投资组合有效边界的图解分析

从均值-方差理论的角度出发，通过投资组合有效边界的数学模型，讨论仅包含3项资产的投资组合在不同资产比例分配下的期望收益和方差，得出不同情形下等收益率线和等方差线的切点连线(临界线)的不同图形表示，从而确定投资组合有效边界在E-V平面图上为一系列相连的抛物线段．从等方差线上所有投资组合的总风险小于单个投资的风险而得出风险分散的结论．

Graphic Analysis of Efficient Frontier of Portfolio

Based on the theory of E-V (expected value-variance) and the mathematical model of the efficient frontier of portfolios, the expected profit and varianc e of a portfolio including three securities under the different allocation propo rtions of capital are discussed, and the graphic expressions of lines linking th e tangent points of isomean lines and isovariance curves under different conditi ons are obtained. The research shows that the efficient frontier is composed of a series of parabolic segments connected each other in an E-V plane and the risk of a compound portfolio is diversified because the variance of the compoun d portfolio is less than that of a single portfolio with the same variance.