A unified view on the optimal solutions to the threemoments portfolio problem

Abstract

This paper brings new results and deeper insights in characterizing the set of solutions to the portfolio selection problem for n risky assets and a riskless one, considering the three first moments and allowing short sales. We examine the three versions associated with this model and find a synthetic equation valid for all of them. With the help of the duality condition linking the optimization problems involved, we are able to introduce the idea of the fundamental equation. This unifying approach sheds light on the understanding of a global efficient frontier in the three-moments model and opens the door to further developments.