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1.1. INTERNATIONAL FINANCIAL MARKETS 11If people believe that W t+1 is normally distributed conditional oncurrently available information, with conditional mean and conditionalvarianceE t W t+1 =·α(1 + i t )+(1− α)(1 + i ∗ t ) E tS t+1S t¸W t , (1.10)Var t (W t+1 )= (1 − α)2 (1 + i ∗ t )2 Var t (S t+1 )Wt2St2 . (1.11)It follows that maximizing (1.9) is equivalent to maximizing the simplerexpressionE t W t+1 − γ 2 Var(W t+1). (1.12)We say that traders are mean-variance optimizers. These individualslike high mean values of wealth, and dislike variance in wealth.Differentiating (1.12) with respect to α and re-arranging the Þrstorderconditions for optimality yields(1 + i t ) − (1 + i ∗ t ) E t[S t+1 ]= −γW t(1 − α)(1 + i ∗ t ) 2 Var t (S t+1 ), (1.13)S twhich implicitly determines the optimal investment share α. Even ifthere is an expected uncovered proÞt available, risk aversion limits thesize of the position that investors will take. If all market participantsare risk neutral, then γ = 0 and it follows that uncovered interest paritywill hold. If γ > 0, violations of uncovered interest parity can occur andthe forward rate becomes a biased predictor of the future spot rate, thereason being that individuals need to be paid a premium to bear foreigncurrency risk. Uncovered interest parity will hold if α = 1, regardlessof whether γ > 0. However, the determination of α requires us to bespeciÞc aboutthedynamicsthatgovernS t and that is information thatwe have not speciÞedhere. Thepointthatwewanttomakehereisthat the forward foreign exchange market can be in equilibrium andthere are no unexploited risk-adjusted arbitrage proÞts even thoughthe forward exchange rate is a biased predictor of the future spot rate.We will study deviations from uncovered interest parity in more detailin chapter 6.S 2 t