Portfolio Optimization Model With CVaR Constraints

Investigating measure theories of risk and approach of securities portfolio, inorder to control finance risk and stabilize finance system, is a common and importantundertaking .In this paper, the theories and approach of several representative measureof risk models are discussed, their localization and shortage are analyzed. A efficiencyapproach to measure risk is presented and tested on applications.In this paper, Introducing the theory of CVaR risk measuring technology, thevirtues and effects of VaR and CVaR risk measuring technology is expounded. Thescale of VaR model is under certain confidence level, to compute the capital's, but itisn't pointed out that once the expected value of maximum loss is exceeded, howmuch the loss of capital will be. Fundamental properties of conditional value-at-risk(CVaR), as a measure of risk with significant advantages over value-at-risk(VaR),CVaR is able to quantify dangers beyond VaR and moreover it is coherent. Thesuperiority of this way is the final solution may be transferred to linear programproblem, and it doesn't only include CVaR's value but also the VaR and the portfolio'sbest ratio can be computed.In addition, based on the theories of CVaR, Mean—CVaR optimization model ofrisk asset portfolio with transaction costs is established and discussed;under thedifferent confidence level, a case study for our stock market is performed ,the efficientfrontier and the optimal portfolio's ratio is analyzed. From the fact of investordecision-making, a portfolio replication with CVaR constraints for the index trackingproblem is established. The index tracking problem consists in minimizing thetracking error between a portfolio and a benchmark. We present an example thatdemonstrates how CVaR constraints can be used efficiently to control such risks.