Abstract: The lower partial moment (LPM) is a more reasonable criteria to measure hedge effectiveness than the variance method,because of its better features to estimate the risk exposure of hedging portfolio.However,there are many limitations in their parametric and non-parametric methods,which are used to estimate the optimal hedging ratio in the framework of LPM.This paper uses time-varying Copula function to introduce the joint density function of return ratios between spot and futures,and then estimates the minimum lower partial moment of the hedge ratios by using the numerical method Empirical comparing the method of copula and the non-parametric methods by using the data of copper futures contract price traded in Shanghai Futures Exchange and copper spot price in the Net of Shanghai Metal,we find that the time-varying correlation coefficient Copula function can get much smaller hedging ratio than the non-para metric method.

Key words: hedging, measurement of risk, LPM, time-varying copula