Calculation Of Portfolio's Value-at-Risk (VaR) By Using Copulas

Variance-Covariance Method is generally used to calculate the portfolio's VaR (Value-at-Risk) in traditional Finance Metrology based on multivariate normal distribution. Being easy to operation is the major advantage of the traditional method, because it's formulized. However, since the price of the assets are not distributed exactly normally and have the characteristic of "sharp peak and fat tail"; meanwhile, the classical correlation coefficient matrix can't describe the non-linear correlationship within the different assets in the portfolio. So we need to develop a better method to compute the portfolio's VaR.In morden statistics, copulas approach has been proved that it's facilitated and highly efficient. At the same time, this new method can resolve the problem of non-normal distribution of the return of assets, so it has a great potential. Both the researchers of universities and the practitioners of finance pay more attentions on copulas in recent years. The major characteristic of the new method is that it computes the portfolio's VaR by using the functions of copula and marginal distributions only, and don't need to confirm the expression of the multivariate distribution. As a result, it expands its applicable range, and improves the accuracy and the efficiency of calculation.This paper not only describes different calculations of VaR, but also introduces the principles and application of copulas. In this paper, we compute the futures portfolio' VaR by using copulas, and obtained a lot of valuable results under different distributions of assets return. Especially, we verify that copula method can obtain more practical VaR value than traditional model of multivariate normal distribution.Due to the disadvantage of time lag, so we try to apply time series and copulas jointly to calculate the portfolio's VaR. The results show that time series with the disturbance of Student's distribution is a preferable method when combining copulas.On the other hand, the calculation of tail-dependence coefficient was also discussed in this paper. And it was applied to calculate the portfolio's VaR more accurately when the distribution of assets return is of "sharp peak and fat tail". Meanwhile, it will help to the practical investment analysis.In the last chapter of this paper, we compute and analyze different kinds of portfolio in Chinese "A share" market including low-profit, high-profit, seasonal and nonseasonal. The conclusion obtained in this chapter is good for confirming and taking safer strategies of investment.