NOISE TRADER RISK 707 mental contexts since Alpert and Raiffa(1982).Noise traders select their portfolios on the basis of such incorrect beliefs.In response to noise traders'actions,it is optimal for sophisticated investors to ex- ploit noise traders'irrational misperceptions.Sophisticated traders buy when noise traders depress prices and sell when noise traders push prices up.Such active contrarian investment strategies push prices toward fundamentals,but not all the way. A.The Model Our basic model is a stripped-down overlapping generations model with two-period-lived agents(Samuelson 1958).For simplicity,there is no first-period consumption,no labor supply decision,and no be- quest.As a result,the resources agents have to invest are exogenous. The only decision agents make is to choose a portfolio when young. The economy contains two assets that pay identical dividends.One of the assets,the safe assets,pays a fixed real dividendr.Asset s is in perfectly elastic supply:a unit of it can be created out of,and a unit of it turned back into,a unit of the consumption good in any period. With consumption each period taken as numeraire,the price of the safe asset is always fixed at one.The dividend r paid on asset s is thus the riskless rate.The other asset,the unsafe asset u,always pays the same fixed real dividend r as asset s.But u is not in elastic supply:it is in fixed and unchangeable quantity,normalized at one unit.The price of u in period t is denoted If the price of each asset were equal to the net present value of its future dividends,then assets u and s would be perfect substitutes and would sell for the same price of one in all periods.But this is not how the price of u is determined in the presence of noise traders. We usually interpret s as a riskless short-term bond and u as aggre- gate equities.It is important for the analysis below that noise trader risk be marketwide rather than idiosyncratic.If noise traders'misper- ceptions of the returns to individual assets are uncorrelated and if each asset is small relative to the market,arbitrageurs would eliminate any possible mispricing for the same reasons that idiosyncratic risk is not priced in the standard capital asset pricing model. There are two types of agents:sophisticated investors(denoted i) who have rational expectations and noise traders (denoted n).We assume that noise traders are present in the model in measure u,that sophisticated investors are present in measure 1 -H,and that all agents of a given type are identical.Both types of agents choose their portfolios when young to maximize perceived expected utility given their own beliefs about the ex ante mean of the distribution of the price of u at t 1.The representative sophisticated investor young in