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6.6. NOISE-TRADERS 197The relevant uncertainty in the model shows up in the forward premiumwhich in turn inherits its uncertainty from the interest rates R t andR ∗ t , through the covered interest parity condition. The randomness ofone of the interest rates is redundant. Therefore, the algebra can besimpliÞed without loss of generality by letting the uncertainty be drivenby R t alone and Þx R ∗ =1.A Fundamentals (µ =1)EconomySuppose everyone is rational (µ = 1) so that E t (·) = E t (·) andV t (·) = V t (·). Second period wealth of the fundamentalist domesticagent is the portfolio payoff plus c dollars of exogenous ‘labor’ incomewhichispaidinthesecondperiod.14 The forward premium,(F t /S t )=(R t /R ∗ )=R t ' 1+x t inherits its stochastic properties fromR t , which evolves according to the AR(1) processx t = ρx t−1 + v t , (6.52)iidwith 0 < ρ < 1, and v t ∼ (0, σv). 2 Second period wealth can now bewritten asW ft+1 =[∆s t+1 − x t ]λ f t + c. (6.53)People evaluate the conditional mean and variance of next periodwealth asE t (Wt+1) f =[E t (∆s t+1 ) − x t ]λ f t + c, (6.54)V t (Wt+1) f =σs 2 (λf t ) 2 , (6.55)where σs 2 = V t (∆s t+1 ). The domestic fundamental trader’s problem isto choose λ f t to maximizewhich is attained by setting[E t (∆s t+1 ) − x t ]λ f t + c − γ 2 (λf t ) 2 σ 2 s , (6.56)λ f t = [E t(∆s t+1 ) − x t ]. (6.57)γσs214 The exogenous income is introduced to lessen the likelihood of negative secondperiod wealth realizations, but as in De Long et. al., we cannot rule out such apossibility.