Cross-Hedging Foreign Exchange Risk with Currency Futures: A New Model for Estimating Hedge Ratios in the Presence of Autocorrelation and Heteroscedasticity

An examination of the hedging literature reveals widespread employment of the Ordinary Least Squares (OLS) regression technique to estimate optimal hedge ratios between cash and futures positions. However, this technique will only provide optimal estimates if the assumptions underlying OLS are satisfied. The objective of this study is to investigate whether simple OLS estimates of hedge ratios are appropriate in crosshedging strategies involving foreign currency markets, where it is unlikely that the restrictive assumptions of OLS will be met. Several II sophisticated II models for hedge ratio estimation are proposed which explicitly model the time-series characteristics inherent in currency markets, and the hedging effectiveness of both simple and sophisticated models is compared to evaluate their relative merits. The results support the contention that simple estimates of hedge ratios are adversely affected by the violation of OLS assumptions in practice. This fact leads to inferior hedging performance by simple estimates relative to more sophisticated hedge ratios. Hedging strategies employing time-varying GARCH hedge ratios were found to consistently provide the lowest risk hedges for a variety of European and Asian currencies. In many cases, the risk reduction achieved by the GARCH model over simple models was economically significant, justifying the use of the more complex technique. These results were robust across different currencies and various parameter estimation periods. The empirical findings also support the viability of cross-hedging foreign currency risk using currency futures, and provide some preliminary indication of which hedging vehicles are most suitable for an exposure in a given currency