In this paper we derive a new mean-risk hedge ratio based on the concept of Value at Risk (VaR). The proposed zero-VaR hedge ratio has an analytical solution and it converges to the MV hedge ratio under a pure martingale process or normality. A bivariate constant correlation GARCH(1,1) model with an error correction term is employed to estimate expected returns and time-varying volatilities of the spot and futures in S&P 500 index. The empirical results indicates that the joint normality and martingale process do not hold for S&P 500 futures and the conventional minimum variance hedge is inappropriate for a hedger who only cares about downside risk. Eventually, this article provides an alternative hedging method for a practitioner to use the concept of Value-at-Risk to reflect the risk-averse level.
