Study On The Portfolio Risk Based On GARCH-EVT Method And Copula

In this paper, we consider a new model named as GARCH-EVT approach to get estimators of measuring for portfolio's Value-at-Risk. The risk of the financial portfolio is mainly influenced by two parts. One part is from the risk in a single market in the portfolios, and the other is from the mutual risks in each single market in the portfolio. Therefore, to make reasonable measure of the risk for the portfolio, people have to make good explanations of the return character for each capital asset. Experiences show that the volatility of a single asset return possesses the heteroscedasticity and clustering. Meanwhile, a distribution of the asset does not follow a normal distribution, but to show that the center of the distribution of the asset has a distinguishing feature of normal, and the shape-style of the two extremities has a feature of the thick-tail distribution. It is well known that the GARCH-EVT method could either show the character of the return volatility or depict the feature of the thick-tail distribution. And then, a Copula links various assets through a link-function, and also shows the relations among each asset in the portfolio. A Copula is the related function to link the joint distribution of the high-dimension random variable through its one-dimension marginal distribution. Thus, this transition has realized from the single asset to a combination of assets.This paper would combine parametric, nonparametric GARCH technique and a GPD distribution in the extreme theory to structure the marginal distribution of the single asset in the financial portfolio. Then, we make a link to these marginal distributions through multi-normal Copula and T-Copula functions to get a joint-distribution model of the financial portfolio. In the paper, we first would give a simple introduction of the GARCH-EVT method, build a parametric GARCH-EVT model and a nonparametric GARCH-EVT model. And then, we would structure a joint distribution function of the portfolio been structured by using multi-normal Copula and T-Copula functions, to realize the transition from the single asset to a combination of assets. Finally, the paper has made the empirical analysis on four professional indexes in Shanghai stock market(the combination would include Shang Zheng Commerce; Shang Zheng Public Business; Shang Zheng Industry; Shang Zheng Landed Property) by using MC simulation to obtain VaR and CVaR of the combination. Furthermore, the effectiveness of the method would inspected by using a return-test. The empirical results show that the method we proposed is a suitable one to measure the extreme risks of a portfolio. It can capture the value of risk of the combination under those extreme financial events. The analysis results in the paper have an activity guidance for those investors.