An Empirical Investigation of Variance Reduction Through Non-Delta Neutral Hedging

The option delta plays a key role in eliminating the risk in continuously rebalanced hedges. This need not be the case in discretely rebalanced hedges. Robins and Schachter (Management Science, June 1994) show how the minimum variance discretely rebalanced (European call) option hedge ratio deviates from the option delta. In this paper, we use the binomial option pricing framework to calculate an analytical approximation to the return variance of a discretely rebalanced (American call) option hedge. We then conduct an empirical examination of the differences between delta-neutral and non-delta neutral (i.e., minimum variance) hedges. We use OEX option quotes for the first 42 trading days of 1986. We construct hedges (buying options at the ask and selling at the bid) with rebalancing intervals of from 1 to 10 days. We categorize realized hedge returns according to rebalancing interval, option time to expiration and degree to which the option is in- or out-of- the-money. Using the heteroskedasticity and autocorrelation consistent test statistic developed by Mizrach (1992) we document statistically significantly smaller hedge variances for the non-delta-based hedges across most categories