The Applications Of CDaR In The Portfolio Theory

The risk measure method of CDaR(Conditional Value-at-Risk)isdeveloped on basis of the VaR(Value-at-Risk)method, which is raised byRockafellar at 2000. The implication of CDaR is the conditional loss overDaR of portfolio, which reflects the average exceed quota. CDaR methodreflects underlying loss better than CVaR method.This paper focuses on the application of CDaR in the protfoliotheory. In the course of researching, I do my best to use the method ofSystem theory, induction and deduction, comparison and empiricalanalysis and so on.Firstly, the paper totally introduces a few kinds of traditionalportfolio theory, including the classical mean-variance theory, meanVaR theory, mean-CVaR theory and their defect. Then put forwardCDaR risk measure method, introduce and analyse the definition, theparameter selecting, the calculation, the properties and applications andso on. The conclusion is that CDaR is better than the traditional one.Then we study the application of CDaR in portfolio theory, considermainly the practical market with friction and the one without friction, weconsider the practical market, affected by tax and the transaction cost. weuse variables of zero and one and turn the portfolio model with centsegment transaction cost into a nonlinear programs. In every market weconsider the mean-CDaR model. Then we put forward a two periodconstrained portfolio optimization by CDaR, which considers the shortaction and the long one of the market and provides a new idea for a longterm investor to establish a rational portfolio. we analysis every modelwith examples and find the models are valid.lastly, we conclude this paper and put forward some view on ourstudy.