The Weakest Link: Sibling Dynamics and Bank Failures in Multi-Bank Holding Companies

Abstract

This paper examines bank failures during the subprime mortgage crisis, emphasizing sibling dynamics within multi-bank holding companies (MBHCs). While traditional risk indicators effectively predict failures for one bank holding companies (OBHCs), they exhibit limited explanatory power for MBHCs, where internal capital markets and interdependencies across affiliates shape risk outcomes. We extend the standard failure framework by incorporating group-level characteristics that capture sibling network structure and the distribution of risk across affiliates. Using pre-crisis data from 2006 to 2007, we show that group structure significantly influences failure risk. Larger sibling networks reduce individual bank failure risk through diversification, while greater size dispersion across affiliates increases vulnerability by constraining internal resource allocation. Beyond these aggregate effects, we introduce a weakest link approach that identifies the most distressed affiliate based on extreme tail risk in capitalization, asset quality, liquidity, earnings, and income volatility, capturing organizational fragility that aggregate measures miss. Concentrated vulnerabilities at a single affiliate significantly amplify failure risk throughout the holding company, even after controlling for traditional bank-level fundamentals and parent-level characteristics. These findings, derived from the 2007–2010 crisis, a severe stress test of holding company structures, identify organizational dynamics: resource competition among siblings and concentrated vulnerabilities at the weakest affiliate. Supervisory frameworks should explicitly account for within-group interdependencies rather than relying solely on individual bank metrics or aggregate indicators when monitoring bank holding company structures.

1. Introduction

Why do traditional bank failure models—proven effective for standalone institutions—perform poorly for banks affiliated with holding companies? The answer lies in what these models ignore.

A substantial body of research has established that bank-specific characteristics predict failure risk with considerable accuracy for standalone institutions. Estrella et al. (2000) demonstrate that capital ratios predict bank failures up to two years in advance, with the equity-to-assets ratio achieving classification accuracy above 80% for standalone banks. Cole and White (2012) extend this framework for the 2007–2010 crisis, showing that traditional measures of asset quality (nonperforming loans, loan loss reserves), capital adequacy, and funding stability (brokered deposits) significantly predict failure risk. Berger and Bouwman (2013) confirm that capital’s protective effect is most pronounced during crises, with well-capitalized banks experiencing failure rates 5–7 percentage points lower than poorly capitalized peers. Wheelock and Wilson (2000) establish that these relationships hold across different regulatory regimes and time periods, cementing the CAMELS framework as the standard approach to failure prediction. DeYoung and Torna (2013) show that nontraditional banking activities—such as heavy reliance on brokered deposits—significantly increased failure risk during the 2007–2010 crisis, using the traditional CAMELS framework.

However, these models were developed and tested primarily on standalone banks or institutions with simple organizational structures. In the United States, a large share of commercial banks operate within holding company structures where sibling dynamics, internal capital markets, and resource competition can fundamentally alter the relationship between bank characteristics and failure risk (Federal Reserve, 2008; Avraham et al., 2012). These organizational structures create interdependencies that standard failure models do not capture. Resources can flow across affiliates, parents may intervene selectively to support distressed subsidiaries, and the performance of sibling banks can influence each affiliate’s access to internal capital. Consequently, traditional predictive models can lose explanatory power for banks embedded in complex holding company structures, where individual bank characteristics may become less tightly linked to failure outcomes.

This organizational complexity persists in contemporary banking, with the vast majority of U.S. commercial banks continuing to operate within holding company structures as of 2023 (Federal Deposit Insurance Corporation, 2023). While industry consolidation has reduced the absolute number of institutions, the multi-bank organizational form remains prevalent among large regional banks and community banking organizations. Large holding companies operate networks of multiple bank charters, facing the same fundamental challenge: how to allocate finite parent resources when multiple subsidiaries require simultaneous support during stress. The structural distinction between one bank holding company (OBHC) and MBHCs thus remains highly relevant for understanding bank stability and informing supervisory policy in the modern banking environment.

Our empirical analysis focuses on the 2007–2010 subprime mortgage crisis as a natural stress test of MBHC organizational structures, for methodological reasons that strengthen the identification of organizational dynamics. This concentrated four-year window provides both the statistical power necessary for multi-level analyses and a homogeneous underlying shock (real estate credit deterioration) that enables clean identification of how holding company structure mediates traditional risk factors. The mechanisms we identify—how finite parent resources are allocated when multiple subsidiaries require simultaneous support, and how concentrated vulnerabilities at one affiliate constrain support available to others—represent structural features of the multi-bank organizational form rather than artifacts of the specific crisis studied. While the precise magnitudes we estimate reflect 2007–2010 crisis conditions and pre-Dodd–Frank regulation, the fundamental resource allocation challenge persists in modern MBHCs regardless of regulatory regime or crisis type, as illustrated by resource allocation questions raised during the 2023 Silicon Valley Bank episode.

The theoretical foundations for understanding resource allocation within multi-unit organizations were established by Stein (1997), who demonstrates that internal capital markets can improve efficiency by reallocating resources to higher value uses but can also create inefficiencies when allocation decisions reflect political power rather than economic merit. Campello (2002) provides early evidence, showing that small banks within holding companies exhibit different responses to monetary policy shocks than standalone banks, indicating active internal capital reallocation. Building on this foundation, a growing empirical literature has begun to unpack how affiliation influences bank stability during crises, revealing important mechanisms through internal capital markets.

Ashcraft (2008) provides foundational evidence that MBHC affiliation reduces failure risk relative to standalone banks, attributing this to geographic diversification and resource pooling advantages. Raykov and Silva-Buston (2020) show these benefits are particularly pronounced during financial shocks, when parents actively reallocate capital to support distressed subsidiaries—increasing capital injections by an average of 15–25% during crisis periods. Wang et al. (2022) establish that this support is institutionalized through the source of strength regulation, which requires parents to serve as a financial backstop, leading to observable adjustments in capital structure and liquidity provision under stress.

However, this support is neither uniform nor unlimited. Ozdemir and Altinoz (2018) demonstrate that within holding companies, the largest banks receive disproportionate assistance during crises, suggesting resource allocation reflects strategic priorities rather than equalizing risk across all affiliates. Matvos and Seru (2014) show that internal capital markets in diversified conglomerates enable resource reallocation during financial market dislocation, but this reallocation can amplify rather than mitigate distress when parent resources are constrained. The stabilizing effects documented by Lu and Whidbee (2013) for the subprime crisis and Argimón et al. (2018) for monetary policy shocks thus depend critically on parent capacity and the distribution of distress across affiliates.

While this research establishes that parent capacity shapes affiliate outcomes, it leaves a complementary dimension unexplored: how do sibling characteristics and organizational fragility affect individual bank failure risk beyond what parent support can explain? When multiple affiliates compete for finite parent resources, does the presence of severely distressed siblings constrain support available to healthier banks? Do concentrated vulnerabilities at one affiliate create spillovers throughout the holding company, even when the parent possesses adequate aggregate resources? Moreover, existing regulatory frameworks often treat affiliated banks as independent entities (Rosen, 2003), potentially overlooking both parent-to-subsidiary linkages and lateral sibling interdependencies. Existing studies focus almost exclusively on parent-to-subsidiary flows, leaving sibling-to-sibling dynamics and the role of the weakest affiliate unexplored.

To capture how concentrated vulnerabilities propagate through holding companies, we draw on the weakest link principle from network and operations theory (Allen & Gale, 2000; detailed in Section 2.3), which holds that system performance is disproportionately influenced by the weakest component when units are interdependent (Snyder et al., 2016). We adapt this framework to the intra-group context: when multiple banks within a holding company compete for finite parent resources, the most distressed affiliate may disproportionately constrain support available to healthier siblings, or concentrated vulnerabilities at one affiliate may signal broader governance or risk management weaknesses throughout the organization. This represents a distinct mechanism from simple aggregation of sibling risks—it posits that the distribution of risk across affiliates, particularly the presence of extreme tail risk at any single affiliate, matters beyond the group’s average risk profile. Operationalizing this principle requires extending existing models of parent–subsidiary relationships to explicitly account for lateral sibling dynamics and concentrated tail risks.

This study complements the parent-centric literature by incorporating sibling-level dynamics and organizational fragility into bank failure analysis. We introduce three complementary approaches. First, we extend the traditional CAMELS framework with group-level characteristics capturing the size and structure of sibling networks, including measures of risk dispersion and size dispersion across affiliates. Second, building on Houston et al. (1997) and Jeon and Wu (2014), we develop a “sibling effect” framework that examines how one affiliate’s resource demands constrain support available to others within the context of limited parent capacity. Third, we apply a “weakest link” approach that identifies whether the most vulnerable affiliate—measured across five dimensions of financial distress—disproportionately influences failure risk throughout the holding company, even after controlling for parent-level characteristics and aggregate group conditions. Building on established evidence of parent-to-subsidiary capital reallocation (Campello, 2002; Ashcraft, 2008; Wang et al., 2022), we examine its consequences for system-wide failure risk within MBHCs.

Using pre-crisis data (2006Q1–2007Q4) and bank failures during 2007–2010, we estimate logit models that decompose failure risk into individual bank fundamentals, group-level characteristics, and concentrated vulnerabilities. This approach allows us to assess not only whether MBHC affiliation matters, but specifically how it matters: through diversification benefits, resource competition, or spillovers from distressed affiliates operating within parent resource constraints.

The empirical analysis reveals several key findings. First, traditional CAMELS indicators perform well in predicting failures for OBHCs but are significantly less effective for MBHCs, highlighting the importance of considering group-level dynamics. Second, group characteristics substantially improve model explanatory power, with larger sibling networks providing diversification benefits that reduce failure risk, while size dispersion among siblings increases vulnerability. Third, the weakest link approach demonstrates that the most vulnerable affiliated bank within an MBHC significantly influences the failure risk of other banks in the group, supporting the hypothesis that systemic risk in MBHCs is shaped by the weakest member in addition to parent capacity and aggregate group resources. These findings have important implications for bank regulation, suggesting that supervisory frameworks should explicitly account for sibling dynamics and group-level risks alongside parent-level oversight to more accurately assess and mitigate systemic vulnerabilities in the banking sector.

2. Methodology

This study employs three complementary approaches to assess bank failure risk within MBHCs: traditional bank-level measures, group-level characteristics, and a weakest link framework that identifies concentrated vulnerabilities at the most distressed affiliate. Appendix C provides a summary table comparing these three approaches along key dimensions. The sections that follow describe our data sources, variable construction, and estimation strategy.

2.1. Data Sources and Sample Construction

This study integrates data from three distinct regulatory sources to construct a comprehensive dataset capturing both individual bank characteristics and holding company structure. The first source is the Consolidated Reports of Condition and Income (Call Reports) filed quarterly by all federally insured commercial banks. Call Reports provide detailed balance sheet and income statement data at the individual bank level, including the CAMELS indicators that form our baseline failure prediction framework. We obtain Call Reports for all U.S. commercial banks from 2006Q1 through 2007Q4 from the Federal Financial Institutions Examination Council (FFIEC) Central Data Repository.

The second source consists of FR Y-9LP (Parent Company Only Financial Statements for Large Holding Companies) and FR Y-9SP (Parent Company Only Financial Statements for Small Holding Companies) reports filed quarterly by bank holding companies. These reports provide information on holding company structure, including the number and identity of all affiliated banks and nonbanks, as well as consolidated financial data at the parent level. We obtain FR Y-9LP and FR Y-9SP data from the Federal Reserve Bank of Chicago’s website for the same 2006Q1–2007Q4 period. The FR Y-9 series is less commonly used in banking research than Call Reports, making our integration of both data sources a distinctive contribution.

The third source is the FDIC Failed Bank List, which identifies all banks whose deposits were insured by the FDIC and that failed between 1 January 2007 and 31 December 2010. Bank failure is defined as closure by federal or state banking regulatory agencies, with the FDIC appointed as receiver. The Failed Bank List provides the bank name, location, closing date, and FDIC certificate number for each failed institution. We accessed this data in January 2026 and manually matched failed banks to our Call Report sample using FDIC certificate numbers and bank charter information.

We merge the three data sources using stable regulatory identifiers. Call Report bank observations are linked to holding company structure in the FR Y-9 data using the bank’s RSSD ID and the parent holding company’s RSSD ID reported in the Call Reports. Failure outcomes are merged from the FDIC Failed Bank List using FDIC certificate numbers. All covariates are constructed from the pre-crisis window 2006Q1–2007Q4 (averaged over available quarters), and failures are defined over 2007–2010, which ensures predictors are measured before outcomes. The match rate between Call Reports and FR Y-9 filings is high; unmatched observations primarily reflect institutions whose parents do not file the relevant FR Y-9 forms or cases with incomplete identifiers, and these are excluded. To keep group measures well defined, we exclude banks that change holding company affiliation during 2006–2007. For data quality, we require non-missing values for the core CAMELS indicators, and we compute group-level dispersion measures only when at least 80% of a holding company’s bank subsidiaries have usable Call Report matches. Appendix A provides additional variable construction details, and Appendix B presents details on sample composition.

By combining these three data sources, the study captures both the micro-level characteristics of individual banks and the macro-level dynamics of BHCs, enabling a nuanced investigation into the interplay between bank-specific vulnerabilities and sibling interactions within MBHCs. This integration of datasets provides a distinctive contribution to the literature, as studies using Call Reports alongside BHC-specific data remain relatively uncommon, particularly in the context of bank failures and group-level risk dynamics.

We focus on the 2007–2010 crisis period for several compelling reasons.

Table 1. U.S. bank failures by year (2001–2025).

Period	Number of Failures	% of Total 2001–2025	Cumulative %
2001–2006	10	1.80%	1.80%
2007	3	0.50%	2.35%
2008	25	4.50%	6.86%
2009	140	25.10%	32.13%
2010	157	28.10%	60.47%
2011	92	16.50%	77.08%
2012	51	9.10%	86.28%
2013	24	4.30%	90.61%
2014	18	3.20%	93.86%
2015	8	1.40%	95.31%
2016–2022	17	3.00%	98.38%
2023	5	0.90%	99.28%
2024–2025	4	0.70%	100.00%
2007–2010 Total	325	58.20%
Total (2001–2025)	554	100.00%

Note: Data from the FDIC Failed Bank List (accessed on 9 January 2026). The 2007–2010 period, highlighted in bold, represents the acute phase of the subprime mortgage crisis and accounts for 325 of 554 failures (58.66%) over the 25 years. No failures occurred in 2005, 2006, 2018, 2021, and 2022.

demonstrates the extraordinary temporal concentration of bank failures during this window: the four years from 2007 to 2010 account for 325 failures. The peak occurred in 2009–2010, when 297 banks failed—more than half of all failures in a quarter-century. This concentration reflects the acute phase of the subprime mortgage crisis, when systemic stress on the banking sector was most severe. After 2010, failures declined sharply to 92 in 2011 and continued declining to single digits in most subsequent years, with no failures whatsoever in 2018, 2021, and 2022.

This concentrated crisis period provides an ideal setting to examine how MBHC structures respond to extreme financial stress, functioning as a crisis stress test, when internal capital markets and resource allocation mechanisms face their greatest test. The homogeneity of the underlying economic shock—widespread deterioration in real estate asset quality—reduces confounding factors that would arise from pooling failures across different macroeconomic environments. For instance, the five failures in 2023 (including Silicon Valley Bank and Signature Bank) were driven by fundamentally different mechanisms: interest rate risk and rapid deposit flight in a rising-rate environment, rather than the credit quality deterioration that characterized 2007–2010. Restricting our analysis to the 2007–2010 period thus ensures we are studying a cohesive crisis episode where sibling dynamics within MBHCs operate under similar stress conditions.

2.2. Standard Variable Construction

Our empirical approach builds on the CAMELS framework, which evaluates bank safety and soundness across six dimensions: capital adequacy, asset quality, management quality, earnings, liquidity, and sensitivity to market risk. We construct bank-level variables corresponding to each CAMELS component and extend this framework with group-level characteristics capturing sibling network structure and concentrated affiliate vulnerabilities.

2.2.1. Dependent Variable

Failure is a binary indicator equal to 1 if a bank failed between 2007 and 2010, as identified in the FDIC Failed Bank List, and 0 otherwise. Bank failures are defined as closures by federal or state banking regulatory agencies where the FDIC is appointed as receiver.

2.2.2. Bank-Level Control Variables (CAMELS)

All bank-level variables are computed using quarterly Call Report data and averaged over the pre-crisis period 2006Q1–2007Q4 to capture banks’ financial condition immediately before the crisis intensified.

Table 2. Descriptive statistics for the MBHC sample.

	N	Mean	SD	Min	Max
Failure	1490	0.07	0.38	0.00	1.00
Equity	1490	0.12	0.10	0.00	1.00
LLR	1490	0.00	0.00	0.00	0.05
NPA	1490	0.01	0.02	0.00	0.23
Securities	1490	0.19	0.15	0.00	0.99
BD	1490	0.03	0.07	0.00	0.90
Cash	1490	0.04	0.06	0.00	1.00
ROA	1490	0.00	0.05	0.00	0.24
Number of siblings	1490	6.94	10.22	2.00	54.00
Risk_dispersion	1490	0.26	0.29	0.00	1.41
Size_dispersion	1490	0.95	0.85	0.00	6.25
Roa_dispersion	1490	0.01	0.03	0.00	0.18
Dominance_ratio	1490	0.55	0.24	0.08	1.00
Sibling_weakest	1490	2.09	0.46	1.00	3.00

presents descriptive statistics, and we discuss each variable’s theoretical role and expected relationship with failure risk below.

Capital Adequacy (C):

Equity Ratio = Total equity capital/Total assets. This measures the bank’s capital cushion available to absorb losses. Higher equity ratios indicate greater capacity to withstand adverse shocks without becoming insolvent. Estrella et al. (2000) demonstrate that capital ratios are among the strongest predictors of bank failure, with well-capitalized banks exhibiting failure rates 5–7 percentage points lower than poorly capitalized peers (Berger & Bouwman, 2013). We expect a negative relationship with failure risk.

Asset Quality (A):

Nonperforming Assets (NPAs) Ratio = Nonperforming loans/Total assets. Nonperforming assets include loans that are 90 or more days past due or on nonaccrual status. This directly measures credit quality deterioration, which was the primary channel through which the subprime crisis affected bank solvency. Cole and White (2012) show that NPAs ratios exhibit the strongest predictive power for 2007–2010 failures. We expect a positive relationship with failure risk.

Loan Loss Reserves (LLRs) Ratio = Allowance for loan and lease losses/Total assets. This captures management’s assessment of potential future losses embedded in the loan portfolio. While higher reserves indicate anticipation of credit problems, they also represent a buffer against losses. The net effect is ambiguous: high reserves may signal either prudent provisioning or deteriorating asset quality. The prior literature finds mixed results depending on context (Wheelock & Wilson, 2000). We expect the sign to be ambiguous.

Securities Ratio = Securities holdings/Total assets. This measures portfolio composition, with higher securities holdings indicating less exposure to loan credit risk but potential exposure to market risk. The expected relationship with failure is ambiguous. While DeYoung and Torna (2013) document elevated failure risk for banks with higher securities ratios during 2007–2010 due to mortgage-backed securities losses, securities also provide liquidity and diversification benefits that enhance stability. We remain agnostic ex ante about the sign, allowing the data to reveal the net effect.

Earnings (E):

Return on Assets (ROA) = Net income/Total assets. This measures profitability and the bank’s ability to generate earnings to absorb losses and build capital organically. Profitable banks are better positioned to weather adverse shocks. Wheelock and Wilson (2000) consistently find that higher pre-crisis profitability reduces failure risk. We expect a negative relationship.

Liquidity (L):

Cash Ratio = Cash and cash equivalents/Total assets. This measures the bank’s ability to meet immediate liquidity demands, including deposit withdrawals. Higher cash holdings provide a buffer against liquidity shocks but may indicate difficulty deploying funds profitably. The relationship with failure risk is theoretically ambiguous but empirically tends to be negative during crises when liquidity constraints bind (Berger & Bouwman, 2013). We expect a negative relationship.

Brokered Deposits Ratio (BD) = Brokered deposits/Total assets. Brokered deposits are purchased through intermediaries and are considered less stable “hot money” that can flee rapidly during distress. Cole and White (2012) find that heavy reliance on brokered deposits significantly increases failure risk during the crisis. We expect a positive relationship.

2.2.3. Group-Level Characteristics

Beyond individual bank fundamentals, we construct variables capturing the structure and risk distribution within MBHCs. These variables are computed at the holding company level using FR Y-9LP and FR Y-9SP reports and assigned to each affiliated bank.

Network Structure:

Number of Siblings = Total number of bank and nonbank subsidiaries affiliated with the same holding company. Larger sibling networks may provide diversification benefits through geographic or business line variety or may create coordination challenges and resource dilution. The expected sign is ambiguous a priori.

Size Dispersion = Standard deviation of log (total assets) across affiliated banks within the holding company. This captures size dispersion among affiliates, which may indicate resource allocation inefficiencies or strategic focus on particular units. Higher dispersion may constrain internal capital market efficiency. We expect a positive relationship if size dispersion creates resource allocation frictions.

Risk Distribution:

Risk Dispersion = Standard deviation of the NPAs across affiliated banks within the holding company, using pre-crisis averages over 2006Q1–2007Q4. This measures the concentration of asset quality problems across affiliates. Higher risk dispersion indicates that credit quality problems are concentrated in specific affiliates rather than evenly distributed. The expected sign depends on whether concentration amplifies stress (weakest link channel) or provides opportunities for cross-subsidization. We expect a positive relationship under the weakest link hypothesis.

ROA Dispersion = Standard deviation of ROA across affiliated banks. This captures earnings dispersion within the group, which may reflect different business strategies or varied success in managing risks. Higher dispersion may indicate internal conflicts over resource allocation. We expect a positive relationship.

Dominance Ratio = Share of total holding company assets held by the largest affiliated bank. This captures concentration of resources within the group. A higher dominance ratio may indicate that the parent’s support will focus disproportionately on the dominant bank (Ozdemir & Altinoz, 2018), potentially increasing failure risk for smaller siblings. We expect a positive relationship for non-dominant banks.

Parent Holding Company Controls:

An important feature of our research design is that parent characteristics are mechanically constant across all banks within the same holding company. When comparing outcomes across siblings sharing the same parent, parent-level heterogeneity does not confound within-group comparisons. Nevertheless, we include parent-level controls—parent total assets, parent equity ratio, parent leverage and parent net income—to ensure that sibling dynamics operate above and beyond parent capacity effects. These variables are measured using consolidated FR Y-9C reports and averaged over 2006Q1–2007Q4. We do not report these coefficients in our results tables because they serve primarily as control variables rather than variables of theoretical interest, and because their effects are mechanically identical for all siblings within the same holding company, making coefficient interpretation less informative in our sibling-focused framework. Our focus remains on the group-level characteristics and sibling dynamics that vary across different holding company structures.

2.3. The Weakest Link Framework

2.3.1. Theoretical Foundation

Our weakest link approach is grounded in established principles from network theory and operations research, where system performance in interconnected settings is disproportionately determined by the weakest component. This principle, formalized in supply chain management and reliability engineering, holds that when units are interdependent, the weakest element constrains overall system capacity regardless of the strength of other components (Snyder et al., 2016). In financial contexts, Allen and Gale (2000) demonstrate that contagion in interconnected financial systems spreads from distressed institutions to healthy ones through network linkages, with system stability determined by the weakest node rather than average system strength. Acemoglu et al. (2015) extend this insight, showing that when financial institutions are interconnected, system-wide failures can be triggered by concentrated vulnerabilities at a single node even when the system appears well-capitalized on average.

We adapt this framework to the intra-group context by recognizing that MBHCs constitute internal networks where siblings are interconnected through competition for finite parent resources. When multiple affiliates require capital or liquidity support simultaneously, parents face binding resource constraints and must allocate selectively. Empirical evidence demonstrates that parents actively reallocate capital to distressed subsidiaries during stress periods, increasing capital injections by 15 to 25 percent under the source of strength doctrine (Wang et al., 2022), with the largest and often most distressed banks receiving disproportionate support (Ozdemir & Altinoz, 2018). This reallocation creates resource scarcity for other affiliates. When one affiliate experiences severe distress requiring substantial parent intervention, the resources diverted to that unit become unavailable to support other siblings, effectively constraining the internal capital market capacity available to healthier banks within the group.

This mechanism differs fundamentally from simple aggregation of sibling risks. Aggregate measures like average affiliate capital ratios or total group NPAs treat all affiliates symmetrically, implying that risk is additive and that all siblings contribute equally to group vulnerability. The weakest link principle instead posits that the distribution of risk matters beyond central tendency. Specifically, concentrated vulnerabilities at a single affiliate may amplify system-wide risk through two channels. First, the severely distressed affiliate directly constrains parent resource availability through intensive support demands, limiting capital and liquidity available for other siblings. Second, the presence of extreme tail risk at any affiliate may signal broader governance or risk management weaknesses that affect the entire organization, even if other affiliates appear healthy on standalone metrics.

Our empirical implementation identifies the most vulnerable affiliate across five dimensions corresponding to CAMELS components: capital adequacy, asset quality, liquidity, earnings, and earnings stability. For each dimension, we focus on banks occupying the extreme tails of the risk distribution, which are most likely to generate binding constraints on internal capital allocation and trigger spillovers within the holding company. This approach captures whether the presence of severely distressed affiliates increases failure risk throughout the group, controlling for the focal bank’s own fundamentals and aggregate group characteristics. If the weakest link mechanism operates, we expect concentrated vulnerabilities at one affiliate to predict failure risk for all banks in the group, even those that appear healthy on individual metrics.

2.3.2. Weakest Link Variables

Building on this framework, we construct measures identifying the most vulnerable affiliate within each holding company. Our weakest link variables capture whether the crowding-out effect operates: if severely distressed siblings predict failure throughout the holding company, this indicates that concentrated vulnerabilities constrain support availability.

We operationalize the weakest link across five risk dimensions corresponding to CAMELS components: capital adequacy (equity ratio), asset quality (NPAs), liquidity (cash holdings), earnings (ROA), and earnings stability (operating income variability). Each affiliated bank is evaluated along one dimension at a time, focusing on extreme tail risk most likely to generate binding constraints on internal capital allocation. For each dimension, banks are assigned risk grades based on their position in the distribution. Banks in the extreme tails—above the 90th percentile for risk factors (NPAs, income volatility) or below the 10th percentile for protective factors (equity, cash, ROA)—are classified as high risk (grade 3), while those in moderate ranges receive grade 2, and those in the opposite tail receive grade 1. The sibling with the highest risk grade within each holding company is identified as the weakest link, and this maximum risk score is assigned to all affiliates in the group.

Specifically, the five weakest link variables are as follows:

Weakest Sibling Risk (Cash-Based): identifies the sibling with the lowest cash ratio (bottom 10th percentile indicates high liquidity risk);

Weakest Sibling Risk (ROA-Based): identifies the sibling with the lowest ROA (bottom 10th percentile indicates earnings weakness);

Weakest Sibling Risk (Operating Income Variability-Based): identifies the sibling with the highest earnings volatility (top 10th percentile indicates unstable earnings);

Weakest Sibling Risk (NPA-Based): identifies the sibling with the highest NPAs ratio (top 10th percentile indicates severe asset quality deterioration);

Weakest Sibling Risk (Equity-Based): identifies the sibling with the lowest equity ratio (bottom 10th percentile indicates capital inadequacy);

These variables test whether the presence of a severely distressed affiliate—across any of these risk dimensions—increases failure probability for all banks in the group, controlling for the bank’s own fundamentals and aggregate group characteristics. Under the weakest link hypothesis, we expect positive relationships: concentrated vulnerabilities at one affiliate amplify risk throughout the holding company.

2.3.3. Illustrative Supervisory Application: Weakest Link Monitoring and Stress Testing

To illustrate how the weakest link concept can be used in contemporary supervision, consider an MBHC. A supervisor can compute the weakest link flags each quarter using the same publicly available regulatory inputs used in this paper (capital, asset quality, liquidity, earnings, and earnings volatility), identifying whether any affiliate falls into an extreme tail (for example, bottom decile of equity or cash, top decile of NPAs or income volatility). The practical output is a simple group-level “attention signal”: even if the median affiliate looks healthy, the presence of one extreme outlier triggers closer monitoring of intra-group resource constraints and spillover exposure.

A natural stress-testing implementation is to pair that signal with a within-group resource allocation overlay. Standard solvency or liquidity scenarios can be run at the consolidated level, but the weakest link framework adds a second step: allocate the parent’s limited support capacity first to the affiliate with the largest modeled shortfall, then evaluate whether remaining affiliates still meet minimum capital or liquidity thresholds under the same scenario. This directly operationalizes the mechanism emphasized in this paper: when support capacity is scarce, one affiliate’s extreme weakness can crowd out support to others.

Suppose a holding company has three bank subsidiaries (A, B, C). A supervisor computes a weakest link liquidity flag using the cash ratio.

Step 1: Identify the weakest affiliate (monitoring).

• Bank A cash ratio: 6.0%;
• Bank B cash ratio: 4.5%;
• Bank C cash ratio: 1.2% (bottom-decile of the system distribution).

Result: the holding company is flagged as having a weakest link liquidity exposure because at least one affiliate (C) sits in the extreme low-liquidity tail.

Step 2: Apply a standard liquidity stress plus limited internal support (stress testing).

Under a common liquidity scenario (for example, a rapid deposit outflow plus haircut on liquid assets), projected 30-day net cash shortfalls are

• Bank A: 0 (still liquid);
• Bank B: 30;
• Bank C: 150.

The parent’s usable liquidity buffer available for downstream support is 120 (after frictions, ring-fencing, and supervisory constraints). If the parent covers Bank C first (120 of 150), the parent buffer is exhausted, and Bank B remains short by 30. Even though Bank B was not the weakest affiliate ex ante, it becomes vulnerable because the group’s support capacity was absorbed by the weakest link.

This kind of overlay converts the weakest link signal into a targeted action: (i) increase the frequency of affiliate-level liquidity/capital monitoring for flagged groups, (ii) require the firm to demonstrate credible internal transfer capacity and contingency funding plans at the subsidiary level, and (iii) design stress scenarios that explicitly test the crowd-out channel by forcing simultaneous needs across multiple affiliates. The key intuition is that supervision should not rely only on averages or consolidated totals when a single extreme affiliate can bind the internal support constraint.

2.4. Descriptive Statistics

Our analysis requires complete quarterly reporting across all eight quarters of the pre-crisis measurement window (2006Q1–2007Q4). This restriction ensures consistent measurement of all covariates and avoids bias from partial reporting histories. Of the 325 banks that failed during 2007–2010 according to FDIC records, our sample includes 290 failures: 108 affiliated with MBHCs and 182 affiliated with OBHCs. The 35 excluded failures represent banks that either merged or underwent significant restructuring during the measurement window or had incomplete Call Report data during 2006–2007. This exclusion ensures all banks in our sample have consistent, complete pre-crisis measurements but does not introduce systematic bias because the excluded failures were predominantly smaller de novo institutions for which pre-crisis conditions cannot be reliably measured.

Table A1. Sample composition and asset size distribution.

Dimension	Category/Statistic	All Banks	MBHC Banks	OBHC Banks
Counts	Number of banks	5962	1490	4472
Counts	Failures in 2007–2010	290	108	182
Size	Mean	1,597,468	4,565,017	546,351
Size	Median	141,249	157,864	130,467.5
Size	10th percentile	34,772	34,550	34,840
Size	25th percentile	64,883	69,780.5	62,886
Size	75th percentile	343,776	409,338	291,822
Size	90th percentile	897,196	1,270,477	629,393

Note: Total assets are taken from Call Reports and reported in thousands of US Dollars. The table summarizes sample composition and asset size by organizational form. Detailed descriptive statistics for the main analysis variables are reported for the MBHC estimation sample in Table 2; OBHC descriptive statistics are available upon request.

reports sample composition for the full matched sample; Table 2 and

Table 3. Differences in means between failed and non-failed banks (MBHC estimation sample).

	Non-Failed Banks	Failed Banks	Difference (Non-Failed–Failed)
Equity	0.12	0.06	0.06
LLR	0.00	0.00	−0.000 *
NPA	0.01	0.02	−0.005 ***
Securities	0.20	0.13	0.064 ***
BD	0.03	0.09	−0.061 ***
Cash	0.04	0.03	0.014 ***
ROA	0.00	0.00	0.001
Number of siblings	7.00	4.48	2.522 ***
Risk_dispersion	0.26	0.30	−0.043
Size_dispersion	0.94	1.26	−0.312 *
Roa_dispersion	0.01	0.01	0.003
Dominance_ratio	0.54	0.62	−0.079
Sibling_weakest	1.09	2.21	−1.120

* p < 0.10, *** p < 0.01.

report descriptive statistics and failed-versus-non-failed comparisons for the MBHC estimation sample used in the main analysis. Table 2 presents descriptive statistics for all variables in our analysis. The sample includes 1490 bank observations, of which 108 failed during the 2007–2010 crisis period. The average bank holds equity equal to 12% of assets, with NPAs averaging 1% of total assets. Group-level characteristics show considerable variation: the average holding company contains approximately seven sibling institutions (ranging from 2 to 54), with substantial dispersion in both size dispersion (mean 0.95, SD 0.85) and risk dispersion (mean 0.26, SD 0.29) across affiliates. The weakest link measure averages 2.09, indicating that most holding companies contain at least one affiliate in a moderate-to-high risk category.

Table 3 compares the means between failed and non-failed banks, revealing patterns consistent with traditional failure prediction. Failed banks exhibit significantly lower equity ratios (0.06 vs. 0.12), higher NPAs (0.02 vs. 0.01), lower securities holdings (0.13 vs. 0.20), and substantially higher reliance on brokered deposits (0.09 vs. 0.03), all significant at conventional levels. Beyond these bank-specific characteristics, important differences emerge in group-level dynamics. Failed banks are affiliated with holding companies that have fewer siblings (4.48 vs. 7.00, p < 0.01), suggesting that larger sibling networks may provide diversification benefits. More strikingly, failed banks exhibit significantly higher size dispersion across siblings (1.26 vs. 0.94, p < 0.10), indicating that dispersion in affiliate size may constrain efficient resource allocation. Most notably, the weakest link measure is substantially higher for banks in holding companies that experienced failures (2.21 vs. 1.09), providing strong preliminary support for our hypothesis that concentrated vulnerabilities at the weakest affiliate predict failure risk throughout the holding company. These univariate patterns motivate the multivariate analysis that follows, where we test whether these group-level dynamics remain significant after controlling for individual bank fundamentals and parent characteristics.

2.5. Empirical Strategy

Our analysis employs cross-sectional logit regression to model bank failure as a discrete, non-repeating event. This design is methodologically necessary for several reasons. First, bank failure is a binary outcome—each bank either fails once during 2007–2010 or survives the entire period—and failed banks exit the sample permanently, making panel methods that require repeated observations inappropriate. Second, we explicitly measure explanatory variables using pre-crisis data to predict crisis outcomes, establishing clear temporal ordering that prevents reverse causality. Third, this approach follows established best practices in the failure prediction literature (Cole & White, 2012; Wheelock & Wilson, 2000; Estrella et al., 2000), where cross-sectional logit is the standard framework for modeling discrete failure events.

We employ a standard logit framework because it best matches our research objectives. Logit provides interpretable estimates and hypothesis tests in a form comparable to the bank failure prediction literature, allowing us to focus on our main contribution: constructing and testing new holding company structure measures rather than proposing a new estimation algorithm. While machine learning and AI-based approaches can achieve higher out-of-sample prediction accuracy, they sacrifice transparency in favor of black-box optimization, making it difficult to isolate specific causal mechanisms or test hypotheses about organizational structure. Our research question—whether and how sibling dynamics and concentrated affiliate vulnerabilities influence failure risk above and beyond traditional indicators—requires interpretable coefficients and hypothesis tests that logit regression provides. Moreover, logit results are directly actionable for supervisors, who can monitor specific group characteristics and weakest link indicators we identify, whereas black-box algorithms provide limited guidance on which organizational features drive risk.

Our explanatory variables are measured using data averaged over the eight quarters preceding the crisis (2006Q1–2007Q4), following the methodology of Berger and Bouwman (2013). This averaging strategy serves three purposes. First, it reduces the influence of short-term fluctuations and measurement error that might obscure underlying financial conditions, ensuring our measures reflect stable structural vulnerabilities rather than quarterly volatility. Second, it establishes clear temporal ordering where independent variables are measured strictly before the dependent variable is realized, which is essential for avoiding reverse causality. Sharp deterioration immediately before failure would be endogenous to the failure process itself rather than a predictor of it. Third, this approach captures banks’ financial condition during the period when they were building the vulnerabilities that would prove decisive once the crisis materialized, rather than capturing the crisis deterioration itself. While averaging necessarily smooths variation across quarters, our objective is to identify which pre-crisis organizational and financial characteristics predict subsequent failures, not to document the timing of deterioration. Section 4 presents robustness tests using alternative measurement windows that confirm our findings are not sensitive to this methodological choice.

The dependent variable, Failure, is a binary indicator that takes the value of one if a bank failed between 2007 and 2010 and zero otherwise. The baseline specification follows the CAMELS framework, which assesses capital adequacy, asset quality, management, earnings, liquidity, and sensitivity to market risk.

2.5.1. Baseline Model: Bank-Level CAMELS

Our baseline model estimates failure probability using only bank-specific fundamentals:

$$\mathrm{P}\left({\mathrm{F}\mathrm{a}\mathrm{i}\mathrm{l}\mathrm{u}\mathrm{r}\mathrm{e}}_{\mathrm{i}}\right)=\mathsf{\Lambda }\left({\mathsf{\beta }}_0+{\mathsf{\beta }}_1{\mathrm{C}\mathrm{A}\mathrm{M}\mathrm{E}\mathrm{L}\mathrm{S}}_{\mathrm{i}}+{\mathsf{\epsilon }}_{\mathrm{i}}\right)$$

(1)

where

Failure_i is a binary indicator equal to 1 if bank i failed during 2007–2010, and 0 otherwise.

$\mathsf{\Lambda }\left(.\right)$ is a logistic cumulative distribution function.

CAMELS_i is a vector of bank-level financial characteristics for bank _i measured over 2006Q1–2007Q4, including the following:

• Capital adequacy: equity ratio
• Asset quality: NPAs ratio, LLRs ratio, securities ratio
• Earnings: ROA
• Liquidity: cash ratio, brokered deposits ratio.
• ${\mathsf{\epsilon }}_{\mathrm{i}}$ is the error term.

This specification serves as our benchmark, replicating the standard approach in the bank failure prediction literature (Cole & White, 2012; Wheelock & Wilson, 2000).

2.5.2. Augmented Model: Group-Level Characteristics

We extend the baseline by adding holding company structure and sibling risk distribution variables:

$$\mathrm{P}\left({\mathrm{F}\mathrm{a}\mathrm{i}\mathrm{l}\mathrm{u}\mathrm{r}\mathrm{e}}_{\mathrm{i}}\right)=\mathsf{\Lambda }\left({\mathsf{\beta }}_0+{\mathsf{\beta }}_1{\mathrm{C}\mathrm{A}\mathrm{M}\mathrm{E}\mathrm{L}\mathrm{S}}_{\mathrm{i}}+{\mathsf{\beta }}_2{\mathrm{G}\mathrm{r}\mathrm{o}\mathrm{u}\mathrm{p}}_{\mathrm{g}}+{\mathsf{\epsilon }}_{\mathrm{i}}\right)$$

(2)

where Group_g is a vector of holding company-level characteristics assigned to all banks within the following:

Network structure: number of siblings, size dispersion;

Risk distribution: risk dispersion, ROA dispersion, dominance ratio.

These variables capture whether the size and composition of the sibling network, and the distribution of risks across affiliates, influence individual bank failure probability beyond the bank’s own fundamentals.

2.5.3. Full Model: Weakest Link

Our primary specification incorporates weakest link measures that identify the most vulnerable affiliate within each holding company:

$$\mathrm{P}\left({\mathrm{F}\mathrm{a}\mathrm{i}\mathrm{l}\mathrm{u}\mathrm{r}\mathrm{e}}_{\mathrm{i}}\right)=\mathsf{\Lambda }\left({\mathsf{\beta }}_0+{\mathsf{\beta }}_1{\mathrm{C}\mathrm{A}\mathrm{M}\mathrm{E}\mathrm{L}\mathrm{S}}_{\mathrm{i}}+{\mathsf{\beta }}_2{\mathrm{G}\mathrm{r}\mathrm{o}\mathrm{u}\mathrm{p}}_{\mathrm{g}}+{\mathsf{\beta }}_3{\mathrm{W}\mathrm{e}\mathrm{a}\mathrm{k}\mathrm{e}\mathrm{s}\mathrm{t}\mathrm{L}\mathrm{i}\mathrm{n}\mathrm{k}}_{\mathrm{g}}+{\mathsf{\epsilon }}_{\mathrm{i}}\right)$$

(3)

where ${\mathrm{W}\mathrm{e}\mathrm{a}\mathrm{k}\mathrm{e}\mathrm{s}\mathrm{t}\mathrm{L}\mathrm{i}\mathrm{n}\mathrm{k}}_{\mathrm{g}}$ is a vector of variables identifying the maximum risk grade across all siblings in group g along five dimensions.

${\mathrm{W}\mathrm{L}}_{\mathrm{g}}^{\mathrm{C}\mathrm{a}\mathrm{s}\mathrm{h}}$: Weakest affiliate liquidity (lowest cash ratio in group).

${\mathrm{W}\mathrm{L}}_{\mathrm{g}}^{\mathrm{R}\mathrm{O}\mathrm{A}}$: Weakest affiliate earnings (lowest ROA in group).

${\mathrm{W}\mathrm{L}}_{\mathrm{g}}^{\mathrm{I}\mathrm{n}\mathrm{c}\mathrm{o}\mathrm{m}\mathrm{e}\mathrm{V}\mathrm{o}\mathrm{l}}$: Weakest affiliate earnings stability (highest income volatility in group).

${\mathrm{W}\mathrm{L}}_{\mathrm{g}}^{\mathrm{N}\mathrm{P}\mathrm{A}}$: Weakest affiliate asset quality (highest NPAs ratio in group).

${\mathrm{W}\mathrm{L}}_{\mathrm{g}}^{\mathrm{E}\mathrm{q}\mathrm{u}\mathrm{i}\mathrm{t}\mathrm{y}}$: Weakest affiliate capital (lowest equity ratio in group).

Each weakest link variable equals 1 if any sibling in the group falls in the bottom (or top, for risk measures) 10th percentile of the distribution, and 0 otherwise. This specification tests whether concentrated vulnerabilities at a single affiliate increase failure probability for all banks in the group.

The coefficient vector ${\mathsf{\beta }}_3$ captures the weakest link effect: positive and significant coefficients indicate that the presence of a severely distressed sibling increases failure risk throughout the holding company, even after controlling for the bank’s own fundamentals (${\mathsf{\beta }}_1$) and aggregate group characteristics (${\mathsf{\beta }}_2$) (See Appendix C 

Table A2. Three complementary approaches to assessing bank failure risk in multi-bank holding companies.

Approach	Focus	Example Measures	Key Insight	Limitation
Traditional Bank-Level	Individual bank fundamentals	Equity ratio, NPL, Cash, ROA	How healthy is this specific bank?	Ignores sibling dynamics and internal capital markets
Group-Level	Holding company structure	Number of siblings, Size dispersion, Risk dispersion	How diversified and balanced is the group?	Treats all siblings symmetrically; misses concentrated weaknesses
Weakest Link	Most vulnerable affiliate	Worst sibling equity, Worst sibling NPL, Worst sibling cash	Which sibling creates the greatest spillover risk?	Requires identifying tail risk across network
Combined Model	All three integrated	All measures above	Captures individual health, group structure, and concentrated vulnerabilities	Most comprehensive; all three needed for MBHCs

for three complementary approaches to assessing bank failure risk).

2.5.4. Estimation and Inference

We estimate all models using maximum likelihood logit regression. Standard errors are clustered at the holding company level to account for potential correlation in unobserved factors affecting multiple banks within the same group.

For interpretation, we report coefficient estimates along with their statistical significance, while marginal effects evaluated at sample means are discussed in the text. Model fit is assessed using the pseudo R² and the log-likelihood. In addition, we evaluate predictive performance using classification metrics derived from confusion matrices, as discussed in Section 3.4.

2.5.5. Interpretation and Scope

Our analysis infers sibling dynamics from statistical relationships between affiliate characteristics and failure outcomes rather than directly observing internal capital reallocation. This follows standard practice in the internal capital markets literature, where researchers document effects through differential outcomes without observing transactions directly (Campello, 2002; Ashcraft, 2008; Wang et al., 2022).

While direct observation of internal transfers would provide more definitive evidence, our approach complements potential case studies by establishing systematic patterns across a large sample of MBHCs during the crisis. As a scope limitation, the estimated crisis-era magnitudes need not carry over to other regimes or shock types.

3. Results

This section presents the empirical results from the logit models described in Section 2. The analysis proceeds in three steps. First, the performance of the traditional CAMELS framework is evaluated separately for banks affiliated with single-bank and multi-bank holding companies. Second, group-level characteristics are introduced to assess how sibling structure and risk distribution within MBHCs influence failure probabilities. Finally, the weakest link approach is applied to examine whether concentrated vulnerabilities at a single affiliate amplify failure risk across the holding company.

Regression results are reported in

Table 4. Regression results for OBHC and MBHC.

	OBHC-Affiliated Banks		MBHC-Affiliated Banks
	b	se	b	se
Equity	−8.86 ***	2.93	1.30	2.05
LLR	305.90 ***	59.36	−26.66	144.92
NPA	13.76 ***	4.51	15.14	12.95
Securities	−5.23 ***	0.95	−3.39 **	1.73
BD	5.69 ***	0.74	5.05 ***	1.53
Cash	−22.71 ***	6.01	−16.29	10.97
ROA	−16.83 ***	5.01	0.49	6.03
_cons	−1.56 ***	0.42	−3.36 ***	0.62
N	4472		1490
chi2	328.15		25.23
ll	−596.86		−151.62
pseudo_r2	0.22		0.08

** p < 0.05; *** p < 0.01.

,

Table 5. Regressions for MBHCs with group characteristics and CAMELS indicators.

	(1)		(2)		(3)
	b	se	b	se	b	se
Equity	1.30	2.05	3.92	2.70	3.09	2.68
LLR	−26.66	144.92	92.73	177.72	86.74	172.85
NPA	15.14	12.95	9.18	14.55	8.58	15.00
Securities	−3.39 **	1.73	−4.83 **	2.06	−5.00 **	2.20
BD	5.05 ***	1.53	5.34 ***	1.70	5.50 ***	1.77
Cash	−16.29	10.97	−19.58	12.26	−20.54 *	10.57
ROA	0.49	6.03	3.65	6.96	−6.19	9.55
Number of siblings			−0.04 **	0.02	−0.06 **	0.03
Risk_dispersion					−2.49 ***	0.89
Size_dispersion					0.92 ***	0.27
Roa_dispersion					−16.90	15.00
Dominance_ratio					−2.11	1.31
_cons	−3.36 ***	0.62	−3.03 ***	0.69	−1.82 *	0.94
N	1490		1490		1490
chi2	25.23		36.39		59.46
ll	−151.62		−136.36		−124.83
pseudo_r2	0.08		0.12		0.19

* p < 0.10; ** p < 0.05; *** p < 0.01.

,

Table 6. Weakest link regressions for MBHCs (Part I).

	Cash-Based WL		ROA-Based WL		Operating Income-Based WL
	b	se	b	se
Equity	1.75	2.74	1.79	2.67	2.69	3.09
LLR	74.28	178.65	63.73	178.87	1.94	200.95
NPA	13.15	15.39	12.18	15.30	12.75	16.63
Securities	−5.31 **	2.19	−4.63 **	2.13	−4.74 **	2.15
BD	5.80 ***	1.79	6.11 ***	1.81	6.94 ***	1.93
Cash	−18.86 *	10.22	−21.26 *	11.78	−26.50 **	11.27
ROA	−8.47	10.10	−11.89	10.44	−9.97	9.59
Number of siblings	−0.07 **	0.03	−0.05 *	0.03	−0.07 ***	0.03
Risk_dispersion	0.20	0.66	0.84	0.63	−2.08 **	0.90
Size_dispersion	0.99 ***	0.28	0.86 ***	0.27	0.82 ***	0.30
Roa_dispersion	−20.52	16.19	−28.23	18.95	−20.98	16.48
Dominance_ratio	−1.08	1.21	−1.34	1.25	−0.90	1.36
Weakest_sibling_risk	0.87 **	0.44	−0.58	0.44	2.05 ***	0.54
_cons	−4.79 ***	1.31	−1.72	1.30	−6.75 ***	1.50
N	1490		1490		1490
chi2	54.51		53.04		68.55
ll	−127.30		−128.04		−120.28
pseudo_r2	0.18		0.20		0.23

* p < 0.10; ** p < 0.05; *** p < 0.01.

and

Table 7. Weakest link regressions for MBHCs (Part II).

	NPA-Based WL		Equity-Based WL
	b	se	b	se
Equity	0.35	2.91	3.05	2.69
LLR	131.62	180.82	32.86	184.66
NPA	−2.54	16.14	19.73	15.64
Securities	−5.14 **	2.19	−4.88 **	2.19
BD	5.86 ***	1.79	6.40 ***	1.79
Cash	−21.94 **	10.67	−23.55 **	10.93
ROA	−9.99	9.43	−7.68	10.71
Number of siblings	−0.07 **	0.03	−0.07 **	0.03
Risk_dispersion	1.52 **	0.59	−0.62	0.83
Size_dispersion	0.94 ***	0.27	1.14 ***	0.31
Roa_dispersion	−22.84	15.96	−17.78	17.15
Dominance_ratio	−0.89	1.26	−1.13	1.27
Weakest_sibling_risk	0.83 *	0.43	1.12 **	0.55
_cons	−4.72 ***	1.28	−5.37 ***	1.56
N	1490		1490
chi2	60.28		54.15
ll	−124.42		−127.48
pseudo_r2	0.22		0.21

* p < 0.10; ** p < 0.05; *** p < 0.01.

. Throughout the analysis, coefficient estimates are interpreted in terms of their sign and statistical significance, with particular emphasis on differences between single-bank and MBHC structures.

Tables report logit coefficients and significance levels. For ease of interpretation, we discuss economically meaningful magnitudes in the text by converting key coefficients to marginal effects—the change in failure probability (in percentage points) associated with a one-unit or one-standard-deviation change in the explanatory variable, evaluated at sample means.

3.1. Traditional CAMELS Indicators and Bank Failures

Table 4 presents estimation results for Equation (1), comparing banks affiliated with OBHCs to those affiliated with MBHCs. The OBHC sample includes banks where the holding company oversees only one institution, while the MBHC sample includes banks operating within networks of sibling affiliates.

The regression results in Table 4 highlight important distinctions between the OBHC sample and the MBHC sample in predicting bank failures. For the OBHC-affiliated banks, the model demonstrates strong explanatory power with a pseudo-R² value of 0.22, and most variables exhibit significant relationships with failure risk. Equity shows a strong negative relationship with failure, indicating that higher equity levels significantly reduce the likelihood of bank failure. Loan loss reserves are positively associated with failure, suggesting that higher provisioning may signal financial distress. Similarly, nonperforming loans emerge as a strong positive predictor of failure, reflecting the role of asset quality in increasing risk. Securities exhibit a negative relationship, indicating that higher holdings in securities reduce failure risk, while brokered deposits are positively associated with failure, pointing to the risks of reliance on less stable funding sources. Cash shows a significant negative relationship, with higher liquidity reducing failure likelihood. Finally, ROA demonstrates a strong negative relationship, where greater profitability is associated with a lower probability of failure.

In contrast, the results for the MBHC-affiliated sample reveal weaker explanatory power, with a pseudo-R² value of only 0.08 and fewer significant predictors. Traditional indicators such as Equity and LLRs are insignificant, highlighting CAMELS-based predictors’ limitations in MBHC settings. However, NPAs remain a positive predictor of failure, consistent with its role as a measure of asset quality risk. Both securities and brokered deposits retain their significance, with similar directional effects as in the OBHC analysis. While Cash exhibits a negative coefficient, it is not statistically significant, and ROA shows no meaningful relationship with failure in this group. The lower chi-squared value and log-likelihood for MBHCs suggest that alternative approaches are needed to better capture the dynamics of group-level risks within MBHCs.

These findings underscore that while traditional CAMELS indicators perform well in predicting failures for the OBHC-affiliated bank sample, they are insufficient for the MBHC-affiliated ones, likely due to the complex interdependencies and group dynamics present in MBHCs. Given these limitations for MBHCs, we next examine whether group structure can explain the gap in predictive power.

The differential performance of CAMELS indicators across organizational forms reflects fundamental structural differences rather than crisis-specific phenomena. In OBHCs, individual bank characteristics directly determine failure outcomes because there are no sibling relationships or internal capital market complications to mediate the relationship between fundamentals and outcomes. Each bank stands or falls based on its own capital, asset quality, liquidity, and earnings. In MBHCs, these direct relationships become attenuated because parents can intervene selectively, resources flow across affiliates, and sibling characteristics influence each bank’s access to support. A well-capitalized bank within a distressed holding company may fail if parent resources are committed to supporting other subsidiaries, while a poorly capitalized bank may survive if it receives priority support from the parent.

These organizational realities persist in contemporary banking. The 2023 Silicon Valley Bank failure illustrates how holding company structure complicates bank stability even under modern regulatory frameworks. SVB Financial Group operated as a bank holding company with multiple subsidiaries, and the rapid failure of Silicon Valley Bank raised immediate questions about the parent company’s obligations to bondholders, the treatment of other subsidiaries, and how resources should be allocated across the holding company structure. While the specific failure mechanism differed from credit-driven 2007–2010 failures, the organizational complexity we studied remained central to understanding the episode and its resolution. The persistence of multi-bank organizational forms in modern banking means that supervisory frameworks must continue to account for how these structures alter the relationship between traditional risk indicators and failure outcomes.

3.2. Group Structure and Sibling Risk Distribution Within MBHCs

Individual bank outcomes may be influenced not only by their own financial conditions but also by holding company structure and the distribution of risk across sibling institutions. Equation (2) extends Equation (1) by introducing group characteristics that capture an individual bank’s demand for limited parent resources. When a sibling bank experiences an urgent need for funds, it can strain parent-level resources and reduce the support available to other affiliates. This effect is captured through the inclusion of several group-level variables.

To measure heterogeneity within the holding company, dispersion variables are constructed at the group level using pre-crisis averages. Risk dispersion is defined as the standard deviation of the risk measure across affiliated banks within the same holding company, capturing the extent to which risk is unevenly distributed across affiliates. Size dispersion is measured as the standard deviation of the logarithm of total assets across affiliated banks, reflecting differences in affiliate size within the group. ROA dispersion is defined as the standard deviation of ROA across affiliated banks and captures variation in profitability among affiliates.

The resulting estimates are reported in Table 5. The three model specifications progressively introduce additional variables to reflect the growing complexity of group-level relationships within MBHCs.

Traditional CAMELS indicators are primarily assessed in the first column of Table 5, as in Table 4. Column 2 introduces the variable number of siblings, representing the total number of banks and nonbanks affiliated with the same holding company. This variable has a significant negative relationship with bank failures, indicating that having more siblings provides a diversification effect, reducing the likelihood of individual bank failure. This aligns with the idea that larger MBHC networks can mitigate risks through resource sharing and internal support mechanisms.

Column (3) incorporates additional sibling-level dynamics and group characteristics. Risk dispersion enters with a negative and statistically significant coefficient, indicating that more evenly distributed risk across affiliated banks is associated with lower failure probabilities. This result suggests that the concentration of risk within a subset of affiliates increases group vulnerability. In contrast, size dispersion is positive and highly significant, highlighting the role of size dispersion in amplifying failure risk. Greater disparities in sibling size may constrain effective resource sharing or limit the parent’s ability to allocate support efficiently across affiliates.

Other group characteristics play a more limited role. The dominance ratio is not statistically significant, indicating that the presence of a single large affiliate does not independently affect failure risk once overall size dispersion is taken into account. ROA dispersion is also insignificant, suggesting that variation in sibling profitability is less relevant than balance-sheet structure and risk concentration in explaining failures within MBHCs. Together, these findings emphasize the importance of group structure and the distribution of risk across affiliates, beyond individual bank fundamentals.

Explanatory power improves substantially across the three specifications in Table 5. Both the chi-squared statistics and pseudo-R² values increase monotonically as sibling-level and group-level variables are added, indicating that these factors significantly enhance explanatory power relative to the model relying solely on traditional CAMELS indicators. This pattern underscores the limitations of standard bank-level measures when applied to MBHCs and highlights the importance of accounting for interdependencies among affiliated banks.

Overall, the results in Table 5 show that group structure and the distribution of risk across sibling institutions play a central role in shaping failure probabilities within MBHCs. While certain CAMELS indicators, such as brokered deposits and securities holdings, remain relevant, incorporating measures of sibling network size and dispersion provides a more complete characterization of risk. These findings suggest that aggregate group characteristics capture important dimensions of vulnerability that are not observable at the individual bank level, motivating a more granular analysis of how concentrated risk within sibling groups affects stability.

3.3. Weakest Link Effects Within MBHCs

To examine whether the specific vulnerabilities matter beyond these aggregate measures, we now turn to the weakest link framework. While Table 5 shows that aggregate group characteristics such as the number of siblings and size dispersion influence failure risk, interconnected structures like MBHCs may also be shaped by the condition of the most vulnerable affiliate. In such settings, distress at a single subsidiary can exert a disproportionate effect on the stability of the entire group.

Table 6 and Table 7 report estimates from five specifications that differ only in the risk dimension used to identify the weakest affiliate. The weakest link is defined using cash holdings, ROA, operating income volatility, NPAs, or equity, allowing the analysis to assess whether vulnerabilities concentrated in different dimensions propagate through the holding company.

Across specifications, the weakest affiliate risk measure is statistically significant in four out of five cases, demonstrating robustness across multiple dimensions of financial distress. Concentrated vulnerabilities in liquidity (cash holdings), earnings stability (operating income volatility), asset quality (NPAs), and capitalization (equity) all significantly predict failure risk throughout the holding company. The ROA-based specification is the exception, remaining statistically insignificant at the 10 percent threshold, which suggests that low profitability—unlike severe distress in capital, liquidity, or asset quality—does not generate strong spillover effects within MBHCs.

Table 6 and Table 7 report coefficients where Weakest_sibling_risk is an ordered categorical variable (1 = low risk, 2 = moderate risk, 3 = high risk) identifying the most vulnerable affiliate based on different CAMELS dimensions. Coefficients represent the change in log-odds per one-grade increase in the weakest affiliate’s risk category. Converting to marginal effects for economic interpretation, the operating income volatility-based measure shows the largest impact: each grade increase raises failure probability by 4.0 percentage points, such that a holding company whose weakest affiliate moves from low to high risk experiences an 8.1 percentage point increase. The equity-based (2.2 percentage point per grade), cash-based (1.6 percentage point per grade), and NPA-based (1.6 percentage point per grade) measures show similar substantial effects, while the ROA-based measure is not statistically significant.

Standard CAMELS variables retain patterns consistent with earlier results. Securities holdings are negatively and significantly associated with failure, while brokered deposits are positively and strongly related to failure risk. Cash holdings are generally negative and significant, underscoring the stabilizing role of liquidity. The number of siblings continues to reduce failure probability, while size dispersion remains positive and significant, indicating that size dispersion amplifies instability even after accounting for weakest link effects.

Overall, the financial condition of the most vulnerable affiliate meaningfully shapes failure risk across the holding company, even after controlling for aggregate group structure and individual bank characteristics. This finding implies that supervisory frameworks focused primarily on average group conditions or individual bank fundamentals may overlook critical sources of systemic vulnerability. Even when overall group characteristics appear stable, severe distress at a single affiliate can materially increase failure risk for the entire organization.

3.4. Model Classification Performance

Beyond statistical significance, we assess the practical value of these findings through classification performance. To assess practical predictive power, we generate predicted failure probabilities from each logit specification. We classify a bank as a predicted failure when its predicted probability exceeds 0.07, the sample failure rate.

Table 8. Confusion matrix classification performance.

Panel A. Baseline Model: Bank-Level CAMELS Variables Only
	Actual Failure	Actual Survival	Total
Predicted Failure	83	151	234
Predicted Survival	25	1231	1256
Total	108	1382	1490
Sensitivity: 76.9%   Specificity: 89.1%   Overall accuracy: 88.2%
Panel B. Augmented Model: CAMELS + Group-Level Characteristics
	Actual Failure	Actual Survival	Total
Predicted Failure	89	155	244
Predicted Survival	19	1227	1246
Total	108	1382	1490
Sensitivity: 82.4%   Specificity: 88.8%   Overall accuracy: 88.3%
Panel C. Full Model: CAMELS + Group-Level Characteristics + Weakest Link Variables
	Actual Failure	Actual Survival	Total
Predicted Failure	95	138	233
Predicted Survival	13	1244	1257
Total	108	1382	1490
Sensitivity: 88.0%   Specificity: 90.0%   Overall accuracy: 89.9%

presents confusion matrices for three specifications: (1) baseline CAMELS-only, (2) augmented with group-level characteristics, and (3) full model with weakest link variables.

The baseline model (Panel A) achieves 76.9% sensitivity and 89.1% specificity, correctly identifying 83 of 108 failures but missing 25. Adding group-level characteristics (Panel B) improves sensitivity to 82.4%, reducing missed failures to 19. The full model with weakest link variables (Panel C) delivers the strongest performance: 88.0% sensitivity and 90.0% specificity, correctly identifying 95 of 108 failures. Relative to baseline, the full model reduces missed failures by nearly half—from 25 to 13—while maintaining high specificity. This improvement is economically meaningful: incorporating information about the most distressed affiliate substantially enhances early warning capabilities.

The weakest link results here use the cash-based definition. Alternative weakest link definitions yield sensitivity ranging from 76% to 82%, though the pattern of improvement relative to baseline remains consistent. These findings demonstrate that sibling dynamics and concentrated affiliate weaknesses improve out-of-sample classification performance beyond statistical significance. The weakest link approach is particularly effective at reducing missed failures, which represent the costliest classification mistakes from a supervisory perspective. At a lower 0.30 threshold, the full model achieves 93.3% sensitivity while maintaining specificity above 85%, offering flexibility for supervisors with differing risk tolerances.

4. Robustness Tests

We conduct several robustness checks to ensure our main findings are not driven by specific modeling choices or variable definitions. For clarity of exposition, we report results using the cash-based weakest link specification throughout the robustness section. This choice is motivated by cash being a direct measure of liquidity—a key concern during the 2007–2010 crisis when funding pressures and deposit flight were prominent failure mechanisms. However, we have conducted all robustness tests using all five weakest link dimensions (cash-based, equity-based, NPA-based, ROA-based, and income volatility-based), and results remain qualitatively similar across all specifications. The consistency across different risk dimensions confirms that our findings capture a general weakest link phenomenon rather than effects specific to a single vulnerability measure. Complete results for all five weakest link specifications are available upon request.

4.1. Alternative Time Periods

Our main analysis averages bank characteristics over eight quarters (2006Q1–2007Q4) to capture stable pre-crisis conditions while mitigating short-term volatility. We test whether results are sensitive to this measurement window by examining single-year observations: 2006 (furthest from crisis onset), 2007 (immediately pre-crisis), 2008 (crisis year one), and 2009 (crisis peak year).

Table 9. Robustness to alternative measurement windows (year-by year specification).

	2006		2007		2008		2009
	b	se	b	se	b	se	b	se
Equity	1.27	1.62	3.31 **	1.40	−14.82 ***	3.94	−71.67 ***	9.71
LLR	39.56	33.99	−61.36	51.45	−26.60 **	13.10	−44.85	31.47
NPA	5.13	8.88	17.64 ***	4.39	23.41 ***	2.92	23.92 ***	4.17
Securities	−6.03 ***	1.11	−4.85 ***	1.09	0.14	1.10	−6.31 ***	2.31
BD	3.92 ***	0.87	5.83 ***	0.87	6.58 ***	0.92	4.23 ***	1.25
Cash	−14.17 ***	4.88	−8.72 **	4.07	−1.96	2.82	2.00	2.18
ROA	40.25	24.97	11.14	16.53	−35.89 ***	8.78	−3.12	11.45
Number of siblings	−0.03 ***	0.01	−0.03 ***	0.01	−0.03 *	0.02	0.02	0.03
Risk_dispersion	2.32 ***	0.43	1.64 ***	0.43	1.47 ***	0.45	3.13 ***	0.80
Size_dispersion	−0.01	0.22	−0.04	0.22	−0.20	0.20	0.67 **	0.33
Roa_dispersion	−53.89 *	28.53	−32.02 ***	11.04	−136.67	102.03	−487.29 **	236.40
Dominance_ratio	46.20 ***	6.29	42.54 ***	5.57	57.78 ***	8.30	47.83 ***	12.36
Sibling weakest	0.51 **	0.22	0.38 *	0.22	0.33 *	0.19	0.36 *	0.18
_cons	−5.24 ***	0.65	−5.39 ***	0.59	−5.23 ***	0.75	−0.51	1.33
N	1490		1490		1490		1490
chi2	197.47		257.49		445.71		487.34
ll	−417.85		−434.06		−364.85		−137.64
pseudo_r2	0.19		0.23		0.38		0.63

* p < 0.10, ** p < 0.05, *** p < 0.01.

presents the results.

The temporal pattern reveals important insights about sibling dynamics in bank failure prediction. Using 2006 data only, the weakest link coefficient (0.51, p < 0.05) indicates that concentrated vulnerabilities predict failure even when measured three to four years in advance, suggesting persistent structural features rather than transitory conditions. In 2007, the coefficient (0.38, p < 0.10) remains significant, though traditional CAMELS indicators strengthen considerably as the crisis approaches—NPAs increase to 17.64 (p < 0.01) and brokered deposits to 5.83 (p < 0.01)—indicating both individual and group-level dynamics matter simultaneously.

During the crisis itself (2008), the weakest link coefficient (0.33, p < 0.10) persists, though interpretation shifts to concurrent rather than predictive relationships. The high NPAs coefficient (23.41, p < 0.01) and capital depletion (−14.82, p < 0.01) reflect acute stress during the crisis year. By 2009, traditional CAMELS indicators dominate prediction entirely, with massive NPAs (23.92, p < 0.01) and equity (−71.67, p < 0.01) coefficients indicating that individual bank distress overwhelms group-level dynamics at peak crisis.

Converting to marginal effects reveals a clear gradient: the weakest link effect is strongest when measured in 2006 (1.1 percentage points per grade increase), declining to 0.9 percentage points in 2007, 0.5 in 2008, and 0.3 in 2009. This pattern confirms that weakest link vulnerabilities are most valuable for early warning, with effects naturally attenuating as the crisis intensifies and individual bank conditions deteriorate. These findings validate our baseline choice to average 2006–2007 data, balancing stability with predictive relevance by measuring conditions when vulnerabilities emerge but failures remain preventable.

4.2. Alternative Failure Period Definitions

Our baseline analysis defines failure as occurring during 2007–2010, capturing 58.66% of all U.S. bank failures from 2001 to 2025. We test robustness by expanding the failure window to include subsequent years (2007–2011, 2007–2012, 2007–2013, and 2007–2014), while continuing to measure explanatory variables using 2006–2007 pre-crisis averages.

Table 10. Robustness to alternative failure horizons, Part I.

	2007–2011		2007–2012		2007–2013
	b	se	b	se	b	se
Equity	0.77	2.73	0.90	2.70	−0.84	2.49
LLR	33.41	170.83	−18.55	174.22	−23.78	154.99
NPA	11.02	14.39	14.13	14.01	11.98	12.63
Securities	−7.33 ***	2.13	−8.12 ***	2.14	−7.92 ***	1.97
BD	5.62 ***	1.68	6.33 ***	1.64	6.79 ***	1.46
Cash	−21.48 **	10.35	−20.50 **	9.94	−13.62	8.63
ROA	−9.71	10.69	−9.12	10.60	−7.18	5.60
Number of siblings	−0.07 **	0.03	−0.08 ***	0.03	−0.02	0.01
Risk_dispersion	−0.25	0.61	−0.34	0.61	−0.40	0.55
Size_dispersion	0.93 ***	0.27	0.97 ***	0.27	0.59 ***	0.23
Roa_dispersion	−23.37	17.11	−23.52	16.88	−5.37	7.18
Dominance_ratio	−0.56	1.14	−0.89	1.11	−0.16	0.90
Sibling_weakest	0.83 **	0.35	1.03 **	0.42	0.58 *	0.33
_cons	−4.01 ***	1.25	−4.18 ***	1.22	−3.55 ***	1.11
N	1490		1490		1490
chi2	67.24		77.68		72.15
ll	−146.94		−152.45		−186.15
pseudo_r2	0.19		0.20		0.17

* p < 0.10, ** p < 0.05, *** p < 0.01.

and

Table 11. Robustness to alternative failure horizons, Part II.

	2007–2014		2007–2010 with Technical Failures
	b	se	b	se
Equity	−0.84	2.49	0.59	2.71
LLR	−23.78	154.99	94.41	171.41
NPA	11.98	12.63	12.24	15.10
Securities	−7.92 ***	1.97	−5.31 **	2.13
BD	6.79 ***	1.46	5.82 ***	1.74
Cash	−13.62	8.63	−13.67	9.23
ROA	−7.18	5.60	−13.43 *	7.67
Number of siblings	−0.02	0.01	−0.05 **	0.02
Risk_dispersion	−0.40	0.55	0.15	0.64
Size_dispersion	0.59 ***	0.23	0.91 ***	0.26
Roa_dispersion	−5.37	7.18	−21.60	13.75
Dominance_ratio	−0.16	0.90	−0.89	1.16
Sibling_weakest	0.58 *	0.33	0.75 *	0.42
_cons	−3.55 ***	1.11	−4.65 ***	1.28
N	1490		1490
chi2	72.15		53.00
ll	−186.15		−135.64
pseudo_r2	0.16		0.16

* p < 0.10, ** p < 0.05, *** p < 0.01.

present the results.

Extending the failure window to include 2011 and 2012 actually strengthens the weakest link effect, with coefficients increasing to 0.83 (p < 0.05) and 1.03 (p < 0.05), respectively. This strengthening likely reflects that banks failing in 2011–2012 (92 and 51 banks, respectively) survived the acute crisis phase but ultimately succumbed due to persistent weaknesses—precisely the type of prolonged stress where resource constraints bind most severely. Further extending to 2013 and 2014 shows modest attenuation, with coefficients of 0.58 (p < 0.10), as failures in these years (24 and 18 banks) likely reflect more idiosyncratic factors rather than systemic stress. Nevertheless, continued significance demonstrates that pre-crisis sibling dynamics predict failure risk six to seven years forward.

Converting to marginal effects, our baseline 2007–2010 window yields 1.6 percentage points per grade increase. Extending to include 2011 strengthens this to 1.9 percentage points, and through 2012 to 2.6 percentage points—indicating that pre-crisis sibling vulnerabilities predict both immediate and delayed failures. Extending to 2013–2014 shows modest attenuation (1.7–1.8 percentage points), yet effects remain significant even six to seven years post-measurement.

Finally, we broaden the dependent variable beyond formal FDIC closures by incorporating “technical failures” following Cole and White (2012). Under this approach, a bank is classified as technically failed when its book capital buffer is insufficient to absorb a moderate write-down of problem assets, operationalized as (Equity + Loan Loss Reserves − 0.5 × NPAs) < 0. We recode failure to equal one for banks that meet this technical failure criterion during 2007–2010, even if they were not formally closed, and re-estimate the model using the same 2006–2007 pre-crisis covariates. The last column of Table 11 shows that the weakest link effect remains positive and statistically significant, with marginal effects of 1.6 percentage points per grade. Overall, this alternative definition suggests our findings capture underlying insolvency risk and holding company resource constraints, not merely the subset of distressed banks that were closed within a particular calendar window.

4.3. Alternative Weakness Level Thresholds

Our baseline analysis identifies the weakest link variables using a 10th percentile cutoff for severely distressed affiliates. We test the sensitivity of this choice by re-estimating the full model using alternative thresholds ranging from the 5th to the 30th percentile, assessing whether weakest link effects are driven by extreme outliers or reflect broader sibling vulnerabilities.

Table 12. Robustness to alternative weakest-link thresholds, Part I.

	5% Threshold		10% Threshold		15% Threshold
	b	se	b	se	b	se
Equity	1.24	2.69	1.75	2.74	1.56	2.87
LLR	104.89	187.09	74.28	178.65	30.21	179.90
NPA	12.70	15.67	13.15	15.39	17.00	16.02
Securities	−5.88 ***	2.27	−5.31 **	2.19	−5.64 **	2.23
BD	5.66 ***	1.82	5.80 ***	1.79	6.15 ***	1.82
Cash	−17.72 *	10.67	−18.86 *	10.22	−15.40	9.75
ROA	−6.98	10.10	−8.47	10.10	−6.56	9.68
Number of siblings	−0.08 **	0.03	−0.07 **	0.03	−0.07 **	0.03
Risk_dispersion	−1.43	1.05	0.20	0.66	0.42	0.67
Size_dispersion	1.25 ***	0.33	0.99 ***	0.28	1.03 ***	0.28
Roa_dispersion	−15.91	15.46	−20.52	16.19	−16.71	14.78
Dominance_ratio	−1.63	1.29	−1.08	1.21	−0.67	1.27
Sibling_weakest	2.09 ***	0.64	0.87 **	0.44	1.69 ***	0.41
_cons	−6.93 ***	1.54	−4.79 ***	1.31	−7.31 ***	1.37
N	1490		1490		1490
chi2	61.45		54.51		73.62
ll	−123.84		−127.30		−117.75
pseudo_r2	0.20		0.18		0.24

* p < 0.10, ** p < 0.05, *** p < 0.01.

and

Table 13. Robustness to alternative weakest-link thresholds, Part II.

	20% Threshold		25% Threshold		30% Threshold
	b	se	b	se	b	se
Equity	1.56	2.90	1.24	2.76	1.57	2.73
LLR	18.06	182.07	71.97	181.92	72.78	181.11
NPA	17.63	15.64	16.87	15.76	15.68	15.53
Securities	−5.18 **	2.19	−5.02 **	2.20	−4.93 **	2.20
BD	5.60 ***	1.74	5.41 ***	1.76	5.67 ***	1.74
Cash	−21.35 **	10.27	−19.85 *	10.35	−18.95 *	10.45
ROA	−7.16	9.42	−8.03	9.59	−7.92	9.46
Number of siblings	−0.06 **	0.03	−0.06 **	0.03	−0.06 **	0.03
Risk_dispersion	1.01 *	0.57	1.19 **	0.56	0.85	0.52
Size_dispersion	0.82 ***	0.27	0.77 ***	0.27	0.79 ***	0.27
Roa_dispersion	−16.66	14.64	−15.62	15.03	−16.50	15.11
Dominance_ratio	−0.12	1.25	−0.38	1.23	−0.50	1.24
Sibling_weakest	1.10 ***	0.35	0.73 **	0.31	0.58 **	0.29
_cons	−6.35 ***	1.34	−5.43 ***	1.28	−4.96 ***	1.30
N	1490		1490		1490
chi2	65.10		59.98		55.49
ll	−122.01		−124.57		−126.81
pseudo_r2	0.21		0.19		0.18

* p < 0.10, ** p < 0.05, *** p < 0.01.

present the results.

Across all thresholds, weakest link coefficients remain positive and statistically significant, with magnitudes generally declining as the definition of weakness becomes more inclusive. The most stringent 5th percentile yields the largest effect, while the baseline 10th percentile balances effect size and sample coverage. More inclusive thresholds continue to exhibit economically meaningful coefficients, indicating that even moderately weak siblings elevate group-level failure risk.

Marginal effects, interpreted as the change in failure probability per one-grade deterioration in the weakest affiliate’s condition, follow a similar pattern. The 5th percentile threshold produces the largest marginal effect at approximately 4.0 percentage points per grade. The baseline 10th percentile yields 1.7 percentage points per grade, while alternative thresholds produce effects of 3.2 (15th percentile), 2.1 (20th), 1.4 (25th), and 1.1 percentage points (30th percentile) per grade. Importantly, marginal effects remain statistically significant across all thresholds, demonstrating that weakest link effects are not confined to extreme cases but represent a persistent feature of holding company dynamics.

Other group-level variables remain stable across threshold definitions. Size dispersion continues to be positively and significantly associated with failure risk, while the number of siblings retains a negative and generally significant relationship, consistent with diversification benefits. Traditional CAMELS indicators show similar magnitudes and significance across specifications. Overall, these results validate our baseline threshold choice while demonstrating robustness across a wide range of alternative definitions, supporting the use of weakest link analysis in supervisory early warning frameworks.

4.4. Alternative Weakest Link Specifications

Column 1 of

Table 14. Robustness to alternative weakest link specifications.

	Baseline		Binary		Continuous
	b	se	b	se	b	se
Equity	1.75	2.74	−0.03	2.57	−0.29	2.43
LLR	74.28	178.65	−50.42	152.83	−62.56	151.55
NPA	13.15	15.39	14.14	12.51	15.21	12.66
Securities	−5.31 **	2.19	−7.51 ***	1.92	−7.71 ***	1.92
BD	5.80 ***	1.79	6.20 ***	1.46	6.24 ***	1.42
Cash	−18.86 *	10.22	−9.54	7.63	−7.10	7.60
ROA	−8.47	10.10	−6.66	5.48	−6.75	5.43
Number of siblings	−0.07 **	0.03	−0.02 *	0.01	−0.02 *	0.01
Risk_dispersion	0.20	0.66	0.00	0.45	0.00	0.4
Size_dispersion	0.99 ***	0.28	0.48 **	0.23	0.44 **	0.22
Roa_dispersion	−20.52	16.19	−9.33	7.15	−6.35	7.15
Dominance_ratio	−1.08	1.21	0.11	0.94	0.19	0.91
Sibling_weakest	0.87 **	0.44	1.08 ***	0.34	4.57 *	2.76
_cons	−4.79 ***	1.31	−3.12 ***	0.77	−1.68 **	0.75
N	1490		1490.00		1490.00
chi2	54.51		79.82		74.98
ll	−127.30		−182.32		−184.74
pseudo_r2	0.18		0.18		0.17

* p < 0.10, ** p < 0.05, *** p < 0.01.

replicates the baseline categorical specification from the main analysis. Columns 2 and 3 examine alternative definitions to ensure that this result is not driven by the categorical measurement choice. Column 2 replaces the three-tier measure with a binary indicator for whether any sibling falls in the bottom decile of the cash ratio. The coefficient increases to 1.08 (p < 0.01) and is more precisely estimated. The corresponding marginal effect implies a 3.2 percentage point increase in failure probability when a holding company includes any high-risk sibling.

Column 3 uses a continuous alternative specification that preserves variation in the severity of liquidity weakness at the most vulnerable affiliate. The weakest link coefficient remains positive and statistically significant, consistent with concentrated weakness at the weakest affiliate increasing failure risk. The implied marginal effect is economically large: a one standard deviation deterioration in the weakest affiliate’s liquidity position increases failure probability by about 18 percentage points (evaluated at sample means). Because this specification uses a different scaling than the categorical and binary measures, magnitudes are not directly comparable across columns.

Across specifications, results for controls are stable. Size dispersion is positive and significant, while the number of siblings is negative and significant, consistent with diversification benefits. CAMELS patterns are also similar across columns, and explanatory power is nearly unchanged (pseudo-R² about 0.17 to 0.18). Overall, weakest link effects are robust across functional forms. The binary specification is estimated most precisely, suggesting that the presence of an extremely weak sibling is a particularly reliable early-warning signal.

5. Discussion

The empirical results presented in Section 3 reveal several important regularities. Bank failure risk within MBHCs is not fully reflected by traditional bank-level indicators alone. Our analysis demonstrates that organizational fragility and systemic vulnerabilities emerge from sibling dynamics—particularly from the weakest affiliate—rather than from aggregate group conditions or individual bank fundamentals. This finding extends prior work on internal capital markets and is consistent with a role for within-group allocation frictions during stress.

The remainder of this section interprets these patterns, delineates the scope of the estimates, and outlines directions for future research.

5.1. Interpretation of Results

The patterns in Section 3 suggest that MBHC affiliation introduces an organizational layer to failure risk. In a multi-bank structure, a subsidiary’s vulnerability reflects not only its own condition but also the holding company’s internal support capacity and the competing demands generated across affiliates. This perspective helps explain why standard bank-level indicators are less informative within MBHCs than for standalone institutions, as internal capital markets and within-group spillovers can weaken the link between a focal bank’s fundamentals and its realized failure outcome.

Group structure helps characterize when internal support is likely to be more constrained. Larger sibling networks are consistent with greater scope for diversification and internal adjustment, while greater dispersion in affiliate size is consistent with frictions that limit effective reallocation, whether through coordination costs or strategic prioritization. Under this view, network size and size dispersion proxy for how smoothly the internal capital market can operate when multiple affiliates face stress simultaneously.

The weakest link results suggest that within-group constraints become binding under stress. Severe weakness at one subsidiary can absorb limited internal capacity and leave other affiliates more exposed, making concentrated tail vulnerability more informative than group averages. Differences across weakest link definitions point to which vulnerabilities matter most for spillovers: measures tied to capital, liquidity, asset quality, and income volatility are more informative than profitability alone in this setting.

We next discuss how the crisis setting and data constraints shape the scope of these inferences.

5.2. Scope Limitations

Several features of our sample and measurement approach bound the scope of the estimates. The banking and regulatory environment has evolved substantially since 2007–2010, including higher capital and liquidity standards, the expansion of stress testing, and broader macroprudential supervision. Accordingly, the estimates are best interpreted as characterizing MBHC risk dynamics under severe, crisis-like conditions driven by widespread credit deterioration, and the crisis-era magnitudes need not carry over to normal times or to stress episodes driven by different mechanisms.

At the same time, the channels highlighted by the results reflect organizational features of multi-bank structures that remain relevant for modern monitoring. Internal capital markets, resource competition among affiliates, and the possibility that weakness at a single subsidiary strains group support capacity are inherent to MBHCs. For this reason, weakest link and group structure measures are best viewed as complements to consolidated and bank-level supervisory metrics, particularly when concern centers on concentrated vulnerabilities within a group.

Our focus on the 2007–2010 window reflects deliberate methodological choices that strengthen identification while imposing interpretive boundaries. The period contains a large share of U.S. bank failures, providing the statistical power needed to study sibling dynamics in a multilevel setting. The relative homogeneity of the underlying shock, centered on real estate credit deterioration, supports cleaner identification of organizational channels than pooling heterogeneous failure episodes across regimes. This design clarifies how MBHC structure mediates traditional risk factors under systemic stress, but it also implies that the estimates primarily reflect responses to credit-crisis conditions. While the organizational mechanisms may operate more broadly, their relative importance and economic magnitudes may differ under alternative stress scenarios, including faster-moving liquidity events. The 2023 bank failures, for example, highlighted resource allocation challenges within holding company structures, although the speed of deposit outflows limited the scope for traditional internal capital market adjustments to operate through standard channels.

Finally, our analysis necessarily infers within-group dynamics from reduced-form relationships rather than directly observing internal capital reallocation or managerial resource allocation decisions. This limitation reflects data constraints: intra-group transfers and allocation processes are not disclosed in public regulatory filings. Consistent with the internal capital markets literature (Campello, 2002; Ashcraft, 2008; Raykov & Silva-Buston, 2020; Wang et al., 2022), we interpret the weakest link patterns as consistent with resource competition and constrained internal support capacity. The persistence of weakest link effects after controlling for parent strength, their stronger presence in larger sibling networks, and their asymmetry relative to aggregate group measures are all consistent with this interpretation, though more direct tests would require confidential supervisory data on intra-group capital flows.

5.3. Directions for Future Research

Motivated by these limitations, we highlight several directions for future research that could provide additional tests of the proposed mechanisms and evaluate whether the results generalize beyond our setting.

We do not explore heterogeneity in effects across MBHCs by size, geographic concentration, subsidiary composition, or governance structure. Splitting the sample along multiple dimensions substantially reduces the number of failures available for estimation, so we leave these heterogeneity analyses for future research with larger samples or confidential supervisory data.

Our baseline analysis uses a standard logit framework consistent with the bank failure prediction literature, prioritizing interpretability and hypothesis testing over purely predictive performance. Future work could combine our conceptual framework with machine learning approaches to assess whether these organizational measures improve algorithmic early-warning systems.

Our weakest link measures are constructed from publicly available regulatory accounting data. They capture concentrated vulnerabilities in capital, asset quality, liquidity, earnings, and income volatility, but do not incorporate market-based signals, supervisory ratings, or funding-run measures. Future work could extend the weakest link framework to these alternative distress indicators when data access permits.

Researchers with access to confidential Federal Reserve data could combine our weakest link framework with granular capital flow information to quantify resource diversion patterns and identify which siblings receive priority support during stress. Examining how post-Dodd–Frank regulatory changes affect sibling dynamics would test whether our 2007–2010 findings persist under the current regime. Exploring whether these patterns vary across different crisis types would provide valuable insights, as banking stress arising from interest rate shocks, liquidity crises, or rapid deposit flight may exhibit different internal capital market dynamics than the gradual credit deterioration that characterized 2007–2010. Natural experiments where holding companies face exogenous shocks to specific subsidiaries could reveal resource reallocation responses through difference-in-differences or event study designs. Understanding these dynamics across varied contexts will be crucial for developing robust regulatory frameworks.

6. Practical and Policy Implications

Our results suggest several actionable ways supervisors and regulators can incorporate within-group tail risk in MBHCs. These implications translate the weakest link and group structure findings into practical applications for monitoring, stress testing, and resolution.

First, monitoring frameworks can be augmented with weakest link measures that flag groups where the weakest affiliate is in an extreme tail of capital, liquidity, asset quality, or earnings stability. For example, supervisors could use these flags as watchlist triggers that prompt targeted subsidiary-level reviews and more frequent follow-up during the examination cycle, even when consolidated indicators appear stable. This provides a simple screening tool that can prioritize more frequent subsidiary-level reviews even when group averages appear healthy.

Second, supervisory stress tests can be strengthened by explicitly modeling within-group spillovers under limited internal support capacity. In addition to applying scenarios to each affiliate, supervisors can evaluate whether capital and liquidity demands at the weakest affiliate would plausibly draw down internal support in ways that leave other affiliates unable to meet minimum requirements under the same scenario.

Third, Basel III and related prudential frameworks can be complemented by assessing whether subsidiary-level requirements remain resilient when internal support is constrained during stress. In groups with large differences across affiliates, reliance on consolidated or “typical” conditions can understate vulnerability to concentrated weakness at specific subsidiaries.

Fourth, data-driven early warning systems can incorporate group structure variables and weakest link indicators as features, complementing traditional bank-level fundamentals by capturing concentrated vulnerabilities that averages can mask.

Finally, resolution planning can incorporate weakest link diagnostics to identify which affiliates pose the greatest threat to group-wide resilience and orderly resolution when internal support capacity is binding.

7. Conclusions

This paper examines how MBHC structure alters the relationship between traditional risk indicators and bank failure outcomes. Using U.S. bank failures during the 2007–2010 crisis, we show that failure risk within MBHCs is not fully captured by bank-level fundamentals or aggregate group measures alone.

Three main findings emerge. First, traditional CAMELS indicators exhibit substantially lower explanatory power for banks operating within MBHCs than for standalone institutions. Second, group structure matters for failure risk: larger sibling networks are associated with lower failure probabilities, while greater size dispersion across affiliates is associated with higher risk, consistent with frictions in internal resource allocation. Third, and most importantly, weakest affiliate vulnerabilities strongly predict failure risk throughout the holding company. Weakest link measures based on capital adequacy, asset quality, liquidity, earnings, and income volatility are associated with economically meaningful increases in failure probability for all affiliated banks, even after controlling for individual bank fundamentals and aggregate group characteristics.

Taken together, these findings demonstrate that sibling dynamics and concentrated affiliate weakness play an important role in shaping failure risk within MBHCs. By identifying the weakest affiliate as a key determinant of group-wide outcomes, the paper highlights an organizational channel through which traditional risk indicators are amplified during periods of systemic stress.