Modelling extreme risk of the South African Financial Index (J580) using the generalised Pareto distribution

Owen Jakata,Delson Chikobvu

doi:10.4102/jef.v12i1.407

Abstract

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.

Highlights

OrientationIn the study and practice of financial risk management, the value at risk (VAR) and expected shortfall (ES) metrics are the most widely used risk measures
Extreme value theory provides a solid framework for estimating the behaviour of extreme events and performs better than other approaches in terms of predicting unexpected extreme movements as it focusses on the tails of the distribution (Longin 2000)
The VAR and ES are used for analysing the extent of potential extreme downside and upside risk of the J580 Index

Summary

Introduction

OrientationIn the study and practice of financial risk management, the value at risk (VAR) and expected shortfall (ES) metrics are the most widely used risk measures. Proper estimation of VAR and ES is necessary in that they need to accurately capture the level of risk exposure (downside and upside risk) that the firm or portfolio is exposed to. Extreme value theory (EVT) application is found in many fields where extreme events may occur, including hydrology (Katz, Parlange & Naveau 2002), insurance (McNeil 1997) and finance (Gencay & Selçuk 2004). EVT is used to estimate financial risk measure in the South African Financial Index. Extreme value theory provides appropriate distributions to capture extreme events. The generalised Pareto distribution (GPD) of the EVT is used to estimate financial risk measures (downside and upside risk) in the form of VAR and ES for the index. The measures are very useful because they are good at assessing the likelihood and impact of a financial crisis

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Conclusion