A Unified View on the Optimal Solutions to the Threemoments Portfolio Problem

This paper brings new results and insights on the set of solutions to the portfolio choice problem for n risky assets and a riskless one, considering the three first moments and allowing short sales. It simultaneously deals with the three possible optimization versions to find a synthetic equation valid for all of them. Duality links the three sets of solutions, leading to and validating the concept of the fundamental equation, here introduced. The unifying approach sheds light on the understanding of a global efficient frontier in either three-moments’ or portfolio weights’ space and opens the door to further developments