A Strategy Which Maximizes the Geometric Mean Return on Portfolio Investments

A common formulation of the portfolio selection problem leads to the prescription of a strategy which maximizes the geometric mean return on investments. In this paper we examine conditions under which solutions exist for the case where the returns distribution is discrete. We establish necessary and sufficient conditions for a solution to exist and give a computationally convenient and exact method for finding a solution in circumstances where (i) a solution exists and (ii) the number of securities equals or exceeds the number of values in the returns distribution.