《金融投资学》教学资源（英文文献）Market efficiency, long-term returns, and behavioral finance

N JOURNAL OF Financial ECONOMICS ELSEVIER Journal of Financial Economics 49 (1998)283-306 Market efficiency,long-term returns,and behavioral finance1 Eugene F.Fama* Graduate School of Business,University of Chicago.Chicago.IL 60637,USA Received 17 March 1997;received in revised form 3 October 1997 Abstract Market efficiency survives the challenge from the literature on long-term return anomalies.Consistent with the market efficiency hypothesis that the anomalies are chance results,apparent overreaction to information is about as common as underreac- tion,and post-event continuation of pre-event abnormal returns is about as frequent as post-event reversal.Most important,consistent with the market efficiency prediction that apparent anomalies can be due to methodology,most long-term return anomalies tend to disappear with reasonable changes in technique.C 1998 Elsevier Science S.A.All rights reserved. JEL classification:G14;G12 Keywords:Market efficiency;Behavioral finance 1.Introduction Event studies,introduced by Fama et al.(1969),produce useful evidence on how stock prices respond to information.Many studies focus on returns in a short window(a few days)around a cleanly dated event.An advantage of this approach is that because daily expected returns are close to zero,the model for expected returns does not have a big effect on inferences about abnormal returns. Corresponding author.Tel.:773 702 7282;fax:773 702 9937;e-mail:eugene.fama@gsb.uchicago. edu. The comments of Brad Barber,David Hirshleifer,S.P.Kothari,Owen Lamont,Mark Mitchell, Hersh Shefrin,Robert Shiller,Rex Sinquefield,Richard Thaler,Theo Vermaelen,Robert Vishny,Ivo Welch,and a referee have been helpful.Kenneth French and Jay Ritter get special thanks. 0304-405X/98/S19.00 C 1998 Elsevier Science S.A.All rights reserved P1S0304-405X(98)00026-9

* Corresponding author. Tel.: 773 702 7282; fax: 773 702 9937; e-mail: eugene.fama@gsb.uchicago. edu. 1The comments of Brad Barber, David Hirshleifer, S.P. Kothari, Owen Lamont, Mark Mitchell, Hersh Shefrin, Robert Shiller, Rex Sinquefield, Richard Thaler, Theo Vermaelen, Robert Vishny, Ivo Welch, and a referee have been helpful. Kenneth French and Jay Ritter get special thanks. Journal of Financial Economics 49 (1998) 283—306 Market efficiency, long-term returns, and behavioral finance1 Eugene F. Fama* Graduate School of Business, University of Chicago, Chicago, IL 60637, USA Received 17 March 1997; received in revised form 3 October 1997 Abstract Market efficiency survives the challenge from the literature on long-term return anomalies. Consistent with the market efficiency hypothesis that the anomalies are chance results, apparent overreaction to information is about as common as underreac￾tion, and post-event continuation of pre-event abnormal returns is about as frequent as post-event reversal. Most important, consistent with the market efficiency prediction that apparent anomalies can be due to methodology, most long-term return anomalies tend to disappear with reasonable changes in technique. ( 1998 Elsevier Science S.A. All rights reserved. JEL classification: G14; G12 Keywords: Market efficiency; Behavioral finance 1. Introduction Event studies, introduced by Fama et al. (1969), produce useful evidence on how stock prices respond to information. Many studies focus on returns in a short window (a few days) around a cleanly dated event. An advantage of this approach is that because daily expected returns are close to zero, the model for expected returns does not have a big effect on inferences about abnormal returns. 0304-405X/98/$19.00 ( 1998 Elsevier Science S.A. All rights reserved PII S0304-405X(98)00026-9

284 E.F.FamafJournal of Financial Economics 49 (1998)283-306 The assumption in studies that focus on short return windows is that any lag in the response of prices to an event is short-lived.There is a developing literature that challenges this assumption,arguing instead that stock prices adjust slowly to information,so one must examine returns over long horizons to get a full view of market inefficiency. If one accepts their stated conclusions,many of the recent studies on long- term returns suggest market inefficiency,specifically,long-term underreaction or overreaction to information.It is time,however,to ask whether this litera- ture,viewed as a whole,suggests that efficiency should be discarded.My answer is a solid no,for two reasons. First,an efficient market generates categories of events that individually suggest that prices over-react to information.But in an efficient market,appar- ent underreaction will be about as frequent as overreaction.If anomalies split randomly between underreaction and overreaction,they are consistent with market efficiency.We shall see that a roughly even split between apparent overreaction and underreaction is a good description of the menu of existing anomalies. Second,and more important,if the long-term return anomalies are so large they cannot be attributed to chance,then an even split between over-and underreaction is a pyrrhic victory for market efficiency.We shall find,however, that the long-term return anomalies are sensitive to methodology.They tend to become marginal or disappear when exposed to different models for expected (normal)returns or when different statistical approaches are used to measure them.Thus,even viewed one-by-one,most long-term return anomalies can reasonably be attributed to chance. A problem in developing an overall perspective on long-term return studies is that they rarely test a specific alternative to market efficiency.Instead,the alternative hypothesis is vague,market inefficiency.This is unacceptable.Like all models,market efficiency(the hypothesis that prices fully reflect available information)is a faulty description of price formation.Following the standard scientific rule,however,market efficiency can only be replaced by a better specific model of price formation,itself potentially rejectable by empirical tests. Any alternative model has a daunting task.It must specify biases in informa- tion processing that cause the same investors to under-react to some types of events and over-react to others.The alternative must also explain the range of observed results better than the simple market efficiency story;that is,the expected value of abnormal returns is zero,but chance generates deviations from zero (anomalies)in both directions. Since the anomalies literature has not settled on a specific alternative to market efficiency,to get the ball rolling,I assume reasonable alternatives must choose between overreaction or underreaction.Using this perspective,Section 2 reviews existing studies,without questioning their inferences.My conclusion is that,viewed as a whole,the long-term return literature does not identify

The assumption in studies that focus on short return windows is that any lag in the response of prices to an event is short-lived. There is a developing literature that challenges this assumption, arguing instead that stock prices adjust slowly to information, so one must examine returns over long horizons to get a full view of market inefficiency. If one accepts their stated conclusions, many of the recent studies on long￾term returns suggest market inefficiency, specifically, long-term underreaction or overreaction to information. It is time, however, to ask whether this litera￾ture, viewed as a whole, suggests that efficiency should be discarded. My answer is a solid no, for two reasons. First, an efficient market generates categories of events that individually suggest that prices over-react to information. But in an efficient market, appar￾ent underreaction will be about as frequent as overreaction. If anomalies split randomly between underreaction and overreaction, they are consistent with market efficiency. We shall see that a roughly even split between apparent overreaction and underreaction is a good description of the menu of existing anomalies. Second, and more important, if the long-term return anomalies are so large they cannot be attributed to chance, then an even split between over- and underreaction is a pyrrhic victory for market efficiency. We shall find, however, that the long-term return anomalies are sensitive to methodology. They tend to become marginal or disappear when exposed to different models for expected (normal) returns or when different statistical approaches are used to measure them. Thus, even viewed one-by-one, most long-term return anomalies can reasonably be attributed to chance. A problem in developing an overall perspective on long-term return studies is that they rarely test a specific alternative to market efficiency. Instead, the alternative hypothesis is vague, market inefficiency. This is unacceptable. Like all models, market efficiency (the hypothesis that prices fully reflect available information) is a faulty description of price formation. Following the standard scientific rule, however, market efficiency can only be replaced by a better specific model of price formation, itself potentially rejectable by empirical tests. Any alternative model has a daunting task. It must specify biases in informa￾tion processing that cause the same investors to under-react to some types of events and over-react to others. The alternative must also explain the range of observed results better than the simple market efficiency story; that is, the expected value of abnormal returns is zero, but chance generates deviations from zero (anomalies) in both directions. Since the anomalies literature has not settled on a specific alternative to market efficiency, to get the ball rolling, I assume reasonable alternatives must choose between overreaction or underreaction. Using this perspective, Section 2 reviews existing studies, without questioning their inferences. My conclusion is that, viewed as a whole, the long-term return literature does not identify 284 E.F. Fama/Journal of Financial Economics 49 (1998) 283—306

E.F.FamafJournal of Financial Economics 49 (1998)283-306 285 overreaction or underreaction as the dominant phenomenon.The random split predicted by market efficiency holds up rather well. Two recent papers,Barberis et al.(1998)and Daniel et al.(1997),present behavioral models that accommodate overreaction and underreaction.To their credit,these models present rejectable hypotheses.Section 3 argues that,not surprisingly,the two behavioral models work well on the anomalies they are designed to explain.Other anomalies are,however,embarrassing.The problem is that both models predict post-event return reversals in response to long-term pre-event abnormal returns.In fact,post-event return continuation is about as frequent as reversal-a result that is more consistent with market efficiency than with the two behavioral models. Section 4 examines the problems in drawing inferences about long-term returns.Foremost is an unavoidable bad-model problem.Market efficiency must be tested jointly with a model for expected (normal)returns,and all models show problems describing average returns.The bad-model problem is ubiqui- tous,but it is more serious in long-term returns.The reason is that bad-model errors in expected returns grow faster with the return horizon than the volatility of returns.Section 4 also argues that theoretical and statistical considerations alike suggest that formal inferences about long-term returns should be based on averages or sums of short-term abnormal returns(AARs or CARs)rather than the currently popular buy-and-hold abnormal returns(BHARs). In categorizing studies on long-term returns,Sections 2 and 3 do not question their inferences.Dissection of individual studies takes place in Section 5.The bottom line is that the evidence against market efficiency from the long-term return studies is fragile.Reasonable changes in the approach used to measure abnormal returns typically suggest that apparent anomalies are methodological illusions. 2.Overreaction and underreaction:An overview One of the first papers on long-term return anomalies is DeBondt and Thaler (1985).They find that when stocks are ranked on three-to five-year past returns, past winners tend to be future losers,and vice versa.They attribute these long-term return reversals to investor overreaction.In forming expectations, investors give too much weight to the past performance of firms and too little to the fact that performance tends to mean-revert.DeBondt and Thaler seem to argue that overreaction to past information is a general prediction of the behavioral decision theory of Kahneman and Tversky (1982).Thus,one could take overreaction to be the prediction of a behavioral finance alternative to market efficiency.For the most part,however,the anomalies literature has not accepted the discipline of an alternative hypothesis. An exception is Lakonishok et al.(1994).They argue that ratios involving stock prices proxy for past performance.Firms with high ratios of earnings to

overreaction or underreaction as the dominant phenomenon. The random split predicted by market efficiency holds up rather well. Two recent papers, Barberis et al. (1998) and Daniel et al. (1997), present behavioral models that accommodate overreaction and underreaction. To their credit, these models present rejectable hypotheses. Section 3 argues that, not surprisingly, the two behavioral models work well on the anomalies they are designed to explain. Other anomalies are, however, embarrassing. The problem is that both models predict post-event return reversals in response to long-term pre-event abnormal returns. In fact, post-event return continuation is about as frequent as reversal — a result that is more consistent with market efficiency than with the two behavioral models. Section 4 examines the problems in drawing inferences about long-term returns. Foremost is an unavoidable bad-model problem. Market efficiency must be tested jointly with a model for expected (normal) returns, and all models show problems describing average returns. The bad-model problem is ubiqui￾tous, but it is more serious in long-term returns. The reason is that bad-model errors in expected returns grow faster with the return horizon than the volatility of returns. Section 4 also argues that theoretical and statistical considerations alike suggest that formal inferences about long-term returns should be based on averages or sums of short-term abnormal returns (AARs or CARs) rather than the currently popular buy-and-hold abnormal returns (BHARs). In categorizing studies on long-term returns, Sections 2 and 3 do not question their inferences. Dissection of individual studies takes place in Section 5. The bottom line is that the evidence against market efficiency from the long-term return studies is fragile. Reasonable changes in the approach used to measure abnormal returns typically suggest that apparent anomalies are methodological illusions. 2. Overreaction and underreaction: An overview One of the first papers on long-term return anomalies is DeBondt and Thaler (1985). They find that when stocks are ranked on three- to five-year past returns, past winners tend to be future losers, and vice versa. They attribute these long-term return reversals to investor overreaction. In forming expectations, investors give too much weight to the past performance of firms and too little to the fact that performance tends to mean-revert. DeBondt and Thaler seem to argue that overreaction to past information is a general prediction of the behavioral decision theory of Kahneman and Tversky (1982). Thus, one could take overreaction to be the prediction of a behavioral finance alternative to market efficiency. For the most part, however, the anomalies literature has not accepted the discipline of an alternative hypothesis. An exception is Lakonishok et al. (1994). They argue that ratios involving stock prices proxy for past performance. Firms with high ratios of earnings to E.F. Fama/Journal of Financial Economics 49 (1998) 283—306 285

286 E.F.FamafJournal of Financial Economics 49 (1998)283-306 price(E/P),cashflow to price(C/P),and book-to-market equity (BE/ME)tend to have poor past earnings growth,and firms with low E/P,C/P,and BE/ME tend to have strong past earnings growth.Because the market over-reacts to past growth,it is surprised when earnings growth mean reverts.As a result,high E/P,C/P,and BE/ME stocks(poor past performers)have high future returns, and low E/P,C/P,and BE/ME stocks(strong past performers)have low future returns. I also classify the poor long-term post-event returns of initial public offerings (IPOs)(Ritter,1991;Loughran and Ritter,1995)and seasoned equity offerings (SEOs)(Loughran and Ritter,1995;Spiess and Affleck-Graves,1995)in the overreaction camp.Mitchell and Stafford(1997)show that SEOs have strong stock returns in the three years prior to the issue.It seems safe to presume that these strong returns reflect strong earnings.It also seems safe to presume that IPOs have strong past earnings to display when going public.If the market does not understand that earnings growth tends to mean revert,stock prices at the time of the equity issue(IPO or SEO)are too high.If the market only gradually recognizes its mistakes,the overreaction to past earnings growth is corrected slowly in the future.Finally,Dharan and Ikenberry(1995)argue that the long- term negative post-listing abnormal stock returns of firms that newly list on the NYSE or Amex are due to overreaction.Firms list their stocks to take advant- age of the market's overreaction to their recent strong performance. If apparent overreaction was the general result in studies of long-term returns, market efficiency would be dead,replaced by the behavioral alternative of DeBondt and Thaler(1985).In fact,apparent underreaction is about as fre- quent.The granddaddy of underreaction events is the evidence that stock prices seem to respond to earnings for about a year after they are announced(Ball and Brown,1968;Bernard and Thomas,1990).More recent is the momentum effect identified by Jegadeesh and Titman(1993);stocks with high returns over the past year tend to have high returns over the following three to six months. Other recent event studies also produce long-term post-event abnormal returns that suggest underreaction.Cusatis et al.(1993)find positive post-event abnormal returns for divesting firms and the firms they divest.They attribute the result to market underreaction to an enhanced probability that,after a spinoff, both the parent and the spinoff are likely to become merger targets,and the recipients of premiums.Desai and Jain (1997)and Ikenberry et al.(1996)find that firms that split their stock experience long-term positive abnormal returns both before and after the split.They attribute the post-split returns to market underreaction to the positive information signaled by a split.Lakonishok and Vermaelen (1990)find positive long-term post-event abnormal returns when firms tender for their stock.Ikenberry et al.(1995)observe similar results for open-market share repurchases.The story in both cases is that the market under-reacts to the positive signal in share repurchases about future perfor- mance.Finally,Michaely et al.(1995)find that stock prices seem to under-react

price (E/P), cashflow to price (C/P), and book-to-market equity (BE/ME) tend to have poor past earnings growth, and firms with low E/P, C/P, and BE/ME tend to have strong past earnings growth. Because the market over-reacts to past growth, it is surprised when earnings growth mean reverts. As a result, high E/P, C/P, and BE/ME stocks (poor past performers) have high future returns, and low E/P, C/P, and BE/ME stocks (strong past performers) have low future returns. I also classify the poor long-term post-event returns of initial public offerings (IPOs) (Ritter, 1991; Loughran and Ritter, 1995) and seasoned equity offerings (SEOs) (Loughran and Ritter, 1995; Spiess and Affleck-Graves, 1995) in the overreaction camp. Mitchell and Stafford (1997) show that SEOs have strong stock returns in the three years prior to the issue. It seems safe to presume that these strong returns reflect strong earnings. It also seems safe to presume that IPOs have strong past earnings to display when going public. If the market does not understand that earnings growth tends to mean revert, stock prices at the time of the equity issue (IPO or SEO) are too high. If the market only gradually recognizes its mistakes, the overreaction to past earnings growth is corrected slowly in the future. Finally, Dharan and Ikenberry (1995) argue that the long￾term negative post-listing abnormal stock returns of firms that newly list on the NYSE or Amex are due to overreaction. Firms list their stocks to take advant￾age of the market’s overreaction to their recent strong performance. If apparent overreaction was the general result in studies of long-term returns, market efficiency would be dead, replaced by the behavioral alternative of DeBondt and Thaler (1985). In fact, apparent underreaction is about as fre￾quent. The granddaddy of underreaction events is the evidence that stock prices seem to respond to earnings for about a year after they are announced (Ball and Brown, 1968; Bernard and Thomas, 1990). More recent is the momentum effect identified by Jegadeesh and Titman (1993); stocks with high returns over the past year tend to have high returns over the following three to six months. Other recent event studies also produce long-term post-event abnormal returns that suggest underreaction. Cusatis et al. (1993) find positive post-event abnormal returns for divesting firms and the firms they divest. They attribute the result to market underreaction to an enhanced probability that, after a spinoff, both the parent and the spinoff are likely to become merger targets, and the recipients of premiums. Desai and Jain (1997) and Ikenberry et al. (1996) find that firms that split their stock experience long-term positive abnormal returns both before and after the split. They attribute the post-split returns to market underreaction to the positive information signaled by a split. Lakonishok and Vermaelen (1990) find positive long-term post-event abnormal returns when firms tender for their stock. Ikenberry et al. (1995) observe similar results for open-market share repurchases. The story in both cases is that the market under-reacts to the positive signal in share repurchases about future perfor￾mance. Finally, Michaely et al. (1995) find that stock prices seem to under-react 286 E.F. Fama/Journal of Financial Economics 49 (1998) 283—306

E.F.FamafJournal of Financial Economics 49 (1998)283-306 287 to the negative information in dividend omissions and the positive information in initiations. Some long-term return anomalies are difficult to classify.For example, Asquith (1983)and Agrawal et al.(1992)find negative long-term abnormal returns to acquiring firms following mergers.This might be attributed to market underreaction to a poor investment decision(Roll,1986)or overreaction to the typically strong performance of acquiring firms in advance of mergers, documented in Mitchell and Stafford(1997).Ikenberry and Lakonishok(1993) find negative post-event abnormal returns for firms involved in proxy contests. One story is that stock prices under-react to the poor performance of these firms before the proxy contest,but another is that prices over-react to the information in a proxy that something is likely to change. Given the ambiguities in classifying some anomalies,and given that the review above is surely incomplete,I shall not do a count of underreaction versus overreaction studies.The important point is that the literature does not lean cleanly toward either as the behavioral alternative to market efficiency.This is not lost on behavioral finance researchers who acknowledge the issue: We hope future research will help us understand why the market appears to overreact in some circumstances and underreact in others.(Michaely et al., 1995,p.606). The market efficiency hypothesis offers a simple answer to this question -chance.Specifically,the expected value of abnormal returns is zero,but chance generates apparent anomalies that split randomly between overreaction and underreaction. Is the weight of the evidence on long-term return anomalies so overwhelming that market efficiency is not a viable working model even in the absence of an alternative that explains both under-and overreaction?My answer to this question is no,for three reasons. First,I doubt that the literature presents a random sample of events.Splashy results get more attention,and this creates an incentive to find them.That dredging for anomalies is a rewarding occupation is suggested by the fact that the anomalies literature shows so little sensitivity to the alternative hypothesis problem.The same authors,viewing different events,are often content with overreaction or underreaction,and are willing to infer that both warrant rejecting market efficiency. Second,some apparent anomalies may be generated by rational asset pricing. Fama and French(1996)find that the long-term return reversals of DeBondt and Thaler(1985)and the contrarian returns of Lakonishok et al.(1994)are captured by a multifactor asset pricing model.In a nutshell,return covariation among long-term losers seems to be associated with a risk premium that can explain why they have higher future average returns than long-term winners. Fama and French(1996)discuss the quarrels with their multifactor model,but

to the negative information in dividend omissions and the positive information in initiations. Some long-term return anomalies are difficult to classify. For example, Asquith (1983) and Agrawal et al. (1992) find negative long-term abnormal returns to acquiring firms following mergers. This might be attributed to market underreaction to a poor investment decision (Roll, 1986) or overreaction to the typically strong performance of acquiring firms in advance of mergers, documented in Mitchell and Stafford (1997). Ikenberry and Lakonishok (1993) find negative post-event abnormal returns for firms involved in proxy contests. One story is that stock prices under-react to the poor performance of these firms before the proxy contest, but another is that prices over-react to the information in a proxy that something is likely to change. Given the ambiguities in classifying some anomalies, and given that the review above is surely incomplete, I shall not do a count of underreaction versus overreaction studies. The important point is that the literature does not lean cleanly toward either as the behavioral alternative to market efficiency. This is not lost on behavioral finance researchers who acknowledge the issue: We hope future research will help us understand why the market appears to overreact in some circumstances and underreact in others. (Michaely et al., 1995, p. 606). The market efficiency hypothesis offers a simple answer to this question — chance. Specifically, the expected value of abnormal returns is zero, but chance generates apparent anomalies that split randomly between overreaction and underreaction. Is the weight of the evidence on long-term return anomalies so overwhelming that market efficiency is not a viable working model even in the absence of an alternative that explains both under- and overreaction? My answer to this question is no, for three reasons. First, I doubt that the literature presents a random sample of events. Splashy results get more attention, and this creates an incentive to find them. That dredging for anomalies is a rewarding occupation is suggested by the fact that the anomalies literature shows so little sensitivity to the alternative hypothesis problem. The same authors, viewing different events, are often content with overreaction or underreaction, and are willing to infer that both warrant rejecting market efficiency. Second, some apparent anomalies may be generated by rational asset pricing. Fama and French (1996) find that the long-term return reversals of DeBondt and Thaler (1985) and the contrarian returns of Lakonishok et al. (1994) are captured by a multifactor asset pricing model. In a nutshell, return covariation among long-term losers seems to be associated with a risk premium that can explain why they have higher future average returns than long-term winners. Fama and French (1996) discuss the quarrels with their multifactor model, but E.F. Fama/Journal of Financial Economics 49 (1998) 283—306 287

288 E.F.FamafJournal of Financial Economics 49 (1998)283-306 their results suffice to illustrate an important point:Inferences about market efficiency can be sensitive to the assumed model for expected returns. Finally,but most important,a roughly even split between overreaction and underreaction would not be much support for market efficiency if the long-term return anomalies are so large they cannot possibly be attributed to chance. Section 5 argues,however,that even viewed individually,most anomalies are shaky.They tend to disappear when reasonable alternative approaches are used to measure them. 3.Behavioral models of underreaction and overreaction Before examining individual long-term return studies,I first consider two behavioral models,recently proposed by Barberis,Shleifer,and Vishny(BSV 1998)and Daniel,Hirshleifer,and Subramanyam(DHS 1997),to explain how the judgment biases of investors can produce overreaction to some events and underreaction to others. The BSV model is motivated by evidence from cognitive psychology of two judgment biases.(i)The representativeness bias of Kahneman and Tversky (1982):People give too much weight to recent patterns in the data and too little to the properties of the population that generates the data.(ii)Conservatism, attributed to Edwards(1968):The slow updating of models in the face of new evidence. In the model of stock prices proposed by BSV to capture the two judgment biases,earnings are a random walk,but investors falsely perceive that there are two earnings regimes.In regime A,which investors assume is more likely, earnings are mean-reverting.When investors decide regime A holds,a stock's price under-reacts to a change in earnings because investors mistakenly think the change is likely to be temporary.When this expectation is not confirmed by later earnings,stock prices show a delayed response to earlier earnings.In regime B,which investors think is less likely,a run of earnings changes of the same sign leads investors to perceive that a firm's earnings are trending.Once investors are convinced that the trending regime B holds,they incorrectly extrapolate the trend and the stock price over-reacts.Because earnings are a random walk,the overreaction is exposed by future earnings,leading to reversal of long-term returns. Regime A in the BSV model is motivated by the evidence of short-term momentum in stock returns (Jegadeesh and Titman,1993)and the evidence of delayed short-term responses of stock prices to earnings announcements(Ball and Brown,1968;Bernard and Thomas,1990).Regime B is meant to explain the long-term return reversals of DeBondt and Thaler(1985)and the returns to the contrarian investment strategies of Lakonishok et al.(1994).How does the model do on other anomalies?

their results suffice to illustrate an important point: Inferences about market efficiency can be sensitive to the assumed model for expected returns. Finally, but most important, a roughly even split between overreaction and underreaction would not be much support for market efficiency if the long-term return anomalies are so large they cannot possibly be attributed to chance. Section 5 argues, however, that even viewed individually, most anomalies are shaky. They tend to disappear when reasonable alternative approaches are used to measure them. 3. Behavioral models of underreaction and overreaction Before examining individual long-term return studies, I first consider two behavioral models, recently proposed by Barberis, Shleifer, and Vishny (BSV 1998) and Daniel, Hirshleifer, and Subramanyam (DHS 1997), to explain how the judgment biases of investors can produce overreaction to some events and underreaction to others. The BSV model is motivated by evidence from cognitive psychology of two judgment biases. (i) The representativeness bias of Kahneman and Tversky (1982): People give too much weight to recent patterns in the data and too little to the properties of the population that generates the data. (ii) Conservatism, attributed to Edwards (1968): The slow updating of models in the face of new evidence. In the model of stock prices proposed by BSV to capture the two judgment biases, earnings are a random walk, but investors falsely perceive that there are two earnings regimes. In regime A, which investors assume is more likely, earnings are mean-reverting. When investors decide regime A holds, a stock’s price under-reacts to a change in earnings because investors mistakenly think the change is likely to be temporary. When this expectation is not confirmed by later earnings, stock prices show a delayed response to earlier earnings. In regime B, which investors think is less likely, a run of earnings changes of the same sign leads investors to perceive that a firm’s earnings are trending. Once investors are convinced that the trending regime B holds, they incorrectly extrapolate the trend and the stock price over-reacts. Because earnings are a random walk, the overreaction is exposed by future earnings, leading to reversal of long-term returns. Regime A in the BSV model is motivated by the evidence of short-term momentum in stock returns (Jegadeesh and Titman, 1993) and the evidence of delayed short-term responses of stock prices to earnings announcements (Ball and Brown, 1968; Bernard and Thomas, 1990). Regime B is meant to explain the long-term return reversals of DeBondt and Thaler (1985) and the returns to the contrarian investment strategies of Lakonishok et al. (1994). How does the model do on other anomalies? 288 E.F. Fama/Journal of Financial Economics 49 (1998) 283—306

E.F.FamafJournal of Financial Economics 49 (1998)283-306 289 The prediction of regime B is reversal of long-term abnormal returns.Specifi- cally,persistent long-term pre-event returns are evidence of market overreaction which should eventually be corrected in post-event returns.In addition to DeBondt and Thaler(1985)and Lakonishok et al.(1994),other events consistent with this prediction are seasoned equity offerings(Loughran and Ritter,1995; Mitchell and Stafford,1997),new exchange listings(Dharan and Ikenberry, 1995),and returns to acquiring firms in mergers(Asquith,1983).All these events are characterized by positive long-term abnormal returns before the event and negative abnormal returns thereafter. But long-term return reversal is not the norm.Events characterized by long-term post-event abnormal returns of the same sign as long-term pre-event returns include dividend initiations and omissions(Michaely et al.,1995),stock splits(Ikenberry et al,1996;Desai and Jain,1997),proxy contests(Ikenberry and Lakonishok,1993),and spinoffs (Miles and Rosenfeld,1983;Cusatis et al. 1993. In short,and not surprisingly,the BSV model does well on the anomalies it was designed to explain.But its prediction of long-term return reversal does not capture the range of long-term results observed in the literature.On the whole, the long-term return literature seems more consistent with the market efficiency prediction that long-term return continuation and long-term return reversal are equally likely chance results. The DHS model has different behavioral foundations than the BSV model.In DHS there are informed and uninformed investors.The uninformed are not subject to judgment biases.But stock prices are determined by the informed investors,and they are subject to two biases,overconfidence and biased self- attribution.Overconfidence leads them to exaggerate the precision of their private signals about a stock's value.Biased self-attribution causes them to downweight public signals about value,especially when the public signals contradict their private signals.Overreaction to private information and under- reaction to public information tend to produce short-term continuation of stock returns but long-term reversals as public information eventually overwhelms the behavioral biases.Thus,though based on different behavioral premises,the DHS predictions are close to those of BSV,and the DHS model shares the empirical successes and failures of the BSV model.This last comment also applies to Hong and Stein(1997). DHS make a special prediction about what they call selective events.These are events that occur to take advantage of the mispricing of a firm's stock.For example,managers announce a new stock issue when a firm's stock price is too high,or they repurchase shares when the stock price is too low.This public signal produces an immediate price reaction that absorbs some of the mispric- ing.But in the DHS model,the announcement period price response is incom- plete because informed investors overweight their prior beliefs about the stock's value.(The conservatism bias of the BSV model would produce a similar result.)

The prediction of regime B is reversal of long-term abnormal returns. Specifi- cally, persistent long-term pre-event returns are evidence of market overreaction which should eventually be corrected in post-event returns. In addition to DeBondt and Thaler (1985) and Lakonishok et al. (1994), other events consistent with this prediction are seasoned equity offerings (Loughran and Ritter, 1995; Mitchell and Stafford, 1997), new exchange listings (Dharan and Ikenberry, 1995), and returns to acquiring firms in mergers (Asquith, 1983). All these events are characterized by positive long-term abnormal returns before the event and negative abnormal returns thereafter. But long-term return reversal is not the norm. Events characterized by long-term post-event abnormal returns of the same sign as long-term pre-event returns include dividend initiations and omissions (Michaely et al., 1995), stock splits (Ikenberry et al., 1996; Desai and Jain, 1997), proxy contests (Ikenberry and Lakonishok, 1993), and spinoffs (Miles and Rosenfeld, 1983; Cusatis et al., 1993). In short, and not surprisingly, the BSV model does well on the anomalies it was designed to explain. But its prediction of long-term return reversal does not capture the range of long-term results observed in the literature. On the whole, the long-term return literature seems more consistent with the market efficiency prediction that long-term return continuation and long-term return reversal are equally likely chance results. The DHS model has different behavioral foundations than the BSV model. In DHS there are informed and uninformed investors. The uninformed are not subject to judgment biases. But stock prices are determined by the informed investors, and they are subject to two biases, overconfidence and biased self￾attribution. Overconfidence leads them to exaggerate the precision of their private signals about a stock’s value. Biased self-attribution causes them to downweight public signals about value, especially when the public signals contradict their private signals. Overreaction to private information and under￾reaction to public information tend to produce short-term continuation of stock returns but long-term reversals as public information eventually overwhelms the behavioral biases. Thus, though based on different behavioral premises, the DHS predictions are close to those of BSV, and the DHS model shares the empirical successes and failures of the BSV model. This last comment also applies to Hong and Stein (1997). DHS make a special prediction about what they call selective events. These are events that occur to take advantage of the mispricing of a firm’s stock. For example, managers announce a new stock issue when a firm’s stock price is too high, or they repurchase shares when the stock price is too low. This public signal produces an immediate price reaction that absorbs some of the mispric￾ing. But in the DHS model, the announcement period price response is incom￾plete because informed investors overweight their prior beliefs about the stock’s value. (The conservatism bias of the BSV model would produce a similar result.) E.F. Fama/Journal of Financial Economics 49 (1998) 283—306 289

290 E.F.FamafJournal of Financial Economics 49 (1998)283-306 Eventually,the mispricing is fully absorbed as further public information con- firms the information implied by the event announcement.The general predic- tion for selective events is thus momentum;stock returns after an event an- nouncement will tend to have the same sign as the announcement period return. Does the DHS prediction about selective events stand up to the data?Table 1 summarizes the signs of short-term announcement returns and long-term Table 1 Signs of long-term pre-event,announcement,and long-term post-event returns for various long- term return studies Event Long-term Announcement Long-term pre-event return post-event return return Initial public offerings (IPOs) Not (Ibbotson,1975;Loughran and Ritter,1995) available Seasoned equity offerings (Loughran and Ritter,1995) Mergers(acquiring firm) (Asquith,1983; Agrawal et al.,1992) Dividend initiations (Michaely et al,1995) Dividend omissions (Michaely et al,1995) Earnings announcements Not (Ball and Brown,1968;Bernard available and Thomas,1990) New exchange listings (Dharan and Ikenberry,1995) Share repurchases(open market) (Ikenberry et al,1995;Mitchell and Stafford,1997) Share repurchases (tenders) (Lakonishok and Vermaelen,1990; Mitchell and Stafford,1997) Proxy fights -(or0) (Ikenberry and Lakonishok,1993) Stock splits (Dharan and Ikenberry,1995;Ikenberry etal,1996) Spinoffs +(or0) (Miles and Rosenfeld,1983;Cusatis etal,1993)

Table 1 Signs of long-term pre-event, announcement, and long-term post-event returns for various long￾term return studies Event Long-term pre-event return Announcement return Long-term post-event return Initial public offerings (IPOs) (Ibbotson, 1975; Loughran and Ritter, 1995) Not available # ! Seasoned equity offerings (Loughran and Ritter, 1995) #! ! Mergers (acquiring firm) (Asquith, 1983; Agrawal et al., 1992) # 0 ! Dividend initiations (Michaely et al., 1995) ## # Dividend omissions (Michaely et al., 1995) !! ! Earnings announcements (Ball and Brown, 1968; Bernard and Thomas, 1990) Not available # # New exchange listings (Dharan and Ikenberry, 1995) ## ! Share repurchases (open market) (Ikenberry et al., 1995; Mitchell and Stafford, 1997) 0 # # Share repurchases (tenders) (Lakonishok and Vermaelen, 1990; Mitchell and Stafford, 1997) 0 # # Proxy fights (Ikenberry and Lakonishok, 1993) !# ! (or 0) Stock splits (Dharan and Ikenberry, 1995; Ikenberry et al., 1996) ## # Spinoffs (Miles and Rosenfeld, 1983; Cusatis et al., 1993) ## # (or 0) Eventually, the mispricing is fully absorbed as further public information con- firms the information implied by the event announcement. The general predic￾tion for selective events is thus momentum; stock returns after an event an￾nouncement will tend to have the same sign as the announcement period return. Does the DHS prediction about selective events stand up to the data? Table 1 summarizes the signs of short-term announcement returns and long-term 290 E.F. Fama/Journal of Financial Economics 49 (1998) 283—306

E.F.FamafJournal of Financial Economics 49 (1998)283-306 291 post-announcement returns for the major long-term return studies.Except for earnings announcements,all these events seem selective.As predicted by DHS, announcement and post-announcement returns have the same sign for SEOs. dividend initiations and omissions,share repurchases,stock splits,and spinoffs. But announcement and post-announcement returns have opposite signs for new exchange listings and proxy fights,and the negative post-event returns to acquiring firms in mergers are not preceded by negative announcement returns. Most embarrassing for the DHS prediction,the long-term negative post-event returns of IPOs(the premier long-term return anomaly)are preceded by positive returns for a few months following the event (Ibbotson,1975;Ritter,1991). Finally,given the demonstrated ingenuity of the theory branch of finance,and given the long litany of apparent judgment biases unearthed by cognitive psychologists(DeBondt and Thaler,1995),it is safe to predict that we will soon see a menu of behavioral models that can be mixed and matched to explain specific anomalies.My view is that any new model should be judged (as above) on how it explains the big picture.The question should be:Does the new model produce rejectable predictions that capture the menu of anomalies better than market efficiency?For existing behavioral models,my answer to this question (perhaps predictably)is an emphatic no. The main task that remains is to examine the long-term return anomalies one at a time to see if they deliver on their claims.We set the stage with a discussion of some of the general problems that arise in tests on long-term returns. 4.Drawing inferences from long-term returns Fama(1970)emphasizes that market efficiency must be tested jointly with a model for expected (normal)returns.The problem is that all models for expected returns are incomplete descriptions of the systematic patterns in average returns during any sample period.As a result,tests of efficiency are always contaminated by a bad-model problem. The bad-model problem is less serious in event studies that focus on short return windows(a few days)since daily expected returns are close to zero and so have little effect on estimates of unexpected(abnormal)returns.But the problem grows with the return horizon.A bad-model problem that produces a spurious abnormal average return of x%per month eventually becomes statistically reliable in cumulative monthly abnormal returns(CARs).The reason is that the mean of the CAR increases like N,the number of months summed,but the standard error of the CAR increases like N1/2.In AARs(averages of monthly abnormal returns),the pricing error is constant at x%,but the standard error of the AAR decreases like N-112.Bad-model problems are most acute with long- term buy-and-hold abnormal returns(BHARs),which compound(multiply)an expected-return model's problems in explaining short-term returns

post-announcement returns for the major long-term return studies. Except for earnings announcements, all these events seem selective. As predicted by DHS, announcement and post-announcement returns have the same sign for SEOs, dividend initiations and omissions, share repurchases, stock splits, and spinoffs. But announcement and post-announcement returns have opposite signs for new exchange listings and proxy fights, and the negative post-event returns to acquiring firms in mergers are not preceded by negative announcement returns. Most embarrassing for the DHS prediction, the long-term negative post-event returns of IPOs (the premier long-term return anomaly) are preceded by positive returns for a few months following the event (Ibbotson, 1975; Ritter, 1991). Finally, given the demonstrated ingenuity of the theory branch of finance, and given the long litany of apparent judgment biases unearthed by cognitive psychologists (DeBondt and Thaler, 1995), it is safe to predict that we will soon see a menu of behavioral models that can be mixed and matched to explain specific anomalies. My view is that any new model should be judged (as above) on how it explains the big picture. The question should be: Does the new model produce rejectable predictions that capture the menu of anomalies better than market efficiency? For existing behavioral models, my answer to this question (perhaps predictably) is an emphatic no. The main task that remains is to examine the long-term return anomalies one at a time to see if they deliver on their claims. We set the stage with a discussion of some of the general problems that arise in tests on long-term returns. 4. Drawing inferences from long-term returns Fama (1970) emphasizes that market efficiency must be tested jointly with a model for expected (normal) returns. The problem is that all models for expected returns are incomplete descriptions of the systematic patterns in average returns during any sample period. As a result, tests of efficiency are always contaminated by a bad-model problem. The bad-model problem is less serious in event studies that focus on short return windows (a few days) since daily expected returns are close to zero and so have little effect on estimates of unexpected (abnormal) returns. But the problem grows with the return horizon. A bad-model problem that produces a spurious abnormal average return of x% per month eventually becomes statistically reliable in cumulative monthly abnormal returns (CARs). The reason is that the mean of the CAR increases like N, the number of months summed, but the standard error of the CAR increases like N1@2. In AARs (averages of monthly abnormal returns), the pricing error is constant at x%, but the standard error of the AAR decreases like N~1@2. Bad-model problems are most acute with long￾term buy-and-hold abnormal returns (BHARs), which compound (multiply) an expected-return model’s problems in explaining short-term returns. E.F. Fama/Journal of Financial Economics 49 (1998) 283—306 291

292 E.F.FamafJournal of Financial Economics 49 (1998)283-306 This section discusses various approaches that attempt to limit bad-model problems.It also discusses a related issue,the relevant return metric in tests on long-term returns.I argue that theoretical and statistical considerations alike suggest that CARs(or AARs)should be used,rather than BHARs. 4.1.Bad-model problems Bad-model problems are of two types.First,any asset pricing model is just a model and so does not completely describe expected returns.For example,the CAPM of Sharpe(1964)and Lintner(1965)does not seem to describe expected returns on small stocks (Banz,1981).If an event sample is tilted toward small stocks,risk adjustment with the CAPM can produce spurious abnormal returns. Second,even if there were a true model,any sample period produces systematic deviations from the model's predictions,that is,sample-specific patterns in average returns that are due to chance.If an event sample is tilted toward sample-specific patterns in average returns,a spurious anomaly can arise even with risk adjustment using the true asset pricing model. One approach to limiting bad-model problems bypasses formal asset pricing models by using firm-specific models for expected returns.For example,the stock split study of Fama et al.(1969)uses the market model to measure abnormal returns.The intercept and slope from the regression of a stock's return on the market return,estimated outside the event period,are used to estimate the stock's expected returns conditional on market returns during the event period.Masulis's (1980)comparison period approach uses a stock's average return outside the event period as the estimate of its expected return during the event period. Unlike formal asset pricing models,the market model and the comparison period approach produce firm-specific expected return estimates;that is, a stock's expected return is estimated without constraining the cross-section of expected returns.Thus,these approaches can be used to study the reaction of stock prices to firm-specific events (splits,earnings,etc.).But they cannot identify anomalies in the cross-section of average returns,like the size effect of Banz (1981),since such anomalies must be measured relative to predictions about the cross-section of average returns. The hypothesis in studies that focus on long-term returns is that the adjust- ment of stock prices to an event may be spread over a long post-event period. For many events,long periods of unusual pre-event returns are common. Thus,the choice of a normal period to estimate a stock's expected return or its market model parameters is problematic.Perhaps because of this problem,event studies often control for expected returns with approaches that constrain the cross-section of expected returns.An advantage of these approaches is that they do not require out-of-sample parameter estimates. A disadvantage is that constraints on the cross-section of expected returns

This section discusses various approaches that attempt to limit bad-model problems. It also discusses a related issue, the relevant return metric in tests on long-term returns. I argue that theoretical and statistical considerations alike suggest that CARs (or AARs) should be used, rather than BHARs. 4.1. Bad-model problems Bad-model problems are of two types. First, any asset pricing model is just a model and so does not completely describe expected returns. For example, the CAPM of Sharpe (1964) and Lintner (1965) does not seem to describe expected returns on small stocks (Banz, 1981). If an event sample is tilted toward small stocks, risk adjustment with the CAPM can produce spurious abnormal returns. Second, even if there were a true model, any sample period produces systematic deviations from the model’s predictions, that is, sample-specific patterns in average returns that are due to chance. If an event sample is tilted toward sample-specific patterns in average returns, a spurious anomaly can arise even with risk adjustment using the true asset pricing model. One approach to limiting bad-model problems bypasses formal asset pricing models by using firm-specific models for expected returns. For example, the stock split study of Fama et al. (1969) uses the market model to measure abnormal returns. The intercept and slope from the regression of a stock’s return on the market return, estimated outside the event period, are used to estimate the stock’s expected returns conditional on market returns during the event period. Masulis’s (1980) comparison period approach uses a stock’s average return outside the event period as the estimate of its expected return during the event period. Unlike formal asset pricing models, the market model and the comparison period approach produce firm-specific expected return estimates; that is, a stock’s expected return is estimated without constraining the cross-section of expected returns. Thus, these approaches can be used to study the reaction of stock prices to firm-specific events (splits, earnings, etc.). But they cannot identify anomalies in the cross-section of average returns, like the size effect of Banz (1981), since such anomalies must be measured relative to predictions about the cross-section of average returns. The hypothesis in studies that focus on long-term returns is that the adjust￾ment of stock prices to an event may be spread over a long post-event period. For many events, long periods of unusual pre-event returns are common. Thus, the choice of a normal period to estimate a stock’s expected return or its market model parameters is problematic. Perhaps because of this problem, event studies often control for expected returns with approaches that constrain the cross-section of expected returns. An advantage of these approaches is that they do not require out-of-sample parameter estimates. A disadvantage is that constraints on the cross-section of expected returns 292 E.F. Fama/Journal of Financial Economics 49 (1998) 283—306