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