Mean-Variance Analysis

Abstract

In a mean–variance portfolio analysis (Markowitz 1959) an n-component vector (portfolio) X is called feasible if it satisfies $$ AX=b\kern2em X\ge O $$ where A is an m × n matrix of constraint coefficients, and b an m-component constant vector. An EV combination is called feasible if $$ \begin{array}{c}E={\mu}^TX\\ {}V={X}^TCX\end{array} $$ for some feasible portfolio. Here E is the expected return of the portfolio, V the variance of the portfolio, μ the vector of expected returns of securities, and C a positive semidefinite covariance matrix of returns among securities.

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