Portfolio optimization

Abstract

Globally, there has been a rapid increase in machine learning (ML) integration within the financial field due to its ability to analyse big data and learn complex patterns to make informed decisions quickly compared to traditional practices. Empirical studies have investigated which traditional methods, such as mean-variance optimization, maximum Sharpe ratio optimization, risk parity, and equal-weighted portfolio, yield optimal returns when compared against each other and similarly when compared against ML methods such as linear regression, decision tree, random forest, and sector vector machine regression model. These studies reflect mixed results where one traditional method, such as mean-variance, outperforms the maximum Sharpe ratio portfolio and, in some cases, is the opposite. However, most literature agrees that implementing machine learning methods will provide higher risk-adjusted returns than traditional methods. While South Africa has surged in research regarding the use-case of machine learning since 2016, it has yet to explore ML's impact within the investment context fully. This study will investigate which traditional and ML methods will yield the highest composite score and which sector has consistently contributed to the optimal portfolio. The study uses daily observations from 30 September 2019 to 30 September 2024, to construct 20 portfolios from randomly selected 27 stocks. In traditional methods, only daily closing prices were used, and in ML, daily opening, closing, high and low prices, and trading volume were used. This study used the following traditional methodologies: (i) Equal Weighted, (ii) Mean Variance, (iii) Maximum Sharpe Ratio, and (iv) Risk Parity optimization. Similarly, machine learning methods consist of (i) Linear Regression, (ii) Decision Tree Regression, (iii) Random Forest Regression, and (iv) Sector Vector Machine Regression models. The evaluation for the predictive analysis includes (i) Mean Absolute Percentage Error, (ii) R-squared, and (iii) Theil's U2. Additionally, the portfolio performance was evaluated by (i) Sharpe ratio, (ii) Tracking Error, (iii) Sortino Ratio, (iv) Information ratio, (v) Beta, and (vi) Treynor Ratio. Finally, a composite z-score ranking system was adopted to determine the optimal portfolio. Our analyses were conducted by executing a series of commands on Python via Google Colab. In traditional methods, results indicated that the Equal Weighted Portfolio had the highest composite score. By contrast, ML tools enhanced each traditional method on 20 different portfolios and obtained an accuracy score between 75% and 98% for all predictive parameters. For ML optimization, it was determined that linear regression was the best ML model, and it was evident that the Mean-Variance portfolio outperformed the Equally Weighted, Mean-Variance, Maximum Sharpe Ratio, and Risk Parity portfolio. The study finds that ML outperforms traditional methods based on the aggregated score. The study's outcome recommends that South African investment professionals integrate ML into their investment strategies as it would be a rewarding opportunity.