Robust estimation of the optimal hedge ratio

✍ Scribed by Richard D. F. Harris; Jian Shen

• Publisher: John Wiley and Sons
• Year: 2003
• Tongue: English
• Weight: 122 KB
• Volume: 23
• Category: Article
• ISSN: 0270-7314
• DOI: 10.1002/fut.10085

✦ Synopsis

Abstract

When using derivative instruments such as futures to hedge a portfolio of risky assets, the primary objective
is to estimate the optimal hedge ratio (OHR). When agents have mean‐variance utility and the
futures price follows a martingale, the OHR is equivalent to the minimum variance hedge ratio,which can be
estimated by regressing the spot market return on the futures market return using ordinary least squares. To
accommodate time‐varying volatility in asset returns, estimators based on rolling windows, GARCH, or EWMA
models are commonly employed. However, all of these approaches are based on the sample variance and covariance
estimators of returns, which, while consistent irrespective of the underlying distribution of the data, are not
in general efficient. In particular, when the distribution of the data is leptokurtic, as is commonly found for
short horizon asset returns, these estimators will attach too much weight to extreme observations. This article
proposes an alternative to the standard approach to the estimation of the OHR that is robust to the
leptokurtosis of returns. We use the robust OHR to construct a dynamic hedging strategy for daily returns on the
FTSE100 index using index futures. We estimate the robust OHR using both the rolling window approach and the
EWMA approach, and compare our results to those based on the standard rolling window and EWMA estimators. It is
shown that the robust OHR yields a hedged portfolio variance that is marginally lower than that based on the
standard estimator. Moreover, the variance of the robust OHR is as much as 70% lower than the variance of
the standard OHR, substantially reducing the transaction costs that are associated with dynamic hedging
strategies. © 2003 Wiley Periodicals, Inc. Jrl Fut Mark 23:799–816, 2003