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 returnsThis 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