条件风险下的两基金分离定理

摘要

Based on the rationality of the conditional value at risk as well as the important role of two fund separation theorem on securities investment,this paper analyzed the two fund separation theorem.For the portfolio with or without risk-free asset,we proved two fund separation theorem under the assumption that the portfolio return follows normal distribution. Further,we find that two fund separation theorem remains valid if the variance-covariance matrix is singular.%鉴于条件风险价值 CVaR 具有风险度量的合理性以及两基金分离定理对证券投资的重要意义，以 CVaR 作为风险度量研究两基金分离定理。在组合收益率服从正态分布的假设下，分别就投资组合含有或没有无风险资产的情形提出并证明了两基金分离定理；放开方差－协方差矩阵为非奇异这一通常假设，证明了 CVaR 风险度量下的两基金分离定理依然成立。