奇异协方差阵及不同借贷利率下均值-方差模型的解析解

摘要

随着金融资产种类的增加，特别是考虑大规模投资组合问题时，很可能出现资产间的多重共线性或相关性，从而出现协方差阵奇异的情况。然而，目前关于投资组合的均值—方差分析大都是在协方差阵正定的条件下得到的，因此，不适用于奇异协方差阵的情形。针对这一问题，利用广义逆矩阵研究了协方差阵奇异时的均值—方差投资组合模型，在不同借贷利率条件下得到了前沿组合和组合前沿的解析解，突破了传统方法中要求协方差阵可逆的限制，推广了经典Markowitz模型。%In the mean-variance portfolio model , the covariance matrix is likely to be singular since the multi-collinearity and correlation can arise from the increase of financial assets , especially when considering a large-scale portfolio .In view of this situation , we reconsider the mean-variance portfolio problem under singular covariance matrix.A new approach based on generalized inverse matrix is proposed as a remedy for the deficien-cy of conventional methods in which covariance matrix is constrained to be invertible .The analytic solutions of frontier portfolio and portfolio frontier are derived with different interest rates for borrowing and lending , which extending successfully the classic Markowitz portfolio model .