The optimal hedge ratio depends on the particular objective function to be optimized. In this article, we apply four approaches—minimum-variance, maximum-sharp ratio, HKL meanvariance utility function and minimum-VaR—as objective function for hedgers to derive optimal hedge ratio. The bivariate constant correlation GARCH model is applied to estimate the withinsample optimal hedge ratios. The hedging performance of these four hedge ratios is evaluated by portfolio coefficient of variation. The empirical results indicates that the martingale process do not hold for china' copper futures and the variances of hedge ratio display a tendency to increase as the risk-averse level decrease. As for hedging performance, the MV hedge ratio performs worst and the HKL mean-variances utility objective function provides better hedging performance than minimum-VaR strategy.