320 N.Barberis et al./Journal of Financial Economics 49 (1998)307-343 data,he does not change his model to something more like a random walk,the true earnings process.His only task is to figure out which of the two regimes of his model is currently generating earnings.This is the only sense in which he is learning from the data. We now provide some preliminary intuition for how investor behavior of the kind described above,coupled with the true random walk process for earnings, can generate the empirical phenomena discussed in Section 2.In particular,we show how our framework can lead to both underreaction to earnings announce- ments and long-run overreaction. In our model,a natural way of capturing overreaction is to say that the average realized return following a string of positive shocks to earnings is lower than the average realized return following a string of negative shocks to earnings.Indeed,after our investor sees a series of positive earnings shocks,he puts a high probability on the event that Model 2 is generating current earnings. Since he believes regime switches to be rare,this means that Model 2 is also likely to generate earnings in the next period.The investor therefore expects the shock to earnings next period to be positive again.Earnings,however,follow a random walk:next period's earnings are equally likely to go up or down.If they go up,the return will not be large,as the investor is expecting exactly that, namely a rise in earnings.If they fall,however,the return is large and negative as the investor is taken by surprise by the negative announcement.10 The average realized return after a string of positive shocks is therefore negative;symmetric- ally,the average return after a string of negative earnings shocks is positive.The difference between the average returns in the two cases is negative,consistent with the empirically observed overreaction. Now we turn to underreaction.Following our discussion in Section 2,we can think of underreaction as the fact that the average realized return following a positive shock to earnings is greater than the average realized return following a negative shock to earnings.Underreaction obtains in our model as long as the investor places more weight on Model 1 than on Model 2,on average.Consider the realized return following a positive earnings shock.Since,by assumption,the investor on average believes Model 1,he on average believes that this positive earnings shock will be partly reversed in the next period.In reality,however, a positive shock is as likely to be followed by a positive as by a negative shock.If the shock is negative,the realized return is not large,since this is the earnings From a mathematical perspective,the investor would eventually learn the true random walk model for earnings if it were included in the support of his prior,from the viewpoint of psychology, though,there is much evidence that people learn slowly and find it difficult to shake off pervasive biases such as conservatism and representativeness. 10A referee has pointed out to us that this is exactly the empirical finding of Dreman and Berry (1995).They find that glamour stocks earn small positive event returns on positive earnings surprises and large negative event returns on negative earnings surprises.The converse holds for value stocks.9From a mathematical perspective, the investor would eventually learn the true random walk model for earnings if it were included in the support of his prior; from the viewpoint of psychology, though, there is much evidence that people learn slowly and find it difficult to shake off pervasive biases such as conservatism and representativeness. 10 A referee has pointed out to us that this is exactly the empirical finding of Dreman and Berry (1995). They find that glamour stocks earn small positive event returns on positive earnings surprises and large negative event returns on negative earnings surprises. The converse holds for value stocks. data, he does not change his model to something more like a random walk, the true earnings process. His only task is to figure out which of the two regimes of his model is currently generating earnings. This is the only sense in which he is learning from the data.9 We now provide some preliminary intuition for how investor behavior of the kind described above, coupled with the true random walk process for earnings, can generate the empirical phenomena discussed in Section 2. In particular, we show how our framework can lead to both underreaction to earnings announce￾ments and long-run overreaction. In our model, a natural way of capturing overreaction is to say that the average realized return following a string of positive shocks to earnings is lower than the average realized return following a string of negative shocks to earnings. Indeed, after our investor sees a series of positive earnings shocks, he puts a high probability on the event that Model 2 is generating current earnings. Since he believes regime switches to be rare, this means that Model 2 is also likely to generate earnings in the next period. The investor therefore expects the shock to earnings next period to be positive again. Earnings, however, follow a random walk: next period’s earnings are equally likely to go up or down. If they go up, the return will not be large, as the investor is expecting exactly that, namely a rise in earnings. If they fall, however, the return is large and negative as the investor is taken by surprise by the negative announcement.10 The average realized return after a string of positive shocks is therefore negative; symmetric￾ally, the average return after a string of negative earnings shocks is positive. The difference between the average returns in the two cases is negative, consistent with the empirically observed overreaction. Now we turn to underreaction. Following our discussion in Section 2, we can think of underreaction as the fact that the average realized return following a positive shock to earnings is greater than the average realized return following a negative shock to earnings. Underreaction obtains in our model as long as the investor places more weight on Model 1 than on Model 2, on average. Consider the realized return following a positive earnings shock. Since, by assumption, the investor on average believes Model 1, he on average believes that this positive earnings shock will be partly reversed in the next period. In reality, however, a positive shock is as likely to be followed by a positive as by a negative shock. If the shock is negative, the realized return is not large, since this is the earnings 320 N. Barberis et al./Journal of Financial Economics 49 (1998) 307—343