A THREE-MOMENT PORTFOLIO SELECTION MODEL: MULTIPLIERS AND DUALITY

This paper addresses the three-moment portfolio selection problem. We develop a comprehensive characterization of this problem through a duality perspective, analyzing the linear systems associated with the multipliers of three interconnected optimization formulations (variance minimization, skewness maximization, and return maximization, each with two moments fixed). Our methodological contribution extends and completes existing analyses, particularly that of Athayde and Flôres [(2004) Finding a maximum skewness portfolio — A general solution to three-moments portfolio choice, Journal of Economic Dynamics and Control 28, 1335–1352, https://doi.org/10.1016/S0165-1889(02)00084-2 ], by providing an alternative, geometrically based approach that deals with the nonlinear nature of these problems without requiring a challenging study of multiplier signs, including in degenerate cases. Our results provide conditions for determining whether a portfolio does not belong to the efficient frontier, thereby enabling a more robust identification of optimal asset allocations in practice. Furthermore, our framework clarifies when solutions deviate from the classical Markowitz mean-variance model, providing deeper insights into the role of higher moments in investment decisions. By relying on computationally efficient checks for linear dependence, our approach not only advances theoretical understanding but also presents a practical and accessible tool for portfolio managers seeking to integrate higher moments into their optimization strategies, ultimately leading to more informed and efficient portfolio construction.