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 subsequentlyprices 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 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 N. Barberis et al./Journal of Financial Economics 49 (1998) 307—343 313