Quantile and Copula Models Reveal How Risk in South Africa’s Stock Market Shifts With the Wind

The Johannesburg Stock Exchange does not behave the same way in calm weather as it does in a storm, and a new statistical study of South Africa’s equity market has now mapped those differences in unusual detail. Precious Mkandla and Fastel Chipepa of the Botswana International University of Science and Technology analyzed nearly eighteen years of monthly data, from August 2007 to July 2025, to examine how the country’s flagship stock index responds to three external forces: the rand–dollar exchange rate, Brent crude oil prices, and gold prices. Their findings, published in Frontiers in Applied Mathematics and Statistics, show that the influence of these variables is not a single fixed number but a shifting pattern that changes depending on whether the market is crashing, cruising, or rallying.

The researchers chose South Africa for a reason. The Johannesburg Stock Exchange is the largest and most liquid equity market in Africa, and the economy behind it is unusually exposed to global conditions. The country relies on imported crude oil, earns substantial revenue from gold mining, and conducts much of its trade in a currency that fluctuates against the dollar. Each of these channels can transmit shocks to corporate earnings and investor sentiment. Yet most earlier studies of such relationships relied on linear regression, which estimates only an average effect, or on correlation measures that capture linear associations but miss the nonlinear comovements that dominate during financial stress. Even widely used GARCH models, which track time-varying volatility, estimate downside risk indirectly and can understate extreme losses when return distributions are fat-tailed.

To get around these limitations, the team assembled a toolkit of quantile-based methods. Quantile regression estimates how explanatory variables affect returns at different points in the return distribution, from the deepest losses to the strongest gains, rather than just at the average. Quantile autoregression extends this by testing whether past returns predict current ones at each quantile. The Conditional Autoregressive Value at Risk framework, known as CAViaR, estimates the fifth percentile of the return distribution directly, without imposing restrictive distributional assumptions. Finally, copula models separate the statistical behavior of each individual series from the dependence structure linking them, allowing the researchers to measure how likely extreme movements are to occur together.

The data itself revealed why such care was needed. Across 215 monthly observations, the JSE and Brent crude oil return series were strongly negatively skewed, meaning large negative moves were more common than large positive ones, and both showed pronounced kurtosis, the statistical signature of fat tails. Brent was by far the most volatile of the four series, with a standard deviation of 10.67 percentage points against 5.48 for the JSE. The worst single month for oil saw a return of nearly minus 80 percent. Formal tests rejected normality for every series, while Augmented Dickey–Fuller tests confirmed that all the return series were stationary, a prerequisite for the modeling that followed.

The quantile regression results delivered the study’s clearest message. The USD/ZAR exchange rate exerted a statistically significant negative effect on JSE returns at every quantile examined, from the fifth to the ninety-fifth percentile, with coefficients ranging from about minus 0.49 to minus 0.69. The effect was strongest in the lower quantiles, where bearish market conditions prevail, suggesting that currency depreciation and equity losses go hand in hand most powerfully when the market is already under pressure. Brent crude oil returns showed positive coefficients across most of the distribution, significant at several quantiles, which the authors interpret as evidence that rising oil prices may often reflect stronger global economic activity rather than simply higher production costs for an oil-importing economy. Gold, by contrast, showed small and mostly insignificant coefficients, with significance appearing only in the lower quantiles.

When the researchers turned to return persistence using quantile autoregression, a different picture emerged. The lagged JSE return was not statistically significant at the lower or median quantiles but was significant at the ninety-fifth percentile, indicating that momentum, if it exists at all, is concentrated in periods of strong market performance. Meanwhile, the lagged values of the exchange rate, oil, and gold provided no significant additional information about subsequent JSE returns at any of the quantiles examined. The authors note that this pattern is consistent with weak-form market efficiency, the idea that past market information should offer little systematic guidance about future returns, and they show that this limited persistence holds across both normal and extreme market conditions.

The downside risk analysis produced perhaps the most practically important findings. In the CAViaR models estimated at the five percent quantile, the autoregressive parameter was positive across all specifications, indicating that Value at Risk is persistent: once elevated, market risk tends to stay elevated for a time. The asymmetric slope specification also showed that negative market shocks affect downside risk differently from positive ones, consistent with the well-documented tendency of investors to react more strongly to losses. Backtesting supported the models: observed violation rates hovered near the nominal five percent level, and the Kupiec, Christoffersen independence, and conditional coverage tests did not reject their null hypotheses. Notably, adding the macroeconomic variables to the risk model barely improved it. The full CAViaR-X specification recorded the lowest quantile loss, at 0.5838 versus 0.5954 for the baseline, but the difference was small, suggesting that exchange rates, oil, and gold add little to short-term downside risk forecasting once past risk and past shocks are accounted for.

The copula analysis then revealed how dependence behaves at the extremes. The JSE and the rand–dollar exchange rate showed strong negative rank dependence, with a Kendall’s tau of minus 0.3422, but the selected Gaussian copula implied no asymptotic tail dependence in either direction. In other words, the two series move together strongly on average, yet simultaneous extreme movements are no more likely than independence would predict. The JSE–Brent relationship told a different story: the Student-t copula, chosen by the Akaike Information Criterion, indicated moderate positive rank dependence of 0.1746 and symmetric tail dependence of about 0.116 in both the lower and upper tails, meaning unusually large moves in oil and equities are more likely to coincide than a tail-free model would suggest. Gold showed the weakest link of all, with an insignificant Kendall’s tau of 0.0383 and a negligible estimated lower-tail dependence whose bootstrap confidence interval included values near zero.

For investors and policymakers, the implications are concrete. Exchange rate movements deserve close monitoring when assessing South African equity exposure, given their consistent association with returns across all market states. Brent crude oil conditions matter most when evaluating the risk of extreme joint comovements, which is relevant for portfolios holding both South African equities and global commodities. And the weak dependence between gold and the JSE cautions against assuming that gold exposure automatically provides protection against severe equity losses, despite South Africa’s status as a major gold producer. The authors also flag their study’s limitations: with only 215 monthly observations, roughly eleven data points fall in the five percent lower tail, which limits the precision of the extreme quantile and tail dependence estimates, and monthly data may miss shorter-term interactions between markets.

What the study ultimately demonstrates is that a single average relationship cannot describe how an emerging equity market responds to the world around it. The exchange rate matters everywhere in the distribution, oil matters most at the extremes, gold barely matters at all, and downside risk feeds on itself and on past shocks rather than on the macroeconomic variables that drive returns. For a market as exposed to global currents as South Africa’s, quantile-based and copula methods offer a way of seeing those currents with far greater resolution, and the authors suggest that future work with higher-frequency data and a broader set of variables could refine the picture further.

Subject of Research: Quantile regression and copula modeling of exchange rate, oil, and gold effects on South African stock returns and downside risk

Article Title: Quantile regression and copula-based analysis of risk and dependence in the South African stock market

Article References: Mkandla, P., & Chipepa, F. (2026). Quantile regression and copula-based analysis of risk and dependence in the South African stock market. Frontiers in Applied Mathematics and Statistics, 12, Article 1934050. https://doi.org/10.3389/fams.2026.1934050

Image Credits: AI Generated

DOI: 10.3389/fams.2026.1934050

Keywords: South African stock market, Johannesburg Stock Exchange, quantile regression, CAViaR, Value at Risk, copula models, tail dependence, exchange rate, Brent crude oil, gold prices, emerging markets, financial risk