On the optimum number of stocks and diversification using Machine Learning techniques

Abstract

The optimum number of stocks prior research specific to South Africa finds that equally-weighted portfolios require about 15-20 stocks for effective diversification, while market capitalization weighted portfolios may need 33-60 stocks due to the concentrated nature of the South African financial market. The optimal number is influenced by market concentration, weighting scheme and stock correlations. There is no universal optimum number to date, but it varies with market conditions and investor preferences. Machine learning (ML) models such as Random Forest (RF) and eXtreme Gradient Boosting (XGBoost) are used to forecast returns and select high-performing stocks. Three portfolio universes of 15 stocks each were constructed and named Factor, Sector and Risk-Adjusted portfolio universes. The predictions are integrated into mean variance (MV), mean valueat-risk (VaR) and risk parity machine learning models to allocate weights and maximize diversification. The proposed Factor Mean-Value at Risk (FM-VaR) strategy achieved a Sharpe ratio of 0.816, outperforming the market benchmark by $\mathbf{6 1. 6 \%}$, while requiring an optimal portfolio of only 15 stocks. Therefore, machine learning techniques are evaluated to significantly enhance stock selection and portfolio diversification.