Page 249 - Contributed Paper Session (CPS) - Volume 6

CPS1909 Retius C. et al.

Evaluating South Africa’s market risk using
APARCH model under heavy-tailed
distributions
Retius Chifurira, Knowledge Chinhamu
School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal,
Westville Campus, South Africa

Abstract
Estimating Value-at-risk (VaR) of stock returns, especially from emerging
economies, has recently attracted attention of both academics and risk
managers. VaR and other risk management tools, such as expected shortfall
(conditional VaR) are highly dependent on an appropriate set of underlying
distributional assumptions. Thus, identifying a distribution that best captures
all aspects of financial returns is of great interest to both academics and risk
managers. This study compares the relative performance of the GARCH-type
model combined with heavy-tailed distributions, namely; the Student- t
distribution, Pearson type-IV distribution (PIVD), Generalized Pareto
distribution (GPD) and stable distribution (SD) in estimating Value-at-Risk of
FTSE/JSE all-share price index (ALSI) returns. Model adequacy is checked by
using the Kupiec likelihood ratio test. The advantage of the proposed models
lies in their ability to capture volatility clustering and the leverage effect on the
returns, through the GARCH framework and at the same time model their
heavy-tailed behaviour. The main findings indicate that the Asymmetric power
ARCH (APARCH) model combined with heavy-tailed distributions performed
well in modelling South African’s market risk. Thus, APARCH model combined
with heavy-tailed distributions provides a good alternative for modelling stock
returns. 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 market.

Keywords
Asymmetric volatility models; Value-at-Risk; Heavy-tailed distributions;
FTSE/JES All share price index

1. Introduction
South Africa is one of the most diverse and promising emerging markets
globally. It is the sixth most outstanding in the emerging economies category,
with vast opportunities within its border. It is a gateway to the rest of the
African continent (a market of more than one billion people) and is a key
investment location. It is the economic powerhouse of Africa and forms part
of BRICS group of countries which includes Brazil, Russia, India and China.
South African stock market, Johannesburg Stock Exchange (JSE) is Africa’s

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