New light on the portfolio allocation problem (Q1812298)

This paper defines the Sharpe ratio of an asset portfolio as its expected return divided by its standard deviation. The paper studies the maximization of this functional, restricted only by the ``full investment'' constraint; short sales are allowed. It solves the optimization problem explicitly and shows that there are two solutions, depending on a sign condition. One solution is the one usually presented in textbooks. The other cannot be achieved exactly for a specified portfolio allocation but can be approached as closely as desired.