Behavioural portfolio optimisation on the Johannesburg stock exchange during COVID-19 Era

Abstract

This study integrates Cumulative Prospect Theory (CPT) with multiple probability weighting function parameters, K-means clustering and a Differential Evolution algorithm to examine portfolio construction during COVID-19 market turbulence. Using daily returns for 88 Johannesburg Stock Exchange stocks from December 2019 to December 2022, CPT-based scores were computed for each stock under a benchmark CPT parameterisation and six alternative parameterisations. For six of the seven parameterisations, the resulting CPT scores selected the same set of extreme low- and high-score stocks, whereas one alternative parameterisation produced a distinct set of portfolios. K-means clustering indicated that the stocks grouped into two profiles that closely aligned with the low- and high-CPT score segments. The resulting portfolios were optimised using Differential Evolution with a Sharpe-ratio objective. The high-CPT portfolio generated under the distinct alternative parameterisation recorded the highest observed risk-adjusted performance among the portfolios examined. Overall, the findings show that CPT parameter choice can affect stock selection and portfolio outcomes, and that behavioural scoring, clustering and evolutionary optimisation can provide complementary information for portfolio construction during periods of severe market stress.