Comparative Analysis on the Application of Markowitz Model and Index Model in Portfolios

Abstract

This article presents a comparison between the Markowitz model and the index model, focusing on their applications in portfolio management. The Markowitz model, also known as the mean-variance model, revolutionized portfolio theory by introducing a quantitative method for balancing risk and return. This model constructs optimal portfolios that maximize expected return for a given level of risk or minimize risk for a given expected return, using a covariance matrix to assess relationships between asset returns. In contrast, index models popularized by William Sharpe offer a simplified approach focused on the relationship between individual asset returns and a common benchmark (usually a market portfolio). The article explores the theoretical foundations of the two models, highlighting their mathematical formulations and assumptions. It also discusses the computational methodologies involved in implementing these models and examines the challenges and advances in optimization techniques. It evaluates how these technological innovations have enhanced portfolio optimization, enabling the handling of larger datasets and more complex market dynamics. In addition to comparing these two models, the article delves deeper into the concepts of efficient frontier, inefficient frontier and minimum variance frontier. The efficient frontier is the portfolios that offer the highest expected return for target risk, while the inefficient frontier includes portfolios that do not offer the best return for the level of risk. Minimum variance frontier focuses on portfolios that minimize risk for target expected return, emphasizing the importance of risk management in investment decisions.