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.
Highlights
South Africa is one of the most diverse and promising emerging markets globally
We examined the suitability of using asymmetric power ARCH (APARCH) (1, 1) framework combined with heavy-tailed distributions for modelling VAR for Johannesburg Stock Exchange (JSE) All Share Index returns
The APARCH framework was used to capture volatility and asymmetric characteristics exhibited by financial returns, while the heavy-tailed distributions are used to capture the heavy-tailedness of actual return distributions
Summary
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. The JSE All Share Index (ALSI) is crafted to represent the performance of South African companies, providing investors with a broad and harmonious set of indices, which compute the performance of the major capital and industry components of the South African stock market. We are interested in the https://www.jefjournal.org.za relative performance of the APARCH model combined with heavy-tailed distributions, namely generalised Pareto distribution (GPD), PIVD and stable distributions (SDs) in estimating the value-at-risk (VAR) for South Africa stock market. We extend the work of Paolella (2016) by proposing GARCH-type models combined with heavy-tailed distributions to model the daily JSE All Share Price returns.
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