CVaR And Mean-CVaR Efficient Frontier For A Portfolio In Elliptically Distribution

In the past twenty years, financial market have presented a large fluctuation, due to the factors of economic globalization, financial deregulation , financial innovation and so on. Financial crisis took place frequently because of financial risk. So, the risk of financial market have become the focus of financial institutions and supervisory authorities. Under this background the risk measure method of VaR (Value-at-Risk) have been developed, which has achieved the high status of being written into industry regulations. But research indicated that VaR method have serious shortcoming, for example it is not a coherent measure of risk; it doesn't have convexity and doesn't deal with the super loss etc.The risk measure method of CVaR(Conditional Value-at-Risk)has been developed on basis of VaR method, the implication of which is the mean of loss's β-tail distribution(0 < β< 1 is the confidence level). The method of CVaR is a coherent measure of risk, can reflect the potential risk of investment portfolio and is more easily to compute. Until now many scholars both at home and abroad have been done a lot of works in CVaR's equivalence definition ,. properties , computing and sample approximation , applications etc. And they have also resolved the Mean-CVaR boundary and Mean-CVaR Efficient Frontier of a portfolio under the assumption of normal risk securities, but they have't resolved the Mean-CVaR boundary and Mean-CVaR Efficient Frontier of a portfolio under the assumption of other distribution risk securities.This paper preliminarily discusses CVaR—the new approach of risk management. The research is split into four parts: The first part introduces the background, the definition and the properties of CVaR and the comparison of the similarities and differences of CVaR and Expected shortfall. The second part is fall into two portions. The first portion studies the formula of CVaR under the assumption of elliptically risk securities; the second portion studies the formula of CVaR under the assumption that the portfolio is made up of risk securities and risk-free securities. Based on the CVaR technique, the third part studies the Mean-CVaR boundary of portfolio under the assumption of elliptically risk securities, compares the Mean-CVaR boundary and Mean-Variance boundary, investigates existence conditions and expression of minimize CVaR portfolio under the assumption of elliptically risk securities. It also studies the Mean-CVaR Efficient Frontier of portfolio and examines the economic implications under the assumption of elliptically risk securities. Moreover, the comparison between the Mean-CVaR Efficient Frontier and...