Comparison, Based On The Variance And The Lpm Method Of Hedging

Hedging is defined as that in order to reduce market risks the market entities have to trade co responsively in another markets. Hedging is designed to realize the main functions of risk reductions and risk transfer in futures markets. The key of hedging is the calculation of the hedging optimal ratios, which is connected with the selection of the risk measures.The paper start with the discussion of the risks in financial markets. Firstly, it discuss the risk theory and methods from the initial risk measures to risk premium models of Neumann & Morgenstern utility functions, to first order stochastic dominance and second order stochastic dominance. And the emphasis is focused to the two quantitive risk measures: variance and lower partial moments, and the latter is divided into two sub-class. in 1952, the Markowitz "Portfolio Selection" theory had firstly introduced variance as one of risk measures. However, variance by the definition is based on the difference between each sample value and the mean. The downside and upside risks are implicitly regarded as the same according to the definition, which is not accord with the usual investment psychologies. Later, Markowitz (1959) had modified his risk measure and introduce the concept of "semi variance". Since Roy(1952) had consider that only the probabilities below a target return are treated as risks on the basis of "Safety First Criterion", there are many studies discussed the measures of "down-side risk", till Bawa & Fishburn had proposed the lower partial moments models theory frame, and finally, formed the family of "lower partial moments"(LPM).After the definition of risk measures , the paper insight into the determination of the optimal hedging ratios on the basis of different risk measures and different hedging strategies, which is followed by a detailed empirical analysis. we choose S&P 500 indices and S&P 500 futures as our analysis sample, and our data method is historical simulation. Through the empirical analysis we can find that: (1)the optimal hedging ratios mostly lie in the 0.99～1.10 though on the basis of different risk measures and different hedge strategies; (2)as a whole, the minimum variance hedge ratios is less than the optimal return-variance hedge ratios ,and the minimum LPM hedge ratios is bigger than the optimal return-LPM hedge ratios; (3)in some futures contracts, the hedge ratios has much discrepancy, which mean different hedging behaviors.In the end, the paper has briefly introduce some measures of hedging performance, and propose some expansions that should be discussed in the future hedging studies.