Can Fund Managers Successfully Time Their Investment Styles?

What is the Wind Behind this Sail? Can Fund Managers Successfully Time Their Investment Styles?

Cranfield School of Management The Centre for Financial Research August 2005 Author: Jeffrey Junhua Lu

Supervisor: Professor Richard Taffler

© Cranfield University 2005. All rights reserved. No part of this publication may be reproduced without the written permission of the copyright owner.

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ABSTRACT

There is a considerable body of literature that examines the behaviour of institutional investors as a potential source of market price movement. Most existing studies focus on the market timing abilities of active fund managers and find mixed evidence for their fund timing skills. However, few studies have investigated fund manager timing abilities within segments of the market, such as factor timing and sector timing. This study investigates the style timing behaviour of US domestic equity funds existing at any time during the period 1992-2002. Specifically, I examine the timing activities of actively managed mutual funds within different market segments based on such established systematic risk factors as size, book-to-market, momentum, and across different fund styles such as aggressive growth, growth and income, and small company funds, etc. Mutual fund timing strategy can be viewed as the fund manager’s response to his/her private information regarding future factor premiums. Instead of directly observing how fund managers make their timing decisions, an alternative approach is to look at the direct outcomes of their decisions, which are related to the factor timing loadings derived from a factor timing model. I significantly expand on the work of Bollen and Busse (2001) and Volkman (1999) by combining systematic risk factors unique to equity markets with timing factors unique to actively managed portfolios. Within this empirical timing-activity evaluation framework, I additionally investigate fund timing behaviour in the context of Morningstar star rating performance record, investment objectives, fund age, turnover, and load expense, etc. This Ph.D. is an original contribution to the literature of fund timing activities, which seeks to contribute to our understanding in terms of investigating mutual fund managers’ timing strategies with respect to specific systematic risk factors and their evolution over time. This research has important implications both for extant asset Ph.D. Thesis: Jeffrey Junhua Lu

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pricing theories and for practitioners especially in the evaluation of portfolio performance and investigation of fund managers’ timing activities.

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ACKNOWLEDGEMENTS

First and foremost, I would like to express my profound gratitude and respect to my supervisor, Professor Richard Taffler, for his valuable guidance, advice, encouragement and backing throughout my studies at the Cranfield University. He kindly allowed me to have access to his every research resource and actively arranged the regular meetings needed for this study. This thesis could not have been completed without his support.

I am also indebted to Professor David Myddelton and Dr. John Towriss for their helpful comments during the first and the second review.

I would like to acknowledge the substantial assistance of Morningstar Inc who provided the data on which this study is built.

I would also like to thank my parents for the moral support they provided during the course of this Ph.D. Without it I would have failed long ago. Special thanks are due to my girl friend Tracy, for her patience and for pushing me over the final finishing line.

Finally, I thankfully acknowledge the financial support provided by Cranfield School of Management during the course of this Ph.D.

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TABLE OF CONTENTS

CHAPTER 1 INTRODUCTION........................................................................................12

CHAPTER 2 INSTITUTIONAL BACKGROUND .........................................................25 2.1. Introduction...............................................................................25 2.2. The Organisation and Structure of the Mutual Fund Industry ..25 2.3. Investment Constraints and Mutual Funds Regulation.............28 2.4. Debate on Active versus Passive Fund Management ...............32

CHAPTER 3 LITERATURE SURVEY............................................................................36 3.1. Introduction...............................................................................36 3.2. Mutual Fund Performance Evaluation ......................................37 3.2.1 Definition of Performance Measures ...............................37 3.2.2 Average Performance of Mutual Funds ...........................41 3.2.3 Differential Performance of Mutual Funds......................43 3.3 Behaviour of Mutual Fund Investors .........................................48 3.3.1 Modeling Mutual Fund Flows .........................................48 3.3.2 Impact of Past Performance on Mutual Fund Flows .......49 3.3.3 Impact of Other Factors on Mutual Fund Flows..............51 3.4 Strategic Behaviour of Mutual Fund Managers.........................54 3.4.1 The Objectives of Fund Managers ...................................54 3.4.2 Managers’ Strategies: Game-Theoretic Analysis .............56 3.4.3 Managers’ Strategies: Empirical Evidence ......................60 3.5 On the Timing Abilities of Fund Managers ...............................63 3.5.1. Stock Return Predictability .............................................63 3.5.2. Market Timing ................................................................65 3.5.3. Timing Strategies in a Broader Sense .............................66 3.5.4. Timing Strategy and Stock Selection ..............................68 3.5.5. Systematic Factors Affecting Funds’ Timing Behaviour 68 3.6 Behavioural Biases in Mutual Fund Investment........................71 3.6.1 Bounded Rationality and Prospect Theory ......................71 3.6.2 Sources of Bias and Behavioural Models ........................73 3.6.3 The Disposition Effect .....................................................76 3.6.4 Overconfidence ................................................................80 Ph.D. Thesis: Jeffrey Junhua Lu

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3.7 Summary and Limitations on Current Studies...........................81 3.7.1 Summary ..........................................................................81 3.7.2 Limitations to Current Studies .........................................85

CHAPTER 4 RESEARCH QUESTIONS AND TESTABLE HYPOTHESES .............89 4.1. Introduction...............................................................................89 4.2. Testable Hypotheses..................................................................90 4.2.1. Market Timing Tests .......................................................90 4.2.2. Style Timing Tests...........................................................91 4.2.3. Tests of Trade-off Associated with Factor Timing..........92 4.2.4. Tests of Factor Timing in the Context of Investment Objectives .................................................................................93 4.2.5. Tests of Factor Timing in the Context of Performance Record .......................................................................................94 4.2.6. Tests of Factor Timing in the Context of Systematic Factors.......................................................................................95 4.3. Summary ...................................................................................98

CHAPTER 5 DATA AND METHODOLOGY ................................................................99 5.1. Introduction...............................................................................99 5.2. Data ...........................................................................................99 5.3. Sample Selection.....................................................................100 5.4. Methodology ...........................................................................105 5.4.1. Multifactor Model.........................................................106 5.4.2. Market Timing Model ...................................................107 5.4.3. Deriving Factor Timing Models............................. 110 5.4.4. Factor Indices’ Construction .........................................115 5.4.5. Synthetic Funds Construction ....................................... 116 5.4.6. Bootstrap Standard Errors.............................................119 5.4.7. Timing Aggressiveness .................................................121 5.4.8. Performance Record Differences ..................................122 5.4.9. Systematic Factors Affecting Fund Timing ..................124 5.4.9.1 Desired Risk Exposure.........................................124 5.4.9.2 Size.......................................................................124 5.4.9.3 Turnover...............................................................125 5.4.9.4 Fund Age..............................................................125 5.4.9.5 Fund Flow ............................................................125 5.5 Summary ..................................................................................126 Ph.D. Thesis: Jeffrey Junhua Lu

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CHAPTER 6 MARKET TIMING ...................................................................................127 6.1. Introduction.............................................................................127 6.2. Market Timing Models ...........................................................128 6.3. Market Timing Results For Sample Funds .............................130 6.4. Market Timing Results For Synthetic Funds ..........................132 6.5. Relationship between Stock Selection and Market Timing ....136 6.6. Summary .................................................................................138

CHAPTER 7 STYLE TIMING........................................................................................140 7.1. Introduction.............................................................................140 7.2. Style Timing Models...............................................................141 7.3. Style Timing Results For Sample Funds.................................143 7.3.1 Joint Tests of Style Timing ...........................................143 7.3.2 Detailed Style Timing for Sample Funds .....................145 7.4. Style Timing Results For Synthetic Funds..............................148 7.4.1 Results on Synthetic Funds ..........................................148 7.4.2 Explanations .................................................................151 7.5. Style Timing Trade-Offs: Style Timing v.s. Stock Selection ..154 7.6. Style Timing Trade-Offs: Different Style Timing ...................156 7.7. Sensitivity Analysis.................................................................158 7.8. Summary .................................................................................160

CHAPTER 8 INVESTMENT OBJECTIVES, PERFORMANCE RECORD AND STYLE TIMING........................................................................................163 8.1. Introduction.............................................................................163 8.2. Investment Objectives and Style Timing ................................165 8.2.1. Factor Loadings on Subgroup of Funds ......................166 8.2.2. Style Timing Preferences by Fund Subgroup ..............169 8.2.3. Style Timing Aggressiveness on Subgroup of Funds ..171 8.2.4. Summary......................................................................173 8.3. Performance Record and Style Timing ...................................174 8.3.1. Introduction .................................................................174 8.3.2. Empirical Results.........................................................178 8.3.2.1. Factor Loadings on Funds Subgroups.................180 Ph.D. Thesis: Jeffrey Junhua Lu

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8.3.2.2. Style Timing Preferences by Fund Morningstar Subgroup ..........................................................................184 8.3.2.3. Style Timing Aggressiveness by Morningstar Subgroup ..........................................................................186 8.3.3. Summary......................................................................189 8.4. Summary of Chapter ........................................................189

CHAPTER 9 FUND SYSTEMATIC FACTORS AFFECTING STYLE TIMING....191 9.1. Introduction.............................................................................191 9.2. Do Small Funds Fare Better?..................................................192 9.2.1 Introduction ..................................................................192 9.2.2 Factor Loadings on Fund Size Subgroups....................194 9.2.3 Style Timing and Fund Size .........................................196 9.2.4 Summary ......................................................................198 9.3. Does Experience Matter?........................................................198 9.3.1 Introduction ..................................................................198 9.3.2 Factor Loadings on Fund Subgroups Classified by Age 201 9.3.3 Style Timing on Subgroup of Funds.............................202 9.3.4 Summary ......................................................................203 9.4. Is High Turnover Rate Justified as Timing? ...........................204 9.4.1 Introduction ..................................................................204 9.4.2 Factor Loadings on Fund Subgroups by Turnover.......205 9.4.3 Style Timing by Fund Turnover Subgroups .................208 9.4.4 Summary ......................................................................211 9.5. Do Investor Flows Affect Factor Timing? ..............................212 9.5.1 Introduction ..................................................................212 9.5.2 Factor Loadings on Subgroup of Funds .......................213 9.5.3 Style Timing on Subgroup of Funds.............................214 9.5.4 Summary ......................................................................215 9.6. Summary .................................................................................215

CHAPTER 10 CONCLUSIONS AND LIMITATIONS ..................................................217 10.1. Introduction...........................................................................217 10.2. Summary and Discussion......................................................217 10.3. Limitations and Further Work...............................................221 10.4. Implications...........................................................................223 10.5. Contribution to the Theory and Practice ...............................224 Ph.D. Thesis: Jeffrey Junhua Lu

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APPENDIX 1 TABLES AND FIGURES .........................................................................227 Table 1 Sample Fund Summary Statistics ...............................................................228 Table 2 Bootstrap Analysis of Market Timing Coefficients ....................................233 Table 3 Correlation Analysis between Market Timing and Selectivity ...................235 Table 4 Joint Tests of Style Timing Coefficients .....................................................236 Table 5 Bootstrap Analysis of Style Timing Coefficients........................................237 Table 6 Summary Statistics for Intercepts and Style Timing Coefficients ..............239 Table 7 Linear Regression Explaining the Relationship between Intercepts and Timing Coefficients……………………………………………………….240 Table 8 Correlation Coefficients Explaining the Relationships between Different Timing Coefficients……………………………………………………….241 Table 9 Factor Loadings on Fund Sub-group Formed According to Investment Objectives…………………………………………………………………243 Table 10 Style Timing on Fund Sub-group Formed According to Investment Objectives ...................................................................................................244 Table 11 Average Style Timing Coefficients within Fund Objective Sub-groups.....247 Table 12 Factor Loadings on Fund Sub-group Formed on Fund Performance .........248 Ph.D. Thesis: Jeffrey Junhua Lu

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Table 13 Average Fund Performance by Morningstar Ranking ................................249 Table 14 Bootstrap Analysis of Style Timing Coefficients by Morningstar Fund Performance Group……………………………………………………….250 Table 15 Style Timing Aggressiveness by Morningstar Fund Performance Group ..253 Table 16 Factor Loadings on Fund Sub-groups Formed on Asset Size…………….254 Table 17 Bootstrap Analysis of style Timing Coefficients within Size Groups ........255 Table 18 Style Timing Aggressiveness within Fund Size Groups .............................258 Table 19 Factor Loadings on Fund Sub-group Formed on Fund Age .......................259 Table 20 Bootstrap Analysis of Factor Timing Coefficients within Age Groups

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Table 21 Style Timing Aggressiveness within Fund Age Groups .............................262 Table 22 Factor Loadings on Fund Turnover Sub-groups .........................................263 Table 23 Average Fund Performance by Fund Turnover...........................................264 Table 24 Bootstrap Analysis of Style Timing Coefficients within Turnover Groups 265 Table 25 Style Timing Aggressiveness within Fund Turnover Groups .....................267 Table 26 Factor Loadings on No-Load and Load of Fund Sub-groups .....................268

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Table 27 Bootstrap Analysis of Factor Timing Coefficients within Load/No-Load Groups.........................................................................................................269 Table 28 Style Timing Aggressiveness within Fund Load Groups............................271 Table 29 Bootstrap Analysis of Style Timing Coefficients........................................272 Figure 1 Timing Aggressiveness by Morningstar Rating..........................................274 Figure 2 Timing Aggressiveness by Size Quintile ....................................................275 Figure 3 Timing Aggressiveness on Age Groups ......................................................276 Figure 4 Timing Aggressiveness by Turnover Group ...............................................277 Figure 5 Timing Aggressiveness on Load/No-Load Groups.....................................278

APPENDIX 2 REFERENCES...........................................................................................280

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CHAPTER 1 INTRODUCTION “My money was in mutual funds. Several of them. They worked like this: When the market went down, my funds went down a lot; when the market went up, my funds went up a little…I thought I could do better.” ---Confessions of a day trader, to Time magazine. The confessions of this do-it-yourself investor typify widely-held doubts concerning active portfolio management: do and can professional money managers time the market? Nowadays, almost 50 percent of US households invest in mutual funds, with an aggregate investment of over five trillion dollars (Investment Company Institute, 2000). Investors who put their money in actively managed mutual funds when index funds are available at a much lower cost hope to “beat the market” instead of merely to “ride with the market.” These investors, not all of whom are aware of the theory of market efficiency in its semi-strong and weak forms, expect professional money managers to be better informed than common people about individual securities or about prospective general market (or segments of the market) movements. If this is true, any special information possessed by a money manager will show up in terms of one or both superior abilities: security selection skills and market (factor) timing. The first ability concerns identifying, and investing disproportionately in, securities that have the potential to outperform the relevant benchmark (usually referring to the market) in risk-adjusted terms. And the second ability is about predicting the overall market movement and adjusting the portfolio’s exposure to systematic risk accordingly. This is why mutual funds sometimes distinguishably market themselves as either “stock pickers” or “market timers.” Timing strategies to exploit cross-sectional return predictability have been widely used by practitioners. Plan sponsors and portfolio managers recognise that style Ph.D. Thesis: Jeffrey Junhua Lu

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decisions can have a large impact on the performance of their equity funds. “Style” is broadly defined as any system of classification by market segments that have distinguishing characteristics. As active managers attempt to differentiate expected returns based on explicit or implicit criteria, they position their portfolios to be out of sync with the broad market. Hence, in a general sense, a manager’s style is that set of investment characteristics that distinguishes the manager from the market. Given the numerous criteria from which active strategies can be devised, academics and practitioners have developed sets of common characteristics or “factors” to characterise style. Beta, size, value, growth, quality, momentum, leverage, and even sectors/industries are criteria commonly used to differentiate investment styles. Although the ability to outperform a benchmark by accurately timing these factors remains debatable, long-term excess return premia are reportedly associated with one side of these factors1. Timing strategies were traditionally concerned with allocating wealth between two asset classes, typically shifting between stocks and bonds, also known as market timing strategy. More recently, more complex style (factor) timing strategies have been successfully tested and implemented. These strategies are based on the recognition that Sharpe’s CAPM (1964) needs to be extended to account for the presence of other pervasive risk factors, e.g., size and book-to-market factors (Fama and French, 1992). In reality, most mutual fund managers actually make discretionary, and sometimes unintended, bets on styles as much as they make bets on individual stocks. The exact proportion of investment funds currently engaged in timing strategies, often referred to as “tactical asset allocation”, is not clear, but it is certainly growing very rapidly. For example, Philip, Rogers, and Capaldi (1996) estimate that in 1996 around $48 billion was being allocated to domestic timing strategies, and Lee (2000) estimated that more than $100 billion dollars was dedicated to domestic timing strategies by the end of 1999. Implementation of timing strategies is often based on the claim of 1

For example, small cap stocks tend to outperform large cap stocks and value stocks tend to outperform growth stocks in the long run.

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superior information. Hence, tests on the timing abilities of these fund managers can be viewed as evidence that is relevant to the efficient market hypothesis and thereby provide insights into the understanding of the process of security price determination, because of its potential implications for differential investment information availability in the marketplace. Why do fund managers engage in style timing strategies or making style bets? I consider two possible explanations. The first relates to the posted superior information and timing skills processed by fund managers. According to this view, fund timing strategies are based on fundamental analysis and implemented by rational and cool-headed managers. In contrast to the investments of individual investors, mutual funds are carefully managed by skilled and trusted professional money managers with enormous information and other resources at their disposal. This puts them in a better position to evaluate the fundamentals and to make style bets. Drawing on the theory of market efficiency with costly information, there has been extensive research measuring the performance of professional money managers along two basic dimensions. The selectivity test seeks to answer the question of whether a fund manager’s portfolio can outperform its benchmark portfolio in risk-adjusted terms.2 The timing test deals with whether a fund manager can outguess the market (or subsets of the market) by moving in and out of “time portfolios.”3 Measures of market timing have fallen into two categories. The first one directly tests whether money managers can successfully allocate funds among different classes of assets to catch market ascendancy and/or to avoid downturns.4 Graham and Harvey (1996) analyse investment newsletters’ suggested allocations between equity and cash, thereby measuring explicitly the ex post performance of timing strategies. Research methodologies in this category require the knowledge of managers’ asset positions at a reasonably high frequency, and have thus been constrained in practice. The second 2

See Jensen (1972); Gruber (1996); Ferson and Schadt (1996); Kothari and Warner (2001). Portfolio proxies for factors. See Treynor and Mazuy (1966); Henriksson and Merton (1981); Admati, et al., (1986). 4 Theoretical work includes studies by Merton (1981) and Cumby and Modest (1987) 3

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category, on the other hand, requires only data on the ex post returns of the funds and the relevant markets. The two most popular methods so far are those proposed by Treynor and Mazuy (1966) and Henriksson and Merton (1981). Most existing studies relating to the timing behaviour of mutual fund managers focus on their timing abilities with respect to the whole market. In general, evidence on the ability of investment managers to time the market is mixed. Several studies of mutual fund timing skill5 generally find little evidence of timing skill. In an early study, Treynor and Mazuy (1966), for example, develop a test of market timing and find significant ability in only 1 fund out of the 57 in their sample. Henriksson (1984) uses the market timing test of Henriksson and Merton (1981) and finds that only 3 funds out of 116 exhibit significant positive market timing ability. On the other hand, in more recent studies, other researchers have demonstrated fund managers’ timing ability. For example, Ferson and Schadt (1996) find some evidence of timing skill when macroeconomic conditions are accounted for. Graham and Harvey (1996) detect evidence of timing skill using certain benchmarks. Wagner, Shellans, and Paul (1992), Brocanto and Chandy (1994), and Chance and Hemler (1999) all uncover some positive timing evidence as well. However, in the studies mentioned thus far, few authors have investigated specific fund manager timing abilities within market segments, which are related to such systematic risk factors as size and book-to-market. One exception is the study of the UK pension funds conducted by Thomas and Tonks (2001). They decompose the abnormal performance of pension funds and find that most of it could be explained by the ability of both large and small funds to time the size premium. For an active fund manager to outperform his passive counterpart, he must possess some sort of superior information and must be capable of exploiting this type of information. Obviously, such information need not be related to the whole market, but can be restricted to subsets of the market. Investment strategies based on size, book-to-market, and 5

See Kon (1983); Chang and Lewellen (1984); Lehmann and Modest (1987), Grinblatt and Titman (1989a), (1994); Daniel, Grinblatt, Titman, and Wermers (1997). Ph.D. Thesis: Jeffrey Junhua Lu

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momentum factors have long been attractive to investors as potential sources of added value, since long-term excess return premia are reportedly associated with one side of these factors. Pioneering work on the predictability of asset class returns grouped by these factors in the US market was carried out by Keim and Stambaugh (1986), Campbell (1987), Campbell and Shiller (1988), Fama and French (1989), and Ferson and Harvey (1991). Moreover, market timing is implicitly incorporated into the model conventionally used in investment performance evaluation. Researchers have long been questioning the appropriate use of the CAPM for the evaluation of mutual fund performance. Several studies reject the CAPM and infer that performance measurement can be sensitive to inefficient benchmarks. 6 Other studies identify the inefficiency of a single-risk-factor model and suggest using multiple conditioned risk factors. Fama and French (1993), Jegadeesh and Titman (1993), and Carhart (1997) demonstrate that factor-mimicking portfolios common to equity markets decrease cross-sectional variability and improve the explanatory power of one-factor models. In addition, other researchers assert that a timing factor unique to managed portfolios is important to measure the cross-sectional variability of mutual fund returns. Bhattacharya and Pfleiderer (1983) and Grinblatt and Titman (1989) assert that traditional performance measures are downward biased if a timing factor that accommodates the nonstationarity of a portfolio’s systematic risk parameter is not included in the performance evaluation model. However, a timing performance parameter is upward biased if the performance evaluation model does not identify perverse or negative timing performance. Most of the work on mutual fund performance measurement extends the alpha-beta analysis of securities and portfolios to mutual funds. There has been controversy over using such a metric to evaluate mutual fund performance. The static alpha-beta analysis misses the diversified and dynamic aspects of managed portfolios.7 In efforts 6 7

See Roll (1978); Breeden, Gibbons, and Lizenberger (1989). See Admati, et al., 1985; Ferson and Schadt, 1996; Becker, et al., 1999; Ferson and Khang, 2000.

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to beat the market, fund managers vary their portfolios’ exposure to market or other risk factors from time to time based on the information they receive. Further, fund managers can alter their funds’ correlation to the benchmark index in order to make the best out of the incentive they face (Chevalier and Ellison, 1997). Consequently, the systematic part of fund risk can be misestimated when the market timing effect is present, and existing measures may fail to attribute superior returns to informed investors if risk aversion varies (Grinblatt and Titman, 1990). To address these issues, there has been a lot of work on the extension of the TM and HM measures in order to capture the effect of conditioning information on timing performance (Ferson and Schadt, 1996; Becker, et al., 1999; Ferson and Khang, 2000), to control for spurious timing arising from not holding the benchmark (Jagannathan and Korazjczyk, 1986; Breen and Jagannathan, 1986), to decompose abnormal performance into selectivity and timing (Admati, et., 1986; Grinblatt and Titman, 1990), and to minimise the loss of test power due to sampling frequencies (Goetzmann, et al., 2000; Bollen and Busse, 2001). In this thesis, I significantly expand on the work of Bollen and Busse (2001) and Volkman (1999) by combining systematic risk factors unique to equity markets with timing factors unique to actively managed portfolios. In other words, I estimate factor timing coefficients for the size, book-to-market, and momentum factors in my factor timing model, in addition to the market factor in the traditional market timing model. In this study, I use “size” to refer to small capitalisation versus large capitalisation, “book-to-market” to refer to value versus growth, and “momentum” to refer to momentum versus contrarian. Factor timing strategies in this thesis thus refer to the style bets that active fund managers make on size, book-to-market, and momentum. Timing strategies based on size, book-to-market, and momentum have long been attractive to investors as potential sources of added value. Hundreds of new funds are launched every year; by the end of 2003, over 8,100 mutual funds existed in the United States, holding assets valued at almost $7.4 trillion

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and accounting for about 22 percent of US equities (ICI Mutual Fund Fact Book, 2004). Given the size of their stake in the equity market, mutual funds’ investment strategies, especially those dynamic strategies such as style (market) timing, could have substantial effects on equity prices, especially when these timing activities amplify financial market turbulence. Timing strategies by mutual funds need not always be destabilising. If fund managers indeed possess superior information and timing skills, their timing activities as timely responses to changes in fundamental information (which are classified as informed tradings), may speed the market’s adjustment to a new equilibrium price and make the equity market more efficient by offsetting irrational shifts in behaviour by other noise traders such as individuals and foreigners. However, if fund managers’ timing activities are not in line with fundamentals and non-profit maximising, which may be a consequence of constraints placed on mutual fund trading activities or fund manager judgement biases (which are classified as uninformed tradings), they will move prices away from fundamental values, thereby exacerbating stock price movements and increasing market volatility. This leads to the second potential explanation for the timing activities of fund managers. Timing strategies implemented by active fund managers may not necessarily be based on fundamentals. Indeed, a growing area of research indicates that institutional investors’ behaviour might be coloured by considerations beyond the maximisation of portfolio return or diversification. Grinblatt, Titman, and Wermers (1995) identify herding activity by mutual fund managers. Brown, Harlow, and Starks (1996) find systematic changes in risk conditional on past performance. There are several reasons why mutual fund managers may implement style timing strategies in a less than economically rational manner. First, a fund manager’s ability to shift a fund’s allocation is constrained to varying degrees by the investment objectives of the fund, as established in the fund’s “Statement of Additional Information.” In addition, fund style timing activity may be hindered by restrictions on the use of leverage and derivatives placed on mutual funds by the Securities and Exchange Commission’s Investment Company Act of 1940. Second, trading costs can substantially reduce the Ph.D. Thesis: Jeffrey Junhua Lu

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notional, or ‘paper,’ return to a timing strategy. Consequently, fund managers might not implement the timing strategy as early as possible due to the higher trading costs associated with it. Third, fund managers provide a great deal of liquidity to investors and thus engage in a material volume of uninformed, liquidity-motivated trading. Unexpected fund inflows and outflows could force the manager to buy or sell investments at the wrong time, which might potentially disturb his/her style timing strategies. Fourth, there are likely to be behavioural biases associated with fund managers’ timing decisions. Fund managers might not be the rational and cool-headed investors normative theory argues them to be. Indeed, they may be subject to related behavioural biases found in the literature relating to individual investors. Finally, incentive problems could affect fund managers’ timing activities leading to their not acting in the best interests of fund investors when making investment decisions. Academic research on mutual fund timing activities in the context of uninformed trading has important implications for both investors and policy makers in terms of the justification of active fund management and the appropriate regulatory policy to promote investors’ best interests and maintain the stability of financial markets. Most studies on fund timing activity, in fact, fail to investigate the different timing behaviours of fund managers under different systematic factor scenarios. To explore this issue, I segregate my data by several systematic factors common to mutual funds, such as: fund size, investment objectives, performance record, manager experience, turnover, and investor flows. In summary, three alternative scenarios under which fund managers implement timing strategies can be postulated: (1) Fund managers correctly implement timing strategies, as they possess superior information and timing ability. (2) Fund managers implement timing strategies incorrectly unintentionally, as they are subject to various trading constraints or behavioural biases.

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(3) Fund managers implement timing strategies wrongly intentionally, as they act in their own interests rather than those of fund investors. This thesis aims to investigate the style timing behaviour of active fund managers over time in line with changes in common risk factors. Further, it makes an attempt to explore the link between fund manager style timing activities and specific systematic factors. My research approach will work backwards from realised fund returns and factor mimicking portfolios to make inferences about fund manager decision processes and attitude towards risk. Two broad perspectives are taken. I first explore whether fund managers possess superior information and timing ability and whether actively managed funds are able to time the factors successfully by profiting from their superior information and skill. In this part of my thesis I start by conducting market timing tests similar to those of prior studies and then extend the market timing test framework to a factor timing test framework by combining Carhart’s (1997) systematic risk factors unique to equity markets with timing factors unique to actively managed portfolios. In the second part of this thesis, I then proceed to explore the linkage between fund style timing activities and specific systematic factors, such as performance record and investment policy etc. In particular, I focus on the way fund managers appear to implement timing strategies in response to their fund-specific characteristics such as past performance or investment objectives. Specifically, this study focuses on the following key issues: (1) Do mutual fund managers engage in style (market) timing activities? Do fund managers possess superior timing abilities? (informed trading hypothesis) (2) How do mutual fund managers implement style timing strategies? Which style among size, value/growth, and momentum do mutual fund managers attend to time? Do they suffer from similar behavioural biases to those of individual investors? (behavioural biases hypothesis) (3) What are the trade-offs associated with style timing strategies faced by mutual

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fund managers? Do mutual fund managers make style bets at the expense of stock selectivity performance? Do mutual fund managers time a particular style at the expense of negative timing with other styles? (4) Do fund investment objectives affect fund style timing activities? What are the differences of style timing behaviour among different groups of funds based on their investment objectives? (5) Do fund performance records affect subsequent fund style timing activities? Do fund managers respond to their performance records by implementing style timing strategies differently? (agency theory hypothesis) (6) Do certain systematic factors affect fund style timing? In particular, do experienced managers do better at style timing? Is it easier for small funds to time their styles? Can the high turnover ratio of actively managed funds be justified as successful attempts to time investment styles? Do investor flows affect fund style timing? The findings of my thesis make the following contributions to the study of the value of active fund management and provide significant insights into the current practice of mutual fund timing strategies: ¾ Providing evidence regarding the validity of the efficient market hypothesis The investment behaviour of mutual funds has been the subject of extensive examination in the finance literature. Implementation of timing strategies is often based on the claim of superior information. Indeed, most fund managers often characterise themselves as market timers. Hence, tests on the timing abilities of these fund managers can be viewed as evidence that is relevant to the efficient market hypothesis and thereby provide insights into the understanding of the process of security price determination, because of its potential implications for differential investment information availability in the marketplace8. 8

Not all Information is ready for all investors in sub-segments of the market. Some investors might be on a better

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Can Fund Managers Successfully Time Their Investment Styles?

¾ Extending extant research on mutual fund timing activities An empirical timing-activity evaluation framework will be developed to combine systematic risk factors unique to equity markets with timing factors unique to actively managed portfolios. Most existing studies relating to the timing behaviour of mutual fund managers focus on their timing abilities with respect to the whole market. However, few studies have investigated their specific timing abilities within market segments, which are related to such systematic risk factors as size and sector. This study seeks to extend the existent mutual fund literature on market timing behaviour to a broader consideration of style timing strategy. I significantly expand on the work of Bollen and Busse (2001) and Volkman (1999) by combining Carhart’s (1997) systematic risk factors unique to equity markets with timing factors unique to actively managed portfolios. I provide a comprehensive examination of mutual fund factor timing activities that explicitly controls for luck without potential bias from misspecification. This is not because I claim my timing models are correctly specified – they may not be. Rather, my approach, which uses a bootstrap statistical approach, is robust to possible misspecification. ¾ A better understanding of the risk-taking behaviour of fund managers under different market conditions and in the light of differential managerial incentives Active fund managers adopt different risk positions in line with changes in market conditions. There are some systematic factors, such as performance record, fund size, and fund age, etc., which can influence the managerial incentives of fund managers, and which in turn, affect their timing behaviour. Hence, the fund manager’s attitude towards risk needs to be understood both in the context of a dynamic market environment as well as the managerial incentives to which he/she responds. I manage to link fund manager timing behaviour to specific systematic factors, such as performance record and investment policy etc., and examine the influences of these systematic factors on fund timing activities. position to possess information in an efficient and timely way while others might not. Ph.D. Thesis: Jeffrey Junhua Lu

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Can Fund Managers Successfully Time Their Investment Styles?

¾ Provide an original contribution on the value of active fund management Investigation of fund timing activities is important for potential mutual fund clients to help them allocate their funds efficiently, since fund investors can assess the timing abilities of the fund manager and essentially “undo” the timing aggressiveness of the manager by investing more or less of their wealth in the fund or by trading in other accounts. Such research is also important for managers to help them evaluate the effectiveness of their timing strategies and set appropriate management fees. A valid question is whether any timing strategies based on superior forecasting skills can generate a sufficient increase in returns to offset the associated information and transaction costs, as well as the management fees charged. Moreover, such information is important for regulators to formulate policy concerning the operations of the market place. ¾ Provide constructive feedback for public policy setters My main findings are: Over the ten-year period of this study (June 1992 to July 2002), my mutual funds are more likely to be successful with respect to book-to-market (value/growth) style timing, and unsuccessful in trying to time size (big cap/small cap) and momentum (winner/loser). These results may be partly due to the institutional factors and transaction costs associated with these timing strategies. Most funds are restricted from taking substantial positions in small-cap stocks and there are relatively higher transaction costs associated with size (big cap/small cap) and momentum (winner/loser) timing strategies when compared to book-to-market (value/growth) timing strategies. There may also be a behavioural explanation which is related to the trading behaviour and preferences of fund managers. Fund managers prefer big-cap stocks to small-cap stocks as safer investments. Also, they tend to sell winners too soon and to hold on to losers too long. Analysis of different fund categories (aggressive growth, growth, income, equity income and small cap) reveals that growth-oriented funds tend to possess better timing abilities and also implement style Ph.D. Thesis: Jeffrey Junhua Lu

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Can Fund Managers Successfully Time Their Investment Styles?

timing strategies more aggressively than other funds. I also find that, on average, funds with previous an extremely good or bad performance record implement timing strategies more aggressively than those with moderate performance. I suggest that style timing ability is fund specific and is difficult to predict by observable fund characteristics. However, style timing aggressiveness is affected significantly by the respective funds characteristics. This can be explained by behavioural factors relating to the potential fund manager biases and incentive structures discussed in the finance literature.

The rest of the thesis is organised as follows: chapters 2 and 3 conduct a critical review of the institutional background and literature, and then, drawing on this, chapter 4 develops testable hypotheses from my research questions. Appropriate empirical methodologies are then established in chapter 5 to test the hypotheses formally adopting both a rational agency and behavioural biases perspective. The first empirical chapter of the thesis, chapter 6, conducts traditional market timing tests on the sample funds. Chapter 7 undertakes general style timing tests on my sample funds by implementing my own style timing models which incorporate additional systematic risk factors unique to equity markets into traditional market timing models. Chapter 8 investigates the style timing ability and activity of active fund managers further in the context of fund investment objectives and fund performance record. The last empirical chapter of the thesis, chapter 9, explores the effect of fund size, manager experience, turnover, and investor flows on the style timing behaviour of active mutual funds. In the final chapter of my thesis, chapter 10, I summarise my main empirical findings and discuss some limitations of my research.

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CHAPTER 2 INSTITUTIONAL BACKGROUND 2.1. Introduction The purpose of this thesis, as presented in the previous chapter, is to investigate the style timing behaviour of active fund managers over time in line with changes in common risk factors. It further makes an attempt to explore the link between fund manager style timing activities and specific systematic factors. This chapter briefly discusses the relevant institutional background, which is crucial for understanding the incentives and actual behaviour of fund managers, and provides the demand for, or motivation of, this research and also helps organise my arguments. The rest of this chapter is organized as follows. Section 2 describes the organisation and structure of the mutual fund industry. Section 3 discusses the investment restrictions placed on mutual funds and section 4 discusses the debate on active versus passive fund management in the investment industry.

2.2. The Organisation and Structure of the Mutual Fund Industry According to the basic definition, a mutual fund is an investment company that pools money from shareholders and invests in a diversified portfolio of securities (see, e.g., Investment Company Institute, 2002). In the US, the most important laws regulating mutual funds and ensuring investor protection are the Investment Company Act (ICA) and the Investment Advisers Act (IAA) of 1940. Mutual funds are typically organized as corporations and have a board of directors or trustees, which is elected by their shareholders. In contrast to most business corporations, mutual funds have very limited internal resources and rely on the provision of specific services by affiliated Ph.D. Thesis: Jeffrey Junhua Lu

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organisations and independent contractors. In particular, the board of directors hires a separate entity – the investment advisor/management company – to provide all management and advisory services to a fund for a fee, which is usually based on a percentage of the fund’s average net assets. In practice，however, the usual procedure is for the management organisation to create the mutual fund itself. To mitigate a potential conflict of interest, the ICA requires that an investment advisor must serve under a written contract approved initially by a vote of the shareholders and thereafter approved annually by the broad of directors. Transactions between a fund and its manager are prohibited and at least 40percent of a fund’s directors must be independent from the fund’s management company or principal underwriter. The IAA imposes recordkeeping, reporting, disclosure, and other requirements on investment advisors and contains several antifraud provisions. An investment advisor has a general fiduciary duty with respect to the compensation for its services, which bars such an advisor from inappropriate increase of its fees. Besides a management company, mutual funds also employ principal underwriters who are responsible for the distribution of fund shares, custodians who hold securities from the fund portfolio, transfer agents who keep records, and administrators who oversee the other agents providing services to the fund. Mutual funds are considered “open-end” companies, since they are obliged to sell or redeem their shares at net asset value (NAV), which is equal to the fund’s total net assets (total assets minus total liabilities) divided by the outstanding number of shares. The NAV must reflect the current market value of the securities in the fund portfolio and is usually calculated daily on the basis of closing prices. Mutual funds can be actively pursuing their own portfolio management strategy or passively tracking the return on some benchmark index. In addition, mutual funds differ with respect to the share distribution method used. Load funds distribute their shares through broker-dealers who charge investors a commission proportional to the amount of their investment. Load fees may be front-end (charged at the time of the

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Can Fund Managers Successfully Time Their Investment Styles?

purchase) or back-end (charged at the time of the redemption). For US funds, the front-end load is on average between 4 percent and 5 percent, while the back-end load usually declines the longer a shareholder holds the fund shares, e.g., from 5 percent after one year to 4 percent after 2 years, etc. (see, e.g., Pozen, 1998). In addition, brokers often receive annual distribution fees, called 12b-1 fees, typically ranging from 25 to 75 basis points of assets under management each year. No-load funds use direct distribution channels such as mail and phone and charge no front- or back-end loads and are limited (up to 25 basis points per year) 12b-1 fees. Many funds have multiple share classes for the same fund corresponding to different combinations of load and 12b-1 fees. For example, class A shares are usually sold with a front-end load, while class B shares – with a back-end load. Besides 12b-1 fees, annual fund operating expenses paid by its shareholders also include the management fee, the recordkeeping fee, etc. There are four basic types of mutual fund: equity, bond, hybrid, and money market (see Investment Company Institute, 2002). Equity and bond funds concentrate their investments in stocks and bonds, respectively. Hybrid funds typically invest in a combination of stocks, bonds, and other securities. These three types of fund are known as long-term funds, whereas money market funds are referred to as short-term funds, since they invest in securities maturing in less than one year. Morningstar, one of the leading mutual fund data providers, divides all long-term funds into four classes: domestic stock, international stock, taxable bond, and municipal bond. Mutual funds have become one of the largest class of financial intermediary in leading world economies, currently controlling about 7 trillion dollars in assets in the US and over 3 trillion euros in assets in Europe (see Investment Company Institute, 2002). Investors can choose from thousands of funds offering a wide range of investment profiles, from relatively safe short-term debt instruments to relatively risky stocks and derivatives. Just as investing in the stock market directly, holding mutual fund shares involves Ph.D. Thesis: Jeffrey Junhua Lu

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financial risks, as the fund’s portfolio may rise or fall in value. Mutual funds claim to provide a number of benefits to their shareholders, compared to investing in other financial intermediaries or directly in the financial markets (see, e.g., Pozen, 1998): 1. Low transaction costs. Mutual funds allow investors including those with limited wealth to hold a diversified portfolio of financial securities at low cost. Mutual fund shares are easy to buy through an intermediary or directly, via telephone or Internet. 2. Customer services. Shareholders can transfer money between funds within the same family at low cost. In addition, they do not run liquidity risk, since they can sell their shares at net asset value at any time. 3. Professional management. The investment strategy of a mutual fund is developed by financial professionals, who are able to select the right stocks at the right time. Thus, mutual funds claim to be especially attractive for small investors who do not have sufficient resources to follow a sound investment strategy at low cost. Two major functions of the mutual fund are professional management and diversification. The money accumulated in a mutual fund is managed by professionals who decide on an investment strategy on behalf of the fund’s shareholders. As economic conditions change, the fund may adjust the mix of its investments to adopt a more aggressive or a more defensive posture to meet its investment objectives. In addition, fund managers typically invest in a variety of securities, seeking portfolio diversification and reducing risks.

2.3. Investment Constraints and Mutual Funds Regulation Mutual funds are investment companies that must register with the US Securities and Exchange Commission (SEC) and, as such, are subject to rigorous regulatory Ph.D. Thesis: Jeffrey Junhua Lu

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Can Fund Managers Successfully Time Their Investment Styles?

oversight. Virtually every aspect of a mutual fund’s structure and operation is subject to strict regulation under four federal laws: the Securities Act of 1933, the Securities Exchange Act of 1934, the Investment Company Act of 1940 and the Investment Advisors Act of 1940. The SEC is charged with overseeing the mutual fund industry’s compliance with these regulations. The Internal Revenue Code sets additional requirements regarding a fund’s portfolio diversification and its distribution of earnings, and the National Association of Securities Dealers, Inc. (NASD) oversees most mutual fund advertising and sales materials. In addition, mutual funds must have directors who are responsible for extensive oversight of the fund’s policies and procedures, and at least a majority of those directors must be independent of the fund’s management. The Investment Company Act is the cornerstone of mutual fund regulation. Its core objectives include ensuring that investors receive adequate and accurate information about the fund, and protecting the integrity of the fund's assets. Mutual funds are subject to regulations concerning the extent to which they may invest in certain types of securities. Under section 8 of the Investment Company Act (ICA) of 1940, a mutual fund must make a registration statement where it defines its investment policy. This statement declares whether the fund is “diversified” or “nondiversified,” and if the fund declares itself “diversified” it can not invest in more than 10 percent of any firm’s voting securities. Also, section 12(e) of the ICA of 1940 forbids the ownership of more than 10 percent of many financial service companies regardless of the fund’s registration statement. The Investment Company Act also severely restricts a mutual fund’s ability to leverage or borrow against the value of securities in its portfolio. The SEC requires that funds engaging in certain investment techniques, including the use of options, futures, forward contracts and short selling, must ‘cover’ their positions. The effect of these constraints has been to strictly limit leveraging by mutual fund portfolio managers. Indeed, section 13(a) of the Act states:

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“No registered investment company shall, unless authorized by the vote of a majority of its outstanding Voting Securities, borrow money.” However, subsequent policy has evolved to the point that funds are now routinely permitted to borrow up to 33 1/3 percent of their total assets in a variety of ways. Not all of the investment restrictions that mutual funds face are necessarily the result of enactment of the Investment Company Act of 1940. The regulatory environment that governs the mutual fund industry provides the framework within which investors and managers negotiate specific investment policy restrictions. Fund managers might be prohibited from taking short positions in stocks, from borrowing to finance the portfolio, or from holding positions in a variety of securities, including equity options, index futures, and restricted stock. Indeed, the cross-sectional and intertemporal variation in the pattern of how investment constraints are adopted in practice, strongly suggests that such restrictions are not mere regulatory prohibitions, but one component of the set of monitoring mechanisms that reduces the costs arising from frictions in the principal-agent relation. Moreover, mutual funds are subject to explicit and/or implicit tracking-error constraints. The explicit tracking-error constraint as specified in investment contracts restricts the maximum possible deviation of a fund manager’s portfolio from a given benchmark. Violation of such a constraint can result in termination of contract or even lawsuits. For example, Pensions & Investments (May 12, 2003) reported that Merrill Lynch Investment Managers agreed to settle a suit brought by the Co-operative Group Pension Fund in London, over investment decisions made in the 1990s by MLIM’s predecessor Mercury Asset Management. The fund had accused Mercury of breaching tracking error limits on its UK equities mandate. Merrill Lynch also settled similar cases with two other pension schemes - the Unilever Pension Fund, and the J. Sainsbury PLC Pension Fund. Merrill Lynch reportedly paid Unilever £75m in settlement.

Even without contractual tracking-error constraints, portfolio managers

have increasingly emphasised the risk of underperfoming a benchmark index or their Ph.D. Thesis: Jeffrey Junhua Lu

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peers in their portfolio decisions. The risk of being wrong and alone, popularly recognised as the “maverick risk”, is viewed as the greatest peril in investment management by many practitioners (see e.g., Arnott, 2003). In addition, because money-managers’ compensation often depends on the performance of their portfolios relative to some benchmark, they may ignore their own superior information and “go with the flow” in order to reduce deviations from their benchmark (see, e.g., Maug and Naik, 1996). The 1940 Act requires that investment companies disclose the restrictions that govern their investment activities in their stated investment policies. Consistent with the notion that the role of investment restrictions goes well beyond regulatory mandates, it is increasingly common practice for a fund to split its stated investment policy into two parts: fundamental and non-fundamental. The purpose of a fund’s fundamental policy, which can only be altered with shareholder approval, is often to provide the manager with as much investment flexibility as possible, within the context of the restrictions dictated by the 1940 Act. On the other hand, the fund’s non-fundamental policy can be altered at the discretion of the fund’s board of directors and includes more business-specific restrictions (e.g., no international securities held in a domestic portfolio, even if the fund’s fundamental policy permits their inclusion). The intention of the non-fundamental policy is to capture the richer set of restrictions that investors and managers feel are necessary to best define the fund’s investment style. Collectively, the fundamental and non-fundamental policies represent the executive contract between the manager and fund investors. These investment restrictions (considering leverage, short sales, and derivatives) placed on mutual funds by the SEC show the concerns of regulators about the dynamic strategies fund managers use and the impact of those strategies on the market. Although the SEC requires mutual funds to invest at least 80 percent of their assets in those securities that the fund’s name suggests, the fact that the SEC mandates that holdings match the fund name, not other style indicators, still gives fund managers the

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flexibility to choose among different asset classes/styles and to employ dynamic trading strategies that frequently involve short sales, leverage, and derivatives, because of the frequently obscure nature of a fund’s name. If these dynamic strategies (such as asset class rotations or style timing) are based on informed trading, they may speed the market’s adjustment to a new equilibrium price and maintain the stability of the market. On the other hand, if these dynamic strategies are driven by other factors rather than fundamentals, they will move prices away from fundamental values, thereby exacerbating stock price movements and increasing market volatility. However, in recent years the SEC has come to consider whether there may be benefits to expanding the kind of investment strategies that are offered to mutual fund investors. The issue arises as to whether average investors could benefit from having access to the professional management of certain dynamic strategies such as style timing strategies. In a recent news article, SEC officials mentioned loosening the restrictions as mutual funds relating to such on tactics as short selling and leverage. We may speculate if the time may have come for the Commission to review whether the investment restrictions imposed on funds through the Investment Company Act continue to be appropriate and necessary for investor protection purposes or whether some of these restrictions place unnecessary constraints on fund managers. Indeed, this issue is closely related to the debate on the value of active fund management using dynamic investment strategies.

2.4. Debate on Active versus Passive Fund Management According to the report of the Investment Company Institute (2001), 88 million individuals now hold investments in US mutual funds, with over 90 percent of the value of these investments being held in actively managed funds. Further, actively managed equity funds gain the lion’s share of investor inflows. Flows of net new money to equity funds (inflows minus outflows) totaled $309 billion in 2000, pushing Ph.D. Thesis: Jeffrey Junhua Lu

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the aggregate value of investments held by these funds to almost $4 trillion at year-end 2000. While the majority of individual investors apparently believe in the virtues of active management in general, many appear to hold even stronger beliefs concerning the talents of subgroups of fund managers --- they believe that, among the field of active managers, superior managers exist that can “beat the market” for long periods of time. In particular, Morningstar and Lipper compete vigorously for the attention of these believers by providing regular fund performance rankings, while popular publications such as Mutual Fund Magazine routinely profile “star” mutual fund managers and “hot” mutual fund companies. To go beyond relying on fund performance ranking, one needs to answer the key question on mutual fund performance: “What is the wind behind this sail?” After all, active fund managers typically transact in similar asset markets to passive fund managers. How then do they deliver superior investment management services in a risk-efficient manner when compared to their passive counterparts? I believe the answer to these questions lies in understanding the value of active fund management from a risk timing perspective. The recently published Sandler (2002) and Pickering (2002) reports commissioned by the UK government question the value of active fund management when compared to passive index trackers, based on the fact that active fund managers are finding it increasingly difficult to justify the higher fees charged to investors when so many funds underperform. Meanwhile, according to research by the Consumers’ Association (2002), only one third of active funds managed to beat the FTSE 100 index during the past 10 years. The consumer body argues that only a minority does so consistently and it is nearly impossible for consumers to pick those in advance. “It is one of the best-kept secrets that the performance of highly paid fund managers in the City leaves much to be desired.” However, the active fund industry defends itself aggressively in an attempt to demonstrate the value added by active fund management services. They argue that the Ph.D. Thesis: Jeffrey Junhua Lu

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above results have merely been driven by a 20-year bull market in equities in the UK. With the benefit of hindsight, passive investment was the right solution. But it cannot be assumed that index tracking will be a sound strategy for the next 20 years. Especially during the current bear market, the distorting effects of trackers are painfully apparent. Huge distortions of value were generated during the technology, media and telecommunications bubble because tracker and benchmarked managers decided that there was no business risk in the main indices. As these companies fell to earth, that only exacerbated investors’ pain. On the contrary, active fund managers can implement more flexible investment strategies to reduce the impact of the overall collapse in market values in a bear market, and identify potentially undervalued stocks. Hence, active fund management may be more valuable during a bear market than a bull market. Although this means active managers are taking big bets on certain stocks, index trackers are not entirely low-risk either. The concentration in leading stock market indices means investors are in effect putting large chunks of their portfolio into a small number of stocks, e.g., BP accounts for 7 percent and Vodaphone Group9 accounts for 5 percent of the total value of FTSE 100 index. As such, it is worthwhile investigating the timing activities of actively managed mutual funds in terms of different market conditions, since this can provide a better understanding of the risk taking behaviour of active fund managers across different states of the market.

In this chapter I have reviewed the present institutional and regulatory environments relating to mutual fund investment strategies in the US to establish the necessary background and framework within which my research is set. In the next chapter, I

9

Vodafone provides a striking example of the risks of investing in index-tracking funds. When the telecommunication group took over the US company Airtouch in June 1999, its increased bulk meant its weighting in the FTSE All-Share doubled to 5%. Less than a year later, the same trick was repeated with the acquisition of German rival Mannesmann. The move more than doubled its weighting in the All-Share to 12.9%. This forced a rush by index funds to increase their exposure to the company. Amid already-hyped sentiment on the company, the buying helped propel the stock to a peak of 399p. On August 16th, 2002, the stock closed at just over 100p. Ph.D. Thesis: Jeffrey Junhua Lu

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review relevant previous work germane to my research.

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CHAPTER 3 LITERATURE SURVEY 3.1. Introduction The preceding chapter reveals that the implementation of fund dynamic investment strategies such as style timing and asset rotation is an issue of desired concern to investors, policy makers and fund managers, especially in the light of the current debate on active versus passive fund management. These issues provide the motivation for examining the dynamic strategies of fund managers in practice. However, empirical research is (or should be) informed by theory, since interpretation of empirical analysis is impossible without theoretical guidance (Kothari, 2000). Timing strategies to exploit cross-sectional return predictability have been widely used by practitioners. Plan sponsors and portfolio managers recognise that style decisions can have a large impact on the performance of their equity funds. In this sense, fund managers implement timing strategies based on fundamental. On the other hand, mutual funds represent one of the organisational forms of delegated portfolio management, in which fund shareholders delegate the task of allocating their money to the fund manager. Since the manager’s objectives are not necessarily identical to those of the fund’s shareholders, a potential agency problem arises: the agent (fund manager) may not pursue investment policies optimal for the principals (fund shareholders). Numerous studies have examined the incentives and the actual behaviour of mutual fund managers and investors. The still dominant hypothesis in finance, that markets are efficient, is based on the premise that investors are rigorously rational. Rationality works well as a first order approximation of investor behaviour although we now recognise that behavioural biases can induce trading patterns at odds with the implications of rationality. It is Ph.D. Thesis: Jeffrey Junhua Lu

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reasonable to suppose that more sophisticated investors such as fund managers might be less susceptible to those behavioural biases from which individual investors suffe. Naïve investor subjects might display cognitive biases that would not be found in professional investors. However, there is strong evidence that “professionalism” or investor sophistication does not bring immunity. It is therefore important to check if such biases are also prevalent among fund managers who are professional investors in the markets. Among the main topics investigated in this literature are mutual fund performance evaluation, determinants of mutual fund flows, strategic behaviour of fund managers, fund timing activities, and the behavioural biases of such investors. In this chapter I review relevant underlying theory and the prior empirical studies. The chapter is organized as follows: section 2 reviews the literature on measurement of mutual fund performance, section 3 reviews the literature on determinants of mutual fund flows, section 4 reviews the literature on strategic behaviour of fund managers, section 5 reviews the literature on fund timing activities, section 6 reviews the literature on behavioural biases and the disposition effect, and section 7 summarises the literature and identifies the gaps to be exploited in this study.

3.2. Mutual Fund Performance Evaluation 3.2.1 Definition of Performance Measures In this section, we discuss the empirical evidence on mutual fund performance. We start by describing typical performance measures used in the literature. The most basic measure of mutual fund performance is a fund’s raw return over a certain period of time. While being the simplest and most appealing to investors, this measure does not allow us to discriminate among managers who have superior skill, those who are lucky, and those who merely earn expected risk premiums on their high-risk investments. There are three factors driving mutual funds’ expected raw returns: (i) the performance of the market and other risk factors, (ii) the fund’s exposure to these Ph.D. Thesis: Jeffrey Junhua Lu

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risk factors, and (iii) the stock picking skill of the portfolio manager. Various risk-adjusted performance measures have been constructed to separate out the third factor, which plays an important role for investors in choosing among funds and for fund management companies devising managerial compensation procedures. Most studies use absolute performance measures defined as a difference between the fund’s return and the return on a passive portfolio with a similar risk profile. The passive portfolio is formed using a return-based approach or a portfolio-based approach; these are explained below. According to the return-based approach, fund performance is defined as the intercept in the time series regression of the excess fund return10 on the excess returns of passive benchmark portfolios (factor-mimicking portfolios, in the context of the arbitrage pricing theory): K

Ri ,t − Rt = α i + ∑ β ik Ft k + ε i ,t

(1)

f

k =1

where Ri ,t is fund i’s return, Rt f is a risk-free rate, and Ft k is the excess return on the k-th benchmark portfolio in period t. This measure is often referred to as Jensen’s alpha, since it was introduced in Jensen (1969), who used the excess market return as a single benchmark. Intuitively, Jensen’s alpha can be interpreted as the difference between the fund’s return and the return of the passive portfolio consisting of

βik units of the k-th benchmark (k=1,…,K) and 1 − ∑ kK=1 βik units of the risk-free asset. A positive Jensen’s alpha implies that mean-variance investors who restrict their attention to the K benchmark assets and a riskless asset only, are able to extend their efficient set by taking a long position in the given fund, neglecting other effects such as transaction costs and taxes. Currently, most studies use multi-factor models to estimate Jensen’s alpha. One of the most frequently used specifications is a three-factor model of Fama and French (1993). 10

Henceforth, the excess return denotes the rate of return in excess of the riskless interest rate.

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Besides an overall market factor, they use two additional stock market factors related to firm size (stock price times number of shares outstanding) and book-to-market equity (the ratio of the book value of the firm’s common stock to its market value). The corresponding factor returns are calculated as the difference between the returns on small- and big-stock portfolios and the returns on portfolios with high and low book-to-market equity, respectively. The four-factor model of Carhart (1997) adds one more factor related to one-year momentum in stock returns. The excess return on the corresponding factor-mimicking portfolio is computed as the difference between returns on stocks with high and low returns over the previous year. Thus, the Fama-French three-factor alpha measures fund performance taking into account exposure to size and growth factors, while the Carhart four-factor alpha in addition adjusts for the momentum effect. In the portfolio-based approach, fund performance is measured as the difference between fund return and return on a passive portfolio with characteristics matching the portfolio of the fund under consideration. For example, Daniel et al. (1997) construct a synthetic portfolio of stocks matching fund holdings along the dimensions of size, book-to-market ratio, and one-year momentum. Zero performance indicates that the fund’s performance could have been replicated by buying stocks with the same three characteristics as those held by the fund, while positive performance suggests that a manager has additional stock selection ability. In practice, funds are often assigned a stylised stock index as a benchmark, e.g., a small-cap index for funds investing in stocks of small companies. The simplicity of measuring fund performance as an index-adjusted return makes it appealing to investors. However, one should keep in mind that indices based on relatively large market segments can provide only a rough approximation of the risk profile of a non-index fund. We will see that benchmarking by a certain index may change the investment strategy of the fund manager in a way detrimental for investors (see Section 3.4).

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So far, I consider absolute performance measures calculated as the difference between the excess fund return and the return on the associated passive portfolio. Another type of absolute performance measure is the fund average excess return earned per unit of risk exposure. The most popular measure of this type is the Sharpe ratio, which is calculated as the average excess return of a fund divided by the standard deviation of the fund’s returns:

Sharpei =

Ri − R f

(2)

σi

If the slope of the capital market line is larger than the fund’s Sharpe ratio (the slope of the line connecting the position of the fund with the point of the risk-free rate), this is taken as evidence that the fund has underperformed the market. Note that in contrast to Jensen’s alpha, which takes the covariance of the fund return with benchmark returns into account, the Sharpe ratio is only based on the characteristics of a given fund. Therefore, the Sharpe ratio does not show whether an investor should add a given fund to his current portfolio, but helps to compare different mutual funds with each other. Specifically, a mean-variance investor restricted to invest either in fund A and a riskless asset or in fund B and a riskless asset will choose the one with the higher Sharpe ratio. Absolute measures discussed above adjust fund performance for exposure to given passive benchmarks or risk factors. Another way to obtain a risk-adjusted performance measure is to evaluate fund performance relative to its peers, funds with a similar investment approach (i.e., funds with similar exposures to common risk factors). A typical relative cardinal measure of fund performance is the fund return in excess of the median or mean return in the fund’s investment style category. Note that this measure may not be appropriate if a fund’s actual investment style differs significantly from those of other funds in the category to which it may be assigned. One should also keep in mind a potential effect of survivorship bias, if the peer group contains only surviving funds (as reported, e.g., by Brown and Goetzmann, 1995, Ph.D. Thesis: Jeffrey Junhua Lu

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disappearing funds tend to have poor performance). As shown in Section 3.4, the use of category-specific returns as a benchmark, similar to benchmarking by stock indices, may lead to undesirable changes in fund strategies. Most of the existing academic studies of mutual funds use cardinal performance measures as described above. However, the financial media as well as fund advertisements pay at least as much attention to ordinal performance measures based on the underlying cardinal measures. A typical ordinal measure is defined as a performance rank of a given fund within its category, which groups funds with a similar investment approach. The main difference between cardinal and ordinal performance measures is that the latter do not take into account by how much one fund outperforms the other. This can induce adverse risk-taking incentives to fund managers competing for the top performance ranks rather than maximising risk-adjusted returns. Besides, ordinal performance measures are susceptible to the same criticisms as their underlying cardinal measures. In Section 3.2.2, I describe the results of studies measuring the average performance of mutual funds, i.e., performance of the mutual fund universe taken as a whole. In Section 3.2.3, I discuss studies investigating whether there are consistent differences between the performance of various mutual funds that can be forecast using various fund-specific and manager-specific characteristics. 3.2.2 Average Performance of Mutual Funds The existing empirical evidence based on both return-based and portfolio-based approaches suggests that an average active mutual fund has negative or neutral risk adjusted performance net of expenses. This is demonstrated, for example, by Gruber (1996) whose main measure of performance is Jensen’s alpha from a four-factor model with market, size, growth, and bond factors. His sample consists of 270 US common stock funds during the period from 1985 to 1994 (almost all funds of this type that existed in 1984) and is free from survivorship bias. He finds that US stock Ph.D. Thesis: Jeffrey Junhua Lu

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funds underperformed an appropriately weighted average of the four benchmark indices by approximately 65 basis points per year. Since the average expense ratio in the sample is about 113 basis points per year, this implies that an average mutual fund earns positive risk-adjusted returns, but charges the investors more than the value added. Similar conclusions are reached by Daniel et al. (1997) who measure the performance of equity holdings of over 2500 US equity funds in 1975-1994 using a portfolio-based approach. They use as a benchmark the return on a portfolio of stocks that is matched to the respective fund’s equity holdings each quarter on the basis of size, book-to-market, and one year momentum characteristics. The authors find that their equity fund managers have some stock selection ability (i.e., buying those growth stocks that have higher expected returns than other growth stocks), but hardly any ability to time the different stock characteristics (e.g., buying growth stocks when they have unusually high returns). Overall, active fund manager performance is not significantly greater than the difference between their expenses and the expenses associated with investing in passive index funds. Using the same sample of funds, Wermers (2000) extends this analysis by considering not only the gross returns on the funds’ equity holdings, but also their net returns to investors. He finds that funds’ stock portfolios outperformed the CRSP value-weighted market index by 1.3 percent per year, with 70 basis points being due to fund managers’ stock picking skills and the rest being due to the stocks’ risk premiums. However, the funds actually underperform the market index by 1 percent per year on average on a net return basis. The 2.3 percent difference between gross and net returns is due to the relatively low returns on fund nonstock holdings (0.7 percent), expense ratios (0.8 percent), and transaction costs (0.8 percent). Thus, a positive abnormal return earned by active mutual funds is more than offset by their expenses and transaction costs. Ferson and Schadt (1996) criticise the standard approach to measuring performance, which relies on unconditional expected returns. They argue that if expected returns

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and risks vary over time, then traditional performance measures may be upward- or downward-biased due to the common time variation in risks and risk premiums. They propose as a benchmark a managed portfolio strategy that can be replicated using publicly available information. Such a conditional performance evaluation approach is consistent with semi-strong form market efficiency. In their model, Jensen’s alpha is based on a factor model with time-varying conditional betas that are linear functions of lagged public information variables including short-term interest rate, dividend yield, term spread, and default spread. Using a sample of 67 US open funds from 1968 to 1990, Ferson and Schadt find that the conditional Jensen’s alphas distribution is consistent with neutral performance by mutual funds, whereas the use of unconditional Jensen’s alphas suggest average underperformance. Edelen (1999) argues that the previously found negative performance of mutual funds may be explained by the costs of providing liquidity to fund investors (open-end funds are obliged to buy and sell their shares at net asset value). In his sample of 166 randomly selected open-end funds between 1985 and 1990, approximately one-half of the average fund’s assets are redeemed in the course of the year and over two-thirds of the average fund’s assets arrived as new inflow in the previous year. The author estimates that a unit of liquidity-motivated trading induced by investor flows, defined as an annual rate of trading equal to 100 percent of fund assets, is associated with a 1.5-2 percent decline in risk-adjusted returns. Controlling for this liquidity cost changes the average Jensen’s alpha from a statistically significant -1.6 percent per year to a statistically insignificant -0.2 percent per year. 3.2.3 Differential Performance of Mutual Funds The previous section suggests that mutual funds as a group have negative or neutral estimated performance adjusted for risk and expenses. However, this does not imply that consumers should avoid all mutual funds. If there exists a subset of funds that are able to consistently earn superior risk-adjusted returns, then investors would like to be able to identify such funds and invest in them. In this section, I discuss the results of Ph.D. Thesis: Jeffrey Junhua Lu

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studies trying to identify consistent performance differences across funds and forecast fund performance. Numerous studies examine whether past fund performance is indicative of future fund performance, i.e., whether there are differences in fund performance that persist over time. For instance, Tonk (2005) measures the abnormal returned generated by fund management houses in managing the equity portfolios of UK pension funds over the period 1983-1997. He finds evidence of significant persistence in the performance of fund managers at the one-year time horizon using a number of different consistency tests. He finds that the returns on a zero investment portfolio of a long position in a portfolio of fund managers that performed well over the previous 12 months and a short position in a portfolio of fund managers that performed poorly, would have yielded an annualised abnormal return of 1.56 percent. Brown and Goetzmann (1995) explore persistence in performance of US equity funds in 1976-1988 using both relative and absolute benchmarks. They find a significant year-to-year persistence in raw and risk-adjusted returns (the latter based on a three-factor model with market, size, and bond factors) relative to the median return of all funds in the sample (relative benchmark) and S&P500 return (absolute benchmark). However, persistence seems to be mostly due to the underperforming funds. In other words, a fund underperforming other funds this year is likely to continue underperforming them next year. The authors note that the persistence pattern depends on the time period and that there was a significant reversal of relative winners and losers in a few years. They conclude that the observed pattern in relative performance could be due to a common component in fund strategies not captured by standard risk-adjustment procedures. This conclusion is supported by Carhart (1997) who demonstrates that most of the performance persistence found in previous studies can be attributed to the one year momentum effect. His database covers US diversified equity funds between 1962 and 1993 and is free of survivor bias. When he sorts funds on the basis of lagged one-year Ph.D. Thesis: Jeffrey Junhua Lu

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raw return, his four-factor model with market, size, book-to-market, and one-year momentum factors explains almost all of the cross-sectional variation in expected returns. In accordance with the previous evidence, funds with better last-year performance have higher a return and one-factor Jensen’s alpha than funds that underperformed in the previous year. However, this difference is mostly due to size, and especially momentum factors, as last-year winners tend to hold more small stocks and momentum stocks than last year losers. The only significant degree of persistence unexplained

by

Carhart’s

model

is

consistent

underperformance

by

his

worst-performing funds, which have significantly negative four-factor alphas. Investigating the factors explaining the differences in fund risk-adjusted performance, Carhart finds a significantly negative relationship between fund four-factor alphas and expense ratios, turnover, and load fees. A 1 percent increase in expense ratio, turnover, and maximum load fee is associated with 1.54 percent, 0.95 percent, and 0.11 percent declines in annual risk-adjusted return, respectively. Testing the consistency in funds’ annual return rankings, Carhart finds that year-to-year rankings of most funds are largely random. Only funds in the top and bottom performance deciles in the last year are likely to remain in these deciles next year. As a result, one-year performance persistence is short-lived, being mostly eliminated after one year. Carhart finds slight evidence of persistence in risk-adjusted performance, as funds with high four-factor alphas tend to have above-average alphas in subsequent periods. However, this result should be treated with caution, since using the same model to sort and estimate performance may pick up model bias that appears between ranking and formation periods. Teo and Woo (2001) examine persistence in style-adjusted fund returns (fund returns in excess of the returns of the average fund in their Morningstar style category). They argue that most funds with high raw returns are clustered into well-performing styles and that a large year-to-year variation in style returns may preclude finding persistence in raw returns. Sorting funds on the basis of lagged three-year style-adjusted returns, they find significant spreads between Carhart’s four-factor Ph.D. Thesis: Jeffrey Junhua Lu

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Jensen’s alphas for funds in the top and bottom deciles. These spreads are larger than those based on raw returns and persist for up to six years. This evidence suggests that some managers do have better abilities than others. Several studies investigate other factors that can explain mutual fund performance. Using a sample of US stock and bond funds in 1990-1999, Elton et al. (2002) examine performance differences between funds using incentive fees (fees dependent on the fund’s benchmark-adjusted return) and other funds using solely fraction-of-funds fees (fees proportional to the fund’s assets). They find that funds with incentive fees earn, on average, an (insignificantly) positive multi-factor alpha of 58 basis points per year, which is higher than the average alpha of other funds. Note, however, that this difference appears to be almost entirely due to the differential expenses of these two classes of funds. Funds using incentive fees have an average expense ratio of 56 basis points per year lower than expense ratios of similar funds with no incentive fees. Among funds with incentive fees, risk-adjusted performance seems to be higher when managers are hired internally by the fund family. Chevalier and Ellison (1999a) study the relationship between fund performance and the characteristics of fund managers that may indicate ability, knowledge, or effort. Their sample consists of 492 managers of growth and growth-and-income funds between 1988 and 1994. They find significant differences between the raw returns of fund managers with different characteristics including manager age, the average SAT score of the manager’s undergraduate institution, and whether the manager has an MBA. However, most of these return differences are attributed to the differences in managers’ investment styles and to the stock selection biases. Nonetheless adjusting for these, the authors do find that managers who attended higher-SAT undergraduate institutions deliver higher risk-adjusted performance. The beliefs of investors, manifested in money flows into mutual funds, also seem to contain some information about future fund performance. Gruber (1996) finds that US stock funds receiving more money subsequently perform significantly better than Ph.D. Thesis: Jeffrey Junhua Lu

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funds suffering fund outflows. Using a sample of US equity funds between 1970 and 1993, Zheng (1999) shows that this “smart money” effect is short-lived and is largely but not completely explained by investors chasing past winners. She demonstrates that the smart money effect is not due to macroeconomic information or style effect, which suggests that investors use fund specific information when choosing between funds. The smart money effect is mostly pronounced in the subset of small funds, whose lagged flows may be used to execute their market beating investment strategies. Several studies use a Bayesian approach for performance evaluation, which combines prior investor beliefs about future fund performance with the information in the fund inflows/outflows data and produces a posterior distribution of fund alphas. Baks et al. (2001) show that even some extremely skeptical priors about the skill of fund managers lead to economically significant allocations of assets to certain active diversified equity funds, based on posterior expectations of the Fama-French (1993) three-factor alpha. Pastor and Stambaugh (2002) develop a framework in which investors’ prior beliefs can distinguish managerial skill from inaccuracy in the pricing model (CAPM, three-factor model of Fama-French, 1993, four-factor model of Carhart, 1997). Using a sample of US domestic equity funds, they demonstrate that optimal mutual fund portfolios are influenced substantially by both types of prior beliefs. Portfolios with the highest Sharpe ratios are constructed when prior beliefs have some confidence in a pricing model. However, investing in equity funds may be optimal even for skeptical investors who rule out the accuracy of pricing models as well as managerial skill. Even if a small group of “star” fund managers earned superior risk-adjusted performance in the past, this may be due to luck. It is natural to expect that some funds out of thousands in the mutual fund universe outperform market indices simply by chance. Using a sample of US equity funds in 1975-1994, Kosowski et al. (2000) apply a bootstrap technique to simulate the distribution of extreme (maximum and

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minimum) performance measures across funds. Using various unconditional and conditional multi-factor models to measure performance, they demonstrate that the performance of the best and worst funds is not a result of sampling variability. To illustrate this point, 41 funds had a risk-adjusted return of at least 1 percent in 1995, while only 15 funds were expected to achieve this level by chance. This finding provides strong evidence of differential stockpicking skills among fund managers and supports the value of the active mutual fund management.

3.3 Behaviour of Mutual Fund Investors 3.3.1 Modelling Mutual Fund Flows In this section, I review studies conducting empirical analysis of the determinants of mutual fund flows, focusing on the impact of past performance. In a typical regression model, the dependent variable is the fund’s net relative or absolute flow. Traditionally (see, e.g., Gruber, 1996), net absolute flows are defined as the change in fund assets net of reinvested dividends:

Fi ,t = TNAi ,t − TNAi ,t −1 (1 + Ri ,t )

(3)

where TNAi ,t denotes fund i’s total net assets at the end of period t and Ri ,t is return of fund i in period t. Similarly, net relative flows are defined as a net percentage growth of fund assets: f i ,t =

TNAi ,t − (1 + Ri ,t )TNAi ,t −1 TNAi ,t −1

=

Fi ,t

(4)

TNAi ,t −1

Both definitions are based on an assumption that all investor earnings are automatically reinvested in the fund and flows occur at the end of period t. A typical model in the literature specifies flows (in this case, net relative flows) as a linear function of past performance and a set of control variables: fi ,t = a + b1ri ,t −1 + ... + bK ri ,t − K + xi' ,t −1c + ui ,t Ph.D. Thesis: Jeffrey Junhua Lu

(5)

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where ri ,t is some measure of fund i’s performance (e.g., raw return, Jensen’s alpha, or corresponding ranking) in period t and xi ,t −1 includes such variables as fund size, age, fees, a measure of riskiness, and performance of other funds in the family. To control for unobserved individual effects (e.g., marketing effort, general reputation, etc.), xi ,t −1 sometimes includes lagged flow fi ,t −1 . The empirical evidence on the impact of past performance and other attributes of mutual funds on their fund flows is described in Sections 3.3.2 and 3.3.3, respectively. 3.3.2 Impact of Past Performance on Mutual Fund Flows

The existing evidence demonstrates a strong positive relationship between mutual fund flows and various measures of their past performance measured over the one-year, three year, and five-year horizons, including Jensen’s alpha and raw return (see, e.g., Gruber, 1996) and category return rankings (see, e.g., Sirri and Tufano, 1998). When taken together, both raw and risk-adjusted performance measures have a significantly positive impact on flows, although the impact of the latter appears to be stronger (see, e.g., Gruber, 1996). This suggests that some investors are style timers choosing funds with high loadings on factors that performed well recently. Note, however, that these effects may be partially offset by the negative impact of fund total risk on flows (see, e.g., Barber et al., 2001). The sensitivity of flows to performance seems to decline with time, i.e., fund last-year performance is more important for investors than fund performance two or three years ago (see Sirri and Tufano, 1998). The flow-performance relationship appears to be asymmetric, as flows to top performers are more sensitive to their performance than flows to poorly performing funds. Using a piecewise linear model in a sample of US growth funds in 1971-1990, Sirri and Tufano (1998) show that flows to funds in the top performance quintile in their objective category are strongly related to their last-year return rankings, whereas for other funds the relationship between flows and performance is weak. For an Ph.D. Thesis: Jeffrey Junhua Lu

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average fund, moving up five percentile points among the top performing funds in the respective category is associated with an 8.4 percent increase in annual relative flow, while a similar move in rankings among funds with bad or intermediate performance results in 0 to 1.4 percent increase in flows. Chevalier and Ellison (1997) use a semiparametric model to estimate the shape of the relationship between fund flows and last-year market-adjusted returns (fund returns in excess of the market return) in a sample of growth and growth-and-income funds in 1982-1992. They demonstrate that this relationship differs considerably bwtween the subsets of young and old funds (funds with age of up to 5 years and over 5 years, respectively). For young funds, the shape of the flow-performance relationship is quite steep and close to linear. A 1 percent rise in the market-adjusted return of an average young fund is associated with about a 4 percent increase in the fund’s annual relative flow. In contrast, expected fund flows to old funds are less sensitive to their last-year performance and the flow-performance sensitivity relationship has a generally convex shape. Old funds outperforming the market are expected to attract about 2.8 percent extra annual flows for a 1 percent rise in the market-adjusted return. Since performance persistence is more pronounced among poor performers than among good performers (see, e.g., Carhart, 1997), one may expect that consumers respond more strongly to low than high performance. The divergence between these expectations and the observed convexity of the flow-performance relationship can be explained by a number of institutional and psychological factors, which prevent large outflows from funds with bad past performance. Market frictions such as the presence of search costs, back-end load charges, tax considerations, and restrictions of the investment retirement plans increase the transaction costs of withdrawing money from the poorly performing funds, while status-quo bias (see Zeckhauser et al., 1991) and cognitive dissonance bias (see Goetzmann and Peles, 1997) make investors ignore information about bad fund performance.

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Capon et al. (1996) use a different approach to examine the allocation rules used by mutual fund investors. They conduct a survey of 3000 consumers investing in US mutual funds who were asked to rate on a five-point scale the importance of given information sources and selection criteria, and to describe their investment approach and demographic characteristics. The results of their survey demonstrate that investors consider performance-related variables as the most important information source (published performance rankings) and selection criterion (performance track record). At the same time, fund characteristics other than return and risk, such as advertising (as an information source) and fund manager reputation, fund family scope, and management fees (as selection criteria), are also important for consumers. The authors also find that mutual fund clienteles consist of several different groups differing considerably from each other in terms of demographic characteristics and investment behaviour. These groups range from the well-informed investors to the naïve ones who are ignorant of their fund investment style and load structure. Further discussion of the non-performance factors driving mutual fund flows is carried on in the next section.

3.3.3 Impact of Other Factors on Mutual Fund Flows

When the information about mutual fund performance is costly, consumers incur search costs to make an allocation decision. Many investors, especially small ones, may choose to save on these costs and make a choice based on the available (incomplete) information. In this case, more visible funds, i.e., those which are heavily advertised and have an established reputation, are expected to attract larger money flows, irrespective of their performance. In addition, flows to these funds may be more sensitive to their performance, since the impact of advertising and established reputation should be even stronger when combined with good performance. Fund flows may be also affected by factors related to other types of transaction costs, such

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as the fee structure (e.g., front load vs annual 12b-1 fee), tax considerations, and the size of the fund family. One proxy for fund visibility is its size. Apparently, large funds spend more on advertising and are more likely to receive media attention. Indeed, money flows to mutual funds are recognised to be roughly proportional to fund size (see, e.g., Gruber, 1996). This is the reason why most studies use the fund’s relative flow as a dependent variable in their regressions. However, the magnitude of relative flows declines with fund size, i.e., large funds tend to attract significantly smaller relative flows than small funds (see, e.g., Sirri and Tufano, 1998). Therefore, a size effect must be taken into account both in regressions of absolute and relative flows. The level of media coverage, which helps to lower search costs, is found to be positively related to fund flows. Sirri and Tufano (1998) show that growth funds whose names are referred to in the major newspapers and periodicals attract larger flows during the same year, while Jain and Wu (2000) find that flows are significantly larger for those equity funds that are advertised in the financial magazines. Fund age may also serve as a proxy for investor awareness about the fund. In contrast to young funds, old funds have an established reputation, which may be good or bad depending on their realised past performance. Therefore, recent performance should be more informative for young funds that do not have such a reputation. Indeed, as discussed in Section 2.3.2, Chevalier and Ellison (1997) find that flows to young funds are more sensitive to their last-year performance than flows to old funds. The effect of fund fees on flows can be twofold. On the one hand, higher fees may lead to lower flows, as investors would like to maximise net-of-fee earnings. In addition, load funds and funds with higher expense ratios have worse a performance than funds charging lower fees (see Carhart, 1997). On the other hand, a higher 12b-1 fee, which is a part of the expense ratio, is associated with larger marketing expenditures and may increase fund flows. The existing evidence is consistent with Ph.D. Thesis: Jeffrey Junhua Lu

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the presence of both effects. Using a sample of US diversified equity funds in 1970-1999, Barber et al. (2001) find that a negative relationship between fund flows and total fees (composed from load fees and expense ratios) is due to the strong negative impact of load fees. However, they find no significant relation between fund flows and expense ratios and even a positive relation in a subset of large funds. These results also suggest that investors pay more attention to salient fees, like loads and commissions, than the expense ratio. The effect of advertising on fund investors may also explain the higher flow-performance sensitivity of high-fee funds found by Sirri and Tufano (1998). Bergstresser and Poterba (2002) study the impact of personal taxation on the investment decisions of consumers who hold mutual fund shares in conventional taxable accounts (not in tax-deferred retirement saving plans). Their sample includes US domestic equity funds in 1993-1999. They find that funds delivering more heavily taxed returns (i.e., returns including more dividends or realised capital gains) attract lower flows than funds with similar pretax returns and lower tax burdens. The flows also appear to be lower for funds with larger stocks of unrealised capital gains (new shareholders of such funds may be taxed on future distributions of these capital gains). The magnitude of the transaction costs incurred by a mutual fund investor is also related to the characteristics of the fund’s family. Since investors are more likely to be aware about the brand name of large and old fund families, funds from these families are more visible. In addition, families offering a large number of funds with a wide range of investment styles decrease the transaction costs for investors who often switch between different types of funds (e.g., stock funds and money market funds). Therefore, funds from large, old, and diverse families are expected to attract higher flows. Indeed, Ivkovic (2000) finds, in a sample of US stock and bond funds in 1991-1999, that funds belonging to larger families attract higher flows. Using a sample of all US open-end funds in 1979-1998, Khorana and Servaes (2001)

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demonstrate that families achieve larger market share when they have more prior experience, offer funds across a wider range of investment objectives, and use more distribution channels. Nanda et al. (2000) explore the performance spillover effects within the fund family, using a sample of US diversified equity funds in 1992-1998. They find that the presence of a star performer (a fund with a return within the top 5 percent in its category) in the family helps to boost flows to the other funds in the family.

3.4 Strategic Behaviour of Mutual Fund Managers 3.4.1 The Objectives of Fund Managers

Similarly to other industries, there is a potential divergence of interests between shareholders and managers of mutual funds. The manager’s strategy consists of two major choices: effort, which allows him to extend his investment opportunities set, and risk. If the principal (fund shareholders) were able to contract directly on actions (effort and risk), it would be possible to achieve the best outcome with properly structured agents’ (fund managers’) incentives. Since, in practice, manager effort is not contractable (i.e., not verifiable by a third party such as a court), the moral hazard problem cannot be eliminated. In a typical mutual fund, two factors influence the manager’s expected payoff: compensation structure and retention policy. Currently, two types of compensation schemes are used by mutual funds: base or fraction-of-funds fee and incentive fee (the latter is always used in combination with the base fee). The base fee is linked to the fund’s size and is charged as a percentage of the average net assets during the year (see, e.g., Khorana, 1996). Deli (2002) reports that in the US, marginal asset-based fee rates are greater for small funds, funds from small families, equity funds (compared to debt funds), and international funds (compared to domestic funds). These differences Ph.D. Thesis: Jeffrey Junhua Lu

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are interpreted as being due to the economies of scale and the difficulties of monitoring the fund performance. The incentive fee depends on the fund’s performance relative to a certain benchmark. The 1970 amendment to the Investment Company Act of 1940 requires the incentive fees of US mutual funds be of a “fulcrum” type. This means that the fee must be symmetric around the benchmark, i.e., the reward for outperformance must be the same as the penalty for underperformance. Probably, this restriction is the reason why only a few US mutual funds use incentive fees. According to Elton et al. (2002), these are mostly large funds accounting for less than 2 percent of the total number of funds in the industry, but controlling more than 10 percent of the total assets under management. Incentive fees can be of the linear or bonus type, being linear or discrete step functions of the benchmark-adjusted fund return, respectively. In most cases, funds use linear incentive fees with a limit (both upper and lower) on the size of the incentive fee, so that the sum of the base and incentive fees cannot be negative. As a result, the incentive fee is usually a piecewise linear function of benchmark-adjusted performance (flat below the lower limit and above the upper limit and increasing between them), which is convex up to the upper fee limit. As was discussed in Section 3.3.2, the sensitivity of flows to performance is higher for well-performing funds than for poor performers (see, e.g., Sirri and Tufano, 1998). This implies that the base fee is a convex function of the fund’s past performance. Thus, fund performance influences the manager’s expected payoff in a convex manner directly, through the incentive fee (over some ranges), and indirectly, through the base fee and the observed flow-performance relationship. Another factor which influences the manager’s strategy is the impact of his actions on the probability of terminating the contract. Several studies demonstrate that fund performance plays a crucial role in the decision to dismiss, retain, or promote the fund’s manager. Khorana (1996) estimates that managers in the lowest performance decile are four times more likely to be replaced than managers in the top performance decile. Chevalier and Ellison (1999b) find that the termination of contract is more performance-sensitive for young Ph.D. Thesis: Jeffrey Junhua Lu

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managers, who do not have an established reputation, than for old managers. For young managers, the probability of termination is a convex function of past performance (over most of the range), decreasing steeply with performance in the case of negative excess returns and being rather insensitive to the differences in performance at positive excess return levels. The authors also find that magnificent deviations in fund sector weightings and level of unsystematic risk from the mean values in the fund’s investment objective category increases the probability of manager termination in case of poor performance, while increasing, although to a smaller extent, the probability of his promotion in the case of good performance. Thus, the convexity of the manager’s expected payoff with respect to the fund’s past performance may be weakened due to the strong impact of manager poor performance on the termination decision. There is vast literature providing extensive game-theoretic analysis of the managerial behaviour in response to different payoff structures (see Section 3.4.2). A number of empirical studies test the predictions concerning the managers’ risk-taking behaviour based on these models as well as other hypotheses (see Section 3.4.3). 3.4.2 Managers’ Strategies: Game-Theoretic Analysis

In this section, we discuss the studies modelling the strategic behaviour of mutual fund managers. Models of delegated portfolio management in the mutual fund industry, in which the agent (fund manager) receives money from the principal (fund shareholder) to invest in financial markets, have their own specifics. Since there are many more investors than funds, fund managers have most of the bargaining power. As a consequence, fund managers and not investors are typically proposing their compensation contracts. Therefore, most models of mutual funds examine pooling equilibrium in which all managers have one type of contract and signal their quality with performance, or separating equilibrium in which managers signal the differences in their abilities by offering different types of contracts. One strand of this literature adopts a behavioural approach and examines the Ph.D. Thesis: Jeffrey Junhua Lu

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equilibrium behaviour of fund managers in response to exogenously given compensation structures observed in the mutual fund industry. Another strand of the literature models both the actions of fund managers and the investment strategies used by fund investors. In this case, the compensation scheme is determined endogenously within the model. In all these studies, the manager’s compensation is some (linear or convex) function of the fund’s performance with respect to some benchmark, which can be absolute (e.g., the return on a market index such as S&P500) or relative (e.g., the best return among other funds). In the former case, the benchmark is exogenous and cannot be influenced by players’ actions. In the latter case, the benchmark is determined endogenously in the equilibrium. I start with the first strand of the literature and exogenous benchmarks. Grinblatt and Titman (1989) use option pricing theory to analyse the impact of convex option-like compensation schemes on the risk-taking behaviour of fund managers. They show that such schemes induce excessive risk-taking from both informed and uninformed fund managers. Moreover, managers with superior information may select the same portfolio as uninformed managers, if the performance fee can be hedged in the manager’s personal portfolio. Carpenter (2000) models the dynamic investment problem of a risk-averse manager who is compensated with a call option on the managed assets with an exercise price equal to a benchmark return and who cannot hedge this position. She demonstrates that option-like compensation does not always lead to greater risk taking. The manager dynamically adjusts volatility in response to changes in the benchmark-adjusted return and may actually decrease risk if the option is in the money or if the evaluation date is far away. Chen and Pennacchi (1999) analyse in a continuous setting the impact of the fund’s prior performance on the portfolio choice of a fund manager with convex benchmark-adjusted compensation. They show that funds with poor performance have an incentive to increase tracking error with respect to the benchmark, which is however not equivalent to an increase in volatility. Admati and Pfleiderer (1996) show that even compensation contracts that are linear in benchmark-adjusted performance are not optimal with respect to efficient Ph.D. Thesis: Jeffrey Junhua Lu

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risk sharing and incentive alignment between managers and investors. In their model, an optimal outcome is achieved when compensation is only based on the total unadjusted return of the manager’s portfolio. Similar conclusions are reached by studies in which managers are rewarded on the basis of relative performance, i.e., when the benchmark is endogenous. Hvide (1999) models the one-period game between fund managers with the tournament reward structure, where only the top performer receives the bonus (resulting, e.g., from the money flows). In his model, managers choose not only effort, which determines the expected return, but also the riskiness of the portfolio. In the extreme case, when there are no limits to possible risk-taking, the tournament breaks down, as managers choose zero effort and infinite risk in equilibrium. When risk-taking is limited, the tournament rewards induce excessive risk-taking and lack of effort from fund managers. The author shows that the scheme with higher reward for modest rather than excellent performance may lead to less risky strategies. Palomino (2002) analyses a different reward structure, in which the manager’s payoff depends linearly on the difference between his return and some function of the returns of other funds (e.g., the mean return in the fund’s category). He shows that even in the case of linear relative performance objectives, managers choose overly risky strategies to outperform their competitors. Furthermore, there is an under acquisition of information in equilibrium. Thus, neither linear, nor convex compensation contracts can optimally (in the best sense) align the interests of managers and investors in mutual funds. What happens if we allow the compensation structure to be determined in the equilibrium? Heinkel and Stoughton (1994) consider the multi period relationship between risk-neutral investor and a pool of risk-neutral fund managers with different, but ex ante unknown abilities. They show that in the first period the investor induces most managers to sign the standard (“boilerplate”) contract with little performance-based component (only a few managers with exceptional ability choose a different contract with a high

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performance-based component). The investor provides proper effort-exerting incentives to fund managers by a credible threat of dismissal following a performance evaluation. The manager is only retained if the return on his portfolio exceeds the benchmark by an appropriate amount (too high return indicates luck rather than skill). These results may provide theoretical justification for the limited use of performance fees in the mutual fund industry. Huddart (1999) examines a similar two-period model with two risk-averse managers of different abilities. In this model, investors also make inferences about managers’ abilities on the basis of their relative performance over the first period. In the second period, investors reallocate their wealth to the fund with the highest first-period return, which is most likely to be informed in equilibrium. However, this allocation rule, which maximises investor perceptions of managerial ability, does not provide proper risk-taking incentives to fund managers. When managers receive a fraction-of-funds fee, they choose overly risky strategies to maximise the chance of becoming the top after the first period. The uninformed manager does it to appear informed, while the informed manager does it to increase the cost of mimicking him. The author shows that the adoption of a performance fee with respect to an exogenous benchmark helps to mitigate these effects. Das and Sundaram (2002) consider the setting in which fund managers choose fee structures to signal their abilities to investors and compare the equilibria with asymmetric incentive fees with the equilibria with (unlimited) fulcrum fees. Consistent with the previous studies, they show that asymmetric incentive fees encourage the adoption of more risky portfolios than fulcrum fees. However, when the entry costs for uninformed managers are low, incentive fees may be more preferable for investors’ welfare than fulcrum fees. Palomino and Uhlig (2002) model a game in which risk-neutral investors choose between an index fund and an active fund. The manager of an active fund may be good or bad (a bad manager is uninformed, while a good manager may be informed Ph.D. Thesis: Jeffrey Junhua Lu

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with some probability) and is compensated with a fraction-of-funds fee. Investors can only observe realised returns, from which can be inferred about the unknown quality of the active fund’s manager. Under the condition that investing in an active fund is not optimal ex ante (i.e., before observing returns), the model has an equilibrium, in which investing in the active fund is optimal ex post, if its return falls within some interval (i.e., is neither too low or too high). In this equilibrium, an informed manager picks a portfolio with minimal riskiness, and an uninformed manager chooses higher risk, gambling on a lucky outcome. When the fee structure is endogenous, both types of active fund manager choose the same fraction-of-funds fee structure. 3.4.3 Managers’ Strategies: Empirical Evidence

In this section, I review empirical evidence on the strategic behaviour of mutual fund managers. I start with the studies testing predictions of the theoretical models discussed in the previous section. Since the calendar year is often used as the performance evaluation period for mutual fund managers,11 they are interested in maximising their calendar-year performance. The convexity of the manager’s payoff function (see Section 3.4.1) suggests that mutual funds will seek to participate in the annual tournaments competing for top year-end rankings. Based on the theoretical models of Carpenter (2000) and Chen and Pennacchi (1999), one can formulate the hypothesis that funds with bad performance after the first part of the year have an incentive to increase risk in the second part of the year, trying to catch up with interim winners at the end of the year. Several studies test this tournament hypothesis examining within-year changes in risk measured on the basis of monthly return data. Applying a contingency table methodology to a sample of US growth funds in 1976-1991, Brown et al. (1996) find that interim losers (defined as funds below the median return category over the first part of the year) increase risk towards the end of 11

In general, two types of evaluation horizon are used: rolling horizon or fixed calendar-year horizon. Mutual fund performance based on the rolling one-year horizon (e.g., fund raw return during the last 12 months) as well as year-to-date performance (e.g., fund raw return from January to the current month) are often published in the financial newspapers. Calendar-year performance is reported in funds’ prospectuses as well as fund listings published on an annual basis by many periodicals and data providers. Ph.D. Thesis: Jeffrey Junhua Lu

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the year relative to interim winners. Using a sample of US domestic equity funds in 1992-1994, Koski and Pontiff (1999) apply regression methodology and find a negative relationship between fund return over the first semester and the change in total, systematic, and unsystematic risk between the first and second semesters. Chevalier and Ellison (1997) use a different approach, measuring fund risk on the basis of the fund’s portfolio holdings. They also find a negative relationship between fund return over the first nine months of the year and the change in fund risk between September and December, using a sample of growth and growth-and-income funds in 1982-1992. However, Busse (2001) finds no such evidence, applying either the contingency table or the regression methodology to the daily returns of 230 US domestic equity funds in 1985-1995 (new entrants after 1984 are not included). He explains this divergence in results by the presence of auto-correlation and cross-correlation in fund returns, which was not accounted for in the standard statistical tests used in the previous studies. A related literature examines strategic changes in fund styles measured as factor loadings from a multi-factor model. Chan et al. (2002) find in a sample of US domestic equity funds in 1976-1997 that fund styles measured on the basis of the Fama-French (1993) three-factor model tend to cluster around a broad market benchmark. When deviating, funds are more likely to favour growth stocks with good recent performance. There is some consistency in styles, although funds with poor past performance are more likely to change styles. Using daily returns of US domestic equity funds in 1985-1995, Lynch and Musto (2000) find that the changes in the factor loadings of the Carhart (1997) four-factor model are larger for funds in the bottom performance quartile than for the other funds. Poorly performing funds tend to increase investments in growth stocks, while good performers are likely to decrease their momentum loadings. The change in strategy as well as managerial replacement among the poor performers seems to lead to some performance improvement. Note, however, that the results of these studies should be treated with caution, since they are

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also subject to the critique of Busse (2001) that statistical tests should account for the auto-correlation and cross-correlation in fund returns. Several studies investigate the gaming behaviour of mutual fund managers around year-ends. Using a database containing the daily returns of US diversified equity funds in 1985-1997, Carhart et al. (2002) find strong evidence that some fund managers mark up their holdings on the last trading day of the year to improve their calendar-year performance (similar although weaker effects are also found at the quarter-ends). By trading aggressively at the end of the trading day, a manager pumps up the closing prices of his portfolio holdings, which determine the fund’s net asset value and daily return. The authors show that funds with the greatest ability and the most incentive to improve their performance rankings are more active in marking up. Musto (1999) presents evidence of window dressing by managers of money market funds in 1987-1997. He demonstrates that funds allocating between government and private issues tend to increase their government holdings around the disclosure dates (at the fiscal year-end and six months later). Since fund performance is reported on the net-of-fee basis, a manager can improve the fund’s relative performance by waiving a part of his contracted fee. Christoffersen (2001) documents that over half of US money market funds waived fees in 1990-1995. This effect is economically significant: institutional funds waive almost half of their contracted advisory fees (19 basis points per year), while retail funds waive about two thirds of their contracted fees (33 basis points per year). Fee waivers allow managers to react flexibly throughout the year to changes in relative performance, which affect fund flows. The link between fund performance and fee waivers appears to be especially strong and statistically significant among poorly performing funds, for which lower performance is associated with larger amounts of waived fees. A convex flow-performance relationship seems to encourage well-performing retail funds to increase waivers as a function of their performance. However, the fee waivers remain

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largely flat among well-performing institutional funds. This is interpreted as evidence of greater price competition among institutional funds than among retail funds. Another strand of the literature tries to classify funds into categories on the basis of their observed investment behaviour. This is important for investors who would like to know the strategy chosen by their funds and identify a relevant peer group for performance comparison. Brown and Goetzmann (1997) classify US equity funds into eight “actual” investment styles according to an algorithm based on funds’ returns. In addition, they estimate the correlation between the style returns and the previous period returns of the S&P 500, T-bills, and foreign equity indices. Some styles are found to exhibit positive correlation (“trend-chasing”), while the others indicate negative correlation (a “contrarian” approach). Teo and Woo (2001) examine persistence in fund performance relative to their peers in the Morningstar style categories. They argue that most funds with good returns are clustered into certain well-performing styles and that a large year-to-year variation in style returns may preclude finding persistence. Indeed, they find strong evidence of persistence in style-adjusted performance measures based on several models including the four-factor model of Carhart (1997).

3.5 On the Timing Abilities of Fund Managers 3.5.1. Stock Return Predictability

There is now a consensus in empirical finance that expected asset returns, and also variances and covariance, are, to some extent, predictable. Pioneering work on the predictability of asset class returns in the US market was carried out by Keim and Stambaugh (1986), Campbell (1987), Campbell and Shiller (1988), Fama and French (1989), and Ferson and Harvey (1991). More recently, some authors have started to investigate this phenomenon on an international basis by studying the predictability of asset class returns in different national markets. 12 Harvey (1989) develops 12

See, for example, Bekaert and Hodrick (1992); Ferson and Harvey (1993, 1995), Harvey (1995); and

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methodologies to implement asset pricing tests with time-varying covariances, variances, and expected risk premiums. Specifically, Ferson and Harvey (1991) find that much of the predicted variation of monthly excess returns of size- and industrygrouped common stock portfolios is associated with their sensitivity to these economic variables. Time variation in the expected compensation for stock beta risk, as opposed to movements in the stock betas themselves, captures most of the predicted variation at the portfolio level. Ferson and Harvey conclude that most of the predictability in portfolio returns is due to a time-varying risk premium. The use of predetermined variables to predict asset returns has produced new insights into asset pricing models, and the literature on optimal portfolio selection recognises that these insights can be exploited to improve on existing policies based upon unconditional estimates of factor coefficients. For example, Kandel and Stambaugh (1996) argue that even a low level of statistical predictability can generate economic significance and abnormal returns may be obtained even if the market is successfully timed only 1 out of 100 times. While Samuelson (1969) and Merton (1969, 1971, 1973) have paved the way by showing that optimal portfolio strategies are significantly affected by the presence of a stochastic opportunity set, optimal portfolio decision rules have subsequently been extended to account for the presence of predictable returns.13 Practitioners also recognise the potential significance of return predictability, starting to engage in timing strategies (also known as “tactical asset allocation strategies”) as early as the 1970s.14 These timing strategies of active mutual funds can be investigated by looking at the covariance matrix between fund systematic exposures to certain risk factors and the risk premia on these risk factors. The key underlying assumption is that from the perspective of uninformed investors, the vector of expected asset returns is constant Harasty and Roulet (2000). 13 See in particular Barberis (2000); Campbell and Viceira (2001); Campbell et al. (2000); Brennan, Schwartz, and Lagnado (1997); Lynch and Balduzzi (1999); Lynch (2000), for a parametric approach in a simple setting or Brandt (1999) and Ait-Sahalia and Brandt (2001) for a non-parametric approach in a more general setting. 14 Wells Fargo is considered to be the first firm to have introduced a tactical asset allocation product, in the 1970s. Ph.D. Thesis: Jeffrey Junhua Lu

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over time, that is, mean assets returns are constant over the sample period. This implies that the systematic exposures to certain risk factors by an uninformed investor cannot be correlated with future risk premia on these risk factors. However, since an informed investor can predict when certain assets will have either higher or lower than average returns, from his perspective the vector of expected returns changes over time. He can therefore profit from these changing expected returns by tilting his portfolio risk exposures over time in favour of factors with expected returns that have increased and away from factors with expected returns that have decreased. Hence, an informed manager whose portfolio systematic exposure to a risk factor is monotonically increasing in its conditional expected return will exhibit a positive unconditional covariance between the systematic exposure to the particular risk factor and the subsequent returns of that factor. 3.5.2. Market Timing

Most existing studies relating to the timing behaviour of mutual funds focus on the market timing abilities of fund managers. Market timing refers to the dynamic allocation of capital among broad classes of investments, often restricted to equities and short-term government debt. The successful market timer increases his/her portfolio weight in equities prior to a rise in the market, and decreases his/her equity weighting prior to a fall in the market. In general, evidence on the ability of investment managers to time the market is mixed. Several studies of mutual fund timing skill15 generally find little evidence of timing skill. In an early study, Treynor and Mazuy (1966), for example, develop a test of market timing and find significant ability in only 1 fund out of 57 in their sample. Henriksson (1984) uses the market timing test of Henriksson and Merton (1981) and finds that only 3 funds out of 116 exhibit significant positive market timing ability. Graham and Harvey (1996) analyse investment newsletters’ suggested allocation between equity and cash, thereby measuring explicitly the ex post performance of timing strategies. Again, they find no 15

See Kon (1983); Chang and Lewellen (1984); Lehmann and Modest (1987), Grinblatt and Titman (1989a), (1994); Daniel, Grinblatt, Titman, and Wermers (1997).

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evidence of timing ability. However, the most puzzling aspect of the empirical evidence is that the average timing measures across mutual funds are negative and that those funds that do exhibit significant timing performance show negative performance more often than positive performance (Volkman, 1999). Also, Kon (1983) and Henriksson (1984) find that there is negative correlation between measures of security selection ability and market timing. Henriksson (1984) suggests a number of potential

explanations

for

these

results,

including

error-in-variables

bias,

misspecification of the market portfolio, and use of a single-factor rather than a multifactor asset-pricing model. On the other hand, when an attempt is made to control for the above issues associated with market timing tests, researchers do demonstrate fund managers’ timing ability. For example, Ferson and Schadt (1996) find some evidence of timing skill when macroeconomic conditions are accounted for. Graham and Harvey (1996) detect evidence of timing skill using certain benchmarks. Wagner et al. (1992), Brocanto and Chandy (1994), and Chance and Hemler (1999) all uncover some evidence of positive timing as well. Brown et al. (1998) find evidence that the Dow Theory works as a timing strategy. Bollen and Busse (2001) demonstrate that using daily rather than monthly fund return data changes inferences regarding the market timing ability of mutual fund managers, and that the standard regression-based tests have more power to detect significant timing activity. 3.5.3. Timing Strategies in a Broader Sense

The active nature of portfolio management is often based on the claim of superior information. If market participants are rational, a necessary condition for superior performance is superior forecasting skills on the part of better performers. Hence, for an active fund manager to outperform his passive counterpart, he must possess some type of superior information and must be capable of exploiting this. Obviously, such information need not be related to the whole market, but can be restricted to subsets of the market. For example, a manager can generate additional performance if size,

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book-to-market, or momentum strategies have time-varying expected returns that can be exploited by changing portfolio weights to exploit these styles when they will be most profitable. Also, some fund managers can be active with regard to sector rotation and try to anticipate and tilt their portfolios toward the sector or sectors they expect to lead the market in future periods. Indeed, market timing is not the only investment strategy employed by active fund managers. What is more, it may not be the main investment strategy used by them. Brown and Goetzmann (1995) carry out an analysis of the risk and return characteristics of chasing the winning funds and find that the average betas for the worst and the best performers are practically the same (same market risk exposure), but the annual standard deviation of returns differs considerably. Because of the correlation across winning funds, it seems that these funds are loading up on macroeconomic factors, unassociated with the major component of equity returns, which is priced as the total market risk premium in the CAPM. Carhart (1997) provides similar evidence that fund return differences are not related to the fund’s risk exposure to the market, since the CAPM betas of his top and bottom performing deciles are virtually identical. Indeed, the size and momentum factors in his 4-factor model account for most of the fund performance spread. A similar idea, expressed in Elton et al.’s (1996) paper, is that the characteristics of top-performing funds change significantly over time. In some periods, small-stock funds do best; in other periods, growth funds do best. In other words, the sensitivity of the top-performing funds to their common risk factors is temporarily unstable. It seems that these top-performing funds successfully take on larger loadings on some risk factors, when the risk premia on these risk factors are high. However, whether these funds intentionally or unintentionally achieve such favourable loadings on relevant common risk factors is still open for discussion.

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3.5.4. Timing Strategy and Stock Selection

Previous studies have documented an inverse relation between the fund managers’ market timing performance and their stock selection performance. The intercept obtained from a timing regression model is often regarded as representing a fund manager’s stock selection ability. Bollen and Busse (2001) find that the average intercept for funds with negative timing coefficients is much higher than the corresponding average for funds with positive timing coefficients as predicted by Jagannathan and Korajczyk (1986). Kon (1983) and Henriksson (1984) also document an inverse relation between timing coefficients and intercepts in timing regressions. Such a negative relation suggests that managers may focus on one source of performance (timing activities) at the expense of the other source of performance (stock selection). This casts doubt on the quality of fund managers’ investment decision processes, that is, whether fund managers can effectively separate their stock-selection activities from their decisions regarding the systematic risk of their funds. 3.5.5. Systematic Factors Affecting Funds’ Timing Behaviour

A growing area of research indicates that institutional investors’ behaviour may be coloured by considerations beyond the maximisation of portfolio return or diversification. Grinblatt et al. (1995) identify herding activity by mutual fund managers. Ferson and Schadt (1996) find that managers rebalance in anticipation of changing economic conditions. Brown et al. (1996) find systematic changes in risk conditional on past performance. Lakonishok et al. (1991) find that “window dressing” accounts for portfolio rebalancing by pension fund managers. Most studies on fund timing activity, in fact, have focused on testing whether fund managers generally possess market (factor) timing skill; few studies try to link the fund manager’s timing behaviour to specific systematic factors, such as market condition, performance record, and investment policy etc., and examine the influences of these systematic factors on fund timing activities. In other words, existing studies fail to

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investigate the different timing behaviours of fund managers under different systematic factor scenarios. Timing strategy is not a free lunch and thus does not come without cost. The major cost associated with an active timing strategy is the resulting increased systematic risk exposure of the fund portfolio. Recall that the major objective of fund managers who implement a market timing strategy is to position their portfolios to be out of sync with the broad market. Instead of acting in advance of market movements, this will put managers at risk of failing to catch up with the market. Because mutual fund companies usually receive a fixed percentage of assets under management as compensation, they will have an incentive to take whatever actions increase the total assets of the fund. Several authors have previously documented a strong relationship between a mutual fund’s past performance and the inflow of new investment into the fund. 16 In effect, the flow-performance relationship then serves as an implicit incentive contract. Chevalier and Ellison (1997) suggest that the risk-taking behaviour of mutual fund managers is consistent with the prospect theory of Kahneman and Tversky (1979). In prospect theory, individuals try to minimise their losses, while “collecting” gains instead of “gambling” for higher profits. To avoid a sure loss of a given quantity, people risk incurring an even greater loss if there is a chance of a better outcome. This surely has implications for fund managers’ timing behaviour, which indeed is responsive to incentives generated by the flow-performance relationship. Funds with bad track records will have greater incentives to pursue timing strategies than funds with good track records, in an effort to enhance performance and attract new investment from fund investors. Moreover, a fund with a smooth track record would be perceived by investors as a preferable investment when compared to a fund with a volatile returns history. Hence, funds with consistently good track records will have fewer incentives to pursue timing strategies than those

16

See, e.g., Patel, Zeckhauser, and Hendricks (1991); Ippolito (1992); Sirri and Tufano (1993); Goetzmann and Peles, in press.

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without consistent track records, such as newly launched funds and funds with volatile performance. In general, market conditions influence fund managers’ timing activities in two ways, affecting not only the value of the timing strategy per se and but also their funds’ inflows themselves. Implementing timing strategies by moving in and out of the market or segments of the market can increase trading costs very significantly, which must be offset by the value added from such timing strategies. Timing strategies exhibit types of option-like payoff (Henriksson and Merton, 1981); hence, the value of the timing strategy depends on the volatility of the underlying market (factor) return. The higher the volatility of return, the higher the value of the strategy. Campbell et al. (2000) find that market volatility increases in down-markets and recessions. Moreover, Duffee (1995) finds that idiosyncratic volatility decreases in down-markets. Both of these effects cause the value of timing strategies (tactical asset allocation) to increase, while decreasing the value of stock selection strategies. Hence, fund managers are more likely to rely on timing strategies during bear markets than they would do so during bull markets. On the other hand, market conditions can affect fund flows in a dramatic way. During bull markets, as the market rally continues, investors become more and more optimistic about equity performance and put money into the equity market. Fund managers can easily attract money as long as their fund performance keeps up with the market. However, during bear markets, investors generally take a pessimistic view of expected equity returns and withdraw money from the equity market. According to the Investment Company Institute, net new cash flows into domestic equity funds shrunk from a peak value of 260 billion dollars in 2000 to 54 billion dollars in 2001, and even a net outflow of 25 billion dollars in 2002. During the same period, the S&P 500 Index dropped from its peak value of 1517 to 911 by the end of July, 2002. In bear markets investors become more risk adverse and avoid investment with a higher perceived expectation of loss. Market timing strategy, which is designed ideally as a tool of riding the bull and hunting the bear, is quite attractive to such risk-averse investors. In order to retain current investors and to Ph.D. Thesis: Jeffrey Junhua Lu

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attract new investors, fund managers have incentives to implement active market timing strategies. Investors have the ability to select funds with significantly different management styles and stated risk objectives. Volkman (1999) investigates the effect of stated risk objectives on the timing performance of funds by segregating his sample into five categories of risk objective: maximum capital gains, growth, growth and income, income, and balanced funds.17 He finds that timing performance is affected by a fund’s stated risk objective. High-risk funds, on average, have a larger degree of significant perverse or negative timing performance than low-risk funds. In addition, the percentage of funds demonstrating significantly positive timing return increases as the stated fund risk objective shifts from high-risk to low-risk funds. These results indicate low-risk funds may be more open to implement timing strategies in anticipation of adverse market movements.

3.6 Behavioural Biases in Mutual Fund Investment The still dominant hypothesis in finance, that markets are efficient, is based on the premise that investors are rigorously rational. Rationality works well as a first order approximation of investor behaviour although it is now recognise that behavioural biases can induce trading patterns at odds with the implications of rationality. In this section, I discuss the studies investigating behavioural biases associated with fund managers’ investment strategies implementation. 3.6.1 Bounded Rationality and Prospect Theory

Many anomalies have been observed in securities markets all around the world. The size effect and the value effect in stock markets are among the most common. Researchers who have been trying to reveal factors underlying these anomalies can be divided into at least two schools: 17

These risk objectives are identified by the Wiesenberger Investment Company Service.

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One school consists of proponents of traditional finance theory. As shown in Fama and French (1998), they try to reconcile seemingly anomalous phenomena by generalising equilibrium models. The most important feature of this school is their insistence that all of the players in the market are rational. Here, rationality means that they conform to the assumptions of expected utility theory (von Neumann and Morgenstern, 1947), and that they can reflect all of the information available in the market in pricing securities prices. The other school consists of researchers opposed to the idea of fully rational market players. They insist that the level of investors’ rationality is seriously limited. Simon (1955, 1956) called it bounded rationality, and was skeptical regarding the assumption made by expected utility theory (von Neumann and Morgenstern, 1947) that decision makers are fully rational. Simon proposed instead the construction of decision-making models that do not assume perfect rationality on the part of decision-makers. Building on Simon’s work, Tversky and Kahneman (1974) introduced the idea of heuristics. This idea means that people tend to use rules of thumb when making a decision due to their lack of ability to process information fully rationally and/or to time pressures, i.e. they have to make a lot of decisions in a limited time. A few years after they presented the idea of heuristics, Kahneman and Tversky (1979) proposed prospect theory, an alternative decision-making model to expected utility theory. Figure 1 represents its value function, where the horizontal axis represents profits/losses and the vertical axis represents the value assigned to each profit/loss by a decision-maker, typically an investor. This figure shows loss aversion, which means that a loss of 1 dollar causes more pain in terms of absolute value than a gain of the same amount provides joy. Figure 1

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Value Function of the Prospect Theory

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This idea of loss aversion was later utilised by some researchers (e.g. Barberis et al., 2001) when they tried to specify factors underlying such anomalies as the equity premium puzzle (Mehra and Prescott, 1985). 3.6.2 Sources of Bias and Behavioural Models

First, as already described, the concept of bounded rationality was first proposed by Simon (1955). This concept implies that human behaviour is not always conducted rationally, as assumed by expected utility theory, which is the basis for traditional finance theory such as the Sharpe-Lintner-Black model (Sharpe, 1964; Lintner, 1965; and Black, 1972). Human judgement, such as selection among several alternatives, is generally made based on past memory and newly collected information. Simon (1955, 1956) suggests that human behaviour can be subject to biases at any of three stages in the decision-making process; recalling memories, selecting information, and making judgements.

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The second source of bias relates to time constraints. Human beings are very busy and have to continuously make many kinds of decisions. As a result, they cannot afford to take a lot of time and try to make an optimal decision in every judgemental situation. Thirdly, emotional factors can be a source of bias in human judgement. In particular, overconfidence and regret aversion are included in biases, which could lead to market anomalies. Fourth and finally come social factors. Human beings tend to create a variety of societies, and to act as members of each society. Meanwhile, they are subject to some kinds of social bias such as exposure to market sentiment, herding, and avoidance of cognitive dissonance. Market sentiment means the general atmosphere of bullishness or bearishness in the market. For example, when market sentiment is very bullish, investors would like to purchase securities even though they are mostly overvalued. On the other hand, herding is the human tendency to act similarly, following other people’s behaviour. To act differently when other people are acting uniformly is mentally very difficult. Lastly, the avoidance of cognitive dissonance refers to the human tendency to try to be consistent in one’s behaviour. Having once expressed a positive or negative opinion on something, people find it difficult to change their position even though they have discovered reasons for doing so. For example, if an analyst has written a report with a buy recommendation for a certain stock, he or she may feel some mental pressure not to express a negative view about the stock even when its issuing firm has announced some detrimental news. Reflecting the sources of bias described so far, some researchers have presented behavioural models which can be more directly connected to market anomalies. The seminal work in the field of behavioural finance is considered to be that of Tversky and Kahneman (1974). It discusses three classes of heuristic to which decision makers are prone. The term heuristics refers to the human tendency to try to intuitively solve problems with limited information by using rules of thumb, even Ph.D. Thesis: Jeffrey Junhua Lu

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when people could derive better answers with more time and information. Although this kind of decision-making rule is generally regarded as an effective way to deal with daily encumbrances, it can lead to systematically biased decisions. Tversky and Kahneman (1974) describe representativeness, availability, and anchoring heuristics. The representativeness heuristic relates to the human tendency to judge A as belonging to a group X (Ａ ∈ Ｘ) if A has any representative feature of that group. The availability heuristic is the human tendency to consider that more familiar things happen more often. Accidents and homicides are generally considered to happen quite often because they receive a lot of coverage in the mass media. People usually take care not to get involved in such affairs since they are a familiar risk. At the same time, people tend to disregard the risk of sicknesses such as diabetes because they are largely ignored by the news media. Anchoring refers to the tendency to consider an arbitrary available number as a starting point for estimating the true value of an unknown matter. The resulting estimate can be affected by the arbitrary number. Prospect theory, first described by Kahneman and Tversky (1979), as indicated above, is intended to be an alternative model to expected utility theory (von Neumann and Morgenstern, 1947). This model is based on five experimentally established aspects of human nature: 1) People tend to evaluate alternatives not by their ultimate asset value but by how far the alternatives depart from a reference value. 2) People tend to be risk averse when making a profit, but reckless when suffering from a loss. 3) People tend to weigh a loss of a certain quantity more than the gain of the same quantity. 4) People tend to value 100 percent certain things much higher than merely probable things. 5) People tend to overvalue the chances of a scenario succeeding when the probability is very small. Finally, the idea of mental accounting is presented by Thaler (1985). It is the human tendency to set up a series of notional local accounts and try to optimise the value of each account separately, rather than considering all accounts together.

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3.6.3 The Disposition Effect

Investors’ reluctance to realise losses has long been noted. Shefrin and Statman (1985) predicted that because people dislike incurring losses much more than they enjoy making gains, and people are willing to gamble in the domain of losses, investors will hold onto stocks that have lost value (relative to the reference point of their purchase) and will be eager to sell stocks that have risen in value. They called this the “disposition effect”. Shefrin and Statman (1985) were the first to draw attention to the potentially substantial impact of this bias on investor behaviour in capital markets and, importantly, to show the scope of Kahneman and Tversky’s (1979) seminal work on prospect theory in generating predictions about the effect. Prospect theory is founded on two propositions. Firstly, investor utility is a function of gains and losses relative to a benchmark, rather than a function of absolute wealth. Secondly, investors’ utility functions are concave for gains and convex for losses (i.e., the regret from a loss is greater than the pleasure from a gain of equivalent magnitude). More specifically, prospect theory implies that investors employ a valuation function which reflects risk aversion in the domain of gains and risk seeking in the domain of losses. Investigations in both experimental settings (eg, Weber and Camerer, 1998) and market settings (eg, Brown et al., 2001; Kaustia, 2000; Ferris et al., 1998; Odean, 1998; Grinblatt and Keloharju, 2001) yield findings consistent with the implications of prospect theory. These latter market-based studies, in fact, indicate the impact of what is substantial, vindicating Shefrin and Statman’s early contention that the assumption of complete rationality is predictively inaccurate in important respects. Given these findings, two questions become interesting. One is whether the disposition effect is truly attributable to behavioural bias rather than other explanations, some of which might be reconcilable with rational behaviour. The other is the extent to which disposition effect biases manifest themselves in capital markets. For instance, it is reasonable to suppose that more sophisticated investors might be less susceptible to the bias given that it can lead to sub-optimal investing, as Odean

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(1998) documents.18. Further, in cases where the wealth loss from exhibiting the disposition effect is salient and substantial, such as failure to capture the tax shields from unrealised capital losses, we might expect virtually all investors to overcome their usual reluctance to sell losing stocks. Explanations that compete with prospect theory to explain the disposition effect include contrarian investment strategies, diversification motives, and transaction cost minimisation. The contrarian explanation posits that investors choose to sell winning stocks and hold losing stocks because they perceive today’s losers to be tomorrow’s winners and vice versa. The diversification explanation is that investors respond to large price increases (decreases) by selling (buying) some of the appreciated (depreciated) stock to restore diversification to their portfolios (Lakonishok and Smidt, 1986). Finally, the disposition effect might be a function of transaction cost minimisation strategies. As trading costs tend to be higher for lower priced stocks and because losing investments are more likely to be lower priced, investors may refrain from selling losers simply to avoid the higher transaction costs (Harris, 1988). Odean (1998) provides persuasive evidence against each of the competing explanations documenting evidence to show that “investors who sell winners and hold losers because they expect the losers to outperform the winners are, on average, mistaken” (p.1790) and that investors who sell all their holdings – and who are thus unlikely to be motivated by diversification motives – remain reluctant to include losing stocks in their sales. He also finds “investors appear to prefer to sell winners and hold losers even when trading costs for both are about the same”. Given that behavioural biases appear to be responsible for the disposition effect, I turn to review evidence on the strength of these biases, an issue of substantial interest to investors and regulators, among others.

18

Statman and Shefrin (1985) cite several anecdotal examples to show professional traders are aware of the pitfalls of succumbing to the disposition effect. Ph.D. Thesis: Jeffrey Junhua Lu

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There is strong evidence that “professionalism” or investor sophistication does not bring immunity. For instance, Coval and Shumway (2001) analyse the trades of Chicago Board of Trade professional market makers. They find that traders with losing mornings (a) place more trades, (b) place trades with larger average size, and (c) assume greater total dollar risk than those with profitable mornings. However, Shapira and Venezia (2000) find that while the disposition effect is pervasive it is significantly weaker among professional investors than among amateurs in Israel, where stock market gains are tax free. The conclusion that greater investor sophistication is associated with less susceptibility to the disposition effect is supported by Locke and Mann (2000). Locke and Mann review the trading behaviour of professional futures traders and find that while all traders hold losers longer than winners, the least successful traders hold losses the longest, while the most successful traders hold losses for the shortest time. One contribution of my thesis is to document the extent fund managers are susceptible to the disposition effect, an issue of interest in light of the agency complications attendant on institutional investment (Odean, 1998). The passage of time and investors’ experience of prior gains and losses could mitigate the influence of the disposition effect (Johnson and Thaler 1990). That is, after a period of time investors “make peace with their losses” (Kahneman and Tversky 1979). The notion that investors’ prior gains and losses influence the operation of the disposition effect is more developed. Johnson and Thaler (1990) contend, and document evidence, that the degree of investors’ loss aversion depends upon prior gains and losses: a loss that comes after prior gains is less painful than otherwise because it is cushioned by the earlier gains. Conversely, a loss that comes after other losses is more painful: after suffering from their first loss, people are even more sensitive to additional setbacks. In short, people are less risk averse following earlier gains and more risk averse after losses, a phenomenon Johnson and Thaler term the “house-money effect” and the “snake-bite effect”. On the one hand, gamblers treat their winnings as house money, not their own money, and thus they tend to take very large risks with their winnings. Similarly, investors face a tendency to treat Ph.D. Thesis: Jeffrey Junhua Lu

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investment gains as house money. Since the gains are viewed as a free opportunity, the investor is more willing to gamble with the gains. In general, the house-money concept predicts that investors will systematically increase risk (implement riskier investment strategies) after earning profits. On the other hand, the snake-bite effect refers to the reluctance to take risks after experiencing losses. Once someone has been bitten by a snake, they will avoid entering locations inhabited by snakes. The snake-bite effect predicts that investors will avoid riskier stocks once they have experienced a loss in the stock market. Besides, there are still other behavioural biases that, it is argued, affect investors’ investment decisions, such as the “trying-to-break-even” effect and the “endowment” effect. The trying-to-break-even effect moves counter to the snake-bite effect. Gamblers have a stronger bias towards “breaking even” after prior losses. The “trying-to-break-even” effect refers to the desire by investors to recoup large losses in one quick long-short (very high-risk) investment. Hence, it predicts that investors will systematically pursue high-risk investments after losing money. The “endowment” effect refers to the tendency by people to place a higher value on what they own than on identical items that they do not own. The endowment effect also can be viewed as a “do nothing” effect. This behavioural bias causes investors to pay little attention to changes in risk and return characteristics, but instead make decisions based on a preference for keeping their original investments. Selling an original investment elicits pain or a feeling of loss. The endowment effect predicts investors will keep their existing portfolio unchanged. A complication with the house-money effect is that it conflicts, prima facie, with prospect theory’s implication that investors are risk-seeking after losses to make up their shortfall. However, Barberis et al. (2001) contend there is no inconsistency. Prospect theory predicts behaviour over the course of a series of associated investments or gambles, e.g., a day at the races or consecutive investments in a single stock. The house-money effect makes predictions about behaviour after the gain or

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loss at the end of the series is experienced, not before. One implication is that after selling out of an investment at a loss, an investor will be more risk averse when making subsequent investment decisions. In summary, the research evidence to date shows that the disposition effect is substantial yet subject to variation in influence and likely caused by behavioural biases. 3.6.4 Overconfidence

One conceptualisation of overconfidence is that traders with this attribute assign excessive weight to their own abilities when things happen to go their way. Gervais and Odean (2001) develop a microstructure model with an informed overconfident trader. The overconfidence bias, coupled with early success, leads to increased risk taking relative to a non-overconfident trader (or an unsuccessful trader). Over time individual overconfidence disappears in their model as traders learn their true abilities. Daniel and Titman (1999) show how market anomalies associated with overconfident investors may be exploited. They term the existence of these persistent exploitable anomalies the lack of adaptive efficiency. Daniel and Titman build directly on Daniel et al. (1998b), who model overconfidence in a multi-security economy. Overconfidence in the models mentioned above has a continuing effect on relative market prices, and leads to profitable “bottom feeding” strategies. The model of Gervais and Odean (2001) predicts that experience and learning will eliminate overconfidence. In their model, traders suffering from overconfidence evolve from somewhat rational, but noisy, to overconfident, and finally, after discovering their true abilities, back to rational. They suggest that overconfidence is a trait that will be exhibited mostly by unseasoned traders with higher abilities, since losses are not discounted, but wins are overvalued. Traders with higher abilities are more likely to have success, and thus build up some overconfidence, until they outgrow the overconfidence and are made aware of their true abilities.

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If experience eliminates overconfidence, then experienced professional investors should exhibit little or no overconfidence. This may have implications for the market effects of retail trader overconfidence, in so far as overconfidence has the potential to generate inefficiencies, which could be arbitraged away by shrewd and rational professionals.

3.7 Summary and Limitations on Current Studies I have reviewed the existing literature on mutual funds in five parts: mutual fund performance evaluation, determinants of mutual fund flows, strategic behaviour of fund managers, fund timing activities, and the behavioural biases of investors. 3.7.1 Summary

The measurement of mutual fund performance is crucial for evaluating fund manager skill. As discussed in Section 3.4.1, past performance of a mutual fund influences both managerial compensation and the decision to retain, promote, or fire the manager. The central question in the recent studies into mutual fund performance is: “Does active fund management add value?” For a mean-variance investor, this question can be reformulated as: “Does the addition of active mutual funds to the portfolio of available assets lead to a shift in the mean-variance frontier?” If the answer is negative, consumers may be better off investing in low-cost index funds and avoiding expensively managed active funds. Two approaches have been used in the literature to measure risk-adjusted performance of mutual funds: return-based (see, e.g., Gruber, 1996) and portfolio-based (see, e.g., Daniel et al., 1997). The former approach employs fund returns, while the latter uses fund portfolio composition in order to construct a passive benchmark replicating the risk characteristics of the fund’s portfolio. The difference between the fund’s return and the benchmark return indicates whether the manager has superior knowledge or skills that allow him to Ph.D. Thesis: Jeffrey Junhua Lu

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outperform the benchmark. The existing empirical evidence suggests that mutual funds, on average, have negative or, at best, neutral risk-adjusted performance after costs. However, this does not necessarily imply that investors should not invest in mutual funds at all. Several studies examine whether there are consistent differences between the performance of various types of mutual funds that can be forecast. It has been found that there is a significant year-to-year persistence in raw returns, i.e., funds with the highest (lowest) raw returns over the last year are likely to be winners (losers) next year as well (see, e.g., Brown and Goetzmann, 1995). However, most of this persistence appears to be due to the differences in fund fees and exposures to the common risk factors (see, e.g., Carhart, 1997). Lesmond et al. (2004) find that the returns associated with momentum strategies do not exceed trading costs. Several studies nevertheless demonstrate that it is possible to identify funds with inferior as well as superior risk-adjusted performance (see Kosowski et al., 2000) and that even investors with skeptical priors about the existence of managerial skill may include the latter funds in their optimal portfolios (see, e.g., Baks et al., 2001). According to standard portfolio theory, an investor should base his allocation decision on the expected return and risk of mutual funds and alternative assets. Since in practice investors incur costs to collect and, maybe even more importantly, to process relevant information, they may limit their attention to a subset of the actual investment opportunity set, which does not necessarily include all mutual funds present in the market. Investors are more likely to consider more visible funds, for which the information or search costs are lower. Other factors related to the transaction costs, such as the fee structure (e.g., front load vs annual 12b-1 fee), size of the fund family, and tax considerations, may also play a role for mutual fund investors. A number of studies investigate the relationship between performance and flows to mutual funds. Consistent with theoretical predictions, it has been demonstrated that better performing funds attract larger flows (see, e.g., Gruber, 1996). The flow-performance relationship appears to be convex, being stronger (weaker) for the best (worst) performers (see, e.g., Sirri and Tufano, 1998). Mutual Ph.D. Thesis: Jeffrey Junhua Lu

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fund flows are found to depend on a number of fund-specific factors, such as fund size, age, and fees (see, e.g., Sirri and Tufano, 1998, and Chevalier and Ellison, 1997), as well as fund family characteristics, such as size and age of the fund’s family and performance of other funds in the family (see, e.g., Nanda et al., 2000). Numerous studies conduct a game-theoretic as well as empirical analysis of the strategic behaviour of mutual fund managers. There are two major factors that influence the expected payoff and, consequently, strategy of a mutual fund manager: compensation structure and retention policy. Several studies model the behaviour of fund managers in response to the exogenously given compensation contracts observed in the mutual fund industry. They demonstrate that contracts, linear or convex, in the fund’s benchmark-adjusted performance are not optimal for the incentive alignment between managers and investors (see, e.g., Admati and Pfleiderer, 1996). In equilibrium, fund managers typically choose lower effort and excessive risk taking (see, e.g., Hvide, 1999). In addition, the fund manager’s risk policy may vary over time depending on his current performance relative to the benchmark (see, e.g., Carpenter, 2000). Some studies use a different approach allowing the compensation structure to be a part of the equilibrium, i.e., being endogenously determined in the model. These show that various types of fees used in the mutual fund industry may arise in equilibrium, including the incentive fee rewarding good performance (see, e.g., Das and Sundaram, 2002) and fraction-of-funds fee based on the fund’s assets (see, e.g., Heinkel and Stoughton, 1994). The existing empirical evidence suggests that fund choice of risk may be related to its past performance (see, e.g., Brown et al., 1996; and Chevalier and Ellison, 1997). However, most of these results should be treated with caution, since they are based on statistical tests that do not take the auto-correlation and cross-correlation in fund returns into account (see Busse, 2001). Several studies find evidence of gaming behaviour, such as window-dressing and marking-up of fund performance, by fund managers around fund year-ends (see, e.g., Musto, 1999, and Carhart et al., 2002).

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Most existing studies related to the timing behaviour of mutual funds focus on the market timing abilities of fund managers. In general, evidence on the ability of investment managers to time the market is mixed. Several studies of mutual fund timing skill19 generally find little evidence of such timing skill. In an early study, Treynor and Mazuy (1966), for example, develop a test of market timing and find significant ability in only 1 fund out of 57 in their sample. Henriksson (1984) uses the market timing test of Henriksson and Merton (1981) and finds that only 3 funds out of 116 exhibit significant positive market timing ability. Graham and Harvey (1996) analyse investment newsletters’ suggested allocation between equity and cash, thereby measuring explicitly the ex post performance of timing strategies. Again, they find no evidence of timing ability. However, the most puzzling aspect of the empirical evidence is that the average timing measures across mutual funds are negative and that those funds which do exhibit significant timing performance show negative performance more often than positive performance (Volkman, 1999). Also, Kon (1983) and Henriksson (1984) find that there is negative correlation between measures of security selection ability and market timing. Henriksson (1984) suggests a number of potential

explanations

for

these

results,

including

error-in-variables

bias,

misspecification of the market portfolio, and use of a single-factor rather than a multifactor asset-pricing model. Shefrin and Statman (1985) introduce the disposition effect, based on the prospect theory of Kahneman and Tversky (1979), as an explanation for the perceived anecdotal evidence at that time of investor reluctance to realise losses. The disposition effect arises when investors focus on a reference point for their position from which gains and losses are calculated, rather than following a portfolio choice model. Agents are alleged to use a form of “frame reference” --- evaluating opportunities to close existing positions as either gains or losses, measured against the reference point. Recent evidence provided by Odean (1998a, 1999), Heisler (1996), and Barber and

19

See Kon (1983); Chang and Lewellen (1984); Lehmann and Modest (1987), Grinblatt and Titman (1989a), (1994); Daniel, Grinblatt, Titman and Wermers (1997).

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Odean (2000a, 2000b) shows that small investors often ignore this well-known rule, and tend to hold losses longer than gains. Early evidence supporting prospect theory is largely experimental (Kahneman and Tversky, 1979; Kahneman et al., 1990). However, this literature has been criticised for a lack of realism due to the absence of a monetary payoff. On the other hand, other research looks at volume patterns for stocks conditioned upon prior price changes, including papers by Shefrin and Statman (1985) and Ferris et al. (1988). More recently, Barberis et al. (1998), Daniel et al. (1998a, 1998b), and Barberis et al. (1999) have examined whether the prospect theory holds in asset prices, in conjunction with the concept of the “house-money” effect. House-money is the issue of altering behaviour upon realising gains and losses, i.e., becoming less risk averse after realising a gain. Fama (1998) points out that “observational” evidence is clearly subject to various, potentially conflicting, interpretations. Odean (1998a, 1999), Heisler (1996), and Barber and Odean (2000a, 2000b), look at direct evidence of the disposition effect in the trading behaviour of small retail investors, or, in the case of Heisler, small off-exchange retail speculators. These studies support the notion that these investors trade in a manner that is consistent with behaviour predicted by prospect theory. That is, they hold their losing trades longer than their winning trades, and this leads to deteriorating profitability, according to the evidence in Odean (1998a). 3.7.2 Limitations to Current Studies

Most current studies on mutual funds market timing activities are based on Jensen’s single factor model. As Roll (1978) and others have noted, performance evaluation with regression based methods is likely to be sensitive to benchmark choice. In particular, benchmarks that are mean-variance inefficient provide erroneous inferences. The well-known size and dividend-yield biases, documented in tests of the CAPM, provide one set of recipes for managers who wish to game an evaluation with CAPM-based benchmarks. The omission of relevant factors in addition to the return on the market portfolio from the return-generating process can create a potential source of error in market timing tests. If the omitted factor can be identified, then the Ph.D. Thesis: Jeffrey Junhua Lu

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return-generating process can be modified to take into account the omitted factor, and a multifactor version of the market timing test can be used. Fama and French (1993) suggest two easily measured variables, size and book-to-market equity, which combine to capture the cross-sectional variation in average stock returns. Carhart (1997) adds in a momentum factor and demonstrates that common factors in stock returns almost completely explain persistence in equity mutual funds’ mean and risk-adjusted returns. These additional factors have been shown to capture the major anomalies of Sharpe’s (1964) single-factor CAPM, and are included so as not to reward managers for simply exploiting these anomalies. Omitting these relevant factors in the market timing test could bias the results of those studies based on a single factor model. Two exceptions are found in the literature: Volkman (1999) and Bollen and Busse (2001). They both incorporate Carhart’s (1997) four-factor model into their market timing test, in an effort to address the problems of benchmark inefficiencies noted by Fama and French (1993) and to correct for biased performance measures created by nonstationary risk. As noted earlier, the timing activities of fund managers are not restricted to market timing, but are open to a broader arena including factor timing, style timing, and sector timing. However, few studies to date address other timing activities besides market timing. Only two studies investigate the style timing abilities of US mutual fund managers. Daniel et al. (1997) introduce a characteristic-based benchmark based on the characteristics of stocks held by the portfolios that are being evaluated. Specifically, they employ a “characteristic timing” measure based on the market capitalisation, book-to-market, and prior-year return characteristics of those stocks in their fund portfolios and detect whether portfolio managers successfully time their portfolio weightings on these characteristics. They find that “characteristic timing” performance is insignificant for all categories of funds in their analysis over the entire sample period and is never significantly positive in any sample sub-period for any category of funds. This indicates that the average mutual fund is not able to effectively time different stock characteristics. Using the same timing measure, Ph.D. Thesis: Jeffrey Junhua Lu

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Wermers (2001) finds similar results showing that none of his fund portfolio categories --- past winners, past losers, or funds in between --- have the ability to successfully time their styles. However, both studies use only quarterly mutual fund portfolio holdings data, and as Wermers (2001) points out, his characteristic timing measure does not capture the ability of fund managers to time styles over other time horizons, such as monthly or semi-annual intervals. In the UK, there is one study investigating the timing ability of pension funds with respect to the size factor. Thomas and Tonks (2001) examine the performance of the UK equity portfolios of 2,175 segregated UK pension funds over the period 1983-97. Specifically, they investigate the sensitivity of the fund returns to the addition of a size premium, which they find to be significant and important for the smaller funds in their sample. Decomposing the abnormal performance of pension funds in the period 1987-92 they find that most of it could be explained by the ability of both large and small funds to time the size premium. Most previous studies have employed a relatively small number of funds, raising the possibility of some selection bias in their samples. For example, due to the limitations on fund data during 1960s, there are only 57 funds in Treynor and Mazuy (1966)’s sample. For those studies carried out in the early 1980s, the sample size still remains quite small: Henriksson (1984) investigates 116 funds while Kon (1983) has only 37 funds in his sample. For the most recent studies conducted in the late 1990s and early 2000s, as more and more fund data became available and easily obtainable through the flourish of new mutual funds and more detailed fund data disclosures, researchers have been able to increase the sample size substantially. There are 230 funds in Bollen and Busse (2001) and 332 funds in Volkman (1999). The biggest sample to date is the one employed by Goetzmann et al. (2000), who include 558 funds in their sample. One exception is Ferson and Schadt (1996) who only use 67 mutual funds. However, they lengthen their sample period to cover 276 monthly observations for each of their sample funds.

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Recent evidence (e.g. Odean, 1998a) describes investor behaviour that is at odds with traditional economic theory. These alternative behaviours, such as those consistent with the disposition effect or overconfidence, form the basis for recent “behavioural” explanations for asset returns (e.g. Daniel et al., 1998a and 1998b; Odean, 1998b; and Shumway, 1998). Notably, the evidence of alternative investor behaviour is based largely on retail customer accounts --- those of amateur traders. For those institutional investors, based on their need for continuing success, the natural assumption should be that market professionals are disciplined traders who are less prone than retail investors to exhibit alternative and costly behavioural tendencies. If so, then behavioural problems may be an annoying but essentially harmless anomaly confined to some retail investors and experimental subjects. On the other hand, evidence that professional traders also exhibit alternative behavioural tendencies would provide increased support for research on the systemic effects of behavioural financial models, as, for example, in the model of Barberis et al. (1999). As fund managers are a substantial group of investors in the market, their investment activities, especially their timing behaviour, are well worth being investigated to see whether these investment professionals suffer from the same behavioural biases as retail investors and to what extent. In the next chapter I build testable hypotheses that address the gaps in the literature identified in this chapter.

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CHAPTER 4 RESEARCH QUESTIONS AND TESTABLE HYPOTHESES 4.1. Introduction In this chapter I derive testable hypotheses that aim at addressing the gaps in the literature identified in chapter 3. The survey of relevant extant literature in the previous chapter demonstrates how tests on whether fund managers possess significant market timing abilities remain inconclusive. Some studies find some evidence of timing skill while others do not. Most studies also suffer from benchmark problems and selection bias, which can potentially affect inferences regarding the timing ability of mutual fund managers. Furthermore, few studies to date address other style timing activities besides market timing. Based on my analysis of the literature and the research gap identified, I draw out below a research route map to describe my research conceptual design in Figure A. The main objective of this study is to test whether fund managers possess significant style timing abilities and how they engage in style timing activities. There are three possible circumstances under which fund managers implement timing strategies: (1) Fund managers implement timing strategies correctly, as they possess superior information and timing ability. (2) Fund managers implement timing strategies incorrectly intentionally, as they act in their own interests rather than those of the fund investors. (3) Fund managers implement timing strategies incorrectly unintentionally, as they are subject to some trading constraints or behavioural biases.

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There is no agreement in the literature about whether fund managers possess superior information and engage in style timing activities successfully. Wermers (2001) finds that none of his fund portfolio categories have the ability to successfully time their styles. However, his characteristic timing measure uses only quarterly mutual fund portfolio holdings data and does not capture the ability of fund managers to time styles over other time horizons, such as monthly or semi-annual intervals. There is no agreement in the literature about whether fund managers implement style timing strategies based on other considerations besides fundamentals. Indeed, a growing area of research indicates that institutional investors’ behaviour might be coloured by considerations beyond the maximisation of portfolio return or diversification. Whether fund managers’ style timing activities differ under different systematic factor scenarios, such as fund size, investment objectives, performance record, and manager experience etc., is an open question that I test in this study. This chapter is organised as follows: section 2 describes the hypotheses to be tested and section 3 summarises the discussion.

4.2. Testable Hypotheses 4.2.1. Market Timing Tests

First, I explicitly seek to answer the following linked research questions: can mutual fund managers time the market successfully? If they can, do they time the market at the expense of stock selectivity performance? I test the market timing ability of fund managers based on the traditional Treynor and Mazuy ((1966), hereafter referred to as TM) model and Henriksson and Merton ((1981), hereafter referred to as HM) model by incorporating the Carhart (1997) four-factor model characteristics. Research Question: can mutual fund managers time the market successfully? H10 : The average mutual fund does not demonstrate a significant ability (positive or negative) to time the market.

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The relationship between funds’ market timing behaviour and stock selection ability is also investigated to test whether mutual fund managers attempt to maximise selectivity performance by sacrificing timing performance. Research Question: do mutual fund managers time the market at the expense of stock selectivity performance? H20 : There is no consistent relationship between funds’ market timing behaviour and their stock selection abilities. 4.2.2. Style Timing Tests

Second, I extend the market timing test framework to a factor timing test framework by adding in Carhart’s (1997) four systematic factors, including market, size, book-to-market, and momentum factors. The test is first carried out on a joint hypothesis basis, that is, to test whether fund managers exhibit factor timing abilities with respect to any of these systematic factors. Research Question: can mutual fund managers time styles/factors successfully? H30 : The average mutual fund does not exhibit a significant timing ability with respect to any of Carhart’s four factors, including market, size, book-to-market, and momentum.

If fund managers do appear to exhibit some degree of factor timing abilities in general, then this leads us to the following research question: which factor(s) do mutual fund managers try to time among Carhart’s four factors? I thus conduct separate tests for each factor to examine whether fund managers exhibit timing abilities with respect to a specific factor. Research Question: which factor(s) do mutual fund managers try to time among all of Carhart’s four factors? H40a : The average mutual fund does not exhibit a significant timing ability with respect to the size factor.

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H40b : The average mutual fund does not exhibit a significant timing ability with respect to the book-to-market factor. H40c : The average mutual fund does not exhibit a significant timing ability with respect to the momentum factor.

Investors’ reluctance to realise losses has long been noted. Odean (1998a, 1999), Heisler (1996), and Barber and Odean (2000a, 2000b), look at direct evidence in the case of trading by small retail investors, or, in the case of Heisler, small off-exchange retail speculators. These studies support the notion that these investors hold their losing trades longer than their winning trades, and this leads to deteriorating profitability according to the evidence in Odean (1998a). Notably, this evidence of “alternative” investor behaviour is based largely on retail customer accounts --- those of amateur traders. However, there is strong evidence that “professionalism” or investor sophistication does not bring immunity. Fund manager investment activities, especially their timing behaviour, may suffer from the same behavioural biases as retail investors to some extent. Momentum style timing can be viewed as follows: an investor goes with loser (winner) stocks when loser (winner) stocks turn out to outperform winner (loser) stocks. If fund managers tend to sell winners (which are momentum stocks) too soon and hold on to losers (which are contrarian stocks) too long, and if momentum stocks outperform contrarian stocks on average, fund managers would time the momentum style poorly. Hence, the two-side test of null hypothesis H40c is further developed as a one-side test as follows. H40d : The average mutual fund does not exhibit a significant poor timing ability with respect to the momentum factor.

4.2.3. Tests of Trade-off Associated with Factor Timing

A fund manager may implement factor timing strategies by sacrificing stock selection Ph.D. Thesis: Jeffrey Junhua Lu

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performance. Also, a fund manager may be good at implementing a specific factor timing strategy according to his/her private information relating to a specific segment of the market. Thus, different fund managers may favour different factor timing strategies and implement their most favourable strategy at the expense of forgoing other strategies or even perversely timing other factors. Similar to my market timing analysis, I will also investigate the relationship between funds’ factor timing behaviour and stock selection ability in parallel as follows: Research Question: do mutual fund managers time styles/factors at the expense of stock selectivity performance? H50 : There is no consistent relationship between funds’ style timing behaviour and stock selection activities.

Also, the relationship between different factor timing strategies are investigated here: Research Question: do mutual fund managers time a specific factor at the expense of pervasively timing other factors? H60 : There is no consistent relationship between different funds’ style timing activities.. 4.2.4. Tests of Factor Timing in the Context of Investment Objectives

Some groups of funds may implement a specific factor timing strategy better than other groups of funds, due to their superior information relating to the factor. Also, some groups of funds may favour a specific factor timing strategy, because of their familiarity with a specific segment of the market in which the factor dominates. To investigate the effect of stated investment objectives on the timing activities of mutual funds, I segregate my sample funds into five Morningstar “investment objectives” (styles): aggressive growth, growth, growth and income, equity income, and small companies. Research Question: are there any differences in style/factor timing activities among

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different groups of funds? H70a : No sub-groups of mutual funds exhibit a significant timing ability with respect to the size factor. H70b : No sub-groups of mutual funds exhibit a significant timing ability with respect to the book-to-market factor. H70c : No sub-groups of mutual funds exhibit a significant timing ability with respect to the momentum factor. 4.2.5. Tests of Factor Timing in the Context of Performance Record

I consider four types of behavioural biases that may affect people’s investment decisions

which

include:

the

“house-money”

effect,

“snake-bite”

effect,

“try-to-break-even” effect, and “endowment” effect. Thaler and Johnson (1990) describe the house-money effect as an increase in risk taking when a trader has recent trading successes. For the mutual funds I am analysing, this could mean that after observing a successful performance record for the fund, the fund manager may feel emboldened and overconfident in his/her ability to time investment styles, and is willing to taking more risk and engage in style timing strategies more aggressively. Thaler and Johnson (1990) describe the snake-bite effect as a decrease in risk taking when a trader has recent trading losses. The snake-bite effect predicts that fund managers will avoid riskier investment strategies once they have experienced a past loss. Contrary to the snake-bite effect, the trying-to-break-even effect refers to the desire by investors to recoup large losses in one quick long-short (very high-risk) investment. Hence, it predicts that fund managers will systematically pursue high-risk investments after poor performance records. For the mutual funds I am analysing, this could mean that after suffering poor fund performance, the fund manager may suffer from both the snake-bite effect and the trying-to-break-even effect. Whether the manager will engage in style timing strategies more or less aggressively depends on which effect will dominate.

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Finally, the “endowment” effect refers to the tendency by people to place higher value on what they own than on identical items that they do not own. The endowment effect also can be viewed as a “do nothing” effect. This behavioural bias causes investors to pay little attention to risk and return characteristics, but instead to make decisions with a strong preference for keeping their original investments. Selling an original investment elicits pain or a feeling of loss. The endowment effect predicts investors will keep their existing portfolio unchanged. I will test the timing abilities of fund managers in the context of their funds’ performance record. Research Question: are fund managers’ style timing activities related to their performance records? H80 : Funds with a moderate performance record are not more likely to implement timing strategies compared to funds with a good performance record. H90 : Sub-group of mutual funds with a poor performance record are not more likely to implement timing strategies compared to funds with a good performance record. 4.2.6. Tests of Factor Timing in the Context of Systematic Factors

In general, investors perceive a well-established fund with a smooth track record as a preferable investment compared to a fund with a short performance history. If established funds are more likely to be run by experienced managers, we can test fund age to see whether experience contributes to better timing ability. The model of Gervais and Odean (2001) predicts that experience and learning will eliminate overconfidence. If experience eliminates overconfidence, then experienced fund managers should exhibit little or no overconfidence, thus we could expect that seasoned funds implement style timing strategies less aggressively than new unseasoned funds.

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Research Question: do experienced managers do better at style timing? do experienced managers engage in style timing less aggressively than inexperienced managers? H100 : There are no differences in the timing behaviour of new funds and old funds.

One common knowledge is that small funds are in a better position to implement timing strategies since it is easy for them to reshuffle their portfolios in a timely manner without affecting the market. This is also consistent with the efficient market hypothesis that activities derived from (costly) superior information must be “small” relative to the market. Research Question: is it easier for small funds to time the styles? H110 : There are no differences in the timing behaviour between small funds and big funds.

The turnover rate of a fund is a proxy for how frequently a manager trades his/her portfolio. The inverse of the fund’s turnover rate is the average holding period for a security in that fund. If one maintains a S&P 500 benchmark portfolio, the average annual turnover rate is about 4-6 percent over the past ten years.20 As a comparison, the average turnover rate of actively managed funds investing in the same market is 85.73 percent over the same time period. Assuming turnover rate is positively correlated with the frequency of timing-oriented trading, we would like to see to what extent high turnover represents successful factor timing. Research Question: can the high turnover ratio of actively managed funds be justified as successful attempts to time styles? H120 : There are no differences in the timing behaviour between low turnover funds

20

Source: Vanguard 500 index fund.

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and high turnover funds.

One plausible explanation of mutual funds’ unsatisfactory timing performance relates to their open nature (as opposed to closed-end funds). While fund managers try to time a specific factor, there are investors who are attempting to time the mutual fund themselves. When the factor fares well, new money flows in, and the associated funds have a higher portion of their portfolios in cash, which results in lower beta. When the factor dips, more investors try to redeem their shares, then cash reserves run low, leading to higher betas. Further, without a stream of new money, big redemption orders can force funds to liquidate shares often at inopportune times, such as selling into a falling market. From this point of view, factor mis-timing of mutual funds constitutes a price that investors have to pay for the liquidity that they enjoy with open-end funds. Edelen (1999) documents a negative relation between a fund’s risk-adjusted return and investor flows, and attributes the negative return performance of open-end mutual funds to the cost of their liquidity-motivated trading. Such logic implicitly assumes that fund investors can time a factor ahead of fund managers. Only if investor money flows in prior to factor ascendancy or flows out prior to factor descent will this offset fund managers’ factor timing endeavours. Gruber (1996) and Zheng (1999) provide some evidence that funds receiving more money subsequently beat the market – the “smart money” effect, but in the aggregate such effect is weak. Warther (1995) documents a positive relation between flows and subsequent returns in terms of the weekly data. Short-term switchers in and out of funds are more likely to attack no-load funds where they can take advantage of cost-free entry and exit. Hence I can look at the possible difference in timing between load and no-load funds and infer whether fund managers’ timing ability is impaired by investor flows. Research Question: do investor flows affect style timing? H130 : There are no differences in the timing behaviour between load funds and Ph.D. Thesis: Jeffrey Junhua Lu

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no-load funds.

4.3. Summary In this chapter I develop testable hypotheses in an attempt to fill important gaps in the existing mutual fund timing literature identified in chapter 3. In the next section I discuss my data and methodology which are employed to test the above hypotheses.

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CHAPTER 5 DATA AND METHODOLOGY 5.1. Introduction In the last chapter I laid out the hypotheses that are to be tested in this study. In this chapter I describe the data used and the methodology employed in order to test these hypotheses. My study covers a period of 10 years and uses the Morningstar database as my major source of fund data. The chapter is organised as follows: section 2 describes the data used in this study, section 3 describes the sample selection procedure, section 4 describes the methodology employed and section 5 summarises what I have covered in the chapter.

5.2. Data 1. Monthly fund net return data is obtained from the Morningstar Principia database. Morningstar reports monthly returns that are computed each month by taking the change in monthly net asset value (NAV), reinvesting all income and capital gains during the month, and dividing by the starting NAV. The return is not adjusted for sale charges (such as front-end or deferred loads and redemption fees), which would give a clearer picture of the fund manager’s investment ability and strategy. However, the published returns do account for management, administrative, 12b-1 fees, and other costs that are automatically taken out of fund assets. 2. Fund characteristics data on an annual basis, such as fund size, expense ratio, turnover ratio, fund age, manager tenure, etc. are taken from the Morningstar Principia database.

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3. The monthly excess return on the market, which is the value-weighted return on all NYSE, AMEX, and NASDAQ stocks taken from CRSP minus the one-month Treasury bill rate taken from Datastream. 4. The monthly 90-day US Treasury bill index which is used to represent the return on the risk-free asset is obtained from Datastream. 5. Monthly equity returns adjusted for dividends and capital changes are obtained from CRSP. 6. The end of month market value of the common equity of the company is calculated as the number of shares as of the end of the month (from CRSP) multiplied by the end of the month CRSP share price. 7. The end of month book-to-market ratio is defined as the book value of equity divided by the market value of equity in that month, where I take book value as the COMPUSTAT book value of shareholders’ equity plus balance sheet deferred taxes and investment tax credit, minus the book value of preferred stock. The book value of preferred stock is taken to be the redemption, liquidation, or par value (in that order) on COMPUSTAT.21

5.3. Sample Selection My study covers US domestic equity funds existing at any time during the period June, 1992 - June, 2002. I use the monthly Morningstar On-Disk or Principia programs from July, 1992 to July, 2002 to select my mutual funds. I start in the year 1992 since this corresponds to the beginning of the On-Disk program.

From the beginning of

the sample period, I select funds based on two criteria. First, I select only “domestic equity” funds as identified by Morningstar’s “Investment Class”. For funds classified

21

To ensure that accounting information is available at the time of portfolio formation, a three month lag between the fiscal year end data and the reporting date is assumed. This will minimise the look-ahead bias. So, for the portfolio formed in August of year t, the book value of equity is obtained from the latest available financial statements with the fiscal year end before February of year t. The market value of equity is as at the end of August of year t.

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to the domestic equity fund class, I then select all funds within each of the following five Morningstar “investment objectives” (styles): aggressive growth, growth, growth and income, equity income, and small companies. This allows me to examine whether there is a “style effect” on fund timing activities. It is important to note that the designation for the “investment objective” is determined by Morningstar, usually based on the wording in the fund’s prospectus. However, in some cases, Morningstar may give a fund an investment objective different from that implied by the fund’s name or by the fund’s prospectus if Morningstar determines that the fund invests in a way that is inconsistent with the wording in its prospectus. There are 15,110 funds in total in the Morningstar database up till the end of my sample period. I exclude international funds (1,807 funds), bond funds (4,401 funds), gold funds (43 funds), real estate funds (161 funds), and all other sector funds (907 funds), as these types of funds generally hold and trade minimal quantities of domestic equities (if any). I also exclude index funds whose managers are not expected to time the market (686 funds). This results in 7,105 domestic equity funds with 466,174 fund-month return observations. Second, I require a fund to have at least 60 valid monthly net return observations to be included in the timing tests. This minimum data requirement, while potentially introducing a survival bias, is necessary to allow more precise regression parameter estimates for my more complex models of timing activity. For robustness checks, the timing tests can be applied with a minimum history requirement of 36 and 48 months, respectively. The results from these robustness tests can be used to determine whether survivorship bias has a significant impact on empirical results. This return observation requirement further reduces the number of funds in my sample. Over 2,700 funds are represented in the remaining database. Table 1 (Page 228)

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Table 1 reports summary statistics on the mutual fund data. My sample includes a total of 2,791 diversified equity funds and 261,138 fund months. Panel A reports annual cross-sectional averages of fund characteristics from 1992 to 2002. In an average year, the sample includes 2,227 funds with average total net assets under management (TNA) of $646.62 million and average expenses of 1.37 percent per year. In addition, funds trade 85.73 percent of the value of their assets (turnover) in an average year. I obtain funds flow by calculating the net growth in fund assets beyond reinvested dividends. The average funds flow in a year is 5.45 percent of the value of the fund’s assets. Note that the sample includes years of high and low returns, as well as a range of standard deviations, suggesting that the sample is rich enough to capture market timing activity. Some interesting patterns are revealed when the historical trend of fund characteristics is examined. On average, funds realised substantial positive returns in the mid 1990s when the market rallied but turned out to lose a lot in 2000 when the market tumbled. Funds flows exhibit relatively high inflow (positive) till the mid 1990s and subsequently drop in 1999, which coincides with the end of the market cycle in the 1990s. It seems investors pursue funds in the bull market and abandon funds in the bear market. Fund expense ratios increase from 1.30 percent in 1992 to 1.43 percent in 2002 (significant at 1 percent level). Similarly, fund turnover ratios increase from 74 percent in 1992 to 90 percent in 2002 (significant at 1 percent level). Funds trade more actively and thus incur more managerial expenses and trading costs. The U-shape of fund age in my sample is due to the proliferation of mutual funds during the mid 1990s. Panel B of Table 1 reports annual cross-sectional averages of fund characteristics by fund category. Most of the funds are grouped within the growth and growth-income investment objectives (70 percent in total). Over the sample period, aggressive growth funds and small company funds realise better performance (with annual return greater than 10 percent) but exhibit more volatile performance (with annual standard

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deviation greater than 21 percent) than other classes of funds. On average, growth and income funds have the largest fund size ($862.64 million) among the five investment objectives. Aggressive growth funds attract the largest funds inflow percentage (6.39 percent) on average while small company funds attract the smallest funds inflow percentage (3.11 percent). Also, the fund expense ratios are higher for aggressive growth funds and small company funds (more than 1.5 percent per year) when compared to those of growth and income funds (1.24 percent per year). Turnover is also substantially higher for aggressive growth funds than other funds. Hence, on the one hand, aggressive growth funds tend to trade actively and frequently in an effort to achieve better performance and attract investor money. On the other hand, these funds incur more expenses and exhibit more volatile performance records. All the above differences are significant at 1 percent level. Panel C of Table 1 reports cross-sectional averages of fund load by fund category. More than one half of the funds are load funds. A load fund is a mutual fund that charges a sales commission when shares are purchased or redeemed. Loads range from as low as 0.5 percent to as high as 8.5 percent. Investing $1,000 in a fund with an 8.5 percent front-end load would put only $915 into investments after the fund deducted its $85 commission. Loads seem to be an important factor to consider. For the load-funds, more have front-end loads and fewer have deferred loads. Aggressive growth funds tend to have lower front-end loads but higher deferred loads, while growth and income funds tend to have higher front-end loads but lower deferred loads. Such load policies serve to cope with the different types of investors that these funds are targeting. Investors who pursue aggressive growth funds tend to focus on short-term performance and could easily change their minds to switch to other hot investment opportunities in the market. Placing higher deferred loads on this type of investor could help the funds retain them and discourage the outflow of monies. Indeed, Chordia (1996) suggests that aggressive growth funds are more sensitive to cash flows, and are more likely to rely on load fees to dissuade redemptions because they hold more of the smaller, less liquid stocks. On the other hand, investors who Ph.D. Thesis: Jeffrey Junhua Lu

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invest in growth and income funds may tend to focus on long-term performance and be less likely to switch funds in the short term. Also, higher front-end loads will spread out over the longer investment horizon. Small company funds exhibit the lowest sales loads among all fund types. These funds seem to rely less on brokers to sell their shares. However, they do exhibit the highest redemption fees imposed on investors. Panel D of Table 1 reports cross-sectional averages of fund characteristics by fund status. Live funds are those in operation at the end of the sample period, June, 2002. Dead funds are those that discontinued operations prior to this date. On average, and not surprisingly, live funds are larger in size, with lower expense ratios and positive fund flows, while dead funds are smaller in fund size, with higher expense ratios and negative fund flows. Panel E of Table 1 lists summary statistics of the fund return distributions. I test the hypothesis that fund returns are normally distributed using the Jarque-Bera (1980) statistic, which is distributed χ 22 under the null. For 62 percent of sample funds normality at the 5 percent level is rejected. The average test statistic is 20.17, whereas a value of 5.99 or higher rejects the null. Evidence of non-normality in the majority of my sample funds is relevant because of the Jagannathan and Korajczyk (1986) suggestion that option-like payoffs can generate spurious evidence of market timing. I will return to this issue when interpreting the results of my factor timing tests. Panel E also lists summary statistics for the factor indices, including the market index, the SMB index, the HML index, and the Momentum index. For all factor indices normality is rejected at the 5 percent level; three exhibit considerable negative skewness except that the SMB index exhibits positive skewness. Furthermore, the factor indices, but the SMB on average, exhibit higher excess kurtosis and larger negative skewness than the mutual fund average. The negative skewness is probably due to the market crash in the late 1990s. Again, the relative degree of non-normality

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in mutual fund returns and the factor indices may explain some of my market timing results, as I discuss in the factor timing tests in chapter 7.

5.4. Methodology Various methodologies have been employed to explore the timing activities of fund managers. Timing strategy refers to the dynamic allocation of capital among broad classes of investments. The successful timer allocates funds among different classes of assets to catch market (or subsets of the market) ascendancy and/or to avoid market downturns.22 If we could observe the portfolio composition of mutual funds at the same frequency as we observe their returns, we would be able to infer funds’ timing activities by testing whether a portfolio’s exposure to the relevant market is pro-trend on average (Merton, 1981; Cumby and Modest, 1987; Ferson and Khang, 2000). In reality, obtaining a mutual fund’s detailed portfolio composition on a timely basis and at a reasonable high frequency is quite difficult.23 Analysis of the timing activity of mutual funds based on less frequent portfolio holdings data may not provide a true picture of the timing behaviour of fund managers. In fact, if a timer could trade several times within each reporting period (that is, not only once, at the very end of each period), then a lower reporting frequency might fail to capture the contribution of a manager’s timing activities to fund returns, because decisions regarding portfolio risk exposures are likely to be made more frequently for most funds. Further, the classification of individual securities into slots based on stock characteristics can involve substantial amounts of judgement.24 Hence, in more practical situations we 22

Theoretical work includes studies by Merton (1981) and Cumby and Modest (1987)

23

The current practice in the industry is that fund companies are only required to show what assets they hold in their portfolios on a semi-annual basis. More timely and more frequent disclosure is on a volunteer basis for each fund.

24

For example, a conglomerate firm would typically have operations in several different sectors of the economy and it may be difficult to identify how much of the firm goes into each sector. Another problem arises from simply calculating portfolio characteristics based on portfolio holdings. A domestic equity mutual fund investing in domestic stocks that derive a majority of their revenue from sales abroad will clearly be influenced by trends in the foreign economies. If the overseas economies go into recession, the fund will be affected. In this way, the fund, although domestic, responds to factors in external markets in a manner similar to an international equity fund. Simply examining fund

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tie our hands to the returns of funds and benchmark portfolios only. The method I employ needs only ex post returns of funds and their benchmark returns. 5.4.1. Multifactor Model

Efforts to systematically analyse the performance of fund managers have been diverse and at times contradictory. Most studies evaluating the performance of fund managers employ an evaluation paradigm based on Jensen’s (1968) model. Jensen recognises the importance of evaluating a fund manager’s performance based on the fund’s systematic risk and employs the CAPM. He assumes returns on a fund have a multivariate normal distribution and the systematic risk of the managed portfolio is stationary over the evaluation period. Given joint normality of returns, Jensen decomposes a fund’s excess return, R pt , into a constant, α p ; a market-related component, β p ; and a conditional mean zero residual, ε pt : R pt = α p + β p Rmt + ε pt

(6)

where Rmt is the excess market return and ε pt is assumed to follow a Brownian motion white noise series. Although Jensen’s model is the standard one used in evaluating mutual fund performance, several researchers note that cross-sectional average returns show little correlation with the systematic risk parameters estimated using the CAPM (Breeden, Gibbons, and Litzenberger (1989)), while other researchers suggest that other systematic factors may influence cross-sectional abnormal performance (Fama and French (1993); Carhart (1997)). Fama and French (1993) note that alone the CAPM systematic risk parameter β has little explanatory power for cross-sectional returns. It is asserted that other systematic factors, such as high- versus low-beta stocks, largeversus small-market capitalisation stocks, and value versus growth stocks affect

portfolio holdings data may not reflect the fact that the fund manager is indeed timing the factors in overseas markets, since all his/her holdings are domestic equities. Ph.D. Thesis: Jeffrey Junhua Lu

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average equity performance. Fama and French (1993) develop a three-factor loading model to explain cross-sectional variability in equity returns. R pt = α p + β 1 RMRFt + β 2 SMBt + β 3 HMLt + ε pt

(7)

In addition to the three factors identified by Fama and French (1993), Carhart (1997) incorporates a fourth systematic factor capturing Jegadeesh and Titman’s (1993) one-year momentum anomaly. Specifically, Carhart employs the following four-factor loading model to analyse abnormal fund performance, R pt = α p + β1 RMRFt + β 2 SMBt + β3 HMLt + β 4 MOM t + ε pt

(8)

where RMRF is the excess return on a value-weighted aggregate market proxy, and SMB, HML, and MOM are returns on value-weighted, zero-investment, factor-mimicking portfolios for size, book-to-market equity, and one-year momentum in stock returns.

5.4.2. Market Timing Model

Several researchers note that studies employing a linear performance paradigm based on intertemporal estimation, such as Jensen’s (1968) alpha or Fama and French’s (1993) three-factor loading model and Carhart’s (1997) four-factor loading model, erroneously assume the risk of the managed portfolio is stationary with a constant covariance relation to the market.25 In reality, the risk of a managed portfolio is not stationary. Fund managers frequently attempt to shift the risk level of the fund by borrowing or lending in the cash market or by adjusting the risk composition of the managed portfolio as they anticipate market (factor) movements. Fund managers can generate additional performance if size, book-to-market, or momentum strategies have time-varying expected returns that the manager can exploit by changing portfolio weights to exploit those styles when they are the most profitable.

25

See Bhattacharya and Pflerderer (1983); Lee and Rahman (1990)

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Fama (1972) and Jensen (1972) addressed this issue and pointed out the empirical measurement problems involved in evaluating properly the constituents of investment performance when portfolio risk levels are nonstationary. A variety of studies have since picked up on the point, including those by Kon and Jen (1979), Fabozzi and Francis (1979), Alexander and Stover (1980), and Miller and Gressis (1980). These papers find at least some evidence that mutual fund portfolios do not in fact maintain a constant risk posture over time and conclude that attempts at market (factor) timing may well be a dimension of fund managers’ decision processes. In an attempt to correct the biased selection measure of Jensen’s alpha, which bias is due to the nonstationary risk exposures of active fund portfolios, and to develop a measure of timing ability, Treynor and Mazuy (1966) assume a stochastic risk relation and use the following quadratic regression to test for market timing: R pt = α p + β p Rmt + γ p Rmt2 + ε pt

(9)

where R pt is the excess return on a portfolio at time t, Rmt is the excess return on the market, and γ p measures the fund manager’s timing ability. If a mutual fund manager increases (decreases) the portfolio’s market exposure prior to a market increase (decrease) then the portfolio’s return will be a convex function of the market’s return, and γ p will be positive. Henrikson and Merton (1981) develop a different test of market timing. In their model, the mutual fund manager allocates capital between cash and equities based on forecasts of the future market return, as before, except now the manager decides between a small number of market exposures levels. The authors test a model with two target betas via the following regression: * R pt = α p + β p Rmt + γ p Rmt + ε pt

(10)

where

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Can Fund Managers Successfully Time Their Investment Styles? * Rmt = I {Rmt > 0}Rmt

(11)

and I {Rmt > 0} is an indicator function that equals one if Rmt is positive and zero otherwise. The magnitude of γ p in Equation 10 measures the difference between the target betas, and is positive for a manager that successfully times the market. Notably, market timing ability is measured as the change in risk from a down- to an up-market condition. The risk levels in these two market conditions, nonetheless, are not identified explicitly. Henriksson and Merton (1981) show this can be accomplished by extending Equation 10: R pt = α p + β u Rmt+ + β d Rmt− + ε pt

(12)

where Rmt+ =max[0, Rmt ] and Rmt− =min[0, Rmt ]. In this model, excess return of a fund is expressed as a linear combination of two market risk premiums: one, Rmt+ , during up-market conditions, and the other, Rmt− , during down-market conditions. Note that both the market timing tests from Equation 9 and 11 are based on the classic Sharpe-Lintner-Mossin CAPM. 26 The CAPM itself and its use in performance measurement have been subjected to strong objections on theoretical grounds. 27 Empirical studies have uncovered risk factors (other than the market) relevant in explaining cross-sectional variation of average asset returns, thus questioning the validity of the CAPM. Among these, size and book-to-market ratio have been studied extensively.28 A multi-factor asset pricing model that, in addition to the market, includes risk factors accounting for size and the book-to-market ratio, as indicated above, has been proposed by Fama and French (1993) and has gained acceptance by academics and practitioners alike. Indeed, any plausible multi-factor asset pricing model can be readily utilised instead of the CAPM. The original market timing 26 27 28

Sharpe (1964); Lintner (1965); Mossin (1966). See Roll (1978); Mayers and Rice (1979); Admati and Ross (1985); Dybvig and Ross (1985). See Banz (1981); Rosenberg, Reid, and Lanstein (1985); Fama and French (1992), (1993), (1996).

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models are robust to the choice to the underlying asset pricing model. Bollen and Busse (2001) and Volkman (1999) propose the following revised version of the Treynor and Mazuy (1966) and Henrikson and Merton (1981) market timing models, by incorporating Carhart’s (1997) four-factor model. The Carhart’s (1997) four-factor TM model is expressed as: R pt = α p + β1 RMRFt + β 2 SMBt + β 3 HMLt + β 4 MOM t + γ p Rmt2 + ε pt

(13)

The Carhart’s (1997) four-factor HM model is expressed as: * R pt = α p + β1 RMRFt + β 2 SMBt + β 3 HMLt + β 4 MOM t + γ p Rmt + ε pt

(14)

Bollen and Busse (2001) find that the magnitude of the average timing coefficient is smaller under the HM model than under the TM model (less positive or less negative). A potential explanation relies on the fact that the TM and HM coefficients essentially measure the expected convexity in the funds’ relation to the market return, which reflects both the probability (related to information quality) and the magnitude (related to risk aversion). A fund manager’s market timing performance depends on both the quality of his/her private information (ability) and the aggressiveness with which the manager reacts to his/her information (response). Jiang (2001) suggests that the HM measure caters more on the information quality side of the market timing while the TM measure basically reflects the intensity of the manager’s reaction. Hence, more aggressive funds can show up as better (or worse if the information is incorrect) market timers with higher (more negative) TM measures. Therefore, the magnitude of these timing coefficients (the absolute value) is used as a proxy for the aggressiveness of fund timing strategies. 5.4.3. Deriving Factor Timing Models

Timing ability on the part of a fund manager traditionally refers to the ability to enhance portfolio performance by using information about the future realisations of the common factors in security returns. Treynor and Mazuy (1966) assume a

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stochastic risk relation and use the following quadratic regression to test for market timing: R p ,t +1 = α p + β p Rm,t +1 + γ p Rm2 ,t +1 + ε p ,t +1

(15)

where R p ,t +1 is the excess return on a portfolio at time t+1, Rm,t +1 is the excess return on the market. Assume the manager observes a private signal yt which equals the future market return plus an independent noise term: yt = Rm ,t +1 + ηt

(16)

This model can be interpreted based on the Capital Asset Pricing Model with a dynamic beta: R p ,t +1 = α p + βˆ p Rm,t +1 + ε p ,t +1 where,

(17)

βˆ p = β p + γ p ( Rm ,t +1 + ηt +1 )

(18)

Equation (17) reflects the essence of market timing in that the beta increases to the timing signal. The market timer will expand allocation to stocks when the timing signal implies a better market return, and vice versa. Substituting (18) into (17) and including noise η in the error term, we obtain the TM model (15). Superior timing ability corresponds to the fact that the variance of the noise term is finite, or σ η2 << ∞ . The manager with constant absolute risk aversion (CARA) preference will respond to the signal by making the portfolio beta a linear function of the signal (Admati, el al., 1986), which in turn makes the portfolio return a quadratic function of the market return as in equation (15). Thus a significantly positive coefficient γ p represents superior market timing performance. We combine the multifactor model and the TM timing model to investigate the factor timing activities of fund managers. Assume the manager observes a private signal yi ,t

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on factor i which equals the future factor index return plus an independent noise term: yi ,t = Ri ,t +1 + ηi ,t

(19)

A TM factor timing model can then be derived based on the Carhart’s four-factor model with dynamic betas: R p ,t +1 = α p + βˆ1 RMRFt +1 + βˆ2 SMBt +1 + βˆ3 HMLt +1 + βˆ4 MOM t +1 + ε p ,t +1 where,

βˆ1 = β1 + γ 1 ( RMRFt +1 + η1,t +1 )

βˆ2 = β 2 + γ 2 ( SMBt +1 + η2,t +1 )

(20) (21) (22)

βˆ3 = β3 + γ 3 ( HMLt +1 + η3,t +1 )

(23)

βˆ4 = β 4 + γ 4 ( MOM t +1 + η 4,t +1 )

(24)

Equations (21) - (24) reflect the essence of factor timing that the betas increase to the timing signal. The factor timer will increase his/her portfolio exposure to a specific factor when the timing signal implies a better factor index return, and vice versa. Substituting (21) - (24) into (20) and including noise ηi in the error term, we obtain the TM Carhart four-factor timing model. R p ,t +1 = α p + β1 RMRFt +1 + β 2 SMBt +1 + β 3 HMLt +1 + β 4 MOM t +1 +

γ 1 RMRFt +21 + γ 2 SMBt2+1 + γ 3 HML2t +1 + γ 4 MOM t2+1 + ε p ,t +1

(25)

If a mutual fund manager increases (decreases) his/her portfolio’s risk exposure to a specific factor prior to the factor index increase (decrease), then the portfolio’s return will be a convex function of the factor index’s return, and γ i will be positive. Henrikson and Merton (1981) develop a different test of market timing. In their model, the mutual fund manager allocates capital between cash and equities based on forecasts of the future market return, as before, except now the manager decides between a small number of market exposures levels. The manager’s timing ability is Ph.D. Thesis: Jeffrey Junhua Lu

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defined as Δ = Pr( Rˆ m ,t +1 > 0 | Rm ,t +1 ) + Pr( Rˆ m ,t +1 < 0 | Rm,t +1 ) − 1

(26)

where Rˆ m,t +1 is the manager’s forecast about Rm ,t +1 . Superior ability corresponds to

Δ being greater than zero. The HM model assumes that the manager sets a higher target beta in an up market (when the excess return on the market portfolio is greater than one) forecast than that in a down market one. Given the magnitude of the manager’s reaction (expressed as the difference between the two betas), the contribution of Δ to the fund return can be inferred by the following regression: R p ,t +1 = α p + β p Rm,t +1 + γ p Rm* ,t +1 + ε p ,t +1

(27)

Rm* ,t +1 = I {Rm ,t +1 > 0}Rm ,t +1

(28)

where

and I {Rm ,t +1 > 0} is an indicator function that equals one if Rm ,t +1 is positive and zero otherwise. The coefficient on Rm* ,t +1 becomes the value added by effective timing that is equivalent to a call option on the market portfolio where the exercise price equals the risk-free rate. Similar to the TM factor timing model, we combine the multifactor model and the HM timing model to investigate the factor timing activities of fund managers. Assume the manager observes a private signal yi ,t on factor i which reflects the future states of factor i (up or down): yi ,t = I {Ri ,t +1 > 0} + ηi ,t +1

(29)

and I {Ri ,t +1 > 0} is an indicator function that equals one if Ri ,t +1 is positive and zero otherwise. An HM factor timing model can be derived based on the Carhart’s four-factor model Ph.D. Thesis: Jeffrey Junhua Lu

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with dynamic betas: R p ,t +1 = α p + βˆ1 RMRFt +1 + βˆ2 SMBt +1 + βˆ3 HMLt +1 + βˆ4 MOM t +1 + ε p ,t +1

where,

(30)

βˆ1 = β1 + γ 1 ( I {RMRFt +1 > 0} + η1,t +1 )

(31)

βˆ2 = β 2 + γ 2 ( I {SMBt +1 > 0} + η2,t +1 )

(32)

βˆ3 = β3 + γ 3 ( I {HMLt +1 > 0} + η3,t +1 )

(33)

βˆ4 = β 4 + γ 4 ( I {MOM t +1 > 0} + η4,t +1 )

(34)

Equations (31) - (34) reflect the essence of factor timing that the betas relate to the timing signal regarding two future states of the factor (up or down). The factor timer will target a higher portfolio exposure to a specific factor when the timing signal implies an up market for the factor, and vice versa. Substituting (31) - (34) into (30) and including noise ηi in the error term, we obtain the HM Carhart four-factor timing model. R p ,t +1 = α p + β1 RMRFt +1 + β 2 SMBt +1 + β 3 HMLt +1 + β 4 MOM t +1 +

γ 1 RMRFt *+1 + γ 2 SMBt*+1 + γ 3 HML*t +1 + γ 4 MOM t*+1 + ε p ,t +1

(35)

where RMRFt*+1 = I {RMRFt +1 > 0}RMRFt +1

(36)

SMBt*+1 = I {SMBt +1 > 0}SMBt +1

(37)

HML*t +1 = I {HMLt +1 > 0}HMLt +1 MOM t*+1 = I {MOM t +1 > 0}MOM t +1

(38) (39)

The magnitude of γ i in Equation (35) measures the difference between the target betas, and is positive for a manager that successfully times factor i. Notably, factor timing

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ability is measured as the change in risk from a down- to an up-market condition. 5.4.4. Factor Indices’ Construction

In this section, I describe the detailed procedure for constructing the factor indices discussed in the previous section when deriving my factor timing models. I construct the size and book-to-market factor indices following the procedure used by Fama and French (1993), except that the factor indices are formed monthly rather than annually. I sort all firms listed on both CRSP and COMPUSTAT and classified as having ordinary common shares (on CRSP) according to their market capitalisation at the end of each month in each year beginning in June of 1990. As in Fama and French (1993), to mitigate the problems associated with COMPUSTAT’s practice in back filling data, firms must exist on COMPUSTAT for two years before I use them. I take market capitalisation to be the number of shares as of the end of the month (per CRSP) multiplied by the end of the month CRSP share price. I also sort these same firms according to their end of calendar year book-to-market ratio, where I take book value as the COMPUSTAT book value of shareholders’ equity plus balance sheet deferred taxes and investment tax credit, minus the book value of preferred stock. I take the book value of preferred stock to be the redemption, liquidation, or par value (in that order) on COMPUSTAT. To ensure that accounting information is available at the time of portfolio formation, a six month lag between the fiscal year end data and the reporting date is assumed. This will minimise the look-ahead bias. So, for the portfolio formed in August of year t, the book value of equity is obtained from the latest available financial statements with the fiscal year end before February of year t. The market value of equity is as at the end of August of year t. I divide all firms (NYSE, AMEX, and Nasdaq) into two groups, big (B) and small(S), where the big group includes all firms greater than or equal to the median market capitalisation of all firms. I also divide all firms into three groups, high book-to-market (H), medium book-to-market (M), and low book-to-market (L), depending on each firm’s book-to-market relative to the 70th and 30th percentiles of all Ph.D. Thesis: Jeffrey Junhua Lu

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firms. Combining the two market capitalisation groups with the three book-to-market groups results in six groups of firms: one that includes big firms with high book-to-market ratios, one with big firms and medium book-to-market ratios, one with big firms and low book-to-market ratios, and an analogous set of three groups of small capitalisation firms. I compute a return index for each of the six groups by weighting their constitutional firm returns by market capitalisation. I form the size factor index by taking the difference between an equally weighted combination of the three small market capitalisation indices and the three big market capitalisation indices. I form the book-to-market index by taking the difference between an equal weighted combination of the two high book-to-market indices and the two low book-to-market indices. I construct the momentum index similar to that of Carhart (1997). For each month t, I rank all firms on CRSP (NYSE, AMEX, and Nasdaq) classified as having ordinary common shares with returns for a month t-12 to t-2 evaluation period by total return from t-12 to t-2. I take the momentum index for month t as the difference between the equal weighted month t return index of the 30 percent of firms with the highest returns during the evaluation period and the equal weighted index of the 30 percent of firms with the lowest returns during the evaluation period. I reallocate firms to the 30 percent highest returns and 30 percent lowest returns groupings monthly. 5.4.5. Synthetic Funds Construction

As shown in Panel E of Table 1, the relative degree of non-normality in the mutual funds and the factor indices may explain some of the style timing results. Jagannathan and Korajczyk (1986) show that standard timing tests spuriously reject the null hypothesis of no timing ability if fund returns are more or less option-like than the market proxy. In an effort to control for possible spurious results, I create a synthetic matched sample of funds that mimics the holdings of the actual funds but that has no timing ability by construction. This section will discuss the detailed procedure for Ph.D. Thesis: Jeffrey Junhua Lu

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constructing my synthetic funds. First of all, I describe in detail the quadratic program which is needed during this procedure. Sharpe’s (1992) return-based style analysis can be considered a special case of the generic factor model discussed above. In return-based style analysis I replicate the performance of a managed portfolio over a specified time period as best as I can by the return on a passively managed portfolio of style benchmark index portfolios. The two important differences when compared to factor models are: (1) every factor is a return on a particular style benchmark index portfolio, and (2) the weights assigned to the factors sum to unity. Sharpe (1992)’s asset class factor model can be expressed as: R pt = [δ 1 X 1t + δ 2 X 2t + ... + δ n X nt ] + ε pt

(40)

where R pt represents the managed portfolio return at time t and X 1t , X 2t ,…, X nt are the returns on style benchmark index portfolios. The slope coefficients δ 1 , δ 2 ,…,

δ n represent the managed portfolio average allocation among the different style benchmark index portfolios – or asset classes during the relevant time period. The sum of the terms in the square brackets is that part of the managed portfolio return that can be explained by its exposure to the different style benchmarks and is termed the style of the manager. The residual component of the portfolio return ---

ε pt reflects the manager decision’s to depart from the benchmark composition within each style benchmark class. This is the part of return attributable to manager stock picking ability and is termed stock selection return. In order to obtain coefficient estimates that closely reflect the fund’s actual investment policy it is important to incorporate restrictions on the style benchmark weights. For example, the following two restrictions are typically imposed:

δ j ≥ 0∀j ∈ {1,2,..., n}

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(41)

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∑δ j =1

j

=1

(42)

The first restriction corresponds to the constraint that the fund manager is not allowed to take short positions in securities, which is standard for pension funds and mutual funds. The second restriction imposes the requirement that we are interested in approximating the managed fund return as closely as possible by the return on a portfolio of passive style benchmark indices. The objective of the analysis is to select a set of coefficients that minimises the “unexplained” variation in returns subject to the stated constraints. The presence of inequality constraints in (6) requires the use of quadratic programming since standard regression analysis packages typically do not allow for imposing such a restriction. It is important to understand that the ‘style’ identified in such an analysis represents an average of potentially changing styles over the period covered. Since a fund’s style can change substantially over time, it is also helpful to study how the exposures to various style benchmark asset classes evolve. For this purpose I will conduct a series of style analyses, using a fixed number of months for each analysis, rolling the time period used for the analysis forward through time.

My synthetic funds are created as in Busse (1999). For each fund in my sample, I determine the fund’s exposure to eight asset classes: the six intersections of the two equally weighted size and the three equally weighted book-to-market indices, the equally weighted momentum index, and the equally weighted contrarian index. If I express fund p’s return in month t as 8

rp ,t = ∑ bp ,i ri ,t + ε p ,t

(43)

i =1

where ri ,t is the return on asset class i in month t, then the bs are selected by

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minimising the variance of ε i ,t , subject to a nonnegativity constraint on the bs. Given these weights on the asset classes, a synthetic fund is constructed by randomly selecting 100 stocks chosen from the different asset classes in proportions to match the fund’s vector of bs. The stocks are initially equally weighted. I replace stocks by other stocks in the same asset class at random, with an average holding period of one year, which is roughly consistent with the 85 percent average annual turnover of my mutual fund sample. When a stock is replaced, weights are reset to equal weights. Between replacements, weights evolve according to a buy and hold strategy. This procedure is similar in spirit to the way Daniel et al. (1997) create characteristic-based benchmarks in order to test for managerial ability, except that Daniel et al. use their funds’ quarterly holdings rather than a quadratic program to, as I do, determine asset class exposures. Since mutual funds are usually not fully invested, but typically hold anywhere from 5 percent to 10 percent of their total net assets in cashlike securities, I give each random portfolio an allocation of 93 percent equity and 7 percent cash. The resulting random control sample consists of 2,792 portfolios, one mimicking portfolio for each fund in the mutual fund sample. 5.4.6. Bootstrap Standard Errors

Assessing the significance of an actual fund’s timing regression coefficients is complicated by the possibility of misspecification of the timing function or of timing strategies that change over time. For example, if a fund manager times the market/factors according to the TM model, but we measure timing ability using the HM specification, we are likely to induce temporary serial correlation in the residuals while the strategy is being executed. Furthermore, there is evidence that fund managers execute timing strategies dynamically. For example, Brown et al. (1996) suggest that fund managers may change their investing strategies over the calendar year depending on year-to-date performance, in an effort to game compensation schemes. Also, Busse (1999) provides evidence that fund managers’ time exposure to Ph.D. Thesis: Jeffrey Junhua Lu

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the market to coincide with low levels of market volatility. Misspecifying the timing function may cause violations of regression assumptions in unknown and possibly time-varying ways, so that standard corrections for heteroskedasticity and serial correlation may not fully capture the effect of these violations on the standard errors of regression coefficients. To overcome this statistical problem, I construct bootstrap standard errors for my timing coefficients following the procedure described by Freedman and Peters (1984). There are three steps in this procedure. Here I illustrate my bootstrapping procedure with the Carhart (1997) four-factor TM timing model of Equation (12). The application of this bootstrap procedure to other factor timing models I use is very similar, with the only modification of the following steps being the substitution of the appropriate timing model in what is to follow. First, for each fund, I use the Carhart four-factor TM timing model to compute the OLS-estimated factor loadings and residuals using the time-series of monthly net returns for fund i: Ri ,t = αˆi + βˆi ,1 RMRFt + βˆi ,2 SMBt + βˆi ,3 HMLt + βˆi ,4 MOM t +

γ 1 RMRFt +21 + γ 2 SMBt2+1 + γ 3 HML2t +1 + γ 4 MOM t2+1 + εˆi ,t

(44)

For each fund i, the coefficient estimates, { αˆ i , βˆ1 , βˆ2 , βˆ3 , βˆ4 , γˆ1 , γˆ2 , γˆ3 , γˆ4 }, are saved, as well as the time-series of estimated residuals, { εˆi ,t , t = 1, Ti }. Second, I generate bootstrap fund returns fund-by-fund as follows. I draw a sample with replacement from the fund i residuals that are saved from the first step, creating a time-series of resampled residuals, { εˆ bi ,t , t = s1b , s1b ,..., sTbi }, where b=1 (for bootstrap resample number one), and, as indicated, where a sample is drawn having the same number of residuals (e.g., the same number of time periods, Ti ) as the original sample for each fund i. This resampling procedure is repeated for the remaining bootstrap iterations, b=2,…,B. For each bootstrap iteration, b, a time-series of (bootstrapped) monthly net returns is constructed for this fund:

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Rib,t = αˆ i + βˆi ,1 RMRFt + βˆi ,2 SMBt + βˆi ,3 HMLt + βˆi ,4 MOM t +

γ 1 RMRFt +21 + γ 2 SMBt2+1 + γ 3 HML2t +1 + γ 4 MOM t2+1 + εˆib,t , t = s1b , s2b ,..., sTb

(45)

i

where s1b , s2b ,..., sTbi is the time reordering imposed by resampling the residuals in bootstrap itereation b. I repeat the process 1,000 times, resulting in 1,000 sets of bootstrap returns for each fund. The third step is to estimate the parameters of the timing models for each set of bootstrap data. For each fund, then, I have 1,000 timing coefficients for both timing models. The standard error of each fund’s 1,000 timing coefficients is the bootstrap standard error of the original timing coefficient, which I use to compute empirical t-statistics of the form t=

γ p ,original σ (γ p ,bootstrap )

(46)

I assess significance at the five percent level and so compare the empirical t-statistic to ± 2, the critical value under the assumption of normality. I repeat this procedure for all other funds in my sample. 5.4.7. Timing Aggressiveness

Bollen and Busse (2001) find that the magnitude of the average timing coefficient is smaller under the HM model than under the TM model (less positive or less negative). A potential explanation relies on the fact that the TM and HM coefficients essentially measure the expected convexity in the funds’ relation to the market return, which reflects both the probability (related to information quality) and the magnitude (related to risk aversion). A fund manager’s market timing performance depends on both the quality of his private information (ability) and the aggressiveness with which the manager reacts to his information (response). Jiang (2001) suggests that the HM measure caters more on the information quality side of the market timing while the TM measure basically reflects the intensity of the manager’s reaction. Hence, more aggressive funds can show up as better (or worse if the information is incorrect) Ph.D. Thesis: Jeffrey Junhua Lu

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market timers with higher (more negative) TM measures. Therefore, the magnitude of these timing coefficients (the absolute value) is used as a proxy for the aggressiveness of fund timing strategies. 5.4.8. Performance Record Differences

To investigate how prior performance record influences fund managers’ timing behaviour as discussed in section 4.2.5, I use the Morningstar rating for each fund as at the beginning of its entire performance history (fund exists during the sample period). Morningstar gives mutual funds one to five stars according to their past investment performance. The highest ranking is five stars, and the lowest ranking is one. As evidence of the importance of the Morningstar five-star rating service, I consider a study reported in both the Boston Globe and The Wall Street Journal, which found that 97 percent of the money flowing into no-load equity funds between January and August 1995 was invested into funds that were rated as five- or four-star funds by Morningstar, while funds with less than three stars suffered a net outflow of funds during the same period. Moreover, the heavy use of Morningstar ratings in mutual fund advertising suggests that mutual fund companies believe that investors care about Morningstar ratings. Indeed, in some cases, the only mention of return performance in the mutual fund advertisement is the Morningstar rating. To calculate its ratings, Morningstar first classifies funds into one of four categories: domestic equity, foreign equity, municipal bond, and taxable bond. The ratings are then based upon an aggregation of the three-, five-, and ten-year risk-adjusted return for funds with 10 years or more of return history, three- and five-year risk-adjusted returns for funds with five to less than 10 years of return data, and three-year risk-adjusted returns for funds with three to less to than five years of return data. To calculate the risk-adjusted return, Morningstar first calculates a load-adjusted return for the fund by adjusting the returns for expenses such as 12b-1 fees, management fees, and other costs automatically taken out of the fund, and then by adjusting for Ph.D. Thesis: Jeffrey Junhua Lu

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front-end and deferred loads. Next, Morningstar calculates a “Morningstar return” in which the expense- and load-adjusted excess return is divided by the higher of two variables: the excess average return of the fund category or the average 90-day US T-bill rate, ( Expense − and Load − Adjusted Return on the Fund − T − Bill ) max[( Average Category Return T − bill ), T − Bill ]

(47)

Morningstar divides through by one of these two variables to prevent distortions caused by having low or negative average excess returns in the denominator of equation (33). Such a situation might occur in a protracted down market. Morningstar then calculates a “Morningstar risk” measure, which is calculated differently from traditional risk measures, such as beta and standard deviation that both see greater-than and less-than-expected returns as added volatility. Morningstar believes that most investors’ greatest fear is losing money, which Morningstar defines as underperforming the risk-free rate of return an investor can earn from the 90-day Treasury bill. Hence, their risk measure only focuses on downside risk. To calculate risk, Morningstar plots monthly returns in relation to T-bill returns, adds up the amounts by which the fund trails the T-bill return each month, and then divides that total by the time horizon’s total number of months. This number, the average monthly underperformance statistic, is then compared with those of other funds in the same broad investment category to assign the risk scores. The resultant Morningstar risk score expresses how risky the fund is relative to the average fund in its category. To calculate a fund’s summary star rating, Morningstar calculates its three-, five-, and ten-year Morningstar return and risk. For each time horizon, the Morningstar risk scores are then subtracted from the Morningstar return scores. The three numbers (one for each time horizon) are then given subjective weights. The three-year number receives a 20 percent weighting, the five-year a 30 percent weighting, and the ten-year a 50 percent weighting. As stated above, in the case of young funds (funds with three to less than five years of return data), the three-year number receives a 100 percent Ph.D. Thesis: Jeffrey Junhua Lu

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weighting; in the case of middle-aged funds (funds with five to less than ten years of return data), the three-year number receives a 40 percent weighting and the five-year number receives a 60 percent weighting. With these weights, Morningstar calculates the weighted average of the numbers. The resulting number is then plotted along a bell curve to determine the fund’s star rating. If the fund scores in the top 10 percent of its broad investment category, it receives a rating of five stars; if the fund falls in the next 22.5 percent, it receives four stars; if it falls in the middle 35 percent, it receives three stars; if it lies in the next 22.5 percent, the fund receives two stars, and if it is in the bottom 10 percent, it receives one star. These Morningstar rankings on fund performance and volatility of performance are divided into five groups based on five star categories and the differences in timing behaviour during the timing implementation period between groups of funds will be examined. 5.4.9. Systematic Factors Affecting Fund Timing

Practitioners and academics have long asserted that certain systematic factors influence mutual fund timing behaviour. To test the influence of systematic factors on fund factor timing activities, as discussed in section 4.2.6, I segregate the data by several systematic factors common to mutual funds: desired risk exposure, size, turnover, fund age, fund flow. 5.4.9.1 Desired Risk Exposure

Investors have the ability to select funds with significantly different management styles and stated risk objectives. To investigate the effect of stated risk objectives on the timing behaviour of funds, I segregate my sample funds into five Morningstar “investment objectives” (styles): aggressive growth, growth, growth and income, equity income, and small companies. 5.4.9.2 Size

Another systematic factor common to mutual funds that affects timing behaviour is Ph.D. Thesis: Jeffrey Junhua Lu

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size of the managed funds as measured by the fund’s total net assets under management (TNA). To investigate the effect of fund size on the timing behaviour of funds, I segregate the sample funds into quintiles by size. The size of the sample funds varies from less than $1m to $9.3bn dollars. The median is $105.2m dollars. I segregate the sample funds into quintiles by size. 5.4.9.3 Turnover

Mutual fund managers claim that turnover does not reduce performance, since investors are paying for the quality of the manager’s information, and because managers trade only to anticipate market/styles movements and to time their styles. To justify their higher charges to customers, funds with higher turnover ratios make a greater attempt to time their styles. Hence, it is expected that an increase in fund timing activities will coincide with higher turnover. To investigate the effect of turnover on the timing behaviour of funds, I segregate my sample funds into three categories according to their average annual turnover rates over the sample period: Low (less than 50 percent), Median (between 50 percent and 100 percent), and High (100 percent or higher). 5.4.9.4 Fund Age

To investigate the effect of fund age on the timing behaviour of funds, I segregate my sample funds into three groups: new funds, old funds and median-aged funds. New funds are defined as those funds with less than 5-year performance history in existence and old funds are defined as those funds with 10-year or more than 10-year performance history. The remainder are defined as median-aged funds. Differences in timing behaviour between these groups of fund managers are investigated to see whether there are any significant differences. 5.4.9.5 Fund Flow

Fund managers provide a great deal of liquidity to investors and thus engage in a material volume of uninformed, liquidity-motivated trading. Ferson and Schadt (1996)

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argue that fund managers might be forced to trade at the wrong time due to unexpected funds flows. Moreover, when market returns are high, investors increase subscriptions to mutual funds, resulting in a temporarily larger cash position and lower fund beta. Warther (1995) shows a strong relation between a fund’s cash inflows and its portfolio weight in cash. Thus, assessing fund managers’ timing ability without considering flow can result in negatively biased inferences. Edelen (1999) finds that funds exhibit negative market timing when, and only when, they experience flow. Absent flow, the inferred market-timing ability of the fund manager is positive. Short-term switchers in and out of funds are more likely to attack no-load funds where they take the advantage of the cost-free entry and exit. Hence, we can look at the possible difference in timing between load and no-load funds and infer whether fund managers’ timing ability is impaired by investor flows.

5.5 Summary In this chapter I have described the data used in this study and the data sources employed. I have also discussed the methodology that I use to test the hypotheses discussed in chapter 4. I significantly expand on the work of Bollen and Busse (2001) and Volkman (1999) by combining systematic risk factors unique to equity markets with timing factors unique to actively managed portfolios. Specifically, I construct a set of synthetic fund returns in order to control for spurious results and apply an innovative bootstrap statistical technique to examine the factor timing behaviour of fund managers within different market segment characterisation, based on such established styles as size, book-to-market, and momentum etc. In the next chapter, I test whether fund managers possess market timing abilities using the Treynor and Mazuy (1966) and Henrikson and Merton (1981) market timing models.

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CHAPTER 6 MARKET TIMING 6.1. Introduction Market timing refers to the dynamic allocation of capital among broad classes of investments, often restricted to equities and short-term government debt. The successful market timer increases his/her portfolio weight in equities prior to a rise in the market, and decreases his/her equity weighting prior to a fall in the market. In general, evidence on the ability of investment managers to time the market is mixed. Several studies of mutual fund timing skill29 generally find little evidence of timing abilities. In an early study, Treynor and Mazuy (1966) find significant ability in only 1 fund out of 57 in their sample. Henriksson (1984) finds that only 3 funds out of 116 exhibit significant positive market timing ability. Graham and Harvey (1996) analyse investment newsletters’ suggested allocation between equity and cash, thereby measuring explicitly the ex post performance of timing strategies. Again, they find no evidence of timing ability. However, the most puzzling aspect of the empirical evidence is that the average timing measures across mutual funds are negative and that those funds that do exhibit significant timing performance show negative performance more often than positive performance (Volkman, 1999). Also, Kon (1983) and Henriksson (1984) find that there is negative correlation between measures of security selection ability and market timing. Henriksson (1984) suggests a number of potential

explanations

for

these

results,

including

error-in-variables

bias,

misspecification of the market portfolio, and use of a single-factor rather than a multifactor asset-pricing model. On the other hand, when an attempt is made to control for the above issues associated

29

See Kon (1983); Chang and Lewellen (1984); Lehmann and Modest (1987), Grinblatt and Titman (1989a), (1994); Daniel, Grinblatt, Titman, and Wermers (1997).

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with market timing tests, other researchers have demonstrated fund managers’ timing ability. For example, Ferson and Schadt (1996) find some evidence of timing skill when macroeconomic conditions are accounted for. Graham and Harvey (1996) detect evidence of timing skill using certain benchmarks. Wagner et al. (1992), Brocanto and Chandy (1994), and Chance and Hemler (1999) all uncover some positive timing evidence as well. Brown et al. (1998) find evidence that the Dow Theory works as a timing strategy. In this chapter I first conduct market timing tests on my sample funds by using the single factor models and the multi-factor models based on Treynor and Mazuy (1966) and Henrikson and Merton (1981). To control for potential Jagannathan and Korajczyk (1986) spurious timing ability bias, I then conduct the same market timing tests on a synthetic matched sample of funds, which are constructed to mimic the holdings of the actual funds, but have no timing ability. Finally, I investigate the relationships between fund managers’ stock selection ability and their timing ability. The chapter is organised as follows: section 2 describes the market timing models, section 3 presents the results of market timing tests on my sample funds, section 4 presents the results of market timing tests on my synthetic funds, section 5 reports the results of tests on the relationship between security selection ability and market timing, and section 6 summarises the results.

6.2. Market Timing Models Treynor and Mazuy (1966, TM hereafter) assume a stochastic risk relation and use the following quadratic regression to test for market timing: 2 R pt = α p + β p Rmt + γ p Rmt + ε pt

(9)

Henrikson and Merton (1981, HM hereafter) test a model with two target betas via the following regression: Ph.D. Thesis: Jeffrey Junhua Lu

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Can Fund Managers Successfully Time Their Investment Styles? * R pt = α p + β p Rmt + γ p Rmt + ε pt

(10)

where * Rmt = I {Rmt > 0}Rmt

(11)

and I {Rmt > 0} is an indicator function that equals one if Rmt is positive and zero otherwise. Henrikson and Merton (1981) also suggest an extended version of Equation 10, which explicitly identifies the risk levels in up- and down-market conditions: + R pt = α p + β u Rmt + β d Rmt− + ε pt

(12)

where Rmt+ =max[0, Rmt ] and Rmt− =min[0, Rmt ]. Empirically, the up-market beta, β u and the down-market beta, β d can be tested to determine whether they are significantly different from each other (H0: β u = β d ). If a manager is a good market timer, his up-market beta should be greater than the down-market beta. Chang and Lewellen (1984) specifically test Equation 12. Bollen and Busse (2001) and Volkman (1999) propose the following revised version of the TM and HM market timing models, by incorporating Carhart’s (1997) four-factor model. Carhart’s (1997) four-factor TM market timing model is expressed as: R pt = α p + β1 RMRFt + β 2 SMBt + β3 HMLt + β 4 MOM t + γ p Rmt2 + ε pt

(13)

Carhart’s (1997) four-factor HM market timing model is expressed as: * R pt = α p + β1 RMRFt + β 2 SMBt + β3 HMLt + β 4 MOM t + γ p Rmt + ε pt

(14)

Grinblatt and Titman (1994) show that tests of performance are quite sensitive to the chosen benchmark. For this reason, the above market timing tests will also be run

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with the Fama and French (1993) three-factor model for robustness check purposes. The Fama and French (1993) three-factor TM market timing model is expressed as: 2 R pt = α p + β 1 RMRFt + β 2 SMBt + β 3 HMLt + γ p Rmt + ε pt

(48)

The Fama and French (1993) three-factor HM market timing model is expressed as: * R pt = α p + β 1 RMRFt + β 2 SMBt + β 3 HMLt + γ p Rmt + ε pt

(49)

6.3. Market Timing Results For Sample Funds To test the null hypothesis of H1, that is, whether the average mutual fund demonstrates a significant ability (either positive or negative) to time the market, I conduct 2,791 time-series regressions for my sample funds using the Treynor and Mazuy (1966) and Henrikson and Merton (1981) market timing models based on the CAPM (CAPM hereafter), the Fama-French three-factor model (FF hereafter), and the Carhart four-factor model (CA hereafter). The timing coefficients obtained from these regressions are first used to carry out significant tests respectively on each sample fund and are then summarised. If substantial percentages of these timing coefficients are significantly different from zero, the null hypothesis is rejected, demonstrating that the average mutual fund demonstrates a significant ability. H10 : The average mutual fund does not demonstrate a significant ability (positive or negative) to time the market.

Table 2 (Page 233)

The results are summarised in Table 2, which shows little evidence of market-timing ability. Table 2 lists the fraction of funds that have positive and negative timing coefficients and the number of funds that have significant positive and negative Ph.D. Thesis: Jeffrey Junhua Lu

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timing coefficients. Panel A, Table 2 shows the results for the mutual fund sample. In most cases, the fraction of funds with positive timing coefficients is similar to that of funds with negative timing coefficients. Around 51 percent of sample funds exhibit positive timing coefficients while 49 percent of sample funds exhibit negative timing coefficients under the TM CA market timing model. Under the HM CA market timing model, around 67 percent of sample funds exhibit positive timing coefficients while 33 percent of sample funds exhibit negative timing coefficients. For comparison purposes, I also conduct the market timing tests under the FF three-factor model and the CAPM single factor model. The results are quantitatively similar.30 Therefore, in terms of the proportion of the sample funds exhibiting positive/negative market timing coefficients, the results under the CA four-factor market timing model and the FF three-factor market timing model are very similar, which indicate that both multi-factor market timing models are able to capture the diversified and dynamic aspects of managed portfolios. However, the results under the CAPM single factor market timing model are somewhat different from those under the above multi-factor market timing models, which indicate that the single factor market timing model misses the diversified and dynamic aspects of managed portfolios. Panel A, Table 2 also reports the percentage of funds that have significantly positive and negative timing coefficients. It seems that mutual funds on average are neither more nor less likely to successfully time the market. Note that there are very few funds exhibiting significantly positive or negative timing coefficients. Under the assumption that the returns earned by the mutual funds and the market portfolio follow a joint-normal distribution, only 1.3 percent of sample funds exhibit significant positive timing coefficients while 1 percent of sample funds exhibit significant

30

There are 53% of sample funds exhibiting positive timing coefficients and 47% of sample funds exhibiting negative timing coefficients under the TM FF marketing timing model. Under the HM FF market timing model, 68% of sample funds exhibit positive timing coefficients while 32% of sample funds exhibit negative timing coefficients. However, under the TM CAPM market timing model, there are 43% of sample funds exhibiting positive timing coefficients and 57% of sample funds exhibiting negative timing coefficients; under the HM CAPM market timing model, there are 53% of sample funds exhibiting positive timing coefficients and 47% of sample funds exhibiting negative timing coefficients.

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negative timing coefficients with 95 percent confidence under the TM CA market timing model. Under the HM CA market timing model, only 2 percent of sample funds exhibit significant positive timing coefficients while 0.3 percent of sample funds exhibit significant negative timing coefficients with 95 percent confidence. For comparison purposes, I also conduct the market timing tests under the FF three-factor model and the CAPM single factor model. The results are quantitatively similar.31

6.4. Market Timing Results For Synthetic Funds A conservative interpretation of the results in Panel A of Table 2 requires the consideration of potential sources of spurious timing coefficients. Jagannathan and Korajczyk (1986) argue that spurious timing ability can be generated when portfolios hold stocks with payoffs that are more, or less, option-like than the market proxy. In particular, funds that tend to invest in stocks with little or no risky debt (less option-like), such as blue chips, will show negative timing coefficients, while funds that invest in small, highly levered stocks (more option-like) will show positive timing coefficients. Recall from Panel E Table 1 that mutual funds exhibit less negative skewness than the market index on average. As such we might expect states in which mutual fund returns and market returns are both negative, due to their correlation, and in which the market returns are more negative than mutual fund returns, due to its greater negative skewness. These states would generate a positive timing coefficient for the market index, even in the absence of market timing activity. To control for Jagannathan and Korajczyk (1986) potential spurious market timing ability, I run my timing tests on a sample of synthetic funds that match the actual

31

There are 1.3% of sample funds exhibiting significant positive timing coefficients and 0.9% of sample funds exhibiting significant negative timing coefficients with 95% confidence under the TM FF marketing timing model. Under the HM FF market timing model, 2.4% of sample funds exhibit significant positive timing coefficients while 0.4% of sample funds exhibit significant negative timing coefficients with 95% confidence. Similarly, under the TM CAPM market timing model, there are 1.1% of sample funds exhibiting significant positive timing coefficients and 2.8% of sample funds exhibiting significant negative timing coefficients with 95% confidence; under the HM CAPM market timing model, there are 1.5% of sample funds exhibiting significant positive timing coefficients and 1.3% of sample funds exhibiting significant negative timing coefficients with 95% confidence.

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funds’ characteristics but have no timing ability by construction, as described earlier. If these synthetic funds exhibit timing ability at the same frequency and magnitude as the actual funds, then the estimated timing coefficients are likely to be spurious rather than evidence of ability. Panel B, Table 2 shows the results of my timing tests when applied to the synthetic funds. In most cases, the fraction of funds with positive timing coefficients is similar to that of funds with negative timing coefficients. Around 50.3 percent of sample funds exhibit positive timing coefficients while 49.7 percent of sample funds exhibit negative timing coefficients under the TM CA market timing model. Under the HM CA market timing model, around 57 percent of sample funds exhibit positive timing coefficients while 43 percent of sample funds exhibit negative timing coefficients. For comparison purposes, I also conduct the market timing tests under the FF three-factor model and the CAPM single factor model. The results are quantitatively similar.32 Panel B, Table 2 also reports the percentage of synthetic funds that have significantly positive and negative timing coefficients. On the assumption that the returns earned by the mutual funds and the market portfolio follow a joint-normal distribution, only 0.5 percent of sample funds exhibit significant positive timing coefficients while 0.7 percent of sample funds exhibit significant negative timing coefficients with 95 percent confidence under the TM CA market timing model. Under the HM CA market timing model, only 2.4 percent of sample funds exhibit significant positive timing coefficients while 0.6 percent of sample funds exhibit significant negative timing coefficients with 95 percent confidence. For comparison purposes, I also report the results for the FF three-factor market timing model and the CAPM single factor

32

There are 50.3% of sample funds exhibiting positive timing coefficients and 49.7% of sample funds exhibiting negative timing coefficients under the TM FF marketing timing model. Under the HM FF market timing model, 56.2% of sample funds exhibit positive timing coefficients while 43.8% of sample funds exhibit negative timing coefficients. However, under the TM CAPM market timing model, there are 23.4% of sample funds exhibiting positive timing coefficients and 76.6% of sample funds exhibiting negative timing coefficients; under the HM CAPM market timing model, there are 27.2% of sample funds exhibiting positive timing coefficients and 72.8% of sample funds exhibiting negative timing coefficients.

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market timing model.33 On average, there are few synthetic funds exhibiting significant timing coefficients under the null of no timing activity. This is consistent with what is expected, since these funds are constructed so that they should have no timing ability. Comparing the results with those of the actual funds, there seem to be no differences in the timing ability between actual funds and their synthetic counterparts. I investigate the relation between the timing ability of actual funds and their synthetic counterparts more formally by computing the differences between their timing coefficients. I assess significance by constructing a standard error for the difference from the bootstrap standard errors of the timing coefficients as follows:

σ (difference) = σ 2 (γ actual ) + σ 2 (γ synthetic )

(50)

Panel C, Table 2 lists the fraction of funds that have timing coefficients larger/smaller than their synthetic counterparts. Under the TM CA market timing model, around 50.9 percent of sample funds exhibit timing coefficients larger than their synthetic counterparts, while 49.1 percent of sample funds exhibit timing coefficients smaller than their synthetic counterparts. Under the HM CA market timing model, around 51.8 percent of sample funds exhibit timing coefficients larger than their synthetic counterparts, while 48.2 percent of sample funds exhibit timing coefficients smaller than their synthetic counterparts. For comparison purposes, I also report the results for the FF three-factor market timing model and the CAPM single factor market timing 33

There are 0.5% of sample funds exhibiting significant positive timing coefficients and 0.8% of sample funds exhibiting significant negative timing coefficients with 95% confidence under the TM FF marketing timing model. Under the HM FF market timing model, 2.1% of sample funds exhibit significant positive timing coefficients while 0.5% of sample funds exhibit significant negative timing coefficients with 95% confidence. Similarly, under the TM CAPM market timing model, there are 0.8% of sample funds exhibiting significant positive timing coefficients and 4.8% of sample funds exhibiting significant negative timing coefficients with 95% confidence; under the HM CAPM market timing model, there are 1.2% of sample funds exhibiting significant positive timing coefficients and 2.7% of sample funds exhibiting significant negative timing coefficients with 95% confidence.

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model.34 Therefore, on average, the sample funds exhibit neither larger nor smaller timing coefficients than their synthetic counterparts. Panel C, Table 2 also lists the percentage of sample funds that have timing coefficients significantly larger/smaller than their synthetic counterparts. Under the TM CA market timing model, around 1.1 percent of sample funds exhibit timing coefficients significantly larger than their synthetic counterparts, while 0.9 percent of sample funds exhibit timing coefficients significantly smaller than their synthetic counterparts. Under the HM CA market timing model, around 1 percent of sample funds exhibit timing coefficients significantly larger than their synthetic counterparts, while 0.8 percent of sample funds exhibit timing coefficients significantly smaller than their synthetic counterparts. For comparison purposes, I also report the results for the FF three-factor market timing model and the CAPM single factor market timing model.35 Again, on average there are very few funds exhibiting significantly larger or smaller timing coefficients than their synthetic counterparts. Therefore, the null hypothesis of H1 can not be rejected and the average mutual fund manager demonstrates little ability to time the market in aggregate over the ten-year period of my study (June

34

Under the TM FF market timing model, around 53% of sample funds exhibit timing coefficients larger than their synthetic counterparts, while 47% of sample funds exhibit timing coefficients smaller than their synthetic counterparts. Under the HM FF market timing model, around 53.2% of sample funds exhibit timing coefficients larger than their synthetic counterparts, while 46.8% of sample funds exhibit timing coefficients smaller than their synthetic counterparts. Similarly, under the TM CAPM market timing model, around 62% of sample funds exhibit timing coefficients larger than their synthetic counterparts, while 38% of sample funds exhibit timing coefficients smaller than their synthetic counterparts. Under the HM CAPM market timing model, around 63.4% of sample funds exhibit timing coefficients larger than their synthetic counterparts, while 36.6% of sample funds exhibit timing coefficients smaller than their synthetic counterparts.

35

Under the TM FF market timing model, around 1% of sample funds exhibit timing coefficients significantly larger than their synthetic counterparts, while 0.9% of sample funds exhibit timing coefficients significantly smaller than their synthetic counterparts. Under the HM CA market timing model, around 1.1% of sample funds exhibit timing coefficients significantly larger than their synthetic counterparts, while 0.8% of sample funds exhibit timing coefficients significantly smaller than their synthetic counterparts. Similarly, under the TM CAPM market timing model, around 4.7% of sample funds exhibit timing coefficients significantly larger than their synthetic counterparts, while 0.8% of sample funds exhibit timing coefficients significantly smaller than their synthetic counterparts. Under the HM CA market timing model, around 3.5% of sample funds exhibit timing coefficients significantly larger than their synthetic counterparts, while 0.1% of sample funds exhibit timing coefficients significantly smaller than their synthetic counterparts.

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1992 to July 2002).

6.5. Relationship between Stock Selection and Market Timing Kon (1983) and Henriksson (1984) also document a negative correlation between regression intercepts and timing coefficients. Both find that most mutual funds in their respective samples exhibit positive intercepts and negative timing coefficients. Sahu et al. (1998) specifically test the relationship between bank funds’ stock selection and market timing abilities by utilising meta-analysis to eliminate such study artefacts as sampling and measurement errors. Their findings suggest that the managers of bank equity investment funds possess superior stock selection abilities and somewhat negative timing skills. Volkman (1999) investigates the relationship between a fund’s timing and selectivity performance and finds a negative correlation. He suggests that mutual fund managers attempt to maximise selectivity performance at the expense of timing performance. To test the null hypothesis of H2, that is, whether there is consistent relationship between funds market timing and stock selection performance, I conduct the following analysis. H20 : There is no consistent relationship between funds market timing behaviour and stock selection activities.

If we cannot reject this hypothesis, we should not expect to see any consistent relationship between the intercepts and the timing coefficients in a market timing regression. Recall that in Panel A of Table 2, there does appear to be an inverse relation between the timing coefficients and intercepts in the timing regressions. In all cases, the average intercept for the funds with negative timing coefficients is much higher than the corresponding average for funds with positive timing coefficients, which are significantly different at the one percent level.

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Table 3 (Page 235) To test the relation more formally, I run a correlation analysis on the intercepts and timing coefficients for each timing model. Table 3 illustrates the correlation between a fund’s timing ability and stock selectivity performance. Both the parametric Pearson correlation coefficient and the nonparametric Spearman rank coefficient indicate a significant negative correlation between a fund’s timing ability and its selectivity performance at the one percent level. For example, under the Carhart four-factor TM market timing model, the Pearson correlation coefficient is -0.344 and the Spearman rank coefficient is -0.378; similarly, under the Carhart four-factor HM market timing model, the Pearson correlation coefficient is -0.531 and the Spearman rank coefficient is -0.573. For comparison purposes, I also report the results for the FF three-factor market timing model and the CAPM single-factor market timing model.36 The negative correlation suggests that managers may focus on one source of performance at the expense of the other source of performance. More informative is the percentage of funds demonstrating abnormal performance (significant alpha). Under the Carhart four-factor TM model, 8.3 percent of funds with significant positive alphas exhibit negative timing coefficients; 2.5 percent of funds with significant positive alphas are accompanied by positive timing coefficients; 1.5 percent of funds with significant negative alpha are associated with a positive timing coefficient; and 0.4 percent of funds with significant negative alpha are associated with a negative timing coefficient. Similarly, under the Carhart four-factor HM model, 3.4 percent of funds with significant positive alphas exhibit negative timing coefficients; 1.6 percent of funds with significant positive alphas are accompanied by 36

Under the Fama-French three-factor TM market timing model, the Pearson correlation coefficient is -0.389 and the Spearman rank coefficient is -0.430; similarly, under the Fama-French three-factor HM market timing model, the Pearson correlation coefficient is -0.518 and the Spearman rank coefficient is -0.538. The correlation coefficients under the CAPM market timing model are more negative than the ones under other market timing models. Under the CAPM single-factor TM market timing model, the Pearson correlation coefficient is -0.408 and the Spearman rank coefficient is -0.422; similarly, under the Fama-French three-factor HM market timing model, the Pearson correlation coefficient is -0.627 and the Spearman rank coefficient is -0.637.

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positive timing coefficients; 1.8 percent of funds with significant negative alpha are associated with a positive timing coefficient; and 0.04 percent of funds with significant negative alpha are associated with a negative timing coefficient. The results are similar for other asset pricing models and timing models. Kon (1983) and Henriksson (1984) also find that most mutual funds in their respective samples exhibit positive intercepts and negative timing coefficients, the same as I find here. Hence, Table 3 rejects the null hypothesis of H2 and supports the assertion that mutual fund managers attempt to maximise selectivity performance at the expense of market timing performance.

6.6. Summary This chapter investigates the market timing ability of fund managers. I conduct market timing tests on my sample funds by using the single factor models and the multi-factor models based on the work of Treynor and Mazuy (1966) and Henrikson and Merton (1981). To control for the Jagannathan and Korajczyk (1986) potential spurious timing ability, I then conduct the same market timing tests on a synthetic matched sample of funds, which are constructed to mimic the holdings of the actual funds but have no timing ability. I find that over the ten-year period (June 1992 to July 2002) of this study, the average mutual fund does not demonstrate a significant ability to time the market. Under the Carhart 4-factor TM timing model, only around 1.1 percent of sample funds exhibit timing coefficients significantly larger than their synthetic counterparts, while only 0.9 percent of sample funds exhibit timing coefficients significantly smaller than their synthetic counterparts. On average there are very few funds exhibiting significantly larger or smaller timing coefficients than their synthetic counterparts. Therefore, the null hypothesis of H1 can not be rejected and the average mutual fund manager demonstrates little ability to time the market in aggregate over the ten-year period of my study (June 1992 to July 2002). I also investigate the relation between fund managers’ stock selection ability and their Ph.D. Thesis: Jeffrey Junhua Lu

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timing ability. There is weak evidence that supports the assertion that mutual fund managers attempt to implement market timing strategies at the expense of poor performance in their stock selection. Based on the Carhart 4-factor TM timing model, 8.3 percent of sample funds with significant positive alphas exhibit negative timing coefficients, though this is not significant. Therefore, the null hypothesis of H2 can be rejected. There is some weak evidence that supports the assertion that mutual fund managers attempt to implement market timing strategies at the expense of poor stock selection performance. In the next chapter I investigate the style timing ability of active fund managers. I significantly expand on the work of Bollen and Busse (2001) and Volkman (1999) by combining systematic risk factors unique to equity markets with timing factors unique to actively managed portfolios. I examine the timing behaviour of fund managers within market segments or styles which are characterised in terms of specific systematic style factors, such as size, book-to-market, and momentum etc.

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CHAPTER 7 STYLE TIMING 7.1. Introduction In chapter 6 I presented evidence that over the ten-year period (June 1992 to July 2002) of this study, the average mutual fund did not demonstrate a significant ability to time the market. I also provide weak evidence that supports the assertion that mutual fund managers attempt to implement market timing strategies at the expense of poor performance in stock selection. In this chapter I turn to investigate the style timing abilities of active fund managers and specifically test the hypotheses addressed in 4.2.2 and 4.2.3. Most existing studies relating to the timing behaviour of mutual funds focus on the general market timing abilities of fund managers. Few have investigated their specific timing abilities within market segments, which are related to such systematic risk factors as size and book-to-market. For an active fund manager to outperform his passive counterpart, he must possess superior information and must be capable of exploiting this information. Obviously, such information need not be related to the whole market, but can be restricted to subsets of the market. Investment strategies based on size (big cap/small cap), book-to-market (value/growth), and momentum (winner/loser) factors have long been attractive to investors as potential sources of added value, since long-term excess return premia are reported associated with one side of these factors. Pioneering work on the predictability of asset class returns grouped by these factors in the US market was carried out by Keim and Stambaugh (1986), Campbell (1987), Campbell and Shiller (1988), Fama and French (1989), and Ferson and Harvey (1991). In this chapter I first conduct style timing tests on my sample funds by using the single factor models and the multi-factor models based on Treynor and Mazuy (1966) Ph.D. Thesis: Jeffrey Junhua Lu

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and Henrikson and Merton (1981). I significantly expand on the work of Bollen and Busse (2001) and Volkman (1999) by implementing my own style timing models which incorporate systematic risk factors unique to equity markets into traditional market timing models. To control for potential Jagannathan and Korajczyk (1986) spurious timing ability bias, I then follow the same procedure implemented in chapter 6 and conduct the same style timing tests on a synthetic matched sample of funds, which are constructed to mimic the holdings of the actual funds but have no timing ability. Specifically, I formally test the hypotheses of H3 and H4 to examine whether fund managers exhibit style timing abilities in general. I also investigate the relationships between fund managers’ stock selection ability and their style timing ability, which is relating to hypothesis H5. Finally, I investigate the relationships between fund managers’ different style timing ability, which is relating to hypothesis H6. Because of concerns about possible survivorship bias, discussed by Brown et al. (1992), it is important to investigate the effect of this restriction on my results. Thus, I next investigate the sensitivity of my results to the choice of minimum number of observations available for each fund. Specifically, I consider a subsample of funds surviving at least 36 months and repeat the major style timing tests on these sample funds. The chapter is organised as follows: section 2 describes the style timing models, section 3 presents the results of these style timing tests on my sample funds, section 4 presents the results of style timing tests on the synthetic funds, section 5 reports the results of tests on the relationship between security selection ability and style timing, section 6 reports the results of tests on the relationship between different style timings, section 7 reports the results of sensitivity analysis on sample funds with at least 36 valid monthly net return observations. Section 8 summarises the chapter.

7.2. Style Timing Models Recall that three additional factors, including size (big cap/small cap), book-to-market (value/growth), and momentum (winner/loser), in Equation 13 on page 110 Ph.D. Thesis: Jeffrey Junhua Lu

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implemented in chapter 6 appear only as linear terms, that is, the model does not estimate “style/factor timing” except for the market factor. To conduct style timing tests based on the Carhart (1997) four-factor TM model, Equation 52 can be revised as: R pt = α p + β1 RMRFt + β 2 SMBt + β3 HMLt + β 4 MOM t +

γ 1 RMRFt 2 + γ 2 SMBt2 + γ 3 HML2t + γ 4 MOM t2 + ε pt

(25)

Similarly, the style timing model based on the Carhart (1997) four-factor HM model is expressed as: R pt = α p + β1 RMRFt + β 2 SMBt + β3 HMLt + β 4 MOM t +

γ 1 RMRFt * + γ 2 SMBt* + γ 3 HML*t + γ 4 MOM t* + ε pt

(35)

where * Rmt = I {Rmt > 0}Rmt

(36)

SMBt* = I {SMBt > 0}SMBt

(37)

HML*t = I {HMLt > 0}HMLt

(38)

MOM t* = I {MOM t > 0}MOM t

(39)

Factor timing tests will also be conducted based on the Fama and French (1993) three-factor model. R pt = α p + β 1 RMRFt + β 2 SMBt + β 3 HMLt +

γ 1 RMRFt 2 + γ 2 SMBt2 + γ 3 HML2t + ε pt R pt = α p + β 1 RMRFt + β 2 SMBt + β 3 HMLt +

γ 1 RMRFt * + γ 2 SMBt* + γ 3 HML*t + ε pt

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(51)

(52)

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7.3. Style Timing Results For Sample Funds 7.3.1

Joint Tests of Style Timing

To test whether the average mutual fund demonstrates a significant ability (either positive or negative) to time the styles, I conduct 2,791 time-series regressions for my sample funds using the TM and HM style timing models based on the Fama-French FF three-factor model and the Carhart CA four-factor model. The timing coefficients obtained from these regressions are first used to carry out significance tests respectively on each sample fund and are then summarised. If substantial percentages of these timing coefficients are significantly different from zero, the relevant null hypothesis is rejected demonstrating that the average mutual fund has significant timing ability. The null hypothesis is developed in 4.2.2 of Chapter 4 as hypothesis H3. H30 : The average mutual fund does not exhibit significant timing ability with respect to any of the stylers, such as market, size (big cap/small cap), book-to-market (value/growth), and momentum (winner/loser).

To test this hypothesis, joint tests of multiple timing coefficients in the style timing models are carried out to test whether any of timing coefficients do not differ significantly from zero. If the null hypothesis can not be rejected at conventional levels and all the timing coefficients are equal to zero, this demonstrates that fund managers demonstrate no style timing abilities or have not engaged in any style timing strategies with respect to the styles considered. I conduct the tests based on the Carhart 4-factor models and these are carried out in the following steps: 1. Create a “full” or “unrestricted” model, one with all coefficients included. R pt = α p + β1 RMRFt + β 2 SMBt + β3 HMLt + β 4 MOM t +

γ 1 RMRFt 2 + γ 2 SMBt2 + γ 3 HML2t + γ 4 MOM t2 + ε pt −unrestricted

(25)

2. Calculate the sum of square errors from that model, call it ESSU

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3. Create a “restricted” model, one with timing coefficients set equal to 0. this amounts to leaving timing variables out of the regression model. R pt = α p + β1 RMRFt + β 2 SMBt + β3 HMLt + β 4 MOM t + ε pt − restricted

(53)

4. Call the sum of square errors for this model ESSR. 5. Compare the two models to find out if the restriction makes a difference. 6. This comparison is conducted using the F test. Let N be the sample size. Let k be the number of independent variables used in the full model. Let q be the number of variables that are excluded from the restricted model. The F statistic is then F=

( ESS R − ESSUR ) / q ESSUR / N − k − 1

(54)

Results are presented in Table 4 Table 4 (Page 236) Table 4 shows that a substantial proportion of my sample funds exhibit significant style timing coefficients and thus engage in style timing activities. With the Carhart 4-factor TM style timing model, around 44 percent of sample funds have significant style timing coefficients with 95 percent confidence. Under the Carhart 4-factor HM style timing model, 22 percent of my sample funds show significant factor timing coefficients with 95 percent confidence. For those sample funds with significant style timing coefficients, on average they exhibit positive timing on the market style, negative timing on the size style, positive timing on the book-to-market style, and negative timing on the momentum style. However, these funds show insignificant positive intercept (0.253 percent per year) or even negative intercept (-1.29 percent per year). Results are very similar to the Fama-French 3-factor TM/HM timing model, except that the average timing coefficients on market style turn negative, albeit their magnitude is very small.

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An interesting pattern is shown in that more funds demonstrate significant timing coefficients under the Carhart 4-factor timing model than under the Fama-French 3-factor timing model. It is possible that some of the factor timing activities not captured by the Fama-French 3-factor model may simply reflect momentum strategy and contrarian strategies implemented by fund managers. Wermers (1999) finds that herds form more often on the buy-side in high past return stocks and on the sell-side in low past return stocks, especially among growth-oriented funds. He suggests that the use of positive-feedback (momentum) strategies by growth-oriented funds is an important source of herding. The Carhart 4-factor model adds in an additional momentum factor. Therefore, it may capture the herding activities among mutual funds and thus increase the power of identifying fund managers’ timing activities. However, the negative sign of the momentum timing coefficient may indicate that fund managers tend to time these momentum and contrarian strategies unsuccessfully. In other words, they are more likely to decrease their position in momentum stocks when these stocks are going to outperform and are less likely to decrease their position in contrarian stocks when these stocks are going to underperform. In short, fund managers are selling winners too soon and holding losers too long. This issue will be investigated further in the following section. 7.3.2

Detailed Style Timing for Sample Funds

As some funds engage in style timing activities, I further investigate their timing activities related to specific styles. If fund managers do appear to exhibit some degree of factor timing abilities in general, then this leads us to the following research question: which factor(s) do mutual fund managers try to time among Carhart’s four factors? I thus conduct separate tests for each factor to examine whether fund managers exhibit timing abilities with respect to a specific factor/style. H40a : The average mutual fund does not exhibit a significant timing ability with respect to the size style (big cap/small cap). H40b : The average mutual fund does not exhibit a significant timing ability with Ph.D. Thesis: Jeffrey Junhua Lu

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respect to the book-to-market style (value/growth) . H40c : The average mutual fund does not exhibit a significant timing ability with respect to the momentum style (winner/loser) .

As discussed in Chapter 4, fund manager investment activities, especially their timing behaviour, may suffer from the same behavioural biases as retail investors to some extent. Momentum style timing can be viewed as follows: an investor goes with loser (winner) stocks when loser (winner) stocks turn out to outperform winner (loser) stocks. If fund managers tend to sell winners (which are momentum stocks) too soon and hold on to losers (which are contrarian stocks) too long, and if momentum stocks outperform contrarian stocks on average, fund managers would time the momentum style poorly. Hence, the two-side test of null hypothesis H40c is further developed as a one-side test as follows. H40d : The average mutual fund does not exhibit a significant poor timing ability with respect to the momentum factor.

Table 5 (Page 237)

Table 5 lists the fractions of funds that have positive and negative timing coefficients and the number of funds that have significantly positive and negative timing coefficients, based on the Carhart 4-factor timing model. It provides evidence that active fund managers engage in some types of style timing activities, consistent with the results of Table 4. Panel A of Table 5 shows the results for my mutual fund sample. For the TM model, the proportion of funds with positive timing coefficients is close to that of funds with negative timing coefficients, with respect to market and size styles. For example, with

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respect to market style, around 58 percent of sample funds possess positive timing coefficients and around 42 percent of sample funds possess negative timing coefficients. Similarly, with respect to size style, about 52 percent of sample funds possess positive timing coefficients and about 48 percent of sample funds possess negative timing coefficients. As such my sample funds do not tend to consistently engage in either type of timing activities (positive or negative). However, there are more funds exhibiting positive book-to-market timing coefficients and negative momentum timing coefficients. In particular, with respect to the book-to-market style, around 77 percent of sample funds have positive timing coefficients and around 23 percent of sample funds possess negative timing coefficients. Similarly, with respect to momentum, about 19 percent of sample funds have positive timing coefficients and about 81 percent of sample funds possess negative timing coefficients. Panel A of Table 5 also reports the percentages of funds that have significantly positive and negative timing coefficients. Few funds show either significant positive (2.2 percent) or significant negative (1.2 percent) market timing coefficients, which is consistent with the results of traditional market timing tests. Few funds show either significant positive (5.6 percent) or significant negative (5.7 percent) size timing coefficients. However, there are more funds exhibiting significant positive book-to-market timing coefficients and negative momentum timing coefficients. For those cases with significant book-to-market timing coefficients, around 30 percent of funds generate positive coefficients and only 2 percent of funds generate negative coefficients. The picture is different for those cases with significant momentum timing coefficients. Only 0.8 percent of funds generate positive coefficients and around 38 percent of funds generate negative coefficients. The HM model results are similar, except that their magnitude is smaller.

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7.4. Style Timing Results For Synthetic Funds 7.4.1

Results on Synthetic Funds

A conservative interpretation of the results requires the consideration of potential sources of spurious timing coefficients. Jagannathan and Korajczyk (1986) argue that spurious timing ability can be generated when portfolios hold stocks with payoffs that are more or less option-like than the market proxy. In particular, funds that tend to invest in stocks with little or no risky debt (less option-like), such as blue chips, will show negative timing coefficients, while funds that invest in small, highly levered stocks (more option-like) will show positive timing coefficients. Recall from Table 1 that the mutual funds in my sample exhibit less negative skewness than the market index, the HML index, the momentum index, and more negative skewness than the SMB index on average. I might expect states in which mutual fund returns and factor returns are both negative, due to their correlation, and in which factor returns are more negative (for the market index, the HML index, and the momentum index) or less negative (for the SMB index) than the mutual funds’ returns, due to their larger (smaller) negative skewness. These states would generate a positive timing coefficient for the market index, the HML index, the momentum index, and a negative timing coefficient for the SMB index, even in the absence of factor timing activity.

Table 6 (Page 239)

Panel A of Table 6 summarises the cross-sectional averages and standard errors of intercepts and timing coefficients for all my sample funds. The relatively large standard errors for the timing coefficients on size suggest far less uniformity of investment strategies with respect to this factor timing activity among sample funds. An interesting pattern emerges when we look at the sign of the average timing coefficient estimates. In all cases, mutual funds on average seem to engage in positive Ph.D. Thesis: Jeffrey Junhua Lu

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market timing, negative size timing, positive value-growth timing, and negative momentum timing. All styles except momentum have timing coefficients whose signs are expected as above. This result suggests that some of the positive/negative timing coefficients in my sample could be spurious. In an effort to control for the JK source of spurious timing ability, I run the timing tests on a sample of synthetic funds that match the actual funds’ characteristics but have no timing ability by construction, as described earlier. If these synthetic funds exhibit timing ability at the same frequency and magnitude as the actual funds, then the estimated timing coefficients are likely to be spurious rather than evidence of ability. I first implement the same joint test on the synthetic funds as I do on the sample funds. The results are reported in Panel B, Table 4. It shows that, for the synthetic control sample, which is constructed under the null hypothesis of no timing ability, fewer funds exhibit significant style timing coefficients, with 12 percent of funds under the Carhart 4-factor TM model and with 3 percent of funds under the HM model. The results are very similar under the Fama-French 3-factor TM/HM timing model, except that the average timing coefficients on the market style turn negative and their magnitude is very small. Hence, to the extent that my synthetic funds control for spurious rejections of the null, significant differences regarding style timing coefficients suggest that a substantial percentage of the sample funds have engaged in timing activities. I then investigate the timing activities related to a specific style for my synthetic funds. Panel B of Table 5 shows the results of the individual style timing tests when applied to the synthetic funds. In all cases, the proportion of funds with positive timing coefficients is close to that of funds with negative timing coefficients, with respect to all styles. For example, under the TM style timing model, there are around 48 percent of synthetic funds exhibiting positive market style timing coefficients and around 52 percent of synthetic funds exhibiting negative market style timing coefficients. With

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respect to size style, there are around 65 percent of synthetic funds exhibiting positive style timing coefficients and around 35 percent of synthetic funds exhibiting negative style timing coefficients. With respect to book-to-market style, there are around 50 percent of synthetic funds exhibiting positive style timing coefficients and around 50 percent of synthetic funds exhibiting negative style timing coefficients. With respect to momentum style, there are around 51 percent of synthetic funds exhibiting positive style timing coefficients and around 49 percent of synthetic funds exhibiting negative style timing coefficients. Therefore, the synthetic funds are not more likely to engage in either kind of timing activities (positive or negative), which is consistent with the fact that these funds are constructed to have no timing ability. Moreover, the synthetic funds do not exhibit substantially more significant timing coefficients than expected under the null of no timing activity. Although, 7.7 percent of the synthetic funds generate significant positive size timing coefficients and 8.5 percent of these funds generate significant positive momentum timing coefficients, on average, the sample funds, as indicated in Panel A of Table 5, tend to reject the null more frequently than the synthetic funds, especially for negative size style timing, positive book-to-market style timing, and negative momentum style timing. The results are very similar under the HM model. The Fama-French 3-factor model results are similar to those using the Carhart 4-factor model with respect to market, size, and book-to-market factors. Note that a larger proportion of sample funds now show negative size timing coefficients, for example, 9.4 percent of funds under the TM model and 12.1 percent of funds under the HM model. Panel B of Table 6 summarises the cross-sectional averages and standard errors of intercepts and timing coefficients for the synthetic control funds. The signs of timing coefficients are completely different and the standard errors of timing coefficients are much lower (on average 40 percent lower) than those of sample funds presented in Panel A of Table 6. To the extent that the synthetic funds control for spurious timing,

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it indicates that sample funds tend to engage in some timing activities. I investigate the relation between the timing ability of my mutual funds and their synthetic counterparts more formally by computing the difference between their timing coefficients. Panel C of Table 5 shows the results. Under the Carhart 4-factor TM style timing model, 1.3 percent (0.4 percent) of funds have market timing coefficients that are significantly larger (smaller) than their synthetic counterparts; 1.9 percent (8.2 percent) of funds have size timing coefficients that are significantly larger (smaller) than their synthetic counterparts; 12.1 percent (0.5 percent) of the funds have book-to-market timing coefficients that are significantly larger (smaller) than their synthetic counterparts; and 1.2 percent (18.8 percent) of the funds have momentum timing coefficients that are significantly larger (smaller) than their synthetic counterparts. The results for the HM model are qualitatively similar. To the extent that the synthetic funds control for spurious rejections of the null, the significant differences above suggest that a substantial proportion of mutual funds have true positive or negative style timing ability. 7.4.2

Explanations

The above results suggest that active fund managers are more likely to engage in positive style timing activities with respect to book-to-market and to engage in negative style timing activities with respect to size and momentum. Style timing activities with respect to size can be referred to as size (big cap/small cap) timing strategies, style timing activities with respect to book-to-market can be labelled as value-growth timing strategies, and the style timing activities with respect to momentum can be classified as active momentum-contrarian timing strategies.37 It is interesting to consider why fund managers apparently seem to favour value-growth timing strategies rather than size timing strategies and momentum-contrarian timing strategies. 37

Carhart (1997) distinguishes the situation when mutual funds just happen by chance to hold relatively larger positions in last year’s winning stocks from the situation where mutual funds actively pursue momentum strategies. The prior can be seen as a perverse momentum strategy while the latter can be seen as an active momentum strategy.

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The first explanation is related to the institutional backgrounds of mutual funds and the market structures that affect fund managers’ investment behaviour. In other words, it might be simply due to the holding restrictions on mutual funds and the transaction costs associated with these strategies. Grinblatt et al. (1995) find that funds following momentum strategies realise better performance before management fees and transaction expenses. On the other hand, Carhart (1997) finds that mutual funds that follow a momentum strategy earn significantly lower abnormal returns after expenses. This suggests that transaction costs consume the gains derivable from following a momentum stock strategy. Similarly, since most funds are restricted from owning more than 10 percent of a firm’s voting shares, there are at least institutional constraints on fund demand for small cap stocks, which are necessary for implementing size timing strategies.38 Furthermore, given the documented existence of upwardly sloped supply curves for stocks, the ownership of a large proportion of a stock may imply a premium must be paid to take on or take off a position.39 This implies that large funds will be discouraged from buying small market capitalisation firms who perceive significant transaction costs in buying and selling shares relative to other, larger stocks. Even if the manager could correctly anticipate that small cap stocks will outperform (underperform) big cap stocks, he/she might not be able to increase (decrease) their position in small cap stocks, simply because of the restrictions placed on fund holdings and the higher transaction costs incurred by trading small cap stocks. On the other hand, value-growth timing strategies are perceived as less expensive in terms of transaction costs than a size timing strategy or a momentum timing strategy, and generally there are no restrictions placed on owning value stocks and growth stocks. Thus, fund managers are more likely to implement book-to-market timing strategies successfully than to implement size and momentum

38

For example, under section 8 of the Investment Company Act (ICA) of 1940, a mutual fund must make a registration statement where it defines its investment policy. This statement declares whether the fund is “diversified” or “nondiversified”, and if the fund declares itself “diversified” it cannot invest in more than 10% of any firm’s voting securities. Also, section 12(e) of the ICA of 1940 forbids the ownership of more than 10% of many financial service companies regardless of the fund’s registration statement. 39 See Bagwell (1992) on the existence of positively sloped supply curves for equities. Ph.D. Thesis: Jeffrey Junhua Lu

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timing strategies. Second, there may be a behavioural explanation, which is related to the trading behaviour and preferences of fund managers. An important factor that affects fund manager’s investment decisions is prudence. Del Guercio (1996) examines the issue of prudence as it relates to stock ownership by banks and mutual funds. She provides intuition and evidence to show that different types of institutions are affected by prudence restrictions to varying degrees. Falkenstein (1996) finds that mutual funds have a significant preference towards stocks with high visibility and large size. Small firms are generally followed by few analysts, and thus may be considered to be investments with low visibility and little information. Fund managers might consider those blue chips stocks with large capitalisation as prudent investments, which could be used to defend themselves in court if future disputes with fund investors arise. Therefore, fund managers might not be willing to increase (decrease) their position in small (large) cap stocks even if small cap stocks are going to outperform (underperform) large cap stocks. This behavioural pattern would lead to a negative size timing coefficient in a timing regression. To be a successful momentum timer, an investor must switch between momentum and contrarian strategies at the right time. In other words, the investor needs to maintain or increase (decrease) his/her position in momentum stocks when these stocks will continue to outperform (underperform); alternatively, the investor needs to maintain or increase (decrease) his/her position in contrarian stocks when these stocks will continue to outperform (underperform). Odean (1999) shows that investors strongly prefer to sell their winning investments too soon and to hold on to their losing investments too long even though the winning investments they sell subsequently outperform the losers they continue to hold. This behaviour is predicted by Shefrin and Stateman’s disposition theory (1985) and, in more general terms, by Kahneman and Tversky’s prospect theory (1979). Grinblatt and Keloharju (2000) find that professional fund managers seem to exhibit a similar disposition effect bias to naïve investors, although less pronounced statistically. If fund managers tend to sell winners too soon (which are momentum stocks) and hold Ph.D. Thesis: Jeffrey Junhua Lu

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on to losers too long (which are contrarian stocks), they will probably exhibit negative momentum timing coefficients in style timing models.40

7.5. Style Timing Trade-Offs: Style Timing v.s. Stock Selection As discussed in chapter 6, fund managers may implement market timing strategies at the expense of stock selection (or the other way round). I investigate whether fund managers appear to implement style timing strategies at the expense of stock selection. H50 : There is no consistent relationship between funds style timing behaviour and stock selection activities.

In Panel A of Table 5, there does appear to be an inverse relation between the market, size, and book-to-market timing coefficients and intercepts in the style timing regressions. In all cases, the average intercept for the funds with negative timing coefficients is much higher than the corresponding average for funds with positive timing coefficients. For example, under the Carhart 4-factor TM style timing model, the average intercept for those funds with positive market timing coefficients is -0.3 percent while the average intercept for those funds with negative market timing coefficients is 2.2 percent; the average intercept for those funds with positive size timing coefficients is -0.2 percent while the average intercept for those funds with negative size timing coefficients is 1.8 percent; the average intercept for those funds with positive book-to-market timing coefficients is 0.6 percent while the average intercept for those funds with negative book-to-market timing coefficients is 1.0 percent. The results for the HM model are qualitatively similar. For those funds with significant positive/negative timing coefficients, the differences

40

A negative momentum timing coefficient could indicate two possible situations: a fund manager goes with contrarian stocks when momentum stocks turn out to outperform contrarian stocks. Alternatively, a fund manager could go with momentum stocks when contrarian stocks turn out to outperform momentum stocks. Given the fact that during the sample period, momentum stocks on average outperform contrarian stocks, I would suggest that the first situation is more likely to apply to the sample period.

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of average intercept between these two groups of funds are even greater. For example, under the Carhart 4-factor TM style timing model, the average intercept for those funds with significant positive market timing coefficients is -2.6 percent while the average intercept for those funds with significant negative market timing coefficients is 7.0 percent; the average intercept for those funds with significant positive size timing coefficients is -3.3 percent while the average intercept for those funds with significant negative size timing coefficients is 3.1 percent; the average intercept for those funds with significant positive book-to-market timing coefficients is 0.1 percent while the average intercept for those funds with significant negative book-to-market timing coefficients is 1.5 percent. The results for the HM model are qualitatively similar. On the other hand, there seems to be a positive relation between the momentum timing coefficients and intercepts in the style timing regressions. The average intercept for the funds with negative momentum timing coefficients is much lower than the corresponding average for funds with positive momentum timing coefficients. For example, under the Carhart 4-factor TM style timing model, the average intercept for those funds with positive momentum timing coefficients is 1.3 percent while the average intercept for those funds with negative momentum timing coefficients is 0.6 percent. In particular, the average intercept for those funds with significant positive market timing coefficients is -0.1 percent while the average intercept for those funds with negative market timing coefficients is -0.3 percent.

Table 7 (Page 240)

To test this relation more formally, I regress intercepts on timing coefficients cross-sectionally for each timing style and for each timing model respectively. The results are reported in Table 7. For the market, size, and book-to-market styles, the slopes are negative and significant for both timing models, indicating that estimates of Ph.D. Thesis: Jeffrey Junhua Lu

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stock selection and style timing with respect to market, size, and book-to-market are significantly negatively related. For example, under the Carhart 4-factor TM Style Timing Model, the coefficients obtained from the linear regressions of intercept on the market, size, book-to-market style timing coefficients are -0.30, -0.27, -0.07 respectively, all significant at the 1 percent level. Similarly, under the Carhart 4-factor HM Style Timing Model, the equivalent market, size, book-to-market style coefficients are -0.40, -0.40, -0.15 respectively, again all significant at the 1 percent level. However, for the momentum style, the slope is positive and significant for both style timing models, indicating that estimates of stock selection and style timing ability with respect to momentum are significantly positively related. Under the Carhart 4-factor TM Style Timing Model, the coefficient obtained from the linear regression of intercept on momentum style timing is 0.04, significant at the 5 percent level. Similarly, under the Carhart 4-factor HM Style Timing Model, the coefficient obtained from the linear regression of intercept on momentum style is 0.07, significant at the 1 percent level. These results suggest that fund managers engage in some style timing activities, for example, market, size, and book-to-market styles, at the expense of stock selection. However, for the momentum style, fund managers tend to realise better (poorer) performance by implementing timing strategies successfully (unsuccessfully). This is consistent with Wermers’ (1999) findings that mutual fund performance persistence is, to a large extent, driven by the persistent use of active momentum investment strategies (and not simply by funds passively holding on to past winner stocks).

7.6. Style Timing Trade-Offs: Different Style Timing As demonstrated earlier, active fund managers are more likely to engage in positive style timing activities with respect to book-to-market and to engage in negative style timing activities with respect to size and momentum. An interesting question to ask is: Ph.D. Thesis: Jeffrey Junhua Lu

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do managers try to time one style (e.g. book-to-market) at the expense of other styles (e.g. size and momentum)? To answer this question, the relation between the timing coefficients is investigated. I conduct a correlation analysis between the factor timing coefficients. Table 8 summarises my results based on the Carhart 4-factor style timing model. H60 : There is no consistent relationship between different funds’ factor timing activities.

Table 8 (Page 241)

As shown in Table 8, on average there exist significant negative relations among the size, book-to-market, and momentum factor timings. In particular, book-to-market timing is strongly negatively correlated with size timing and momentum timing. With the Carhart 4-factor TM Style Timing Model the Pearson correlation coefficient between book-to-market style timing and size style timing is -0.46 with the corresponding Spearman ρ of -0.45. Similarly, the Pearson correlation coefficient between book-to-market style timing and momentum style timing is -0.47 with the corresponding Spearman ρ of -0.48. All these correlation coefficients are significant at the 1 percent level. In particular, momentum timing is negatively correlated with all other timing styles. With the Carhart 4-factor TM Style Timing Model, the Pearson correlation coefficient between momentum style timing and market style timing is -0.17 with the corresponding Spearman ρ of -0.22, and the Pearson correlation coefficient between momentum timing and size timing is -0.15 with the corresponding Spearman ρ of -0.18. All coefficients are significant at the 1 percent level. The magnitudes of these correlation coefficients are similar under the HM model. The relation between market timing and other style timings is, however, less Ph.D. Thesis: Jeffrey Junhua Lu

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conclusive, because under the Carhart 4-factor TM Style Timing Model, market style timing is positively related to book-to-market style timing (though not significant) while under the HM model the opposite relationship appears (significant at 1 percent level). Also, the positive relation between market style timing and size style timing is statistically insignificant. However, market style timing is indeed significantly negatively related to momentum style timing, with coefficient values range from -0.17 to -0.28. The above analysis is also carried out on the Fama-French 3-factor model and the results are very similar. There seem to be trade-offs in implementing different style timing strategies, at least among the size, book-to-market, and momentum style timings. If the manager tries to time the B/M style, he may bear the costs of negative timing with respect to the size and momentum styles and vice versa. There is no “free lunch” for implementing a style timing strategy with respect to a specific style, which is consistent with the argument presented in section 7.4.2.

7.7. Sensitivity Analysis In the last section, I conduct style timing tests on my sample funds. A long record of past returns is needed for the factor loadings to be estimated reliably. The baseline bootstrap results imposed a minimum of 60 observations to excluded funds that are very short-lived. Because of concerns about possible survivorship bias, discussed by Brown et al. (1992), it is important to investigate the effect of this restriction on my results. Thus, I next investigate the sensitivity of my results to the choice of minimum number of observations available for each fund. Specifically, I consider a subsample of funds surviving at least 36 months and repeat the major style timing tests conducted in Table 5 on these sample funds. Total sample size increases to 4,586 funds. The results are reported in Table 29. Table 29 lists the fractions of funds that have positive and negative timing coefficients and the number of funds that have significantly positive and negative timing Ph.D. Thesis: Jeffrey Junhua Lu

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coefficients, based on the Carhart 4-factor timing model.

Table 29 (Page 272)

Panel A of Table 29 shows the results for mutual fund sample having at least 36 observations. For the TM model, the proportion of funds with positive timing coefficients is close to that of funds with negative timing coefficients, with respect to market and size styles. For example, with respect to market style, around 57 percent of sample funds possess positive timing coefficients and around 43 percent of sample funds possess negative timing coefficients. Similarly, with respect to size style, about 52 percent of sample funds possess positive timing coefficients and about 48 percent of sample funds possess negative timing coefficients. These funds do not tend to consistently engage in either type of timing activities (positive or negative). However, there are more funds exhibiting positive book-to-market timing coefficients and negative momentum timing coefficients. In particular, with respect to the book-to-market style, around 77 percent of sample funds have positive timing coefficients and around 23 percent of sample funds possess negative timing coefficients. Similarly, with respect to momentum, about 20 percent of sample funds have positive timing coefficients and about 80 percent of sample funds possess negative timing coefficients. Panel A of Table 29 also reports the percentages of funds that have significantly positive and negative timing coefficients. Few funds show either significant positive (2.3 percent) or significant negative (0.9 percent) market timing coefficients, which is consistent with the results of traditional market timing tests. Few funds show either significant positive (4.8 percent) or significant negative (5.4 percent) size timing coefficients. However, there are more funds exhibiting significant positive book-to-market timing coefficients and negative momentum timing coefficients. For those cases with significant book-to-market timing coefficients, around 25 percent of Ph.D. Thesis: Jeffrey Junhua Lu

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funds generate positive coefficients and only 1 percent of funds generate negative coefficients. The picture is different for those cases with significant momentum timing coefficients. Only 0.6 percent of funds generate positive coefficients and around 31 percent of funds generate negative coefficients. The HM model results are similar, except that their magnitude is smaller. Panel B of Table 29 reports the results for the corresponding synthetic funds, which are quantitatively similar to those presented in Panel B of Table 5. I also investigate the relation between the timing ability of my mutual funds and their synthetic counterparts more formally by computing the difference between their timing coefficients. Panel C of Table 29 shows the results. Under the Carhart 4-factor TM style timing model, 2.0 percent (1.7 percent) of funds have market timing coefficients that are significantly larger (smaller) than their synthetic counterparts; 1.7 percent (5.8 percent) of funds have size timing coefficients that are significantly larger (smaller) than their synthetic counterparts; 10.9 percent (2.1 percent) of the funds have book-to-market timing coefficients that are significantly larger (smaller) than their synthetic counterparts; and 1.7 percent (20.0 percent) of the funds have momentum timing coefficients that are significantly larger (smaller) than their synthetic counterparts. Again, the results are quantitatively similar to those presented in Panel C of Table 5 Therefore, these results show that my inferences about the style timing activities of my sample funds are largely unaffected when funds with only 36 months of return observations are included in my tests, as compared to my baseline results shown in Table 5 when I restrict my tests to funds having at least 60 months of return observations.

7.8. Summary This chapter investigates the style timing ability of fund managers. I conduct style timing tests on my sample funds by implementing my own style timing models which Ph.D. Thesis: Jeffrey Junhua Lu

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incorporate systematic risk factors unique to equity markets into traditional market timing models. To control for potential Jagannathan and Korajczyk (1986) spurious timing ability, I also conduct the same style timing tests on a synthetic matched sample of funds, which are constructed to mimic the holdings of the actual funds but that have no timing ability. I find that over the ten-year period (June 1992 to July 2002) of this study, some active mutual funds engage in style timing activities. Most obviously, under the Carhart 4-factor TM style timing model, there are more funds exhibiting positive book-to-market style timing coefficients (around 30 percent) and negative momentum timing coefficients (around 38 percent). Moreover, 12.3 percent of the funds have book-to-market style timing coefficients that are significantly larger than their synthetic counterparts; and 19.0 percent of the funds have momentum timing coefficients that are significantly smaller than their synthetic counterparts. Active fund managers are more likely to engage in positive style timing activities with respect to book-to-market (value/growth) and to engage in negative style timing activities with respect to size (big cap/small cap) and momentum (winner/loser). First, this may be partly due to the institutional backgrounds and transaction costs associated with these timing strategies. Most funds are restricted from taking substantial positions in small-cap stocks and there are relatively higher transaction costs associated with size (big cap/small cap) and momentum (winner/loser) timing strategies when compared to book-to-market (value/growth) timing strategies. Second, there may be a behavioural explanation which is related to the trading behaviour and preferences of fund managers. Fund managers prefer big-cap stocks to small-cap stocks as safer investments. Also, they tend to sell winners too soon and to hold on to losers too long. I also investigate the relationships between fund managers’ stock selection ability and their style timing ability. Similar to the results in my market timing tests, I find fund managers implement style timing strategies at the expense of poor stock selection performance. Moreover, implementing a timing strategy with respect to a specific style (such as value/growth) may bear the costs of negative timing with respect to Ph.D. Thesis: Jeffrey Junhua Lu

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other styles (such as size and momentum). In a word, timing strategies are not a free lunch. My inferences about the style timing activities of my sample funds are largely unaffected when funds with only 36 months of return observations are included in my tests, as compared to my baseline results when I restrict my tests to funds having at least 60 months of return observations. In the next chapter I investigate the style timing ability and activity of active fund managers in the context of fund investment objectives and fund performance record. Specifically, I explore the effect of stated risk objectives on the style timing behaviour of active mutual funds by dividing my sample funds into sub-groups based on their self-claimed investment objectives. I also investigate how prior performance record influences fund managers’ style timing behaviour.

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CHAPTER 8 INVESTMENT OBJECTIVES, PERFORMANCE RECORD AND STYLE TIMING 8.1. Introduction In chapter 7 I presented evidence that over the ten-year period (June 1992 to July 2002) of this study, some active mutual funds engage in style timing activities. Active fund managers are more likely to engage in positive style timing activities with respect to book-to-market (value/growth) and to engage in negative style timing activities with respect to size (big cap/small cap) and momentum (winner/loser). I also provide evidence that implementing a timing strategy with respect to a specific style (such as value/growth) may bear the costs of negative timing with respect to other styles (such as size and momentum). In this chapter I investigate the style timing abilities of active fund managers within the context of their fund investment objectives and performance record. Some groups of funds may implement a specific style timing strategy better than other groups of funds, due to their superior information relating to the style they adopt. Also, some groups of funds may favour a specific style timing strategy, because of their familiarity with a specific segment of the market in which the style dominates. Grinblatt and Titman (1989) and Volkman and Wohar (1995) generally find a positive correlation between risk-adjusted performance and stated fund goals. Volkman (1999) investigates the effect of stated risk objectives on the market timing performance of funds and finds that a fund’s market timing activities are affected by its stated investment objectives. In a typical mutual fund, two factors influence the manager’s expected payoff: compensation structure and retention policy. A manager’s compensation usually

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depends on the fund’s performance relative to a certain benchmark. Moreover, fund performance also plays a crucial role in the decision to dismiss, retain, or promote the fund’s manager. Huddart (1999) examines a two-period model with two risk-averse managers of different abilities. In this model, investors make inferences about managers’ abilities on the basis of their relative performance in the first period. In the second period, investors reallocate their wealth to the fund with the highest first-period return, which is most likely to be informed in equilibrium. However, this allocation rule, which maximises investor perceptions of managerial ability, does not provide proper risk taking incentives to fund managers. When managers receive a fraction-of-funds fee, they may choose overly risky strategies to maximise the chance of becoming the top performing fund in the first period. The uninformed manager does it to appear informed, while the informed manager does it to increase the cost of mimicking him. In this chapter I first conduct style timing tests on the sub-groups of my sample funds which are segregated based on their self-claimed investment objectives. The tested null hypotheses are presented in Chapter 4 as H7a, H7b, and H7c. Second, I investigate the effect of fund performance record on fund managers’ timing behaviour by grouping the sample funds by their Morningstar category rating. The tested null hypotheses are presented in Chapter 4 as H8 and H9. Recall that the expected change in a manager’s factor exposure across time depends not only on his aggressiveness, but also the precision of his forecast. The precision of the fund manager’s timing forecast, thus the timing ability of the fund manager, is generally reflected by the signs of the timing coefficients derived from the style timing regression. Thus a significantly positive style timing coefficient represents superior style timing ability. The aggressiveness with which the fund manager reacts to his forecast, as suggested by Jiang (2001), could be reflected by the magnitude (or the absolute value) of the timing coefficients derived from the TM style timing regression. Based on this approximation, I also explore how fund investment objectives and performance record affect the aggressiveness of fund managers’ timing activities. Ph.D. Thesis: Jeffrey Junhua Lu

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The chapter is organised as follows: section 2 presents the results of style timing tests within each sub-group of sample funds classified according to their self-claimed investment objectives, section 3 presents the results of style timing tests on sub-groups of sample funds classified based on their prior performance record, and section 4 summarises the results.

8.2. Investment Objectives and Style Timing The style timing analysis in chapter 7 is based on all the mutual funds in my sample pooled together. Investors have the ability to select funds with significantly different management styles and stated risk objectives. Volkman (1999) investigates the effect of stated risk objectives on the market timing performance of funds and finds that fund market timing activities are affected by a fund’s stated investment objectives. From the inception of the industry, mutual funds have attempted to inform potential investors about their intended investment strategy by committing to a specific objective classification. These investment objectives, which currently number 33 according to the Investment Company Institute, are listed in the fund’s prospectus and include such categories as aggressive growth, growth, growth and income, balanced, global, and income. To investigate the effect of stated risk objectives on the timing behaviour of my sample funds, I segregate these funds into five Morningstar “investment objectives” (style) categories or sub-groups: aggressive growth (131), growth (1,326), growth and income (627), equity income (180), and small companies (527). If a fund manager’s style timing decision is not affected by the fund’s stated risk objective, then little variance in style timing activities should be observed between the above five sub-groups of funds. The null hypotheses are developed in Chapter 4 and are reintroduced here as follows: H70a : No sub-groups of mutual funds exhibit a significant timing ability with respect to the size factor. Ph.D. Thesis: Jeffrey Junhua Lu

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H70b : No sub-groups of mutual funds exhibit a significant timing ability with respect to the book-to-market factor. H70c : No sub-groups of mutual funds exhibit a significant timing ability with respect to the momentum factor.

8.2.1. Factor Loadings on Subgroup of Funds

Before the investigation of the effects of fund investment objectives on fund timing activities, I first examine the factor loadings on each investment objective subgroup of funds. In this analysis, I focus on the Carhart (1997) four-factor model, which augments the Fama-French three-factor model by a momentum factor. The regression model is as follows:

R pt = α p + β1 RMRFt + β 2 SMBt + β3 HMLt + β 4 MOM t + ε pt

(8)

Where RMRF is the market factor, SMB is the size factor, HML is the book-to-market factor, and MOM is the momentum factor. I employ the portfolio regression approach. I compute the set of equally weighted monthly return of the fund portfolio which comprises all funds with the same investment objectives and then use this monthly return as the dependent variable in the above regression.

Table 9 (Page 243)

Table 9 summarises the fund factor loadings of the five fund portfolios, which are constructed based on the funds’ investment objectives, for the portfolio regression approach. For comparison purposes, I also include the factor loadings of the Russell 3000 Index as a proxy for the general market index. On average, the sample mutual funds have an alpha of 10 basis points per month (1.2

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percent per year), while during the same sample period the Russell 3000 Index has an alpha of 8 basis points per month (0.96 percent per year). So after controlling for risk, I find that the sample funds as a whole have outperformed the market, although the differences between them and the Russell 3000 are relatively small and insignificant. Growth and income funds achieve the best performance with a significant alpha of 16 basis points per month (1.92 percent per year), while small company funds achieve the worst performance with an alpha of minus 1 basis point per month (-0.12 percent per year), though not significant. Recall that in Panel B, Table 1, small company funds deliver the best performance with a raw return of 10.91 percent per year, while the growth and income funds achieve relatively poor performance with a raw return of 9.66 percent per year, which is significant different at 5 percent level. However, after controlling for risk, a different picture appears. Small company funds seem to generate better performance by taking more risk. The other three groups, aggressive growth, growth, and equity income, perform in much the same way, which is around 10 basis points per month (1.2 percent per year) and not significant. The signs and magnitudes of the factor loadings for each sub-group of funds illustrate their own investment styles over the sample period. Aggressive growth funds tend to have relatively large market exposures (around 1.09 compared to Russell 3000’s 0.99), and favour small (0.46 loading on SMB) and growth stocks (-0.30 loading on HML). It is not surprising that these funds invest heavily in smaller stocks and growth stocks in the pursuit of above average growth. The insignificant positive average estimate of momentum loading and its small magnitude (near zero) indicates that these funds are indifferent to momentum or contrarian strategies. Growth funds appear to closely index the market (around 1.00 loading on RMRF), weakly favour small stocks (0.12 loading on SMB), although significant at the 1 percent level, invest equally among value stocks and growth stocks to balance between long-term and intermediate-term growth targets (near zero loading on HML), and are also indifferent to momentum or contrarian strategies (near zero loading on MOM). Growth and income funds are less exposed to the market (around 0.91 loading Ph.D. Thesis: Jeffrey Junhua Lu

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on RMRF), have preferences towards large (-0.09 loading on SMB) and value stocks (0.17 loading on HML) (all coefficients significant at the 1 percent level), and are also indifferent to momentum or contrarian strategies (near zero on momentum). Equity income funds exhibit the lowest exposures to the market (around 0.82 loading on RMRF), indicating that these funds tend to hold more cash than other funds. They also prefer large (-0.08 loading on SMB) stocks, invest heavily in value stocks (0.32 loading on HML), and follow momentum strategies (0.07 loading on MOM, significant at 1 percent level). Small company funds also index the market (1.00 loading on RMRF), not surprisingly invest most heavily in small stocks (0.71 loading on SMB, significant at 1 percent level) and also appear to weakly favour value stocks (0.08 loading on HML, although the coefficient is only significant at the 10 percent level), in an effort to identify under-valued stocks in the less efficient small-cap market. These funds also follow momentum strategies actively (0.13 loading on MOM, significant at the 1 percent level). In summary, I find some evidence that growth and income funds outperform the market and other groups of funds. In particular, growth and income funds achieve superior performance with moderate risk exposures to general market risk factors. On the contrary, although small company funds deliver the best performance in terms of raw returns, they produce negative abnormal returns after controlling for risk. These findings are potentially consistent with the view that (1) growth and income fund managers have superior investment skills; and (2) the interests of growth and income fund managers are more closely aligned with the interests of their shareholders, so they invest more conservatively in the markets. Different sub-groups of funds tend to favour stocks with different characteristics, which indicates that fund managers do appear to follow specific investment styles when making their investment decisions. I will next examine the style timing activities of fund managers within each fund investment objective.

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8.2.2. Style Timing Preferences by Fund Subgroup

To investigate the effect of stated risk objectives on the timing behaviour of my sample funds, the null hypotheses H7a, H7b, and H7c are tested and the results are summarised in Table 10. Table 10 lists the fraction of funds that have positive and negative timing coefficients and the number of funds that have significantly positive and negative timing coefficients for each sub-group of funds grouped by investment objective. The bootstrap analysis of style timing coefficients is based on my Carhart 4-factor style timing model.

Table 10 (Page 244)

Table 10 provides the patterns of timing behaviour within each sub-group of funds with different stated investment objectives. I first examine the results under the Carhart 4-factor TM style timing model. Panel A reports the results for aggressive growth funds: more funds demonstrate positive timing coefficients with respect to book-to-market style (86 percent of funds) and negative timing coefficients with respect to size (76 percent of funds) and momentum style (71 percent of funds). Panel B reports the results for equity income funds: more funds demonstrate positive timing coefficients with respect to size style (77 percent of funds) and negative timing coefficients with respect to book-to-market (52 percent of funds) and momentum style (90 percent of funds). Panel C reports the results for growth funds: more funds demonstrate positive timing coefficients with respect to book-to-market style (82 percent of funds) and negative timing coefficients with respect to size (55 percent of funds) and momentum style (78 percent of funds). Panel D reports the results for growth and income funds: more funds demonstrate positive timing coefficients with respect to size (67 percent of funds) and book-to-market style (66 percent of funds)

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and negative timing coefficients with respect to momentum style (81 percent of funds). Panel E reports the results for small company funds: more funds demonstrate positive timing coefficients with respect to book-to-market style (85 percent of funds) and negative timing coefficients with respect to size (51 percent of funds) and momentum style (89 percent of funds). For growth-oriented funds, i.e., aggressive growth, growth, and small company funds, there are more funds exhibiting negative timing coefficients with respect to size, especially in the case of aggressive growth funds, where nearly 76 percent of funds in this group demonstrate negative size timing coefficients, as shown in panel A. For the income-oriented funds, i.e., equity income, and growth and income funds, on the other hand, there are more funds exhibiting positive timing coefficients with respect to size, especially in the case of equity income funds, where nearly 77 percent of funds in this group demonstrate negative size timing coefficients, as shown in panel B. On the other hand, compared to other funds, there are more growth-oriented funds exhibiting positive timing coefficients with respect to book-to-market. Around 80 percent of growth-oriented funds show positive timing coefficients with respect to book-to-market, while less than half of equity income funds do so. All groups have substantial percentages of funds showing negative momentum timing coefficients. However, among all groups, fewer aggressive growth funds do so (around 70 percent of funds, compared to more than 80 percent of funds on average in the other groups). Different sub-groups of funds seem to possess different preferences in timing different market styles. Growth-oriented funds seem to time the book-to-market style at the expense of negative timing on the size and momentum styles, while equity income funds try to time the size style at the expense of negative timing on the book-to-market and momentum styles. Growth and income funds appear to time the size and book-to-market styles at the expense of negative timing on the momentum style. For those funds with significant timing coefficients, aggressive growth funds, as Ph.D. Thesis: Jeffrey Junhua Lu

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shown in panel A, are more likely to time the book-to-market factor successfully (more than 53 percent of funds, the highest among all groups) and less likely to time the momentum factor unsuccessfully (less than 21 percent of funds, the lowest among all groups). However, these funds are slightly more likely to time the size factor unsuccessfully (more than 14 percent of funds, the highest among all groups). Equity income funds, as shown in panel B, tend to be good at timing the size factor (more than 11 percent of funds, the highest among all groups) but be extremely poor at timing the momentum factor (55 percent of funds, the highest among all groups). Growth funds, as shown in panel C, are more likely to be good book-to-market timers (38 percent of funds) but relatively poor momentum timers (32 percent of funds). These funds are neither good timers nor bad timers on size. Growth and income funds, as shown in panel D, seems to exhibit the worst timing abilities, with a relatively low percentage of funds demonstrating timing ability on size (5.7 percent of funds) and book-to-market (8.9 percent of funds), and relatively high percentage of funds showing poor timing ability on momentum (37 percent of funds). Small company funds behave similarly to growth funds. As can be seen from the four columns to the right of Table 10, results are quantitatively similar under the Carhart 4-factor HM style timing model. 8.2.3. Style Timing Aggressiveness on Subgroup of Funds

Note however, the magnitude of the average timing coefficient is smaller under the HM model than under the TM model (less positive or less negative). A potential explanation relies on the fact that the TM and HM timing coefficients essentially measure the expected convexity in the funds’ relation to the market return, which reflects both the probability (related to information quality) and the magnitude (related to risk aversion). A fund manager’s market timing performance depends on both the quality of his private information (ability) and the aggressiveness with which the manager reacts to his information (response). Jiang (2001) suggests that the HM timing measure caters more to the information quality side of market timing while the

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TM measure basically reflects the intensity of a manager’s reaction. Hence more aggressive funds can show up as better (or worse if the information is incorrect) market timers with higher (more negative) TM measures.

Table 11 (Page 247)

Table 11 summarises the average TM and HM estimates of style timing ability within the mutual fund sub-groups. All groups of funds show negative signs on their momentum style timing coefficients. Income-oriented funds (growth and income and equity income funds), together with small company funds, show larger magnitudes of negative timing coefficients, when compared to growth-oriented funds. For example, the average TM (HM) style timing coefficient for aggressive growth funds is -0.33 (-0.08), while the average TM style timing coefficient for equity income funds is -0.61 (-0.12). This indicates that these income-oriented funds are more likely to be subject to the disposition effect, and selling winners too soon and holding on to losers too long. Aggressive growth funds, growth funds, and small company funds on average exhibit positive book-to-market style timing coefficients. The higher HM timing coefficients indicate that these funds tend to possess better timing ability or more accurate private information regarding the book-to-market style. Meanwhile, these funds also respond to their private information in a much more aggressive manner, as shown by their higher TM timing coefficients. For example, the average TM (HM) style timing coefficient for aggressive growth funds is 1.72 (0.41), the average TM (HM) style timing coefficient for growth funds is 0.91 (0.23), and the average TM (HM) style timing coefficient for small company funds is 1.04 (0.25) On the other hand, income-oriented funds tend to possess poor timing ability or less accurate private information regarding this factor, as shown by their close to zero HM timing coefficients. These funds also respond to their private information in a much less Ph.D. Thesis: Jeffrey Junhua Lu

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aggressive manner, as shown by their lower TM timing coefficients. For example, the average TM (HM) style timing coefficient for equity income funds is -0.05 (-0.02), and the average TM (HM) style timing coefficient for growth and income funds is 0.11 (0.01). No funds seem to possess accurate private information regarding the size style, since the HM timing coefficients are either negative or close to zero. Interestingly, aggressive growth funds respond to their poor information much more aggressively than other funds, as indicated by their larger magnitudes of negative TM coefficients (-1.20). Moreover, except for aggressive growth funds, all funds show positive signs on their market timing coefficients, though few of them are statistically significant. Growth-oriented funds, together with small company funds, show relatively large cross-sectional standard deviation for their timing coefficients on average, suggesting far less uniformity of investment strategies with respect to these fund styles timing activities. For example, for aggressive growth funds, the standard deviations of the HM style timing coefficients with respect to size, book-to-market, and momentum are 0.34, 0.38, and 0.23, respectively. For small company funds, the standard deviation of the HM style timing coefficients with respect to size, book-to-market, and momentum are 0.31, 0.33, and 0.23, respectively. However, for growth and income funds, the standard deviations of the HM style timing coefficients with respect to size, book-to-market, and momentum are only 0.15, 0.15, and 0.11, respectively. 8.2.4. Summary

In summary, analysis of these different fund categories (aggressive growth, growth, income, equity income and small cap) reveals that growth-oriented funds tend to possess better timing abilities and also implement style timing strategies more aggressively than other funds. Specifically, aggressive growth funds are excellent book-to-market (value/growth) timers without bearing the costs of poor momentum (winner/loser) timing, while growth funds time book-to-market (value/growth) style correctly, but at the expense of negative timing on size (big cap/small cap) and Ph.D. Thesis: Jeffrey Junhua Lu

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momentum (winner/loser). Equity income funds tend to be good at timing size (big cap/small cap) but be poor at timing momentum (winner/loser). Income funds are bad factor timers, especially with respect to size (big cap/small cap) and momentum (winner/loser) styles. Growth-oriented funds respond to their private information on future factor performance more aggressively than income-oriented funds. There is far less uniformity of investment strategies with respect to style timing activities among growth-oriented funds.

8.3. Performance Record and Style Timing 8.3.1. Introduction

One strand of research analyses potential agency problems between a mutual fund’s shareholders and its portfolio manager. This literature highlights how the structure of managerial compensation can lead a portfolio manager to shift a fund’s risk based on its prior performance. This adverse incentive arises from the nature of mutual fund inflows. A mutual fund’s investment advisor, the entity responsible for portfolio management, typically is paid a fixed percentage of the fund’s assets. However, the level of these assets depends on the fund’s past returns and the inflow of new investment money. Importantly, empirical evidence indicates that a fund’s past performance, relative to that of other funds or of a benchmark index, has a positive effect on net new inflows.41 In other words, mutual fund investors “chase returns” by channelling new investment into better performing funds. Their behaviour creates a situation that has been described as a “tournament” in which portfolio managers compete for greater fund inflows and, ultimately, greater compensation. While inflows increase with a fund’s relative performance, the relation appears nonlinear. Numerous studies document that mutual funds with the best recent performance experience the lion’s share of new inflows. But while top performers do exceptionally well, the worst performing funds are not penalised with sharply higher 41

See, for example, Ippolito (1992), Gruber (1996) and Sirri and Tufano (1998) for evidence linking fund flows to past performance. Ph.D. Thesis: Jeffrey Junhua Lu

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outflows. Hence, a fund’s net inflows appear to be an increasing, convex function of its recent return performance. Since the compensation of portfolio managers is likely to depend on their success in generating greater fund inflows, this convex performance - fund flow relation produces a convex performance - compensation structure. Various authors have considered the implications of this convexity for managers’ portfolio decisions. Chevalier and Ellison (1997) estimate the shape of the performance - fund flow relation from which they then infer different funds’ risk-taking incentives. They suggest that the incentives to alter the riskiness of a portfolio are derived from the fact that flows are a nonlinear function of calendar year returns. They find that: (1) Funds with bad performance have an incentive to gamble (take on more risk) to try to catch up. (2) Funds with relatively good performance have an incentive to “lock in” their gains by indexing the market. (3) Funds with extremely good performance may have a strong incentive to gamble. Other research, such as Huberman and Kandel (1993), Heinkel and Stoughton (1994), and Huddart (1999), considers environments where fund managers possess different abilities that are unbeknownst to investors. In these game-theoretic models, there is typically an initial period when investors learn of managers’ abilities based on their relative performances, followed by a second period during which investors may switch their investments to those managers perceived to have the highest abilities. Hence, these “investor learning” models can be viewed as explaining the link between fund flows and prior performance. As such, most existing studies examine the link between a fund manager’s compensation contract and his choice of the fund’s portfolio, and are based on the assumption that fund managers are rational investors and they make investment decisions based on the maximisation of their interests in the fund portfolio. Recent evidence (e.g. Odean, 1998a) describes investor behaviour that is at odds with traditional economic theory. These alternative behaviours, such as those consistent Ph.D. Thesis: Jeffrey Junhua Lu

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with the disposition effect or overconfidence, form the basis for recent “behavioural” explanations for asset returns (e.g. Daniel et al., 1998a and 1998b, Odean 1998b, and Shumway, 1998). Notably, the evidence of alternative investor behaviour is based largely on retail customer accounts - those of amateur traders. For institutional investors, based on their need for continuing success, the natural assumption should be that market professionals are disciplined traders who are less prone than retail investors to exhibit alternative and costly behavioural tendencies. If so, then behavioural problems may be an annoying but essentially harmless anomaly confined to some retail investors and experimental subjects. On the other hand, evidence that professional traders also exhibit a tendency towards behavioural biases would provide increased support for research on the systemic effects of behavioural financial models, as, for example, in the model of Barberis et al. (1999). Johnson and Thaler (1990) suggest that people are less risk averse following earlier gains and more risk averse after losses, phenomena they term the “house-money effect” and the “snake-bite effect”. On the one hand, gamblers treat their winnings as house money, not their own money, and thus they tend to take very large risks with their winnings. Similarly, so it can be argued, fund managers face a tendency to treat investment gains as house money. Since the gains are viewed as a free opportunity, the fund manager is more willing to gamble with the gains. In general, the house-money concept predicts that fund managers will systematically increase risk (implement riskier investment strategies) after earning profits. On the other hand, the snake-bite effect refers to the reluctance to take risks after experiencing losses. Once someone has been bitten by a snake, they will avoid entering locations inhabited by snakes. The snake-bite effect predicts that fund managers will avoid riskier stocks once they have experienced a loss in the stock market. There are other established behavioural biases that may also affect fund managers’ investment decisions, such as the “trying-to-break-even” effect and the “endowment” effect. The trying-to-break-even effect moves counter to the snake-bite effect.

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Gamblers have a stronger bias towards “breaking even” after prior losses. The “trying-to-break-even” effect refers to the desire by investors to recoup large losses in one quick long-short (very high-risk) investment. Hence, it predicts that fund managers will systematically pursue high-risk investments after losing money. The “endowment” effect refers to the tendency by people to place a higher value on what they own than on identical items that they do not own. The endowment effect also can be viewed as a “do nothing” effect. This behavioural bias causes investors to pay little attention to risk and return characteristics, but instead make decisions that lead them to stay with their original investments. The endowment effect predicts fund managers will keep their existing portfolio unchanged. Fund managers are a substantial group of investors in the market. As such, their investment activities, especially their timing behaviour, are well worth investigating to see whether these investment professionals suffer from the same behavioural biases as retail investors and if so to what extent. As evidence of the importance of the Morningstar five-star rating service, I consider a study reported in both the Boston Globe and The Wall Street Journal, which found that 97 percent of the money flowing into no-load equity funds between January and August 1995 was invested into funds that were rated as five- or four-star funds by Morningstar, while funds with less than three stars suffered a net outflow of funds during the same period. Moreover, the heavy use of Morningstar ratings in mutual fund advertising suggests that mutual fund companies believe that investors care about Morningstar ratings. Indeed, in some cases, the only mention of return performance in the mutual fund advertisement is the Morningstar rating. Therefore, the Morningstar five-star rating system is used in this study as a proxy for a fund’s prior performance record. The key differences between my thesis and previous work are the assumptions made about fund managers’ investment decisions. Previous studies assume that the fund manager is rational and his/her choice of the fund’s portfolio is based on the maximisation of his/her compensation, which is linked to the fund’s prior performance record. My study assumes that the fund manager might not be rational. Ph.D. Thesis: Jeffrey Junhua Lu

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His/her choice of the fund’s portfolio is not only based on the maximisation of his/her compensation, but is also subjected to some potential behavioural biases, which have been documented in studies of retail investors. Therefore, the current thesis clarifies issues in the mutual fund tournament literature by providing new theoretical and empirical insights into risk-taking by mutual funds and potential behavioural biases exhibited by institutional investors. 8.3.2. Empirical Results

To investigate how fund prior performance record influences fund managers’ timing behaviour, for each sample fund I use the fund Morningstar rating at the beginning of its entire performance history during the sample period. Morningstar awards mutual funds one to five stars according to their past investment performance. The highest ranking is five stars, and the lowest ranking is one. I investigate fund style timing activities over the long run (during the whole sample period of my study) instead of the short run. The Morningstar five star rating is also based on a medium- to long-term performance evaluation period, and thus the star rating should affect fund managers’ investment decisions not only in the short run, but also in the medium to long run. Therefore, I examine whether Morningstar rating is associated with subsequent medium to long run fund style timing activities during the sample period. Since Morningstar does not rate those funds that have been in existence for less than three years, this reduces my sample to a total of 2,286 funds. If prior fund performance record does not affect fund managers’ subsequent portfolio choices, there should be no differences in style timing activities between fund managers with different performance records. The null hypotheses are developed in Chapter 4 as H8 and H9 and will be tested here. H80 : Funds with a moderate performance record are not more likely to implement style timing strategies compared to funds with a good performance record. H90 : Sub-group of mutual funds with a poor performance record are not more likely to implement timing strategies compared to funds with a good performance Ph.D. Thesis: Jeffrey Junhua Lu

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record.

If the above null hypothesis does not hold and prior fund performance does affect fund style timing activities significantly, fund managers will be implementing style timing strategies differently depending on their specific performance records. Indeed, the traditional fund manager rationality assumption predicts that top-performing funds will have incentives to “lock in” their winning positions and reduce their fund portfolio risk exposures, and thus implement style timing strategies in a less aggressive manner. In the case of those moderate-performing funds, these are expected to seek to “catch up with” their better-performing counterparts and increase the fund portfolio risk exposures, leading to style timing strategies being implemented in a more aggressive manner. In the extreme case, when a fund is well behind its counterparts, the fund manager may have fewer or even no incentives to increase his fund’s risk exposure, since it seems impossible for him to catch up with his counterparts, and increased portfolio risk may also affect future performance negatively. Hence, such funds are expected to implement style timing strategies in a less aggressive manner. However, if fund managers are not rational and are also influenced by similar behavioural biases as retail investors, their style timing activities will be somewhat different from those predicted above under the rationality assumption. Indeed, under the behavioural bias assumption, top-performing funds might be influenced by the “house-money” effect, that is, tending to treat investment gains as house money and, as

a

result,

implementing

style

timing

strategies

more

aggressively.

Bottom-performing funds might exhibit the “trying-to-break-even” effect, that is, being willing to take very high risks to try to recoup the loss immediately, as such, implementing

style

timing

strategies

more

aggressively,

similar

to

their

top-performing counterparts. Funds in the middle might be affected by the “endowment” effect, that is, they will keep their existing portfolio unchanged and “lock in” their gains, thus implementing style timing strategies in a less aggressive manner. Ph.D. Thesis: Jeffrey Junhua Lu

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8.3.2.1. Factor Loadings on Funds Subgroups

Before investigating the effects of fund investment objectives on fund timing activities, I first examine the factor loadings on subgroups of funds within each prior performance ranking category. I focus on the Carhart (1997) four-factor model. The regression model is as follows:

R pt = α p + β1 RMRFt + β 2 SMBt + β3 HMLt + β 4 PR1YRt + ε pt

(8)

Where RMRF is the market factor, SMB is the size factor, HML is the book-to-market factor, and PR1YR is the momentum factor. I employ two different regression approaches: the portfolio regression approach and the fund regression approach. In the portfolio regression approach, I compute the equally weighted monthly return of the fund portfolio comprising all funds classified as having the same Morningstar rating and then use this return as the dependent variable in the above regression. In the fund regression approach, I use the individual monthly fund returns in the above regression and then report the average coefficient estimates.

Table 12 (Page 248)

Table 12 summarises the factor loadings for five fund portfolios, which are constructed using the Morningstar five-star rating categories for the portfolio regression approach. For comparison purposes, I also include the factor loadings of the Russell 3000 Index as a proxy for the general market index. The results show that high-rated funds continue to perform well and low-rated funds continue to perform poorly during the sample period. Five-star (highest-rated) funds on average achieve significant positive abnormal returns of 32 basis points per month (3.84 percent per year, significant at the 1 percent level), and four-star funds achieve significant positive abnormal returns of 18 basis points per month (2.16 percent per year, significant at the 1 percent level), while during the sample period, the Russell 3000 achieves significant Ph.D. Thesis: Jeffrey Junhua Lu

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positive abnormal returns of 8 basis points per month (0.96 percent per year, significant at the 1 percent level). Therefore, both groups of funds, have on average, outperformed the market index during the sample period. Three-star funds trail the market by achieving abnormal returns of 11 basis points per month (1.32 percent per year), though not significant at even the five percent level. Two-star and one-star funds, in fact, appear to achieve negative abnormal returns of 4 basis points per month (-0.48 percent per year) and 12 basis points per month (-1.44 percent per year), respectively. However, neither monthly alpha differs significantly to a conventional level. Top-performing funds (five-star funds) outperform bottom-performing funds (one-star funds) by a spread of 44 basis points per month (5.28 percent per year), which is significant at the 1 percent level. The spread of alpha between top-performing funds (five-star funds) and moderate-performing funds (three-star funds) is 22 basis points per month (2.64 percent per year), which is significant at the 5 percent level. The spread of alpha between moderate-performing funds (three-star funds) and bottom-performing funds (one-star funds) is also 22 basis points per month (2.64 percent per year), but not significant. The spread of alpha between top-performing funds (five-star funds) and next-to-top-performing funds (four-star funds) is also not significant. Therefore, most of the differences in abnormal performance between the above two ranking groups of funds are attributable to the differences in abnormal performance between top-performing funds (five-star funds) and moderate-performing funds (three-star funds). Funds with less than three stars generally have a much worse future performance than other groups. There are also differences in the subsequent factor loadings between different fund rating groupings. Top-performing funds (five-star funds) tend to have a market exposure above one (around 1.03 compared to Russell 3000’s 0.99), and to favour small (0.23 on size, significant at the 1 percent level) and growth stocks (-0.11 on B/M, significant at the 1 percent level). The insignificant positive average estimate of the momentum loading (t=1.57) and its small magnitude (near zero) indicates that these funds do not invest significantly in momentum or contrarian stocks. Ph.D. Thesis: Jeffrey Junhua Lu

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Next-to-top-performing funds (four-star funds) are less exposed to the market (a loading of 0.96), have weak preferences towards small (0.06 on size, significant at the 1 percent level) and value stocks (0.04 on B/M, significant at the 1 percent level), and are also indifferent to momentum or contrarian stocks (near zero loading on momentum). The moderate and below-moderate performing funds, the three-star and two-star funds, tend to favour small stocks and value stocks, and follow momentum strategies actively (0.04 loading on momentum, significant at 1 percent level). Bottom-performing funds (one-star funds) favour small stocks (0.51 on size, significant at 1 percent level) and follow momentum strategies actively (0.06 loading on momentum, significant at the 5 percent level). However, these funds are indifferent to value or growth stocks (insignificant on B/M). The spreads on size and book-to-market loadings between five-star funds and one-star funds are -0.283 and -0.151, which are both significant at the 1 percent level. The spread on the momentum loading between five-star funds and one-star funds is -0.022, which is not significant at any conventional level. Therefore, I conclude funds with good historical performance (five-star funds) will tend to hold fewer small stocks, fewer value stocks, and fewer stocks with good recent performance, when compared to those funds with poor historical performance (one-star funds). The above analysis is based on the portfolio regression approach. I then implement the fund regression approach to further investigate whether there exists a relationship between fund Morningstar ranking at the beginning of the sample period and subsequent fund performance during the entire sample period. I use three performance metrics from the existing fund performance literature to measure subsequent fund performance: the Sharpe (1966) ratio, mean monthly excess raw returns, and Carhart (1997) four-factor alpha. The goal is to examine whether the Morningstar star ranking at the beginning of the sample period is associated with the values of the performance measures during the sample period. If the Morningstar ranking predicts future performance well, then there should be a close correlation

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between them.

Table 13 (Page 249)

Table 13 reports average fund performance by Morningstar ranking. Each sample fund is classified into one of five fund ranking groups, based on its Morningstar star ranking at the beginning of its performance history during the sample period. Group sample period performance measure averages are then computed. The three fund performance measures decrease more or less monotonically as fund ranking groups move from five-star to one-star. The five-star group of funds clearly outperforms the one-star group of funds during the sample period. For example, for the five-star group, the average monthly raw excess return (net of 30 day T-bill rate) is 1.09 percent, the average monthly Sharpe ratio is 0.157, and the average Carhart 4-factor alpha is 27 basis points per month; for the one-star group, the average monthly raw excess return (net of 30 day T-bill rate) is 0.78 percent, the average monthly Sharpe ratio is 0.108, and the average Carhart 4-factor alpha is minus 47 basis points per month. For the mean monthly raw excess return, the spread between five-star funds and one-star funds is 31 basis points per month (significant at 1 percent level); the spread between five-star funds and three-star funds is 24 basis points per month (significant at 1 percent level); the spread between three-star funds and one-star funds is 7 basis points per month (significant at 1 percent level). Therefore, more than 60 percent of the spread between top-performing funds and bottom-performing funds is attributable to the spread between top-performing funds and moderate-performing funds. For the risk-adjusted performance measures, the Sharpe ratio and Carhart 4-factor alpha, the picture is similar. For example, for the Sharpe ratio, the spread between five-star funds and one-star funds is 0.049 (significant at 1 percent level); the spread between five-star funds and three-star funds is 0.008 (significant at 1 percent level); the spread between three-star funds and one-star funds is 0.041 (significant at 1 Ph.D. Thesis: Jeffrey Junhua Lu

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percent level). Therefore, more than 80 percent of the spread between top-performing funds and bottom-performing funds is attributable to the spread between moderate-performing funds and bottom-performing funds. For the Carhart 4-factor alpha, the spread between five-star funds and one-star funds is 74 basis points per month (significant at 1 percent level); the spread between five-star funds and three-star funds is 30 basis points per month (significant at 1 percent level); the spread between three-star funds and one-star funds is 44 basis points per month (significant at 1 percent level). Therefore, nearly 40 percent of the spread between top-performing funds and bottom-performing funds is attributable to the spread between moderate-performing funds and bottom-performing funds. 8.3.2.2. Style Timing Preferences by Fund Morningstar Sub-group

Different sub-groups of funds tend to favour stocks with different characteristics, which indicates that fund managers tend to favour specific styles when making investment decisions. I next examine the style timing activities of fund managers within each fund prior performance ranking group. Table 14 describes timing behaviour within each Morningstar ranking sub-group of funds. In particular, it lists the fraction of funds that have positive and negative timing coefficients and the number of funds that have significantly positive and negative timing coefficients within each rating group. The bootstrap analysis of style timing coefficients is based on the Carhart 4-factor style timing model.

Table 14 (Page 250)

I first examine the results under the Carhart 4-factor TM style timing model. Except for the five-star fund group, all other ranking groups (panel B to panel E) exhibit the following pattern: there are more funds demonstrating positive timing coefficients Ph.D. Thesis: Jeffrey Junhua Lu

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with respect to size (more than 50 percent of funds) and book-to-market style (more than 75 percent of funds), and negative timing coefficients with respect to momentum style (more than 80 percent of funds). However, for the five-star fund group, panel A shows more funds demonstrate positive timing coefficients with respect to book-to-market style (85 percent of funds), negative timing coefficients with respect to size (66 percent of funds) and momentum style (79 percent of funds). Therefore, top-performing funds (five-star funds) seem to time the book-to-market style at the expense of negative timing on the size and momentum styles, while all other funds try to time the size and book-to-market styles at the expense of negative timing on the momentum style. For those funds with significant timing coefficients, top-performing funds (five-star funds) exhibit more significant positive book-to-market timing coefficients and less significant negative momentum timing coefficients than low-rated funds during the sample period. For the TM model, for example, 44 percent of the five-star funds have significantly positive book-to-market timing coefficients, while only 32 percent of the one-star funds do so. Also, only 27 percent of the five-star funds have significantly negative momentum timing coefficients, while more than 42 percent of the one-star funds do so. However, there are more five-star funds exhibiting significant negative size timing coefficients (more than 11 percent compared to around 5 percent of other fund groups). The results are quantitatively similar under the Carhart 4-factor HM style timing model. It seems that top-performing funds tend to implement style timing strategies with respect to book-to-market and momentum styles more successfully than their counterparts after they received the Morningstar ranking. However, five-star funds do time the size style unsuccessfully. This might be due to the fact that after these funds receive their high rankings, they attract more and more fund investors’ money and fund size becomes inevitably larger and larger. Ciccotello and Grant (1996) suggest that yesterday’s best performing funds tend to become today’s largest funds as individuals invest heavily in response to the communications about the fund’s past Ph.D. Thesis: Jeffrey Junhua Lu

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success. Implementing size style timing strategies would indicate frequent buying/selling small-cap stocks in an effort to time size successfully. Finding “diamonds in the rough” may become more difficult as the fund grows. Moreover, getting in or out of small-cap stocks quickly without a significant impact on the market price of these stocks also becomes more difficult as the funds investment in such stocks increase in size. Therefore, as fund size increases, the fund manager will find it more difficult to successfully implement style timing strategies with respect to size when compared to their counterparts with fewer assets to manage. 8.3.2.3. Style Timing Aggressiveness by Morningstar Subgroup

As discussed earlier, the TM timing coefficients reflect the aggressiveness with which the fund manager implements his/her timing strategy, either positively or negatively. Hence, magnitude of these timing coefficients (absolute value) is used as a proxy for the aggressiveness of fund timing strategies. The goal is to examine whether the Morningstar star ranking at the beginning of the sample period corresponds to subsequent fund style timing aggressiveness during the sample period. If the Morningstar ranking is associated with fund managers’ investment decisions and their choices of fund portfolios, then there should be differences in style timing aggressiveness between different subgroups of funds based on their initial Morningstar star ranking.

Table 15 (Page 253)

Table 15 summarises the results based on the Carhart 4-factor timing model. It demonstrates that, on average, there are significant differences in style timing aggressiveness between different subgroups of funds. The spreads of style timing aggressiveness between one-star funds and three-star funds are 0.36, 0.54, 0.66, and 0.32 for market, size, book-to-market, and momentum styles respectively, which are

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all significant at the 1 percent level. The spreads of style timing aggressiveness between one-star funds and two-star funds are 0.27, 0.15, 0.35, and 0.20 for market, size, book-to-market, and momentum styles respectively, which are all significant at the 1 percent level, except for the size style. Therefore, the style timing aggressiveness of bottom-performing funds (one-star funds) is consistently larger than that of their average or just below average performing counterparts (three-star funds and two-star funds). Similarly, the spreads of timing aggressiveness between five-star funds and three-star funds are 0.11, 0.44, 0.59, and 0.01 for the four styles respectively, which are all significant at the 1 percent level except for the momentum style. When we look at the spreads between five-star funds and four-star funds, which are 0.13, 0.49, 0.58, and 0.10 for the four styles respectively, all are significant at the 1 percent level. Therefore, the style timing aggressiveness of top-performing funds (five-star funds) is consistently larger than that of their average or just above average performing counterparts (three-star funds and four-star funds). In summary, funds with moderate performance implement timing strategies less aggressively than those with an extremely good or bad performance record. Interestingly, the style timing aggressiveness of the bottom-performing funds (one-star funds) is larger than that of the top-performing funds (five-star funds), but is only significant at the 1 percent level for the market and momentum factors. Moreover, the magnitudes of these spreads are smaller than the spreads between one-star funds and three-star funds. Therefore, there is little statistical evidence that the style timing aggressiveness of bottom-performing funds (one-star funds) is consistently larger than that of their top-performing counterparts (five-star funds), or vice versa. Therefore, funds with moderate historical performance (three- and four-star funds) seem to be not keen on enhancing their performance and thus are the least willing to gamble and implement timing strategies. It seems that the “endowment” effect dominates these groups of funds. The endowment effect refers to the tendency by

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people to place higher value on what they own than on identical items that they do not own. It predicts that these fund managers will keep their existing portfolio unchanged and “lock in” their gains by indexing the market. On this basis they will implement timing strategies in a relatively passive manner. Top-performing funds (five-star funds) have an incentive to index the market and “lock in” a winning position, which is the optimal choice for fund managers under the rational agency assumption, but they still appear to want to and are capable of gambling using so-called “house-money”. Gamblers treat their winnings as house money, not their own money, and thus they tend to take very large risks with their winnings. The house-money effect seems to dominate this group of funds. Thaler and Johnson (1990) describe the house-money effect as an increase in risk taking when an investor has recent trading successes, which is also related to investor overconfidence. The theory predicts that these fund managers face a tendency to treat investment gains as house money and will be more willing to gamble with the gains. This is consistent with implementing timing strategies in a relatively aggressive manner. The worst-performing funds (one-star funds) also have a strong interest in factor timing strategies, since these funds are already in trouble and factor timing strategies could possibly help them out. It seems that the “trying-to-break-even” effect dominates this group of funds. The “trying to break even” effect refers to the desire by fund managers to recoup large losses in one quick long-shot (very high-risk) investment. This form of behavioural bias predicts that these fund managers who have lost money are more willing to take very high risks to try to recoup the loss immediately. Indeed, the results show that they implement timing strategies in the most aggressive manner. Given the results presented in Table 15, the null hypotheses of H8 and H9 are rejected. As such, prior fund performance does seem to systematically affect funds’ subsequent timing behaviour. The lines of U-shape in Figure 1 show this intuitively.

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Figure 1 (Page 274)

8.3.3. Summary

On average, the lowest Morningstar rating funds tend to underperform their top performing counterparts by substantial amounts in terms of risk-adjusted future returns, while the highest Morningstar rating funds only outperform their average counterparts by a relative small amount in terms of risk-adjusted returns in the future. It seems that top-performing funds tend to implement style timing strategies with respect to book-to-market and momentum styles more successfully than their counterparts after they received the Morningstar ranking. However, five-star funds do time the size style unsuccessfully. Funds with an extreme good or bad performance record implement timing strategies more aggressively than those with a moderate performance record. Therefore, funds with middling performance seem to be keen on maintaining their performance and thus appear to be less willing to take bets on a style, while funds at the two ends of the performance spectrum (stars or dogs) have more incentives to do so. On average, top-performing funds are influenced by the “house-money” effect; bottom-performing funds exhibit “trying-to-break-even” effect; funds in the middle are affected by the “endowment” effect.

8.4. Summary of Chapter This chapter investigates the style timing abilities of active fund managers within the context of their fund investment objectives and performance record. Dividing my sample funds into sub-groups based on their self-stated investment objectives reveals that growth-oriented funds tend to possess better timing abilities and also implement style timing strategies more aggressively than other funds. Specifically, aggressive Ph.D. Thesis: Jeffrey Junhua Lu

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growth funds are excellent book-to-market (value/growth) timers without bearing the costs of poor momentum (winner/loser) timing, while growth funds time the book-to-market (value/growth) style at the expense of negative timing on the momentum (winner/loser) style. Equity income funds tend to be good at timing the size (big cap/small cap) style but be poor at timing the momentum (winner/loser) style. Growth and income funds are bad factor timers, especially with respect to size (big cap/small cap) and momentum (winner/loser) styles. Growth-oriented funds respond to their private information on future style performance more aggressively than income-oriented funds. I also find that, on average, funds with an extremely good or bad performance record implement timing strategies more aggressively than those with a moderate performance record. Funds with middling performance seem to be keen on maintaining their performance and thus appear to be less willing to take bets on a style, while funds at the two ends of the performance spectrum (stars or dogs) have more incentives to do so. On average, top-performing funds are influenced by the “house-money” effect; bottom-performing funds exhibit “trying-to-break-even” effect; funds in the middle are affected by the “endowment” effect. In the next chapter I investigate the style timing ability and activity of active fund managers in the context of specific fund characteristics. Specifically, I explore the effect of fund size, manager experience, turnover, and investor flows on the style timing behaviour of active mutual funds by dividing my sample funds into sub-groups based on these fund characteristics.

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CHAPTER 9 FUND SYSTEMATIC FACTORS AFFECTING STYLE TIMING 9.1. Introduction In chapter 8 I presented evidence that growth-oriented funds tend to possess better timing abilities and also implement style timing strategies more aggressively than other funds. I also find that on average, funds with an extremely good or bad performance record implement timing strategies more aggressively than those with a moderate performance record. In this chapter I turn to investigate the style timing abilities of active fund managers within the context of specific fund characteristics. Common knowledge has it that fund characteristics such as size, manager experience, turnover, and investor flows affect fund timing activities. Small funds are in a better position to time the market since it is easy for them to reshuffle their portfolios in a timely manner without a large impact on the market. Experienced managers should be better informed when making investment decision and implementing style timing strategies. If fund turnover rate is positively correlated with the frequency of timing-oriented trading, to what extent does high turnover represent successful style timing? Also, while fund managers may be trying to time investment styles, there are investors who are attempting to time the mutual funds, therefore, investors’ inflows and outflows may directly affect fund style timing activities. In this chapter I conduct style timing tests on sub-groups of my sample funds, segregated based on their specific fund characteristics. Recall that the expected change in a manager’s factor exposure over time depends not only on his/her aggressiveness, but also the precision of his/her forecast. The precision of the fund manager’s timing forecast, thus the timing ability of the fund manager, is generally

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reflected by the sign of the timing coefficients derived from the style timing regression. Thus a significantly positive style timing coefficient represents superior style timing ability. The aggressiveness with which the fund manager reacts to his forecast, as suggested by Jiang (2001), could be reflected by the magnitude (or the absolute value) of the timing coefficients derived from the TM style timing regression. Based on this approximation, I also explore how fund-specific characteristics affect the aggressiveness of sample fund managers’ timing activities. The chapter is organised as follows: section 2 presents the results of style timing tests within sub-groups of sample funds classified by fund size, section 3 presents the results of style timing tests on sub-groups of sample funds classified by fund age, section 4 presents the results of style timing tests on sub-groups of sample funds classified by fund turnover, section 5 presents the results of style timing tests on sub-groups of sample funds classified by fund inflows/outflows and section 6 summarises the results.

9.2. Do Small Funds Fare Better? 9.2.1

Introduction

The issue of the relationship between size of assets under management and fund performance has been examined by other researchers. Grinblatt and Titman (1989) study the performance of mutual fund portfolios over the period from 1975 to 1984. Mutual funds are ranked by asset size and then divided into quintiles. Using 1975 asset size, they find some evidence of abnormal performance in gross returns over the following 10-year period (1975-1984) in their smaller asset-size quintiles, especially with more aggressive fund objectives. Droms and Walker (1994) find no relationship between fund size and performance in their study of international mutual funds. Ciccotello and Grant (1996) suggest that more aggressive funds have a smaller optimal size than less aggressive funds and the advantages of being small appear to outweigh the disadvantages. Thomas and Tonks (2001) investigate the performance of Ph.D. Thesis: Jeffrey Junhua Lu

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the UK equity portfolios of 2,175 segregated UK pension funds over the period 1983-97. They examine the sensitivity of the fund returns to the addition of a size premium, which they find to be significant and important for the smaller funds in their sample. The average size timing coefficient for the small fund sample is greater than that for the large fund sample. Thomas and Tonks suggest that the small funds are more able to time the size premium. One common view is that small funds are in a better position to time the market since it is easy for them to reshuffle their portfolio in a timely manner without a large impact on the market. Big funds present management challenges. Continuing to find worthwhile investment opportunities as the fund grows may strain the capabilities of even a top manager or management team. Phalon (1994) outlines the circumstances associated with the closing of the highly-successful SoGen International Fund. How much strain may depend upon the investment strategy of the fund being managed. If more aggressive investment strategies (such as those style timing strategies) involve buying or selling stocks frequently, then rapid asset growth may be more difficult to manage. Large asset size also reduces a fund’s “nimbleness.” The manager becomes less able to quickly move in or out of positions without attracting a great deal of attention. Managing the fund becomes like “manoeuvring a battleship in a bathtub.” Beating the styles becomes difficult as the fund itself grows to become a style proxy. These challenges support the assertion that funds can grow too big, and that optimal performance occurs in smaller funds. Small funds are able to invest in small companies, whereas large funds are unable to take advantage of movements in the size premium, because it is more difficult for them to invest in small companies on account of their large size. Hence it is argued that smaller funds are more likely to implement timing strategies than other funds. As such, I set up null H110 to test this proposition. H110 : There are no differences in the timing behaviour between small funds and big funds.

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The size of a mutual fund is measured by the fund’s total net assets under management. I segregate my sample funds into quintiles by size. 9.2.2

Factor Loadings on Fund Size Subgroups

Before the investigation of the effects of fund sizes on fund timing activities, I first examine the factor loadings within each fund size quintile subgroup. In this study, I focus on the Carhart (1997) four-factor model, which augments the Fama-French three-factor model by a momentum factor. The regression model is as follows:

R pt = α p + β1 RMRFt + β 2 SMBt + β3 HMLt + β 4 MOM t + ε pt

(8)

where RMRF is the market factor, SMB is the size factor, HML is the book-to-market factor, and MOM is the momentum factor. I employ two different regression approaches: the portfolio regression approach and the fund regression approach. In the portfolio regression approach, I compute the set of equally weighted monthly returns of the fund portfolio, which comprises all funds within the same fund size subgroup, and then use this return as the dependent variable in the above regression. In the fund regression approach, I use the individual monthly fund returns in the above regression and then report the average coefficient estimates.

Table 16 (Page 254)

Table 16 summarises the fund factor loadings for the five fund size portfolios for the portfolio regression approach. For comparison purposes, I also include the factor loadings of the Russell 3000 Index as a proxy for the general market index. Table 16 shows that large funds tend to outperform small funds during my sample period in terms of alpha. In the largest quintile (quintile 5), funds on average achieve positive abnormal returns of 19 basis points per month (2.28 percent per year), which is significant at the 1 percent level. The funds in size quintile 4 achieve positive Ph.D. Thesis: Jeffrey Junhua Lu

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abnormal returns of 14 basis points per month (1.68 percent per year), which is significant at the 5 percent level. During the sample period, the Russell 3000 achieves significant positive abnormal returns of 8 basis points per month (0.96 percent per year). Therefore, both groups of funds have on average outperformed the market index during the sample period. Funds in size quintiles 3 and 2 trail the market by achieving abnormal returns of 9 basis points per month (1.08 percent per year) and 3 basis points per month (0.36 percent per year), though not significantly different to zero at even the five percent level. Funds in quintile 1, the smallest quintile, in fact, even achieve negative abnormal returns of 4 basis points per month (-0.48 percent per year), although not significantly different to zero. Funds in size quintile 5 outperform funds in quintile 1 by a spread of 23 basis points per month (2.76 percent per year), which is significant at the 1 percent level. Funds in quintile 5 also outperform funds in quintile 2 by a spread of 16 basis points per month (1.92 percent per year), which is significant at the 10 percent level. The spread of alpha between moderate-size funds (quintile 3) and the smallest funds (quintile 1) is also 22 basis points per month (2.64 percent per year), but not significant. The spread of alpha between the largest funds (quintile 5) and moderate-size funds (quintile 3) is also not significant. Therefore, as fund size increases funds achieve better abnormal performance. The funds in the largest fund size group significantly outperform the funds in below-average fund size groups. There are also differences in the factor loadings between different fund size groups. The funds in the largest fund size group (quintile 5) tend to index the market (0.99 on market), and, not surprisingly have relatively lower exposures to small-cap stocks (0.10 on size compared to other funds’ 0.20). The insignificant and close-to-zero estimates of B/M loading and momentum loading indicate that these funds invest in growth/value stocks and momentum/contrarian stocks in a balanced way. The funds in quintiles 3 and 2 tend to invest in momentum stocks, as indicated by their significant positive momentum loadings. The funds in the smallest fund size group (quintile 1) are the least exposed to the market (around 0.95 on market). These funds also have the Ph.D. Thesis: Jeffrey Junhua Lu

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highest exposures to small-cap stocks (around 0.22 on size), indicating that small funds favour small-cap stocks. Large funds tend to have market exposures closer to one, and tend to hold less small stocks, when compared to small funds. For example, the spread on size between the largest funds (quintile 5) and the smallest funds (quintile 1) are -0.11, which is significant at the 1 percent level. However, large funds and small funds tend to have identical loadings on B/M and Momentum. 9.2.3

Style Timing and Fund Size

Table 17 lists the fraction of funds that have positive and negative timing coefficients and the number of funds that have significantly positive and negative timing coefficients within each size group. The bootstrap analysis of style timing coefficients is based on the Carhart 4-factor style timing model.

Table 17 (Page 255)

I first examine the results under the Carhart 4-factor TM style timing model. Except for the size style, all fund size groups (as reviewed in panel A to panel E) exhibit the following pattern: there are more funds demonstrating positive timing coefficients with respect to book-to-market style (more than 70 percent of funds on average), and negative timing coefficients with respect to momentum style (more than 80 percent of funds on average). For those funds with average and below average fund size (quintile 3 to quintile 1), as shown in panel A to panel C, there are relatively more funds demonstrating positive timing coefficients with respect to size style (more than half of funds on average), while for those funds with above average fund size (quintile 4 and quintile 5), as shown in panel D and panel E, there are relatively more funds demonstrating negative timing coefficients with respect to size style (more than half of funds on average). Ph.D. Thesis: Jeffrey Junhua Lu

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For those funds with significant timing coefficients, small funds exhibit more significant

positive

size

timing

coefficients

and

less

significant

positive

book-to-market timing coefficients than large funds. For example, 9 percent of funds in the smallest quintile (quintile 1 shown in panel A) have significantly positive style timing coefficients with respect to size style, while only 3 percent of funds in the largest quintile (quintile 5 shown in panel E) do so. Also, only 26 percent of the funds in the smallest quintile (quintile 1 shown in panel A) have significantly positive book-to-market style timing coefficients, while more than 31 percent of the funds in the largest quintile (quintile 5 shown in panel E) do so. Therefore, small funds tend to be good timers on the size style, when compared to large funds. Recall that sample funds on average demonstrate a negative size timing coefficient. This is consistent with the conjecture that small funds are in a better position to implement timing strategies with respect to the size style, since implementing these strategies needs to establish and rebalance positions in small stocks frequently, which is not easy for large funds. As discussed earlier, the TM timing coefficients reflect the aggressiveness with which the fund manager implements his/her timing strategy, either positively or negatively. Hence, the magnitude of these timing coefficients (the absolute value) is used as a proxy for the aggressiveness of fund timing strategies. Table 18 summarises the results based on the Carhart 4-factor timing model.

Table 18 (Page 258)

Table 18 demonstrates that, on average, there are significant differences in style timing aggressiveness between different subgroups of funds. The spreads of timing aggressiveness between quintile 3 (median-size funds) and quintile 5 (largest funds) are 0.08, 0.30, 0.30, and 0.22 for market, size, book-to-market, and momentum styles

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respectively, which are all significant at the 1 percent level. Similarly, the spreads of timing aggressiveness between quintile 1 (smallest funds) and quintile 5 are 0.19, 0.46, 0.24, and 0.27 for the four styles respectively, which are all significant at the 1 percent level. Therefore, style timing aggressiveness of the smallest funds (quintile 1) is consistently larger than that of their median-size and the largest size counterparts (quintile 3 and quintile 5). As shown in figure 2, the larger the funds, the lower their style timing aggressiveness. In other words, small funds tend to implement timing strategies more aggressively than large funds.

Figure 2 (Page 275)

9.2.4

Summary

Large funds tend to outperform small funds during the sample period in terms of risk-adjusted returns. Smaller funds tend to favour small-cap stocks when compared to their larger counterparts. Small funds tend to be good timers on the size style, which indicates that these funds are in a better position to implement style timing strategies with respect to the size style, since implementing these strategies needs to establish and rebalance positions in small stocks frequently, which is not easy for large funds. Moreover, small funds tend to implement style timing strategies far more aggressively than large funds.

9.3. Does Experience Matter? 9.3.1

Introduction

Fund management groups appear to have an incentive to close down poorly Ph.D. Thesis: Jeffrey Junhua Lu

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performing funds which would otherwise reduce the average performance of the funds in their stable. There is a literature which shows that, in general, poor job performance leads to poor labour market outcomes for managers. Kaplan and Reishus (1990) show that CEOs who perform poorly are less likely to become outside members of the boards of directors of other firms. For those funds that survive and become seasoned funds, their fund managers are more likely to possess superior investment abilities. Lunde et al. (1999) argue that fund investors are unlikely to know ex ante which funds will outperform in the future and hence have to learn this gradually as a fund’s track record is established. After sufficient data have been accumulated, investors may recognise that certain funds underperform, withdraw their money, and thereby cause the funds to close. Funds that survive this treatment are more likely to be perceived as having a good track record and having sufficient experiences. Tweddell (2002) suggests that few advisers or planners seem to take new funds seriously. The primary reason for professionals’ disdain is the belief that new fund outperformance is largely the result of sponsors’ shenanigans; regulators’ disciplinary actions and unfavourable press reports have reinforced these suspicions. The other reason that new funds often do not gain the respect they arguably deserve is probably due to the popularity of Morningstar rating system, which is often deemed by the public to have “a good housekeeping seal of approval” (Franecki, 2000). In fact, some financial planners report that investors require them to invest only in funds with 4- or 5-star ratings. However, Morningstar does not rate funds that have fewer than 3 years of historical returns. Therefore, for a fund to have a superior Morningstar rating that stands out in advertisements, it has to stay in existence for more than 3 years, which puts new funds in a position of competitive disadvantage. As such, a more experienced manager will be more inclined to run a seasoned fund when confronted with opportunities in both new funds and seasoned funds, since a seasoned fund will attract new money more easily from fund investors. If established funds are more likely to be run by experienced managers, we can test

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using fund age whether experience contributes to better timing ability. To do this, I segregate my sample funds into three groups: new funds, old funds and median-aged funds. New funds are defined as those funds with less than a 5-year performance history in existence and old funds are defined as those funds with a 10-year or more performance history. The remainders are defined as median-aged funds. As such, I set up null H100 to test this proposition. H100 : There are no differences in the timing behaviour between new funds and old funds.

As mentioned earlier, fund management groups tend to close down poorly performing funds in an effort to maintain the average performance of the group. If these funds are not to be closed down after only a very short period, then their fund managers can be expected to be under significant pressure to perform in the short run. This might give the fund manager in new funds a strong incentive to follow short-term investment strategies, such as style timing strategies. Moreover, since investors use the Morningstar rating as an important criterion when selecting mutual funds in which to invest, a new fund will need an outstanding track record to obtain a superior Morningstar rating in an effort to attract fund investors’ investment. In order to properly balance long-term performance and short-term performance, Morningstar uses a specific weighting system that depends upon the age of the fund to calculate the fund’s overall star rating. Morningstar first calculates a fund’s star rating for each of three different time horizons: 3 years, 5 years and 10 years. Then for funds with 10 years or more of returns, Morningstar weights the 3-year star rating by 20 percent, the 5-year star rating by 30 percent and the 10-year rating by 50 percent. For funds with 5 to less than 10 years of return data, Morningstar weights the 3-year star rating 40 percent and the 5-year star rating by 60 percent. For funds with less than 5 but at least 3 years of return data, Morningstar weights the 3-year star rating by 100 percent. Therefore, for younger funds, especially those funds with less than 5 years of return data, their overall star ratings mainly depend on their

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most recent performance over a relatively short evaluating period. This would also give the fund manager in new funds a strong incentive to follow style timing strategies aggressively. 9.3.2

Factor Loadings on Fund Subgroups Classified by Age

Before investigating the effects of fund age on fund timing activities, I first examine the factor loadings within each fund age subgroup. In this study, I focus on the Carhart (1997) four-factor model, which augments the Fama-French three-factor model by a momentum factor. Table 19 summarises the fund factor loadings of my three fund portfolios, which are constructed based on fund age. I segregate all my sample funds into three groups: new funds, seasoned funds and median-aged funds. New funds are defined as those funds with less than a 5-year performance history in existence and seasoned funds are defined as those funds with 10-years or more performance history. The remainder are defined as median-aged funds. For comparison purposes, I also include the factor loadings of the Russell 3000 Index as a proxy for the general market index.

Table 19 (Page 259)

The results show little evidence that seasoned funds outperform new funds during the sample period in terms of alpha, or vice versa. No age group delivers a significant alpha. Seasoned funds outperform new funds by a spread of only 2 basis points per month (0.24 percent per year), which is not significant. There are also no significant differences in the factor loadings between different fund age groups. New funds have relatively larger exposures to small-cap stocks (0.20 on size compared to other funds’ 0.14) and smaller exposures to value stocks (0.03 on B/M compared to other funds’ 0.05). However, the spreads on all style loadings between new funds and seasoned funds are all small in magnitude and not significant. In summary, there is no evidence Ph.D. Thesis: Jeffrey Junhua Lu

Cranfield School of Management 201

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showing that different age groups of funds achieve different risk-adjusted performance during the sample period. Also, there is no evidence demonstrating that different age groups of funds favour stocks with different characteristics. 9.3.3

Style Timing on Subgroup of Funds

Table 20 lists the fraction of funds that have positive and negative style timing coefficients and the number of funds that have significantly positive and negative style timing coefficients within each age group. The results show little evidence of better timing abilities of seasoned funds when compared to their younger counterparts. The distribution of funds showing positive and negative (or significant positive and negative) style timing coefficients are similar across all three fund age groups. Therefore, there is no evidence that seasoned funds possess better style timing abilities than young funds.

Table 20 (Page 260)

As discussed earlier, the TM timing coefficients reflect the aggressiveness with which the fund manager implements his/her timing strategy, either positively or negatively. Hence, the magnitude of these timing coefficients (the absolute value) is used as a proxy for the aggressiveness of fund timing strategies. Table 21 summarises the results based on the Carhart 4-factor timing model.

Table 21 (Page 262)

On average, new funds tend to implement style timing strategies more aggressively than their older counterparts. The spreads of style timing aggressiveness between young funds and seasoned funds are 0.09, 0.20, and 0.12 for size, book-to-market, and Ph.D. Thesis: Jeffrey Junhua Lu

Cranfield School of Management 202

Can Fund Managers Successfully Time Their Investment Styles?

momentum styles respectively; all of them are statistically significant42. Similarly, the spreads of style timing aggressiveness between young funds and median aged funds are 0.02, 0.19, 0.30, and 0.09 for the four styles respectively, which are all significant at the 1 percent level except for the market style. For comparison purposes, I also group the seasoned funds and the median-aged funds together and label them as old funds. A clearer picture is presented by style timing aggressiveness spreads between young funds and old funds (funds classified as with more than 5 years) which are 0.14, 0.25, and 0.11 for the three styles respectively, and are all significant at the 1 percent level. The results on style timing aggressiveness are also visualised and presented in figure 3.

Figure 3 (Page 276)

9.3.4

Summary

There is little evidence that seasoned funds outperform new funds during the sample period in terms of alpha, or vice versa. Despite the arguments that established funds are more likely to be run by experienced managers and thus possess better timing ability, there is no statistical evidence that seasoned funds implement style timing strategies more successfully when compared to their younger counterparts. However, new funds do tend to implement style timing strategies more aggressively than their older counterparts. They are, however, unsuccessful in generating superior performance. Note, however, that my results may be biased in that I do not rebase my analysis for funds that reach/change age thresholds during my sample period.

42

Indeed, the spreads of timing aggressiveness between young funds and seasoned funds are significant at the 1% level for the B/M and momentum style, and significant at the 10% level for the size style. Ph.D. Thesis: Jeffrey Junhua Lu

Cranfield School of Management 203

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9.4. Is High Turnover Rate Justified as Timing? 9.4.1

Introduction

A number of studies examine the relationship between performance and portfolio turnover and provide conflicting findings. Ippolito (1989) finds no correlation between fund performance and portfolio turnover. However, Grinblatt and Titman (1989) find a positive relation between turnover and gross performance (i.e. before expenses) and Wermers (2000) finds that high turnover funds are better able to select stocks that earn higher returns (and beat an appropriate benchmark net of fees) than low turnover funds, although their transaction costs and expenses are higher. On the other hand, Carhart (1997) finds a negative relation between turnover and net mutual fund returns. Khorana (2001) examines the level of portfolio turnover contingent on performance and management turnover, arguing that underperforming fund managers, facing the threat of dismissal, will increase trading activity (and therefore fund turnover) by window dressing their portfolios. Khorana finds empirical support for this hypothesis, in that underperforming managers experience significantly higher levels of portfolio turnover prior to termination. Mutual fund managers claim that turnover does not reduce performance, since investors are paying for the quality of the manager’s information, and because managers trade only to anticipate market/style movements and to style time. To justify their higher charges on customers, funds with higher turnover ratios should make a greater attempt to style time. Hence, it is expected that an increase in fund timing activities will coincide with higher turnover. 2,744 out of 2,791 of my sample funds report their annual turnover rates in the Morningstar database. To investigate the effect of turnover on the timing behaviour of funds, I segregate my sample funds into three categories according to their average annual turnover rates over the sample period: Low (less than 50 percent), Median (between 50 percent and 100 percent), and High (100 percent or higher).

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Turnover is defined as the percentage of a mutual fund portfolio’s holdings that has changed over the past year. Morningstar measures portfolio turnover as the minimum of purchases or sales, divided by the average total net assets of the fund in the period: PortfolioTurnoverpt =

min( Purchase pt , Sales pt ) averageTNApt

(48)

where Purchasespt is the total value of stock purchases by portfolio p during period t, Salespt is the total value of stock sales by portfolio p during period t, and TNApt is the total average net assets of portfolio p during period t. Portfolio turnover is measured annually. The turnover rate of a fund is a proxy for how frequently a manager trades his/her portfolio. The inverse of the fund’s turnover rate is the average holding period for a security in that fund. If one maintains a Russell 3000 benchmark portfolio, the average annual turnover rate is about 4-6 percent for the previous ten years. As a comparison, the average turnover rate of actively managed funds investing in the same market is 85.7 percent. Assuming turnover rate is positively correlated with the frequency of timing-oriented trading, to what extent does high turnover represent successful factor timing and aggressiveness of factor timing activities? As such, I set up null H120 to test this proposition. H120 : There are no differences in the timing behaviour between low turnover funds and high turnover funds. 9.4.2

Factor Loadings on Fund Subgroups by Turnover

Before investigating the effects of fund turnover on fund timing activities, I first examine the factor loadings within each fund turnover subgroup. In this study, I focus on the Carhart (1997) four-factor model, which augments the Fama-French three-factor model by a momentum factor. I employ two different regression approaches: the portfolio regression approach and the fund regression approach. In the portfolio regression approach, I compute the set of equally weighted monthly return of

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Cranfield School of Management 205

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the fund portfolio which comprises all funds within the same fund turnover subgroup and then use this return as the dependent variable in the above regression. In the fund regression approach, I use the individual monthly fund returns in the above regression and then report the average coefficient estimates.

Table 22 (Page 263)

Table 22 summarises the fund factor loadings of my three fund portfolios constructed by fund turnover ratio, for the portfolio regression approach. For comparison purposes, I also include the factor loadings of the Russell 3000 Index as a proxy for the general market index. Table 22 shows that low turnover funds tend to outperform high turnover funds during the sample period in terms of alpha. In the low turnover group, the average fund demonstrates a positive abnormal return of 19 basis points per month (2.28 percent per year), which is significant at the 1 percent level; while the average fund in the high turnover group achieves a negative abnormal return of 4 basis points per month (0.48 percent per year), which is not statistically significant. As turnover rate increases funds achieve worse abnormal performance. High turnover funds underperform low turnover funds by a spread of 15 basis points per month (1.80 percent per year), although not significant at conventional levels. There are also differences in the factor loadings between different fund turnover groups. Low turnover funds tend to have relatively lower market exposures (around 0.91 compared to Russell 3000’s 0.99, significant at the 1 percent level), favour small (0.05 on size, significant at the 1 percent level) and value stocks (0.13 on B/M, significant at the 1 percent level). The insignificant positive average estimate of momentum loading and its small magnitude (near zero) indicate that these funds are indifferent to momentum or contrarian stocks. Median turnover funds on average track the market index (0.97 compared to Russell 3000’s 0.99, significant at the 1 percent level), have preferences towards small (0.17 on size, significant at the 1 Ph.D. Thesis: Jeffrey Junhua Lu

Cranfield School of Management 206

Can Fund Managers Successfully Time Their Investment Styles?

percent level) and value stocks (0.10 on B/M, significant at the 1 percent level), and are also indifferent to momentum or contrarian stocks (near zero on momentum). High turnover funds tend to have relatively large market exposures (around 1.04 compared to Russell 3000’s 0.99, significant at the 1 percent level), favour small (0.33 on size, significant at the 1 percent level) and growth stocks (-0.11 on B/M, significant at the 1 percent level). These funds also follow momentum strategies actively (around 0.06 on momentum, significant at 1 percent level). The spread on market, size, and book-to-market loadings between high turnover funds and low turnover funds are 0.13, 0.29, and -0.24, which are all significant at 1 percent level. The spread on momentum loading between high turnover funds and low turnover funds is 0.05, which is not significant at the 10 percent level. Moreover, when high turnover funds are compared to median turnover funds and median turnover funds are compared to low turnover funds, similar results appear. Therefore, higher turnover funds tend to have higher market exposures, and tend to hold more small stocks, more growth stocks, and probably more stocks with good recent performance, when compared to lower turnover funds. The above analysis is based on the portfolio regression approach. I then implement the fund regression approach to further investigate whether there exists a relationship between fund turnover and fund performance during the entire sample period. I use three performance metrics from the existing fund performance literature to measure subsequent fund performance during the entire sample period: the Sharpe (1966) ratio, mean monthly excess raw returns, and Carhart (1997) four-factor alpha. Table 23 reports the results of average fund performance by fund turnover. Each sample fund is classified into one of three fund turnover groups, based on its average annual turnover ratio during the sample period. The group average performance measures during the sample period are then computed. When using the mean monthly raw excess return, there is no significant difference in results between high turnover funds, median turnover, and low turnover funds. In particular, the average monthly

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raw excess returns (net of 30 day T-bill rate) for high turnover funds, median turnover funds, and low turnover funds are 0.91 percent, 0.88 percent, and 0.90 percent, respectively.

Table 23 (Page 2643)

However, for the risk-adjusted performance measures, the Sharpe ratio and Carhart 4-factor alpha, the picture is different. For high turnover funds, the average monthly Sharpe ratio is 0.13, and the average Carhart 4-factor alpha is 2.1 basis points per month; for low turnover funds, the average monthly Sharpe ratio is 0.17, and the average Carhart 4-factor alpha is -17.2 basis points per month. There is a significant difference in results (at well beyond to 1 percent level) between high turnover funds and low turnover funds under these two performance measures. Moreover, as the fund turnover ratio increases, the fund becomes more and more volatile measured in terms of monthly volatility. Since the Sharpe ratio and Carhart 4-factor alpha provide for better risk adjustment for mutual funds than does simple raw excess return and they reflect true fund performance, the above results indicate that high turnover funds tend to underperform strongly their low turnover counterparts in terms of risk-adjusted returns. 9.4.3

Style Timing by Fund Turnover Subgroups

Table 24 lists the fraction of funds that has positive and negative timing coefficients and the number of funds that have significantly positive and negative timing coefficients within each fund turnover group. I first examine the results under the Carhart 4-factor TM style timing model.

Table 24 (Page 265)

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Except for the size style, all fund turnover groups (as presented in panels A to C) exhibit the following pattern: there are more funds demonstrating positive timing coefficients with respect to book-to-market style (more than 70 percent of funds on average), and negative timing coefficients with respect to momentum style (more than 80 percent of funds on average). For median turnover funds and low turnover funds, as shown in panels A and B, there are relatively more funds demonstrating positive timing coefficients with respect to size style (more than half of funds on average), while for high turnover funds, as shown in panel C, there are relatively more funds demonstrating negative timing coefficients with respect to size style (less than half of funds on average). For those funds with significant timing coefficients, the results show some evidence of better timing abilities of higher turnover funds when compared to their lower turnover counterparts. For the book-to-market style, high turnover funds have substantially more funds showing significant positive timing coefficients (more than 45 percent) and slightly fewer funds showing significant negative timing coefficients (1.6 percent), while only 19 percent of low turnover funds show significant positive timing coefficients and 2.3 percent of these funds show significant negative timing coefficients. This suggests that high turnover funds are good book-to-market timers. For the momentum style, the differences are less impressive. The high turnover group has 1 percent (36 percent) of funds showing significant positive (negative) timing coefficients, while the low turnover group has 0.7 percent (37 percent) of funds showing significant positive (negative) timing coefficients. For the size style, there are more funds demonstrating significant positive timing coefficients than those funds demonstrating significant negative timing coefficients in the low turnover group, while there are fewer funds demonstrating significant positive timing coefficients than those funds demonstrating significant negative timing coefficients in the high turnover group. This suggests that high turnover funds demonstrate worse style timing abilities with respect to the size style than low turnover funds. Ph.D. Thesis: Jeffrey Junhua Lu

Cranfield School of Management 209

Can Fund Managers Successfully Time Their Investment Styles?

As discussed earlier, the TM timing coefficients reflect the aggressiveness with which the fund manager implements his/her timing strategy, either positively or negatively. Hence, the magnitude of these timing coefficients (the absolute value) is used as a proxy for the aggressiveness of fund timing strategies. Table 25 summarises the results based on the Carhart 4-factor timing model.

Table 25 (Page 268)

On average, high turnover funds tend to implement timing strategies more aggressively than low turnover funds. The spreads of timing aggressiveness between high turnover funds and low turnover funds are 0.24, 0.63, 0.91, and 0.30 for market, size, book-to-market, and momentum styles respectively; all differences are statistically significant at the 1 percent level. Similarly, the spreads of timing aggressiveness between high turnover funds and median turnover funds are 0.45, 0.68, and 0.21 for the three styles respectively, which are all significant at the 1 percent level. On average, more than 70 percent of the differences on timing aggressiveness between higher turnover funds and lower turnover funds can be attributed to the differences between high turnover funds and median turnover funds. Therefore, the higher the turnover ratio, the more aggressive the implementation of fund style timing strategies, as shown visually in figure 4.

Figure 4 (Page 277)

It seems that high turnover funds implement timing strategies more aggressively than their low turnover counterparts, and most of their timing activities are related to the book-to-market style, as shown by the largest spread of timing aggressiveness on this style. This is consistent with the results shown in table 24, where substantially higher Ph.D. Thesis: Jeffrey Junhua Lu

Cranfield School of Management 210

Can Fund Managers Successfully Time Their Investment Styles?

percentages of high turnover funds (45 percent compared to 20 percent on average for other funds) show timing abilities on this style. However, though the spread of timing aggressiveness in size is relatively large between high turnover funds and low turnover funds, high turnover funds demonstrate worse timing abilities with respect to size than low turnover funds. It could be the case that their fund managers are timing one style at the expense of mistiming on other styles. There could also be other behavioural explanations related to fund managers’ investment activities. Dow and Gorton (1997) consider a model where portfolio managers trade even though they have no reason to because their clients cannot distinguish “actively doing nothing” from “simply doing nothing.” Fund managers might be engaging in timing strategies not because they possess superior forecasting skill, but because they use it as a marketing strategy to distinguish themselves from their competitors by providing a “so-called” extra investment service. Lakonishok et al. (1991) tell a story that fund managers dress up their portfolios, and selling off the losers in particular, before disclosing their holdings to the public in order to make the composition look “smart.” Haugen and Lakonishok (1988) suggest window dressing by professional money managers as a possible explanation of the “January Effect.” Funds engaging in such window dressing activities are selling to avoid apologising for and defending a losing stock’s presence to clients even though the investment judgement may be to hold (Lakonishok et al., 1991). As such, a high turnover rate can go with mis-timing. 9.4.4

Summary

High turnover funds appear to underperform their low turnover counterparts in terms of risk-adjusted returns. Higher turnover funds tend to have higher market exposures, and tend to hold more small stocks, more growth stocks, and more stocks with good recent performance, when compared to lower turnover funds. Higher turnover funds on average are good book-to-market style timers but bad size style timers, and they also implement timing strategies more aggressively than low turnover funds.

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Cranfield School of Management 211

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Therefore, the above analysis provides evidence to reject the null hypothesis of H12, suggesting that there are significant differences in the timing behaviour between low turnover funds and high turnover funds.

9.5. Do Investor Flows Affect Factor Timing? 9.5.1

Introduction

One plausible explanation for mutual funds’ unsatisfactory timing performance might be their open nature (as opposed to closed-end funds); this is described as the cash-flow hypothesis in Warther (1995), Ferson and Warther (1996), and Edelen (1999). While fund managers try to time the market, there are investors who attempt to time the mutual funds themselves. When the market fares well, new money flows in, and funds have a higher portion of their portfolio in cash, which results in lower betas. When the market dips, more investors try to redeem their shares, then the cash reserve runs low, which leads to higher betas. Further, Ferson and Schadt (1996) argue that without a stream of new money, big redemption orders can force funds to liquidate shares often at an inopportune time, such as selling into a falling market. From this point of view, style mis-timing of mutual funds constitutes a price that investors have to pay for the liquidity they enjoy with open-end funds. Therefore, fund managers provide a great deal of liquidity to investors and thus arguably need to engage in a material volume of uninformed, liquidity-motivated trading. Edelen (1999) finds that funds exhibit negative market timing when, and only when, they experience flow. He attributes the negative return performance of open-end mutual funds to the cost of liquidity-motivated trading. Such logic implicitly assumes that fund investors can time the market/styles ahead of fund managers. Only if investor money flows in prior to market/styles ascendancy or flows out prior to market/styles descent will this offset fund managers’ style timing endeavours. Works by Gruber (1996) and Zheng (1999) show some evidence that funds receiving more money subsequently beat the market --- the “smart money” Ph.D. Thesis: Jeffrey Junhua Lu

Cranfield School of Management 212

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effect, but in the aggregate such an effect is weak. Warther (1995) documents a positive relation between flows and subsequent returns in the fund weekly data. Short-term switchers in and out of funds are more likely to attack on no-load funds where they can take advantage of cost-free entry and exit. Hence, I can look at the possible difference in timing activity between load and no-load funds and infer whether fund managers’ timing ability is impaired by investor flows. Out of my 2,791 sample funds, 1,334 are no-load funds. As such, I set up null H130 to test this proposition. H130 : There are no differences in the timing behaviour between load funds and no-load funds. 9.5.2

Factor Loadings on Subgroup of Funds

Before investigating the effects of fund turnover on fund timing activities, I first examine the factor loadings within each fund turnover subgroup. In this study, I focus on the Carhart (1997) four-factor model, which augments the Fama-French three-factor model by a momentum factor. I compute the set of equally weighted monthly return of the fund portfolio which comprises all funds within the same fund turnover subgroup and then use this return as the dependent variable in the above regression.

Table 26 (Page 268)

Table 26 summarises the factor loadings of my two fund portfolios, constructed based on the fund load/no-load. For comparison purposes, I also include the factor loadings of the Russell 3000 Index as a proxy for the general market index. The average no-load fund demonstrates a positive abnormal return of 13 basis points per month (1.56 percent per year), which is significant at the 90 percent confidence level; while the average load fund achieves a positive abnormal return of 7 basis points per month Ph.D. Thesis: Jeffrey Junhua Lu

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(0.84 percent per year), which is not statistically significant. No-load funds underperform load funds by a spread of 6 basis points per month (0.72 percent per year), albeit this is not significant. Therefore, there is no significant difference in alphas between no-load funds and load funds. Moreover, there is also clearly no difference in the factor loadings between no-load funds and load funds. 9.5.3

Style Timing on Subgroup of Funds

Table 27 lists the fraction of funds that have positive and negative timing coefficients and the number of funds that have significantly positive and negative timing coefficients within the no-load and load subgroups. I first examine the results under the Carhart 4-factor TM style timing model. There are more load funds demonstrating significant positive book-to-market timing coefficients (33 percent vs 27 percent), but there are still more load funds demonstrating significant negative momentum timing coefficients (40 percent vs 35 percent), when compared to no-load funds. The results are pretty much the same under the HM model. The load fund group may have more successful book-to-market timers, but this is offset by the fact that this group also has more poor momentum timers. In any cases the percentage differences are not large. The effect of investor flows on fund managers’ style timing performance is thus obscure.

Table 27 (Page 269)

Figure 5 (Page 278)

Table 28 summarises the results of timing aggressiveness based on the Carhart 4-factor style timing model for the two groups of funds. As demonstrated in Figure 5,

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there are no differences on timing aggressiveness between load funds and no-load funds. Thus, the null hypothesis of H13 cannot be rejected. Combined with the results in Table 27, this suggests that investor flows affect funds’ style timing in a limited way, if at all.

Table 28 (Page 271)

9.5.4

Summary

There is no significant difference in alphas between no-load funds and load funds. Moreover, there is also no difference in the factor loadings between no-load funds and load funds. The obscure effect of investor flows on fund managers’ style timing activities suggests that investor flows affect funds’ style timing in a limited way.

9.6. Summary This chapter investigates the style timing abilities of active fund managers within the context of specific fund characteristics. Common knowledge has it that fund characteristics such as size, manager experience, turnover, and investor flows affect fund timing activities. I find that small funds tend to be good timers on the size (big cap/small cap) style and these funds implement timing strategies more aggressively than large funds. Although there is little evidence of better timing abilities by young funds, when compared to their longer established counterparts, these funds tend to implement timing strategies more aggressively. It would appear their managers take higher risk positions in their portfolios in an effort to establish their performance records. High turnover funds implement timing strategies more aggressively than their low turnover counterparts. Most of their timing activities relate to the value/growth style, with a substantially higher percentage of these funds demonstrating timing abilities on this style. On the Ph.D. Thesis: Jeffrey Junhua Lu

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other hand, high turnover funds demonstrate worse or no distinctly different timing abilities compared with low turnover funds for size (big cap/small cap) and (winner/loser) styles. There are few differences in the timing behaviour between load funds and no-load funds, suggesting that investor flows affect funds’ timing activities in a limited way. In general, my findings show that differences in the average style timing ability of funds with different characteristics are too small to have any economic significance, suggesting that style timing ability is fund-specific and is difficult to predict by observable systematic factors. However, differences in average style timing aggressiveness between different fund types are relatively large, suggesting that style timing aggressiveness is affected significantly by fund characteristics. In the final chapter I summarise the findings of this study, discuss its limitations and bring out its principal contributions to the academic literature and investment practice.

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CHAPTER 10 CONCLUSIONS AND LIMITATIONS 10.1. Introduction This study is primarily concerned with the style timing behaviour of US domestic equity funds existing at any time during the period 1992-2002. In undertaking this research, I first conducted a critical review of the institutional background and literature, and then, drawing on this, developed testable hypotheses from my research questions. Appropriate empirical methodologies were then established to test the hypotheses formally adopting both a rational agency and behavioural biases perspective. The first empirical chapter of the thesis, Chapter 6, conducts the traditional market timing tests on my sample funds. Chapter 7 conducts the general style timing tests on the sample funds by implementing my own style timing models which incorporate systematic risk factors unique to equity markets into traditional market timing models. Chapter 8 investigates the style timing ability and activity of active fund managers further in the context of their fund investment objectives and fund performance record. The last empirical chapter of the thesis, chapter 9, explores the effect of fund size, manager experience, turnover, and investor flows on the style timing behaviour of active mutual funds. In this final chapter of my thesis, I first summarise and discuss my main empirical findings in the next section and then discuss some limitations of my research and outline possible future developments of my work. The final section stresses the original contribution of this study to the theory and practice.

10.2. Summary and Discussion Most existing studies relating to the timing behaviour of mutual funds focus on the market timing abilities of fund managers, and find mixed evidence of such skills. Few Ph.D. Thesis: Jeffrey Junhua Lu

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studies have investigated mutual fund factor style timing abilities. Based on a novel empirical timing-ability evaluation framework that combines systematic risk factors and portfolio-specific characteristics, I investigate the specific style timing behaviour of mutual fund managers using a database of 2,791 US mutual funds provided by Morningstar. I find that over the ten-year period of this study (June 1992 to July 2002), the average mutual fund manager demonstrates little ability to time the market in aggregate. In fact, using my empirical factor timing model, I find only 8.3 percent of my funds had significant positive alphas. There is even some weak evidence that supports the assertion that mutual fund managers attempt to implement market timing strategies at the expense of poor stock selection performance. Using my style timing model, on average, my mutual funds are more likely to be successful with respect to book-to-market (value/growth) style timing, and unsuccessful in trying to time size (big cap/small cap) and momentum (winner/loser). These results may be partly due to the institutional factors and transaction costs associated with these timing strategies. Most funds are restricted from taking substantial positions in small-cap stocks and there are relatively higher transaction costs associated with size (big cap/small cap) and momentum (winner/loser) timing strategies when compared to book-to-market (value/growth) timing strategies. There may also be a behavioural explanation which is related to the trading behaviour and preferences of fund managers. Fund managers prefer big-cap stocks to small-cap stocks as safer investments. Also, they tend to sell winners too soon and to hold on to losers too long. Similarly to the results in my aggregate market timing analysis, fund managers also appear to be implementing style timing strategies at the expense of poor stock selection performance. Moreover, implementing a timing strategy with respect to a specific style (such as value/growth) may bear the costs of negative timing with respect to other styles (such as size and momentum). In a word, timing strategies are

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not a free lunch. In further analysis, I divide my sample funds into sub-groups based on their stated investment objectives. Analysis of these different fund categories (aggressive growth, growth, income, equity income and small cap) reveals that growth-oriented funds tend to possess better timing abilities and also implement style timing strategies more aggressively than other funds. Specifically, aggressive growth funds are excellent book-to-market (value/growth) timers without bearing the costs of poor momentum (winner/loser) timing, while growth funds time book-to-market (value/growth) style correctly, but at the expense of negative timing on size (big cap/small cap) and momentum (winner/loser). Equity income funds tend to be good at timing size (big cap/small cap) but be poor at timing momentum (winner/loser). Income funds are bad factor timers, especially with respect to size (big cap/small cap) and momentum (winner/loser) styles. Growth-oriented funds respond to their private information on future factor performance more aggressively than income-oriented funds. I also find that, on average, funds with previous extreme good or bad performance record implement timing strategies more aggressively than those with moderate performance. Funds with middling performance appear to prefer to play safe and seek to maintain their performance, appearing to be less willing to take bets on a factor style, while funds at the two ends of the performance spectrum (stars or dogs) have more incentives to do so. On average, top-performing funds seem to be influenced by the

“house-money”

effect;

bottom-performing

funds

exhibit

the

“trying-to-break-even” effect; funds in the middle are affected by the “endowment” effect. Common knowledge has it that fund characteristics such as size, manager experience, turnover, and investor flows affect fund timing activities. I find that small funds tend to be good timers on the size (big cap/small cap) style and these funds implement timing strategies more aggressively than large funds. Although there is little evidence of better timing abilities by young funds, when compared to their longer established

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counterparts, these funds tend to implement timing strategies more aggressively. It would appear their managers take higher risk positions in their portfolios in an effort to establish their performance records. High turnover funds implement timing strategies more aggressively than their low turnover counterparts. Most of their timing activities relate to the value/growth style, with a substantially higher percentage of these funds demonstrating timing abilities on this style. On the other hand, high turnover funds demonstrate worse or no distinctly different timing abilities compared with low turnover funds for size (big cap/small cap) and (winner/loser) styles. There are few differences in the timing behaviour between load funds and no-load funds, suggesting that investor flows affect funds’ timing activities, if at all, in a limited way. In general, my findings show that differences in the average style timing ability of funds with different characteristics are too small to have any economic significance, suggesting that style timing ability is fund specific and is difficult to predict by observable systematic factors. However, differences in average style timing aggressiveness between different fund types are relatively large, suggesting that style timing aggressiveness is affected significantly by funds characteristics. I conclude that investors in mutual funds need to recognise that fund managers find it very difficult to time their investment strategies to capitalise on market-wide style preferences. However, aggressive growth funds as a class tend to be more able to do this than other fund categories. In addition, funds with more extreme performance history (both good and bad) are likely to trade more actively in an attempt to exploit style timing. Small funds and new funds similarly trade more aggressively despite no evidence of superior timing abilities, presumably in an attempt to establish a success track record. Many of my findings can be explained by behavioural factors relating to fund manager bias and incentive structures discussed in the finance literature.

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10.3. Limitations and Further Work 1. My study currently covers a ten-year period (1992-2002), which begins with a relatively long bull market followed by a relatively short bear market starting in 2000. My reported findings can hence be specific to this period and may not be applicable to other periods. A longer period might be needed to cover several bull and bear markets and to obtain more meaningful and reliable results regarding fund managers’ timing activities under different market conditions. 2. In line with most other studies in the literature, this study uses monthly mutual fund return data to conduct style timing tests. As discussed by Goetzmann, Ingersoll, and Ivkovic (2000), monthly frequency might fail to capture the contribution of a manager’s timing activities to fund returns, because decisions regarding market exposure are likely to be made more frequently than monthly for most funds. Therefore, other mutual fund returns observation frequencies, such as semi-monthly, weekly, or even daily, might yield results different to those I obtain in this study. 3. The study employs the multi-factor regression model to investigate the timing activities of mutual fund managers. A long record of past returns is needed for the factor loadings to be estimated reliably, at least 60 valid monthly net return observations should be included in the timing tests. Hence, short-lived funds are dropped out, which could potentially bias my findings. I thus repeat my main style timing tests with requirements of at least 36 valid monthly net return observations included. The results are quantitatively similar compared to those presented in chapter 7. 4. Also, since all the returns used are equally important in the regression-based timing analysis, the returns earned on the fund some time ago may contain far less information about the fund’s current timing strategies than the most recent returns. A detailed examination of fund actual portfolio holdings could provide a

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timelier and more accurate picture of fund managers’ timing behaviours. However, it is not possible to implement such a detailed examination of fund portfolio holdings and their evolution over time for all the sample funds, given the coverage of this study. 5. Morningstar database has a well known feature --- survivorship bias. The influences of survivorship bias in this study depend on how differently managers of perished funds implement timing strategies or possess timing abilities compared to those of live funds. My results should hence be interpreted with this caveat in mind. However, as mention earlier, I conduct a robustness check by extending the requirements on the length of past return record to 36 valid monthly net return observations for each fund. The results of the general style timing tests are quantitatively similar to those obtained under the original requirements. Therefore, survivorship bias should have limited effects on the style timing test results. 6. Market timing ability can only be accurately measured under the assumptions of highly stylised models. The style timing models employed in my study are derived from traditional market timing models. Traditional market timing models, in addition to their strong assumptions about how managers use their abilities, have taken the view that any information correlated with future market returns is superior information. In other words, they are unconditional models. Therefore, my inferences about fund managers’ style timing activities do not distinguish “style timing” based on public information from “style timing” based on fund managers’ superior private information. Ferson and Schadt (1996) advocate conditional performance evaluation in order to distinguish timing ability that merely reflects publicly available information from timing based on better information. They use a collection of public information variables which are useful for predicting security returns and risks over time. 43 However, these 43

The variables are (1) the lagged level of the one-month Treasury bill yield, (2) the lagged dividend yield of the CRSP value-weighted New York Stock Exchange (NYSE) and American Stock Exchange (AMEX) stock index, (3) a lagged measure of the slope of the term structure, (4) a lagged quality spread in the corporate bond market, and Ph.D. Thesis: Jeffrey Junhua Lu

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information variables may not be suitable for predicting style returns in a subset of the stock market. In the context of style timing, the relevant information variables for each investment style in the market need to be identified. A further study on fund managers’ conditional style timing abilities could be done in the context of public information relevant for the prediction of style returns in the market.

10.4. Implications This thesis explicitly investigates the style timing activities of active fund managers. Many of my findings can be explained by behavioural factors relating to fund manager bias and incentive structures discussed in the finance literature. For example, on average, my mutual funds are more likely to be successful with respect to book-to-market (value/growth) style timing, and unsuccessful in trying to time size (big cap/small cap) and momentum (winner/loser), which might indicate that fund managers prefer big-cap stocks to small-cap stocks as safer investments and tend to sell winners too soon and to hold on to losers too long. Moreover, funds with more extreme performance history (both good and bad) are likely to trade more actively in an attempt to exploit style timing. Small funds and new funds similarly trade more aggressively despite no evidence of superior timing abilities, presumably in an attempt to establish a success track record. All these suggest that fund managers might not make investment decisions regarding style timing strategies merely based on fundamentals and their superior information on style performance. Fund managers might be engaging in timing strategies not because they possess superior forecasting skill, but because they use it as a marketing strategy to distinguish themselves from their competitors by providing a “so-called” extra investment service. Therefore, behavioural biases and incentives structures could affect fund style timing activities in a significant way. Style timing strategies implemented by active fund

(5) a dummy variable for the month of January. Ph.D. Thesis: Jeffrey Junhua Lu

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managers might not be always motivated by an informational advantage nor by “genuine” motives such as hedging, portfolio rebalancing, or liquidity needs. These strategies could be pure noise trades: they do not maximise the welfare of the owner of the fund portfolio. There is a long-standing debate concerning whether price movements and trading in equity market reflect fundamentals or “animal spirits.” On the one hand, there is the belief that participants in markets are “rational,” and the few who are not are quickly eliminated by the natural selection effects of arbitrage. On the other hand, there is the belief that many individuals may not be rational and that there is no necessary tendency for irrationality to disappear in the aggregate. In other words, a market may display aggregate “irrationality,” “fads,” or “herding.” Dow and Gorton (1997) consider a model where portfolio managers trade even though they have no reason to because their clients cannot distinguish “actively doing nothing” from “simply doing nothing.” Portfolio managers who engage in producing information do not always uncover profitable trading opportunities. It can happen that inactivity (i.e. not trading) is the optimal decision because the portfolio manager’s effort at finding mispriced securities did not uncover any. However, it is not easy for the delegated portfolio manager to convince the client/employer that inactivity is his/her best strategy. If the manager is rewarded for not trading, he/she might simply do nothing, no matter whether he/she is a competent manager or not. If this makes it impossible to reward inactivity, and limited liability prevents punishing ex post incorrect decisions, then the optimal contract may induce trading by the portfolio manager which is simply a gamble to produce a satisfactory outcome by chance.

10.5. Contribution to the Theory and Practice The findings of my thesis make the following contributions to the study of the value of active fund management and provide significant insights into the current practice of mutual fund timing strategies: ¾ Providing evidence regarding the validity of the efficient market hypothesis Ph.D. Thesis: Jeffrey Junhua Lu

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The investment behaviour of mutual funds has been the subject of extensive examination in the finance literature. Implementation of timing strategies is often based on the claim of superior information. Indeed, most fund managers often characterise themselves as market timers. Hence, tests on the timing abilities of these fund managers can be viewed as evidence that is relevant to the efficient market hypothesis and thereby provide insights into the understanding of the process of security price determination, because of its potential implications for differential investment information availability in the marketplace44. ¾ Extending extant research on mutual fund timing activities

An empirical timing-activity evaluation framework will be developed to combine systematic risk factors unique to equity markets with timing factors unique to actively managed portfolios. Most existing studies relating to the timing behaviour of mutual fund managers focus on their timing abilities with respect to the whole market. However, few studies have investigated their specific timing abilities within market segments, which are related to such systematic risk factors as size and sector. This study seeks to extend the existent mutual fund literature on market timing behaviour to a broader consideration of style timing strategy. I significantly expand on the work of Bollen and Busse (2001) and Volkman (1999) by combining Carhart’s (1997) systematic risk factors unique to equity markets with timing factors unique to actively managed portfolios. I provide a comprehensive examination of mutual fund factor timing activities that explicitly controls for luck without potential bias from misspecification. This is not because I claim my timing models are correctly specified – they may not be. Rather, my approach, which uses a bootstrap statistical approach, is robust to possible misspecification. ¾ A better understanding of the risk-taking behaviour of fund managers under

different market conditions and in the light of differential managerial incentives Active fund managers adopt different risk positions in line with changes in market 44 Not all information is ready for all investors in sub-segments of the market. Some investors might be in a better position to possess information in an efficient and timely way while others might not.

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conditions. There are some systematic factors, such as performance record, fund size, and fund age, etc., which can influence the managerial incentives of fund managers, and which in turn, affect their timing behaviour. Hence, the fund manager’s attitude towards risk needs to be understood both in the context of a dynamic market environment as well as the managerial incentives to which he/she responds. I manage to link fund manager timing behaviour to specific systematic factors, such as performance record and investment policy etc., and examine the influences of these systematic factors on fund timing activities. ¾ Provide an original contribution on the value of active fund management

Investigation of fund timing activities is important for potential mutual fund clients to help them allocate their funds efficiently, since fund investors can assess the timing abilities of the fund manager and essentially “undo” the timing aggressiveness of the manager by investing more or less of their wealth in the fund or by trading in other accounts. Such research is also important for managers to help them evaluate the effectiveness of their timing strategies and set appropriate management fees. A valid question is whether any timing strategies based on superior forecasting skills can generate a sufficient increase in returns to offset the associated information and transaction costs, as well as the management fees charged. Moreover, such information is important for regulators to formulate policy concerning the operations of the market place.

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APPENDIX 1 TABLES AND FIGURES

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Table 1 Sample Fund Summary Statistics

Panel A: Time-series of annual cross-sectional averages from June 1992 to June 2002. Raw TNA Fund Expense Volatility Turnover Age Num Return ($ Flow Ratio (%/year) (%/year) (years) (%/year) Millions) (%/year) (%/year)

By year-end

a

1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002

949 1272 1615 1979 2462 2791 2791 2756 2709 2632 2540

9.26% 11.93% -1.10% 28.85% 18.11% 24.36% 14.42% 26.70% -1.22% -9.87% -11.49%

5.81% 8.35% 5.24% 11.24% 8.49% 10.02% 15.51% 29.67% 15.16% 14.76% 8.74%

469.69 417.79 370.04 450.75 495.23 597.53 755.56 967.77 947.22 854.90 786.34

-1.71% 12.20% 12.38% 6.38% 12.07% 9.29% 7.39% -6.61% 2.34% 3.51% 2.71%

1.30 1.30 1.34 1.38 1.39 1.38 1.37 1.39 1.37 1.39 1.43

74.00 74.00 76.00 82.00 90.00 85.00 87.00 90.00 100.00 95.00 90.00

10.65 8.87 7.85 7.34 6.66 6.98 7.97 8.93 9.92 10.95 11.52

Mean Median Std.

2227 2540 667

10.00% 12.09% 646.62 11.93% 10.02% 597.53 14.27% 6.83% 221.84

5.45% 6.38% 6.12%

1.37 1.38 0.04

85.73 87.00 8.55

8.88 8.87 1.68

Variable definitions

Raw return Volatility TNA Funds flow

= = = =

Expense ratio

=

Turnover

=

Age

=

annualised fund net return annualised standard deviation of fund net return total net assets net growth in fund assets beyond reinvested dividends, which reflects the percentage growth of a fund in excess of the growth that would have occurred had no new funds flowed in and had all dividends been reinvested total annual management and administrative expenses divided by average TNA the percentage of the value of fund assets that the fund trades during a year the number of years since the inception of the fund

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Table 1 cont. Sample Fund Summary Statistics

Panel B: Time-series average of annual cross-sectional averages by fund category Raw Fund Expense Volatility TNA Turnover Return Flow Ratio Age (years) (%/year) ($ millions) (%/year) (%/year) (%/year) (%/year)

By fund category

Num

Aggressive Growth Equity Income Growth Growth and Income Small Company b Variable definitions

131 180 1326

10.59% 9.28% 9.75%

28.78% 13.77% 20.94%

477.96 508.84 558.95

6.39% 4.39% 4.88%

1.60% 1.29% 1.42%

136.00% 67.00% 97.00%

7.91 7.29 7.89

627

9.66%

16.12%

862.64

6.01%

1.24%

65.00%

9.39

527

10.91%

21.39%

242.86

3.11%

1.51%

98.00%

5.89

Raw return Volatility TNA Funds flow

Expense ratio Turnover Age

= annualised fund net return = annualised standard deviation of fund net return = total net assets = net growth in fund assets beyond reinvested dividends, which reflects the percentage growth of a fund in excess of the growth that would have occurred had no new funds flowed in and had all dividends been reinvested = total annual management and administrative expenses divided by average TNA = the percentage of the value of fund assets that the fund trades during a year = the number of years since the inception of the fund

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Table 1 cont. Sample Fund Summary Statistics

Panel C: Time-series average of annual cross-sectional averages by fund category By fund category

Percentage Fload with load

Dload

Rload

b_1

Maxload

Aggressive Growth Equity Income Growth Growth and Income Small Company

53.44% 53.33% 53.17% 52.15% 49.15%

1.22 1.39 1.39 1.34 1.08

0.94 0.86 0.84 0.84 0.76

0.05 0.03 0.04 0.03 0.10

0.30 0.25 0.25 0.24 0.23

2.22 2.28 2.27 2.21 1.93

Total c Variable definitions

52%

1.31

0.83

0.05

0.25

2.19

Percentage with load Fload Dload Rload b_1 Maxload

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= the percentage of funds with load = front load as a percentage of the investment = deferred load as a percentage of the investment = redemption fee as a percentage of the investment = 12B-1 fee as a percentage of the investment = the total of maximum front-end, rear-end, and deferred sales charges as a percentage of the investment

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Table 1 cont. Sample Fund Summary Statistics

Panel D: Cross sectional averages of fund characteristics by fund status

By fund status

Num

2350 441

Live Dead c

TNA Fund Flow ($millions) (%/year) 645.36 105.69

6.07% -1.97%

Expense Ratio (%/year)

Turnover (%/year)

Age

1.39 1.46

90 88

11.65 9.11

Variable definitions

TNA Fund flow

Expense ratio Turnover Age

= total net assets = net growth in fund assets beyond reinvested dividends, which reflects the percentage growth of a fund in excess of the growth that would have occured had no new funds flowed in and had all dividends been reinvested = total annual management and administrative expenses divided by average TNA = the percentage of the value of fund assets that the fund trades during a year = the number of years since the inception of the fund

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Table 1 cont. Sample Fund Summary Statistics

Panel E: Sample fund monthly return summary statistics Listed are average summary statistics of the sample funds and the factor indices (including market index, SMB index, HML index, momentum index). The sample period is June, 1992 to June, 2002, a total of 121 trading months. Mean (μ ) and standard deviation ( σ ) are sample estimates. Skewness (S) is computed as S=

1 σ 3T

T

∑ (R − μ )

3

t

t =1

and excess kurtosis (K) is computed as K=

1 σ 4T

T

∑ (R − μ ) t =1

4

t

−3

χ2 The Jarque-Bera (JB) test for normality is distributed by 2

under the null and is given

T ⎡ 2 K2 ⎤ JB = ⎢ S + ⎥ 6⎣ 4 ⎦

μ

σ

S

K

JB − Test

Mutual Funds

0.895%

5.520%

-0.436

1.289

20.165

Factor Indices Market SMB HML Momentum

0.601% 0.231% 0.144% 1.258%

4.296% 3.709% 4.537% 5.144%

-0.804 0.463 -0.820 -0.671

1.112 1.780 5.304 6.256

19.280 20.303 155.374 206.366

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Table 2 Bootstrap Analysis of Market Timing Coefficients

Listed are the fractions, mean timing coefficients, and mean intercept of 2,791 mutual funds that exhibit positive/negative (+/-) and significant positive/significant negative (++/--) market timing abilities. The sample period is June 1992 to June 2002, a total of 121 trading months. The intercepts are converted to annualized percentages. Timing ability is measured using the Carhart (1997) four-factor, Fama-French three-factor, and CAPM Treynor and Mazuy (1966; TM) and Henriksson and Merton (1981; HM) market timing models. Significance is at the five percent level (two-tailed) and is based on bootstrap standard errors. Panel A shows the results from the mutual fund sample, and Panel B shows the results from the synthetic control sample. A synthetic fund is constructed under the null hypothesis of no timing ability for each fund in the sample by forming an index portfolio to match the fund's investment style. Panel C shows the fraction of funds for which the difference between the fund's timing coefficient and the timing coefficient of the corresponding synthetic fund is positive/negative (+/-) and significantly positive/significantly negative (++/--). Panel A: Mutual Fund Sample Carhart four-factor +

+

Fama-French three-factor

CAPM

+

-

+

-

++

--

+

-

++

--

0.568 0.468

Fraction (%) TM HM

0.508 0.508 0.667 0.667

0.432 0.532

0.568 0.468

0.525 0.680

0.475 0.320

0.013 0.024

0.009 0.004

0.432 0.532

0.011 0.015

0.028 0.013

Timing coefficients TM HM

0.521 0.521 0.124 0.124

0.488 0.122

-0.988 -0.219

0.529 0.129

-0.450 -0.113

2.125 0.377

-2.610 -0.776

0.488 -0.988 2.070 0.122 -0.219 0.336

-2.711 -0.639

Intercept TM HM

0.321 0.321 0.538 -0.739 -0.739 -0.466

5.352 7.444

-0.359 -1.953

2.314 3.707

-4.507 8.922 0.538 5.352 -3.444 11.175 -6.824 15.810 -0.466 7.444 -4.973 17.331

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Table 2 cont. Bootstrap Analysis of Market Timing Coefficients

Panel B: Synthetic Control Sample Carhart four-factor Fama-French three-factor + ++ -+ ++ --

+

CAPM ++

--

Fraction (%) TM HM

0.503 0.497 0.566 0.434

0.005 0.024

0.007 0.006

0.503 0.562

0.497 0.438

0.005 0.021

0.008 0.005

0.234 0.272

0.008 0.012

0.048 0.027

Timing coefficients TM HM

0.769 -0.648 2.110 0.183 -0.151 0.488

-2.302 -0.538

0.738 0.178

-0.654 -0.154

2.075 0.466

-2.277 -0.551

0.211 -0.257 2.829 0.193 -0.263 0.684

-2.561 -0.606

Intercept TM HM

0.590 3.568 -1.474 8.369 1.673 -1.339 4.941 -5.963 14.438 -0.663

3.867 5.721

-0.011 8.845 2.385 7.017 -0.143 12.404 -5.268 16.337 -0.372 10.003 -8.151 18.520

Panel C: Differences in Timing Coefficients Carhart four-factor Fama-French three-factor + ++ -+ ++ -Fraction (%) TM HM

0.509 0.491 0.518 0.482

0.011 0.010

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0.009 0.008

0.530 0.532

0.470 0.468

0.010 0.011

0.009 0.008

+ 0.620 0.634

0.766 0.728

CAPM ++ 0.380 0.366

0.047 0.035

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Can Fund Managers Successfully Time Their Investment Styles?

Table 3 Correlation Analysis between Market Timing and Selectivity

This table illustrates the correlation between a fund’s market timing coefficients, which are based on the Carhart (1997) four-factor, Fama-French three-factor, and CAPM Treynor and Mazuy (1966; TM) and Henriksson and Merton (1981; HM) market timing models. The relevant timing coefficients and selectivity intercepts are obtained from the market timing models. The correlation is tested based on both the Pearson measure and the Spearman rank measure. Significance is at the one percent level (two-tailed). Correlation Estimates Between Timing Coefficients and Selectivity Intercepts

Percentage of Funds with Significant Alpha (at the 5% level)

Person Correlation

Spearman Rank Correlation

Positive Timing and Positive Selectivity

Negative Timing and Positive Selectivity

Positive Timing and Negative Selectivity

Negative Timing and Negative Selectivity

TM

-0.344

-0.378

2.47%

8.31%

1.47%

0.36%

Sig. (2-tailed) HM Sig. (2-tailed)

0.000

0.000

-0.531 0.000

-0.573 0.000

TM

-0.389

-0.430

Sig. (2-tailed) HM Sig. (2-tailed)

0.000

0.000

-0.518 0.000

Market Timing Model

Carhart four-factor model

Fama-French three-factor model

CAPM

TM Sig. (2-tailed) HM Sig. (2-tailed)

Ph.D. Thesis: Jeffrey Junhua Lu

1.61%

3.37%

1.83%

0.04%

3.65%

10.82%

1.29%

0.39%

-0.538 0.000

1.76%

2.97%

1.00%

0.04%

-0.408 0.000

-0.422 0.000

1.68%

10.07%

0.93%

0.36%

-0.627 0.000

-0.637 0.000

0.14%

3.40%

0.72%

0.14%

Cranfield School of Management 235

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Table 4 Joint Tests of Style Timing Coefficients

Listed are the fractions, mean timing coefficients, and mean intercept of 2,791 mutual funds that exhibit significant style timing coefficients. The sample period is June 1992 to June 2002, a total of 121 trading months. The intercepts are converted to annualized percentages. Timing coefficients are measured using the Carhart (1997) four-factor, Fama-French three-factor, and CAPM Treynor and Mazuy (1966; TM) and Henriksson and Merton (1981; HM) market timing models. Significance is at the five percent level (two-tailed) and is based on bootstrap standard errors. Panel A shows the results for the mutual fund sample, and Panel B shows the results from the synthetic control sample. A synthetic fund is constructed under the null hypothesis of no timing ability for each fund in the sample by forming an index portfolio to match the fund’s style. Panel A: Mutual Fund Sample 4 Factors - TM

4 Factors - HM

3 Factors - TM

3 Factors - HM

Fraction (%)

44.00

22.39

11.68

9.96

Timing coefficients Market Size B/M Momentum

0.178 -0.072 1.048 -0.727

0.046 -0.086 0.307 -0.139

-0.038 -0.931 1.146

-0.030 -0.194 0.340

Intercept

0.253

-1.289

0.295

-0.569

Panel B: Synthetic Control Sample 4 Factors - TM

4 Factors - HM

3 Factors - TM

3 Factors - HM

Fraction (%)

12.11

3.05

2.94

0.75

Timing coefficients Market Size B/M Momentum

-0.180 1.283 -0.092 1.139

-0.111 0.076 -0.048 0.274

-0.848 2.688 0.166

-0.162 0.215 -0.071

Intercept

1.368

0.913

-1.683

1.954

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Table 5 Bootstrap Analysis of Style Timing Coefficients

Listed are the fractions, mean timing coefficients, and mean intercept of 2,791 mutual funds that exhibit positive/negative (+/-) and significant positive/significant negative (++/--) style timing abilities. The sample period is June 1992 to June 2002, a total of 121 trading months. The intercepts are converted to annualised percentages. Timing ability is measured using the Carhart (1997) four-factor Treynor and Mazuy (1966; TM) and Henriksson and Merton (1981; HM) style timing models. Significance is at the five percent level (two-tailed) and is based on bootstrap standard errors. Panel A shows the results from the mutual fund sample, and Panel B shows the results from the synthetic control sample. A synthetic fund is constructed under the null hypothesis of no timing ability for each fund in the sample by forming an index portfolio to match the fund’s style. Panel C shows the fraction of funds for which the difference between the fund's timing coefficient and the timing coefficient of the corresponding synthetic fund is positive/negative (+/-) and significantly positive/significantly negative (++/--). Panel A: Mutual Fund Sample TM

HM

+

-

++

--

+

-

++

--

Market

58.366

41.634

2.221

1.182

64.063

35.937

4.694

0.932

Size

51.630

48.370

5.589

5.697

45.038

54.962

1.935

4.085

B/M

76.890

23.110

30.061

1.935

73.558

26.442

24.149

1.863

Momentum

18.739

81.261

0.752

37.513

22.537

77.463

0.502

10.928

Market

0.540

-0.458

1.774

-2.353

0.152

-0.130

0.354

-0.721

Size

1.046

-1.216

2.955

-3.150

0.148

-0.200

0.526

-0.533

B/M

1.166

-0.712

2.065

-2.772

0.291

-0.139

0.559

-0.417

Momentum

0.580

-0.782

1.917

-1.133

0.110

-0.172

0.380

-0.361

Market

-0.317

2.208

-2.634

6.986

-1.669

1.713

-4.215

13.517

Size

-0.228

1.756

-3.347

3.101

-3.072

1.717

-7.704

5.693

B/M

0.633

1.040

0.099

1.510

-0.807

0.490

-1.989

1.533

Momentum

1.329

0.589

-0.148

-0.324

0.056

-0.617

-1.159

-4.731

Fraction (%)

Timing coefficients

Intercept

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Table 5 cont. Bootstrap Analysis of Style Timing Coefficients Panel B: Synthetic Control Sample TM

HM

+

-

++

--

+

-

++

--

Market

47.832

52.168

0.466

0.788

49.445

50.555

1.039

0.717

Size

64.601

35.399

7.739

0.824

57.542

42.458

1.218

0.860

B/M

49.731

50.269

1.218

2.902

48.836

51.164

1.111

1.147

Momentum

51.415

48.585

8.563

4.228

62.307

37.693

3.511

0.358

Market

0.670

-0.692

1.765

-2.128

0.178

-0.193

0.479

-0.635

Size

1.668

-1.193

3.956

-4.337

0.255

-0.215

0.753

-0.794

B/M

0.638

-0.995

1.745

-4.564

0.203

-0.220

0.523

-0.689

Momentum

1.125

-0.576

2.594

-1.336

0.244

-0.132

0.768

-0.418

Market

-0.134

2.083

-2.386

4.873

-2.097

2.333

-6.869

6.063

Size

-0.516

3.870

-2.582

7.211

-2.633

3.964

-4.621

12.860

B/M

0.296

1.735

0.967

6.435

-1.656

1.841

-0.439

5.628

Momentum

1.768

0.228

4.042

-1.158

0.575

-0.629

3.334

-2.161

Fraction (%)

Timing coefficients

Intercept

Panel C: Differences in Timing Coefficients TM

HM

+

-

++

--

+

-

++

--

Market

57.184

42.816

1.290

0.430

60.050

39.950

1.218

0.860

Size

38.552

61.448

1.899

8.241

38.552

61.448

0.860

2.042

B/M

73.737

26.263

12.110

0.537

68.613

31.387

8.742

0.609

Momentum

26.693

73.307

1.218

18.846

24.257

75.743

0.179

7.023

Fraction (%)

Ph.D. Thesis: Jeffrey Junhua Lu

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Table 6 Summary Statistics for Intercepts and Style Timing Coefficients

Listed are the cross-sectional means and standard errors of intercepts and timing coefficients of 2,791 mutual funds. The sample period is June 1992 to June 2002, a total of 121 trading months. The intercepts are converted to annualised percentages. Timing coefficients is obtained from the Carhart (1997) four-factor and Fama-French three-factor Treynor and Mazuy (1966; TM) and Henriksson and Merton (1981; HM) style timing models. Panel A shows the results from the mutual fund sample, and Panel B shows the results from the synthetic control sample. A synthetic fund is constructed under the null hypothesis of no timing ability for each fund in the sample by forming an index portfolio to match the fund's style. Panel A: Mutual Fund Sample Carhart 4-factor Style Timing TM

Fama-French 3-factor Style Timing

HM

TM

HM

Means

Std

Means

Std

Means

Std

Means

Std

0.727

0.003

-0.466

0.005

1.767

0.003

1.308

0.005

Market

0.124

0.705

0.051

0.177

-0.036

0.734

0.013

0.178

Size

-0.048

1.097

-0.043

0.211

-0.402

1.109

-0.115

0.205

B/M

0.732

0.686

0.178

0.172

0.363

0.599

0.125

0.151

Momentum

-0.527

0.487

-0.109

0.155

Intercept (%) Timing coefficients

Panel B: Synthetic Control Sample Carhart 4-factor Style Timing TM

Fama-French 3-factor Style Timing

HM

TM

HM

Means

Std

Means

Std

Means

Std

Means

Std

1.017

0.006

0.120

0.009

0.591

0.005

-0.899

0.009

Market

-0.040

1.205

-0.010

0.323

0.000

1.293

0.019

0.314

Size

0.656

1.861

0.055

0.386

0.889

1.940

0.109

0.362

B/M

-0.183

1.154

-0.013

0.313

-0.048

1.042

0.032

0.266

Momentum

0.299

0.813

0.102

0.281

Intercept (%) Timing coefficients

Ph.D. Thesis: Jeffrey Junhua Lu

Cranfield School of Management 239

Can Fund Managers Successfully Time Their Investment Styles?

Table 7 Linear Regression Explaining the Relationship between Intercepts and Timing Coefficients

Listed are the coefficient and t-statistics obtained from the cross-sectional regression of 2,791 mutual funds, in which the intercepts are regressed on the timing coefficients for each timing style factor and for each timing model respectively. The intercepts and the timing coefficients are obtained from the Carhart (1997) four-factor and Fama-French three-factor Treynor and Mazuy (1966; TM) and Henriksson and Merton (1981; HM) style timing models. The sample period is June 1992 to June 2002, a total of 121 trading months.

Panle A:

Carhart 4-factor Style Timing Model

TM

HM

Coefficient t-stat R Square F-value

Coefficient t-stat R Square F-value

Timing coefficients Market

-0.304

-16.828

0.092

283.171

-0.401

-23.138

0.161

535.379

Size

-0.271

-14.843

0.073

220.321

-0.403

-23.107

0.164

533.947

B/M

-0.068

-3.573

0.005

12.770

-0.147

-7.828

0.021

61.280

Momentum

0.040

2.108

0.002

4.443

0.068

3.595

0.005

12.923

Panle B:

Fama-French 3-factor Style Timing

TM

HM

Coefficient t-stat R Square F-value

Coefficient t-stat R Square F-value

Timing coefficients Market

-0.358

-20.233

0.128

409.392

-0.297

-16.433

0.088

270.034

Size

-0.251

-13.715

0.063

188.097

-0.476

-28.595

0.227

817.672

B/M

-0.11

-5.831

0.012

33.995

-0.169

-9.054

0.029

81.98

Ph.D. Thesis: Jeffrey Junhua Lu

Cranfield School of Management 240

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Table 8 Correlation Coefficients Explaining the Relationships between Different Timing Coefficients

Listed are the Pearson (parametric) correlation coefficients and the Spearman ρ (non-parametric) correlation coefficients between different style timing coefficients for 2,791 mutual funds. The timing coefficients are obtained from the Carhart (1997) four-factor Treynor and Mazuy (1966; TM) and Henriksson and Merton (1981; HM) style timing models. The sample period is June 1992 to June 2002, a total of 121 trading months. Panel A: Timing Styles

Timing Model

Size

TM HM

BM

TM HM

Pearson Correlation Market

TM

0.011

Sig. (2-tailed)

0.549

Correlation coefficient

0.072

Sig. (2-tailed)

0.000

Correlation coefficient

0.009

-0.460

Sig. (2-tailed)

0.640

0.000

-0.163

-0.398

0.000

0.000

-0.165

-0.153

-0.473

0.000

0.000

0.000

-0.270

-0.045

-0.480

0.000

0.017

0.000

Correlation coefficient

Correlation coefficient Sig. (2-tailed)

HM

Correlation coefficient Sig. (2-tailed)

Ph.D. Thesis: Jeffrey Junhua Lu

BM

Correlation coefficient

Sig. (2-tailed) Momentum

Size

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Table 8 cont. Correlation Coefficients Explaining the Relationships between Different Timing Coefficients Panel B: Timing Styles

Timing Model

Size

TM HM

BM

TM HM

Spearman

ρ Correlation Market

TM

0.021

Sig. (2-tailed)

0.265

Correlation coefficient

0.062

Sig. (2-tailed)

0.001

Correlation coefficient

0.039

-0.459

Sig. (2-tailed)

0.040

0.000

-0.234

-0.325

0.000

0.000

-0.216

-0.182

-0.405

0.000

0.000

0.000

-0.275

-0.008

-0.407

0.000

0.062

0.000

Correlation coefficient

Correlation coefficient Sig. (2-tailed)

HM

Correlation coefficient Sig. (2-tailed)

Ph.D. Thesis: Jeffrey Junhua Lu

BM

Correlation coefficient

Sig. (2-tailed) Momentum

Size

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Table 9 Factor Loadings on Fund Sub-group Formed According to Investment Objectives

Sample mutual funds are grouped into five objective portfolios based on Morningstar “investment objectives”: categories are aggressive growth, growth, growth and income, equity income, and small companies. The portfolios are equally reweighted monthly so the weights are readjusted whenever a fund disappears. Market, Size, HML, and Momentum are Carhart’s (1997) market proxy and factor-mimicking portfolios for size, book-to-market, and momentum equity. Alpha is the intercept of the Model. The t-statistics are in parentheses. Fund Objectives

Number of Funds

Alpha RMRF

SMB HML

MOM

R-square

Aggressive Growth

131

0.11% (0.711)

1.088 0.464 -0.298 (28.156) (11.216) (-5.939)

0.036 (0.979)

0.950

Equity Income

180

0.10% (1.020)

0.818 -0.084 0.321 (30.526) (-2.924) (9.226)

0.071 (2.812)

0.908

Growth

1326

0.11% (1.550)

0.999 (53.224)

0.119 -0.044 (5.897) (-1.791)

0.004 (0.232)

0.977

Growth and Income

627

0.16% (2.627)

0.914 -0.089 0.165 (57.841) (-5.256) (8.044)

0.001 (0.029)

0.976

Small Company

527

-0.01% 1.004 0.709 0.084 (-0.072) (28.265) (18.619) (1.831)

0.127 (3.785)

0.942

Total

2791

0.10% (1.353)

0.183 0.040 (9.215) (1.677)

0.032 (1.810)

0.975

0.08% 0.991 -0.066 0.040 (2.794) (139.082) (-8.672) (4.3600

-0.010 (-1.433)

0.996

Russell 3000

Ph.D. Thesis: Jeffrey Junhua Lu

0.973 (52.441)

Cranfield School of Management 243

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Table 10 Style Timing on Fund Sub-group formed According to Investment Objectives

Listed are the fractions, mean timing coefficients, and mean intercept of 2,791 mutual funds that exhibit positive/negative (+/-) and significant positive/significant negative (++/--) style timing abilities. Sample mutual funds are grouped into objective sub-groups based on Morningstar “investment objectives”: categories are aggressive growth, growth, growth and income, equity income, and small companies. The sample period is June 1992 to June 2002, a total of 121 trading months. The intercepts are converted to annualized percentages. Timing ability is measured using the Carhart (1997) four-factor Treynor and Mazuy (1966; TM) and Henriksson and Merton (1981; HM) style timing models. Significance is at the five percent level (two-tailed) and is based on bootstrap standard errors. Each panel shows the results for the relevant fund group. Panel A: Aggressive Growth TM +

-

HM ++

--

+

-

++

--

Fraction (%) Market

60.305

39.695

3.053

3.817

49.618

50.382

1.527

3.817

Size

23.664

76.336

3.817 14.504

25.191

74.809

1.527

8.397

B/M

86.260

13.740

3.053

87.786

12.214

41.985

5.344

Momentum

29.008

70.992

5.344 20.611

32.824

67.176

3.053

8.121

Market

0.680

-1.178

1.743

-6.780

0.181

-0.266

0.347

-1.290

Size

1.643

-2.085

4.382

-4.600

0.229

-0.334

0.268

-0.702

B/M

2.144

-0.942

2.479

-0.913

0.499

-0.262

0.677

-0.267

Momentum

0.938

-0.853

1.353

-1.384

0.160

-0.200

0.071

-0.032

Market

-1.826

4.144

-1.626

2.546

-5.222

4.478

Size

-0.001

0.663

-8.357

5.250

-3.354

0.555

B/M

0.342

1.537

-0.230

-3.183

-0.921

3.054

Momentum

1.135

0.249

-3.858

0.488

2.167

-1.697

53.435

Timing coefficients

Intercept

Ph.D. Thesis: Jeffrey Junhua Lu

-7.799 20.653 -10.307

8.748

-1.414 12.694 -7.221

7.598

Cranfield School of Management 244

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Table 10 cont. Panel B: Equity Income TM + Fraction (%) Market Size B/M Momentum

-

HM ++

--

+

-

++

--

61.667 77.222 48.333 10.000

38.333 22.778 51.667 90.000

2.778 11.111 2.778 0.000

0.000 2.222 3.889 55.000

80.556 45.000 43.889 16.111

19.444 55.000 56.111 83.889

6.111 0.000 2.778 0.000

0.000 4.444 4.444 15.000

Timing coefficients Market Size B/M Momentum

0.440 1.090 0.438 0.557

-0.373 -0.653 -0.500 -0.744

0.867 1.891 0.905 0.000

0.000 -2.376 -0.822 -0.947

0.146 0.162 0.097 0.079

-0.087 -0.122 -0.119 -0.162

0.265 0.000 0.271 0.000

0.000 -0.427 -0.216 -0.258

Intercept Market Size B/M Momentum

0.501 1.163 1.845 2.224

4.088 4.266 1.879 1.822

1.575 0.212 1.933 2.897

0.263 13.622 0.606 1.881

0.923 -0.439 0.985 0.612

5.949 3.820 2.591 2.129

0.682 6.053 5.788 6.053

-1.249 11.203 -0.548 1.952

Panel C: Growth TM + Fraction (%) Market Size B/M Momentum

-

HM ++

--

+

-

++

--

58.673 45.023 81.900 21.795

41.327 54.977 18.100 78.205

2.564 5.204 37.858 0.603

1.207 7.466 2.036 31.900

60.709 44.796 80.166 23.002

39.291 55.204 19.834 76.998

4.902 1.735 32.428 0.603

0.754 4.751 1.282 11.991

Timing coefficients Market Size B/M Momentum

0.544 1.052 1.272 0.480

-0.447 -1.194 -0.730 -0.765

1.951 2.790 2.016 2.153

-1.730 -2.850 -2.879 -1.169

0.150 0.148 0.325 0.108

-0.125 -0.194 -0.141 -0.179

0.363 0.454 0.549 0.391

-0.512 -0.500 -0.458 -0.365

Intercept Market Size B/M Momentum

-0.261 -0.863 0.641 1.502

1.974 1.917 0.731 0.423

-4.481 -3.607 0.314 -1.543

4.247 1.794 -1.435 0.049

-2.204 -3.675 -1.261 -0.412

0.890 1.222 0.065 -1.174

-6.490 -6.159 -2.288 -1.742

9.695 3.766 1.799 -2.363

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Table 10 cont.

+ Fraction (%) Market Size B/M Momentum

Panel D: Growth and Income TM ++ --

HM +

-

++

--

53.429 66.667 65.869 18.979

46.571 33.333 34.131 81.021

2.552 5.742 8.931 0.797

2.233 1.754 1.754 37.480

69.856 52.632 60.447 24.561

30.144 47.368 39.553 75.439

6.539 2.392 6.699 0.638

0.797 1.914 3.030 7.815

Timing coefficients Market Size B/M Momentum

0.430 0.665 0.414 0.345

-0.289 -0.603 -0.473 -0.525

1.128 2.321 1.120 0.427

-0.981 -1.067 -2.446 -0.772

0.128 0.095 0.101 0.073

-0.068 -0.128 -0.118 -0.103

0.300 0.340 0.306 0.144

-0.173 -0.281 -0.309 -0.212

Intercept Market Size B/M Momentum

1.207 1.804 2.129 1.987

3.154 2.723 2.072 2.138

1.639 -1.790 1.164 3.812

4.889 3.775 0.042 1.533

0.842 0.009 1.613 1.365

3.006 3.159 1.303 1.531

-0.341 -3.533 -1.385 1.023

3.932 6.015 -0.134 0.068

+

Panel E: Small Company TM ++ --

Fraction (%) Market Size B/M Momentum

HM +

-

++

--

61.860 48.577 84.820 11.195

38.140 51.423 15.180 88.805

1.518 5.882 39.469 0.759

0.380 5.503 1.898 50.095

63.567 41.556 79.127 18.596

36.433 58.444 20.873 81.404

3.226 3.416 27.324 0.380

1.898 4.175 1.139 14.042

Timing coefficients Market Size B/M Momentum

0.642 1.558 1.495 1.316

-0.575 -1.511 -1.492 -1.098

1.897 3.946 2.285 1.741

-0.945 -3.718 -3.760 -1.424

0.185 0.210 0.357 0.159

-0.167 -0.269 -0.178 -0.232

0.437 0.650 0.616 0.362

-0.613 -0.633 -0.580 -0.466

Intercept Market Size B/M Momentum

-1.905 -2.779 -0.908 -0.963

0.357 0.614 -1.822 -1.058

-3.264 -5.118 -0.657 5.620

-3.740 4.266 -1.750 -0.867

-4.009 -6.857 -2.122 -1.602

0.998 -5.754 1.219 -11.113 -2.553 -1.739 -2.351 -13.462

13.673 6.369 -4.133 -0.476

Ph.D. Thesis: Jeffrey Junhua Lu

Cranfield School of Management 246

Can Fund Managers Successfully Time Their Investment Styles?

Table 11 Average Style Timing Coefficients within Fund Objective Sub-groups

This table summarises the cross-sectional average estimates of fund style timing coefficients within sub-groups of mutual funds derived from Carhart 4-factor Treynor and Mazuy (1966; TM) and Henriksson and Merton (1981; HM) factor timing models. Sample mutual funds are grouped into objective sub-groups based on Morningstar “investment objectives”: categories are aggressive growth, growth, growth and income, equity income, and small companies. The sample period is June 1992 to June 2002, a total of 121 trading months. The standard deviations are in parentheses.

Objectives Aggressive Growth

TM HM

Equity Income

TM HM

Growth

TM HM

Growth and Income

TM HM

Small Company

TM HM

Ph.D. Thesis: Jeffrey Junhua Lu

Market

Size

B/M

Momentum

-0.057 (1.913) -0.044 (0.411)

-1.203 (2.586) -0.192 (0.337)

1.720 (1.581) 0.406 (0.375)

-0.334 (1.233) -0.082 (0.234)

0.128 (0.629) 0.101 (0.147)

0.693 (1.577) 0.006 (0.370)

-0.046 (0.760) -0.024 (0.191)

-0.614 (0.659) -0.123 (0.163)

0.134 (0.727) 0.042 (0.184)

-0.183 (1.530) -0.041 (0.238)

0.910 (1.332) 0.233 (0.318)

-0.494 (0.804) -0.113 (0.187)

0.095 (0.499) 0.069 (0.130)

0.242 (0.973) -0.011 (0.152)

0.112 (0.728) 0.014 (0.154)

-0.360 (0.554) -0.060 (0.109)

0.178 (0.817) 0.057 (0.231)

-0.020 (2.081) -0.070 (0.314)

1.042 (1.560) 0.245 (0.331)

-0.828 (1.083) -0.159 (0.231)

Cranfield School of Management 247

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Table 12 Factor Loadings on Fund Sub-group Formed on Fund Performance

This table summarises the fund factor loadings for sub-groups of mutual funds derived from Carhart 4-factor model. Sample mutual funds are grouped into objective portfolios based on their Morningstar five star ranking. Portfolios are equally reweighted monthly so weights are readjusted whenever a fund disappears. I use a fund’s Morningstar rating at the beginning of its entire performance history during the sample period. Since Morningstar does not give star rating to those funds that have been in existence in less than three years, total sample size is 2,286 funds. The sample period is June 1992 to June 2002, a total of 121 trading months. Morningstar awards mutual funds one to five stars according to their past investment performance. The highest ranking is five stars, and the lowest ranking is one. The Russell 3000 Index serves as a proxy for the general market index. The t-statistics are in parentheses.

5 Star

Number of Funds 323

4 Star

588

3 Star

698

2 Star

505

1 Star

172

No. Rating.

505

Fund Ranking

Russell 3000

5 Star – 1 Star spread 5 Star – 4 Star spread 5 Star – 3 Star spread 3 Star – 1 Star spread

Ph.D. Thesis: Jeffrey Junhua Lu

Alpha

Market

Size

B/M

Momentum R-square

0.32% (3.616) 0.18% (3.247) 0.11% (1.525) 0.04% (0.496) -0.12% (-0.991) -0.04% (-0.596) 0.08% (2.794)

1.034 (44.122) 0.963 (65.322) 0.944 (50.777) 0.998 (42.525) 0.977 (32.195) 0.958 (50.685) 0.991 (139.082)

0.231 (9.198) 0.061 (3.882) 0.104 (5.231) 0.285 (11.335) 0.514 (15.795) 0.189 (9.323) -0.066 (-8.672)

-0.112 (-3.689) 0.035 (1.809) 0.111 (4.620) 0.062 (2.038) 0.039 (0.995) 0.012 (0.484) 0.040 (4.360)

0.035 (1.573) 0.016 (1.163) 0.036 (2.061) 0.049 (2.222) 0.057 (1.983) 0.007 (0.394) -0.010 (-1.433)

0.44%

0.057

-0.283

-0.151

-0.022

(2.943)

(1.464)

(-6.760)

(-2.990)

(-0.597)

0.14%

0.070

0.170

-0.147

0.019

(1.395)

(2.669)

(5.992)

(-4.283)

(0.746)

0.22%

0.090

0.127

-0.224

-0.001

(1.781)

(2.834)

(3.736)

(-5.446)

(-0.046)

0.22%

-0.033

-0.409

0.072

-0.021

(1.447)

(-0.807)

(-9.458)

(1.380)

(-0.541)

0.971 0.983 0.971 0.964 0.950 0.975 0.996

Cranfield School of Management 248

Can Fund Managers Successfully Time Their Investment Styles?

Table 13 Average Fund Performance by Morningstar Ranking

This table summarises the cross-sectional average estimates of fund performance within sub-groups of mutual funds. Sample mutual funds are grouped into objective portfolios based on their Morningstar five star ranking. I use the Morningstar rating at the beginning of the fund’s entire performance history during the sample period. Since Morningstar does not give star rating to those funds that have been in existence in less than three years, total sample size is 2,286 funds. The sample period is June 1992 to June 2002, a total of 121 trading months. Morningstar gives mutual funds one to five stars according to their past investment performance. The highest ranking is five stars, and the lowest ranking is one. The standard deviations are in parentheses.

5 Star

323

1.09% (0.004)

0.066 (0.023)

Monthly Sharpe Ratio 0.157 (0.068)

4 Star

588

0.88% (0.003)

0.052 (0.015)

0.149 (0.063)

0.09% (0.004)

3 Star

698

0.85% (0.003)

0.050 (0.013)

0.149 (0.064)

-0.03% (0.005)

2 Star

505

0.88% (0.003)

0.058 (0.017)

0.134 (0.067)

-0.18% (0.005)

1 Star

172

0.78% (0.004)

0.067 (0.024)

0.108 (0.069)

-0.47% (0.008)

5 Star – 1 Star spread

Mean t-stat

0.31% 8.411

-0.001 -0.406

0.049 7.628

0.74% 11.366

5 Star – 4 Star spread

Mean t-stat

0.21% 10.003

0.014 10.522

0.007 1.578

0.18% 5.172

5 Star – 3 Star spread

Mean t-stat

0.24% 11.426

0.016 13.996

0.008 1.730

0.30% 8.049

3 Star – 1 Star spread

Mean t-stat

0.07% 2.601

-0.017 -12.592

0.041 7.471

0.44% 8.895

Fund Ranking

Ph.D. Thesis: Jeffrey Junhua Lu

Number of Mean-Monthly Monthly Funds Raw Return Volatility

Carhart 4-factor Alpha 0.27% (0.006)

Cranfield School of Management 249

Can Fund Managers Successfully Time Their Investment Styles?

Table 14 Bootstrap Analysis of Style Timing Coefficients by Morningstar Fund Performance Group

Fund Morningstar rating at the beginning of its entire performance history is used. Morningstar awards mutual funds one to five stars according to their past investment performance. The highest ranking is five stars, and the lowest ranking is one. Since Morningstar does not rate funds that have been in existence in less than three years, total sample size is 2,286 funds. Listed are the fractions, mean timing coefficients, and mean intercept of 2,286 mutual funds that exhibit positive/negative (+/-) and significant positive/significant negative (++/--) style timing abilities within each fund performance group. The sample period is June 1992 to June 2002, a total of 121 trading months. The intercepts are converted to annualised percentages. Timing ability is measured using the four-factor Treynor and Mazuy (1966; TM) and Henriksson and Merton (1981; HM) style timing models. Significance is at the five percent level (two-tailed) and is based on bootstrap standard errors. Panel A: 5 Star TM + Fraction (%) Market Size B/M Momentum

47.988 33.127 85.759 21.053

-

HM ++

--

52.012 1.858 0.619 66.873 1.858 11.146 14.241 43.653 0.929 78.947 1.548 27.554

+ 51.393 30.650 84.520 17.957

Timing coefficient Market Size B/M Momentum

0.662 0.765 1.549 0.344

-0.422 -1.589 -0.395 -0.749

3.030 2.060 2.531 0.972

-1.787 -3.218 -0.983 -1.259

0.160 0.116 0.414 0.082

Intercept Market Size B/M Momentum

2.915 2.861 4.160 6.624

5.434 4.897 4.572 3.586

2.135 3.229 3.434 6.640

9.877 8.073 2.733 2.942

0.241 0.430 3.230 3.690

Ph.D. Thesis: Jeffrey Junhua Lu

-

++

--

48.607 1.858 69.350 0.929 15.480 38.080 82.043 0.310

1.548 5.882 0.619 11.146

-0.151 -0.245 -0.105 -0.190

-0.493 -0.537 -0.257 -0.453

0.327 0.114 0.689 -0.150

6.593 -2.404 12.197 4.569 3.331 11.943 3.578 1.901 0.230 3.195 12.081 2.454

Cranfield School of Management 250

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Table 14 cont. Panel B: 4 Star TM + Fraction (%) Market Size B/M Momentum

-

HM ++

--

+

-

++

--

57.313 51.871 77.551 18.197

42.687 48.129 22.449 81.803

1.701 3.061 28.912 0.510

0.850 5.612 0.680 36.224

65.136 44.048 75.850 21.939

34.864 55.952 24.150 78.061

3.741 0.510 24.320 0.510

1.020 3.571 0.510 12.925

Timing coefficient Market Size B/M Momentum

0.443 0.650 0.957 0.253

-0.356 -1.011 -0.266 -0.631

1.085 2.231 1.833 0.396

-0.916 -2.609 -1.208 -0.995

0.128 0.100 0.241 0.063

-0.100 -0.169 -0.083 -0.148

0.267 0.207 0.496 0.123

-0.324 -0.502 -0.241 -0.299

Intercept Market Size B/M Momentum

1.287 1.680 2.022 2.975

3.290 2.634 2.539 1.953

-0.138 -1.777 1.223 1.629

3.403 3.108 2.666 1.726

0.359 -0.842 0.650 1.742

2.390 2.586 2.369 0.873

-0.514 -1.260 -0.666 3.616

5.455 6.660 0.772 0.080

++

--

Panel C: 3 Star TM + Fraction (%) Market Size B/M Momentum

-

HM ++

--

+

-

59.312 58.883 77.364 12.607

40.688 41.117 22.636 87.393

3.152 6.734 27.221 0.143

1.576 3.152 0.573 47.278

70.201 46.275 73.496 16.762

29.799 53.725 26.504 83.238

6.7340.287 1.7193.438 20.7740.860 0.43013.897

Timing coefficient Market Size B/M Momentum

0.469 0.891 0.920 0.206

-0.362 -0.855 -0.349 -0.723

1.472 2.303 1.704 -0.897

-0.947 -2.054 -0.769 -1.000

0.143 0.126 0.227 0.075

-0.096 -0.158 -0.101 -0.155

0.352-0.350 0.327-0.390 0.460-0.248 0.076-0.296

Intercept Market Size B/M Momentum

-0.237 0.217 0.689 1.730

2.418 1.727 1.338 0.707

-3.171 -3.070 -0.133 -1.651

4.189 1.276 0.820 0.668

-1.062 -2.910 -0.755 0.414

1.322 1.892 0.755 -0.511

-4.7247.070 -5.7791.982 -3.8194.029 0.174-3.032

Ph.D. Thesis: Jeffrey Junhua Lu

Cranfield School of Management 251

Can Fund Managers Successfully Time Their Investment Styles?

Table 14 cont. Panel D: 2 Star TM + Fraction (%) Market Size B/M Momentum

-

HM ++

--

+

-

++

--

63.366 51.683 79.010 14.059

36.634 48.317 20.990 85.941

3.168 8.911 36.436 0.990

0.990 6.931 1.188 42.376

63.960 44.752 76.832 19.604

36.040 55.248 23.168 80.396

6.337 3.168 28.911 0.594

1.386 4.950 1.188 7.921

Timing coefficient Market Size B/M Momentum

0.553 1.265 1.287 0.439

-0.463 -1.261 -0.414 -0.836

1.633 2.736 1.987 0.884

-1.090 -3.188 -0.535 -1.180

0.174 0.157 0.316 0.115

-0.131 -0.223 -0.122 -0.169

0.354 0.481 0.531 0.224

-0.488 -0.542 -0.165 -0.367

Intercept Market Size B/M Momentum

-1.199 -1.411 -0.598 -0.215

0.383 0.227 -0.714 -0.689

-2.354 -3.380 -1.574 0.841

7.879 0.276 -4.466 -0.917

-2.918 -4.276 -2.285 -1.157

-0.691 -0.343 -1.574 -2.355

-3.460 -8.508 -3.124 -5.011

11.363 2.097 -4.695 -0.975

Panel E: 1 Star TM + Fraction (%) Market Size B/M Momentum

-

HM ++

--

+

-

++

--

69.767 52.326 90.116 13.953

30.233 47.674 9.884 86.047

4.070 4.070 31.977 1.163

1.744 4.070 2.907 42.442

67.442 44.767 80.233 22.093

32.558 55.233 19.767 77.907

7.558 2.326 25.581 1.744

1.744 4.070 1.744 9.302

Timing coefficient Market Size B/M Momentum

0.705 1.468 1.474 0.727

-0.967 -1.355 -1.244 -1.021

1.479 3.530 2.503 3.229

-6.585 -3.014 -1.748 -1.398

0.205 0.199 0.385 0.191

-0.231 -0.230 -0.189 -0.211

0.408 0.551 0.717 0.720

-1.526 -0.453 -0.235 -0.477

Intercept Market Size B/M Momentum

-4.047 -5.861 -3.155 -3.418

-1.696 -5.272 -0.505 -8.469 -5.028 -2.248 -3.329 -15.504

1.016 -2.002 -9.675 -2.601

-7.813 -9.573 -5.450 -5.812

Ph.D. Thesis: Jeffrey Junhua Lu

-0.702 -9.057 10.249 -2.172 -14.591 0.248 -5.960 -4.050 -13.033 -5.477 -20.577 -5.261

Cranfield School of Management 252

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Table 15 Style Timing Aggressiveness by Morningstar Fund Performance Group

This table summarises the cross-sectional average estimates of fund style timing aggressiveness within sub-groups of mutual funds. Absolute values of the TM timing coefficient (which are obtained from the Carhart 4-factor style timing model) are used to proxy for the aggressiveness of fund timing strategies. Sample mutual funds are grouped into objective portfolios based on Morningstar five star ranking. Morningstar rating at the beginning of a fund’s entire performance history during the sample period is used. Since Morningstar does not award a star rating to those funds that have been in existence in less than three years, total sample size is 2,286 funds. The sample period is June 1992 to June 2002, a total of 121 trading months. Morningstar gives mutual funds one to five stars according to their past investment performance. The highest ranking is five stars, and the lowest ranking is one. Standard deviations are in parentheses.

5 Star

Number of Funds 323

5 Star

588

3 Star

698

2 Star

505

1 Star

172

1 Star – 5 Star spread

Mean T-stat

0.247 2.403

0.098 0.883

0.067 0.566

0.317 4.659

1 Star – 3 Star spread

Mean T-stat

0.359 3.686

0.538 5.831

0.661 6.725

0.323 5.248

1 Star – 2 Star spread

Mean T-stat

0.265 2.691

0.151 1.518

0.348 3.369

0.200 3.184

5 Star – 3 Star spread

Mean T-stat

0.112 2.823

0.440 5.771

0.594 7.578

0.006 0.155

5 Star – 4 Star spread

Mean T-stat

0.131 3.283

0.493 6.321

0.583 7.166

0.102 2.609

Fund Ranking

Ph.D. Thesis: Jeffrey Junhua Lu

Market

Size

B/M

0.537 (0.657) 0.406 (0.394) 0.426 (0.394) 0.520 (0.462) 0.785 (1.262)

1.316 (1.2440 0.824 (0.869) 0.876 (0.848) 1.263 (1.112) 1.414 (1.135)

1.384 (1.306) 0.802 (0.884) 0.791 (0.776) 1.104 (0.972) 1.452 (1.230)

Momentu m 0.664 (0.611) 0.562 (0.464) 0.658 (0.469) 0.781 (0.489) 0.980 (0.772)

Cranfield School of Management 253

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Table 16 Factor Loadings on Fund Sub-groups Formed on Asset Size

This table summarises the fund factor loadings for sub-groups of mutual funds derived from the Carhart 4-factor model. Sample mutual funds are grouped into fund size portfolios based on fund size. The portfolios are equally weighted and reweighted monthly so the weights are readjusted whenever a fund disappears. The fund’s total net assets under management at the beginning of its entire performance history during the sample period. The sample period is June 1992 to June 2002, a total of 121 trading months. The Russell 3000 Index serves as a proxy for the general market index. The t-statistics are in parentheses. Size Quintile

Number Alpha of Funds

Quintile 5: TNA>443.9 ($ millions) Quintile 4: 156.1
Total

557

556

557

557

564

2791

Russell 3000

Quintile 5 - quintile 1 spread

Mean

Quintile 5 - quintile 2 spread

Mean

Quintile 5 - quintile 3 spread

Mean

Quintile 3 - quintile 1 spread

Mean

Ph.D. Thesis: Jeffrey Junhua Lu

Momentu R-square m

Market

Size

B/M

0.192%

0.992

0.104

0.014

0.019

(3.002)

(59.273)

(5.809)

(0.628)

(1.177)

0.141%

0.975

0.193

0.042

0.033

(1.970)

(51.086)

(9.423)

(1.677)

(1.830)

0.094%

0.975

0.206

0.019

0.040

(1.235)

(48.897)

(9.620)

(0.746)

(2.127)

0.029%

0.964

0.199

0.069

0.040

(0.383)

(49.505)

(9.512)

(2.738)

(2.174)

-0.039%

0.947

0.216

0.050

0.022

0.980

0.974

0.973

0.972

0.971

(-0.513) (47.692) (10.151) (1.922)

(1.155)

0.10% (1.353)

0.040 (1.677)

0.032 (1.810)

0.975

0.08% 0.991 -0.066 0.040 (2.794) (139.082) (-8.672) (4.360)

-0.010 (-1.433)

0.996

0.231% (2.325) 0.164% (1.667) 0.098% (0.984) 0.133% (1.238)

0.973 (52.441)

0.183 (9.215)

0.046 -0.112 -0.036 -0.003 (1.757) (-4.010) (-1.063) (-0.123) 0.028 -0.094 -0.056 -0.021 (1.106) (-3.425) (-1.667) (-0.881) 0.017 -0.101 -0.006 -0.021 (0.662) (-3.633) (-0.168) (-0.872) 0.028 -0.010 -0.030 0.018 (1.010) (-0.343) (-0.827) (0.693) Cranfield School of Management 254

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Table 17 Bootstrap Analysis of style Timing Coefficients within Size Groups

Listed are the fractions, mean timing coefficients, and mean intercept of 2,791 mutual funds that exhibit positive/negative (+/-) and significant positive/significant negative (++/--) factor timing abilities within each fund performance group. Mutual fund size is measured by fund total net assets under management. Sample funds are segregated into quintiles by size. The sample period is June 1992 to June 2002, a total of 121 trading months. The intercepts are converted to annualised percentages. Timing ability is measured using the four-factor Treynor and Mazuy (1966; TM) and Henriksson and Merton (1981; HM) factor timing models. Significance is at the five percent level (two-tailed) and is based on bootstrap standard errors.

+ Fraction (%) Market Size B/M Momentum

54.399 47.935 81.688 17.235

Panel A: Size Quintile 5: TNA >$443.9M TM ++ -+ 45.601 1.257 1.436 52.065 3.411 7.540 18.312 31.239 0.718 82.765 0.718 36.984

61.400 40.575 77.558 17.056

HM -

++

--

38.600 5.745 1.436 59.425 1.257 4.488 22.442 25.314 0.539 82.944 0.539 10.952

Timing coefficient Market Size B/M Momentum

0.445 0.666 0.980 0.339

-0.383 -1.099 -0.437 -0.628

1.160 2.193 1.819 0.933

-0.974 -2.665 -2.098 -0.990

0.127 0.094 0.252 0.079

-0.124 -0.177 -0.097 -0.132

0.289 0.266 0.502 0.159

-0.472 -0.451 -0.247 -0.267

Intercept Market Size B/M Momentum

1.678 1.703 2.361 3.606

3.359 3.126 2.800 2.201

1.213 -0.579 1.709 4.100

5.121 4.374 1.362 1.464

0.666 -0.269 1.586 2.507

3.212 2.966 1.838 1.465

-0.347 -1.742 0.586 3.218

11.203 5.713 -0.028 -0.306

Ph.D. Thesis: Jeffrey Junhua Lu

Cranfield School of Management 255

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Table 17 cont.

+ Fraction (%) Market Size B/M Momentum

Panel B: Size Quintile 4: $156.1M
--

54.856 48.561 76.799 19.424

45.144 51.439 23.201 80.576

1.619 4.317 32.734 0.540

1.799 5.036 1.799 35.971

62.590 39.928 75.899 24.820

37.410 60.072 24.101 75.180

4.317 1.619 26.439 0.540

1.079 3.597 1.799 10.791

Timing coefficient Market Size B/M Momentum

0.497 0.845 1.172 0.443

-0.399 -1.245 -0.535 -0.760

1.311 2.397 1.926 0.771

-1.386 -3.273 -2.093 -1.104

0.136 0.124 0.280 0.091

-0.118 -0.210 -0.121 -0.159

0.348 0.394 0.520 0.127

-0.368 -0.529 -0.254 -0.341

Intercept Market Size B/M Momentum

0.591 0.954 1.564 2.739

3.115 2.455 2.251 1.480

-2.420 -1.281 0.681 1.040

0.903 4.624 1.705 0.854

-0.490 -1.818 0.371 1.433

2.935 2.539 2.072 0.564

-3.177 -5.164 -0.931 -0.045

2.754 6.114 3.222 0.196

+ Fraction (%) Market Size B/M Momentum

Panel C: Size Quintile 3: $61.4M
--

60.682 51.346 79.354 18.851

39.318 48.654 20.646 81.149

2.693 5.386 29.982 0.898

0.718 5.925 1.616 39.497

63.734 46.320 75.224 20.826

36.266 53.680 24.776 79.174

6.643 1.795 25.494 0.539

0.539 4.488 2.154 9.874

Timing coefficient Market Size B/M Momentum

0.544 1.116 1.260 0.618

-0.436 -1.270 -0.861 -0.844

1.603 2.938 2.258 1.316

-0.628 -3.235 -1.698 -1.162

0.157 0.160 0.321 0.101

-0.128 -0.217 -0.153 -0.182

0.313 0.491 0.612 0.209

-0.326 -0.538 -0.202 -0.365

Intercept Market Size B/M Momentum

-0.435 -0.146 0.658 1.331

2.526 1.640 0.954 0.578

-0.871 -3.013 -0.227 1.739

6.037 3.300 2.049 0.266

-1.708 -3.129 -1.091 0.098

1.420 1.661 0.971 -0.763

-3.655 -7.839 -1.816 -1.268

13.024 4.330 -0.081 -1.154

Ph.D. Thesis: Jeffrey Junhua Lu

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Table 17 cont.

+ Fraction (%) Market Size B/M Momentum

Panel D: Size Quintile 2: $19.6M
HM -

++

--

62.837 53.321 72.352 19.031

37.163 46.679 27.648 80.969

2.873 6.643 30.162 1.436

1.257 5.386 2.693 37.702

69.120 47.038 69.659 25.135

30.880 52.962 30.341 74.865

4.488 2.693 23.698 0.539

1.436 5.027 1.436 12.208

Timing coefficient Market Size B/M Momentum

0.548 1.117 1.198 0.736

-0.539 -1.195 -0.844 -0.811

1.699 2.576 2.095 1.858

-3.403 -2.725 -3.656 -1.188

0.160 0.147 0.294 0.121

-0.151 -0.201 -0.138 -0.187

0.406 0.407 0.553 0.163

-0.970 -0.468 -0.340 -0.367

Intercept Market Size B/M Momentum

-0.663 -0.477 0.186 0.314

1.656 0.965 0.213 0.165

-1.879 -3.843 -0.580 -0.986

4.565 2.533 -1.604 0.037

-2.334 -3.132 -1.349 -0.154

1.652 0.701 -0.589 -1.441

-5.983 -6.093 -3.625 -2.066

15.005 5.171 0.394 -1.617

+ Fraction (%) Market Size B/M Momentum

Panel E: Size Quintile 1: TNA<$19.6M TM ++ -+

HM -

++

--

59.043 56.915 74.291 19.149

40.957 43.085 25.709 80.851

3.369 9.043 26.418 0.887

1.596 4.965 3.723 38.121

63.475 51.241 69.504 24.823

36.525 48.759 30.496 75.177

3.014 3.191 20.035 1.241

1.064 3.191 4.255 11.702

Timing coefficient Market Size B/M Momentum

0.652 1.404 1.230 0.740

-0.552 -1.283 -0.804 -0.870

2.196 3.412 2.197 2.046

-3.227 -3.748 -2.102 -1.195

0.176 0.199 0.312 0.144

-0.133 -0.197 -0.172 -0.204

0.463 0.621 0.602 0.448

-0.630 -0.653 -0.497 -0.427

Intercept Market Size B/M Momentum

-2.441 -2.623 -1.744 -1.050

0.181 0.298 -0.300 -1.451

-5.914 -5.007 -1.454 -7.026

16.408 0.175 -3.767 -0.837

-4.230 -6.045 -3.795 -2.728

-0.701 -11.285 0.393 -11.583 -1.014 -4.947 -3.029 -12.294

14.955 7.437 2.065 -2.545

Ph.D. Thesis: Jeffrey Junhua Lu

Cranfield School of Management 257

Can Fund Managers Successfully Time Their Investment Styles?

Table 18 Style Timing Aggressiveness within Fund Size Groups

This table summarises the cross-sectional average estimates of fund style timing aggressiveness within sub-groups of mutual funds. The absolute value of the TM timing coefficients (which are obtained from the Carhart 4-factor style timing model) is used as a proxy for the aggressiveness of fund timing strategies. Sample mutual funds are grouped into fund size quintiles based on fund net assets under management at the beginning of each fund’s entire performance history during the sample period. The sample period is June 1992 to June 2002, a total of 121 trading months. The standard deviations are in parentheses. Fund Size

Number of Funds

Market

Size

B/M

Momentu m

Quintile 5: TNA>443.9 ($ millions)

557

0.417

0.891

0.880

0.578

(0.392)

(0.941)

(0.956)

(0.474)

0.453

1.051

1.024

0.698

(0.437)

(1.124)

(1.032)

(0.585)

0.501

1.191

1.178

0.802

(0.536)

(1.370)

(1.178)

(0.764)

0.545

1.153

1.100

0.797

(0.819)

(1.054)

(1.162)

(0.675)

0.611

1.352

1.121

0.845

(0.792)

(1.442)

(1.085)

(0.758)

Quintile 4: 156.1
556

557

557

564

Quintile 1 - Quintile 2 spread

Mean t-stat

0.066 1.369

0.198 2.619

0.021 0.311

0.049 1.129

Quintile 1 - Quintile 3 spread

Mean t-stat

0.110 2.714

0.161 1.911

-0.057 -0.844

0.044 0.963

Quintile 1 - Quintile 5 spread

Mean t-stat

0.194 5.190

0.461 6.323

0.241 3.938

0.268 7.076

Quintile 3 - Quintile 5 spread

Mean t-stat

0.084 3.001

0.300 4.259

0.298 4.631

0.224 5.876

Quintile 4 - Quintile 5 spread

Mean t-stat

0.036 1.453

0.159 2.566

0.144 2.412

0.120 3.762

Ph.D. Thesis: Jeffrey Junhua Lu

Cranfield School of Management 258

Can Fund Managers Successfully Time Their Investment Styles?

Table 19 Factor Loadings on Fund Sub-group Formed on Fund Age

This table summarises the fund factor loadings for sub-groups of mutual funds derived from the Carhart 4-factor model. Sample mutual funds are grouped into fund age portfolios based on fund age. The portfolios are equally weighted and reweighted monthly so the weights are readjusted whenever a fund disappears. Fund age is measured by years since inception at the beginning of its entire performance history during the sample period. Sample funds are segregated into three groups: new funds, seasoned funds and median-aged funds. New funds are defined as those funds with less than 5-year performance history and seasoned funds are defined as those funds with 10-year or more than 10-year performance history. The remainders are defined as medium-aged funds. I also group seasoned funds and median-aged funds together and label them as old funds. The sample period is June 1992 to June 2002, a total of 121 trading months. The Russell 3000 Index serves as a proxy for the general market index. The t-statistics are in parentheses. Size Quintile Young Funds: 0
Number Alpha Market of Funds 1821 0.095% 0.972 (1.250) (48.663)

Median Aged Funds: 5 ≤ AGE<10

483

Seasoned Funds: AGE ≥ 10

487

Old Funds: AGE ≥ 5

970

Total

2791

Russell 3000

Young Funds - Seasoned Funds spread

Mean

t-stat Young Funds - Median Aged Mean Funds spread t-stat Mean Young Funds - Old Funds spread t-stat

Ph.D. Thesis: Jeffrey Junhua Lu

Size

B/M Momentum R-square

0.202 (9.458)

0.026 (0.997)

0.034 (1.783)

0.972

0.977

0.114%

0.970

0.152

0.063

0.018

(1.698) 0.078% (1.193) 0.096% (1.455) 0.10% (1.353)

(55.141) 0.970 (56.722) 0.970 (56.260) 0.973 (52.441)

(8.060) 0.143 (7.786) 0.147 (7.977) 0.183 (9.215)

(2.777) 0.052 (2.335) 0.058 (2.579) 0.040 (1.677)

(1.075) 0.029 (1.804) 0.024 (1.448) 0.032 (1.810)

0.08% 0.991 -0.066 0.040 (2.794) (139.082) (-8.672) (4.360)

-0.010 (-1.433)

0.017%

0.002

0.060

-0.026

0.978 0.978 0.975

0.996

0.004

(0.115) (0.054) -0.019% 0.001

(1.408) (-0.505) 0.050 -0.038

(0.120) 0.016

(-0.124) 0.001%

(0.037) 0.002

(1.181) (-0.727) 0.055 -0.032

(0.419) 0.010

(-0.004)

(0.057)

(1.705) (-0.815)

(0.353)

Cranfield School of Management 259

Can Fund Managers Successfully Time Their Investment Styles?

Table 20 Bootstrap Analysis of Factor Timing Coefficients within Age Groups

Listed are the fractions, mean timing coefficients, and mean intercepts of 2,791 mutual funds that exhibit positive/negative (+/-) and significant positive/significant negative (++/--) factor timing abilities within each fund performance group. Fund age is measured by years since inception at the beginning of its entire performance history during the sample period. Sample funds are segregated into three age groups: new funds, old funds and median-aged funds. New funds are defined as those funds with less than 5-year performance history in existence and seasoned funds are defined as those funds with 10-years or more performance history. The remainder are defined as medium-aged funds. The sample period is June 1992 to June 2002, a total of 121 trading months. The intercepts are converted to annualised percentages. Timing ability is measured using the four-factor Treynor and Mazuy (1966; TM) and Henriksson and Merton (1981; HM) factor timing models. Significance is at the five percent level (two-tailed) and is based on bootstrap standard errors. Panel A: Young Funds: 0
--

Fraction (%) Market Size B/M Momentum

56.398 50.632 78.089 18.616

43.602 2.087 0.879 49.368 5.437 5.272 21.911 31.741 2.032 81.384 0.659 38.001

61.724 45.854 76.496 21.472

38.276 2.416 0.879 54.146 1.867 3.789 23.504 26.469 1.812 78.528 0.549 11.697

Timing coefficient Market Size B/M Momentum

0.554 1.117 1.252 0.590

-0.445 -1.239 -0.777 -0.825

1.941 3.142 2.179 1.205

-1.940 -3.192 -2.860 -1.178

0.152 0.160 0.314 0.117

-0.122 -0.212 -0.150 -0.189

0.385 0.569 0.592 0.281

-0.604 -0.541 -0.467 -0.392

Intercept Market Size B/M Momentum

-0.802 -0.588 0.565 1.322

2.470 1.858 0.782 0.451

-2.781 11.537 -4.332 3.729 0.170 -1.809 0.105 0.140

-2.297 -3.938 -1.008 -0.309

1.834 2.055 0.162 -0.850

-7.557 -9.380 -2.172 -5.310

13.860 6.683 2.254 -1.360

Ph.D. Thesis: Jeffrey Junhua Lu

Cranfield School of Management 260

Can Fund Managers Successfully Time Their Investment Styles?

Table 20 cont. Panel B: Median Aged Funds: 5
--

Fraction (%) Market Size B/M Momentum

61.284 54.865 75.776 19.048

38.716 45.135 24.224 80.952

2.484 5.797 25.673 0.828

2.070 4.969 1.449 37.474

69.772 44.306 68.737 25.673

30.228 55.694 31.263 74.327

9.731 1.863 18.427 0.621

1.242 4.555 2.277 8.489

Timing coefficient Market Size B/M Momentum

0.515 0.857 0.940 0.588

-0.430 -1.138 -0.556 -0.714

1.276 2.185 1.734 2.693

-1.956 -3.173 -2.493 -1.076

0.148 0.121 0.224 0.090

-0.130 -0.176 -0.114 -0.139

0.334 0.336 0.449 0.522

-0.530 -0.456 -0.288 -0.298

Intercept Market Size B/M Momentum

0.537 0.628 0.851 1.807

2.049 1.721 1.967 0.959

-0.317 -0.767 -0.064 -1.596

3.853 2.722 -2.406 0.529

-0.575 -1.341 -0.369 1.013

1.794 1.325 1.253 -0.166

-2.921 -4.094 -1.456 -3.153

13.405 5.665 1.668 -0.307

Panel C: Seasoned Funds: 10
--

Fraction (%) Market Size B/M Momentum

62.834 52.156 73.511 18.891

37.166 47.844 26.489 81.109

3.080 6.571 28.542 1.437

2.053 8.419 2.669 36.140

67.146 42.710 67.351 23.409

32.854 57.290 32.649 76.591

8.830 2.875 21.561 0.821

1.437 5.133 2.259 10.883

Timing coefficient Market Size B/M Momentum

0.515 0.986 1.055 0.532

-0.543 -1.197 -0.651 -0.690

1.386 2.611 1.849 1.992

-2.674 -2.604 -2.245 -0.998

0.155 0.128 0.261 0.103

-0.165 -0.183 -0.130 -0.140

0.317 0.374 0.492 0.255

-0.806 -0.472 -0.332 -0.267

Intercept Market Size B/M Momentum

0.492 0.192 0.681 0.878

1.231 1.395 1.002 0.740

-2.548 -1.717 -0.019 2.023

1.147 1.468 0.285 0.859

-0.624 -1.334 -0.396 0.273

1.119 0.909 0.653 -0.154

-1.599 -3.530 -1.531 1.623

6.442 2.154 -1.405 -1.016

Ph.D. Thesis: Jeffrey Junhua Lu

Cranfield School of Management 261

Can Fund Managers Successfully Time Their Investment Styles?

Table 21 Style Timing Aggressiveness within Fund Age Groups

This table summarises the cross-sectional average estimates of fund style timing aggressiveness within sub-groups of mutual funds. The absolute value of the TM timing coefficients (which are obtained from the Carhart 4-factor style timing model) is used as a proxy for the aggressiveness of fund timing strategies. Fund age is measured by years since inception at the beginning of its entire performance history during the sample period. Sample funds are segregated into three groups: new funds, seasoned funds and medium-aged funds. New funds are defined as those funds with less than 5-year performance history and seasoned funds are defined as those funds with 10-years or more performance history. The remainder are defined as medium-aged funds. I also group seasoned funds and median-aged funds together and label them as old funds. The sample period is June 1992 to June 2002, a total of 121 trading months. Standard deviations are in parentheses. Fund Age Young Funds: 0
Medium Aged Funds: 5
Number of Funds 1821

483

Market

Size

B/M

0.505 (0.545)

1.177 (1.242)

1.148 (1.158)

Momentu m 0.781 (0.662)

0.482

0.984

0.847

0.690

(0.706)

(1.216)

(0.910)

(0.784)

Seasoned Funds: AGE ≥ 10

487

0.525 (0.798)

1.087 (1.068)

0.948 (0.945)

0.660 (0.537)

Old Funds: AGE ≥ 5

970

0.504 (0.753)

1.036 (1.145)

0.898 (0.929)

0.675 (0.671)

Young Funds - Seasoned Funds Spread

Mean

-0.019

0.090

0.200

0.121

t-stat

-0.489

1.596

3.936

4.184

Mean

0.024

0.193

0.301

0.091

t-stat

0.699

3.093

6.079

2.331

Mean

0.003

0.142

0.250

0.106

t-stat

0.105

3.018

6.203

3.983

Young Funds - Medium Aged Funds Spread

Young Funds - Old Funds Spread

Ph.D. Thesis: Jeffrey Junhua Lu

Cranfield School of Management 262

Can Fund Managers Successfully Time Their Investment Styles?

Table 22 Factor Loadings on Fund Turnover Sub-groups

This table summarises the fund factor loadings for sub-groups of mutual funds derived from Carhart 4-factor model. Sample mutual funds are grouped into fund turnover portfolios based on fund turnover. The portfolios are equally weighted and reweighted monthly so the weights are readjusted whenever a fund disappears. Turnover is measured by the percentage of the mutual fund’s holdings that change over year. 2,744 funds out of 2,791 report their annual turnover rates in the Morningstar database. Sample funds are segregated into three categories according to their average annual turnover rates over the sample period: Low (less than 50%), Median (between 50% and 100%), and High (100% or higher). The sample period is June 1992 to June 2002, a total of 121 trading months. The Russell 3000 Index serves as a proxy for the general market index. The t-statistics are in parentheses. Fund Turnover

Number Alpha of Funds

Low Turnover Funds (<50%/annual ) Median Turnover Funds (50%100%/annual) Total

Size

B/M

0.187%

0.914

0.046

0.134

0.010

(3.007)

(56.116)

(2.611)

(6.339)

(0.624)

0.084%

0.967

0.165

0.096

0.027

(1.135)

(49.919)

(7.965)

(3.830)

(1.502)

895

0.036%

1.039

0.334

-0.108

0.059

0.963

2744

(0.337) 0.098% (1.353)

(37.621) (11.296) (-3.019) 0.973 0.183 0.040 (52.441) (9.215) (1.677)

(2.258) 0.032 (1.810)

0.975

0.08% 0.991 -0.066 0.040 (2.794) (139.082) (-8.672) (4.360)

-0.010 (-1.433)

777

1072

Russell 3000

High Turnover Funds - Low Turnover Funds Spread High Turnover Funds Median Turnover Funds Spread Median Turnover Funds Low Turnover Funds Spread

Ph.D. Thesis: Jeffrey Junhua Lu

Momentu R-square m

Market

Mean

-0.152%

0.125

t-stat Mean

(-1.191) -0.048%

(3.760) 0.072

(8.092) (-5.604) 0.169 -0.204

(1.568) 0.031

t-stat Mean

(-0.384) -0.103%

(2.197) 0.053

(4.787) (-4.781) 0.120 -0.038

(1.010) 0.018

t-stat

(-1.013)

(1.982)

(4.194) (-1.091)

(0.710)

0.289

-0.242

0.975

0.971

0.996

0.049

Cranfield School of Management 263

Can Fund Managers Successfully Time Their Investment Styles?

Table 23 Average Fund Performance by Fund Turnover

This table summarises the cross-sectional average estimates of fund performance within sub-groups of mutual funds. Sample mutual funds are grouped into fund turnover portfolios based on fund turnover. The portfolios are equally weighted and reweighted monthly so the weights are readjusted whenever a fund disappears. Turnover is measured by the percentage of the mutual fund’s holdings that change over year. 2,744 funds out of 2,791 report their annual turnover rates in the Morningstar database. Sample funds are segregated into three categories according to their average annual turnover rates over the sample period: Low (less than 50%), Median (between 50% and 100%), and High (100% or higher). The sample period is June 1992 to June 2002, a total of 121 trading months. The Russell 3000 Index serves as a proxy for the general market index. The standard deviations are in parentheses.

Fund Turnover Low Turnover Funds (<50%/annual )

Median Turnover Funds (50%
High Turnover Funds (>100%/annual)

High Turnover Funds - Low Turnover Funds Spread

High Turnover Funds - Median Turnover Funds Spread

Median Turnover Funds - Low Turnover Funds Spread

Ph.D. Thesis: Jeffrey Junhua Lu

Number Mean-Monthly Monthly of Funds Raw Return Volatility 777

Monthly Sharpe Ratio

Carhart 4-factor Alpha

0.901%

0.047

0.169

0.172%

(0.003)

(0.016)

(0.097)

(0.004)

0.882%

0.052

0.153

0.052%

(0.003)

(0.015)

(0.116)

(0.004)

0.914%

0.066

0.127

0.021%

(0.004)

(0.022)

(0.087)

(0.005)

Mean

0.013%

0.019

-0.042

-0.151%

t-stat

0.386

20.451

-9.35

-8.301

Mean

0.032%

0.014

-0.026

-0.031%

t-stat

1.643

16.890

-5.538

-3.077

Mean

-0.019%

0.005

-0.016

-0.124%

t-stat

-1.355

7.221

-3.148

-6.788

1072

895

Cranfield School of Management 264

Can Fund Managers Successfully Time Their Investment Styles?

Table 24 Bootstrap Analysis of Style Timing Coefficients within Turnover Groups

Listed are the fractions, mean timing coefficients, and mean intercepts of 2,744 mutual funds that exhibit positive/negative (+/-) and significant positive/significant negative (++/--) factor timing abilities within each fund performance group. I segregate the sample funds into three categories according to their average annual turnover rates over the sample period: Low (less than 50%), Median (between 50% and 100%), and High (100% or higher). The sample period is June 1992 to June 2002, a total of 121 trading months. The intercepts are converted to annualised percentages. Timing ability is measured using the four-factor Treynor and Mazuy (1966; TM) and Henriksson and Merton (1981; HM) factor timing models. Significance is at the five percent level (two-tailed) and is based on bootstrap standard errors. Panel A: Low Turnover Funds (<50%/annual ) TM + ++ -+ Fraction (%) Market Size B/M Momentum

54.745 59.124 71.898 17.032

45.255 1.825 0.973 40.876 5.353 2.190 28.102 19.100 2.311 82.968 0.730 37.470

Timing coefficient Market Size B/M Momentum

0.476 0.877 0.710 0.522

-0.329 -0.833 -0.617 -0.636

Intercept Market Size B/M Momentum

1.017 1.480 1.635 2.207

3.195 2.751 2.931 1.955

Ph.D. Thesis: Jeffrey Junhua Lu

1.262 2.303 1.508 1.366

69.708 52.068 65.815 23.358

HM -

++

--

30.292 6.083 47.932 1.582 34.185 13.869 76.642 0.608

0.487 2.311 2.190 8.637

-1.580 -2.119 -2.145 -0.937

0.133 0.126 0.168 0.085

-0.083 -0.141 -0.133 -0.131

0.305 0.395 0.400 0.184

-0.098 -0.361 -0.413 -0.289

-0.841 14.996 -1.912 5.564 1.079 0.194 1.921 1.154

-0.017 -0.932 0.316 1.364

2.963 2.877 1.966 0.729

-1.647 -6.567 -0.712 -5.020

2.262 4.559 5.939 -0.636

Cranfield School of Management 265

Can Fund Managers Successfully Time Their Investment Styles?

Table 24 cont. Panel B: Median Turnover Funds (50%
--

59.870 54.655 74.767 20.298

40.130 45.345 25.233 79.702

1.769 6.983 25.978 0.745

1.210 5.587 2.235 38.827

65.922 44.134 71.229 24.395

34.078 55.866 28.771 75.605

4.097 2.793 20.205 0.838

0.279 3.445 2.142 10.335

Timing coefficient Market Size B/M Momentum

0.475 1.038 0.988 0.500

-0.428 -1.036 -0.672 -0.754

1.584 2.911 1.781 1.501

-1.067 -2.632 -2.872 -1.084

0.146 0.153 0.243 0.106

-0.120 -0.176 -0.126 -0.156

0.340 0.524 0.476 0.289

-0.209 -0.464 -0.354 -0.297

Intercept Market Size B/M Momentum

-0.442 -0.405 0.484 1.176

2.047 1.712 0.744 0.391

-1.845 -3.109 0.351 1.442

4.562 1.658 -0.926 0.385

-1.591 -3.413 -1.008 0.076

1.271 1.630 0.332 -0.849

-2.533 -6.910 -1.846 -3.798

3.664 3.231 -0.548 -0.086

++

--

+ Fraction (%) Market Size B/M Momentum

Panel C: High Turnover Funds (>100%/annual) TM ++ -+

HM -

59.888 41.117 84.022 18.436

40.112 58.883 15.978 81.564

3.464 4.469 45.140 1.006

1.676 9.274 1.564 36.201

69.708 52.068 65.815 23.358

30.292 47.932 34.185 76.642

4.469 1.564 38.436 0.335

2.458 6.704 1.564 14.078

Timing coefficient Market Size B/M Momentum

0.670 1.282 1.713 0.734

-0.626 -1.626 -0.941 -0.952

1.977 3.402 2.473 1.792

-3.359 -3.595 -2.970 -1.368

0.133 0.126 0.168 0.085

-0.083 -0.141 -0.133 -0.131

0.407 0.460 0.663 0.500

-0.790 -0.594 -0.466 -0.445

Intercept Market Size B/M Momentum

-1.276 -2.166 0.010 0.791

1.386 1.166 -1.398 -0.443

-3.389 -4.847 -0.451 -2.119

3.990 3.482 -4.041 -0.525

-0.017 -0.932 0.316 1.364

2.963 2.877 1.966 0.729

-8.755 -8.698 -2.495 -1.627

14.963 7.221 -1.092 -2.382

Ph.D. Thesis: Jeffrey Junhua Lu

Cranfield School of Management 266

Can Fund Managers Successfully Time Their Investment Styles?

Table 25 Style Timing Aggressiveness within Fund Turnover Groups

This table summarises the cross-sectional average estimates of fund style timing aggressiveness within sub-groups of mutual funds. The absolute value of the TM timing coefficients (which is obtained from the Carhart 4-factor style timing model) is used as a proxy for the aggressiveness of fund timing strategies. Turnover is measured by the percentage of the mutual fund’s holdings that change in a year. 2,744 funds out of 2,791 report their annual turnover rates in the Morningstar database. Sample funds are segregated into three categories according to their average annual turnover rates over the sample period: Low (less than 50%), Median (between 50% and 100%), and High (100% or higher). The sample period is June 1992 to June 2002, a total of 121 trading months. Standard deviations are in parentheses. Fund Age

Number of Funds

Market

Size

B/M

Momentum

Low Turnover Funds (<50%/annual )

777

0.410

0.859

0.683

0.616

(0.453)

(0.990)

(0.819)

(0.606)

0.456

1.037

0.909

0.703

(0.434)

(1.049)

(0.928)

(0.555)

0.652

1.484

1.590

0.912

(0.878)

(1.467)

(1.273)

(0.798)

Mean

0.243

0.626

0.907

0.295

t-stat

7.275

10.430

17.691

8.677

Mean

0.196

0.447

0.681

0.209

t-stat

6.085

7.640

13.333

6.610

Mean

0.047

0.178

0.225

0.087

t-stat

2.256

3.785

5.599

3.192

Median Turnover Funds (50%
High Turnover Funds (>100%/annual)

High Turnover Funds - Low Turnover Funds Spread

High Turnover Funds - Median Turnover Funds Spread

Median Turnover Funds - Low Turnover Funds Spread

Ph.D. Thesis: Jeffrey Junhua Lu

1072

895

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Table 26 Factor Loadings on No-Load and Load of Fund Sub-groups

This table summarises the fund factor loadings for sub-groups of mutual funds derived from Carhart 4-factor model. Sample mutual funds are grouped into no-load and load portfolios. The portfolios are equally weighted and reweighted monthly so the weights are readjusted whenever a fund disappears. Fund load is the total of maximum front-end, rear-end, and deferred sales charges as a percentage of the investment. 1,344 funds out of 2,791 are no-load funds. The sample period is June 1992 to June 2002, a total of 121 trading months. The Russell 3000 Index serves as a proxy for the general market index. The t-statistics are in parentheses. Fund Turnover No-Load Fund

R-square Number Alpha Market Size B/M Momentum of Funds 1334 0.126% 0.967 0.178 0.046 0.034 0.976 (1.827) (53.5340 (9.181) (1.973) (2.006)

Load Fund

1457

0.068% (0.932)

0.978 (50.993)

0.188 (9.154)

0.035 (1.423)

0.030 (1.634)

0.974

Total

2794

0.10% (1.353)

0.973 (52.441)

0.183 (9.215)

0.040 (1.677)

0.032 (1.810)

0.975

0.08% 0.991 -0.066 0.040 (2.794) (139.082) (-8.672) (4.360)

-0.010 (-1.433)

0.996

Russell 3000

No-Load Fund - Load Fund Spread

Ph.D. Thesis: Jeffrey Junhua Lu

Mean

0.058%

t-stat

(0.572)

-0.011

-0.010

0.011

(-0.402) (-0.366) (0.316)

0.005 (0.185)

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Table 27 Bootstrap Analysis of Factor Timing Coefficients within Load/No-Load Groups

Listed are the fractions, mean timing coefficients, and mean intercept of 2,791 mutual funds that exhibit positive/negative (+/-) and significant positive/significant negative (++/--) factor timing abilities within load and no-load group. Fund load is the total of maximum front-end, rear-end, and deferred sales charges as a percentage of the investment. The sample period is June 1992 to June 2002, a total of 121 trading months. The intercepts are converted to annualised percentages. Timing ability is measured using the four-factor Treynor and Mazuy (1966; TM) and Henriksson and Merton (1981; HM) factor timing models. Significance is at the five percent level (two-tailed) and is based on bootstrap standard errors.

+

Panel A: No-Load Funds TM ++ --

HM +

-

++

--

Fraction (%) Market Size B/M Momentum

56.897 53.748 73.913 21.139

43.103 2.249 1.424 46.252 5.397 5.322 26.087 26.687 2.474 78.861 0.750 34.558

63.343 46.627 70.315 24.588

36.657 5.247 1.049 53.373 1.649 3.598 29.685 20.915 2.324 75.412 0.600 10.045

Timing coefficient Market Size B/M Momentum

0.557 1.059 1.125 0.645

-0.496 -1.235 -0.808 -0.790

1.605 2.797 2.065 1.094

-3.165 -2.990 -2.722 -1.163

0.152 0.153 0.277 0.114

-0.133 -0.195 -0.151 -0.168

0.355 0.442 0.569 0.248

-0.778 -0.506 -0.432 -0.357

Intercept Market Size B/M Momentum

0.003 0.288 1.123 1.701

2.916 2.375 1.606 1.128

-1.803 10.069 -2.427 5.138 0.626 -0.207 1.654 0.639

-1.272 -2.342 -0.332 0.830

2.552 2.306 1.178 -0.118

-3.917 -5.538 -0.972 -3.393

13.195 6.752 3.586 -0.769

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Table 27 cont.

Panel B: Load Funds TM

HM

+

-

++

--

+

-

++

--

Fraction (%) Market Size B/M Momentum

59.712 49.691 79.616 16.541

40.288 50.309 20.384 83.459

2.334 5.903 33.219 0.824

1.098 6.108 1.579 40.288

64.722 43.583 76.527 20.659

35.278 56.417 23.473 79.341

4.324 2.334 27.179 0.549

0.961 4.598 1.579 11.874

Timing coefficient Market Size B/M Momentum

0.525 1.033 1.200 0.503

-0.420 -1.199 -0.599 -0.776

1.813 2.950 2.060 2.237

-1.107 -3.161 -2.624 -1.106

0.152 0.143 0.303 0.105

-0.127 -0.205 -0.125 -0.176

0.339 0.520 0.552 0.410

-0.549 -0.529 -0.370 -0.358

Intercept Market Size B/M Momentum

-0.596 -0.737 0.218 0.895

1.519 1.237 0.382 0.124

-2.757 -3.857 -0.278 -0.625

2.869 1.395 -3.020 0.082

-2.024 -3.782 -1.206 -0.782

0.921 1.210 -0.300 -1.049

-4.269 -8.389 -2.689 -3.750

11.746 4.727 -1.338 -1.450

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Table 28 Style Timing Aggressiveness within Fund Load Groups

This table summarises the cross-sectional average estimates of fund style timing aggressiveness within load and no-load sub-groups of mutual funds. The absolute value of the TM timing coefficients (which is obtained from the Carhart 4-factor style timing model) is used as a proxy for the aggressiveness of fund timing strategies. Fund load is the total of maximum front-end, rear-end, and deferred sales charges as a percentage of the investment. 1,344 funds out of 2,791 are no-load funds. The sample period is June 1992 to June 2002, a total of 121 trading months. Standard deviations are in parentheses.

No-Load Fund

Number of Funds 1334

Load Fund

1457

0.483 (0.486)

1.117 (1.154)

1.077 (1.052)

0.731 (0.563)

No-Load Fund - Load Fund Spread

Mean

0.048

0.024

-0.035

0.028

T-stat

1.996

0.510

-0.842

1.099

Fund Age

Ph.D. Thesis: Jeffrey Junhua Lu

Market

Size

B/M

0.531 (0.747)

1.140 (1.271)

1.043 (1.130)

Momentu m 0.759 (0.764)

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Table 29 Bootstrap Analysis of Style Timing Coefficients

Listed are the fractions, mean timing coefficients, and mean intercept of 4,586 mutual funds that exhibit positive/negative (+/-) and significant positive/significant negative (++/--) style timing abilities. Mutual funds with at least 36 monthly observations are included in the analysis. The sample period is June 1992 to June 2002, a total of 121 trading months. The intercepts are converted to annualised percentages. Timing ability is measured using the Carhart (1997) four-factor Treynor and Mazuy (1966; TM) and Henriksson and Merton (1981; HM) style timing models. Significance is at the five percent level (two-tailed) and is based on bootstrap standard errors. Panel A shows the results from the mutual fund sample, and Panel B shows the results from the synthetic control sample. A synthetic fund is constructed under the null hypothesis of no timing ability for each fund in the sample by forming an index portfolio to match the fund's style. Panel C shows the fraction of funds for which the difference between the fund's timing coefficient and the timing coefficient of the corresponding synthetic fund is positive/negative (+/-) and significantly positive/significantly negative (++/--). Panel A: Mutual Fund Sample TM +

-

HM ++

--

+

-

++

--

Fraction (%) Market

56.716

43.284

2.311

0.872

59.856

40.144

2.791

0.720

Size

51.701

48.299

4.775

5.364

45.813

54.187

1.854

3.533

B/M

77.148

22.852

25.185

1.031

75.556

24.444

20.279

1.221

Momentum

20.519

79.481

0.589 31.225

24.051

75.949

0.371

9.049

Market

0.758

-0.704

2.775

-3.826

0.172

-0.215

0.442

-0.853

Size

1.244

-1.460

3.378

-3.865

0.291

-0.252

0.497

-0.737

B/M

1.211

-0.984

2.145

-4.044

0.320

-0.164

0.580

-0.542

Momentum

0.841

-0.840

2.678

-1.203

0.138

-0.222

0.566

-0.314

Market

-0.561

3.946

-6.752

6.723

-2.081

5.036

-7.393

4.841

Size

-0.378

3.282

-4.255

7.179

-3.075

4.400

-8.726 13.404

B/M

0.585

0.732

1.377

2.847

-0.857

0.658

1.459

2.964

Momentum

2.486

1.107

-0.245

-0.599

1.197

0.685

4.534

0.312

Timing coefficients

Intercept

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Table 29 cont. Bootstrap Analysis of Style Timing Coefficients Panel B: Synthetic Control Sample TM +

-

HM ++

--

+

-

++

--

Fraction (%) Market

50.018

49.982

1.334

0.455

60.301

39.699

1.513

0.977

Size

63.657

36.343

7.849

2.777

48.372

51.628

0.523

1.611

B/M

40.727

59.273

1.998

1.923

34.254

65.746

1.063

1.337

Momentum

56.821

43.179

7.266

5.509

61.942

38.058

3.845

0.342

Market

1.384

-0.022

0.182

-1.353

1.981

-0.130

0.371

-1.240

Size

3.077

-2.885

3.962

-3.196

1.262

-0.200

3.222

-0.749

B/M

0.101

-0.888

2.725

-6.508

1.137

-0.139

0.075

-1.777

Momentum

0.865

-0.486

2.754

-2.543

1.827

-0.172

0.716

-0.278

-0.784

2.591

-2.560

4.509

-1.789

2.518

-7.399

5.953

Size

0.752

3.694

-3.210

7.699

-2.600

4.146

-5.261 12.946

B/M

0.040

2.086

1.609

6.014

-1.930

1.105

-0.056

6.491

Momentum

1.899

0.769

4.018

-1.228

-1.143

-1.246

3.837

-2.771

Timing coefficients

Intercept Market

Panel C: Differences in Timing Coefficients TM +

-

HM ++

--

+

-

++

--

Fraction (%) Market

79.293

20.707

1.985

1.696

47.636

52.364

0.588

0.689

Size

33.943

66.057

1.685

5.826

50.157

49.843

0.093

2.450

B/M

64.623

35.377

10.940

2.052

55.332

44.668

7.478

0.553

Momentum

21.134

78.866

1.717 19.982

27.678

72.322

1.386

7.587

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Figure 1 Timing Aggressiveness by Morningstar Rating

This figure graphs the cross-sectional average estimates of fund style timing aggressiveness within sub-groups of mutual funds. Absolute values of the TM timing coefficient (which are obtained from the Carhart 4-factor style timing model) are used to proxy for the aggressiveness of fund timing strategies. Sample mutual funds are grouped into objective portfolios based on Morningstar five star ranking. Morningstar rating at the beginning of a fund’s entire performance history during the sample period is used. Since Morningstar does not award a star rating to those funds that have been in existence in less than three years, total sample size is 2,286 funds. The sample period is June 1992 to June 2002, a total of 121 trading months. Morningstar gives mutual funds one to five stars according to their past investment performance. The highest ranking is five stars, and the lowest ranking is one.

Timing Aggressiveness on Moringstar Rating Groups 1.6 1.4

Timing Aggressiveness

1.2 1

Market Size

0.8

B/M MOM

0.6 0.4 0.2 0 1

2

3

4

5

Morningstar Rating

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Figure 2 Timing Aggressiveness by Size Quintile This figure graphs the cross-sectional average estimates of fund style timing

aggressiveness within sub-groups of mutual funds. The absolute value of the TM timing coefficients (which are obtained from the Carhart 4-factor style timing model) is used as a proxy for the aggressiveness of fund timing strategies. Sample mutual funds are grouped into fund size quintiles based on fund net assets under management at the beginning of each fund’s entire performance history during the sample period. The sample period is June 1992 to June 2002, a total of 121 trading months. The standard deviations are in parentheses.

Timing Aggressiveness on Size Quintiles 1.6

Tim ing A ggressiveness

1.4 1.2 1

Market Size

0.8

B/M MOM

0.6 0.4 0.2 0 1

2

3

4

5

Size Quintiles

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Figure 3 Timing Aggressiveness on Age Groups

This figure graphs the cross-sectional average estimates of fund style timing aggressiveness within sub-groups of mutual funds. The absolute value of the TM timing coefficients (which are obtained from the Carhart 4-factor style timing model) is used as a proxy for the aggressiveness of fund timing strategies. Fund age is measured by years since inception at the beginning of its entire performance history during the sample period. Sample funds are segregated into three groups: new funds, seasoned funds and medium-aged funds. New funds are defined as those funds with less than 5-year performance history and seasoned funds are defined as those funds with 10-years or more performance history. The remainder are defined as medium-aged funds. The sample period is June 1992 to June 2002, a total of 121 trading months. Standard deviations are in parentheses.

Timing Aggressiveness on Age Groups 1.3 1.2

Tim ing A g g ressiv eness

1.1 1 Market 0.9

Size

0.8

B/M MOM

0.7 0.6 0.5 0.4 Young

Median Aged

Seasoned

Age Groups

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Figure 4 Timing Aggressiveness by Turnover Group

This figure graphs the cross-sectional average estimates of fund style timing aggressiveness within sub-groups of mutual funds. The absolute value of the TM timing coefficients (which is obtained from the Carhart 4-factor style timing model) is used as a proxy for the aggressiveness of fund timing strategies. Turnover is measured by the percentage of the mutual fund’s holdings that change in a year. 2,744 funds out of 2,791 report their annual turnover rates in the Morningstar database. Sample funds are segregated into three categories according to their average annual turnover rates over the sample period: Low (less than 50%), Median (between 50% and 100%), and High (100% or higher). The sample period is June 1992 to June 2002, a total of 121 trading months. Standard deviations are in parentheses.

Timing Aggressiveness on Turnover Groups 1.8

Tim ing A ggressiveness

1.6 1.4 Market

1.2

Size B/M

1

MOM

0.8 0.6 0.4 Low

Median

High

Turnover Groups

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Figure 5 Timing Aggressiveness on Load/No-Load Groups

This figure graphs the cross-sectional average estimates of fund style timing aggressiveness within load and no-load sub-groups of mutual funds. The absolute value of the TM timing coefficients (which is obtained from the Carhart 4-factor style timing model) is used as a proxy for the aggressiveness of fund timing strategies. Fund load is the total of maximum front-end, rear-end, and deferred sales charges as a percentage of the investment. 1,344 funds out of 2,791 are no-load funds. The sample period is June 1992 to June 2002, a total of 121 trading months. Standard deviations are in parentheses.

Timing Aggressiveness on Load/No-Load groups 1.2

Tim ing Aggressiveness

1.1 1 0.9

Market Size

0.8

B/M MOM

0.7 0.6 0.5 0.4 No-Load

Load

Load/No-Load Funds

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Cranfield School of Management 278

Figure A

Research Route Map

Can Fund Managers Successfully Time Their Investment Styles?

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