The Research For The Measurement Of Portfolio Risk Based On Copula Functions

According to Modern Portfolio Theory, Constructing different assets Portfolio can disperse the risk of a single idiosyncratic risk to a certain extent, that is to say some non-systematic risk of portfolio is dispersed. The assets in the portfolio may not be negative correlation. The constructed portfolio can not completely eliminate the non-systematic risk, and portfolio systems also bear the risk. Modern Portfolio Theory and models of measurement tool for portfolio risk is theβcoefficient and the VaR as the representative, which is inadequate measure for leptokurtosis and fat-tail of Portfolio risk distribution. And they are built on the assumption of portfolio income under the normal distribution. Therefore, it has become a trend to study measurement method of leptokurtosis and fat-tail of portfolio risk in the field. Copula function makes the joint distribution of multivariate random variables connect with a one-dimensional marginal distribution, whose advantages are that can use the joint distribution function of portfolio to analysis portfolio rate of return dependent structure and make marginal distribution and their related structures studied separately. Based on its analysis for leptokurtosis and fat-tail risk characteristics, nonlinear correlation coefficient of the tail of Clayton Copula and Gumbel Copula functions from the Archimedean-Copula Functions is selected, because it can better describe the tail characteristics of portfolio instead of the linear correlation coefficient in the traditional portfolio VaR measure. The aim is to characterize the status of loss in the joint distribution of the different asset risk, and to provide theoretical guidance for investment decisions.Based on defining the application conditions of the mean - variance portfolio model of modern portfolio theory and capital asset pricing model,βcoefficient of portfolio risk metrics and the applicability of VaR are analyzed. The feasibility and the described conditions which have leptokurtosis and fat-tail and the risk of financial assets are analyzed by Copula function measure. In order to verify the validity of portfolio risk measured by Copula function, the stock market is measured by the tail correlation coefficient of Copula function instead of the linear correlation coefficient of VaR. The panel data of daily logarithmic return rate of Shanghai Composite Index and Shenzhen Component Index are empirically tested in the period from January 4, 2005 to 2010 on January 4. The empirical results show that using the tail correlation coefficient to measure portfolio risk is closer than linear correlation coefficient to the real distribution of the portfolio risk.