Original Research

Modelling extreme risk of the financial index (J580) using the general Pareto distribution

Owen Jakata, Delson Chikobvu
Journal of Economic and Financial Sciences | Vol 12, No 1 | a407 | DOI: https://doi.org/10.4102/jef.v12i1.407 | © 2019 Owen Jakata, Delson Chikobvu | This work is licensed under CC Attribution 4.0
Submitted: 17 August 2018 | Published: 29 May 2019

About the author(s)

Owen Jakata, Department of Mathematical Statistics and Actuarial Sciences, University of the Free State, Bloemfontein, South Africa
Delson Chikobvu, Department of Mathematical Statistics and Actuarial Sciences, University of the Free State, Bloemfontein, South Africa

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Orientation: In light of the global financial instabilities, investors and risk analysts need extreme risk management tools to help them accurately monitor and reduce market exposure in an investment portfolio.

Research purpose: The main aim of the study was to apply extreme value theory results to quantify the extreme downside risk and upside risk of the South African Financial Index (J580).

Motivation for the study: Financial markets have been characterised by significant instabilities caused by occurrence of extreme events. This means there is a need to develop proper risk management models that can accurately assess these extreme events.

Research approach, design and method: The peak over threshold approach was used to obtain the excess returns over the threshold. The generalised Pareto distribution (GPD) was fitted to the excess returns over the threshold to estimate the parameters, which were used to quantify the downside and upside risk in the form of value at risk and expected shortfall.

Main findings: The findings indicate that the upside risk of the Financial Index (J580) outweighs the downside risk.

Practical/managerial implications: These findings would be important for hedging purposes, investment decision-making and help risk analysts to monitor the exposure of market risk and protect their investment portfolios accordingly.

Contribution/value-add: This article will contribute to empirical evidence of the research into the behaviour of the extreme returns on the Johannesburg Stock Exchange. The GPD model formulated will be used to assess tail-related risk.


extreme value theory; peak over threshold; generalised Pareto distribution; financial index (J580); value at risk; expected shortfall; downside risk; upside risk


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