Underreaction,Momentum Trading,and Overreaction 2149 each subinnovation of e+1has been seen by a fraction 2/z of the total population.This rotation process continues until time t +z-1,at which point every one of the z groups has directly observed each of the subinno- vations that comprise+1.So+1 has become totally public by time t+z-1.Although this formulation may seem unnecessarily awkward,the rotation feature is useful because it implies that even as information moves slowly across the population,on average everybody is equally well-informed.12 This symmetry makes it transparently simple to solve for prices,as is seen momentarily. In this context,the parameter z can be thought of as a proxy for the (lin- ear)rate of information flow-higher values of z imply slower information diffusion.Of course,the notion that information spreads slowly is more ap- propriate for some purposes than others.In particular,this construct is fine if our goal is to capture the sort of underreaction that shows up empirically as unconditional positive correlation in returns at short horizons.However, if we are also interested in capturing phenomena like post-earnings- announcement drift-where there is apparently underreaction even to data that is made available to everyone simultaneously-we need to embellish the model.We discuss this embellishment later;for now it is easiest to think of the model as only speaking to the unconditional evidence on underreaction. All the newswatchers have constant absolute risk aversion(CARA)utility with the same risk-aversion parameter,and all live until the terminal date T.The riskless interest rate is normalized to zero,and the supply of the asset is fixed at Q.So far,all these assumptions are completely orthodox.We now make two that are less conventional.First,at every time t,newswatch- ers formulate their asset demands based on the static-optimization notion that they buy and hold until the liquidating dividend at time T.13 Second, and more critically,while newswatchers can condition on the information sets described above,they do not condition on current or past prices.In other words,our equilibrium concept is a Walrasian equilibrium with pri- vate valuations,as opposed to a fully revealing rational expectations equilibrium. As suggested in the Introduction,these two unconventional assumptions can be motivated based on a simple form of bounded rationality.One can think of the newswatchers as having their hands full just figuring out the implications of the e's for the terminal dividend D.This leaves them unable to also use current and past market prices to form more sophisticated fore- casts of D(our second assumption);it also leaves them unable to make any forecasts of future price changes,and hence unable to implement dynamic strategies (our first assumption). 12 Contrast this with a simpler setting where group 1 always sees all of+-1first,then group 2 sees it second,etc.In this case,group 1 newswatchers are better-informed than their peers. 1a There is an element of time-inconsistency here,since in fact newswatchers may adjust their positions over time.Ignoring the dynamic nature of newswatcher strategies is more sig- nificant when we add momentum traders to the model,so we discuss this issue further in Section II.B.each subinnovation of et1z21 has been seen by a fraction 20z of the total population. This rotation process continues until time t 1 z 21, at which point every one of the z groups has directly observed each of the subinno￾vations that comprise et1z21. So et1z21 has become totally public by time t 1 z 2 1. Although this formulation may seem unnecessarily awkward, the rotation feature is useful because it implies that even as information moves slowly across the population, on average everybody is equally well-informed.12 This symmetry makes it transparently simple to solve for prices, as is seen momentarily. In this context, the parameter z can be thought of as a proxy for the ~lin￾ear! rate of information flow—higher values of z imply slower information diffusion. Of course, the notion that information spreads slowly is more ap￾propriate for some purposes than others. In particular, this construct is fine if our goal is to capture the sort of underreaction that shows up empirically as unconditional positive correlation in returns at short horizons. However, if we are also interested in capturing phenomena like post-earnings￾announcement drift—where there is apparently underreaction even to data that is made available to everyone simultaneously—we need to embellish the model. We discuss this embellishment later; for now it is easiest to think of the model as only speaking to the unconditional evidence on underreaction. All the newswatchers have constant absolute risk aversion ~CARA! utility with the same risk-aversion parameter, and all live until the terminal date T. The riskless interest rate is normalized to zero, and the supply of the asset is fixed at Q. So far, all these assumptions are completely orthodox. We now make two that are less conventional. First, at every time t, newswatch￾ers formulate their asset demands based on the static-optimization notion that they buy and hold until the liquidating dividend at time T. 13 Second, and more critically, while newswatchers can condition on the information sets described above, they do not condition on current or past prices. In other words, our equilibrium concept is a Walrasian equilibrium with pri￾vate valuations, as opposed to a fully revealing rational expectations equilibrium. As suggested in the Introduction, these two unconventional assumptions can be motivated based on a simple form of bounded rationality. One can think of the newswatchers as having their hands full just figuring out the implications of the e’s for the terminal dividend DT. This leaves them unable to also use current and past market prices to form more sophisticated fore￾casts of DT ~our second assumption!; it also leaves them unable to make any forecasts of future price changes, and hence unable to implement dynamic strategies ~our first assumption!. 12 Contrast this with a simpler setting where group 1 always sees all of et1z21 first, then group 2 sees it second, etc. In this case, group 1 newswatchers are better-informed than their peers. 13 There is an element of time-inconsistency here, since in fact newswatchers may adjust their positions over time. Ignoring the dynamic nature of newswatcher strategies is more sig￾nificant when we add momentum traders to the model, so we discuss this issue further in Section II.B. Underreaction, Momentum Trading, and Overreaction 2149