EMPIRICAL STUDIES ON THE MARKOWITZ PORTFOLIO OPTIMIZATION PROBLEM THROUGH METAHEURISTIC ALGORITHMS

Abstract

Portfolio optimization remains a critical task in finance, guiding investment decisions and risk management strategies. This thesis investigates various aspects of single-period deterministic portfolio optimization, focusing on the application of Metaheuristic techniques and their efficacy in addressing real-world constraints incorporated in the portfolio optimization problem. The study begins with an exploration of Modern Portfolio Theory (MPT) and its significance in finance, tracing its historical development and examining its enduring relevance in contemporary investment practices. Subsequent chapters delve into the application of EAs, such as Genetic Algorithms (GAs) and Multi-Objective Evolutionary Algorithms (MOEAs), to solve constrained portfolio optimization problems. Through empirical studies and comparative analyses, the effectiveness of these algorithms in handling complex optimization tasks is evaluated, considering factors such as cardinality constraint and budget constraint. The primary objectives addressed in this study include the theoretical conclusion on the equivalence of solving the weighted sum approach of portfolio optimization or its multi-objective formulation. This theoretical result is verified through an empirical study employing a proposed Genetic Algorithm (GA). Additionally, the thesis conducts a comparative analysis of a Swarm Intelligence technique versus an Evolutionary Optimization technique, accompanied by a sensitivity analysis of varying upper bound and cardinality constraints. Moreover, this research addresses the lack of selection strategies in the field by showcasing the efficiency of exponential sorting paired with SPEA2 to solve the Cardinality Constrained Portfolio Optimization Problem (CCPOP). Furthermore, a novel contribution is made by proposing a modification to the CCPOP model with soft constraints, studying the effect of modifications, and deploying three large-scale datasets for empirical validation. Comparative analysis of state-of-the-art evolutionary algorithms for Large-Scale Sparse Multi-Objective Optimization Problems (LSSMOPs) further highlights the effectiveness of the proposed approach. In essence, this thesis contributes significantly to the ongoing evolution of studies deploying Metaheuristic techniques to solve the single-period cardinality-constrained deterministic portfolio optimization problem. Through a judicious blend of theoretical insights, empirical validations, and innovative methodologies, the research not only advances our understanding of portfolio optimization but also sets the stage for future breakthroughs in this critical domain of finance.