A Primer on Hedging with Stock Index Futures

Abstract

In this article, the authors discuss the various approaches and issues associated with hedging with stock index futures. The most common approach used in practice is based on minimizing the variance of the hedge within the mean-variance framework to obtain the optimal hedge ratio. In determining the optimal hedge ratio, consideration must be given to the basis risk to which a fund is exposed when using stock index futures. An optimal hedge ratio based on variance minimization is the slope coefficient estimated from an ordinary least squares (OLS) regression of the returns of the portfolio to be hedged on the returns of the stock index futures contract. The estimated slope coefficient is referred to as beta. The optimal hedge ratio can be further refined by adjusting for the beta estimated from an OLS regression of the return on the underlying stock index on the return on the stock index futures. A criticism of the OLS model is twofold. The first is that there are statistical issues in estimating beta using the basic OLS regression model. Several models that employ advanced econometric techniques have been proposed for estimating hedge ratios. The second criticism is that the OLS model assumes a constant hedge ratio, despite the theoretical and empirical evidence showing the hedge ratio should be time varying. Evidence suggests that employing advanced econometric models to estimate the slope coefficient offers little improvement in hedging effectiveness—and even if there is some improvement, the modeling cost may not justify the extra effort. As for the second criticism, the well-known autoregressive conditional heteroscedasticity (ARCH) and the generalized ARCH (GARCH) have been used to allow for time-varying hedge ratios. Although some studies have reported that ARCH and GARCH can improve hedge effectiveness, the effort may not be warranted due to the additional modeling as well as the time-varying hedge ratios involving rebalancing the portfolio periodically, which can add significantly to the cost of hedging.