Hedging and Value at Risk: A Semi-Parametric Approach

The non-normality of financial asset returns has important implications for hedging. In particular, in contrast with the unambiguous effect that minimum-variance hedging has on the standard deviation, it can actually increase the negative skewness and kurtosis of hedge portfolio returns. Thus the reduction in Value at Risk (VaR) and Conditional Value at Risk (CVaR) that minimum-variance hedging provides can be significantly lower than the reduction in standard deviation. In this paper, we provide a new, semi-parametric method of estimating minimum-VaR and minimum-CVaR hedge ratios based on the Cornish-Fisher expansion. We apply the method to four equity index positions hedged with equity index futures. We find that the semiparametric approach is superior to the standard minimum-variance approach, and to the non-parametric approach of Harris and Shen (2006). In particular, it provides a greater reduction in both negative skewness and excess kurtosis, and consequently generates hedge portfolios that have lower VaR and CVaR.