Original Research

Evaluating South Africa’s market risk using asymmetric power auto-regressive conditional heteroscedastic model under heavy-tailed distributions

Retius Chifurira, Knowledge Chinhamu
Journal of Economic and Financial Sciences | Vol 12, No 1 | a475 | DOI: https://doi.org/10.4102/jef.v12i1.475 | © 2019 Retius Chifurira, Knowledge Chinhamu | This work is licensed under CC Attribution 4.0
Submitted: 12 April 2019 | Published: 30 October 2019

About the author(s)

Retius Chifurira, School of Mathematics, Statistics and Computer Sciences, University of KwaZulu-Natal, Durban, South Africa
Knowledge Chinhamu, School of Mathematics, Statistics and Computer Sciences, University of KwaZulu-Natal, Durban, South Africa


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Abstract

Orientation: Value-at-risk (VAR) and other risk management tools, such as expected shortfall (conditional VAR), are heavily reliant on a suitable set of underlying distributional conjecture. Thus, distinguishing the underlying distribution that best captures all properties of stock returns is of great interest to both scholars and risk managers.

Research purpose: Comparing the execution of the generalised auto-regressive conditional heteroscedasticity (GARCH)-type model combined with heavy-tailed distributions, namely the Student’s t-distribution, Pearson type-IV distribution (PIVD), generalised Pareto distribution (GPD) and stable distribution (SD), in estimating VAR of Johannesburg Stock Exchange (JSE) All Share Price Index (ALSI) returns.

Motivation for the study: The proposed models have the potential to apprehend volatility clustering and the leverage effect through the GARCH scheme and at the same time model the heavy-tailed behaviour of the financial returns.

Research approach/design and method: The GARCH-type model combined with heavy-tailed distributions, namely the Student’s t-distribution, PIVD, GPD and SD, is developed to estimate VAR of JSE ALSI returns. The model performances are assessed through Kupiec likelihood ratio test.

Main findings: The results show that the asymmetric power auto-regressive conditional heteroscedastic models combined with GPD and PIVD are the robust VAR models for South African’s market risk.

Practical/managerial implications: The outcomes of this study are expected to be of salient value to financial analysts, portfolio managers, risk managers and financial market researchers, thus giving a better understanding of the South African financial market.

Contributions/value-add: Asymmetric power auto-regressive conditional heteroscedastic model combined with heavy-tailed distributions provides a good option for modelling stock returns.


Keywords

asymmetric volatility models; value-at-risk; heavy-tailed distributions; JSE All Share Index, backtesting

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