One-sided underreaction in stock prices Adriaan R. Soetevent∗

Sibrand J. Drijver

May 31, 2000

Abstract In this paper, we will add new evidence for the proposition that the Efficient Market Hypothesis is violated in financial markets. Nearly all stocks in the Euro Stoxx 50 have the characteristic that if they perform one day extremely bad, they will tend to perform the following day also extremely bad. Moreover, this underreaction effect does not occur when a stock performs exceptionally well on a certain day. The usual arguments put forward to argue that market efficiency holds notwithstanding this phenomenon are discussed, together with the existing models in the literature which produce under and overreaction. It will turn out that these models lack explanatory power for our results. For this reason, we propose a design for a model that probably could explain one-sided underreaction.

1

Introduction

The strongest form of the Efficient Market Hypothesis (EMH) alleges that the information set on which trading is based, includes all public as well as privately available information. (See e.g. Campbell, Lo and MacKinlay, 1997). If this hypothesis is true, asset prices should follow a random walk with the possibilities of earning a positive or a negative return in the next time-period being equally likely. Observations of non-zero autocorrelations of stock returns indicate in this case violation of the EMH, because not all information seems to be reflected immediately in the prices, but with a time lag. Positive autocorrelations are consistent with the underreaction hypothesis, which states that stock prices incorporate information slowly. On the contrary, negative autocorrelations are consistent with the overreaction hypothesis, which states that stock prices react too sensitive to information. The estimation of autocorrelations can be of great help both to detect short-term as well as long-term violations of the EMH. However, to infer ∗

Corresponding author. Faculty of Economics, University of Groningen, P.O. Box 800, 9700 AV Groningen, The Netherlands, Ph: +31 - (0) 50 - 363 37 66; E-mail: [email protected].

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whether short-term returns obey the EMH, one can also make use of the concept of Markov chains. This is the approach taken in Section 2 of this paper. Markov chain models are especially suited to test the short-term implications of the EMH, since they make use of states and conditional transition probabilities. Defining the states by the stock returns rit with i and t denoting the stock and the time respectively, the EMH implies that the probability of being in a certain state at time t is independent from the state the stock return was in in period t − 1. An overview of the empirical evidence on under and overreaction can be found in e.g. Barberis, Shleifer and Vishny (1998) and Fama (1998). Underreaction to news takes place over horizons of 1-12 months and overreaction of stock prices to consistent patterns of news pointing in the same direction seems to take place over horizons of 3-5 years. Fama defends the EMH by arguing that in the first place, these facts do not contradict the EMH, because in the empirical evidence, apparent underreaction is about as frequent as overreaction and are therefore mere chance results, as assumed by the EMH. Second, and more important, long-term anomalies are sensitive to the methodology used, as they tend to become marginal when exposed to different models for expected returns or when they are measured differently. Nevertheless, Barberis et al. (1998) and Daniel et al. (1998) present alternative behavioral models in which the judgments of investors are biased. These models account for both under and overreaction, implying that news is only slowly incorporated in market prices, and that these prices are therefore inefficient. These two models will be discussed in Section 3 together with the critique of Fama and the question to which extent our results fit into these frameworks. In the foregoing section, we will present our own empirical evidence on the violation of the EMH by means of a Markov chain model. It turns out that our results only show underreaction when prices go down, a fact that cannot be explained in the framework of the two discussed behavioral models. Therefore, we propose another behavioral model in Section 4, in which underreaction is explained by the fact that investors are partly led by the actions of other investors. We argue that elaborating on non-market interactions between investors may prove to be fruitful in explaining one-sided underreaction. Section 5 explains in which way investors can exploit the fact that stock returns are not independent and identically distributed. Section 6 summarizes and concludes.

2

Empirical evidence of market inefficiency

In this section, we look at empirical evidence of market inefficiency. We do this by defining a Markov chain model in Section 2.1. With this Markov chain model, we show in Section 2.2 that stock returns are not independent

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and identically distributed random variables. In Section 2.3 the conflict between the EMH and our and other empirical results is described. Section 2.4 describes how the results can be exploited in portfolio management decisions.

2.1

The Markov Chain Model

We define for each stock a first-order Markov chain model, based on the past returns rit := log(Sit ) − log(Si,t−1 ), where Sit is the price of stock i at time t and i = 1, . . . , 50 denotes the stock. Define gi := µˆi − 2σˆi where µˆi is the extimated mean return and σˆi is the estimated standard deviation, based on sixty past returns. The Markov model has the 6 states Sti = j for i = 1, . . . , 50, with:    j=1

j = 2, . . . , 5   j=6

if rit ∈ (−∞; gi ] if rit ∈ (gi + (j − 1)σi ; gi + (j − 1)σi ] if rit ∈ (gi + 4σi ; ∞)

Denote the conditional transition probability by P ri (a, b) = Pi,a,b = P r(St+1,i = a|St,i = b); a, b = 1, . . . , 6. In the sequel we suppress the subscript i. The Markov model is Πt+1 = P Πt with P = [Pab ] a 6x6 matrix of transition probabilities. Now, we can state the following null-hypothesis: P r(rt+1 < µ − 2σ|rt < µ − 2σ) = F (µ − 2σ), with F (.) the cumulative distribution function of the lognormal distribution with mean µ and standard deviation σ. That is, we test whether the returns are IID drawings from a lognormal distribution, given that we observed the last period a return less than µ − 2σ. To test the null-hypothesis, we use the following test-statistic: z=

P r(rt+1 < µ − 2σ|rt < µ − 2σ) − F (µ − 2σ) q

F (µ−2σ)(1−F (µ−2σ)) n

,

(1)

where n is the number of times we observed rt < µ − 2σ .

2.2

Results

We test the null-hypothesis for the Euro Stoxx 50 stocks. Therefore, we used data from Datastream. We used daily data and calculated P11 for series consisting of 3 and 5 years data respectively. The results are displayed in the next table. If we had not enough data to do the calculations, we put a ∗ on the corresponding position. 3

Table 1: Results for the Stoxx 50 stocks Company Abn Amro Holding Aegon Ahold Air Liquide Alcatel Alliantz Assicurazioni Generali Aventis AXA Banco Bilbao BASF Bayer Bayer. Hypo-Vereinsbank Banco Santander Banque Nationale de Paris Carrefour Compagnie de Saint-Gobain Daimlerchrysler Deutsche Bank Deutsche Telekom Dresdner Bank Electrabel Endesa Eni Fortis France Telecom ING Groep Koninklijke KPN Koninklijke Philips Electronics Koninklijke Olie LVMH Mannesmann Metro M¨ unchener R¨ uckversicherung Nokia

t-value (3 years) 4.18 -3.49 8.31 -3.49 10.45 23.58 6.74 -3.49 3.18 24.40 -3.49 8.31 * * 14.55 8.31 -3.49 * 8.31 19.52 28.80 -3.49 -3.49 20.11 28.80 * 12.66 8.31 6.74 4.58 -3.49 6.74 6.10 6.74 5.03

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t-value (5 years) 17.30 -4.93 1.64 4.92 13.9 15.39 3.41 2.81 9.06 31.20 -4.93 9.06 * * 12.41 12.41 -4.93 * 9.06 * 23.97 19.85 3.10 * 17.30 * 21.51 9.06 19.16 1.44 2.29 2.81 * 1.64 1.64

Table 1: Results for the Stoxx 50 stocks (continued) Company l’Oreal Pinault-Printemps-Redoute Repsol RWE Sanofi-Synthelabo Siemens Soci´et´e G´enerale Suez Lyonnaise des Eaux Telecom Italia Telefonica Total Fina Elf Unicredito Italiano Unilever Veba Vivendi

t-value (3 years) 13.55 6.74 18.42 14.55 -3.49 -3.49 23.18 20.11 29.38 44.44 8.31 -3.49 15.68 -3.49 24.40

t-value (5 years) 12.65 2.54 16.75 7.46 -4.93 8.21 17.89 12.41 20.08 35.72 4.10 14.78 23.97 1.09 27.59

From the results in Table 1 we conclude that for most of the stocks in the Stoxx50 index, a large drop in the price of the stock will be followed by a further drop. Many restults are highly significant, with even a t-statistic of 44.44 for Telefonica. The results are not very sensitive to the period considered (three or five years daily data). On the other hand, we did not find evidence for the hypothesis that very large positieve returns are also followed by a further large increase. A typical graph of the excess probabilities if in the previous period we observed a return less than µˆi − 2σˆi is given in Figure 1.

5

0.12

0.1

0.08

excess probability

0.06

0.04

0.02

0

−0.02

−0.04

−0.06

−0.08

1

2

3

4

5

6

state

Figure 1. Example of excess probabilities in the Markov chain given state 1 in the previous period. It is also interesting to test whether these results can only be drawn for individual stocks or also for (broadly) diversified stock indices. Therefore, we also tested the null-hypothesis for some (major) stock indices. The results are displayed in the next table. We tested not only on daily data over 3 and 5 years, but also used weekly data over the past 13 years. We could do calculations on weekly data, since for stock indices more data were available than for individual stocks. Again, a ∗ denotes that we did not have enough data to do the calculations. From Table 2 we conclude that return processes for stock indices are also not independent and identically distributed random drawings from a lognormal probability distribution. Again, the period over which the calculations are done does not seem to be relevant.

2.3

The conflict with market efficiency

From the two tables in the previous section, we conclude that returns on stocks and on stock indices are not independent and identically distributed drawings from a lognormal probability distribution. These results, which are in conflict with market efficiency, cannot only be explained by the observation that tails of the empirical return distribution are fatter than those of a lognormal return distribution. Other factors, like psychological, may also play an important role in explaining these results.

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Table 2: Results for some major stock indices Stock index AEX DAX FTSE100 CAC40 MIB SMI Topix Hang Seng Dow Jones Nasdaq SandP500

t-value (3 years) -4.26 18.78 10.18 23.55 28.39 14.52 3.89 31.49 -0.51 13.61 -0.51

t-value (5 years) 4.58 13.50 6.62 17.04 28.14 9.96 7.95 23.87 5.26 12.65 9.33

t-value (13 years) 16.02 * 11.64 * * * 4.12 41.21 2.85 13.14 2.35

From behavioral finance, which studies how people actually behave and not how people should behave, the following is known: • Markets are dominated by people and there is no universal rationality. • Numerous psychological factors influence the decision making process of individuals. In the table listed below, some assumptions underlying modern finance theory are given together with some real world facts. Table 3: Assumptions modern finance theory and facts Modern finance theory Changes in prices reflect new information Everyone buys the market portfolio Virtually no trading (Groucho Marx theorem) Stock splits are irrelevant and is costly, will not be observed

facts October 19, 1987 Most portfolios are poorly diversified Most equity funds are actively managed; turnover is high The average nominal stock price on the NYSE is the same as it was 70 years ago

We conclude from Table 3 that psychological factors influence investor behavior and that not all investors are completely rational. Therefore, we look at two behavioral finance models on under and overreaction in more 7

detail in the next section, to see if they are able to give an explanation for the observed facts.

2.4

Making investment decisions

From tables 1 and 2 we conclude that stock returns are not independent and identically distributed random variables. This observation naturally leads to the question how to exploit this information, for example to generate an outperformance with respect to a benchmark. Drijver and Otter (2000) used static Markowitz portfolio optimization to outperform a broadly diversified portfolio, in which stocks were grouped in sectors. They generated a statistically significant outperformance by giving upper and lower bounds on the asset classes, which explicitly depend on previous realizations of stock returns. If in the last period, the return was less than µˆi − 2σˆi , the weight of the sector in the next period in the portfolio was not allowed to exceed its weight in the benchmark portfolio. Drijver, Klein Haneveld and Van der Vlerk (2000) used this return dependent process in an Asset Liability Management model for pension funds. If a large drop was observed in the last period, a position in derivative secturies is allowed, otherwise not. These two modeling aspects can also be combined. Instead of giving a stock in a portfolio a lower weight than in the benchmark, we could also take a long position in put options or take a short position in futures contracts. This may be profitable as long as the gains from this strategy outperform the additional transactions costs.

3

Two behavioral models on under and overreaction

In this section, two recently proposed behavioral models are discussed, which were devised in such a way that they can explain both under and overreaction. Barberis, Shleifer and Vishny (BSV, 1998) generate an asset-pricing model that explains returns which produces underreaction to earning announcements in the short-run and overreaction in the long-run. Daniel, Hirshleifer and Subrahmanyam (DHS, 1998) also develop a model that explains under and overreaction, but their mechanism is based on a distinction between uninformed and informed investors. Prices are set by the latter, who are subject to overconfidence and biased self-attribution.

3.1

The investor sentiment model of Barberis et al.

The study of Barberis et al. separates the earnings process of a firm — which follows a random walk — and the price process, which is determined by investors under and overreacting on earnings announcements. An earnings 8

announcement at time t, zt , can be either good or bad, i.e. zt = G or zt = B. By underreaction, they mean that the average return on the company’s stock in the period following an announcement of good news is higher than the average return in the period following bad news: E(rt+1 |zt = G) > E(rt+1 |zt = B).

(2)

They define overreaction as occurring when the average return following not one but a series of announcements of good news is lower than the average return following a series of bad news announcements: E(rt+1 |zt = G, zt−1 = G, . . . , zt−j = G) < E(rt+1 |zt = B, Zt−1 = B, . . . , zt−j = B),

(3)

where j is at least one but probably rather higher. Note the asymmetry between these two definitions: the first is aimed at the short-term and the second at the long-term. The authors derive their approach from the work of Griffin and Tversky (1992): ”In their framework, people update their beliefs based on the ’strength’ and the ’weight’ of new evidence. Strength refers to such aspects of the evidence as salience and extremity, whereas weight refers to statistical informativeness, such as sample size. According to Griffin and Tversky, in revising their forecasts, people focus too much on the strength of the evidence, and too little on its weight, relative to a rational Bayesian.” Barberis et al. suppose that corporate earning announcements represent information that is of low strength but of significant statistical weight, thereby leading to underreaction. On the other hand, they suppose that consistent patterns of news represent information that is of high strength and low weight, leading to the hypothesis of underreaction. Barberis et al. work with a representative risk-neutral investor who beliefs that the earnings follow either a mean-reverting or a trending regime. In the first regime, it is likely that the earnings in the next period are opposite to those in the current period, whereas in the trending regime it is likely that earnings in both periods will have the same sign. The investor is convinced that he knows these probabilities, and moreover, he is also convinced that he knows the probabilities from switching from one regime to another. He is stubborn in the sense that does not change his model, even after observing a long stream of earnings data. His only task is to figure out which of the two regimes of his model is currently generating earnings. In this sense, the learning process in this model is minimal, which is not totally satisfactionary. Explanatory power of the BSV-model in the current case Can the facts we observed in Section 2 be explained by the BSV-model? The first thing to note in answering this question is that our data only 9

contain information over subsequent (daily or weekly) returns but that they say next to nothing about long term relationships. Therefore, given the definition (3) of overreaction, our data say nothing about it, and this part of the BSV-model is not of use to explain our results. Another weak point in the modelling is that it contains no information on how decisions and trade on a micro-level take place. The only thing the investor does, is adapting the subjective probabilities by which regime the earnings stream is generated, on basis of the observations. According to Barberis, Shleifer and Vishny, the beliefs of the representative investor reflect the ’consensus’1 , even if different investors have different beliefs. In this way, they neglect the question how trade takes place in order to reach a new price and how different investors interact with each other.

3.2

The investor psychology model of Daniel et al.

Whereas Barberis et al. ground their model of under and overreaction on the terms ’strength’ and ’weight’, Daniel, Hirschleifer and Subrahmanyam (1998) depart from the psychological biases of investor overconfidence and biased self-attribution, resulting in giving greater weight to private relative to public information2 . An overconfident investor is one who overestimates the precision of private signals but not of public signals, thereby leading stock prices to overreact to the arrival of private signals and to underreact to the arrival of public signals. Moreover, according to Daniel et al., investors update their confidence in their own ability in a biased manner. Individuals tend to attribute too strongly events that confirm the validity of their actions to high ability, and events that disconfirm the action to external noise or sabotage. Confirming public information makes his confidence rise but disconfirming public information causes his confidence only to fall modestly. Due to this different impact, new public signals will on average strengthen his confidence, leading to further overreaction to a preceding private signal. This causes both positive short-term autocorrelations as well as long-term reversals, as prices return to their fundamentals as further public information becomes available. The testable prediction that Daniel et al. make, is about so-called selective events. Selective events are events that are partly triggered by under or overreaction of the stock price. They include the issue of new stocks when the management of a firm considers its stocks overvalued and the repurchase 1

the equilibrium price of the security is supposed equal to the net present value of future earnings, as forecasted by the representative investor 2 In the terminology of Barberis et al., one could say that private information has on average higher strength but lower statistical significance compared to public information.

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of shares when it considers the price below the fair value. Due to overconfidence of the informed investors, the stock price will adjust only gradually when management makes this kind of plans public.

3.3

Support of the BSV and DHS model in empirical studies

In the paper in which Fama (1998) argues that the supposed long-term anomalies are consistent with the EMH, he counters with respect to the BSVmodel, that certainly, it explains reversal of long-term abnormal returns, but that long-term returns are not the norm. To show this, he mentions a number of articles which give evidence of long-term post-event returns of the same sign as long-term pre-event returns. Moreover, as the DHS-model makes in large the same long-term predictions as the BSV-model, it falls prey to the same criticism. Fama does not comment on the short-term implications of the two behavioral models. That is a pity since, as noted before, our data focus not so much on long-term as well on short-term behavior: only couples of two subsequent returns are considered and not the returns on more adjacent time periods3 . Our results have one characteristic that is not accounted for by both the BSV and the DHS model. Our data give evidence to short-term underreaction to bad news announcements but they do not lend support to the hypothesis that there is a lagged price response to good news. Neither the BSV-model, nor the DHS-model make a difference between an underreaction to good news and an underreaction to bad news. The question is, why should such a difference be extant in reality? The following possible explanations can be given for this: • After a downfall in prices, banks will send margin calls to their investors in order to ascertain that their clients can still meet their obligations. These calls may urge clients to sell. • A stock market drop is on an average given more attention on television and in the newspapers than stock market rises, so bad news will reach investors in a different way than good news. This information is received with a time lag and upon receiving the investor may be incited to give as yet an order to sell; • It is a well-known fact (See e.g. De Bondt and Thaler,1995) that people are more sensitive to loss as they are to gains; human beings are not as much risk averse as well loss averse. This may cause the observed difference in reaction to good and bad news. 3

It is possible to do this kind of research within the framework of Markov chain models, but then the states have to be modelled accordingly. This is left for future research.

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The first explanation is the most testable. It would be worthwhile to gather information on margin calls by banks to see how they influence everyday trade. The second assertion is more difficult to verify since it requires the identification of the uninformed and informed group of investors at each time point. This is calling for a testable model of information spreading through the economy. The final assertion could be verified by developing and testing a model in which people behave loss averse. In the next section we will investigate still another possible explanation for our results, namely that the time lag in price reaction to bad news is caused by investors influencing each other in their decisions; investors are partly led by the actions of the other investors, but they receive the information on these actions with a time lag.

4

Interdependent preferences of actors on the stockmarket

De Bondt and Thaler (1995) notice that it is an obvious fact of life that people are influenced by each other and that fashions and fads are as likely to emerge in financial markets as anywhere else. We strongly agree with this point of view. To give an example, in recent years many households entered the stock market in the Netherlands financing their stocks with investment mortgages. These mortgages used to be considered risky, but the attitude to these products seems to be altered. The question remains unanswered whether this is caused by a change in the degree of risk aversion of people, or by a collective change in the estimation of the riskiness of investment mortgages. In both cases however, the preferences of people seem to influence each other. Another example concerns the behavior of pension funds. Most funds increased the last few years the percentage they invested in stocks relative to the amount invested in bonds (see e.g. the annual report on 1999 of PGGM pension fund). The EMH however predicts, that the only difference in yield between bonds and stocks is the risk premium earned for investing in stocks. Therefore, also pension funds seem to have collectively changed either their degree of risk aversion or their perception of the risk on stock investments. In the nineties, a series of interesting empirical studies appeared, in which interdependent preferences were incorporated. These include studies on consumption decisions (Blundell and Robin, 1999), saving decisions (Kapteyn, 2000), and labor supply decisions (Aronsson, Blomquist and Sackl´en, 1999, Woittiez and Kapteyn, 1998). As far as we know, no empirical work on interdependent preferences in investment decisions is done, although the examples show that also in financial markets, not all interactions take place via the market. In the studies on consumer interdependence with respect to expenditures, 12

the budget share wgn consumer n spends on good g is made dependent on the prices of all goods i, with i ∈ {1, . . . , G}, in the economy, on the income yn earned by consumer n and on the budget shares wij other consumers in the economy give to the available goods, where i ∈ {1, . . . , G}, j ∈ {1, . . . , N }. The consumers whose budget shares influence the budget shares of consumer g are called the reference group of consumer g. The identification of reference groups is a difficult problem as clarified by Manski (1993). In most studies, reference groups are formed on basis of people sharing certain social characteristics, like age, education or family size. In the study of Woittiez and Kapteyn (1998), the grouping is done on basis of direct survey information. Noteworthy is, that hitherto the reference groups are nonoverlapping. That means that a person can belong to only one group. It is an attractive idea to do a same kind of study for investment goods. We could start with a simple economy with N investors where only two different assets are present (G = 2), stocks and bonds. The share wgn (t) of fund value that investor n, with n ∈ {1, . . . , N } spends on asset g at time t could be made dependent on the total fund value yn (t − 1) in the previous period, risk measures σi (t) of the different assets i ∈ {1, . . . , G}, a stochastic variable g (t) which accounts for the arrival of news relevant to the asset value, and the share distribution wij (t − 1), i ∈ {1, . . . , G}, j ∈ {1, . . . , N }, of all investors in the economy as perceived by investor g. We suppose these investment shares are observed with a lag of one period. This functional relationship is shown in (4): wgn = f (yn , σ1 , . . . , σG , w1,1 , . . . , w1,N , w2,1 , . . . , w2,N , . . . , wG,1 , . . . , wG,N , g ), ∀g∀n.

(4)

We omitted the time variables in this last equation. When switching from consumption to investment goods, we have to be aware of fundamental differences. The largest of these is the investment character of assets. Price changes influence the amount of money available for investments in future periods, whereas in consuming non-durable goods, future income can be assumed independent of current expenditures. Another point is the assumption of non-overlapping reference groups which is usually made in studies about interdependence. Intuitively, we think that reference groups could be well formed around fund size, with large funds being most sensitive to the actions of other large funds, small investors being most influenced by the actions of other small investors, whom they meet at work and at birthday parties. However, it is likely that small investors will give considerable weight to the actions of large investors in forming their opinion as these actions are transmitted to them by newspapers and personal mailings. This gives rise to the formation of overlapping reference groups where one investor can participate in more than one group. 13

In future research, these issues have to be addressed properly. Main questions are, which interdependence relationships exist in practice and how do they influence the pricing process in asset markets? Relation of interdependent preferences to the empirical results How should a model taking non-market interactions between investors into account be able to explain the empirical results in Section 2? In a model with interdependence, an underreaction of the stock price to company news occurs if investors too slowly adjust their perceptions of other investors investment shares over the different assets. Notice that this is a fundamental difference with the models of Barberis et al. and Daniel et al. discussed in Section 3, where underreaction results from investors being conservative in updating their own perceptions about the fair price. It is this distinction that enables us to incorporate one-sided underreaction into our model, by making investors react more heavily to a reduction in investment share by other investors than to a increase. This makes sense when investors behave loss averse instead of risk averse. Another notable difference between our set-up and the BSV- and DHSmodel is, that we explicitly introduce a microstructure into our approach, whereas the other models work with the concept of a representative investor.

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Conclusion

We have shown that returns on stocks and returns on stock indices are not independent and identically distributed drawings from lognormal probability distributions. Often, large drops in stock prices are followed by a further drop in the price in the next period. To explain these results, two behavioral finance models were introduced which were able to explain underreaction in asset prices. However, they were not able to explain the one-side underreaction we observed. For this reason, we made a set-up for a different approach in which individual investors’ preferences are interdependent. In future research, we want to build a complete model in which investors take notice of each other in this way and run simulations to see how the prices of the assets in the economy develop. Complementary research would involve the identification of reference groups in reality and the estimation of the interrelationships.

References “Http://www.dehypotheekadviseur.nl/hypotheekvormen.html”. “Jaarverslag PGGM 1999”.

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Aronsson, T., Blomquist S. and H. Sackl´en (1999), “Identifying interdependent behaviour in an empirical model of labor supply”, Journal of Applied Econometrics, 14, 607–626. Barberis, N., A. Shleifer and R. Vishny (1998), “A model of investor sentiment”, Journal of Financial Economics, 49, 307–343. Campbell, J.Y., A.W. Lo and A.C. MacKinlay (1997), The Econometics of Financial Markets, Princeton University Press, 41 William Street, Princeton, New Jersey. De Bondt, W.F.M. and R.H. Thaler (1995), “Financial decision-making in markets and firms: A behavioral perspective”, in R. Jarrow et al., editor, Handbooks in OR & MS, Vol., Elsevier Science B.V., chapter 13, 385–411. Drijver, S.J. and P.W. Otter (2000), “On rebalancing a sector portfolio model based on predictions of sector returns and markov chain models”, unpublished manuscript. Drijver, S.J, W.K Klein Haneveld and M.H. Van der Vlerk (2000), “Asset Liability Management modeling using multistage mixed-integer stochastic programming.”, unpublished manuscript. Fama, E.F. (1998), “Market efficiency, long-term returns, and behavioral finance”, Journal of Financial Economics, 49, 283–306. Griffin, D. and A. Tversky (1992), “The weighing of evidence and the determinants of confidence”, Cognitive Psychology, 24, 411–435. Kapteyn, A. (2000), “Saving and reference groups”, unpublished manuscript. Manski, C. (1993), “Identification of endogeneous social effects: The reflection problem”, The review of Economic Studies, 60, 531–542. Woittiez, I. and A. Kapteyn (1998), “Social interactions and habit formation in a model of female labour supply”, Journal of Public Economics, 70, 185–205.

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