This section is divided into the following sub-sections:
Section 4.1 A graphical representation and analysis of the returns of the sectors, depicting the trends.
Section 4.2. Descriptive statistics will be discussed to provide a summary and an understanding of the dataset.
Section 4.3. An assessment of the correlation between the sector index and the market index.
Section 4.4. An analysis of the correlation between the SA equity market and policy uncertainty.
Section 4.5. The stationarity of the data will be detected by making use of the ADF and KPSS tests.
Section 4.6. The conditional volatilities of the sectors and the market by performing ARCH-LM tests and GARCH models.
4.2. Descriptive Statistics
Table 2 provides a summary of the descriptive statistics of the daily returns of all the sectors during the chosen COVID-19 sample period. It can be deduced from
Table 2 that during the COVID-19 period, there were positive mean returns for all sectors, excluding the Industrials and Technology sectors, indicating that the South African stock market withstood the economic storm caused by the pandemic and that the sectors maintained positive returns over time. Additionally, the positive mean indicates that the daily prices of the indices increased over the observed period. On the contrary, although very small, the negative mean returns for the industrials and technology sectors point out that, on average, the two sectors had negative returns, which led to an overall loss again. This generally means the sectors were not performing well due to the effects of the pandemic and that they did not adapt to the shock that resulted from the pandemic.
When a sector’s median return is positive, it indicates that over 50% of its companies or data points had positive returns during the period under analysis.
Table 2 exhibits that over 50% of companies in all the sectors had positive returns during the COVID-19 pandemic period.
Table 2 reveals that the energy sector was the most volatile, with a value of 0.043, while the consumer staples sector had the lowest standard deviation of 0.014. Thus, it can be deduced that the energy sector is likely to have experienced larger fluctuations in stock prices relative to the other sectors. The high standard deviation can be a result of travel restrictions and lockdowns that were imposed in different countries, which decreased the demand for energy products, particularly oil. Conversely, the low standard deviation for consumer staples implies that the sector was less volatile and relatively stable, which may be because companies in this sector trade in essential goods and services, including food and drinks, among others.
From
Table 2, it can be deduced that the energy and technology sectors were the only two indices that exhibited positive skewness. This means that the returns are not symmetric, and instead, the sectors have small losses and few large gains. The positive skewness may mean that energy prices and stocks had periodic, notable recoveries despite overall poor performance, resulting in a few large gains. Additionally, some investors may have taken speculative bets on a recovery as oil prices plummeted. When these recoveries happened, they produced significant returns in an otherwise struggling industry, which further skewed the distribution positively. Similarly, cloud computing, remote work, and e-commerce tech companies benefited from the pandemic’s acceleration of digital technology use. As a result, several tech stocks saw significant gains, which caused the overall returns of the industry to skew positively. All the other sectors, including the JSE ALSI, deviated from zero and showed negative skewness during the COVID-19 pandemic. Financial returns with negative skewness are more likely to have extreme negative returns, which may indicate more downside risk.
Kurtosis is a statistical metric that measures the tailedness of a distribution, as this is often where the outliers occur (
DeCarlo, 1997). The kurtosis values for the JSE and all the sectors were observed to be leptokurtic, meaning that they did not follow a normal distribution but rather were fat-tailed during the pandemic. This means that the returns of the indices had more pronounced peaks or fluctuations. Finally, the Jarque–Bera test is a goodness-of-fit test that determines if the skewness and kurtosis of sample data are comparable to those of a normal distribution (
Koizumi et al., 2009). In contrast to the EMH, the high values of the Jarque–Bera statistic for all sectors offered additional evidence that the null hypothesis of normality could be rejected for all indices.
4.3. Correlation Between Each Sector and the Market
Portfolio diversification is important for every investor to cushion negative returns, and correlation is a metric often used when building diverse portfolios (
H. K. Baker et al., 2020). Thus, to spread risk, investors often use correlation to identify sectors or stocks that have negative or low correlations with each other so that when one stock is underperforming, the other stocks are not impacted.
Figure 2 reveals the relationship between different equity sectors and the JSE ALSI from 1 January 2020 to 31 March 2022. It can be deduced from
Figure 2 that all sectors have a positive correlation with the JSE ALSI, being a proxy of the entire equity market. Therefore, this implies that the performance of the sectors has a significant influence on the performance of the ALSI.
Notably, consumer staples, industrials, and telecommunications have a moderately positive correlation with the JSE ALSI. These sectors have an impact on the market, but not as much as the sectors that are more strongly correlated (basic materials, consumer discretionary, and financials). In contrast, the energy sector exhibits the lowest correlation with the JSE ALSI, suggesting that the sector performs largely independently of the overall market. Thus, it could be a strong option for portfolio diversification because it could not be as impacted by changes in the market as a whole.
Figure 2 also exhibits a low correlation between the health care sector and the JSE ALSI, which indicates that the former often moved independently of broader market movements during the pandemic. Regulation changes and public health crises may be some of the driving forces behind the healthcare sector. Since health care services and goods are necessities or non-cyclical, they are often in constant demand regardless of the state of the economy. Thus, the sector often performs better during economic downturns. Similarly, the technology sector also exhibits a low correlation with the overall market, which suggests that the sector is heavily influenced by industry-specific dynamics like innovation cycles, technology adoption, and consumer demand for tech products, and less by the broader market dynamics.
The correlation analysis is insightful, showing that the energy sector had the lowest correlation with the overall market, making it a useful diversification tool. Most sectors showed a weak negative correlation with policy uncertainty, contradicting global studies. In order to create a diversified portfolio, investors must take these correlations into consideration. With their low correlations to the ALSI, sectors like energy can aid in lowering the overall portfolio risk. On the other hand, although they might provide less diversity, sectors with strong correlations to the ALSI can also be used to support market-aligned strategies.
4.6. Diagnostics and Robustness Checks
To ensure the reliability of the GARCH family estimates, several diagnostic and robustness checks were performed.
Post-estimation ARCH-LM tests were conducted on the residuals to verify whether conditional heteroskedasticity remained. The null hypothesis of no ARCH effects was consistently rejected at conventional significance levels before model estimation, confirming the presence of volatility clustering and justifying the use of GARCH-type models. After estimation, the ARCH-LM tests showed no remaining ARCH effects, indicating that the models adequately captured volatility dynamics.
Standardized residuals and squared standardized residuals were examined through autocorrelation (ACF) and partial autocorrelation (PACF) plots. The absence of significant autocorrelation in residuals indicates that volatility shocks were well captured by the models. Jarque–Bera tests, however, confirmed departures from normality, which is common in financial return series. To account for this, robust standard errors were used in the estimation process.
To ensure robustness, three complementary models were estimated:
GARCH (1,1) for baseline persistence and clustering;
E-GARCH to capture asymmetries (leverage effects of good vs. bad news);
T-GARCH to explicitly model the impact of positive vs. negative shocks.
Across specifications, consistent patterns emerged: volatility persistence was high in all sectors, the Energy sector showed the strongest and longest-lasting volatility, and asymmetry effects were significant, with most sectors exhibiting stronger reactions to negative shocks. This cross-model consistency strengthens the robustness of the findings.
While the study focused on univariate models for sector-level clarity, alternative models such as multivariate GARCH (BEKK, DCC-GARCH) could capture interlinkages across sectors. However, given the study’s focus on sector-specific volatility behavior during COVID-19, the univariate framework provides clearer sectoral insights. Future work could extend the analysis by applying multivariate models to test for volatility spillovers and co-movements across sectors.
The persistence estimates (α + β) were consistently close to or above unity across all models, supporting the interpretation of prolonged volatility during COVID-19. The consistency of persistence across different specifications confirms the robustness of this result, particularly for the Energy and Consumer Staples sectors, which exhibited the highest persistence.
Based on the diagnostic tests and information criteria, the E-GARCH model emerges as the most suitable specification for the South African equity market during COVID-19, as it effectively captures the leverage effect and asymmetric responses to shocks, which were a defining feature of pandemic-induced volatility. While the GARCH (1,1) adequately explains baseline volatility clustering, it underestimates the asymmetric impact of bad news. The T-GARCH also highlights asymmetry, but its performance is weaker in several sectors compared to E-GARCH.
Unlike previous South African studies that focused mainly on aggregate market indices using standard GARCH models, this study contributes by providing a sector-level analysis with asymmetric GARCH models. The results demonstrate that volatility drivers differ substantially across sectors, with Energy exhibiting persistence dominated by positive news, in contrast to the rest of the market, where negative news drives volatility. This sectoral heterogeneity provides a novel insight for portfolio managers and policymakers.