SUMMARY
AbstractOrientation: 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.