MOMENTUM EFFECT IN INDIVIDUAL STOCKS AND HETEROGENEOUS BELIEFS AMONG FUNDAMENTALISTS

Transcription

1 MOMENTUM EFFECT IN INDIVIDUAL STOCKS AND HETEROGENEOUS BELIEFS AMONG FUNDAMENTALISTS Sandrine Jacob Leal Assistant Professor, ICN Business School Nancy-Metz CEREFIGE Address: 13, rue Michel Ney, Nancy (France). Tel: Fax: address: 1

2 MOMENTUM EFFECT IN INDIVIDUAL STOCKS AND HETEROGENEOUS BELIEFS AMONG FUNDAMENTALISTS Sandrine Jacob Leal 1 CEREFIGE, ICN Business School Nancy-Metz (France) sandrine.jacob-leal@icn-groupe.fr Abstract This paper investigates whether the observed momentum effect in individual stocks, caused by positive serial correlations in returns over short horizons, can be explained by fundamentalists heterogeneous beliefs when chartists are present in the market. For this purpose, we propose a heterogeneous agent model wherein agents follow different strategies and where information about asset fundamentals diffuses slowly. Computer-based simulations reveal that the interplay of fundamentalists and chartists can robustly generate positive serial correlations in returns over short horizons. Especially, short-term momentum is explained by trend-following strategies and slow diffusion of information. Furthermore, our model is able to simultaneously generate the momentum effect in individual stock returns, asset price overreaction and misalignments often observed in real financial time series. Keywords: momentum effect, return predictability, bounded rationality, trading strategies, computer-based simulations. Résumé: Dans cet article, nous abordons la question du «momentum effect», souvent observé dans le cours des actions et dû à l émergence de corrélations positives des rendements à court terme, à travers la coexistence sur le marché de chartistes et de fondamentalistes, lorsque ces derniers ont des croyances hétérogènes. À cette fin, nous proposons un modèle à agents hétérogènes dans lequel les agents adoptent différentes stratégies mais où la diffusion de l information concernant les fondamentaux des actifs est progressive. Les simulations numériques menées révèlent que les interactions entre fondamentalistes et chartistes peuvent causer, et ce de façon robuste, des corrélations positives des rendements à court terme. En particulier, notre modèle démontre que ces dynamiques des rendements observées à court terme s expliquent par les stratégies chartistes de type «trend-following» et la diffusion lente de l'information. En outre, notre modèle est capable de produire conjointement le «momentum effect» des rendements boursiers, la sur-réaction du prix des actifs et les anomalies de prix souvent observés sur les marchés d actions. Mots-clés: momentum effect, prévisibilité des rendements, rationalité limitée, stratégies de trading, simulations numériques. 1 This paper was presented at the 17 th Annual Workshop on Economic Heterogeneous Interacting Agents (W.E.H.I.A. 2012) held in Paris from June, 21 to June The author would like to thank the participants of W.E.H.I.A for very stimulating remarks. This paper will also be presented at the 61 st AFSE Congres held in Paris from July, 2 to July The author is also particularly grateful to Alain Raybaut, Patrick Musso and Olivier Bruno for fruitful discussions, very helpful comments and suggestions. 2

3 1 Introduction This paper investigates whether the momentum effect in individual stocks, caused by positive serial correlations in returns at short-term horizons ranging from three to twelve months (e.g., Jegadeesh and Titman, 1993; Chan, Jegadeesh, and Lakonishok, 1996; Rouwenhorst, 1998; Hong, Lim, and Stein, 2000; Jegadeesh and Titman, 2001; Doukas and McKnight, 2005), can be explained by the interplay of fundamentalists and chartists. Empirical evidence of return predictability is one of the most important challenge for the efficient market theory. Indeed such patterns in stock returns are inconsistent with the classical asset pricing theory. However, a well-documented explanation for the emergence of positive serial correlations in returns rely on the tendency of stock prices to underreact to news events in the short run (e.g., Chan, Jegadeesh, and Lakonishok, 1996; Barberis, Shleifer, and Vishny, 1998; Hong and Stein, 1999; Hong, Lim, and Stein, 2000). Behavioral theories further support stock prices underreaction to new information relying on some form of investor irrationality. From this viewpoint, such a predictibility in stock returns arises from investor psychological biases. Owing to biased self-attribution, representativeness heuristic and/or conservatism, investors are kept from quickly adapting their beliefs to new and convincing information. As a result, investors tend to underreact to news (see, for instance, Barberis, Shleifer, and Vishny, 1998; Daniel, Hirshleifer, and Subrahmanyam, 1998). Individual stock returns therefore exhibit positive short-lag autocorrelation. According to these works, the way investors interpret available information becomes crucial in explaining short-term momentum. 2 Another explanation for the above anomaly emphasizes the key role played by the diffusion of information. In this case, the momentum effect arises because the market responds only gradually to new information (see, for instance, Chan, Jegadeesh, and Lakonishok, 1996; Hong and Stein, 1999; Hong, Lim, and Stein, 2000). Overall, these earlier works suggest that information - both the diffusion process and the way investors interpret it - seems to play a crucial role in explaining the momentum effect in individual stocks. However, financial economists are from reaching a consensus on the source of this market anomaly. This paper contributes to the ongoing debate on the explanation of the above-described anomaly by studying autocorrelation patterns of returns in a heterogeneous agents model wherein fundamentalists have heterogeneous beliefs, due to slow diffusion of firm-specific information. To be precise, we investigate whether positive serial correlations in returns over short horizons can be explained by the interplay of fundamentalists, who set their strategies from the inference of asset fundamentals, and chartists, who set their strategies on the observation of past price movements. Indeed, the above works focus either on pervasive psychological biases which affect investors decisions or on market statistics to explain the emergence of short-term momentum in real financial time series. We rather propose to fill the gap by spelling out the source of the above anomaly at an intermediate level, i.e., by focusing on the effect of the interplay of common trading strategies on market dynamics. The main novelty of our study consists in the assumption regarding the knowledge of fundamentals. In fact, most of the works based on the explicit distinction between fundamentalists and chartists assume that fundamentalists know the fundamental value of 2 Behavioral explanations of the momentum effect in individual stocks also rely on overreaction to new information. Earlier works suggest that investor overconfidence causes stock prices movements to persist in the short run (i.e., positive serial correlation in returns) and reverse in the long run (i.e., negative serial correlation in returns) (e.g., Daniel, Hirshleifer, and Subrahmanyam, 1998, 2001). 3

4 the asset (e.g., Beja and Goldman, 1980; Lux, 1995, 1998; Farmer and Joshi, 2002; Westerhoff, 2003). In this work, we depart from this assumption by allowing fundamentalists to be sequentially aware of any news about asset fundamentals (e.g., Abreu and Brunnermeier, 2002, 2003). As a result, fundamentalists have, for some period of time, heterogeneous beliefs about asset fundamentals and they may not be able to recognize misalignments in asset prices. This departure is justified by earlier empirical and theoretical works which suggest that slow diffusion of information plays a key role in explaining momentum effect in individual stocks (see, for instance, Chan, Jegadeesh, and Lakonishok, 1996; Hong and Stein, 1999; Hong, Lim, and Stein, 2000; Doukas and McKnight, 2005). Furthermore, in contrast to previous works in the literature (e.g., Abreu and Brunnermeier, 2002, 2003), we assume that fundamentalists are boundedly rational. This departure is justified by extensive works on bounded rationality, which seems highly relevant in a heterogeneous world (Arthur, 1995; Hommes, 2001, 2006). Lastly, while most of the earlier heterogeneous agent models consider that the very figure of technical analysis is a trend follower, we depart from this assumption. In line with earlier works, we rather assume that the chartist population is composed of both trend followers and contrarian traders (see, for instance, Lux, 1995; Lux and Marchesi, 2000; Mannaro, Marchesi, and Setzu, 2008). Our study reveals that our model offers a qualitative description of asset prices dynamics and enables us to simultaneously explain momentum in individual stocks, asset price overreaction to news events and price misalignments. In particular, computer-based simulations reveal that the interplay of fundamentalists and chartists can robustly generate short-term momentum in returns. This phenomenon is mainly driven by slow diffusion of firm-specific information and the pervasive presence of chartists. Moreover, we find that, when trend followers dominate the market, owing to slow diffusion of firm-specific information, asset price overreacts and subsequently corrects. This price dynamics generates positive as well as negative serial correlations in returns over differing horizons. This paper is organized as follows. In Section 2, we present the model of linear price formation with sequentially informed fundamentalists. In Section 3, we present and discuss the results of the model. Section 4 summarizes the main findings of this work and concludes. 2 The model We consider a market in which there is a single risky asset with price P t and fundamental value V t. The fundamental value of the asset is based on the asset future payoffs i.e., on the prospects of future cash flows only. The evolution of the asset fundamental value over time is formalized as follows: V t Vt 1 t = +ε (1) 2 where { ε t } is a sequence of i.i.d. random variables with E [ ε t ] = 0, var[ ε t ] = σ ε and cov( εt, ε t j ) = 0 for j 0, so that E[ V t ] = V t 1. In the market, there are N agents, who are assumed to be of two types, namely, fundamentalists and chartists. The number of fundamentalists and chartists in the market is 4

5 denoted n f and n c respectively, with n f + nc = N. The portion of fundamentalists is denoted η n / N. The chartist population is composed of two subgroups, namely, trend f followers and contrarian traders. Their respective numbers are denoted n TF and n CT with ntf + nct = nc. The portion of trend followers among the chartist population is denoted z ntf / nc. In each period, agents can place buy or sell orders in the market. First, fundamentalists base their trading strategy upon any differential between the observed asset price and its fundamental value. Fundamentalists orders are captured as follows: F X = t 1 β ( E[ Vt ] + Pt ) (2) where the term β is a positive reaction coefficient. Second, chartists set their trading strategies based on the observation of past prices. Trend followers believe that any observed trend in prices will persist in the future. Their orders are as follows: X = ϕ( P P ) (3) TF t+ 1 t t 1 where the term ϕ is a positive reaction coefficient. Contrarian traders rather believe that any observed trend in prices will revert in the future. Their orders are therefore expressed as: X = ϕ( P P ) (4) CT t+ 1 t t 1 In each period, the market maker mediates transactions by matching agents demand and supply and sets the new asset price according to aggregate excess demand in the market as follows: P = P + µ ( n X + n X + n X ) (5) F TF CT t+ 1 t f t+ 1 TF t+ 1 CT t+ 1 where the term µ is a positive price adjustment parameter. Substituting eq. (2), eq. (3) and eq. (4) into eq. (5) yields: P = µ n β V + (1 n µβ + µϕ ( n n )) P + µϕ( n n ) P (6) t+ 1 f t 1 f TF CT t CT TF t 1 which constitutes our stochastic model driving the price dynamics. In the market, at some point in time, t 0, there is a positive shock on the asset fundamental value. 3 This shock captures any good news events which markedly alters future cash flows of the asset and as a consequence its intrinsic value. However, we assume 4 that information about the asset fundamentals diffuses slowly. Consequently, fundamentalists are only sequentially aware of the true fundamentals. In each period, an additional fraction of fundamentalists ( n inc ) is informed of the true asset fundamentals. All fundamentalists are therefore not immediately able to recognize that the asset fundamentals have markedly changed. For a while, fundamentalists have heterogeneous beliefs about 3 Similar results of the model would be derived if a negative shock on t V were considered. 4 The foregoing assumption may also capture situations in which there is asymmetric information or differential interpretation of such an information among fundamentalists. 5

6 asset future payoffs and fundamentalists perceived asset fundamental value does not always coincide with the true one. After t 0, some fundamentalists know the true asset fundamental value (i.e., fundamentalists with realistic beliefs ) and are immediately able to recognize that the asset is mispriced i.e., it is undervalued. Others stick to a misleading asset fundamental value (i.e., fundamentalists with unrealistic beliefs ) and they are therefore not able to recognize that the asset is mispriced. As a result, for a while, fundamentalists with realistic and unrealistic beliefs about asset fundamentals coexist in the market. 3 Numerical analysis We consider the above-described model and seek to investigate, through such a parsimonious model with linear behavioral rules and linear price formation rule, under which conditions the momentum effect in individual stocks, caused by positive serial correlations in returns over short horizons, emerges when fundamentalists and chartists coexist in the market. In what follows, we mainly focus on autocorrelation patterns in returns from the simulated time series. Computer-based simulations are required due to the stochasticity of the model driving price dynamics and the heterogeneity within the agent population. For this purpose, we simulate the model with 500 time steps and we check the robustness of the simulation results by implementing Monte Carlo simulations over 50 runs. 5 The parameter values used in simulations are reported in Table 1. The main criterion for choosing parameter values was to match one of the crucial efficient market hypothesis prediction according to which stock prices should reflect asset fundamentals and arbitrage does work. A preliminary study of the deterministic version of the model, described in eq. (6), provides the required background to set the appropriate framework as well as parameter values used in computer simulations. 6 In particular, this study reveals that, first, consistent with the efficient market theory, when there are only well-informed and well-funded fundamentalists, arbitrage works. Second, we identified the parameter values (i.e., β, ϕ and µ ) which ensure that the system is stable, so that any non-stationary behavior of { P t } sequence is precluded from this work. To be precise, we show that the { P t } sequence is stable for a wide range of parameter values. 7 Lastly, given the stability conditions on parameter values, we show that the { P t } sequence is stable whatever the composition of the population (i.e., η and z ). 5 The code, written in Java and Matlab, is available from the author upon request. 6 In the deterministic model, we relax the sequential awareness assumption by rather assuming that fundamentalists know the fundamental value of the asset in each period. 7 The study of the stability of the solution of the deterministic version of the model is available from the author upon request. 6

7 Table 1: Parameters for the simulations. Our investigation of the statistical properties of artificially generated series is presented in the following subsections. As a preliminary step in this study, we implement some baseline cases which include, first, a setting in which there are only fundamentalists (i.e., η = 1 ) (baseline 1). This setting enables us to determine whether slow diffusion of information suffices to explain short-term trends in prices (i.e., positive serial correlations in returns over short horizons). Second, we study a setting where chartists are present as well in the market, although their trading activity does not further affect price dynamics (baseline 2). This is done by setting the portion of trend followers equal to the portion of contrarian traders (i.e., z = 0.5 ). 8 This setting enables us to focus on the effect of fundamentalist strategies on price dynamics, when chartists are present in the market. Finally, in order to investigate under which conditions the momentum effect in individual stocks emerges when fundamentalists and chartists - both trend followers and contrarian traders - are present in the market, we present the results from the setting of major interest to us i.e., when trend-following and contrarian strategies actually affect price dynamics. This is done by varying the portion of trend followers versus contrarian traders (i.e., 0 z 1). 8 In this case, according to eq. (3) and eq. (4) from Section 2, trend follower s orders and contrarian trader s ones exactly compensate, so that chartist trading activity does not further affect the evolution of the asset price. 7

8 3.1 A Market with only Fundamentalists As a preliminary step, we focus on return predictability when there are only fundamentalists in the market (i.e., η = 1 ): baseline 1. This setting enables us to spell out the effect of slow diffusion of firm-specific information on price dynamics. By assuming sequential awareness, after the shock on V t and so long as all fundamentalists do not share the same information about asset fundamentals (i.e., during the awareness window) 9, they have heterogeneous beliefs. Consequently, for the awareness window, asset price does not coincide with its fundamental value (i.e., there is mispricing). Mispricing persistence arises from the heterogeneity in fundamentalists beliefs, which prevents fundamentalists from simultaneously trading against the mispricing. However, although mispricing persists over time, computer simulations reveal that when there are only fundamentalists in the market (i.e., η = 1), returns from the simulated time series are not predictable. Fig. 1 shows the sample autocorrelation functions of returns from the simulated time series when η = 1. Figure 1: Sample autocorrelation functions of returns when η = 1. Fig. 1 shows that, when η = 1, positive serial correlations in returns over short horizons do not emerge. As a result, we can assert that, when there are only fundamentalists in the market, fundamentalists heterogeneous beliefs, owing to slow diffusion of information, is not sufficient to explain the momentum effect in individual stocks. The smoothness of the convergence process of the asset price towards its fundamental value prevents returns from being predictable. Contrary to earlier works which suggest that gradual diffusion of firm-specific information helps to explain short-term momentum, in our model, slow information dissemination across market participants does not suffice to explain the momentum effect in returns. 9 As shown in Table 1, in this work, the awareness window is assumed to be 10 periods. 8

9 3.2 A Market with Fundamentalists and Neutral Chartists We now turn to focus on the effect of fundamentalist strategies on the price dynamics when chartists - both trend followers and contrarian traders - are present in the market. To this end, as a first step, we study the price dynamics that emerge in the market when chartist trading activity does not further affect the evolution of the asset price (i.e., z = 0.5 ): baseline 2. This setting enables us to focus on the effect of fundamentalist strategies on price dynamics, when chartists are present in the market. This is done by varying the portion of fundamentalists (i.e., η ) from 0 to First, simulations reveal that mispricing duration is decreasing in the portion of fundamentalists in the market (i.e., η ). In other words, the greater the portion of fundamentalists in the market, the shorter will last the mispricing. Fig. 2 shows the values of the autocorrelation coefficients at lag 1 of mispricing duration for differing values of η. Figure 2: Relationship between mispricing duration and η when z = 0.5. Furthermore, mispricing correction tends to be markedly delayed only for low portion of fundamentalists (i.e., 0.1 η 0.2 ). The presence of chartists therefore prevents fundamentalists from correcting the mispricing only when chartists widely dominate the market. As a result, we show that the presence of fundamentalists is crucial in explaining mispricing correction. Second, simulations bring out that autocorrelation patterns only emerge when chartists dominate the market ( η < 0.5 ). Fig. 3 shows the sample autocorrelation function of returns for differing values of η. 10 To be precise, we restrict this analysis to 0 < η < 1 because first when there are no fundamentalists in the market (i.e., η = 0 ), the asset price will remain constant at its pre-shock level and chartists have no incentive to trade in this market. Second, the price dynamics that emerges in the market when there are only fundamentalists was the purpose of the previous subsection. 9

10 Figure 3: Sample autocorrelation function of returns for differing values of η and z = 0.5. In particular, we find that, as shown in Fig. 3c and Fig. 3d, positive coefficients over small lags, reflecting short-term trends in prices, only arise when η < 0.5. In contrast, when fundamentalists dominate the market ( η > 0.5 ), as shown in Fig. 3a and Fig. 3b, such autocorrelation patterns do not emerge and no sign of return predictability is detected. Unlike when there are only fundamentalists in the market, short-term momentum (i.e., positive serial correlation in returns) is driven by slow diffusion of firm-specific news events and the pervasive presence of chartists in the market. Overall, we find that first fundamentalists play a key role in explaining mispricing correction. Second, the pervasive presence of chartists is a necessary condition for explaining the emergence of the momentum effect in individual stocks (i.e., positive short-term autocorrelation of stock returns). Lastly, we find that slow diffusion of firm-specific information plays a crucial role in explaining short-term momentum only when chartists dominate the market. This result is consistent with earlier works which suggest that the source of short-term momentum is stock price underreaction to news events 10

11 (e.g., Jegadeesh and Titman, 1993; Chan, Jegadeesh, and Lakonishok, 1996; Hong and Stein, 1999; Jegadeesh and Titman, 2001). 3.3 A Market with Fundamentalists and Active Chartists We now investigate the price dynamics that emerge in the market for differing portions of trend followers versus contrarian traders. This is done by varying the portion of trend followers (i.e., z ) from 0 to 1. First, simulations reveal that trend following (contrarian) strategies quicken (slow) mispricing correction. Fig. 4 shows the relationship between the autocorrelation coefficient at lag 1 of mispricing duration and the portion of trend followers in the market ( z ) for differing portions of fundamentalists (η ). Figure 4: Relationship between mispricing duration and z for differing values of η. The dash line represents ACF(1) of mispricing duration when z = 0.5 (i.e., baseline 2). 11

12 This figure clearly shows that, on one hand, when chartists mainly use trend-following strategies ( z > 0.5 ), mispricing duration tends to be shortened with respect to baseline 2 (i.e., when z = 0.5), depicted by the dash line in Fig. 4. However, it is worth stressing that the lower the portion of fundamentalists in the market, the greater the extent of mispricing correction driven by trend-following strategies, with respect to baseline 2. So, contrary to earlier results (see, for instance, Lux, 1995, 1998; Farmer and Joshi, 2002; De Grauwe and Grimaldi, 2005), we find that, when trend followers dominate the market, trend-following strategies facilitate market efficiency thanks to slow diffusion of information. This result is explained by the fact that trend-following strategies tend to amplify trends in prices triggered by fundamentalists who sequentially trade against the mispricing. As a result, price correction is faster. On the other hand, contrarian strategies (i.e., when z < 0.5 ) tend to lengthen mispricing duration with respect to baseline 2, especially when the portion of fundamentalists is high ( η > 0.5 ). Contrarian strategies prevent fundamentalists from efficiently trading against the mispricing, even when the latter widely dominate the market. Nevertheless, simulations unveil that when the portion of fundamentalists is high ( η 0.5 ), whatever the portion of trend followers in the chartist population, positive serial correlations in returns over short horizons do not emerge. Fig. 5 shows the sample autocorrelation functions of returns from the simulated time series for high and low portion of trend followers ( z = 0.7 and z = 0.3, respectively). Figure 5: Sample autocorrelation functions of returns when η = 0.7 and for differing values of z. Fig. 5 illustrates that, when fundamentalists dominate the market, whatever the portion of trend followers, fundamentalist strategies prevent returns from being predictable. Returns are not predictable because, when fundamentalists dominate the market, the effect of chartist trading activity does not outweight the effect of fundamentalist trading activity on price dynamics. 12

13 Second, simulations reveal that when chartists widely dominate the market (i.e., η 0.2 ), trend-following (contrarian) strategies amplify (reduce) short-term momentum. Fig. 6 shows the sample autocorrelation functions of returns when η = 0.2, for differing portions of trend followers (i.e., z ). Figure 6: Sample autocorrelation function of returns when η = 0.2 for differing values of z. 13

14 The returns from the simulated time series exhibit positive serial correlations over short horizons, whatever the portion of trend followers versus contrarian traders in the chartist population. However, on one hand, when the chartist population is mainly composed of contrarian traders ( z < 0.5 ), positive coefficients at small lag are smaller than in baseline 2 (i.e., z = 0.5 ) but emerge at higher lags than in baseline 2. In other words, the greater the portion of contrarian traders in the market, the longer is mispricing correction. Contrarian strategies therefore increase mispricing duration. On the other hand, when the chartist population is mainly composed of trend followers ( z > 0.5 ), the extent of positive coefficients is greater than in baseline 2 (i.e., z = 0.5 ) but positive correlations emerge at smaller lags than in baseline 2. That is, the greater the portion of trend followers in the chartist population, the more pronounced short-term positive correlations in returns. Trend-following strategies therefore amplify short-term momentum which, in this case, fasten mispricing correction. Overall, these results suggest that momentum effect is mainly driven by slow diffusion of information and the composition of the market population. Lastly, simulations bring out that when there are only trend followers within the chartist population (i.e., z = 1 ), the asset price overshoots before converging towards the asset fundamental value. Fig. 7 shows the simulated time series as well as the sample autocorrelation function of returns from the simulated time series when η = 0.2 and z = 1. Figure 7: Price dynamics when η = 0.2 and z = 1. In Fig. 7a, convergence towards the asset fundamentals occurs through dampened oscillations and the asset price clearly overreacts then corrects. As a result, when trend followers dominate the market, positive as well as negative serial correlations in returns over differing horizons emerge, as shown in Fig. 7b. Price misalignment therefore persists longer in the market. In fact, when fundamentalists are present in the market, trend following strategies, which, according to eq. (3) (see also Fig. 6), primarily induce trends in price, amplify the foremost trend in prices initiated by fundamentalists, causing the asset price to overreact. Under some circumstances, our model is therefore able to simultaneously generate short-term positive serial correlations in returns (i.e., price trends) and long-term negative serial correlation in returns (i.e., asset price reversals). These results are consistent with earlier works which suggest that stock prices overreaction to news events and 14

15 subsequent correction is the source of the momentum effect often observed in real financial time series (as in, for instance, De Bondt and Thaler, 1985, 1987; DeLong, Shleifer, Summers, and Waldmann, 1990). 4 Conclusions In this paper, we model a financial stock market wherein fundamentalists have heterogeneous beliefs, owing to slow diffusion of firm-specific information. In line with earlier works, we assume that fundamentalists are sequentially informed about any new information about asset fundamentals (see, for instance, Abreu and Brunnermeier, 2002, 2003). The purpose of this work is to assess whether positive serial correlations in returns can be explained by the interplay of fundamentalists and chartists - both trend followers and contrarian traders, when fundamentalists have heterogeneous beliefs. This work reveals that this parsimonious model offers a qualitative description of asset prices dynamics and enables us to simultaneously explain the momentum effect in individual stocks as well as asset price overreaction and price misalignments. First, our study brings out that slow diffusion of information and the resulting heterogeneous beliefs among fundamentalists play a crucial role in explaining price misalignments. Indeed, when fundamentalists, altogether, are not able to trade against asset mispricing, it can persist for some period of time. This finding is consistent with earlier works which suggest that synchronized risk tends to prevent fundamentalists from bringing back asset prices towards its fundamentals (Abreu and Brunnermeier, 2002, 2003). However, in constrast with earlier works (e.g., Chan, Jegadeesh, and Lakonishok, 1996; Hong and Stein, 1999), we show that, when there are only fundamentalists in the market, slow diffusion of information does not suffice to explain the momentum effect in individual stocks, caused by positive serial correlations in returns. Second, our framework is able to reproduce positive serial correlations in returns over short horizons, often observed in real financial markets. In particular, we suggest that, when firm-specific information diffuses slowly, short-term momentum arises from chartists strategies. This finding is consistent with the explanation of the momentum effect relying on stock price underreaction to news events. Third, our investigation unveils that trend-following strategies play a key role in explaining the momentum effect in individual stocks, when there is slow diffusion of information. More precisely, consistent with earlier works on the destabilizing effect of trend followers (e.g., DeLong, Shleifer, Summers, and Waldmann, 1990, Lux, 1995; Farmer and Joshi, 2002; De Grauwe and Grimaldi, 2005), we show that when chartists dominate the market, trend-following strategies generate short-term positive serial correlations in returns (i.e., price trends). However, by amplifying trends in prices, trend-following strategies subsequently fasten mispricing correction, triggered by fundamentalists. Consequently, when information diffuses slowly, trend followers also facilitate price correction and market efficiency. Lastly, in contrast to earlier works which suggest that the momentum effect is explained by stock price underreaction (e.g., Jegadeesh and Titman, 1993; Chan, Jegadeesh, and Lakonishok, 1996; Hong, Lim, and Stein, 2000; Jegadeesh and Titman, 2001), our results reveal that trends in stock returns reverse over long horizons. Our model is therefore able to simultaneously generate positive serial correlations in returns over short horizons and 15

16 negative serial correlations in returns over long horizons. Our results further support empirical evidence which suggest that the momentum effect is better characterized as a stock price overreaction, as for instance in De Bondt and Thaler (1985, 1987); Doukas and McKnight (2005). However, our findings reveal that the market composition plays a key role in interpreting the momentum effect. Given that chartists dominate the market and that firm-specific information diffuses slowly, when trend followers dominate the market, we show that asset price overreacts then corrects. Returns from the simulated time series therefore exhibit both positive serial correlations in returns over short horizons and negative serial correlations in returns over long horizons. Such a price behavior explains that misalignments can markedly persist in the market. Consequently, our parsimonious model is able to simultaneously generate momentum effect in individual stocks, asset price overreaction and price misalignments. Extensions of this work can be conducted along the following lines. First, in this work, we assume that agents are well-funded. Agents are rather likely to face financial constraints which would limit their trading strategies and would lead to more complex price dynamics. This would enable us to account for the evolution of agents wealth and of the market composition over time. Second, in this work, the learning process is quite simple allowing, in each period, a constant fraction of fundamentalists to be aware of the true asset fundamental value. However, the diffusion of firm-specific information is likely to be better approximated by a more complex rule. This would enable us to further understand the effect of the information diffusion process on price dynamics. We leave these extensions for future research. 16

17 References Abreu, D. and M. Brunnermeier (2002), Synchronization risk and delayed arbitrage, Journal of Financial Economics, 66: Abreu, D. and M. Brunnermeier (2003), Bubbles and crashes, Econometrica, 71(1): Arthur, W. (1995), Complexity in economic and financial markets, Complexity, 1(1): Barberis, N., A. Shleifer and R. Vishny (1998), A model of investor sentiment, Journal of Financial Economics, 49: Beja, A. and M. Goldman (1980), On the dynamic behavior of prices in disequilibrium, The Journal of Finance, 35(2): Chan, L., N. Jegadeesh and J. Lakonishok (1996), Momentum strategies, The Journal of Finance, 51(5): Daniel, K., D. Hirshleifer and A. Subrahmanyam (1998), Investor psychology and security market under- and overreactions, The Journal of Finance, 53(6): Daniel, K., D. Hirshleifer and A. Subrahmanyam (2001), Overconfidence, arbitrage, and equilibrium asset pricing, The Journal of Finance, 56(3): De Bondt, W. and R. Thaler (1985), Does the stock market overreact?, The Journal of Finance, 40(3): De Bondt, W. and R. Thaler (1987), Further evidence on investor overreaction and stock market seasonality, The Journal of Finance, 42(3): De Grauwe, P. and M. Grimaldi (2005), Heterogeneity of agents, transactions costs and the exchange rate, Journal of Economic Dynamics and Control, 29(4): DeLong, J. B., A. Shleifer, L. Summers and R. Waldmann (1990), Positive feedback investment strategies and destabilizing rational speculation, The Journal of Finance, 45: Doukas, J. and P. McKnight (2005), European momentum strategies, information diffusion, and investor conservatism, European Financial Management, 11(3): Farmer, J. and S. Joshi (2002), The price dynamics of common trading strategies, Journal of Economic Behavior and Organization, 49(2): Hommes, C. (2001), Financial markets as nonlinear adaptive evolutionary systems, Quantitative Finance, 1(1): Hommes, C. (2006), Heterogeneous agent models in economics and finance, in Tesfatsion, L. and K. L. Judd (eds.), Handbook of Computational Economics, Vol. 2, chap. 23, pp Elsevier. Hong, H., T. Lim and J. Stein (2000), Bad news travels slowly: Size, analyst coverage, and the profitability of momentum strategies, The Journal of Finance, 55(1): Hong, H. and J. Stein (1999), A unified theory of underreaction, momentum trading, and overreaction in asset markets, The Journal of Finance, 54(6): Jegadeesh, N. and S. Titman (1993), Returns to buying winners and selling losers: Implications for stock market efficiency, The Journal of Finance, 48(1): Jegadeesh, N. and S. Titman (2001), Profitability of momentum strategies: An evaluation of alternative explanations, The Journal of Finance, 56(2): Lux, T. (1995), Herd behaviour, bubbles and crashes, The Economic Journal, 105(431):

18 Lux, T. (1998), The socio-economic dynamics of speculative markets: Interacting agents, chaos, and the fat tails of return distributions, Journal of Economic Behavior and Organization, 33(2): Lux, T. and M. Marchesi (2000), Volatility clustering in financial markets: A microsimulation of interacting agents, International Journal of Theoretical and Applied Finance, 3(4): Mannaro, K., M. Marchesi and A. Setzu (2008), Using an artificial financial market for assessing the impact of Tobin-like transaction taxes, Journal of Economic Behavior & Organization, 67(2): Rouwenhorst, K. (1998), International momentum strategies, The Journal of Finance, 53(1): Westerhoff, F. (2003), Market-maker, inventory control and foreign exchange dynamics, Quantitative Finance, 3(5):