Cvar Based Portfolio Optimization Problem

Portfolios theory is one of the important research contents in Economics. It aimsto attain the portfolios of the maximum of the investment' s return with the givenvalue of the risk of portfolios or of the minimum of investment's risk with the givenlevel of the investment's return. VaR,CVaR and CDaR, which are new risk measurementmethods, are put forth recently. Because of its easy definition and eminentproperties, CVaR is given attentions by more and more researchers in particular, andbecomes a latest research content in financial risk management.On the foundation of the definitions of VaR,CVaR and CDaR, their advantages aredescribed and the methods of applying CVaR and CDaR to decision are analysed,There are two kinds of applications about portfolio selection decision based onCVaR:Mean-CVaR model and CVaR-constrained Mean-Variance model.The efficient frontiers of Mean-CVaR model are obtained by solving Mean-Variancemodel. Mean-CVaR efficient set are subset of the Mean-Variance efficient frontierunder the assumption that returns are normally distributed.The efficient frontiers of CVaR-constrained Mean-Variance model is the sectionof efficient frontier of Mean-Variance model above a line with intercept-k and slopet(β).When the interest rate of the borrowed money is not equal to the interest rateof the deposit, the efficient frontier of portfolio is no longer a straight line.Finally, risk measure index CVaR and CDaR are applied in Chinese stock marketand other fields, and they are verified effective.