Portfolio Selection Decision Based On Risk Measurement Of VaR

Variance of returns is regarded as risk in the model of Mean-variance. Although this kind of method can reduce the fluctuation of return effectively, the Minimization of variance can not only reduce the shortfall of return, but also reduce the surplus of return ,so it may confine the potential return.VaR is the statisticial measurement of potential loss under the condition of market varying normally. Having known the return's distribution of future, the possible loss of invest to a given confidence level is equivalent to VaR, VaR represents the value at risk to the confidence level in the formula , where denotes the return of invest.There are two kinds of applications about portfolio selection decision based on VaR: Mean-VaR model and VaR-constrained Mean-variance model.We study the efficient frontiers of Mean-VaR model obtained by solving Mean-variance model. Mean-VaR efficient set are subset of the Mean –variance efficient frontier under assumption that returns are normally distributed. A characterization of the existence of the global minimum VaR portfolio suggests that one must be careful in choosing the confidence level at which VaR is determined, otherwise there may be no solution to the model.The efficient frontier of VaR-constrained Mean-variance model is the section of efficient frontier of Mean-variance model lies on or above a line with intercept and slope .When the interest rate of the borrowed money is not equal to the interest rate of the deposit, we can prove that the efficient frontier of portfolio with risk-less asset is no longer a straight line.Research on VaR under the condition of fat-tail distribution has won tremendous development in recent years. But VaR has enormous defect not only in theory but also in application, CVaR(Conditional VaR) becomes the new research focus as a kind of improvement of VaR.