关键词: 投资组合, 协方差矩阵, 有效子集

Abstract: This paper studies the properties of portfolio’s covariance matrix.We obtained a sufficient condition for a portfolio’s covariance matrix to be positive.Meanwhile,we discussed the optimal portfolio selection under the covariance matrix being not positive definite.We concluded that the covariance matrix is nonpositive definite, there is either arbitrage opportunity or efficient subset.

Key words: portfolio, covariance, efficient subset