International macroe.. - Free

10 CHAPTER 1. SOME INSTITUTIONAL BACKGROUNDhas a positive payoff in expectation. We use the uncovered interestparity condition as a Þrst-approximation to characterize internationalasset market equilibrium, especially in conjunction with the monetarymodel (chapters 3, 10, and 11). However, as you will see in chapter 6,violations of uncovered interest parity are common and they present animportant empirical puzzle for international economists.(2)⇒Risk Premia. What reason can be given if uncovered interest paritydoes not hold? One possible explanation is that market participantsare risk averse and require compensation to bear the currency risk involvedin an uncovered foreign currency investment. To see the relationbetween risk aversion and uncovered interest parity, consider the followingtwo-period partial equilibrium portfolio problem. Agents takeinterest rate and exchange rate dynamics as given and can invest a fractionα of their current wealth W t in a nominally safe domestic bondwith next period payoff (1+i t )αW t . The remaining 1−α of wealth canbe invested uncovered in the foreign bond with future home-currencypayoff (1 + i ∗ t ) S t+1S t(1 − α)W t . We assume that covered interest parityis holds so that a covered investment in the foreign bond is equivalentto the investment in the domestic bond. Next period nominal wealthis the payoff from the bond portfolioW t+1 =·α(1 + i t )+(1− α)(1 + i ∗ t ) S t+1S t¸W t . (1.8)Domestic market participants have constant absolute risk aversion utilitydeÞned over wealth, U(W )=−e −γW where γ ≥ 0isthecoefficientof absolute risk aversion. The domestic agent’s problem is to choosethe investment share α to maximize expected utilityE t [U(W t+1 )] = −E t³e−γW t+1´. (1.9)Notice that the right side of (1.9) is the moment generating function ofnext period wealth. 33 The moment generating function for the normally distributed random variableX ∼ N(µ, σ 2 )isψ X (z) =E ¡ e zX¢ ¢ ¡µz+= eσ2 z 22. Substituting W for X, −γ for z,E t W t+1 for µ, andVar(W t+1 )forσ 2 and taking logs results in (1.12).