Quantifying Foreign Exchange Risk in the Selected Listed Sectors of the Johannesburg Stock Exchange: An SV-EVT Pairwise Copula Approach

Abstract

This paper attempted to apply an EVT-based pairwise copula method for modelling risk interaction between foreign exchange rates and equity indices of the Johannesburg Stock Exchange (JSE) and to model the dependence structure of the underlying assets with some selected listed stock indices. We filtered the return residuals using the stochastic volatility and GJR-GARCH (1,1) models with different distributions, and we selected the best-fitted model in the GARCH framework. We applied the peaks-over-threshold (POT) method to the filtered residuals to fit it by the generalised Pareto distribution (GPD), and we used the vine copula to model the co-movement between foreign exchange rates and equity indices and value at risk (VaR) for risk quantification. We used three exchange rates (USD, GDP, and EUR) against the South African rand (ZAR) and six industry indices (banking, life insurance, non-life insurance, leisure, telecommunications, and mining). Our empirical findings show that the GJR-GARCH with Student’s t-distribution, combined with a regular (R)-vine copula, outperforms the alternatives models. Dependence structure analysis reveals a strong co-dependency between the stock from the financial industry and foreign exchange rates. The results also show that VaR-based R-vine copula outperforms the model compared to VaR-based D-vine and C-vine before the COVID-19 outbreak, while the D-vine copula produced appears to be the most suitable risk model specification for quantifying risk during the COVID-19 pandemic. Therefore, VaR-based R-vine copula is suitable for risk quantification, while GJR-GARCH with Student’s t-distribution produces better results in the GARCH framework. Further, we find that equity indices and foreign exchange rates exhibit higher tail risk contagion during the COVID-19 pandemic, with the non-life-insurance and telecommunications sectors appearing to be the investor’s safe haven among the listed sectors of the JSE. Our results will help South African investors seek risk-adjusted returns to substantially reduce the hedging cost of potential loss due to the misspecification of a risk model and make an investment decision during the global health crisis.