The risk-return relationship in South Africa: tail optimization of the GARCH-M approach

Abstract

<abstract> <p>The risk-return relationship is of fundamental significance in the field of economics and finance. It is used to structure investment strategies, allocate resources, as well as assist in the construction of policy and regulatory frameworks. The accurate forecast of the risk-return relationship ensures sound financial decisions, whereas an inaccurate one can underestimate risk and thus lead to losses. The GARCH-M approach is one of the foremost models used in South African literature to investigate the risk-return relationship. This study made a novel and significant contribution, on a local and international level, as it was the first study to investigate GARCH-M type models with different innovation distributions. This study analyzed the JSE ALSI returns of the South African market for the sample period from 05 October 2004 to 05 October 2021. Results revealed that the EGARCH (1, 1)-M with the Skewed Student-t distribution (Skew-t) is optimal relative to the standard GARCH, APARCH and GJR. However, the EGARCH-M Skew-t failed to capture the financial data's asymmetric, volatile and random nature. To improve forecast accuracy, this study applied different nonnormal innovation distributions: the Pearson Type Ⅳ distribution (PIVD), Generalized Extreme Value distribution (GEVD), Generalized Pareto distribution (GPD) and Stable. Model diagnostics revealed that the nonnormal innovation distributions adequately captured asymmetry. The Value at Risk and backtesting procedure found that the PIVD, followed by Stable, outperformed the Extreme Value Theory distributions (GEVD and GPD). Thus, investors, risk managers and policymakers would opt to use the EGARCH-M in combination with the PIVD when modelling the risk-return relationship. The main contribution of this study was to confirm that applying GARCH type models with the conventional and normal type distributions, to a volatile emerging market, is considered ineffective. Therefore, this study recommended the exploration of other innovation distributions, that were not included in the scope of this study, for future research purposes.</p> </abstract>