The Research Of Hedging Efficiency Of Commodity Futures Based Lower Partial Moment

Hedging is an important means of risk management to the enterprise. The first problem of risk management is how to measure risk, and the second is how to minimize the risk under the established framework of measuring risk. Because the purpose of hedging is to reduce the exposure risk of assets. In theory ,all methods that can be applied to measure the risk are suit to measure the hedge effectiveness. But it is not precision in the practice because the focus on the various aspects of risk measurement methods are not the same and the hedging issue has its own character. In fact , not all methods applied to measure the risk are suit to measure the hedging effectiveness. Even if we have established measurement criteria for hedging effectiveness, the models of hedging ratio that worked out according to this criteria of measurement to minize risks are various.This article reviewed those properties and assumptions of some methods about risk measurement such as Variance, VaR(Value at Risk), ES (Expected shortfall) and LPM(lower partial moment) and found, during these, lower partial moment is a more reasonable measure of hedging effectiveness relatively. However, there are many limitations in the parametric and non-parametric methods, which used to estimate the optimal hedging ratio in the framework of LPM. In the non-parametric method, the length of the time window that used to estimate joint density function is selected subjectively by researchers and the different select influences the stability of the result. In order to simplify the model, the parameter method assumes two relevant coefficients that the rate of return is changeless in the entire sample period. This assumption is obviously discrepancy with the characteristic of commodity futures markets. Because the prices of commodities are often seasonal and on different seasons the returns of cash and futures may present a different correlation. Therefore, this paper use time-varing Copula function to estimate the joint density function of ratios, which is the return of the spot and futures. And then use this joint density function with the numerical method to estimate the minimum lower partial moment hedge ratios. Do empirical studies through comparing the data of copper futures contract price traded in Shanghai Futures Exchange with the published data of copper spot price in the Net of Shanghai Metal, The method of copula and the traditional non-parametric methods were compared. We find that using a time-varying correlation coefficient Copula function to calculate optimal hedging ratio can get the hedging portfolio with smaller value of LPM than the traditional methods.