A Comparative Analysis of The Markowitz Model and The Single-Index Model: Mathematical Efficiency Vs. Practical Simplicity

Abstract

With the increasing interest of emerging economies in the stock market, single asset investment is also shifting towards diversified portfolio strategies, and the trade-off between Markowizt model and index model in terms of evaluation correctness and practical effectiveness is also arising. Based on the historical daily total return data of 21 OEX member companies' stocks over the past 20 years, as well as a S&P 500 stock index and risk-free rate (one month federal funds rate), this article uses a structured data-driven approach to analyze and compare the difficulty of data and computation between the two models, as well as to compare the accuracy of capturing the trade-off between risk and return. Research has found that an increase in the number of assets will bring significant computational pressure to the Markowitz model, and the calculation speed of single indicator models will be faster and more accurate; The Markowitz model framework theoretically captures correlations between assets more accurately, but also faces the phenomenon of high risk and high return, while the single index model tangent investment portfolio has a milder balance of expected risk and return at the cost of slightly lower expected returns.