N JOURNAL OF Financial ECONOMICS ELSEVIER Journal of Financial Economics 49(1998)307-343 A model of investor sentiment' Nicholas Barberis",Andrei Shleifer.*,Robert Vishny? Graduate School of Business,University of Chicago.Chicago.IL 60637.USA Harvard University.Cambridge,MA 02138.USA Received 29 January 1997;received in revised form 10 February 1998 Abstract Recent empirical research in finance has uncovered two families of pervasive regulari- ties:underreaction of stock prices to news such as earnings announcements,and overreac- tion of stock prices to a series of good or bad news.In this paper,we present a parsimoni- ous model of investor sentiment,or of how investors form beliefs,which is consistent with the empirical findings.The model is based on psychological evidence and produces both underreaction and overreaction for a wide range of parameter values.C 1998 Elsevier Science S.A.All rights reserved. JEL classification:G12;G14 Keywords:Investor sentiment;Underreaction;Overreaction 1.Introduction Recent empirical research in finance has identified two families of pervasive regularities:underreaction and overreaction.The underreaction evidence shows that over horizons of perhaps 1-12 months,security prices underreact to news.2 *Corresponding author.Tel:617/495-5046;fax:617/496-1708;e-mail:ashleifer@harvard.edu. We are grateful to the NSF for financial support,and to Oliver Blanchard,Alon Brav,John Campbell (a referee),John Cochrane,Edward Glaeser,J.B.Heaton,Danny Kahneman,David Laibson,Owen Lamont,Drazen Prelec,Jay Ritter (a referee),Ken Singleton,Dick Thaler,an anonymous referee,and the editor,Bill Schwert,for comments. 2Some of the papers in this area,discussed in more detail in Section 2,include Cutler et al.(1991), Bernard and Thomas(1989),Jegadeesh and Titman(1993),and Chan et al.(1997). 0304-405X/98/S19.00 C 1998 Elsevier Science S.A.All rights reserved P1S0304-405X(98)00027-0
* Corresponding author. Tel.: 617/495-5046; fax: 617/496-1708; e-mail: ashleifer@harvard.edu. 1We are grateful to the NSF for financial support, and to Oliver Blanchard, Alon Brav, John Campbell (a referee), John Cochrane, Edward Glaeser, J.B. Heaton, Danny Kahneman, David Laibson, Owen Lamont, Drazen Prelec, Jay Ritter (a referee), Ken Singleton, Dick Thaler, an anonymous referee, and the editor, Bill Schwert, for comments. 2 Some of the papers in this area, discussed in more detail in Section 2, include Cutler et al. (1991), Bernard and Thomas (1989), Jegadeesh and Titman (1993), and Chan et al. (1997). Journal of Financial Economics 49 (1998) 307—343 A model of investor sentiment1 Nicholas Barberis!, Andrei Shleifer",*, Robert Vishny! ! Graduate School of Business, University of Chicago, Chicago, IL 60637, USA " Harvard University, Cambridge, MA 02138, USA Received 29 January 1997; received in revised form 10 February 1998 Abstract Recent empirical research in finance has uncovered two families of pervasive regularities: underreaction of stock prices to news such as earnings announcements, and overreaction of stock prices to a series of good or bad news. In this paper, we present a parsimonious model of investor sentiment, or of how investors form beliefs, which is consistent with the empirical findings. The model is based on psychological evidence and produces both underreaction and overreaction for a wide range of parameter values. ( 1998 Elsevier Science S.A. All rights reserved. JEL classification: G12; G14 Keywords: Investor sentiment; Underreaction; Overreaction 1. Introduction Recent empirical research in finance has identified two families of pervasive regularities: underreaction and overreaction. The underreaction evidence shows that over horizons of perhaps 1—12 months, security prices underreact to news.2 0304-405X/98/$19.00 ( 1998 Elsevier Science S.A. All rights reserved PII S0304-405X(98)00027-0
308 N.Barberis et al./Journal of Financial Economics 49 (1998)307-343 As a consequence,news is incorporated only slowly into prices,which tend to exhibit positive autocorrelations over these horizons.A related way to make this point is to say that current good news has power in predicting positive returns in the future.The overreaction evidence shows that over longer horizons of perhaps 3-5 years,security prices overreact to consistent patterns of news pointing in the same direction.That is,securities that have had a long record of good news tend to become overpriced and have low average returns after- wards.3 Put differently,securities with strings of good performance,however measured,receive extremely high valuations,and these valuations,on average, return to the mean.4 The evidence presents a challenge to the efficient markets theory because it suggests that in a variety of markets,sophisticated investors can earn superior returns by taking advantage of underreaction and overreaction without bearing extra risk.The most notable recent attempt to explain the evidence from the efficient markets viewpoint is Fama and French(1996).The authors believe that their three-factor model can account for the overreaction evidence,but not for the continuation of short-term returns(underreaction).This evidence also pres- ents a challenge to behavioral finance theory because early models do not successfully explain the facts.3 The challenge is to explain how investors might form beliefs that lead to both underreaction and overreaction. In this paper,we propose a parsimonious model of investor sentiment-of how investors form beliefs-that is consistent with the available statistical evidence.The model is also consistent with experimental evidence on both the failures of individual judgment under uncertainty and the trading patterns of investors in experimental situations.In particular,our specification is consistent with the results of Tversky and Kahneman(1974)on the important behavioral heuristic known as representativeness,or the tendency of experimental subjects to view events as typical or representative of some specific class and to ignore the laws of probability in the process.In the stock market,for example,investors might classify some stocks as growth stocks based on a history of consistent 3 Some of the papers in this area,discussed in more detail in Section 2,include Cutler et al.(1991). De Bondt and Thaler(1985),Chopra et al.(1992),Fama and French (1992),Lakonishok et al.(1994), and La Porta (1996). +There is also some evidence of nonzero return autocorrelations at very short horizons such as a day (Lehmann,1990).We do not believe that it is essential for a behavioral model to confront this evidence because it can be plausibly explained by market microstructure considerations such as the fluctuation of recorded prices between the bid and the ask. sThe model of De Long et al.(1990a)generates negative autocorrelation in returns,and that of De Long et al.(1990b)generates positive autocorrelation.Cutler et al.(1991)combine elements of the two De Long et al.models in an attempt to explain some of the autocorrelation evidence.These models focus exclusively on prices and hence do not confront the crucial earnings evidence discussed in Section 2
3 Some of the papers in this area, discussed in more detail in Section 2, include Cutler et al. (1991), De Bondt and Thaler (1985), Chopra et al. (1992), Fama and French (1992), Lakonishok et al. (1994), and La Porta (1996). 4There is also some evidence of nonzero return autocorrelations at very short horizons such as a day (Lehmann, 1990). We do not believe that it is essential for a behavioral model to confront this evidence because it can be plausibly explained by market microstructure considerations such as the fluctuation of recorded prices between the bid and the ask. 5The model of De Long et al. (1990a) generates negative autocorrelation in returns, and that of De Long et al. (1990b) generates positive autocorrelation. Cutler et al. (1991) combine elements of the two De Long et al. models in an attempt to explain some of the autocorrelation evidence. These models focus exclusively on prices and hence do not confront the crucial earnings evidence discussed in Section 2. As a consequence, news is incorporated only slowly into prices, which tend to exhibit positive autocorrelations over these horizons. A related way to make this point is to say that current good news has power in predicting positive returns in the future. The overreaction evidence shows that over longer horizons of perhaps 3—5 years, security prices overreact to consistent patterns of news pointing in the same direction. That is, securities that have had a long record of good news tend to become overpriced and have low average returns afterwards.3 Put differently, securities with strings of good performance, however measured, receive extremely high valuations, and these valuations, on average, return to the mean.4 The evidence presents a challenge to the efficient markets theory because it suggests that in a variety of markets, sophisticated investors can earn superior returns by taking advantage of underreaction and overreaction without bearing extra risk. The most notable recent attempt to explain the evidence from the efficient markets viewpoint is Fama and French (1996). The authors believe that their three-factor model can account for the overreaction evidence, but not for the continuation of short-term returns (underreaction). This evidence also presents a challenge to behavioral finance theory because early models do not successfully explain the facts.5 The challenge is to explain how investors might form beliefs that lead to both underreaction and overreaction. In this paper, we propose a parsimonious model of investor sentiment — of how investors form beliefs — that is consistent with the available statistical evidence. The model is also consistent with experimental evidence on both the failures of individual judgment under uncertainty and the trading patterns of investors in experimental situations. In particular, our specification is consistent with the results of Tversky and Kahneman (1974) on the important behavioral heuristic known as representativeness, or the tendency of experimental subjects to view events as typical or representative of some specific class and to ignore the laws of probability in the process. In the stock market, for example, investors might classify some stocks as growth stocks based on a history of consistent 308 N. Barberis et al./Journal of Financial Economics 49 (1998) 307—343
N.Barberis et al./Journal of Financial Economics 49 (1998)307-343 309 earnings growth,ignoring the likelihood that there are very few companies that just keep growing.Our model also relates to another phenomenon documented in psychology,namely conservatism,defined as the slow updating of models in the face of new evidence(Edwards,1968).The underreaction evidence in particu- lar is consistent with conservatism. Our model is that of one investor and one asset.This investor should be viewed as one whose beliefs reflect 'consensus forecasts'even when different investors hold different expectations.The beliefs of this representative investor affect prices and returns. We do not explain in the model why arbitrage fails to eliminate the mispric- ing.For the purposes of this paper,we rely on earlier work showing why deviations from efficient prices can persist(De Long et al.,1990a;Shleifer and Vishny,1997).According to this work,an important reason why arbitrage is limited is that movements in investor sentiment are in part unpredictable,and therefore arbitrageurs betting against mispricing run the risk,at least in the short run,that investor sentiment becomes more extreme and prices move even further away from fundamental value.As a consequence of such 'noise trader risk,'arbitrage positions can lose money in the short run.When arbitrageurs are risk-averse,leveraged,or manage other people's money and run the risk of losing funds under management when performance is poor,the risk of deepen- ing mispricing reduces the size of the positions they take.Hence,arbitrage fails to eliminate the mispricing completely and investor sentiment affects security prices in equilibrium.In the model below,investor sentiment is indeed in part unpredictable,and therefore,if arbitrageurs were introduced into the model, arbitrage would be limited. While these earlier papers argue that mispricing can persist,they say little about the nature of the mispricing that might be observed.For that,we need a model of how people form expectations.The current paper provides one such model. In our model,the earnings of the asset follow a random walk.However,the investor does not know that.Rather,he believes that the behavior of a given firm's earnings moves between two'states'or 'regimes'.In the first state,earnings are mean-reverting.In the second state,they trend,i.e.,are likely to rise further after an increase.The transition probabilities between the two regimes,as well as the statistical properties of the earnings process in each one of them,are fixed in The empirical implications of our model are derived from the assumptions about investor psychology or sentiment,rather than from those about the behavior of arbitrageurs.Other models in behavioral finance yield empirical implications that follow from limited arbitrage alone,without specific assumptions about the form of investor sentiment.For example,limited arbitrage in closed-end funds predicts average underpricing of such funds regardless of the exact form of investor sentiment that these funds are subject to (see De Long et al.,1990a;Lee et al.,1991)
6The empirical implications of our model are derived from the assumptions about investor psychology or sentiment, rather than from those about the behavior of arbitrageurs. Other models in behavioral finance yield empirical implications that follow from limited arbitrage alone, without specific assumptions about the form of investor sentiment. For example, limited arbitrage in closed-end funds predicts average underpricing of such funds regardless of the exact form of investor sentiment that these funds are subject to (see De Long et al., 1990a; Lee et al., 1991). earnings growth, ignoring the likelihood that there are very few companies that just keep growing. Our model also relates to another phenomenon documented in psychology, namely conservatism, defined as the slow updating of models in the face of new evidence (Edwards, 1968). The underreaction evidence in particular is consistent with conservatism. Our model is that of one investor and one asset. This investor should be viewed as one whose beliefs reflect ‘consensus forecasts’ even when different investors hold different expectations. The beliefs of this representative investor affect prices and returns. We do not explain in the model why arbitrage fails to eliminate the mispricing. For the purposes of this paper, we rely on earlier work showing why deviations from efficient prices can persist (De Long et al., 1990a; Shleifer and Vishny, 1997). According to this work, an important reason why arbitrage is limited is that movements in investor sentiment are in part unpredictable, and therefore arbitrageurs betting against mispricing run the risk, at least in the short run, that investor sentiment becomes more extreme and prices move even further away from fundamental value. As a consequence of such ‘noise trader risk,’ arbitrage positions can lose money in the short run. When arbitrageurs are risk-averse, leveraged, or manage other people’s money and run the risk of losing funds under management when performance is poor, the risk of deepening mispricing reduces the size of the positions they take. Hence, arbitrage fails to eliminate the mispricing completely and investor sentiment affects security prices in equilibrium. In the model below, investor sentiment is indeed in part unpredictable, and therefore, if arbitrageurs were introduced into the model, arbitrage would be limited.6 While these earlier papers argue that mispricing can persist, they say little about the nature of the mispricing that might be observed. For that, we need a model of how people form expectations. The current paper provides one such model. In our model, the earnings of the asset follow a random walk. However, the investor does not know that. Rather, he believes that the behavior of a given firm’s earnings moves between two ‘states’ or ‘regimes’. In the first state, earnings are mean-reverting. In the second state, they trend, i.e., are likely to rise further after an increase. The transition probabilities between the two regimes, as well as the statistical properties of the earnings process in each one of them, are fixed in N. Barberis et al./Journal of Financial Economics 49 (1998) 307—343 309
310 N.Barberis et al./Journal of Financial Economics 49 (1998)307-343 the investor's mind.In particular,in any given period,the firm's earnings are more likely to stay in a given regime than to switch.Each period,the investor observes earnings,and uses this information to update his beliefs about which state he is in.In his updating,the investor is Bayesian,although his model of the earnings process is inaccurate.Specifically,when a positive earnings surprise is followed by another positive surprise,the investor raises the likelihood that he is in the trending regime,whereas when a positive surprise is followed by a nega- tive surprise,the investor raises the likelihood that he is in the mean-reverting regime.We solve this model and show that,for a plausible range of parameter values,it generates the empirical predictions observed in the data. Daniel et al.(1998)also construct a model of investor sentiment aimed at reconciling the empirical findings of overreaction and underreaction.They,too, use concepts from psychology to support their framework,although the under- pinnings of their model are overconfidence and self-attribution,which are not the same as the psychological ideas we use.It is quite possible that both the phenomena that they describe,and those driving our model,play a role in generating the empirical evidence. Section 2 of the paper summarizes the empirical findings that we try to explain.Section 3 discusses the psychological evidence that motivates our approach.Section 4 presents the model.Section 5 solves it and outlines its implications for the data.Section 6 concludes. 2.The evidence In this section,we summarize the statistical evidence of underreaction and overreaction in security returns.We devote only minor attention to the behavior of aggregate stock and bond returns because these data generally do not provide enough information to reject the hypothesis of efficient markets.Most of the anomalous evidence that our model tries to explain comes from the cross- section of stock returns.Much of this evidence is from the United States, although some recent research has found similar patterns in other markets. 2.1.Statistical evidence of underreaction Before presenting the empirical findings,we first explain what we mean by underreaction to news announcements.Suppose that in each time period,the investor hears news about a particular company.We denote the news he hears in period t as z This news can be either good or bad,i.e,z=G or z=B.By underreaction we mean that the average return on the company's stock in the period following an announcement of good news is higher than the average
the investor’s mind. In particular, in any given period, the firm’s earnings are more likely to stay in a given regime than to switch. Each period, the investor observes earnings, and uses this information to update his beliefs about which state he is in. In his updating, the investor is Bayesian, although his model of the earnings process is inaccurate. Specifically, when a positive earnings surprise is followed by another positive surprise, the investor raises the likelihood that he is in the trending regime, whereas when a positive surprise is followed by a negative surprise, the investor raises the likelihood that he is in the mean-reverting regime. We solve this model and show that, for a plausible range of parameter values, it generates the empirical predictions observed in the data. Daniel et al. (1998) also construct a model of investor sentiment aimed at reconciling the empirical findings of overreaction and underreaction. They, too, use concepts from psychology to support their framework, although the underpinnings of their model are overconfidence and self-attribution, which are not the same as the psychological ideas we use. It is quite possible that both the phenomena that they describe, and those driving our model, play a role in generating the empirical evidence. Section 2 of the paper summarizes the empirical findings that we try to explain. Section 3 discusses the psychological evidence that motivates our approach. Section 4 presents the model. Section 5 solves it and outlines its implications for the data. Section 6 concludes. 2. The evidence In this section, we summarize the statistical evidence of underreaction and overreaction in security returns. We devote only minor attention to the behavior of aggregate stock and bond returns because these data generally do not provide enough information to reject the hypothesis of efficient markets. Most of the anomalous evidence that our model tries to explain comes from the crosssection of stock returns. Much of this evidence is from the United States, although some recent research has found similar patterns in other markets. 2.1. Statistical evidence of underreaction Before presenting the empirical findings, we first explain what we mean by underreaction to news announcements. Suppose that in each time period, the investor hears news about a particular company. We denote the news he hears in period t as z t . This news can be either good or bad, i.e., z t "G or z t "B. By underreaction we mean that the average return on the company’s stock in the period following an announcement of good news is higher than the average 310 N. Barberis et al./Journal of Financial Economics 49 (1998) 307—343
N.Barberis et al./Journal of Financial Economics 49 (1998)307-343 311 return in the period following bad news: E(r+2=G)>E(r+=B). In other words,the stock underreacts to the good news,a mistake which is corrected in the following period,giving a higher return at that time.In this paper,the good news consists of an earnings announcement that is higher than expected,although as we discuss below,there is considerable evidence of underreaction to other types of news as well. Empirical analysis of aggregate time series has produced some evidence of underreaction.Cutler et al.(1991)examine autocorrelations in excess returns on various indexes over different horizons.They look at returns on stocks,bonds, and foreign exchange in different markets over the period 1960-1988 and generally,though not uniformly,find positive autocorrelations in excess index returns over horizons of between one month and one year.For example,the average one-month autocorrelation in excess stock returns across the world is around 0.1 (and is also around 0.1 in the United States alone),and that in excess bond returns is around 0.2(and around zero in the United States).Many of these autocorrelations are statistically significant.This autocorrelation evidence is consistent with the underreaction hypothesis,which states that stock prices incorporate information slowly,leading to trends in returns over short horizons. More convincing support for the underreaction hypothesis comes from the studies of the cross-section of stock returns in the United States,which look at the actual news events as well as the predictability of returns.Bernard(1992) surveys one class of such studies,which deals with the underreaction of stock prices to announcements of company earnings. The finding of these studies is roughly as follows.Suppose we sort stocks into groups (say deciles)based on how much of a surprise is contained in their earnings announcement.One naive way to measure an earnings surprise is to look at standardized unexpected earnings (SUE),defined as the difference between a company's earnings in a given quarter and its earnings during the quarter a year before,scaled by the standard deviation of the company's earnings.Another way to measure an earnings surprise is by the stock price reaction to an earnings announcement.A general (and unsurprising)finding is that stocks with positive earnings surprises also earn relatively high returns in the period prior to the earnings announcement,as information about earnings is incorporated into prices.A much more surprising finding is that stocks with higher earnings surprises also earn higher returns in the period after portfolio formation:the market underreacts to the earnings announcement in revising a company's stock price.For example,over the 60 trading days after portfolio formation,stocks with the highest SUE earn a cumulative risk-adjusted return that is 4.2%higher than the return on stocks with the lowest SUE(see Bernard, 1992).Thus,stale information,namely the SUE or the past earnings announce- ment return,has predictive power for future risk-adjusted returns.Or,put
return in the period following bad news: E(r t`1 Dz t "G)'E(r t`1 Dz t "B). In other words, the stock underreacts to the good news, a mistake which is corrected in the following period, giving a higher return at that time. In this paper, the good news consists of an earnings announcement that is higher than expected, although as we discuss below, there is considerable evidence of underreaction to other types of news as well. Empirical analysis of aggregate time series has produced some evidence of underreaction. Cutler et al. (1991) examine autocorrelations in excess returns on various indexes over different horizons. They look at returns on stocks, bonds, and foreign exchange in different markets over the period 1960—1988 and generally, though not uniformly, find positive autocorrelations in excess index returns over horizons of between one month and one year. For example, the average one-month autocorrelation in excess stock returns across the world is around 0.1 (and is also around 0.1 in the United States alone), and that in excess bond returns is around 0.2 (and around zero in the United States). Many of these autocorrelations are statistically significant. This autocorrelation evidence is consistent with the underreaction hypothesis, which states that stock prices incorporate information slowly, leading to trends in returns over short horizons. More convincing support for the underreaction hypothesis comes from the studies of the cross-section of stock returns in the United States, which look at the actual news events as well as the predictability of returns. Bernard (1992) surveys one class of such studies, which deals with the underreaction of stock prices to announcements of company earnings. The finding of these studies is roughly as follows. Suppose we sort stocks into groups (say deciles) based on how much of a surprise is contained in their earnings announcement. One naive way to measure an earnings surprise is to look at standardized unexpected earnings (SUE), defined as the difference between a company’s earnings in a given quarter and its earnings during the quarter a year before, scaled by the standard deviation of the company’s earnings. Another way to measure an earnings surprise is by the stock price reaction to an earnings announcement. A general (and unsurprising) finding is that stocks with positive earnings surprises also earn relatively high returns in the period prior to the earnings announcement, as information about earnings is incorporated into prices. A much more surprising finding is that stocks with higher earnings surprises also earn higher returns in the period after portfolio formation: the market underreacts to the earnings announcement in revising a company’s stock price. For example, over the 60 trading days after portfolio formation, stocks with the highest SUE earn a cumulative risk-adjusted return that is 4.2% higher than the return on stocks with the lowest SUE (see Bernard, 1992). Thus, stale information, namely the SUE or the past earnings announcement return, has predictive power for future risk-adjusted returns. Or, put N. Barberis et al./Journal of Financial Economics 49 (1998) 307—343 311
312 N.Barberis et al./Journal of Financial Economics 49 (1998)307-343 differently,information about earnings is only slowly incorporated into stock prices. Bernard also summarizes some evidence on the actual properties of the time series of earnings,and provides an interpretation for his findings.The relevant series is changes in a company's earnings in a given quarter relative to the same calendar quarter in the previous year.Over the period 1974-1986,using a sample of 2626 firms,Bernard and Thomas(1990)find that these series exhibit an autocorrelation of about 0.34 at a lag of one quarter,0.19 at two quarters, 0.06 at three quarters,and -0.24 at four quarters.That is,earnings changes exhibit a slight trend at one-,two-,and three-quarter horizons and a slight reversal after a year.In interpreting the evidence,Bernard conjectures that market participants do not recognize the positive autocorrelations in earnings changes,and in fact believe that earnings follow a random walk.This belief causes them to underreact to earnings announcements.Our model in Section 3 uses a related idea for generating underreaction:we suppose that earnings follow a random walk but that investors typically assume that earnings are mean- reverting.The key idea that generates underreaction,which Bernard's and our analyses share,is that investors typically (but not always)believe that earnings are more stationary than they really are.As we show below,this idea has firm foundations in psychology. Further evidence of underreaction comes from Jegadeesh and Titman(1993), who examine a cross-section of U.S.stock returns and find reliable evidence that over a six-month horizon,stock returns are positively autocorrelated.Similarly to the earnings drift evidence,they interpret their finding of the 'momentum'in stock returns as pointing to underreaction to information and slow incorpora- tion of information into prices.?More recent work by Rouwenhorst(1997) documents the presence of momentum in international equity markets.Chan et al.(1997)integrate the earnings drift evidence with the momentum evidence They use three measures of earnings surprise:SUE,stock price reaction to the earnings announcement,and changes in analysts'forecasts of earnings.The authors find that all these measures,as well as the past return,help predict subsequent stock returns at horizons of six months and one year.That is,stocks with a positive earnings surprise,as well as stocks with high past returns,tend to subsequently outperform stocks with a negative earnings surprise and poor returns.Like the other authors,Chan,Jegadeesh,and Lakonishok conclude that investors underreact to news and incorporate information into prices slowly. In addition to the evidence of stock price underreaction to earnings announcements and the related evidence of momentum in stock prices,there is also a body of closely related evidence on stock price drift following many other announcements and events.For example,Ikenberry et al.(1995)find that stock 7Early evidence on momentum is also contained in De Bondt and Thaler(1985)
7Early evidence on momentum is also contained in De Bondt and Thaler (1985). differently, information about earnings is only slowly incorporated into stock prices. Bernard also summarizes some evidence on the actual properties of the time series of earnings, and provides an interpretation for his findings. The relevant series is changes in a company’s earnings in a given quarter relative to the same calendar quarter in the previous year. Over the period 1974—1986, using a sample of 2626 firms, Bernard and Thomas (1990) find that these series exhibit an autocorrelation of about 0.34 at a lag of one quarter, 0.19 at two quarters, 0.06 at three quarters, and !0.24 at four quarters. That is, earnings changes exhibit a slight trend at one-, two-, and three-quarter horizons and a slight reversal after a year. In interpreting the evidence, Bernard conjectures that market participants do not recognize the positive autocorrelations in earnings changes, and in fact believe that earnings follow a random walk. This belief causes them to underreact to earnings announcements. Our model in Section 3 uses a related idea for generating underreaction: we suppose that earnings follow a random walk but that investors typically assume that earnings are meanreverting. The key idea that generates underreaction, which Bernard’s and our analyses share, is that investors typically (but not always) believe that earnings are more stationary than they really are. As we show below, this idea has firm foundations in psychology. Further evidence of underreaction comes from Jegadeesh and Titman (1993), who examine a cross-section of U.S. stock returns and find reliable evidence that over a six-month horizon, stock returns are positively autocorrelated. Similarly to the earnings drift evidence, they interpret their finding of the ‘momentum’ in stock returns as pointing to underreaction to information and slow incorporation of information into prices.7 More recent work by Rouwenhorst (1997) documents the presence of momentum in international equity markets. Chan et al. (1997) integrate the earnings drift evidence with the momentum evidence. They use three measures of earnings surprise: SUE, stock price reaction to the earnings announcement, and changes in analysts’ forecasts of earnings. The authors find that all these measures, as well as the past return, help predict subsequent stock returns at horizons of six months and one year. That is, stocks with a positive earnings surprise, as well as stocks with high past returns, tend to subsequently outperform stocks with a negative earnings surprise and poor returns. Like the other authors, Chan, Jegadeesh, and Lakonishok conclude that investors underreact to news and incorporate information into prices slowly. In addition to the evidence of stock price underreaction to earnings announcements and the related evidence of momentum in stock prices, there is also a body of closely related evidence on stock price drift following many other announcements and events. For example, Ikenberry et al. (1995) find that stock 312 N. Barberis et al./Journal of Financial Economics 49 (1998) 307—343
N.Barberis et al./Journal of Financial Economics 49 (1998)307-343 313 prices rise on the announcement of share repurchases but then continue to drift in the same direction over the next few years.Michaely et al.(1995)find similar evidence of drift following dividend initiations and omissions,while Ikenberry et al.(1996)document such a drift following stock splits.Finally,Loughran and Ritter (1995)and Spiess and Affleck-Graves (1995)find evidence of a drift following seasoned equity offerings.Daniel et al.(1998)and Fama (1998) summarize a large number of event studies showing this type of underreaction to news events,which a theory of investor sentiment should presumably come to grips with. 2.2.Statistical evidence of overreaction Analogous to the definition of underreaction at the start of the previous subsection,we now 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.Using the same notation as before, E+1l2,=G,2-1=G,3-j=G) <E+a,=B,z-1=B,,-j=B), where j is at least one and probably rather higher.The idea here is simply that after a series of announcements of good news,the investor becomes overly optimistic that future news announcements will also be good and hence over- reacts,sending the stock price to unduly high levels.Subsequent news an- nouncements are likely to contradict his optimism,leading to lower returns. Empirical studies of predictability of aggregate index returns over long horizons are extremely numerous.Early papers include Fama and French(1988) and Poterba and Summers (1988);Cutler et al.(1991)examine some of this evidence for a variety of markets.The thrust of the evidence is that,over horizons of 3-5 years,there is a relatively slight negative autocorrelation in stock returns in many markets.Moreover,over similar horizons,some measures of stock valuation,such as the dividend yield,have predictive power for returns in a similar direction:a low dividend yield or high past return tend to predict a low subsequent return(Campbell and Shiller,1988). As before,the more convincing evidence comes from the cross-section of stock returns.In an early important paper,De Bondt and Thaler(1985)discover from looking at U.S.data dating back to 1933 that portfolios of stocks with extremely poor returns over the previous five years dramatically outperform portfolios of stocks with extremely high returns,even after making the standard risk adjust- ments.De Bondt and Thaler's findings are corroborated by later work (e.g,Chopra et al.,1992).In the case of earnings,Zarowin (1989)finds that firms that have had a sequence of bad earnings realizations subsequently
prices rise on the announcement of share repurchases but then continue to drift in the same direction over the next few years. Michaely et al. (1995) find similar evidence of drift following dividend initiations and omissions, while Ikenberry et al. (1996) document such a drift following stock splits. Finally, Loughran and Ritter (1995) and Spiess and Affleck-Graves (1995) find evidence of a drift following seasoned equity offerings. Daniel et al. (1998) and Fama (1998) summarize a large number of event studies showing this type of underreaction to news events, which a theory of investor sentiment should presumably come to grips with. 2.2. Statistical evidence of overreaction Analogous to the definition of underreaction at the start of the previous subsection, we now 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. Using the same notation as before, E(r t`1 Dz t "G, z t~1"G,2, z t~j "G) (E(r t`1 Dz t "B, z t~1"B,2, z t~j "B), where j is at least one and probably rather higher. The idea here is simply that after a series of announcements of good news, the investor becomes overly optimistic that future news announcements will also be good and hence overreacts, sending the stock price to unduly high levels. Subsequent news announcements are likely to contradict his optimism, leading to lower returns. Empirical studies of predictability of aggregate index returns over long horizons are extremely numerous. Early papers include Fama and French (1988) and Poterba and Summers (1988); Cutler et al. (1991) examine some of this evidence for a variety of markets. The thrust of the evidence is that, over horizons of 3—5 years, there is a relatively slight negative autocorrelation in stock returns in many markets. Moreover, over similar horizons, some measures of stock valuation, such as the dividend yield, have predictive power for returns in a similar direction: a low dividend yield or high past return tend to predict a low subsequent return (Campbell and Shiller, 1988). As before, the more convincing evidence comes from the cross-section of stock returns. In an early important paper, De Bondt and Thaler (1985) discover from looking at U.S. data dating back to 1933 that portfolios of stocks with extremely poor returns over the previous five years dramatically outperform portfolios of stocks with extremely high returns, even after making the standard risk adjustments. De Bondt and Thaler’s findings are corroborated by later work (e.g., Chopra et al., 1992). In the case of earnings, Zarowin (1989) finds that firms that have had a sequence of bad earnings realizations subsequently N. Barberis et al./Journal of Financial Economics 49 (1998) 307—343 313
314 N.Barberis et al./Journal of Financial Economics 49 (1998)307-343 outperform firms with a sequence of good earnings.This evidence suggests that stocks with a consistent record of good news,and hence extremely high past returns,are overvalued,and that an investor can therefore earn abnormal returns by betting against this overreaction to consistent patterns of news. Similarly,stocks with a consistent record of bad news become undervalued and subsequently earn superior returns. Subsequent work has changed the focus from past returns to other measures of valuation,such as the ratio of market value to book value of assets(De Bondt and Thaler,1987;Fama and French,1992),market value to cash flow (Lakonishok et al.,1994),and other accounting measures.All this evidence points in the same direction.Stocks with very high valuations relative to their assets or earnings(glamour stocks),which tend to be stocks of companies with extremely high earnings growth over the previous several years,earn relatively low risk-adjusted returns in the future,whereas stocks with low valuations (value stocks)earn relatively high returns.For example,Lakonishok et al.find spreads of 8-10%per year between returns of the extreme value and glamour deciles.Again,this evidence points to overreaction to a prolonged record of extreme performance,whether good or bad:the prices of stocks with such extreme performance tend to be too extreme relative to what these stocks are worth and relative to what the subsequent returns actually deliver.Recent research extends the evidence on value stocks to other markets,including those in Europe,Japan,and emerging markets(Fama and French,1998;Haugen and Baker,1996). The economic interpretation of this evidence has proved more controversial, since some authors,particularly Fama and French(1992,1996),argue that glamour stocks are in fact less risky,and value stocks more risky,once risk is properly measured.In a direct attempt to distinguish risk and overreaction, La Porta (1996)sorts stocks on the basis of long-term growth rate forecasts made by professional analysts,and finds evidence that analysts are excessively bullish about the stocks they are most optimistic about and excessively bearish about the stocks they are most pessimistic about.In particular,stocks with the highest growth forecasts earn much lower future returns than stocks with the lowest growth forecasts.Moreover,on average,stocks with high growth fore- casts earn negative returns when they subsequently announce earnings and stocks with low growth forecasts earn high returns.All this evidence points to overreaction not just by analysts but more importantly in prices as well:in an efficient market,stocks with optimistic growth forecasts should not earn low returns. Finally,La Porta et al.(1997)find direct evidence of overreaction in glamour and value stocks defined using accounting variables.Specifically,glamour stocks earn negative returns on the days of their future earnings announcements, and value stocks earn positive returns.The market learns when earnings are announced that its valuations have been too extreme
outperform firms with a sequence of good earnings. This evidence suggests that stocks with a consistent record of good news, and hence extremely high past returns, are overvalued, and that an investor can therefore earn abnormal returns by betting against this overreaction to consistent patterns of news. Similarly, stocks with a consistent record of bad news become undervalued and subsequently earn superior returns. Subsequent work has changed the focus from past returns to other measures of valuation, such as the ratio of market value to book value of assets (De Bondt and Thaler, 1987; Fama and French, 1992), market value to cash flow (Lakonishok et al., 1994), and other accounting measures. All this evidence points in the same direction. Stocks with very high valuations relative to their assets or earnings (glamour stocks), which tend to be stocks of companies with extremely high earnings growth over the previous several years, earn relatively low risk-adjusted returns in the future, whereas stocks with low valuations (value stocks) earn relatively high returns. For example, Lakonishok et al. find spreads of 8—10% per year between returns of the extreme value and glamour deciles. Again, this evidence points to overreaction to a prolonged record of extreme performance, whether good or bad: the prices of stocks with such extreme performance tend to be too extreme relative to what these stocks are worth and relative to what the subsequent returns actually deliver. Recent research extends the evidence on value stocks to other markets, including those in Europe, Japan, and emerging markets (Fama and French, 1998; Haugen and Baker, 1996). The economic interpretation of this evidence has proved more controversial, since some authors, particularly Fama and French (1992, 1996), argue that glamour stocks are in fact less risky, and value stocks more risky, once risk is properly measured. In a direct attempt to distinguish risk and overreaction, La Porta (1996) sorts stocks on the basis of long-term growth rate forecasts made by professional analysts, and finds evidence that analysts are excessively bullish about the stocks they are most optimistic about and excessively bearish about the stocks they are most pessimistic about. In particular, stocks with the highest growth forecasts earn much lower future returns than stocks with the lowest growth forecasts. Moreover, on average, stocks with high growth forecasts earn negative returns when they subsequently announce earnings and stocks with low growth forecasts earn high returns. All this evidence points to overreaction not just by analysts but more importantly in prices as well: in an efficient market, stocks with optimistic growth forecasts should not earn low returns. Finally, La Porta et al. (1997) find direct evidence of overreaction in glamour and value stocks defined using accounting variables. Specifically, glamour stocks earn negative returns on the days of their future earnings announcements, and value stocks earn positive returns. The market learns when earnings are announced that its valuations have been too extreme. 314 N. Barberis et al./Journal of Financial Economics 49 (1998) 307—343
N.Barberis et al./Journal of Financial Economics 49 (1998)307-343 315 In sum,the cross-sectional overreaction evidence,like the cross-sectional underreaction evidence,presents rather reliable regularities.These regularities taken in their entirety are difficult to reconcile with the efficient markets hypothesis.More important for this paper,the two regularities challenge behav- ioral finance to provide a model of how investors form beliefs that can account for the empirical evidence. 3.Some psychological evidence The model we present below is motivated by two important phenomena documented by psychologists:conservatism and the representativeness heuristic. In this subsection,we briefly describe this psychological evidence as well as a recent attempt to integrate it(Griffin and Tversky,1992). Several psychologists,including Edwards(1968),have identified a phenom- enon known as conservatism.Conservatism states that individuals are slow to change their beliefs in the face of new evidence.Edwards benchmarks a subject's reaction to new evidence against that of an idealized rational Bayesian in experiments in which the true normative value of a piece of evidence is well defined.In his experiments,individuals update their posteriors in the right direction,but by too little in magnitude relative to the rational Bayesian benchmark.This finding of conservatism is actually more pronounced the more objectively useful is the new evidence.In Edwards'own words: It turns out that opinion change is very orderly,and usually proportional to numbers calculated from the Bayes Theorem-but it is insufficient in amount. A conventional first approximation to the data would say that it takes anywhere from two to five observations to do one observation's worth of work in inducing a subject to change his opinions.(p.359) Conservatism is extremely suggestive of the underreaction evidence described above.Individuals subject to conservatism might disregard the full information content of an earnings (or some other public)announcement,perhaps because they believe that this number contains a large temporary component,and still cling at least partially to their prior estimates of earnings.As a consequence, they might adjust their valuation of shares only partially in response to the announcement.Edwards would describe such behavior in Bayesian terms as a failure to properly aggregate the information in the new earnings number with investors'own prior information to form a new posterior earnings estimate.In particular,individuals tend to underweight useful statistical evidence relative to the less useful evidence used to form their priors.Alternatively,they might be characterized as being overconfident about their prior information. A second important phenomenon documented by psychologists is the repre- sentativeness heuristic(Tversky and Kahneman,1974):"A person who follows this heuristic evaluates the probability of an uncertain event,or a sample,by the
In sum, the cross-sectional overreaction evidence, like the cross-sectional underreaction evidence, presents rather reliable regularities. These regularities taken in their entirety are difficult to reconcile with the efficient markets hypothesis. More important for this paper, the two regularities challenge behavioral finance to provide a model of how investors form beliefs that can account for the empirical evidence. 3. Some psychological evidence The model we present below is motivated by two important phenomena documented by psychologists: conservatism and the representativeness heuristic. In this subsection, we briefly describe this psychological evidence as well as a recent attempt to integrate it (Griffin and Tversky, 1992). Several psychologists, including Edwards (1968), have identified a phenomenon known as conservatism. Conservatism states that individuals are slow to change their beliefs in the face of new evidence. Edwards benchmarks a subject’s reaction to new evidence against that of an idealized rational Bayesian in experiments in which the true normative value of a piece of evidence is well defined. In his experiments, individuals update their posteriors in the right direction, but by too little in magnitude relative to the rational Bayesian benchmark. This finding of conservatism is actually more pronounced the more objectively useful is the new evidence. In Edwards’ own words: It turns out that opinion change is very orderly, and usually proportional to numbers calculated from the Bayes Theorem — but it is insufficient in amount. A conventional first approximation to the data would say that it takes anywhere from two to five observations to do one observation’s worth of work in inducing a subject to change his opinions. (p. 359) Conservatism is extremely suggestive of the underreaction evidence described above. Individuals subject to conservatism might disregard the full information content of an earnings (or some other public) announcement, perhaps because they believe that this number contains a large temporary component, and still cling at least partially to their prior estimates of earnings. As a consequence, they might adjust their valuation of shares only partially in response to the announcement. Edwards would describe such behavior in Bayesian terms as a failure to properly aggregate the information in the new earnings number with investors’ own prior information to form a new posterior earnings estimate. In particular, individuals tend to underweight useful statistical evidence relative to the less useful evidence used to form their priors. Alternatively, they might be characterized as being overconfident about their prior information. A second important phenomenon documented by psychologists is the representativeness heuristic (Tversky and Kahneman, 1974): “A person who follows this heuristic evaluates the probability of an uncertain event, or a sample, by the N. Barberis et al./Journal of Financial Economics 49 (1998) 307—343 315
316 N.Barberis et al./Journal of Financial Economics 49 (1998)307-343 degree to which it is(i)similar in its essential properties to the parent popula- tion,(ii)reflects the salient features of the process by which it is generated" (p.33).For example,if a detailed description of an individual's personality matches up well with the subject's experiences with people of a particular profession,the subject tends to significantly overestimate the actual probability that the given individual belongs to that profession.In overweighting the representative description,the subject underweights the statistical base rate evidence of the small fraction of the population belonging to that profession. An important manifestation of the representativeness heuristic,discussed in detail by Tversky and Kahneman,is that people think they see patterns in truly random sequences.This aspect of the representativeness heuristic is suggestive of the overreaction evidence described above.When a company has a consistent history of earnings growth over several years,accompanied as it may be by salient and enthusiastic descriptions of its products and management,investors might conclude that the past history is representative of an underlying earnings growth potential.While a consistent pattern of high growth may be nothing more than a random draw for a few lucky firms,investors see 'order among chaos'and infer from the in-sample growth path that the firm belongs to a small and distinct population of firms whose earnings just keep growing.As a conse- quence,investors using the representativeness heuristic might disregard the reality that a history of high earnings growth is unlikely to repeat itself;they will overvalue the company,and be disappointed in the future when the forecasted earnings growth fails to materialize.This,of course,is what overreaction is all about. In a recent study,Griffin and Tversky (1992)attempt to reconcile conserva- tism with representativeness.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.In the Griffin-Tversky framework,conservatism like that documented by Edwards would occur in the face of evidence that has high weight but low strength:people are unimpressed by the low strength and react mildly to the evidence,even though its weight calls for a larger reaction.On the other hand,when the evidence has high strength but low weight,overreaction occurs in a manner consistent with representativeness.Indeed,representativeness can be thought of as excessive attention to the strength of particularly salient evidence,in spite of its relatively low weight. To illustrate these concepts,Griffin and Tversky use the example of a recommendation letter. The'strength'of the letter refers to how positive and warm its content is;'weight'on the other hand, measures the credibility and stature of the letter-writer
8To illustrate these concepts, Griffin and Tversky use the example of a recommendation letter. The ‘strength’ of the letter refers to how positive and warm its content is; ‘weight’ on the other hand, measures the credibility and stature of the letter-writer. degree to which it is (i) similar in its essential properties to the parent population, (ii) reflects the salient features of the process by which it is generated” (p. 33). For example, if a detailed description of an individual’s personality matches up well with the subject’s experiences with people of a particular profession, the subject tends to significantly overestimate the actual probability that the given individual belongs to that profession. In overweighting the representative description, the subject underweights the statistical base rate evidence of the small fraction of the population belonging to that profession. An important manifestation of the representativeness heuristic, discussed in detail by Tversky and Kahneman, is that people think they see patterns in truly random sequences. This aspect of the representativeness heuristic is suggestive of the overreaction evidence described above. When a company has a consistent history of earnings growth over several years, accompanied as it may be by salient and enthusiastic descriptions of its products and management, investors might conclude that the past history is representative of an underlying earnings growth potential. While a consistent pattern of high growth may be nothing more than a random draw for a few lucky firms, investors see ‘order among chaos’ and infer from the in-sample growth path that the firm belongs to a small and distinct population of firms whose earnings just keep growing. As a consequence, investors using the representativeness heuristic might disregard the reality that a history of high earnings growth is unlikely to repeat itself; they will overvalue the company, and be disappointed in the future when the forecasted earnings growth fails to materialize. This, of course, is what overreaction is all about. In a recent study, Griffin and Tversky (1992) attempt to reconcile conservatism with representativeness. 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.8 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. In the Griffin—Tversky framework, conservatism like that documented by Edwards would occur in the face of evidence that has high weight but low strength: people are unimpressed by the low strength and react mildly to the evidence, even though its weight calls for a larger reaction. On the other hand, when the evidence has high strength but low weight, overreaction occurs in a manner consistent with representativeness. Indeed, representativeness can be thought of as excessive attention to the strength of particularly salient evidence, in spite of its relatively low weight. 316 N. Barberis et al./Journal of Financial Economics 49 (1998) 307—343