Applications Of VaR And CVaR In The Portfolio Theory

VaR and CVaR has many applications, such as measuring credit risk, deciding inner risk capital, allocating asset, supervising finance etc. This article focuses on VaR and CVaR in the portfolio theory.In this paper, by use of theoretical research and empirical study. Firstly, we introduce the definition and property of the VaR and CVaR risk measure methods, and some related model: mean-VaR and mean- CVaR , make some study of the bound and efficient frontier of mean- CVaR , then we put forward the mathematical statement of CVaR risk measure and its picture. Given the return rate and some CVaR constraint, we put forward the portfolio optimization model, which is the new ideas of this paper. Two questions have been solved , one is the selecting range of target yield, which avoids the selecting with experience in the past; another is seting VaR as the first line of defense and seting consistency of risk measurement CVaR as the objective function to create a model and to find its solution, which effectively conquers the lack of consistency and convex of the risk measure and can use the merits of the two methods to measure risks. Finally, we select the actual stock data of China's securities market, in a given target rate of return, determine the VaR , calculate out the minimum loss of over-subscription CVaR and decide the optimal portfolio strategy under the corresponding conditions .which is meaningful for investors in the practical investment.