Optimal currency hedge ratios and interest rate risk

Abstract

The objective of this article is to provide a framework for the interpretation of the optimal currency hedge ratios on foreign investments, taking into account interest rate risk. This is made possible by using a continuous-time setting in the spirit of Merton (1969). We focus on the importance of the interest rate differential (forward basis) in setting the optimal currency hedge because of the influence of interest rates on exchange rates. More specifically, we consider two discount bonds, a domestic and a foreign one, which follow stochastic processes possibly correlated with the other state variables of the model. It is shown that the optimal hedge ratio can be split into five components: (a) a ‘macro-economic’ component which is a function of the volatility of the interest rate differential and its covariance with currency movements; this term depends on the currency considered but not on the asset being hedged; (b) an ‘asset-specific’ term which is directly related to the covariance of the foreign currency asset return with exchange and interest rate movements; (c) a ‘speculative’ term function of the investor's risk preference and of the conditional risk premium on the exchange rate, and (d) two stochastic opportunity set hedging terms. The analysis of the optimal hedge ratio is illustrated on the period December 1970–1989 for stock and bond investments in seven countries. (JEL G15, F31)