A new mean‐risk hedge ratio based on the concept of generalized semivariance (GSV) is proposed. The proposed mean‐GSV (M‐GSV) hedge ratio is consistent with the GSV‐based risk–return model developed by Fishburn (1977), Bawa (1975, 1978), and Harlow and Rao (1989). The M‐GSV hedge ratio can also be considered an extension of the GSV‐minimizing hedge ratio considered by De Jong, De Roon, and Veld (1997) and Lien and Tse (1998, 2000). The M‐GSV hedge ratio is estimated for Standard & Poor's (S&P) 500 futures and compared to six other widely used hedge ratios. Because all the hedge ratios considered are known to converge to the minimum‐variance (Johnson) hedge ratio under joint normality and martingale conditions, tests for normality and martingale conditions are carried out. The empirical results indicate that the joint normality and martingale hypotheses do not hold for the S&P 500 futures. The M‐GSV hedge ratio varies less than the GSV hedge ratio for low and relevant levels of risk aversion. Furthermore, the M‐GSV hedge ratio converges to a value different from the values of the other hedge ratios for higher values of risk aversion.
Journal of Futures Markets, Vol.21, No.6, pp.581-598