Modelling South Africa's market risk using the APARCH model and heavy-tailed distributions.

Abstract

Estimating Value-at-risk (VaR) of stock returns, especially from emerging economies has recently attracted attention of both academics and risk managers. This is mainly because stock returns are relatively more volatile than its historical trend. VaR and other risk management tools, such as expected shortfall (conditional VaR) are highly dependent on an appropriate set of underlying distributional assumptions being made. Thus, identifying a distribution that best captures all aspects of financial returns is of great interest to both academics and risk managers. As a result, this study compares the relative performance of the GARCH-type model combined with heavy-tailed distribution, namely Skew Student t distribution, Pearson Type IV distribution (PIVD), Generalized Pareto distribution (GPD), Generalized Extreme Value distribution (GEVD), and stable distribution in estimating Value-at-Risk of South African all share index (ALSI) returns. Model adequacy is checked through the backtesting procedure. The Kupiec likelihood ratio test is used for backtesting. The proposed models are able to capture volatility clustering (conditional heteroskedasticity), and the asymmetric effect (leverage effect) and heavy-tailedness in the returns. The advantage of the proposed models lies in their ability to capture volatility clustering and the leverage effect on the returns, though the GARCH framework and at the same time model their heavy tailed behaviour through the heavy-tailed distribution. The main findings indicate that APARCH model combined with this heavy-tailed distribution performed well in modelling South African market’s risk at both the long and short position. It was also found that when compared in terms of their predictive ability, APARCH model combined with the PIVD, and APARCH model combined with GPD model gives a better VaR estimation for the short position while APARCH model combined with stable distribution give the better VaR estimation for long position. Thus, APARCH model combined with heavy-tailed distribution model provides a good alternative for modelling stock returns. The outcomes of this research are expected to be of salient value to financial analysts, portfolio managers, risk managers and financial market researchers, therefore giving a better understanding of the South African market.