Distance functions and portfolio selection : a multi-factor and multi-moment approach
Safa Bouchnak · theses.fr (ABES) · 2024
Decision-making in investment remains a central concern in the fields of financial economics and portfolio management. The aim here is to extend evaluation methodologies by exploring multidimensional criteria that encompass multi-factors and multi-moments, as well as general and partial moments, to better reflect market realities and address investor preferences. First, we extend the shortage function to a multifactorial space through risk decomposition. This extension enables a new geometric representation of the non-parametric frontier, which is capable of representing two risk factors in a three-dimensional space. Secondly, the multi factor Capital Asset Pricing Model, based on the decomposition of market portfolio returns, captures the sensitivity of asset returns to multifactorial market risk and provides a representation of a market hyperplane. The shortage function is also extended within a multifactorial CAPM framework, to account for multi-factor market risk and riskless assets. Thirdly, the MMFV and MVSK shortage functions were extended to the risk-loving case to determine the impact of investor attitude on portfolio performance. Finally, the boundaries of the selection problem are pushed by considering strongly efficient portfolios, thereby introducing a new general shortage function in a multidimensional general and partial moment space