A Simple Solution for Optimal Currency Hedging

Abstract

Rather than relying on historical experience to determine the optimal currency hedging strategy for portfolios that include foreign assets, one can use a simple procedure adapted from portfolio management theory. This procedure specifies the utility of a portfolio, given the investor's risk tolerance, asset and currency returns, standard deviations, weights and covariances. The sensitivity of the portfolio's utility can then be measured as a function of currency exposure. The portfolio's exposure to each currency to which utility is related positively is increased, and its exposure to each currency to which utility is related negatively is decreased. The portfolio's exposure to the currency with the largest sensitivity (in absolute terms) is iteratively adjusted until all the portfolio's sensitivities equal zero. This currency exposure represents the optimal portfolio-the one that offers the highest return for the chosen risk level. In some special cases, the optimal hedging strategy can be determined more directly. For example, the minimum-risk strategy for a single foreign asset can be identified by measuring the currency's beta relative to the underlying portfolio. For a portfolio with several foreign assets, the minimum-risk strategy can be defined by regressing the portfolio's returns on the currencies' returns. The basic procedure can also be adjusted to take inflation into account and to incorporate liabilities.