Structural instability and volatility shifts in emerging-market banking equities: evidence from South Africa's big five banks

1 Introduction

Financial returns rarely evolve according to a stable data-generating process over long samples. Episodes such as pandemic shocks, monetary-policy tightening, inflation surprises, geopolitical uncertainty and capital-flow reversals can alter volatility, market liquidity and investor risk perception. Adarov [1] shows that financial cycles differ across countries and are shaped by macro-financial conditions. Potjagailo and Wolters [2] provide long-run evidence that global financial cycles have changed over time rather than followed a stable pattern. Wan et al. [3] show that return and volatility connectedness across global environmental, social and governance stock indices varies across time and frequency domains. These findings make structural instability an important empirical issue in financial-market analysis.

Banking equities are especially relevant because banks occupy a central role in credit intermediation, liquidity provision, payment systems and the transmission of financial shocks. Bank share prices reflect expectations about profitability, credit quality, interest rates, funding conditions, sovereign risk, regulatory pressure and macroeconomic stability. Chatterjee and Sing [4] show that market-based systemic-risk measures are useful for monitoring vulnerabilities in South African banks. Foggitt et al. [5] provide evidence that systemic-risk measurement can reveal banking-sector vulnerability in South Africa. Mashimbye and Fanta [6] show that systemic risk can intensify during crisis periods. These findings suggest that changes in banking equity volatility may reveal not only firm-specific developments, but also broader financial-sector stress.

South Africa provides a useful emerging-market setting for this analysis. The country has a developed equity market and a concentrated banking sector, but it has also faced weak growth, fiscal pressure, sovereign-risk concerns, exchange-rate volatility, electricity-supply disruptions and the financial effects of the COVID-19 pandemic. South African Reserve Bank [7] highlights vulnerabilities associated with sovereign-financial linkages, weak growth and the exposure of financial institutions to government debt. South African Reserve Bank [8] further notes that regulated financial institutions remain resilient despite persistent domestic and global risks. These conditions create an environment in which banking equity risk may shift across time rather than remain constant.

Recent South African studies have examined aggregate equity volatility, investor sentiment, market uncertainty and macro-financial connectedness. Mloyi and Vengesai [9] show that global risk aversion and domestic macroeconomic factors influence dynamic conditional correlations among South African financial markets. Naidoo et al. [10] find that investor sentiment helps explain stock-market volatility in Johannesburg Stock Exchange size-based indices. Ramakau et al. [11] show that South African equity-market volatility during COVID-19 contains both market-wide and sector-specific components. Maingo et al. [12] confirm the continued relevance of GARCH-family volatility modelling for the Johannesburg Stock Exchange All Share Index. However, less is known about structural instability in individual listed banking equities.

This gap matters because bank-level breaks may reveal risk adjustments that aggregate indices conceal. The paper does not claim novelty from documenting higher volatility during COVID-19. Its contribution is an integrated diagnostic framework that separates four dimensions of instability: changes in typical return magnitude, changes in high-intensity volatility, persistent unconditional-variance shifts, and bank-specific movements after common banking variation is removed.

Absolute and squared returns capture different features of risk. The robust ICSS κ² test assesses whether these changes amount to a persistent shift in unconditional variance. Common banking-factor analysis then examines whether the estimated breaks survive after shared movements are removed. Finally, placebo partitions and no-break BIC comparisons assess whether the selected regimes separate the data more effectively than random dates or a constant-parameter model.

The study has five objectives: (i) to detect breaks in absolute and squared log returns; (ii) to test unconditional variance stability using the robust ICSS κ² procedure; (iii) to describe distributional and scale changes across adjacent regimes; (iv) to identify shared cross-bank instability windows; and (v) to distinguish common banking movements from bank-specific instability.

2 Literature review

Financial return behavior is widely understood to be unstable across time, particularly in markets exposed to macroeconomic shocks, liquidity pressure and changing investor sentiment. Volatility clustering, heavy tails, excess kurtosis and abrupt changes in risk dynamics remain central features of financial return series. Although the early foundations of volatility modelling were established through the autoregressive conditional heteroskedasticity model of Engle [13] and the generalized autoregressive conditional heteroskedasticity model of Bollerslev [14], recent empirical work increasingly emphasizes that volatility should not be treated as stable over long samples. In this context, structural instability becomes important because an apparently persistent volatility process may partly reflect shifts between regimes rather than a single unchanged data-generating mechanism.

Recent international evidence confirms the importance of break-aware volatility modelling. Hasanov et al. [15] re-examine structural breaks in GARCH exchange-rate volatility models and show that models incorporating structural changes perform better than models that ignore instability. Chung et al. [16] study volatility forecasting under structural breaks in Latin American equity markets and show that neglecting structural breaks can overstate volatility persistence and weaken predictive accuracy. Their use of ICSS-type break detection and regime segmentation is particularly relevant to the present study because it supports the treatment of volatility breaks as an empirical feature that should be identified before long-sample risk behavior is interpreted.

These recent studies move the literature beyond the general observation that volatility changes over time, and instead show that explicitly accounting for breaks can improve the reliability of volatility modelling. These findings are reinforced by recent regime-aware studies. Erol and Dogan [17] apply least-squares breakpoint methods to the Istanbul stock market and identify a major change around March 2020 in a setting characterized by herding and severely negative macroeconomic fundamentals. Their study provides a close emerging-market comparator, but it focuses on an aggregate market index and behavioral dynamics rather than heterogeneous listed banks. Ding et al. [18] show that smooth-transition and Markov-switching specifications improve realized-volatility forecasting across international equity markets, illustrating the predictive value of regime-aware modelling.

At a broader emerging-market level, Benigno et al. [19] develop an endogenous regime-switching model of financial crises and show that crisis dynamics can be understood as state-dependent rather than as responses to unusually large shocks alone.

The methodological foundation for detecting structural breaks remains important. Bai and Perron [20] introduce a formal framework for estimating multiple structural breaks in linear models, while Bai and Perron [21] provide the computational procedures for dating and analyzing multiple structural changes. This framework is useful in the present paper because absolute returns and squared returns can be represented as transformed risk measures whose regime-specific mean levels may change across the sample. In volatility applications, Inclan and Tiao [22] introduce the Iterated Cumulative Sum of Squares procedure for detecting shifts in unconditional variance. These older sources are retained not as the main international literature, but as the statistical foundation for the break-detection procedures applied in this study.

South African equity-market evidence also supports the need for volatility models that allow instability. Babikir et al. [23] show that structural breaks affect GARCH-based modelling of stock-return volatility on the Johannesburg Stock Exchange. More recent evidence confirms that South African equity volatility remains an active empirical concern. Maingo et al. [12] model volatility in the Johannesburg Stock Exchange All Share Index using the family of GARCH models and show that volatility persistence and leverage effects remain important features of South African equity returns. Ramakau et al. [11] examine South African equity-market volatility during the COVID-19 period and show that volatility responses contain both market-wide and sector-specific components. Naidoo et al. [10] show that investor sentiment helps explain volatility behavior in Johannesburg Stock Exchange size-based indices.

Together, these studies indicate that South African equity-market risk is dynamic and that aggregate market behavior may not be sufficient for understanding risk at the firm level.

Related South African and applied risk-modelling studies also support the need to account for instability in financial-return behavior. Chifurira and Chinhamu [24] evaluate South Africa's market risk using an asymmetric power autoregressive conditional heteroskedastic model under heavy-tailed distributions, showing that local financial returns may exhibit asymmetry, heavy tails and changing risk dynamics. Basira et al. [25] apply long-memory volatility models to commodity returns and show that persistence in volatility is important for estimation and prediction. Similarly, Subramoney et al. [26] examine long-memory volatility models with heavy-tailed distributions for value-at-risk estimation. Although these studies do not directly estimate structural breaks in listed banking equities, they support the use of flexible risk-modelling frameworks when financial returns exhibit persistence, asymmetry and heavy tails.

The banking sector provides an especially important setting for structural-break analysis because bank share prices respond to both institution-specific information and broader financial-system conditions. Banks are exposed to credit risk, liquidity risk, funding conditions, sovereign-financial linkages, interest-rate changes and shifts in investor confidence. Chatterjee and Sing [4] show that market-based systemic-risk measures are useful for monitoring vulnerabilities in South African banks. Foggitt et al. [5] provide evidence that systemic-risk measurement can reveal banking-sector vulnerability in South Africa. More recently, Mashimbye and Fanta [6] show that systemic risk can intensify during crisis periods, while Sithole and Eita [27] highlight the role of asset volatility in the transmission of systemic risk within South Africa's banking sector.

This literature strengthens the motivation for analyzing listed banking equities separately rather than relying only on broad market indices.

Recent South African macro-financial studies further suggest that instability may arise from both domestic and external sources. Mloyi and Vengesai [9] show that global risk aversion and domestic macroeconomic factors influence dynamic conditional correlations among South African financial markets. Magubane [28] uses a Markov-switching framework to show that South African financial-cycle behavior is regime-dependent. The domestic financial system remains exposed to risks linked to sovereign-financial linkages, weak economic growth and institutional exposure to government debt [7]. Regulated financial institutions remain resilient, although global uncertainty and domestic vulnerabilities continue to shape the financial-stability outlook [8]. These conditions provide a strong empirical basis for expecting bank-equity volatility to shift across time rather than remain constant over a ten-year sample.

Alternative regime-based methods address related but distinct questions. Recent Markov-switching applications model volatility as evolving across latent states and use regime transitions to improve realized-volatility forecasting [18]. Endogenous regime-switching models similarly treat financial crises as state-dependent processes rather than as responses to unusually large shocks alone [19]. Structural-break-adjusted GARCH models instead focus on conditional-volatility dynamics while allowing observed instability to influence forecasting performance [15]. These approaches complement the present framework, which identifies transparent historical break dates in observed return-based risk measures and distinguishes transformed-return breaks, robust unconditional-variance shifts and residual bank-specific instability.

The preceding literature demonstrates that structural instability cannot be viewed as a single phenomenon. Rather, different statistical procedures capture different dimensions of instability. Building on this literature, the present study interprets structural instability as a layered process rather than a single event. A break in the mean of absolute returns is not equivalent to a break in squared returns because squared returns place greater weight on extreme observations. Moreover, a break in either transformation does not necessarily imply a persistent change in the unconditional variance of the original return series.

Common banking-factor analysis adds a further distinction. A break that remains after shared banking movements are removed provides stronger evidence of bank-specific adjustment than a break observed only in the raw transformation. The framework therefore separates changes in typical risk magnitude, extreme volatility intensity, unconditional variance and institution-specific instability. Agreement across procedures strengthens the evidence of broad instability. Disagreement is also informative because it identifies the statistical dimension in which the change occurs. This distinction matters for model recalibration: a temporary stress episode, a firm-specific adjustment and a persistent variance-regime change should not be treated as equivalent.

Four gaps motivate the study. South African research has concentrated mainly on aggregate indices, sector portfolios and systemic-risk measures rather than individual listed banks. Existing studies also rarely distinguish transformed-return breaks from robust variance shifts, assess whether breaks survive common-factor adjustment, or compare selected partitions with random and no-break alternatives. The present firm-level framework addresses these gaps by combining Bai–Perron segmentation, robust ICSS inference, common banking-factor analysis and supplementary partition-comparison checks.

3 Methods and research design

This section describes the statistical framework. Reproducible Python scripts were used for return construction, structural-break estimation, common banking-factor analysis, robust variance-stability testing, regime characterization, placebo assessment, break clustering and graphical presentation. Further computational implementation and reproducibility details are provided in Appendix A.

3.1 Return construction and risk transformations

Let P_{*i, t*} denote the daily closing price of banking equity i on trading day t, where i = 1,…, N and t= 1,…, T. The continuously compounded daily return is defined as

ri,t=100[ln(Pi,t)-ln(Pi,t-1)], t=2,…,T.(1)

ri,t=100ln(Pi,tPi,t-1).(2)

The factor (100) expresses returns in percentage form. The use of logarithmic returns is consistent with recent South African equity-volatility studies that model risk using return-based transformations rather than price levels [10–12].

The transformed-return process is defined as

yi,t(q)={|ri,t|,if q=A,ri,t2,if q=S,(3)

where q = A denotes absolute returns and q = S denotes squared returns. The daily log-return and transformed-risk measures used throughout the analysis are defined in Equations 1–3. This notation allows the same break-detection framework to be applied separately to changes in return magnitude and volatility intensity.

Throughout the paper, structural instability is used as the broad term for parameter changes over time. A structural break refers to an estimated discrete change in a regime-specific parameter. A volatility shift denotes a broader change in return-magnitude or volatility-intensity behavior, while a variance shift is reserved specifically for a statistically supported change in unconditional variance. The term regime refers to the segment between estimated break dates; it is not used interchangeably with a latent Markov state.

3.2 Break-aware stationarity assessment

Before applying the structural-break procedures, the stationarity of the daily log-return series is assessed using the Zivot–Andrews unit-root test. This test is useful because it allows for one endogenously determined structural break [29]. Since the study is based on returns rather than prices, the test is used as a preliminary check that the return series are suitable for break-detection analysis.

Δri,t=αi+βit+θiDUi,t(τ)+γiri,t-1+∑k=1pici,kΔri,t-k+εi,t,(4)

where r_{*i, t*} denotes the daily log return, Δr_{*i, t*} = r_{*i, t*}-r_{*i, t*−1}, p_*i* is the selected lag length and ε_{*i, t*} is an error term. The break dummy is defined as

DUi,t(τ)={1,t>Tτ,0,t≤Tτ,(5)

where τ∈ (0,1) is the unknown break fraction and Tτ is the corresponding break location. The null hypothesis is that the return series contains a unit root, H₀: γ_*i* = 0, while the alternative is stationarity around a broken intercept, H₁: γ_*i* < 0. The break date is selected endogenously as

τ^i=argminτtγi(τ).(6)

The break-aware stationarity specification is summarized in Equations Equations 4–6. The Zivot–Andrews test is used only as a supporting stationarity diagnostic. The Bai–Perron framework remains the main method for detecting multiple structural breaks, while the robust ICSS κ² procedure is used to test unconditional variance stability.

3.3 Multiple structural break framework

The multiple structural-break analysis is based on the Bai-Perron framework, which allows several unknown breakpoints to be estimated within a linear modelling setting [21]. This approach is preferred over the Chow test because the timing and number of volatility shifts are not specified in advance. The procedure is applied separately to absolute and squared returns to detect shifts in return magnitude and volatility intensity.

Let yi,t(q) denote the transformed return series for bank i. Suppose that the sample is divided into m+1 regimes by m unknown break dates,

0=T0<T1<T2<⋯<Tm<Tm+1=T.(7)

Within regime j, the transformed return process is represented by the intercept-only model

yi,t(q)=θi,j(q)+ui,t(q), t=Tj-1+1,…,Tj, j=1,…,m+1.(8)

Here, θi,j(q) is the regime-specific mean level of the transformed risk measure. A structural break occurs when θi,j(q)≠θi,j+1(q) for at least one adjacent pair of regimes. For absolute returns, this represents a change in return magnitude; for squared returns, it represents a change in volatility intensity.

For a fixed number of breaks m, the estimated break dates solve the global least-squares problem

(T^1,…,T^m)=argminT1,…,Tm∑j=1m+1∑t=Tj-1+1Tj(yi,t(q)-θ^i,j(q))2.(9)

The optimization is subject to the minimum-regime-size restriction

Tj-Tj-1≥⌊hT⌋, j=1,…,m+1,(10)

where h∈(0, 1) is the trimming parameter. This restriction prevents the procedure from selecting very short regimes driven by isolated extreme observations.

For a given partition, the regime-specific mean is

θ^i,j(q)=1Tj-Tj-1∑t=Tj-1+1Tjyi,t(q).(11)

The residual sum of squares associated with m breaks is

RSSi(q)(m)=∑j=1m+1∑t=Tj-1+1Tj(yi,t(q)-θ^i,j(q))2.(12)

The number of breaks is selected using the Bayesian Information Criterion of Schwarz [30], which penalizes unnecessary over-parameterization. The criterion is minimized as

BICi(q)(m)=Tln(RSSi(q)(m)T)+kmln(T),(13)

where k_*m* is the number of estimated parameters. For the intercept-only specification, the parameter count includes the m+1 regime-specific means and the m estimated break locations, so that k_*m* = 2m+1. The selected number of breaks is

m^i(q)=argminm∈MBICi(q)(m), M={0,1,…,M}.(14)

The multiple structural-break framework and BIC-based break-selection procedure are defined in Equations 7–14. In the empirical implementation, the maximum number of candidate breaks is set to five and the trimming parameter is fixed at h = 0.15 across banks and transformations. The same information criterion and trimming rule are used throughout to ensure comparability.

3.4 Common banking-factor analysis

To separate shared banking movements from institution-specific dynamics, a common factor is constructed separately for each bank. For bank i, the factor is the equal-weight average return of the other four banks:

f-i,t=1N-1∑j=1j≠iNrj,t,(15)

where N = 5. The bank under examination is excluded from its own factor to avoid mechanical overlap.

The following regression is estimated:

ri,t=αi+βif-i,t+εi,t.(16)

The common banking factor and corresponding residual-return specification are defined in Equations 15 and 16. The residual ε_{*i, t*} is the component of bank i's return that is not explained by contemporaneous movements in the other banks. The Bai–Perron procedure is then applied to |ε_{*i, t*}| and εi,t2.

Breaks that remain in the residual series provide stronger evidence of bank-specific instability. Breaks that disappear are more consistent with shared banking movements. Because the factor is constructed internally, it is not equivalent to an external FTSE/JSE banking or broad-market index. The common and bank-specific components are therefore interpreted cautiously.

The leave-one-bank-out factor provides a within-sample adjustment for shared contemporaneous movements among the five banking equities. It does not, however, constitute a complete decomposition of market-wide and idiosyncratic risk because an external banking-sector index or broad-market index is not included. The residual analysis is therefore interpreted as providing stronger, but not definitive, evidence of institution-specific adjustment.

3.5 Robust ICSS κ² variance-stability test

The original ICSS procedure of Inclan and Tiao [22] can over-reject variance stability under excess kurtosis and serial dependence in squared returns. Because these features are prominent in the present data, inference is based on the κ² statistic of Sansó and Aragó [31], which uses a heteroskedasticity- and autocorrelation-consistent estimate of the long-run variance of squared returns.

Let

εi,t=ri,t-r̄i, r̄i=1T∑t=1Tri,t,(17)

and

σ^i2=1T∑t=1Tεi,t2.(18)

Define z_{*i, t*} = εi,t2-σ^i2 and

Si,k=∑t=1kzi,t=∑t=1kεi,t2-kσ^i2.(19)

The long-run variance of z_{*i, t*} is estimated using a Bartlett-kernel HAC estimator,

ω^i2=γ^i,0+2∑ℓ=1L(1-ℓL+1)γ^i,ℓ,(20)

where

γ^i,ℓ=1T∑t=ℓ+1Tzi,tzi,t-ℓ.(21)

The Bartlett-kernel truncation lag, denoted by L, was selected using the sample-size-based rule

L=⌊4(T100)2/9⌋.(22)

For the present sample of T = 2,495 daily returns, this rule produced L = 8. The same bandwidth-selection rule was applied consistently across all five banking-equity return series.

The robust statistic is

κi2=max1≤k≤T|Si,k|Tω^i2.(23)

The null hypothesis is constant unconditional variance. At the 5% level, variance stability is rejected when κi2 > 1.358. The candidate location is

k^i=argmax1≤k≤T|Si,k|.(24)

The robust ICSS κ² variance-stability procedure is defined in Equations 17–24. The date associated with the maximum cumulative deviation is treated as a confirmed variance break only when the test rejects the null.

3.6 Post-estimation regime characterization and break clustering

After break detection, adjacent regimes are compared to describe how the estimated segments differ in distribution and scale. Because the break dates are selected to maximize between-regime separation, these tests are treated as post-estimation characterization rather than independent validation. Distributional differences are assessed using the Kolmogorov–Smirnov test [32, 33]. Let F_{*i, j*}(x) denote the distribution function of returns for bank i in regime j. The null hypothesis is

H0D:Fi,j(x)=Fi,j+1(x) for all x,(25)

against the alternative that the adjacent-regime distributions differ. The test statistic is

Di,j=supx|F^i,j(x)-F^i,j+1(x)|.(26)

Variance differences are assessed using the Fligner–Killeen test, which is robust to departures from normality [34]. Levene's test is used as a robustness-oriented alternative when appropriate [35]. For each bank, the reported characterization count is the number of adjacent-regime comparisons for which either the distributional test, the variance test, or both indicate statistically significant differences at the 5% level. Finally, detected break dates are grouped by calendar month to identify cross-bank clustering windows. Let Bi(q) denote the set of detected break dates for bank i and transformed series q. For each month s, the number of breaks is counted as

Ns(q)=∑i=1N∑b=1m^i(q)I(M(T^i,b(q))=s),(27)

where I(·) is an indicator function and M(T^i,b(q)) maps a break date to its calendar month. Months with several breaks across banks are described as shared instability windows, while isolated dates indicate less-synchronized firm-level adjustment. The common banking-factor analysis provides a within-sample adjustment for shared banking movements. It is not equivalent to an external FTSE/JSE market index and does not support causal attribution. The adjacent-regime comparisons and monthly break-clustering measure are defined in Equations 25–27.

3.7 Placebo partition and no-break model comparisons

To provide supplementary evidence on the strength of the selected Bai–Perron partitions, the estimated break specifications are compared with random admissible partitions and with the corresponding no-break models. These comparisons are not treated as fully independent breakpoint validation. Instead, they quantify the regime separation and relative model fit achieved by the selected partitions.

BSSi(q)=∑j=1m^i(q)+1ni,j(q)(ȳi,j(q)-ȳi(q))2,(28)

where ni,j(q) and ȳi,j(q) denote the size and mean of regime j, and ȳi(q) is the full-sample mean. Between-regime separation is measured using Equation 28. A larger value indicates stronger separation between regime-specific means.

For each bank and transformation, B = 5,000 random partitions are generated with the same number of breaks as the selected model and subject to a minimum regime length of 120 observations. The empirical placebo probability is

pi,pl(q)=1+∑b=1BI(BSSi,b(q)≥BSSi,obs(q))B+1.(29)

A small value indicates that the selected partition produces stronger regime separation than random break dates. In addition, the selected break specification is compared with the no-break model through

ΔBICi(q)=BICi(q)(0)-BICi(q)(m^i(q)),(30)

where a positive value favors the selected break model. The simulation uses a fixed random seed of 20260717 to ensure reproducibility. The improvement in BIC relative to the no-break model is defined in Equation 30.

3.8 Multidimensional instability profile

The study reports the underlying instability dimensions separately rather than combining them into a single composite score. This avoids arbitrary equal weighting and min–max normalization over only five banks, which would mechanically assign sample minima and maxima values of zero and one. Separate reporting preserves the interpretation of absolute-return breaks, squared-return breaks, robust variance-stability evidence and temporal clustering.

4 Results and discussion

This section presents the empirical results from the structural-break procedures described above. It begins with the data source and descriptive return features, followed by break detection in absolute returns, squared returns and robust unconditional-variance inference. It then reports post-estimation regime characterization, placebo and no-break robustness evidence, and monthly clustering of detected dates.

4.1 Data source and description

The dataset consists of daily closing prices for Standard Bank, FirstRand, Absa, Nedbank and Capitec, obtained from the IRESS Research Domain dataset. The common sample period runs from 27 January 2016 to 23 January 2026, yielding 2,496 daily price observations and 2,495 daily log returns for each bank after first differencing. The analysis is conducted on daily log returns and their transformations. This bank-level design helps reveal differences that may be hidden in aggregate market or sector indices.

Figure 1 shows that daily log returns fluctuate around zero, but with visibly time-varying variance. Calm periods are interrupted by clusters of large positive and negative movements, especially around 2020, providing preliminary evidence of volatility clustering. The timing and magnitude of these volatility bursts differ across banks, supporting the need for firm-level break-detection analysis.

Table 1 reports descriptive statistics and Jarque-Bera normality results for the daily log returns. Mean returns are close to zero across all banks, while the standard deviations, extreme values, negative skewness and positive excess kurtosis indicate volatile, asymmetric and heavy-tailed return distributions. Capitec records the widest return range and highest excess kurtosis, suggesting stronger sensitivity to unusually large shocks. The Jarque–Bera statistics reject normality for all banks, confirming that the return series exhibit stylised features that justify break-aware volatility analysis. After examining the descriptive properties of the return series, the Zivot–Andrews test is applied as a break-aware stationarity diagnostic. The results are reported in Table 2.

Table 1. Descriptive statistics and normality test of daily log returns.

Daily log returns are expressed in percentages. JB denotes the Jarque–Bera normality test.

Table 2. Zivot–Andrews unit-root test with one endogenous structural break.

Zivot–Andrews test applied to daily log returns with an intercept break; lags selected by AIC.

Table 2 shows that the unit-root null is rejected for all five daily log-return series at the 5% level. This indicates that the return series are stationary even when one endogenous break is allowed. The identified break dates are treated as preliminary single-break diagnostics, while the Bai–Perron framework remains the main multiple-break procedure.

4.2 Structural breaks in absolute returns

This subsection presents the structural breaks detected in the absolute-return series. Since absolute returns measure the size of daily movements irrespective of direction, breaks in this series indicate changes in the typical magnitude of bank-equity risk.

Figure 2 displays the detected absolute-return breaks for each bank, while Table 3 reports the break counts, Bayesian Information Criterion (BIC) values and estimated break dates.

Table 3. Structural breaks detected in the absolute-return series.

Absolute-return breaks indicate changes in the average magnitude of return movements.

Figure 2 and Table 3 show that all five banks experienced structural breaks in absolute returns. FirstRand records the largest number of breaks, indicating more frequent changes in the average magnitude of daily return movements. The clearest common pattern is the clustering of break dates around February and March 2020, consistent with a shared cross-bank stress window during the onset of COVID-19. Additional breaks in late 2020 suggest that the adjustment in banking equity risk occurred in phases rather than through a single shift. Breaks in 2016–2018 and 2022 further indicate that structural instability was not confined to the pandemic period, although these non-COVID breaks should be interpreted as contextual rather than causal evidence.

4.3 Structural breaks in squared returns

This subsection examines structural breaks in squared returns. Squared returns place greater weight on extreme observations and are therefore useful for detecting changes in volatility intensity.

Figure 3 and Table 4 present the structural breaks detected in the squared-return series. The break dates are more concentrated around 2020 than those obtained from absolute returns, indicating that the largest changes in volatility intensity occurred during the pandemic-related stress period.

Table 4. Structural breaks detected in the squared-return series.

Squared-return breaks indicate changes in volatility intensity.

All banks record at least two squared-return breaks, while Standard Bank and Nedbank record three. Most breaks occur between February 2020 and March 2021, indicating that high-volatility regimes were concentrated during and immediately after the initial pandemic shock. The squared-return evidence strengthens the absolute-return results by showing that 2020 was not only a period of larger daily movements, but also a period of intensified extreme-return behavior. The smaller number and tighter clustering of squared-return breaks suggest that squared returns mainly identify high-intensity volatility episodes, whereas absolute returns also capture broader shifts in the average magnitude of daily price changes. Because squared returns magnify extreme observations, their concentration around 2020 provides strong evidence of a crisis-period volatility shift.

4.4 Common banking-factor results

Table 5 reports the common banking-factor regressions. The factor explains 67.7%–72.6% of daily return variation for Absa, FirstRand, Nedbank and Standard Bank. Its explanatory power is lower for Capitec, with an R² of 38.3%.

Table 5. Common banking-factor regression results.

Table 6 reports the selected breaks in absolute and squared residual returns.

Table 6. Breaks in common-factor-adjusted residual returns.

Several early-2020 breaks remain after common-factor adjustment. The pandemic-period instability was therefore not explained entirely by contemporaneous movements in the other banks. A second cluster appears in August–September 2021, indicating renewed heterogeneity after the common component is removed.

Capitec differs from the other banks because the no-break model is selected for squared residual returns. Its raw squared-return instability therefore appears to be associated more closely with shared banking movements than with a persistent bank-specific change in volatility intensity. Overall, clustering in the raw transformations identifies shared timing, whereas residual breaks provide stronger, although not definitive, evidence of institution-specific adjustment after contemporaneous movements in the other four banks have been controlled for.

The common-factor results should be interpreted with two qualifications. First, the factor is constructed internally from the returns of the remaining four banks and is therefore not equivalent to an external banking-sector or broad-market factor. Second, the regression assumes a constant full-sample factor loading, β_*i*. If a bank's exposure to shared banking movements changes over time, some residual break patterns may partly reflect changes in factor sensitivity rather than purely idiosyncratic instability.

4.5 Robust variance-stability results

Table 7 reports the robust ICSS κ² variance-stability results. A candidate date identifies the largest cumulative deviation in squared demeaned returns, whereas a confirmed break requires the robust statistic to exceed the 5% critical value of 1.358.

Table 7. Robust ICSS κ² variance-stability results.

The null hypothesis is constant unconditional variance. A candidate date is interpreted as a confirmed variance break only when κ² > 1.358. Capitec's candidate date is therefore not treated as a confirmed variance break.

The test rejects the null hypothesis of constant unconditional variance for Standard Bank, FirstRand, Absa and Nedbank. Their statistics range from 1.5419 to 1.8816, all exceeding the 5% critical value of 1.358. Capitec records a statistic of 0.8839, and the null hypothesis of constant unconditional variance is therefore not rejected for that bank.

The confirmed variance-break dates are concentrated between November 2020 and February 2021. Standard Bank records a confirmed break on 21 December 2020, FirstRand on 11 January 2021, Absa on 30 November 2020 and Nedbank on 12 February 2021. These dates broadly overlap with the later stages of the pandemic-related instability windows identified in the absolute- and squared-return analyses.

Capitec also records its largest cumulative deviation on 21 December 2020. However, because its robust statistic remains below the critical value, this date is treated only as a candidate location and not as a confirmed unconditional-variance break.

The robust ICSS evidence therefore supports persistent unconditional-variance instability for four of the five banks. This strengthens the Bai–Perron results for Standard Bank, FirstRand, Absa and Nedbank by showing that their transformed-return breaks are accompanied by statistically supported changes in unconditional variance. Capitec presents a different pattern: it exhibits breaks in absolute and squared returns, but the robust variance-stability test does not confirm a persistent unconditional-variance shift.

4.6 Structural break counts

Figure 4 summarizes the structural break counts across the Big Five South African banking equities. The figure provides a compact comparison of the number of breaks detected for each bank and helps identify which institutions experienced more frequent changes in risk behavior.

FirstRand records the largest number of absolute-return breaks, while Standard Bank and Nedbank record the largest number of squared-return breaks. The robust ICSS κ² test confirms one unconditional-variance break for Standard Bank, FirstRand, Absa and Nedbank, whereas no confirmed robust variance break is recorded for Capitec. The banks therefore differ in both the frequency and form of structural instability. Capitec exhibits transformed-return breaks without a confirmed persistent variance shift, while the remaining four banks display evidence across both transformed-return and unconditional-variance diagnostics.

4.7 Post-estimation regime characterization and break clustering

After the breakpoints are identified, adjacent regimes are compared to determine whether the estimated breaks correspond to meaningful changes in return behavior. Table 8 summarizes the number of significant distributional and scale differences across adjacent regimes.

Table 8. Post-estimation characterization of adjacent-regime differences.

KS denotes the Kolmogorov–Smirnov distributional comparison. “Total significant comparisons” counts adjacent-regime comparisons with at least one significant distributional or variance difference at the 5% level.

Table 8 shows that all five banks exhibit significant adjacent-regime differences. FirstRand records seven significant adjacent-regime comparisons, the largest count among the five banks. Standard Bank, Absa, Nedbank and Capitec also show substantial post-estimation differences, with most adjacent regimes differing significantly in variance and/or distributional behavior. These comparisons show that the estimated segments differ in distribution and/or scale. They are interpreted as descriptive characterization rather than independent proof of the selected break dates.

4.8 Placebo and no-break robustness results

Table 9 reports the random-partition placebo assessment and the improvement in BIC relative to the no-break model. For every bank and both transformations, none of the 5,000 random admissible partitions produces a between-regime sum of squares as large as the observed partition. With the finite-simulation correction in Equation 29, the empirical probability is therefore 1/5001 ≈ 0.0002 in every case.

Table 9. Placebo-partition and no-break model assessment.

Each placebo assessment uses 5,000 random partitions with the selected number of breaks and a minimum regime length of 120 observations. ΔBIC =BIC(0)-BIC(m^); positive values favor the selected break model.

The observed partitions achieve substantially greater between-regime separation than the randomly generated admissible partitions. The BIC improvements are also positive throughout, ranging from 99.0456 for Capitec squared returns to 413.2016 for Nedbank absolute returns. These results provide supplementary partition-comparison evidence in favor of the selected break specifications relative to random-date and no-break alternatives. However, the placebo results are not interpreted as fully independent validation of the estimated break dates. The Bai–Perron procedure selects partitions that optimize within-regime fit and therefore maximize between-regime separation for a given number of breaks. Some superiority over randomly generated partitions is consequently expected. The placebo analysis is therefore treated as a calibration of the magnitude of regime separation, while the BIC comparison summarizes the relative fit of the selected break model against the constant-parameter alternative.

Table 10 groups detected break dates by calendar month to distinguish shared clustering windows from less-synchronized bank-level breaks. The strongest transformed-return clusters occur in 2020, particularly around February, March, September, November and December. Confirmed robust ICSS variance breaks are concentrated from November 2020 to February 2021, indicating that persistent variance changes emerged during the later stages of the broader pandemic-related instability window. The non-pandemic transformed-return breaks in 2016–2018 and 2022 should be interpreted as statistical evidence of changes in return behavior rather than causal proof of specific events. They may reflect domestic macro-financial pressure, monetary-policy repricing, investor sentiment, electricity-supply disruptions, regulatory developments, bank-specific news or broader emerging-market risk conditions. Their presence is nevertheless important because it shows that bank-equity instability was not limited to COVID-19.

Table 10. Monthly clustering of detected transformed-return breaks and confirmed robust ICSS variance breaks.

Break dates are grouped by calendar month to identify cross-bank clustering windows across the Big Five South African banking equities. Robust ICSS dates are included only where the κ² statistic exceeds the 5% critical value of 1.358. Candidate locations associated with a non-rejection decision are excluded. Clustering remains descriptive and does not formally decompose market-wide and bank-specific components.

4.9 Economic context of the detected instability windows

The detected dates are interpreted as statistical break locations and not as formal event-study estimates. Nevertheless, placing them within broad macro-financial periods helps explain their practical relevance. The breaks in 2016–2018 occurred during a period of weak domestic growth, heightened sovereign-risk concerns, political uncertainty and changing expectations about interest rates and fiscal sustainability. Because these dates differ across banks, they are more consistent with a mixture of common domestic pressure and heterogeneous institution-level repricing than with a single uniform sector event.

The strongest clustering in February and March 2020 coincides with the global escalation of COVID-19 uncertainty and the rapid repricing of financial assets before and during the initial South African containment measures. The additional September–November 2020 breaks are consistent with a multi-stage adjustment process involving the reopening of economic activity, reassessment of credit losses, changing policy support and revisions to bank earnings expectations. The factor-adjusted residual results show that several early-2020 changes remain after contemporaneous common banking movements are removed, suggesting that the shared shock was transmitted differently across institutions.

The 2022 Absa absolute-return break occurred during a broader period of accelerating inflation, global monetary-policy tightening, exchange-rate pressure and severe domestic electricity-supply constraints. These conditions can affect banks through funding costs, borrower repayment capacity, credit-growth expectations and investor risk premia. The date should therefore be viewed as economically plausible contextual evidence rather than proof that any one factor caused the break.

Regulatory developments, including the continuing implementation and refinement of Basel capital, liquidity and loss-absorbing requirements, may also influence bank-equity valuation over time. However, such reforms are gradual and often overlap with macroeconomic developments. The present design cannot identify a discrete Basel-related causal effect, and no break is attributed exclusively to regulation. Overall, the economic interpretation is deliberately cautious: temporal alignment supports risk-monitoring relevance, while causal attribution requires a dedicated event-study or structural macro-financial model.

4.10 Multidimensional bank-level instability profile

The separate diagnostics show that no single measure captures every form of instability. FirstRand records the largest number of absolute-return breaks, while Standard Bank and Nedbank record the largest number of squared-return breaks. The robust ICSS κ² procedure confirms unconditional-variance instability for Standard Bank, FirstRand, Absa and Nedbank, but not for Capitec.

Capitec's results illustrate the importance of separating transformed-return breaks from persistent unconditional-variance shifts. Although its absolute and squared returns contain statistically selected breaks, its robust ICSS statistic remains below the critical value. Structural instability should therefore be interpreted as multidimensional rather than reduced to a single bank ranking or diagnostic outcome.

Overall, the evidence indicates heterogeneous bank-level adjustment within several shared instability windows. Break dates may be used as diagnostic triggers for model recalibration, stress-window definition and closer institution-specific monitoring, but temporal clustering alone should not be interpreted as a formal market-factor decomposition.

5 Conclusion

This study examined structural instability in the Big Five South African banking equities using daily prices over a common ten-year period. The empirical framework combined Bai–Perron multiple-break estimation for absolute and squared returns, the robust ICSS κ² variance-stability test, post-estimation regime characterization and monthly clustering. The design distinguishes changes in typical return magnitude, changes in high-intensity volatility and persistent shifts in unconditional variance rather than treating them as interchangeable manifestations of one process.

All five banks exhibit structural breaks in absolute and squared returns. The strongest cross-bank clustering occurs around February and March 2020, with further shared windows in September and November 2020. These dates are temporally consistent with successive phases of pandemic-related financial stress, but the analysis does not claim formal causal attribution. Additional breaks in 2016–2018 and 2022 indicate that transformed-return instability was not confined to COVID-19. FirstRand records the largest number of absolute-return breaks, while Standard Bank and Nedbank record the largest number of squared-return breaks.

A central methodological finding is that the robust ICSS κ² test rejects unconditional variance stability for Standard Bank, FirstRand, Absa and Nedbank, but not for Capitec. The confirmed variance-break dates are concentrated between November 2020 and February 2021, broadly overlapping with the later pandemic-related instability windows identified by the Bai–Perron analysis. These findings show that transformed-return breaks and unconditional-variance shifts are related but not interchangeable. For four banks, evidence from absolute returns, squared returns and robust variance testing points to instability across several statistical dimensions. Capitec, however, exhibits transformed-return breaks without a confirmed persistent unconditional-variance shift. The selected transformed-return partitions also outperform 5,000 random admissible partitions and the corresponding no-break models in every case, providing supplementary evidence on regime separation and relative fit.

For practice, bank-level break dates can serve as diagnostic triggers for volatility-model recalibration, stress-window construction, portfolio-risk review and intensified supervisory monitoring. Heterogeneity across banks cautions against relying exclusively on aggregate market indicators or applying a single risk adjustment uniformly across institutions. Monthly clustering remains descriptive, but the common banking-factor analysis provides additional evidence on whether breaks persist after shared banking movements are removed.

The study is limited to five listed South African banks and excludes Investec and unlisted institutions. The common banking factor is constructed internally from the remaining four banks rather than from an external FTSE/JSE banking-sector or broad-market index. The resulting residual analysis therefore provides a within-sample adjustment for shared banking movements, but it does not constitute a complete market-factor decomposition. The factor regressions also assume constant full-sample loadings, although banks' exposures to shared market movements may themselves vary over time. Although the adjacent-regime comparisons are descriptive, the placebo and no-break comparisons provide supplementary evidence on the regime separation and relative fit achieved by the selected partitions. Because the Bai–Perron partitions are selected through fit optimization, the placebo results should not be interpreted as fully independent confirmation of the estimated break dates.

Future research may incorporate an external market or banking-sector factor and extend the analysis through structural-break-adjusted GARCH, Markov-switching, hidden Markov and Bayesian change-point models. These extensions would allow latent-state dynamics, transition uncertainty, volatility persistence and forecasting performance to be examined directly.

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Supplementary material

The Supplementary Material for this article can be found online at: https://www.frontiersin.org/articles/10.3389/fams.2026.1922013/full#supplementary-material

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Footnotes

Edited by: Yu Mu, Libero Capital, United States

Reviewed by: Raphael Tabani Mpofu, University of South Africa, South Africa

Derese Teklie, Istanbul Technical University, Türkiye