Optimal Hedging of the Currency Exchange Risk Exposure of Dynamically Balanced Strategic Asset Allocations

Abstract

This paper presents theoretical and empirical results on the magnitude of optimal hedge ratios for a dynamically balanced strategic asset allocation with multiple currencies. Optimality refers to a mean-variance objective function with a time-varying risk-aversion parameter. A data driven choice of this parameter is proposed, which is suggested by a Sharpe ratio maximization criterion and renders the vector of optimal hedge ratios scale invariant. Empirical results are given for an EMU based investor with USD, GBP and JPY assets and an US based investor with assets in EUR, GBP and JPY. Since the vector of optimal hedge ratios depends on the conditional variance-covariance matrix of the involved exchange rate return time series, multivariate GARCH models are estimated. In particular, ML estimation of the DCC-GARCH model is performed, which remains computationally attractive in large dimensional cases. A fixed-mix rebalancing investment rule is applied in order to maintain the strategic asset allocation over time. Finally, hedging strategies for subsidiary companies are investigated, which account for the hedging interests of their mother company. Keywords: Currency overlay management, optimal hedging, DCC-GARCH