Portfolio Optimization Model Based On TheMean-CVaR -Entropy And Empirical Study

In the situation of stock market keep rising in recent years of China equity investment has become the major choice of people.How to select the stock portfolio and to measure the risk in investment process become more and more important. The portfolio investment theory has always been a immortal research subject from ancient times to present. It mainly solves the problem that how to distribute some amount of capital into different kinds of assets, it can maximum returns under the condition of less-than a given level of risk or minimize the returns under the condition of a certain risk. In order to obtain the best stock portfolio, many researchers,on the basis of modern portfolio theory, respectively use Variance、Value at Risk(VaR)、Conditional Value at Risk(CVaR) to measure the risk. In recent years, some researchers put forward a theory that comentropy can be used to measure risk, they put it into practice and obtain a ideal result. The concept of entropy is very simple and it can satisfy the requirement of consistency risk measurement, so that it has become a frontier subject to research the management of finance risk for researchers. In this paper I put forward a new risk measurement model:Mean-CVaR-Entropy Model,which I add a constraint condition of entropy on the base of CVaR risk measurement.In this paper I elaborate the characteristics of coherent risk measurement first, and then I introduce the Markowitz’s investment portfolio theory, and then describe the VaR in theory aspect and compare it with CVaR so that I can put forward the concept of CVaR. analysis the property、advantage and disadvantage of both VaR and CVaR. As a result, entropy can be a method to measure risk and it can satisfy the requirement of coherent risk measurement. It also can remedy disadvantages of other measure methods, so entropy is suitable to be used in risk measuring.After the analysis of theory aspect, the core of this paper is that,in premise of ensuring the rate of return of portfolio, using liner combination of CVaR and entropy function as the minimum function to construct a stock portfolio model based on the Mean-CVaR-Entropy model which is not lowed short selling. After constructing Mean-CVaR-Entropy model,I compare it with Mean-Variance model and Mean-CVaR model and analysis their advantages and disadvantages.The last part of this paper is about analysing the three established models in practical, first I chose thirty stocks in Shanghai A shares in a number different industries as the data selected object, take use of the finincon function in Matlab to calculate the optimal solution and the distributed proportion of corresponding assets of Mean-Variance model、Mean-CVaR model、Mean-CVaR-Entropy model, and then analyse the optimum results and use data out of sample to calculate the Sharp rate of each combination, then test the validity of the result of model. Finally I analyse how parameters influence the Mean-CVaR-Entropy model.