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6.6. NOISE-TRADERS 199ANoiseTrader(µ 0 for they believe the dollarwill be weaker in the future than what is justiÞed by the fundamentals.We specify the noise distortion to conform with the evidence fromsurvey expectations in which respondents appear to place excessiveweight on the forward premium when predicting future changes in theexchange raten t = kx t + u t , (6.62)iidwhere k>0,u t ∼ N(0, σu). 2 The domestic noise trader’s problem isto maximize λ n t (E t ∆s t+1 − x t + n t ) − γ(λ n t ) 2 σs/2. 2 The solution is tochooseλ n t = λf t + n t. (6.63)γσs2The noise trader’s position deviates from that of the fundamentalist bya term that depends on the distortion in their beliefs, n t .The foreign noise trader holds similar beliefs, solves an analogousproblem and choosesλ n ∗t = S tλ n t . (6.64)Substituting these optimal portfolio positions into the market clearingcondition (6.49) yields the stochastic difference equation[E t ∆s t+1 − x t ]+(1− µ)n t = Γ t ([E t−1 ∆s t − x t−1 ]+(1− µ)n t−1 ). (6.65)