Underreaction,Momentum Trading,and Overreaction 2145 prices.Momentum traders,in contrast,do condition on past price changes. However,their limitation is that their forecasts must be "simple"(i.e.,uni- variate)functions of the history of past prices.4 In addition to imposing these two constraints on the information process- ing abilities of our traders,we make one further assumption,which is more orthodox in nature:Private information diffuses gradually across the news- watcher population.All our conclusions then flow from these three key as- sumptions.We begin by showing that when only newswatchers are active, prices adjust slowly to new information-there is underreaction but never overreaction.As is made clear later,this result follows naturally from com- bining gradual information diffusion with the assumption that newswatch- ers do not extract information from prices. Next,we add the momentum traders.It is tempting to conjecture that because the momentum traders can condition on past prices,they arbitrage away any underreaction left behind by the newswatchers;with sufficient risk tolerance,one might expect that they would force the market to become approximately efficient.However,it turns out that this intuition is incom- plete if momentum traders are limited to simple strategies.For example, suppose that a momentum trader at time t must base his trade only on the price change over some prior interval,say from t-2 to t-1.We show that in this case,momentum traders'attempts to profit from the underreaction caused by newswatchers lead to a perverse outcome:The initial reaction of prices in the direction of fundamentals is indeed accelerated,but this comes at the expense of creating an eventual overreaction to any news.This is true even when momentum traders are risk neutral. Again,the key to this result is the assumption that momentum traders use simple strategies-that is,they do not condition on all public informa- tion.Continuing with the example,if a momentum trader's order at time t is restricted to being a function of just the price change from t-2 to t-1,it is clear that it must be an increasing function.On average,this simple trend- chasing strategy makes money.But if one could condition on more informa- tion,it would become apparent that the strategy does better in some circumstances than in others.In particular,the strategy earns the bulk of its profits early in the "momentum cycle"-by which we mean shortly after substantial news has arrived to the newswatchers-and loses money late in the cycle,by which time prices have already overshot long-run equilibrium values. To see this point,suppose that there is a single dose of good news at time t and no change in fundamentals after that.The newswatchers cause prices to jump at time t,but not far enough,so that they are still below their 4 The constraints that we put on traders'information-processing abilities are arguably not as well-motivated by the experimental psychology literature as the biases in Barberis et al.(1998) or Daniel et al.(1998),and so may appear to be more ad hoc.However,they generate new and clear-cut asset-pricing predictions,some of which have already been supported in recent tests. See Section IV below.prices. Momentum traders, in contrast, do condition on past price changes. However, their limitation is that their forecasts must be “simple” ~i.e., uni￾variate! functions of the history of past prices.4 In addition to imposing these two constraints on the information process￾ing abilities of our traders, we make one further assumption, which is more orthodox in nature: Private information diffuses gradually across the news￾watcher population. All our conclusions then flow from these three key as￾sumptions. We begin by showing that when only newswatchers are active, prices adjust slowly to new information—there is underreaction but never overreaction. As is made clear later, this result follows naturally from com￾bining gradual information diffusion with the assumption that newswatch￾ers do not extract information from prices. Next, we add the momentum traders. It is tempting to conjecture that because the momentum traders can condition on past prices, they arbitrage away any underreaction left behind by the newswatchers; with sufficient risk tolerance, one might expect that they would force the market to become approximately efficient. However, it turns out that this intuition is incom￾plete if momentum traders are limited to simple strategies. For example, suppose that a momentum trader at time t must base his trade only on the price change over some prior interval, say from t 2 2 to t 2 1. We show that in this case, momentum traders’ attempts to profit from the underreaction caused by newswatchers lead to a perverse outcome: The initial reaction of prices in the direction of fundamentals is indeed accelerated, but this comes at the expense of creating an eventual overreaction to any news. This is true even when momentum traders are risk neutral. Again, the key to this result is the assumption that momentum traders use simple strategies—that is, they do not condition on all public informa￾tion. Continuing with the example, if a momentum trader’s order at time t is restricted to being a function of just the price change from t 2 2 to t 2 1, it is clear that it must be an increasing function. On average, this simple trend￾chasing strategy makes money. But if one could condition on more informa￾tion, it would become apparent that the strategy does better in some circumstances than in others. In particular, the strategy earns the bulk of its profits early in the “momentum cycle”—by which we mean shortly after substantial news has arrived to the newswatchers—and loses money late in the cycle, by which time prices have already overshot long-run equilibrium values. To see this point, suppose that there is a single dose of good news at time t and no change in fundamentals after that. The newswatchers cause prices to jump at time t, but not far enough, so that they are still below their 4 The constraints that we put on traders’ information-processing abilities are arguably not as well-motivated by the experimental psychology literature as the biases in Barberis et al. ~1998! or Daniel et al. ~1998!, and so may appear to be more ad hoc. However, they generate new and clear-cut asset-pricing predictions, some of which have already been supported in recent tests. See Section IV below. Underreaction, Momentum Trading, and Overreaction 2145