Portfolio Optimization Model With Transaction Costs Based On CVaR And Empirical Study

Portfolios theory is one of the important research contents in Economics. The main problem which portfolio solves is how to distribute some amount of capital into different kinds of assets to make sure that the return is the maximum under the condition that the risk is below some scalar or the risk is the minimum under the condition that the return is greater than the given constant. On the one hand VaR(Value at Risk) and CVaR(Conditional Value at Risk) which are new risk measurement methods, are put forth recently. Because of its easy definition and eminent properties, CVaR is given attentions by more and more researchers in particular, and becomes a latest research content in financial risk management. On the other hand transaction costs are popular kinds of frictions in the real market. The effect of transaction costs to the portfolio optimization is dominant. It will lead to invalid portfolio if transaction costs are neglected and transaction costs also have a great effect to the portfolio selection. This paper considers transaction costs into portfolio problems based on CVaR(Conditional Value at Risk), and gains results as follows:Firstly, it introduces preliminary knowledge, that is, research the CVaR risk measure method in-depth in theory, there list the definition, the character, the numeration, the application and the merit and demerit of CVaR. It makes a conclusion that CVaR is better than VaR.Secondly, there construct mean-variance/CVaR models with assets without risk and transaction costs, which is the innovation of this paper. The models are onefold aim, which consider the minimum risk under the condition that the return is the given constant.At last, it is the empirical study. Firstly, it is the empirical study on models without transaction costs, it chooses data of ten stocks from Shanghai stock bourse, it uses Matlab7.0 software to obtain the optimum portfolios.Then it is the empirical study on models with transaction costs and it have three contents. Firstly, it uses Matlab7.0 software to solve the models in order to obtain the optimum portfolios. Then it analyses the optimum results. Last it is the effect on mean-CVaR model with transaction costs from parameters, it process three times numeric tests:changing the transaction costs, changing the value of confidence level and changing the risk-free rate. We find that the effect is prominent on portfolio when you change the transaction costs, the value of confidence level and the risk-free rate.