Notes on the Markowitz Portfolio Selection Method

摘要

A proof of the validity of Markowitz's critical line method is given for a more general situation than discussed by Markowitz. Next, for the Markowitz case with a positive definite covariance matrix, explicit expressions are derived for all efficient portfolios. Using these expressions, it can be shown that the critical line in the (mu, sigma squared) plane is a representation of a function which is not necessarily differentiable everywhere.