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196CHAPTER 6. FOREIGN EXCHANGE MARKET EFFICIENCY1+x t − ∆s t+1 , the net euro payoff is 13[∆s t+1 − x t ]R ∗ λ ∗tt . (6.48)S tThe foreign exchange market clears when net dollar sales of thecurrent young equals net dollar purchases of the current oldλ t + λ ∗t =Fundamental and Noise TradersS tS t−1R ∗ t−1λ t−1 + R t−1 λ ∗t−1 . (6.49)Afractionµ of domestic and foreign traders are fundamentalists whohave rational expectations. The remaining fraction 1 − µ are noisetraders whose beliefs concerning future returns from their portfolio investmentsare distorted. Let the speculative positions of home fundamentalistand home noise traders be given by λ f t and λ n t respectively.Similarly, let foreign fundamentalist and foreign noise trader positionsbe λ f ∗t and λ n ∗t. The total portfolio position of domestic residents isλ t = µλ f t +(1− µ)λ n t and of foreign residents is λ ∗t = µλ f ∗t +(1− µ)λ n ∗t.We denote subjective date—t conditional expectations genericallyas E t (·). When it is necessary to make a distinction we will denotethe expectations of fundamentalists denoted by E t (·). Similarly, theconditional variance is generically denoted by V t (·) with the conditionalvariance of fundamentalists denoted by V t (·).Utility displays constant absolute risk aversion with coefficient γ.The young construct a portfolio to maximize the expected utility ofnext period wealth³E t −e−γW t+1´. (6.50)Both fundamental and noise traders believe that conditional on time-tinformation, W t+1 is normally distributed. As shown in chapter 1.1.1,maximizing (6.50) with (perceived) normally distributed W t+1 is equivalentto maximizingE t (W t+1 ) − γ 2 V t(W t+1 ). (6.51)13 To get (6.48), −(R t /S t+1 − R ∗ t /S t)λ ∗t = −λ ∗t [(R ∗ t F t)/(S t S t+1 ) − (R ∗ t /S t)]= −λ ∗t (R ∗ t /S t)[(S t F t )/(S t S t+1 ) − 1] =−λ ∗t R ∗ t /S t[1 + x t − ∆s t+1 ]