Extreme Value Modelling of the Monthly South African Industrial Index (J520) Returns

An Application of the Generalised Pareto Distribution

  • Owen Jakata University of the Free State, Faculty of Natural and Agricultural Sciences, Department of Mathematical Statistics and Actuarial Science, Box 339 Bloemfontein 9300, South Africa https://orcid.org/0000-0001-7058-4337
  • Delson Chikobvu University of the Free State, Faculty of Natural and Agricultural Sciences, Department of Mathematical Statistics and Actuarial Science, Box 339, Bloemfontein 9300,South Africa https://orcid.org/0000-0003-3979-658X
Keywords: Extreme Value Theory, Generalised Pareto Distribution, Peak-over-Threshold method, Value-at-Risk, Expected Shortfall, Tail-related risk, monthly South African Industrial Index (J520), South African equity market


This study uses Extreme Value Theory (EVT), Value-at-Risk (VaR) and Expected Shortfall (ES) analysis as a unified tool for managing extreme financial risk. The study extends the application of the generalised Pareto distribution (GPD) by modelling monthly South African Industrial Index (J520) returns (years: 1995-2018) to quantify the tail-related risk measures. The GPD is used to estimate the tail-related risk measures using the Peak over Threshold (PoT) method. Maximum Likelihood Estimates (MLE) of model parameters were obtained and the models goodness of fit was assessed graphically using Quantile-Quantile (QCQ) plots, Probability (PCP) plots, scatter plots, residuals, return levels and density plots. The findings are that the GPD provides an adequate fit to the data of excesses (extreme losses or gains). Low frequency but very high or very low returns impact on investment decisions. Calculations of the VaR and ES tail-related risk measures based on the fitted GPD model are given. The results reveal that for an investment in the South African Industrial Index (J520), the prospect of potential extreme losses is less than the prospect of potential extreme gains. There seems to be an upper bound where losses do not seem to exceed easily. The study concluded that EVT, together with VaR and ES analysis are useful tools that can be applied in practice to manage index/stock price risk and help investors improve their investment decisions and trading strategies through better quality information derived from the tools. This study contributes to empirical evidence on EVT methods that help to protect financial systems against unpredictable fluctuations and losses of extreme nature.

Author Biographies

Owen Jakata, University of the Free State, Faculty of Natural and Agricultural Sciences, Department of Mathematical Statistics and Actuarial Science, Box 339 Bloemfontein 9300, South Africa
Department of Mathematical Statistics and Actuarial Science PhD student, research interests: Financial Risk Modelling
Delson Chikobvu, University of the Free State, Faculty of Natural and Agricultural Sciences, Department of Mathematical Statistics and Actuarial Science, Box 339, Bloemfontein 9300,South Africa
Department of Mathematical Statistics and Actuarial Science Senior Lecturer


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How to Cite
Jakata, O., & Chikobvu, D. (2021). Extreme Value Modelling of the Monthly South African Industrial Index (J520) Returns. Statistics, Optimization & Information Computing, 10(2), 383-400. https://doi.org/10.19139/soic-2310-5070-906
Research Articles