Risk Measurement Technique VAR And CVAR And Their Application In Portfolio Optimization

As financial market develops, risk that we meet grows much more complicated, risk is unsure about future loss, risk is caused by capital wave, or debt wave, how to measure it accurately turn out to be solved. Financial regulator, financial consultation and private financial groups now pay much attention to it. VaR, value at risk, enable us to quantify the maximum loss of financial portfolios in certain period. Till now, risk measurement become much more popular in the financial market. CVaR come from VaR, and it play the same important part as VaR. Use VaR and CVaR to control risk in the portfolios is popular all over the world.This paper introduces VaR and CVaR research background, applied range, current situation. Then introduces VaR and CVaR measurement system, include their conception, properties, merit and demerit, comparison. After that it introduces several classic models in portfolios and improve one of them. Depend CVaR, the min lost optimization problem is: The first formula is the objective function; the first limiting condition is CVaR condi-tion; xj≥0 means no short purchase. To solve this linear programming problem, we can get the optimal vector x*,its VaR isξ*. The max optimal profit isΣi=1n E[yi]xi. After that, we use the model in practice. We download the stock data from Sina net, we choose ten stocks for applying. They are as follows: For each stock i, its profit is: yij=ln(pitj-1+7/Pitj-1),j=1,2,…,10 So we get (yij)10×10 from the data, as the follow table:So we use the results,with the help of matlab,solve different risk optimal problem, get the optimal vecter x*, the first component is VaRChange the value ofα, we get different VaR of different risk, as follows: This result is perfect, and agrees with the theoretical,too.At last, we also discuss the improvement of the model, we present several methods which is very practicable.