Underreaction,Momentum Trading,and Overreaction 2151 price changes.We assume that these forecasts take an especially simple form:The only conditioning variable is the cumulative price change over the past k periods;that is,(P-1-P-1). As it turns out,the exact value of k is not that important,so in what follows we simplify things by setting k =1,and using(P-1-P-2)=AP:-1 as the time-t forecasting variable.15 What is more significant is that we restrict the momentum traders to making univariate forecasts based on past price changes.If,in contrast,we allow them to make forecasts using n lags of price changes,giving different weights to each of the n lags,we suspect that for sufficiently large n,many of the results we present below would go away.Again,the motivation is a crude notion of bounded rationality:Mo- mentum traders simply do not have the computational horsepower to run complicated multivariate regressions. With k=1,the order flow from generation-t momentum traders,F,is of the form F=A+中△P-1 (3) where the constant A and the elasticity parameter have to be determined from optimization on the part of the momentum traders.This order flow must be absorbed by the newswatchers.We assume that the newswatchers treat the order flow as an uninformative supply shock.This is consistent with our prior assumption that the newswatchers do not condition on prices. Given that the order flow is a linear function of past price changes,if we allowed the newswatchers to extract information from it,we would be indi- rectly allowing them to learn from prices. To streamline things,the order flow from the newswatchers is the only source of supply variation in the model.Given that there are j generations of momentum traders in the market at any point in time,the aggregate supply S,absorbed by the newswatchers is given by: 8=Q-含+1=Q-A-含1R4 (4) We continue to assume that,at any time t,the newswatchers act as if they buy and hold until the liquidating dividend at time T.This implies that prices are given exactly as in equation(1),except that the fixed supply Q is replaced by the variable St,yielding B二=D,+2-1)e+1+2-2e+2+…++-k-Q+jA+ 中AP-i (5) 15 In the NBER working paper version,we provide a detailed analysis of the comparative statics properties of the model with respect to k.price changes. We assume that these forecasts take an especially simple form: The only conditioning variable is the cumulative price change over the past k periods; that is, ~Pt21 2 Pt2k21!. As it turns out, the exact value of k is not that important, so in what follows we simplify things by setting k 5 1, and using ~Pt21 2 Pt22! [ DPt21 as the time-t forecasting variable.15 What is more significant is that we restrict the momentum traders to making univariate forecasts based on past price changes. If, in contrast, we allow them to make forecasts using n lags of price changes, giving different weights to each of the n lags, we suspect that for sufficiently large n, many of the results we present below would go away. Again, the motivation is a crude notion of bounded rationality: Mo￾mentum traders simply do not have the computational horsepower to run complicated multivariate regressions. With k 5 1, the order flow from generation-t momentum traders, Ft, is of the form Ft 5 A 1 fDPt21, ~3! where the constant A and the elasticity parameter f have to be determined from optimization on the part of the momentum traders. This order flow must be absorbed by the newswatchers. We assume that the newswatchers treat the order flow as an uninformative supply shock. This is consistent with our prior assumption that the newswatchers do not condition on prices. Given that the order flow is a linear function of past price changes, if we allowed the newswatchers to extract information from it, we would be indi￾rectly allowing them to learn from prices. To streamline things, the order flow from the newswatchers is the only source of supply variation in the model. Given that there are j generations of momentum traders in the market at any point in time, the aggregate supply St absorbed by the newswatchers is given by: St 5 Q 2 ( i51 j Ft112i 5 Q 2 jA 2 ( i51 j fDPt2i. ~4! We continue to assume that, at any time t, the newswatchers act as if they buy and hold until the liquidating dividend at time T. This implies that prices are given exactly as in equation ~1!, except that the fixed supply Q is replaced by the variable St, yielding Pt 5 Dt 1 $~z 2 1!et11 1 ~z 2 2!et121{{{1et1z21%0z 2 Q 1 jA 1 ( i51 j fDPt2i. ~5! 15 In the NBER working paper version, we provide a detailed analysis of the comparative statics properties of the model with respect to k. Underreaction, Momentum Trading, and Overreaction 2151