Robust- extended goal programming with uncertainty sets: an application to a multi-objective portfolio selection problem leveraging DEA

Abstract

This study presents a two-phase approach of Data Envelopment Analysis (DEA) and Goal Programming (GP) for portfolio selection representing a pioneering attempt at combining these techniques within the context of portfolio selection. The approach expands on the conventional risk and return framework by incorporating additional financial factors and addressing data uncertainty which allows for a thorough examination of portfolio outcomes while accommodating investor preferences and conservatism levels. The initial phase employs a super-efficiency DEA model to streamline asset selection by identifying suitable investment candidates based on efficiency scores setting the stage for subsequent portfolio optimization. The second phase leverages the Extended GP (EGP) framework which facilitates the comprehensive incorporation of investor preferences to determine the optimal weights of the efficient assets previously identified within the portfolio. Each goal is tailored to reflect specific financial factors spanning both technical and fundamental aspects. To tackle data uncertainty robust optimization is applied. The research contributes to the robust GP (RGP) literature by analyzing new RGP variants overcoming limitations of traditional and other uncertain GP models by incorporating uncertainty sets. Robust counterparts of the EGP models are accordingly developed using polyhedral and combined interval and polyhedral uncertainty sets providing a flexible representation of uncertainty in financial markets. Empirical results based on real data from the Tehran Stock Exchange comprising 779 assets demonstrate the superiority of the proposed approach over traditional portfolio selection methods across various uncertainty settings. Additionally a comprehensive sensitivity analysis investigates the impact of uncertainty levels on the robust EGP models. The proposed framework offers guidance to investors and fund managers through a pragmatic approach enabling informed and robust portfolio decisions by considering efficiency uncertainty and extended financial factors.