Hedging downside risk with futures contracts

This paper considers a futures hedge strategy that minimizes the lower partial moments; such a strategy minimizes the downside risk and is consistent with the expected utility hypothesis. Two statistical methods are adopted to estimate the optimal hedge ratios: the empirical distribution function method and the kernel density estimation method. Both methods are applied to the Nikkei Stock Average (NSA) spot and futures markets. It is found that, for a hedger who is willing to absorb small losses but otherwise extremely cautious about large losses, the optimal hedge strategy that minimizes the lower partial moments may be sharply different from the minimum variance hedge strategy. If a hedger cares for downside-only risk, then the conventional minimum variance hedge strategy is inappropriate. The methods presented in this paper will be useful in these scenarios.