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