Are mutual fund managers investors or speculators?

May 2007

Jeffrey Junhua Lu

Jeffrey Junhua Lu Global Wealth Management Citi UK

e-mail: [email protected]

Are mutual fund managers investors or speculators?

Abstract The quantification of speculative risk appears to be useful for measuring risk in diversified portfolio, such as mutual funds. Based on the measure of systematic skewness, I explore the alleged shift among mutual funds toward more highly aggressive investment policies and the apparent increase in the diversity of investment policies from fund to fund. My sample covers 485 randomly selected mutual funds listed on Datastream for the period from April, 1997 to July, 2002. The risk taking behavior by mutual fund managers are investigated by linking to different market conditions and managerial incentives based on fund flow-performance relationship. Fund managers with enhanced performance tend to decrease the speculative risk of fund portfolios while fund managers with deteriorative performance tend to increase the speculative risk of fund portfolios. However, implementing speculative investment strategies and hence increasing portfolio speculative risk may not come without cost. The evidence of this article has some important implications with respect to behavioral finance.

Keywords: speculative risk, systematic skewness

Are mutual fund managers investors or speculators? 1． Introduction Many investors use a consistent, long-term strategy to build a more secure financial future through steady purchases of well-diversified investments. Speculators and market (or sector) timers are usually less concerned about consistency. They may switch investment philosophies on an emotional whim, sometimes treating their investments more like play money than the serious money needed for future security. The commentary on mutual fund behavior during the last decade has shown rather consistent concern over a shift toward speculative investment policies---most obviously in soaring portfolio turnover and the dramatic changing characteristics of top performing funds. According to numbers compiled by the Investment Company Institute, a mutual fund research firm, fund portfolio turnover ratio has grown from 16% in 1965 to an astonishing average annual rate of 110%! Compared to that earlier six-year standard that prevailed for so long, the average stock is now held for just eleven months. As Bogle (2003) puts it: “We are no longer stock owners. We are stock traders”. Moreover, mutual fund investment in letter stock and small, less seasoned corporations has also risen, as an effort by active fund managers to beat the market. Elton, Gruber, and Blake (1996) find 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. 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. The driving forces behind this trend towards short-term speculation are the coming of more aggressive funds, the burgeoning emphasis on short-term performance, and the move from investment committees to portfolio managers. Aggressive fund managers often follow major trends in the market, such as some momentum style funds, or make “sector” bets and concentrate their holdings in a few industries or stocks that

expect to do well. These fund portfolios are actively traded and reflects the investment philosophy of fund managers. The appearances of hundreds of more aggressive performance funds have brought in new game rules in the investment management industry, which call for free-wheeling individual talent. About 3,200 funds of the 3,650 stock funds listed in Morningstar in 2002 are run by portfolio managers, while management teams run the remaining 450 funds. The tenure of portfolio managers lasted only as long as they produced performance1, and the managers with the hottest short-term records had been transformed by their employers' vigorous public relations efforts and the enthusiastic cooperation of the media, into "stars." As the industry brought out funds that were more and more performance-oriented, often speculative, specialized, and concentrated—funds that behaved increasingly like individual stocks—it attracted more and more investors for whom the long-term didn’t seem to be relevant. Fund investors have thus become more and more short-term oriented, as the fund redemptions rate has risen from 6% in the 1950s to 45% last year2. Such a focus on short-term performance probably makes the agency problem more severe, which will be discussed later in this paper. Given the shift toward speculative investment policies within the mutual fund industry, the risk associated with these fund investment behaviors is of great concern to fund investors. The risk derives from the vulnerability of such strategies to a severe fall in value which may result from a downturn in market prices generally. However, as shown below, traditional risk measures (i.e., variance and beta) are somewhat deficient for dealing with the rich set of portfolio objectives and constrains that investment managers often formulate, as it is not able to assess the potential speculative risk of the investment portfolio. Instead, the third moment of the distribution of portfolio returns is a potentially useful means with which to quantity the speculative risk incurred by managers of mutual funds. By implementing a 1 2

According to Morningstar (2002), the tenure of the average portfolio manager is just five years.

6% of fund redemption rate suggests an average holding period of 16 years for a fund investor, while 45% of fund redemption rate suggests an average holding period of 2 years. In this case, the time horizon for the typical fund investor had tumbled by fully 90%.

speculative risk measure developed by Simonson (1972), I investigate the characteristics of investment behavior of fund managers under different market conditions. Specifically, I examine the relationship between fund performance and speculative behavior of fund managers and try to determine whether any systematic changes in portfolio risk are consistent with the previously identified incentives, which are generally generated from the well-known fund flow-performance relationship. By ting the behavior of fund managers to their incentives, I illustrate the applicability of agency models in the problem of risk taking behavior of fund managers. The remaining of the paper is organized as follows. Section 2 discusses the role of skewness in investors’ preferences and addresses the speculative trading activities associated with fund managers. Section 3 describes the data employed in this study. Section 4 examines the investment behavior of 485 mutual funds by implementing a speculative risk measure during 1997-2002. Section 5 investigates the portfolio risk changes by fund managers between two sub-periods in order to test whether these portfolio changes reflect the incentives to take risk. Section 6 concludes.

2. Speculative risk and fund investment strategies 2.1. The role of skewness The probability distribution of the rate of return can be characterized by its moment. The reward for taking risks is measured by the first moment, which is the mean of the return distribution. Higher moments characterize the volatility risk and the asymmetry in payoffs. Investors’ risk preferences can be characterized by their preferences for the various moments of the distribution. The fundamental approximation theorem by Samuelson (1972) shows that when portfolios are revised often enough, and prices are continuous, the desirability of a portfolio can be measured by its mean and variance alone. The rate of return on well-diversified portfolios for holding periods that are not too long can be approximated by a normal distribution. Unfortunately, in reality the

two assumptions underlying Samuelson’s theorem do not hold. Portfolio revisions entail transaction costs, meaning that rebalancing must necessarily be limited. Price continuation rules out certain phenomena such as the major stock price jumps that occur in response to takeover attempts. It also rules out such dramatic events as the 25% one-day decline of the stock market in October 1987. Therefore, the second moment (variance) alone is generally not an adequate measure of risk Even though small losses occur more likely than with a normal distribution investors prefer positively skewed distributions of their portfolio value. They do so because big losses are less probable than in a normally or a negatively skewed distribution. As most investors are risk averse, they view the disutility of a loss as unevenly greater than the utility of a gain in the same proportion. Harvey and Siddique (2000) show that systematic skewness earns a risk premium and thus matters in the composition of portfolios. As investors desire positive skewness in portfolio returns, the risky asset will be held in higher proportion than predicted by a mean-variance framework due to its positive skewness. However, such positive skewness in portfolio returns do not come without a cost. Harvey and Siddique (2000) demonstrate that at any level of variance, there is a negative trade-off of mean return and skewness. That is, to get investors to hold low or negatively skewed portfolios, the expected return needs to be higher, to compensate investors for the increased probability of shortfall. Therefore, as the average risk-averse investor desires low downside risk and high upside potential, volatility or variance become inadequate as risk measures 3 . Skewness in combination with the first two moments is able to mirror the investor’s attitude towards both the upper and the lower part of the distribution. Skewness preferences becomes increasingly important as a decision making criterion when the investor has to choose among different risk levels that correspond to distinctly differently skewed return distributions. Skewness increases both with the risk levels as well as with the time horizon of the investment due to the compounding effect over

3

Other risk measures such as Value-at-Risk or Lower Partial Moments focus on the lower end of the distribution and do not capture the degree of upside potential the investor desires to achieve.

long time periods. 2.2. Fund speculative trading activities Recent studies of mutual fund manager behavior report unambiguous evidence of speculative trading activities associated with most funds. Grinblatt, Titman, and Wermers (1995) identify herding activity by mutual fund managers. Ferson and Schadt (1996) find that managers rebalance in anticipation of changing economic conditions. Brown, Harlow, and Starks (1996) find systematic changes in risk conditional on past performance. Lakonishok, Shleifer, Thaler, and Vishny (1991) find that “window dressing” accounts for portfolio rebalancing by pension fund managers. Apparently, such a disposition of fund managers to strive for quick gains from short-term speculative trading, can probably impose undesirable risk upon fund investors, who show great concerns on the measurement of such risk. In the typical mean-variance framework, investors have preferences over the mean and the variance of portfolio returns. The systematic risk of a security is measured as the contribution to the variance of a well-diversified portfolio. However, there is considerable evidence that the unconditional returns distributions cannot be adequately characterized by mean and variance alone. This leads us to the next moment---skewness. Skewness may be important in investment decisions because of induced asymmetries in realized returns. First, some fund managers specializes in groups of securities such as the smallest market-capitalized deciles or favor in specific strategies such as ones based on momentum. These assets are also the ones with the most skewed returns. Second, the presence of limited liability in all equity investments may induce option-like asymmetries in returns 4 . Third, the agency problem may induce asymmetries in portfolio returns5. That is, a manager has a call option with respect to the outcome of his investment strategies. Managers may prefer portfolios with high positive skewness (or low negative skewness).

4

See Nelson (1991), Golec and Tamarkin (1998)

5

See Brennan (1993)

3. Data The following analysis is performed on 485 mutual funds over the period April, 1997July, 2002 and sub-periods April, 1997 – December, 1999 and January, 2000 – July 2002. Monthly total return index data for virtually all equity mutual funds (unit trusts) that existed during any given quarter between April, 1997 and July, 2002 (inclusive) were extracted from Datastream. The definition of return index is expressed as: RI t = RI t − k ×

Pt + Dt Pt − k

(1)

RI t , return index on day t RI t − k , return index on day t-k Pt , the closing bid price on ex-date t Pt − k , the closing bid price on date t-k Dt , the dividend payment associated with ex-date t Hence, the monthly returns for each fund can be expressed as: Rt = RI t / RI t −k − 1

(2)

A similar expression is used for returns on the market portfolio proxy the S&P 500 Index. The 485 sample funds are drawn from the universe of 2,400 funds identified in this database over the sample period. The fund category is identified by examining the fund name and more than 20 such categories are identified. The main U.S. mutual fund categories include bond fund, equity fund, international funds, global funds and sector funds. In this study, I focus on actively managed equity funds and investigate mainly 5 types of equity funds, including aggressive growth, growth, growth & income, value, and balanced funds. Funds within the aggressive growth and growth sector invest in stocks that provide capital growth. Funds within the value sector

invest in stocks that have a good earnings track record and provide income. Funds within the growth & income sector invest in stocks that provide moderate income with decent growth prospects. Balanced funds invest in multiple assets in the market in an attempt to time the market. For aggressive growth and growth funds, I allocate small-cap growth funds to the aggressive growth sector while including large-cap growth funds in the growth sector, as small-cap companies on average exhibit a higher growth rate than large-cap companies. Among these five types of mutual funds, I randomly select an arbitrary number of funds in each category6.

4. Measuring fund speculative risk Markowitz (1952) formally associated the notion of speculative behavior with the third moment or skewness of portfolio returns. Everything else being equal, investors should prefer portfolios that are right-skewed to portfolios that are left-skewed. This is consistent with the Arrow-Pratt notion of risk aversion. Recall that for an asset, the only variability risk that matters in a well-diversified portfolio is its systematic risk, which is referring to its contribution to the variance of the portfolio (often cited as the market)’s return (denoted as beta). Similarly, for an asset, the only speculative risk that matters in a well-diversified portfolio is its coskewness with respect to the market, which is referring to its contribution to the skewness of the portfolio. Based on the above spirit, Simonson (1972) proposes a measure for the speculative risk of an asset, which can be termed systematic skewness, given by the formula below:

{

E [Rit − E (Ri )][RMt − E (RM )] Γi = Skewness M

2

}

(3)

where Rit is the return of an asset at time t, RMt is the return of the market at time t, and SkewnessM is the skewness of the market. The relevant measure of systematic skewness is denoted as Γi . Empirically, the values of the fund’s beta and systematic skewness are nearly always 6

See Table 1 for the number of funds in each category.

positive which suggests that fund and market returns are positively correlated. In such circumstances, speculative risk is present in fund i when the distribution of returns on the market portfolio is negatively skewed. The magnitude of Γi then describes the degree of i’s participation in the market’s negative skewness. For the sample period under consideration, the market portfolio returns are negatively skewed

7

.

Conceptually, the distribution of returns of a fund with higher value of Γi was more negatively skewed relative to the market’s negative skewness during the sample period than that of a fund with lower value of Γi . Table 1 presents a statistical description of the returns and parameters βi and Γi for the sample funds. The mean values forβi and Γi equal to 0.926 and 0.856 respectively for the five year holding period, are both close to one. This suggests that risk-bearing among the sample funds closely emulated most risk inherent in the market. A striking feature of Table 1 is the comparison of averageβi and Γi values for the sub-periods 1997.04-1999.12 and 2000.01- 2002.07. The average Γi value rose from 0.591 in the first period to 1.292 in the second period, an increase of 118%, while the averageβi rose only 6% from 0.917 to 0.975. It seems that mutual funds shifted toward more highly speculative investment policies during the second sub-sample period. It is interesting to note that in this latter period the allegedly exhaustive measure of risk generally applied in the studies of investment performance, i.e., standard deviation and beta, does not exceed the market’s risk level. The implication from the more traditional capital market theory that this sample of mutual funds incurred no greater risk during the second sub-period than the risk inherent in the market as a whole is strongly challenged by the measure of speculative risk. Note that the variances of βi and Γi for the second sub-period is significantly greater than that for the first sub-period. This suggests far less uniformity of investment 7

See Figure 4

policies with respect to speculative risk-taking in the later sub-period than in the earlier. It will be demonstrated below that the sample funds which claim a growth investment policy contributed disproportionately to the upward shift in Γi in the second sub-period. Table 2 shows the risk characteristics of the sample funds segregated according to different investment objectives and policies. For the whole sample period, both of the average risk measuresβi and Γi for the various types of funds are positive related to the relative degree of aggressiveness suggested by the investment objectives. As we proceed along the spectrum of mutual funds from the conservative value funds which focus on current income and price stability, to the aggressive growth funds which strive only for rapid capital appreciation, we should expect to encounter greater and greater risk. The fact that the risk measures for variability and speculative risk follow such a pattern lends support to their validity as risk measures. As noted previously, the surge in risk-taking by mutual funds in the second sub-period has been associated with the growth and performance-oriented funds (i.e., aggressive growth and growth funds). Curiously, the average of the more conventional risk measureβi for these funds increased slightly from the first sub-period to the second sub-period. On the other hand, a dramatic increase in Γi incurred by these two types of funds relates far more faithfully to the increase in risky investment behavior said to have occurred in the mutual fund industry. These results suggest that the degree of systematic risk for growth funds was roughly constant but that these funds significantly increased their participation in and exposure to the occasional fall or collapse of returns in the market. Besides growth oriented funds, balanced funds also exhibit dramatic increase in their speculative risk measures. Funds generally seek both income and capital appreciation by investing in a fixed combination of stocks and bonds. The results infer that these funds may participate in some sorts of speculative investment strategies.

5. Do funds alter their risk in response to incentives? The above findings are relevant in examining a potential agency problem within mutual fund companies and their investors. We take the basic agency problem between a mutual fund and its investors to be that, while investors would like the fund to use whatever private information it may have to maximize risk-adjusted returns, the mutual fund itself will instead take whatever action maximizes its value as a concern given the incentive it faces. 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. Previous research on the relationship between investment flows and past performance has demonstrated that consumers react strongly to historical returns8. Hence, many potential investors see and react to fund performance; a fund may at times increase its expected inflow of investment by altering the risk of its portfolio. 5.1. Market conditions and speculative risk bearing The dramatic increase in the systematic skewness of fund portfolios can be explained as the fund managers’ response to adverse market conditions and managerial incentives. The average monthly returns for the market (S&P 500) are 2.16% and -1.30% respectively for the two sub-periods. The first sub-period exhibits some characteristics of bull market, while the second sub-period exhibits some characteristics of bear market. During bull market, as the market rally continues, investors become more and more optimistic about equity performance and put money into the equity market. Fund manager can easily attract money as long as the fund performance catches up with the market. However, during bear market, investors generally take a pessimistic view of expected equity return and withdraw money from equity market. According to Investment Company Institute, net new cash flow to domestic equity funds has shrunk from a peak value of 260 billions dollars in 2000 to

8

See Patel, Zeckhauser, and Hendricks (1991); Ippolito (1992); Sirri and Tufano (1993).

54 billions dollars in 2001, and even an outflow of 25 billions dollars in 20029. During the same period, the S&P 500 Index has dropped from its peak value of 1517 to 911 at end of July, 2002. Moreover, investors would become more risk adverse and avoid investment with higher probability of under-performance. In other words, investment with positively skewed return distributions limits losses and provides the investor with downside protection10. In order to retain current investors and to attract new investors, fund managers have incentives to implement some kinds of speculative investment strategies, which subsequently increase the skewness of the portfolio. 5.2. Fund performance and speculative risk changes Given that a mutual fund wishes to maximize its value as a concern, how might it have an incentive to distort its portfolio? Recall the facts that the inflow of new investment is strongly related to the fund’s past performance and management fees are proportional to the assets under management, the flow-performance relationship11 can be thought of as an implicit incentive contract. That is, fund managers alter the speculative risk of fund portfolios as responses to investors’ different preferences for positive skewness in different circumstances. Moreover, a fund with a smooth track record would be perceived by the investors as a preferable investment compared to a fund with a volatile return history. Hence, performance persistence is unassailably a key issue in assessing the investment skill of a fund manager and is important to the portfolio decisions of investors. 9

See figure 1

10

For example, Cooley (1977) conducts an experiment to test the perception of risk on the part of institutional investors and finds that, among 56 institutional investors who were asked to rate distributions according to perceived risk, at least 29 associated the asymmetry of return distributions with risk. Particularly, the investors associated increases in risk with increases in negative skewness, indicating a preference for positive skewness.

11

Chevalier and Ellison (1997) suggest a model of fund investor behavior in which heterogeneously informed potential investors try to assess the quality of various funds. They find that when the fund’s return is 15 or more points below the target, funds flow out quickly and the rate is sensitive to performance, as though increasingly even investors who pay little attention begin to take notice of the fund’s poor performance. For somewhat less disastrous results (say between 15 and 8 points below the target), the fund attracts few or no new investors but does retain many of its old investors. At more typical performance levels, flow is increasing in performance and increases sharply at extremely good performance (say 15 points above the target).

Therefore, if a fund falls short of its performance target slightly, the fund manager may have incentives to implement speculative investment strategies to catch up with his previous performance, in an effort to retain current investors or even attract new investment from potential investors. In the extreme case when a fund is well behind its performance target, the fund manager may have fewer incentives or even no incentives to implement speculative strategies, since it seems impossible to catch up with the target and increased portfolio speculative risk may affect next year’s performance. However, if a fund is somewhat ahead of its target, the fund manager may have incentives to reduce the speculative risk of the fund portfolio and to lock in the gain achieved. My analysis thus allows me to address several interesting issues, which are addressed by the following hypotheses: 1. If a fund trails its previous performance, the fund manager has an incentive to “gamble” and increase the speculative risk of the fund portfolio. 2. If a fund is well behind its previous performance, the fund manager has fewer incentives or no incentive to increase the speculative risk of the fund portfolio. 3. If a fund surpasses its previous performance, the fund manager has an incentive to “lock in” the gain and decrease the speculative risk of the fund portfolio. Systematic skewness defined in the previous section is used as a proxy for the speculative risk of the fund portfolio. I plot the change in fund excess return and the change in fund systematic skewness on the graph to see there exit any relationships between them. These two variables are defined as follows:

Δ(ri − rM ) = (rit − rMt ) − (rit −1 − rMt −1 )

(4)

where rit is the fund average monthly return during period t, and rMt is the market average monthly return during period t

Δsyskewi = syskewit − syskewit −1

(5)

where syskewit is the fund’s systematic skewness during period t. The reason that I use change in fund performance rather then absolute fund performance is that investors tend to make investment decisions based on most recent performance or changes since previous investment performance, which is referred to the habit of anchoring12. The results are presented in Figure 2. Clearly, the graph shows that the two variables are negatively correlated. That is, an increase (decrease) in fund excess return would indicate a decrease (increase) in fund systematic skewness. This is consistent with the hypothesis 1 and 2. Drawing a trend line across the plotted graph manifests such relationship. First, I draw a straight line based on the linear regression and obtain the following equation, accompanying statistical results13.

Δsyskewi = 1.0198 - 40.945Δ(ri − rM )

(6)

That is, additional 1% increase (decrease) in fund excess return would cause the fund manager to decrease (increase) the fund’s systematic skewness by 0.41. The slope of the line indeed reflects the manager’s incentive to alter the speculative risk of the fund portfolio. Since the slope is negative, the larger the slope (less negative), the flatter the line, and the fewer incentives for the manager to change the fund’s speculative risk. It is interesting to see that the trend line does not go through the origin and the intercept is positive, which suggests that not all the funds that have surpassed their previous performance have incentives to decrease the speculative risk of the fund portfolios. Indeed, for a decrease in fund excess return or a moderate increase in fund excess return (less than 2.5%), the fund manager has an incentive to increase the speculative risk (systematic skewness) of the fund. On the other hand, for a relatively large increase in fund excess return (more than 2.5%), the fund manager has an incentive to decrease the speculative risk (systematic skewness) of the fund. 12

The habit of anchoring is a common bias in which the decision maker chooses an inappropriate reference point upon which he bases further decisions.

13

See table 3

5.3. Further tests on speculative risk bearing While the simple regression above provide a straightforward test of the hypothesis that fund managers have incentives to alter the speculative risk of fund portfolios based on previous performance, they may leave one wondering exactly how these incentives evolve with performance change. I thus turn now to the task of providing a more detailed picture of actual risk changes. As mentioned earlier, a fund manager may have fewer incentives or even no incentives if the fund performance is well below its previous level. That is, for large decrease in fund excess return from previous period (the north-west part of the graph), the slope of the trend line is a non-decreasing function of the magnitude of decrease in fund performance. I then conduct polynomial regression to figure out whether there exists such a non-linear relationship. Table 3 summarizes the results with polynomial order from 2 to 4 and the graphs for the regression lines are presented in Figure 3. Clearly, the convex shape of the regression lines is in accord with the intuition developed above and indicates that funds that trail their previous performance have an incentive to “gamble” with increasing speculative risk in the fund portfolios, whereas funds that surpass their previous performance by certain amounts (2.5% in this case) have an incentive to “lock in” the gain and decrease the speculative risk of the fund portfolio. The figure suggests in addition that these incentives decrease at extreme positions: funds that are well behind their previous performance may have fewer incentives or no incentives to increase the speculative risk of the fund portfolio, as the regression line appears to be flat at the left-end. Given the pattern of the trend line reviewed in Figure 3, it seems that funds with good performance may have different incentives to alter their speculative risk positions when compared to funds with poor performance14. To assess whether the above argument holds true in detail, I conduct a piecewise linear regression to model the relationship between risk changes and performance changes. The equation is given as 14

Funds with good performance are those have positive performance changes, while funds with poor performance are those have negative performance changes.

follows:

Δsyskewi = α 0 + α 1 Δ(ri − rm ) + α 2 Δ(ri − rm )dummyi

(7)

where Δsyskewi and Δ(ri − rm ) are defined as previously, dummyi is 1 if Δ(ri − rm ) >0 and 0 if Δ(ri − rm ) ≤0. As shown in Table 4, all the coefficients are statistically significant, which demonstrates that funds with good performance have different incentives to alter their speculative risk positions when compared to funds with poor performance. Specifically, according to the results, funds with good performance have the following risk taking incentive equation:

Δsyskewi = α 0 + (α 1 + α 2 )Δ(ri − rm ) = 1.265 − 53.229Δ(ri − rm )

(8)

while funds with poor performance have the following risk taking incentive equation:

Δsyskewi = α 0 + α 1 Δ(ri − rm ) = 1.265 − 18.341Δ(ri − rm )

(9)

Predicted values from this regression are graphed in Figure 5. It suggests that poor performing funds have fewer incentives to change their speculative risk positions when compared to their good performing counterparts. In other words, good performing funds are more willing to decrease their speculative risk as performance improves while poor performing funds are less willing to increase their speculative risk as performance deteriorates. This suggests that implementing speculative investment strategies and hence increasing portfolio speculative risk may not come without cost. Poor performing funds are faced with a more severe situation associated with a trade-off between improving performance and increased speculative risk.

6. Conclusion The quantification of speculative risk appears to be useful for measuring risk in diversified portfolio, such as mutual funds. Thus, the measure of systematic skewness appears to explain the alleged shift among mutual funds toward more highly

aggressive investment policies and the apparent increase in the diversity of investment policies from fund to fund. Such a risk taking behavior by mutual fund managers is directly linked to different market conditions and managerial incentives based on fund flow-performance relationship. During the bear market, fund managers tend to take on more speculative risk. Changes in fund speculative risk are negatively related to fund performance changes. Fund managers with enhanced performance tend to decrease the speculative risk of fund portfolios while fund managers with deteriorative performance tend to increase the speculative risk of fund portfolios. However, implementing speculative investment strategies and hence increasing portfolio speculative risk may not come without cost. The evidence of this article has some important implications with respect to behavioral finance. The risk taking behavior of mutual fund managers demonstrate that individuals try to minimize their losses which are consistent with the prospect theory of Kahnernan and Tversky (1979). They take chances to decrease them, 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 for a better outcome. As demonstrated that fund risk taking behavior are responses to incentives generated from flow-performance relationship, it may leave one wondering what performance evaluation procedure is relevant for fund investors’ decision making. The significant influences of fund performance changes (from previous performance) on fund risk taking behavior suggests that the reference point is changed every time the fund investors reaches a new level of wealth, which is called aspiration level by March (1987); and such a change in the performance reference point plays an important role in fund investors’ decision making process. Under the premise that mutual fund managers intensively implement speculative investment strategies, the payoff structure of these funds will be asymmetric. In that case variance and beta become inadequate as risk measures, as the average risk-averse investor desires low downside risk and high upside potential. Incorporating the

speculative risk measure will therefore result in a more precise picture of the portfolio risk profile relevant for fund investors. A diversification strategy employing multiple funds may achieve the desired level of speculative for some fund investors.

Table 1 Return and Risk Parameters for 485 Mutual Funds for 1997-2002

1997.04-2002.07

Mean

Z-value

Variance

F-value

Minimum

Maximum

Ri

-0.0012

0.0001

-0.0195

0.1400

βi

0.9264

0.0899

0.1792

2.7886

Γi

0.8585

0.0579

-0.0903

1.6313

Rm

0.0046

0.0027

-

-

1997.04-1999.12

Mean

Variance

Minimum

Maximum

Ri

0.0123

0.0003

-0.0231

0.3007

βi

0.9167

0.0690

0.1204

2.4756

Γi

0.5906

0.1618

-1.0816

1.8050

Rm

0.0216

0.0024

-

-

2000.01-2002.07

Mean

Variance

Minimum

Maximum

Ri

-0.0151

0.0001

-0.0438

0.0142

βi

0.9754

5.1760***

0.1121

2.6422***

0.1831

2.3888

Γi

1.2916

17.6050***

0.3634

5.0440***

-0.6731

2.5423

Rm

-0.0130

-

-

0.0025

*** Significant at the 1% level Z-value tests for the difference in mean values of βi and Γi for the sub-periods. F-value tests for the difference in variance values of βi and Γi for the sub-periods.

Table 2 Risk Parameters for 485 Mutual Funds Classified by Investment Objectives and Policies for 1997-2002

Type AGGRESSIVE

βi

Z-value

Variance (βi)

F-value

Γi

Z-value

Variance (Γi)

All period

1.2101

0.0456

1.0853

0.0302

1st period

1.2048

0.0465

0.5366

0.1348

2nd period

1.2092

GROWTH

All period

1.0800

0.0590

0.8900

0.0378

193 Funds

1st period

1.0121

0.0402

0.4291

0.1508

2nd period

1.1455

All period

0.7933

0.0235

0.8329

0.0380

1st period

0.8240

0.0198

0.7192

0.0816

2nd period

0.8247

VALUE

All period

0.7370

0.0202

0.7089

0.0567

95 Funds

1st period

0.8095

0.0177

0.9072

0.1365

2nd period

0.7804

BALANCED

All period

0.5576

0.0188

0.7548

0.0620

69 Funds

1st period

0.5580

0.0159

0.5672

0.0949

2nd period

0.5925

GROWTH 73 Funds

GROWTH & INCOME 50 Funds

0.1270

6.3710***

0.0230

-2.0620**

1.5670

*** Significant at the 1% level ** Significant at the 5% level * Significant at the 10% level

0.0844

0.0932

0.0463

0.0327

0.0361

1.8134**

2.3181***

2.3341***

1.8499***

2.2725***

1.8506

1.5291

1.1056

0.6317

1.0860

20.1800***

22.1250***

4.4940***

-3.8010***

6.8270***

0.0930

0.1790

0.2474

0.2521

0.2573

F-value

1.4499*

1.1873

3.0326***

1.8467***

2.7126***

Table 3 Polynomial Regression for Risk Changes and Performance Changes Dependent Variable ΔSYSKEWi Polynomial Order 1 R

2

Adjusted R

2

2

3

4

0.70

0.73

0.74

0.74

0.70

0.73

0.73

0.73

SE

0.4821

0.4527

0.4520

0.4510

F

1110.69

662.78

444.03

335.20

1.0198

1.1445

1.1609

1.1902

<0.0001

(<0.0001)

(<0.0001)

(<0.0001)

-40.9452

-35.3923

-37.6559

-35.7943

<0.0001

(<0.0001)

(<0.0001)

(<0.0001)

-443.0755

-501.4179

-710.0985

(<0.0001)

(<0.0001)

(<0.0001)

3387.7615

918.1257

(0.1165)

(0.7214)

Independent Variables Intercept ΔERi ΔERi2 ΔERi3 ΔERi4

156399.8238 (0.0815)

Note: ΔERi = Δ(ri − rM ) = (rit − rMt ) − (rit −1 − rMt −1 )

Δsyskewi = syskewit − syskewit −1 p value for the estimated coefficients in parentheses.

Table 4 Piecewise Linear Regression for Risk Changes and Performance Changes Independent Variables Dependent Variables ΔSYSKEWi Coefficient

p-value

Intercept

1.2647

(<0.0001)

ΔERi

-18.3410

(<0.0001)

ΔERi × Dummyi

-34.8882

(<0.0001)

R2

0.85

Adjusted R

2

0.73

SE

0.46

F

653.37

Dummyi is 1 if Δ(ri − rm ) >0 and 0 if Δ(ri − rm ) ≤0.

Figure 1 Net New Cash Flow to Domestic Equity Funds, 1997-2002 Net New Cash Flow to Domestic Equity Funds, 1997-2002 300

Billons of Dollars

250 200 150 100 50 0 -50

1997

1998

1999

2000

2001

2002

Figure 2 Plot Graph for Risk Changes and Performance Changes 3 2.5 2

Change in Systematic Skewness

1.5 1 y = -40.945x + 1.0198 R2 = 0.6974

0.5 0 -0.05

-0.04

-0.03

-0.02

-0.01

0

0.01

-0.5 -1 -1.5 -2 -2.5 Change in Returns

0.02

0.03

0.04

0.05

0.06

Figure 3 Graphs of Polynomial Regression for Risk Changes and Performance Changes

Order = 1

Change in Systematic Skewness

3

2

1

0

-1

-2 -0.05

-0.03

-0.01

0.01

2.5

0.03

1

0

-1

-2

-0.01

0.01

Order = 3

Order = 4 2

y = 3387.8x - 501.42x - 37.656x + 1.1609

0.5

-0.5

-1.5

4

2.5

-0.01

0.01

Change in Returns

0.03

0.05

0.03

3

0.05

2

y = 156400x + 918.13x - 710.1x 35.794x + 1.1902

1.5

0.5

-0.5

-1.5

-2.5 -0.05

-0.03

-0.03

Change in Returns

1.5

-2.5 -0.05

2

-3 -0.05

0.05

2

y = -443.08x - 35.392x + 1.1445

Change in Returns

3

Change in Systematic Skewness

3

y = -40.945x + 1.0198

Change in Systematic Skewness

Change in Systematic Skewness

4

Order = 2

-0.03

-0.01

0.01

Change in Returns

0.03

0.05

Figure 4 Frequency Distribution of Monthly Rates of Return on Standard and Poor Composite 500 Index for 1997-2002

SP500 10

8

6

FREQUENCY

4

2

Std. Dev = .05 Mean = .005 N = 63.00

0 -.150

-.100 -.125

-.050 -.075

.000 -.025

.050 .025

.100 .075

SP500

Figure 5 Patterns of Fund Speculative Risk Change on Fund Performance Change

Changes in Speculative Risk

2.5 2 1.5 1 0.5 0 -0.06

-0.04

-0.02

-0.5 0

0.02

-1 -1.5 -2 Changes in Performance

0.04

0.06

Reference Brennan, M. (1993)

Agency and asset pricing. Unpublished manuscript, UCLA

and London Business School

Brown, K.C., W. Van Harlow and Laura T. Starks (1996)

Of tournaments and

temptations: An analysis of managerial incentives in the mutual fund industry.

Journal of Finance, 51(1), 85-110.

Chevalier, J. and Glenn Ellison (1997)

Risk taking by mutual funds as a response to

incentives. Journal of Political Economy,

Cooley, P.L. (1977) of risk.

105(6), 1167-1200.

A multidimensional analysis of institutional investor perception

Journal of Finance 32, 67-78.

Elton, E.J., Martin J. Gruber and Christopher R. Blake (1996) risk-adjusted mutual fund performance.

The persistence of

Journal of Business, 69(2), 133-157.

Ferson, W.E. and Rudi W. Schadt (1996)

Measuring fund strategy and performance

in changing economic conditions. The Journal of Finance, 51(2), 425-461.

Golec, J. and Tamarkin, M. (1998) Bettors love skewness, not risk, at the horse track. Journal of Political Economy 106, 205-225.

Grinblatt, M., Sheridan Titman and Russ Wermers (1995) Momentum investment strategies, portfolio performance, and herding: A study of mutual fund behavior.

The American Economic Review, 85(5), 1088-1105.

Harvey, C.R. and Siddique, A. (2000)

Conditional skewness in asset pricing tests.

The Journal of Finance 55, 1263-1295. Ippolito, R.A. (1992)

Consumer reaction to measures of poor quality: Evidence

from the mutual fund industry. Journal of Law and Economics, Chicago, 35(1), 45-70.

John C. Bogle. The Mutual Fund Industry in 2003: Back to the Future. Investing Under Fire: Winning Strategies from the Masters for Bulls, Bears, and the Bewildered. 2-13. 2003.

Bloomberg Press.

Kahneman, D. and Amos Tversky (1979)

Prospect theory: An analysis of decision

under risk. Econometrica, 47(2), 263-292.

Lakonishok, J., Andrei Shleifer, Richard Thaler and Robert Vishny (1991) dressing by pension fund managers.

Window

The American Economic Review, 81(2),

227-231.

March, J. (1987)

Variable risk preferences and adaptive aspirations. Journal of

Economic Behavior and Organization 9, 5-24.

Markowitz, H. (1952)

Nelson, D. (1991)

Portfolio selection. Journal of Finance 77-91.

Conditional heteroskedasticity in asset returns. Econometrica

59, 347-370.

Patel, J., Richard Zeckhauser and Darryl Hendricks (1991)

The rationality struggle:

Illustrations from financial markets. American Economic Review, 81(2), 232-236.

Samuelson, P. (1972) The fundamental approximation theorem of portfolio analysis in terms of means, variances, and higher order moments. Cambridge, Mass.: The

MIT Press III,

Simonson, D.D. (1972)

Finance

The speculative behavior of mutual funds. Journal of

27, 381-392.

Sirri, E.R. and Peter Tufano (1993) Competition and change in the mutual fund industry.

Samuel L. Hayes III, Ed.: Financial Services: Perspectives and Challenges

Harvard Business School Press, Boston, Mass,