Comprehensive Analysis of Portfolio Optimization Using the Markowitz and Index Models

Abstract

Harry Markowitz’s 1952 systematic approach to optimizing the trade-off between risk and return, known as Modern Portfolio Theory (MPT), revolutionized investment strategy. The objective of this final project is to apply the Markowitz and index models to provide a comprehensive analysis of portfolio optimization and conduct a comparative examination of the two models. By utilizing 20 years of historical daily total return data for 10 selected stocks within the S&P 500 Index, the study will develop optimal portfolios under various realistic constraints, such as typical leverage limitations and short selling restrictions. Additionally, the study evaluates the performance of these models and demonstrates that while index models offer computational simplicity, there are some drawbacks. In this scenario, a Markowitz model will generally provide a more precise risk-return optimization. Finally, the findings highlight the substantial influence of real-world constraints on portfolio management, which can significantly alter the efficient frontier and the structure of the optimal portfolio. This article, in the chapter on future research, proposes some possible future research directions, including the integration of behavioral finance elements and dynamic portfolio optimization, and furthermore discusses the implications of these research results.