Analysis Of Portfolio CVaR Based On Pair-Copula Scenario Generation

In order to describe the risk of portfolio,Markowitz put forward the model of M-V,which used the variance of return on assets to describe the risk.The variance of return on assets is a statistic to measure the discrete degree of random variables.It includes the upward and downward fluctuations around the average of random variables.Later,researchers have proposed the Value at Risk as a statistic to describe the risk.The Value at Risk means the possible maximum loss of the portfolio in a certain period of time at a given confidence level.So,to compared with the variance of return,the Value at Risk pay close attention to the risk when the return on assets goes down.But in the calculation of the Value at Risk,Usually,the distribution of the return on assets are assumed to be normal distribution.It has a big difference with the actual situation.Therefore,we need to use copula link function to describe the dependency relationship between return on assets and find the joint distribution of the return on assets.In the study of financial asset allocation and portfolio we would use the stochastic programming model as the analysis tool.The main idea of the Stochastic programming model is to need to generate future yields of tectonic scene tree as input variables of the model,and use it to optimize the results.K-means Clustering analysis is a mature method to generate scenario of the rate of return.It needs to decide the number of categories based on experience.It is subjectivity and uncertainty.So we use copula link function to describe the dependency relationship between return on assets and find the joint distribution of the return on assets and use Monte Carlo simulation technique to generate scenario of the rate of return based on copula link function.The scenario of the rate of return is used as input variables of the Portfolio model and we get the optimal portfolio.Based on the above ideas,this paper introduces copula link function and the related Marginal distribution modeling method.Then this paper introduces the Value at Risk model and the Conditional Value at Risk model.Next this paper presents a method to find the optimal portfolio weights,which uses GARCH model and copula method to construct the marginal distribution and joint distribution of the rate of return.Then Monte Carlo simulation technique is used to generate scenario of the rate of return,which is regarded as the input variable in the model of the Conditional Value at Risk with constraint of generalized entropy.In the empirical analysis,we randomly selected four stocks from China's stock market to construct a portfolio.The empirical result indicates that the optimal portfolio weights we get perform better than the M-V model in diversification and profitability in consideration of dependency structure between the assets in the portfolio.