《金融投资学》教学资源（英文文献）A Unified Theory of Underreaction, Momentum Trading and Overreaction in Asset Markets

THE JOURNAL OF FINANCE.VOL.LIV,NO.6.DECEMBER 1999 A Unified Theory of Underreaction, Momentum Trading,and Overreaction in Asset Markets HARRISON HONG and JEREMY C.STEIN* ABSTRACT We model a market populated by two groups of boundedly rational agents:"news- watchers"and "momentum traders."Each newswatcher observes some private in- formation,but fails to extract other newswatchers'information from prices.If information diffuses gradually across the population,prices underreact in the short run.The underreaction means that the momentum traders can profit by trend- chasing.However,if they can only implement simple(i.e.,univariate)strategies, their attempts at arbitrage must inevitably lead to overreaction at long horizons. In addition to providing a unified account of under-and overreactions,the model generates several other distinctive implications. OVER THE LAST SEVERAL YEARS,a large volume of empirical work has docu- mented a variety of ways in which asset returns can be predicted based on publicly available information.Although different studies have used a host of different predictive variables,many of the results can be thought of as belonging to one of two broad categories of phenomena.On the one hand, returns appear to exhibit continuation,or momentum,in the short to me- dium run.On the other hand,there is also a tendency toward reversals,or fundamental reversion,in the long run.1 It is becoming increasingly clear that traditional asset-pricing models- such as the capital asset pricing model(CAPM)of Sharpe(1964)and Lint- ner (1965),Ross's (1976)arbitrage pricing theory (APT),or Merton's (1973) intertemporal capital asset pricing model (ICAPM)-have a hard time ex- plaining the growing set of stylized facts.In the context of these models,all of the predictable patterns in asset returns,at both short and long horizons, must ultimately be traced to differences in loadings on economically mean- ingful risk factors.And there is little affirmative evidence at this point to suggest that this can be done. Stanford Business School and MIT Sloan School of Management and NBER.This re- search is supported by the National Science Foundation and the Finance Research Center at MIT.We are grateful to Denis Gromb,Rene Stulz,an anonymous referee,and seminar par. ticipants at MIT,Michigan,Wharton,Duke,UCLA,Berkeley,Stanford,and Illinois for help- ful comments and suggestions.Thanks also to Melissa Cunniffe for help in preparing the manuscript. We discuss this empirical work in detail and provide references in Section I below. 2143

A Unified Theory of Underreaction, Momentum Trading, and Overreaction in Asset Markets HARRISON HONG and JEREMY C. STEIN* ABSTRACT We model a market populated by two groups of boundedly rational agents: “news￾watchers” and “momentum traders.” Each newswatcher observes some private in￾formation, but fails to extract other newswatchers’ information from prices. If information diffuses gradually across the population, prices underreact in the short run. The underreaction means that the momentum traders can profit by trend￾chasing. However, if they can only implement simple ~i.e., univariate! strategies, their attempts at arbitrage must inevitably lead to overreaction at long horizons. In addition to providing a unified account of under- and overreactions, the model generates several other distinctive implications. OVER THE LAST SEVERAL YEARS, a large volume of empirical work has docu￾mented a variety of ways in which asset returns can be predicted based on publicly available information. Although different studies have used a host of different predictive variables, many of the results can be thought of as belonging to one of two broad categories of phenomena. On the one hand, returns appear to exhibit continuation, or momentum, in the short to me￾dium run. On the other hand, there is also a tendency toward reversals, or fundamental reversion, in the long run.1 It is becoming increasingly clear that traditional asset-pricing models— such as the capital asset pricing model ~CAPM! of Sharpe ~1964! and Lint￾ner ~1965!, Ross’s ~1976! arbitrage pricing theory ~APT!, or Merton’s ~1973! intertemporal capital asset pricing model ~ICAPM!—have a hard time ex￾plaining the growing set of stylized facts. In the context of these models, all of the predictable patterns in asset returns, at both short and long horizons, must ultimately be traced to differences in loadings on economically mean￾ingful risk factors. And there is little affirmative evidence at this point to suggest that this can be done. * Stanford Business School and MIT Sloan School of Management and NBER. This re￾search is supported by the National Science Foundation and the Finance Research Center at MIT. We are grateful to Denis Gromb, René Stulz, an anonymous referee, and seminar par￾ticipants at MIT, Michigan, Wharton, Duke, UCLA, Berkeley, Stanford, and Illinois for help￾ful comments and suggestions. Thanks also to Melissa Cunniffe for help in preparing the manuscript. 1 We discuss this empirical work in detail and provide references in Section I below. THE JOURNAL OF FINANCE • VOL. LIV, NO. 6 • DECEMBER 1999 2143

2144 The Journal of Finance As an alternative to these traditional models,many are turning to"be- havioral"theories,where "behavioral"can be broadly construed as involving some departure from the classical assumptions of strict rationality and un- limited computational capacity on the part of investors.But the difficulty with this approach is that there are a potentially huge number of such de- partures that one might entertain,so it is hard to know where to start. In order to impose some discipline on the process,it is useful to articulate the criteria that a new theory should be expected to satisfy.There seems to be broad agreement that to be successful,any candidate theory should,at a minimum:(1)rest on assumptions about investor behavior that are either a priori plausible or consistent with casual observation;(2)explain the exist- ing evidence in a parsimonious and unified way;and(3)make a number of further predictions that can be subject to "out-of sample"testing and that are ultimately validated.Fama (1998)puts particular emphasis on the lat- ter two criteria:"Following the standard scientific rule,market efficiency can only be replaced by a better model....The alternative has a daunting task.It must specify what it is about investor psychology that causes simul- taneous underreaction to some types of events and overreaction to oth- ers....And the alternative must present well-defined hypotheses,themselves potentially rejectable by empirical tests." A couple of recent papers take up this challenge.Both Barberis,Shleifer, and Vishny (1998)and Daniel,Hirshleifer,and Subrahmanyam (1998)as- sume that prices are driven by a single representative agent,and then posit a small number of cognitive biases that this representative agent might have. They then investigate the extent to which these biases are sufficient to si- multaneously deliver both short-horizon continuation and long-horizon reversals.2 In this paper,we pursue the same goal as Barberis et al.(1998)and Dan- iel et al.(1998),that of building a unified behavioral model.However,we adopt a fundamentally different approach.Rather than trying to say much about the psychology of the representative agent,our emphasis is on the interaction between heterogeneous agents.To put it loosely,less of the action in our model comes from particular cognitive biases that we ascribe to in- dividual traders,and more of it comes from the way these traders interact with one another. More specifically,our model features two types of agents,whom we term “newswatchers'”and“momentum traders..”Neither type is fully rational in the usual sense.Rather,each is boundedly rational,with the bounded ra- tionality being of a simple form:each type of agent is only able to "process" some subset of the available public information.3 The newswatchers make forecasts based on signals that they privately observe about future funda- mentals;their limitation is that they do not condition on current or past 2 We have more to say about these and other related papers in Section V below. 3 Although the model is simpler with just these two types of traders,the results are robust to the inclusion of a set of risk-averse,fully rational arbitrageurs,as shown in Section III.B

As an alternative to these traditional models, many are turning to “be￾havioral” theories, where “behavioral” can be broadly construed as involving some departure from the classical assumptions of strict rationality and un￾limited computational capacity on the part of investors. But the difficulty with this approach is that there are a potentially huge number of such de￾partures that one might entertain, so it is hard to know where to start. In order to impose some discipline on the process, it is useful to articulate the criteria that a new theory should be expected to satisfy. There seems to be broad agreement that to be successful, any candidate theory should, at a minimum: ~1! rest on assumptions about investor behavior that are either a priori plausible or consistent with casual observation; ~2! explain the exist￾ing evidence in a parsimonious and unified way; and ~3! make a number of further predictions that can be subject to “out-of sample” testing and that are ultimately validated. Fama ~1998! puts particular emphasis on the lat￾ter two criteria: “Following the standard scientific rule, market efficiency can only be replaced by a better model. . . . The alternative has a daunting task. It must specify what it is about investor psychology that causes simul￾taneous underreaction to some types of events and overreaction to oth￾ers. . . . And the alternative must present well-defined hypotheses, themselves potentially rejectable by empirical tests.” A couple of recent papers take up this challenge. Both Barberis, Shleifer, and Vishny ~1998! and Daniel, Hirshleifer, and Subrahmanyam ~1998! as￾sume that prices are driven by a single representative agent, and then posit a small number of cognitive biases that this representative agent might have. They then investigate the extent to which these biases are sufficient to si￾multaneously deliver both short-horizon continuation and long-horizon reversals.2 In this paper, we pursue the same goal as Barberis et al. ~1998! and Dan￾iel et al. ~1998!, that of building a unified behavioral model. However, we adopt a fundamentally different approach. Rather than trying to say much about the psychology of the representative agent, our emphasis is on the interaction between heterogeneous agents. To put it loosely, less of the action in our model comes from particular cognitive biases that we ascribe to in￾dividual traders, and more of it comes from the way these traders interact with one another. More specifically, our model features two types of agents, whom we term “newswatchers” and “momentum traders.” Neither type is fully rational in the usual sense. Rather, each is boundedly rational, with the bounded ra￾tionality being of a simple form: each type of agent is only able to “process” some subset of the available public information.3 The newswatchers make forecasts based on signals that they privately observe about future funda￾mentals; their limitation is that they do not condition on current or past 2 We have more to say about these and other related papers in Section V below. 3 Although the model is simpler with just these two types of traders, the results are robust to the inclusion of a set of risk-averse, fully rational arbitrageurs, as shown in Section III.B. 2144 The Journal of Finance

Underreaction,Momentum Trading,and Overreaction 2145 prices.Momentum traders,in contrast,do condition on past price changes. However,their limitation is that their forecasts must be "simple"(i.e.,uni- variate)functions of the history of past prices.4 In addition to imposing these two constraints on the information process- ing abilities of our traders,we make one further assumption,which is more orthodox in nature:Private information diffuses gradually across the news- watcher population.All our conclusions then flow from these three key as- sumptions.We begin by showing that when only newswatchers are active, prices adjust slowly to new information-there is underreaction but never overreaction.As is made clear later,this result follows naturally from com- bining gradual information diffusion with the assumption that newswatch- ers do not extract information from prices. Next,we add the momentum traders.It is tempting to conjecture that because the momentum traders can condition on past prices,they arbitrage away any underreaction left behind by the newswatchers;with sufficient risk tolerance,one might expect that they would force the market to become approximately efficient.However,it turns out that this intuition is incom- plete if momentum traders are limited to simple strategies.For example, suppose that a momentum trader at time t must base his trade only on the price change over some prior interval,say from t-2 to t-1.We show that in this case,momentum traders'attempts to profit from the underreaction caused by newswatchers lead to a perverse outcome:The initial reaction of prices in the direction of fundamentals is indeed accelerated,but this comes at the expense of creating an eventual overreaction to any news.This is true even when momentum traders are risk neutral. Again,the key to this result is the assumption that momentum traders use simple strategies-that is,they do not condition on all public informa- tion.Continuing with the example,if a momentum trader's order at time t is restricted to being a function of just the price change from t-2 to t-1,it is clear that it must be an increasing function.On average,this simple trend- chasing strategy makes money.But if one could condition on more informa- tion,it would become apparent that the strategy does better in some circumstances than in others.In particular,the strategy earns the bulk of its profits early in the "momentum cycle"-by which we mean shortly after substantial news has arrived to the newswatchers-and loses money late in the cycle,by which time prices have already overshot long-run equilibrium values. To see this point,suppose that there is a single dose of good news at time t and no change in fundamentals after that.The newswatchers cause prices to jump at time t,but not far enough,so that they are still below their 4 The constraints that we put on traders'information-processing abilities are arguably not as well-motivated by the experimental psychology literature as the biases in Barberis et al.(1998) or Daniel et al.(1998),and so may appear to be more ad hoc.However,they generate new and clear-cut asset-pricing predictions,some of which have already been supported in recent tests. See Section IV below

prices. Momentum traders, in contrast, do condition on past price changes. However, their limitation is that their forecasts must be “simple” ~i.e., uni￾variate! functions of the history of past prices.4 In addition to imposing these two constraints on the information process￾ing abilities of our traders, we make one further assumption, which is more orthodox in nature: Private information diffuses gradually across the news￾watcher population. All our conclusions then flow from these three key as￾sumptions. We begin by showing that when only newswatchers are active, prices adjust slowly to new information—there is underreaction but never overreaction. As is made clear later, this result follows naturally from com￾bining gradual information diffusion with the assumption that newswatch￾ers do not extract information from prices. Next, we add the momentum traders. It is tempting to conjecture that because the momentum traders can condition on past prices, they arbitrage away any underreaction left behind by the newswatchers; with sufficient risk tolerance, one might expect that they would force the market to become approximately efficient. However, it turns out that this intuition is incom￾plete if momentum traders are limited to simple strategies. For example, suppose that a momentum trader at time t must base his trade only on the price change over some prior interval, say from t 2 2 to t 2 1. We show that in this case, momentum traders’ attempts to profit from the underreaction caused by newswatchers lead to a perverse outcome: The initial reaction of prices in the direction of fundamentals is indeed accelerated, but this comes at the expense of creating an eventual overreaction to any news. This is true even when momentum traders are risk neutral. Again, the key to this result is the assumption that momentum traders use simple strategies—that is, they do not condition on all public informa￾tion. Continuing with the example, if a momentum trader’s order at time t is restricted to being a function of just the price change from t 2 2 to t 2 1, it is clear that it must be an increasing function. On average, this simple trend￾chasing strategy makes money. But if one could condition on more informa￾tion, it would become apparent that the strategy does better in some circumstances than in others. In particular, the strategy earns the bulk of its profits early in the “momentum cycle”—by which we mean shortly after substantial news has arrived to the newswatchers—and loses money late in the cycle, by which time prices have already overshot long-run equilibrium values. To see this point, suppose that there is a single dose of good news at time t and no change in fundamentals after that. The newswatchers cause prices to jump at time t, but not far enough, so that they are still below their 4 The constraints that we put on traders’ information-processing abilities are arguably not as well-motivated by the experimental psychology literature as the biases in Barberis et al. ~1998! or Daniel et al. ~1998!, and so may appear to be more ad hoc. However, they generate new and clear-cut asset-pricing predictions, some of which have already been supported in recent tests. See Section IV below. Underreaction, Momentum Trading, and Overreaction 2145

2146 The Journal of Finance long-run values.At time t+1 there is a round of momentum purchases,and those momentum buyers who get in at this time make money.But this round of momentum trading creates a further price increase,which sets off more momentum buying,and so on.Later momentum buyers(i.e.,those buying at t+i for some i)lose money,because they get in at a price above the long-run equilibrium. Thus a crucial insight is that "early"momentum buyers impose a negative externality on "late"momentum buyers.5 Ideally,one uses a momentum strat- egy because a price increase signals that there is good news about funda- mentals out there that is not yet fully incorporated into prices.But sometimes, a price increase is the result not of news but just of previous rounds of momentum trade.Because momentum traders cannot directly condition on whether or not news has recently arrived,they do not know whether they are early or late in the cycle.Hence they must live with this externality,and accept the fact that sometimes they buy when earlier rounds of momentum trading have pushed prices past long-run equilibrium values. Although we make two distinct bounded-rationality assumptions,our model can be said to "unify"underreaction and overreaction in the following sense. We begin by modeling a tendency for one group of traders to underreact to private information.We then show that when a second group of traders tries to exploit this underreaction with a simple arbitrage strategy,they only par- tially eliminate it,and in so doing,create an excessive momentum in prices that inevitably culminates in overreaction.Thus,the very existence of un- derreaction sows the seeds for overreaction,by making it profitable for mo- mentum traders to enter the market.Or,said differently,the unity lies in the fact that our model gets both underreaction and overreaction out of just one primitive type of shock:Gradually diffusing news about fundamentals. There are no other exogenous shocks to investor sentiment and no liquidity- motivated trades. In what follows,we develop a simple infinite-horizon model that captures these ideas.We begin in Section I by giving an overview of the empirical evidence that motivates our work.In Section II,we present and solve the basic model,and do a number of comparative statics experiments.Sec- tion III contains several extensions.In Section IV,we draw out the model's empirical implications.Section V discusses related work,and Section VI concludes I.Evidence of Continuation and Reversals A.Continuation The continuation evidence can be decomposed along the following lines. First,returns tend to exhibit unconditional positive serial correlation at ho- rizons on the order of three to twelve months.This is true both in cross 5 As we discuss below,this "momentum externality"is reminiscent of the herding models of Banerjee(1992),Bikhchandani,Hirshleifer,and Welch(1992),and Scharfstein and Stein(1990)

long-run values. At time t 1 1 there is a round of momentum purchases, and those momentum buyers who get in at this time make money. But this round of momentum trading creates a further price increase, which sets off more momentum buying, and so on. Later momentum buyers ~i.e., those buying at t 1 i for some i! lose money, because they get in at a price above the long-run equilibrium. Thus a crucial insight is that “early” momentum buyers impose a negative externality on “late” momentum buyers.5 Ideally, one uses a momentum strat￾egy because a price increase signals that there is good news about funda￾mentals out there that is not yet fully incorporated into prices. But sometimes, a price increase is the result not of news but just of previous rounds of momentum trade. Because momentum traders cannot directly condition on whether or not news has recently arrived, they do not know whether they are early or late in the cycle. Hence they must live with this externality, and accept the fact that sometimes they buy when earlier rounds of momentum trading have pushed prices past long-run equilibrium values. Although we make two distinct bounded-rationality assumptions, our model can be said to “unify” underreaction and overreaction in the following sense. We begin by modeling a tendency for one group of traders to underreact to private information. We then show that when a second group of traders tries to exploit this underreaction with a simple arbitrage strategy, they only par￾tially eliminate it, and in so doing, create an excessive momentum in prices that inevitably culminates in overreaction. Thus, the very existence of un￾derreaction sows the seeds for overreaction, by making it profitable for mo￾mentum traders to enter the market. Or, said differently, the unity lies in the fact that our model gets both underreaction and overreaction out of just one primitive type of shock: Gradually diffusing news about fundamentals. There are no other exogenous shocks to investor sentiment and no liquidity￾motivated trades. In what follows, we develop a simple infinite-horizon model that captures these ideas. We begin in Section I by giving an overview of the empirical evidence that motivates our work. In Section II, we present and solve the basic model, and do a number of comparative statics experiments. Sec￾tion III contains several extensions. In Section IV, we draw out the model’s empirical implications. Section V discusses related work, and Section VI concludes. I. Evidence of Continuation and Reversals A. Continuation The continuation evidence can be decomposed along the following lines. First, returns tend to exhibit unconditional positive serial correlation at ho￾rizons on the order of three to twelve months. This is true both in cross 5 As we discuss below, this “momentum externality” is reminiscent of the herding models of Banerjee ~1992!, Bikhchandani, Hirshleifer, and Welch ~1992!, and Scharfstein and Stein ~1990!. 2146 The Journal of Finance

Underreaction,Momentum Trading,and Overreaction 2147 sections of individual stocks(Jegadeesh and Titman(1993))and for a variety of broad asset classes(Cutler,Poterba,and Summers(1991)).6 One possible interpretation of this unconditional evidence-which fits with the spirit of the model below-is that information which is initially private is incorpo- rated into prices only gradually. Second,conditional on observable public events,stocks tend to experience post-event drift in the same direction as the initial event impact.The types of events that have been examined in detail and that fit this pattern include: Earnings announcements (perhaps the most-studied type of event in this genre;see e.g.,Bernard (1992)for an overview);stock issues and repur- chases;dividend initiations and omissions;and analyst recommendations.? Recent work by Chan,Jegadeesh,and Lakonishok (1996)shows that these two types of continuation are distinct:In a multiple regression,both past returns and public earnings surprises help to predict subsequent returns at horizons of six months and one year. B.Reversals and Fundamental Reversion One of the first and most influential papers in the reversals category is DeBondt and Thaler(1985),who find that stock returns are negatively cor- related at long horizons.Specifically,stocks that have had the lowest returns over any given five-year period tend to have high returns over the subsequent five years,and vice versa.8 A common interpretation of this result is that when there is a sustained streak of good news about an asset,its price overshoots its "fundamental value"and ultimately must experience a correction.More re- cent work in the same spirit has continued to focus on long-horizon predict- ability,but has used what are arguably more refined indicators of fundamental value,such as book-to-market,and cash flow-to-price ratios.(See,e.g.,Fama and French(1992)and Lakonishok,Shleifer,and Vishny (1994).)9 C.Is It Risk? In principle,the patterns noted above could be consistent with traditional models,to the extent that they reflect variations in risk,either over time or across assets.Fama and French (1993,1996)argue that many of the long- 6 Rouwenhorst(1998,1999)finds that Jegadeesh and Titman's(1993)U.S.results carry over to many other developed and emerging markets,though they are not statistically significant for every country individually (see,e.g.,Haugen and Baker(1996)on weak momentum in Japan). 7 References include:Bernard and Thomas(1989,1990)on earnings announcements;Lough- ran and Ritter(1995)and Spiess and Affleck-Graves(1995)on stock issues;Ikenberry,Lakon- ishok,and Vermaelen(1995)on repurchases;Michaely,Thaler,and Womack(1995)on dividend initiations and omissions;and Womack(1996)on analyst recommendations. 8 These results have been controversial,but seem to have stood up to scrutiny (Chopra, Lakonishok,and Ritter(1992)).There are also direct analogs in the time series of aggregate market returns,although the statistical power is lower.See Fama and French(1988),Poterba and Summers (1988),and Cutler,Poterba,and Summers (1991). s These results have also been found to be robust in international data.(Fama and French (1998),Rouwenhorst (1999))And again,there are analogous fundamental reversion patterns in the time-series literature on aggregate market predictability (Campbell and Shiller(1988))

sections of individual stocks ~Jegadeesh and Titman ~1993!! and for a variety of broad asset classes ~Cutler, Poterba, and Summers ~1991!!. 6 One possible interpretation of this unconditional evidence—which fits with the spirit of the model below—is that information which is initially private is incorpo￾rated into prices only gradually. Second, conditional on observable public events, stocks tend to experience post-event drift in the same direction as the initial event impact. The types of events that have been examined in detail and that fit this pattern include: Earnings announcements ~perhaps the most-studied type of event in this genre; see e.g., Bernard ~1992! for an overview!; stock issues and repur￾chases; dividend initiations and omissions; and analyst recommendations.7 Recent work by Chan, Jegadeesh, and Lakonishok ~1996! shows that these two types of continuation are distinct: In a multiple regression, both past returns and public earnings surprises help to predict subsequent returns at horizons of six months and one year. B. Reversals and Fundamental Reversion One of the first and most influential papers in the reversals category is DeBondt and Thaler ~1985!, who find that stock returns are negatively cor￾related at long horizons. Specifically, stocks that have had the lowest returns over any given five-year period tend to have high returns over the subsequent five years, and vice versa.8 A common interpretation of this result is that when there is a sustained streak of good news about an asset, its price overshoots its “fundamental value” and ultimately must experience a correction. More re￾cent work in the same spirit has continued to focus on long-horizon predict￾ability, but has used what are arguably more refined indicators of fundamental value, such as book-to-market, and cash flow-to-price ratios. ~See, e.g., Fama and French ~1992! and Lakonishok, Shleifer, and Vishny ~1994!.!9 C. Is It Risk? In principle, the patterns noted above could be consistent with traditional models, to the extent that they reflect variations in risk, either over time or across assets. Fama and French ~1993, 1996! argue that many of the long- 6 Rouwenhorst ~1998, 1999! finds that Jegadeesh and Titman’s ~1993! U.S. results carry over to many other developed and emerging markets, though they are not statistically significant for every country individually ~see, e.g., Haugen and Baker ~1996! on weak momentum in Japan!. 7 References include: Bernard and Thomas ~1989, 1990! on earnings announcements; Lough￾ran and Ritter ~1995! and Spiess and Affleck-Graves ~1995! on stock issues; Ikenberry, Lakon￾ishok, and Vermaelen ~1995! on repurchases; Michaely, Thaler, and Womack ~1995! on dividend initiations and omissions; and Womack ~1996! on analyst recommendations. 8 These results have been controversial, but seem to have stood up to scrutiny ~Chopra, Lakonishok, and Ritter ~1992!!. There are also direct analogs in the time series of aggregate market returns, although the statistical power is lower. See Fama and French ~1988!, Poterba and Summers ~1988!, and Cutler, Poterba, and Summers ~1991!. 9 These results have also been found to be robust in international data. ~Fama and French ~1998!, Rouwenhorst ~1999!! And again, there are analogous fundamental reversion patterns in the time-series literature on aggregate market predictability ~Campbell and Shiller ~1988!!. Underreaction, Momentum Trading, and Overreaction 2147