Modelling Financial Risk in the South African Stock Market: An Application of the Generalised Extreme Value Distribution (GEVD)

This study analyses the return characteristics of the South African Industrial Index (J520) and South African Financial Index (J580) using the Generalized Extreme Value Distribution (GEVD) to estimate return levels, Value-at-Risk (VaR) and Expected Shortfall (ES). Results show that losses in the Industrial Index follow a short-tailed negative Weibull distribution, indicating bounded downside risk, while its gains follow a light-tailed Gumbel distribution, suggesting limited but unbounded positive returns. In contrast, losses in the Financial Index exhibit a heavy-tailed Frechet distribution, pointing to the potential for extreme, unbounded losses during market downturns, whereas its gains are bounded and follow a short-tailed Weibull distribution. These findings highlight the Financial Index's greater vulnerability to extreme losses, especially under volatile conditions, warranting higher risk-based capital allocation. The GEVD model proves to be a robust and flexible tool for modelling extreme return behaviour and enhances portfolio risk management by enabling more accurate estimation of return levels, VaR and ES, thereby supporting better-informed investment decisions under financial stress.