We have estimated optimal hedge ratio based on HKM [Herbst, Kare and Marshall (1993)] methodology with benchmark model JSE [Johnson (1960), Stein (1961) and Ederington (1979)] methodology for futures. In case of estimating optimal hedge ratio for options, we have used fBM [Fractional Brownian Motion] methodology with benchmark model BSM [Black-Scholes Model (1973)] methodology. For empirical validation of the efficiency of the optimal hedge ratios, we have estimated return on hedged positions using the hedge ratios to present comparative study. A study of hedging of Nifty {National Stock Exchange of India (NSE) - 50 Index) price risk through index futures and options is conducted using high frequency data (from 01.01.2002 to 28.03.2002 for futures and 01.01.2002 to 31.01.2002 for options). We find that estimates of optimal hedge ratio based on competing models (HKM in case of futures, and fBM in case of options) are better than those estimated using benchmark models (JSE for futures and BSM for options respectively). The results are statistically significant at 95% confidence level. However, the returns on hedged positions using the superior optimal hedge ratios are not significantly different. This is quite puzzling, and requires a plausible explanation.