Research On Securities Portfolio

The main purpose of portfolio investment is to gain benefit. Actually, the returns are always accompanied by risk, the higher the risk and the greater the benefits.In order to diversify risk, Investors always diversified investment portfolio, which is known as portfolio, this makes the investment portfolio be a major issue in financial sector.In1952, Markowitz founded the mean-variance model and set up making use of quantitative mathematical analysis methodology. Now, VaR method is a new method to measure financial market risk,which is developed to respond the financial disaster in 1990s. However, the traditional research on VaR of portfolio approach is mainly based on the joint normal distribution, while the actual distribution of asset returns is not completely normal, which is peak, thick tail and partial, while the portfolio of the relationship between each asset is not just linear relationship, the traditional matrix can not respond related coefficiency between the various assets. Therefore, we need to research VaR of portfolio based on a biased and fat tail distribution and to consider the non-linear relationship between each securities assets.This article first gives a comprehensive research on VaR, about historical background of VaR models, calculation methods and their strengths and weaknesses.Secondly, this article assumes a single asset return follows the asymmetric Laplace distribution, the distribution is better than the normal distribution to describe financial data which is biased and fat-tail. The article also described in detail the nature of asymmetric Laplace distribution and parameter estimation methods, and fitting with the distribution of several stock portfolios' return data in Chinese stock market.Empirical analysis shows that asymmetric Laplace distribution fits the stock portfolio return data which is biased, peak and fat-tail better than the normal distribution, symmetric Laplace distribution.Finally, based on the Copula theory, we assume return of a single asset rate subject to asymmetric Laplace distribution, with the Archimedean Copula function to reflect the correlation between the portfolio assets, derived the joint distribution of binary and multi-asset, we also gives the prediction of VaR of binary and multi-asset portfolio of Monte Carlo simulation method. In the end, selected a group of Chinese stock portfolio to empirical analysis,the results show that the method to calculate the value of portfolio VaR is more accurate.