Robust estimation of the optimal hedge ratio

When using derivative instruments such as futures to hedge a portfolio of risky assets, the primary objectiveis to estimate the optimal hedge ratio (OHR). When agents have mean‐variance utility and thefutures price follows a martingale, the OHR is equivalent to the minimum variance hedge ratio,which can beestimated by regressing the spot market return on the futures market return using ordinary least squares. Toaccommodate time‐varying volatility in asset returns, estimators based on rolling windows, GARCH, or EWMAmodels are commonly employed. However, all of these approaches are based on the sample variance and covarianceestimators of returns, which, while consistent irrespective of the underlying distribution of the data, are notin general efficient. In particular, when the distribution of the data is leptokurtic, as is commonly found forshort horizon asset returns, these estimators will attach too much weight to extreme observations. This articleproposes an alternative to the standard approach to the estimation of the OHR that is robust to theleptokurtosis of returns. We use the robust OHR to construct a dynamic hedging strategy for daily returns on theFTSE100 index using index futures. We estimate the robust OHR using both the rolling window approach and theEWMA approach, and compare our results to those based on the standard rolling window and EWMA estimators. It isshown that the robust OHR yields a hedged portfolio variance that is marginally lower than that based on thestandard estimator. Moreover, the variance of the robust OHR is as much as 70% lower than the variance ofthe standard OHR, substantially reducing the transaction costs that are associated with dynamic hedgingstrategies. © 2003 Wiley Periodicals, Inc. Jrl Fut Mark 23:799–816, 2003