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Loan portfolio diversification and bank insolvency risk
January 13, 2015
ABSTRACT
This paper examines whether banks’ loan portfolio diversification is associated with bank insolvency risk using the samples of U.S. commercial banks over the period 2005:Q1-2013:Q3. The empirical analysis is conducted with two-stage estimation procedures to address potential endogenous concerns. We also analyze the probability of banks’ being closed as a function of loan diversity and other bank characteristics using the probit regression. The results show that loan diversification is inversely related to bank insolvency risk, indicating that banks may be able to diminish financial fragility by diversifying their loan portfolios. The results also suggest that bank size, income diversity, liquidity, core deposits, tier 1 capital, profitability and residential single-family mortgages are negatively associated with bank insolvency risk, while non-interest income, brokered deposits, non-performing loans and unemployment rate are positively related to the likelihood of bank insolvency.
Keywords: Commercial banks; Insolvency risk; Loan and income diversification
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Loan portfolio diversification and bank insolvency risk
1. Introduction
The number of bank closures has sharply risen during a period of recent economic
downturn in the United States. The Federal Deposit Insurance Corporation (FDIC) reports that 465
insured U.S. commercial banks failed between January 2008 and December 2012, while only 27
banks closed from October 2000 to December 2007. These developments have severely strained
the resources of the FDIC.1 The burden could eventually fall on the general taxpayers in the form
of higher taxes as noted by Kane (1985) and exemplified by the recent bailouts for the demise of
large financial institutions. The high failure of commercial banks is a concern for banking
supervisors because bank safety and soundness is a major regulatory responsibility.
A number of studies have investigated the factors influencing bank failures. Earlier studies
rely on the standard proxies for the CAMEL ratings2 and show that these CAMEL-type variables
are useful to explain the likelihood of bank failures (e.g., Sinkey, 1975; Thomson, 1992; Cole and
Gunther, 1995). Wheelock and Wilson (2000) use typical measures of productive inefficiency as
proxies for management quality and find evidence that managerial inefficiency increases the
likelihood of bank failure. Reinhart and Rogoff (2011) argue that external debt surges are a
1 From 2008 through 2011, bank failures cost the deposit insurance fund an estimated $88 billion, and with failures
accelerating, the fund’s balance turned negative in 2009. 2 The acronym "CAMELS" refers to the six components of a bank's financial condition that are assessed: Capital
adequacy, Asset quality, Management, Earnings, Liquidity, and Sensitivity to market risk. During an on-site bank
examination, bank supervisory authorities assign each bank a score on a scale of 1 to 5 for each component. A 1(5)
indicates the highest (lowest) rating and represents the least (greatest) supervisory concern. The Federal Reserve,
FDIC, and other financial supervisory agencies employ this rating system to provide a summary of bank conditions at
the time of an exam.
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recurrent antecedent to banking crises. Berger and Bouwman (2013) show that capital has a
substantial impact on the probability of survival for small banks at all times (during banking crises,
market crises, and normal times). DeYoung (2003) finds that aggressive lending, expensive deposit
funding and cost inefficiencies are significant predictors of bank failure. Cole and White (2012)
and Government Accountability Office (2013) report that the concentration on real estate loans is
among the contributing factors that led to an increased likelihood of recent bank closures across
all states. These observations raise the following questions: Would a recent wave of bank failures
have been avoided if banks had diversified more in their loan portfolios? Do banks reduce financial
fragility from diversification of their products and loan portfolios? Does diversification diminish
or increase the chances of bank failure? What are the major determinants of recent bank failures?
In this paper, we address these unanswered questions by undertaking an empirical investigation
using the samples of U.S. commercial banks over the period 2005-2012.
The corporate finance literature documenting the drawbacks of diversification suggests that
firms should concentrate their activities on specialized area to take greatest advantage of
management’s expertise and reduce agency problems (Jensen, 1986; Berger and Ofek, 1995;
Servaes, 1996). Berger and Ofek (1995), and Servaes (1996) show that diversified firms trade at a
substantial discount relative to focused firms. On the other hand, diversification proves to be
important in the theoretical literature of financial intermediation. Froot et al. (1993) and Froot and
Stein (1998) argue that diversification across sectors is a hedge against insolvency risk that reduces
the firm’s probability of costly financial distress. Diamond (1984) develops a theory implying that
banks diversifying their credit portfolio into new sectors can reduce their probability of default.
Banks that provide diverse financial services could achieve economies of scope that boost
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performance and market valuations.3 However, diversification benefits will be limited if
diversified banks lend more of their assets to risky borrowers and operate with greater financial
leverage. Froot et al. (1993) and Froot and Stein (1998) present that banks that engage in active
risk management hold less capital and invest more aggressively in risky and illiquid loans.
Cebenoyan and Strahan (2004) find that banks that manage their credit risk through loan sales and
purchases hold more risky loans (commercial real estate loans). Diversification may aggravate
bank performance if banks diversify into new lines of business where management does not have
expertise and experience (Stiroh, 2006; Mercieca et al., 2007). The diversity of activities could
intensify agency problems and thereby lower the market valuations of financial conglomerates
(Laeven and Levine, 2007).
Despite the growing empirical studies on the effects of diversification on performance of
banks, there is no general consensus as to whether it is advantageous for banks to diversify or to
focus on the specialized area. DeYoung and Roland (2001) provide evidence that U.S. commercial
banks shifting product mix in the directions of more non-interest and fee-based activities increase
their revenue volatility, implying that an ongoing trend toward these fee-based activities is
associated with higher earnings volatility. Stiroh and Rumble (2006) show that benefits of revenue
diversification exist between U.S. financial holding companies, but these gains are offset by the
costs of increased exposure to volatile non-interest activities. Rossi et al. (2009) find that
diversification across industries and loan book granularity dampens cost efficiency, but increases
profit efficiency and reduces banks’ realized risk for large Austrian commercial banks. Berger et
al. (2010) examine the effects of product and geographical focus versus diversification on
3 Laeven and Levine (2007) argue that it is extremely challenging to measure economies of scope in the provision of
financial services.
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performance of Chinese banks and find that diversification is associated with decreased profits and
increased costs. Sanya and Wolfe (2011) show that diversification across and within both interest
and non-interest income generating activities increases risk-adjusted profits and decreases
insolvency risk for banks in emerging economies. Shim (2013) provides evidence that the
probability of insolvency risk decreases for diversified U.S. bank holding companies that have
broader sources of operating revenue.
Given the conflicting views and inconsistent empirical results in the literature, the issue of
net effects of diversification on bank performance and financial stability still draws attention to
the need for additional investigation. Unlike the prior studies that focus on the link between
revenue diversification and financial performance of banks, this paper intends to provide evidence
on whether banks’ loan portfolio diversification influences their insolvency risk. We test the effect
of loan diversity on bank insolvency risk by measuring insolvency risk using the Z-score of each
bank. Following the literature, we define the Z-score as the return on assets (ROA) plus the capital
to asset ratio divided by the standard deviation of asset returns (e.g., Stiroh and Rumble, 2006;
Laeven and Levine, 2009; Shim, 2013). The Z-score measures the inverse of the probability of
insolvency. We regress the Z-score on the bank’s loan diversification and a broad set of control
variables.
To shed further light on the factors of recent bank failures and to obtain more insights on
the relationship between loan diversification and the likelihood of bank failures, we additionally
analyze the probability of banks’ being closed as a function of loan diversity and other bank
characteristics using probit regressions. We observe failed banks from the FDIC’s Failed Bank list.
By investigating the bank specific characteristics associated with closures of commercial banks,
we can identify important drivers that cause a wave of recent U.S. bank failures.
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Our study adds to the literature by building on previous studies of impact of portfolio
diversification on bank stability in several ways. First, U.S. banks have been shifting away from
traditional lending activities toward a broader range of financial services such as brokerage,
insurance underwriting, and other types of activities that generate non-interest income. The non-
interest income share for the U.S. bank holding companies accounts for 45.63% of total operating
revenue in 2011:Q1, compared to 15.24% in 1990:Q1 (Shim, 2013). The increased shifts toward
non-interest activities draw attention for researchers to investigate the consequences of these
diversification choices on bank performance (e.g., DeYoung and Roland, 2001; Stiroh and Rumble,
2006). Despite its growing importance in bank revenue, the empirical analysis on whether greater
reliance on non-interest income can lower bank risk is surprisingly limited. In this paper, we are
particularly interested in examining how increased non-interest income is associated with bank
insolvency risk. This paper helps to fill the gap in the extant banking diversification-performance
literature which is mostly focused on examining how noninterest income affects the volatility of
bank profits and revenues. The evidence of this paper should provide some insights for industry
practitioners as well as regulators who consider encouraging or discouraging the bank’s
diversification choice into non-interest activities to keep the likelihood of bank failure low.
Second, we attempt to identify key factors that have contributed to a wave of recent bank
failures. This study employs a much larger sample of closed banks than previous studies. Given
the significant impact of bank failures on the overall health of the US economy, it would seem
worthwhile to revisit this issue. Our new evidence can provide important implications for
regulators in the monitoring of safety and financial soundness of commercial banks and control of
limiting banks’ exposures to concentrated forms of credit risk.
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Finally, we perform various robustness checks. It is well documented in the corporate
finance literature that estimated results may be biased if the firm’s decision to diversify is
endogenous (Campa and Kedia, 2002; Villalonga, 2004a). Our regression analyses initially use the
lagged-structure model to lessen endogeneity concerns. Additionally, we address this potential
endogeneity problem employing two-stage estimation procedures. To examine whether our main
results are sensitive to the definition of key independent variables, we use alternative measures of
the bank’s loan diversification.
The paper is structured as follows. Section 2 reviews existing theories and formulates main
hypotheses. Section 3 discusses variables used in the analysis. The regression methodology is
described in Section 4. Section 5 presents the data and analyzes empirical results. Section 6
concludes.
2. Formulation of main hypotheses
The costly bank failure provides incentives for the bank to minimize its chance of
insolvency by monitoring loan contracts. Some theoretic models suggest that diversification helps
financial institutions attain credibility in their role as monitors of borrowers. Diamond (1984) in
his delegated monitoring model shows that diversification serves to reduce the financial
intermediary’s delegation costs and financial intermediaries (such as banks) can lower the
probability of their default by adding more independent risks. Similar results are obtained by the
related work of Ramakrishnan and Thakor (1984), and Boyd and Prescott (1986).
However, this argument is challenged by a theoretical framework that incorporates
financial intermediary’s monitoring incentives. Winton (1999) argues that credit risk on most bank
loans is endogenously affected by the intensity and efficacy of the bank’s loan monitoring. Banks
can influence the credit risk of a loan investment by improving monitoring quality and screening
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expertise. Effective monitoring enables the bank to identify troubled loans before they worsen too
far, improving loan returns. Acharya et al. (2006) imply that weakened monitoring incentives and
a poorer-quality loan portfolio result in diseconomies of scope when a risky bank expands loan
activity into new industries and sectors. The theoretical work done by Dell'Ariccia et al. (1999),
Dell'Ariccia (2001) and Marquez (2002) suggests that banks suffer an adverse-selection effect
when they enter new sectors where incumbent banks have an informational advantage over new
entrants by virtue of their established relationships with borrowers (the “winner’s curse”). This
puts entrants in a worse position than the incumbents and may make diversification into new
sectors more likely to increase the bank’s likelihood of failure and less likely to enhance the bank’s
monitoring incentives (Winton, 1999).
This paper aims to shed light on these contradicting implications by analyzing the loan
portfolio diversification of U.S. commercial banks. We expect the loan diversity to be positively
associated with bank insolvency risk if banks diversifying their loan portfolios into new sectors
face the winner’s curse problem. If diversification involves in expanding into sectors where
monitoring expertise is lacking, then the worse returns in new sectors may reduce the bank’s
average loan returns and increase the probability of bank insolvency. On the other hand, we predict
that the loan diversity is negatively related to the likelihood of insolvency if engaging in various
loan activities that have low or negative correlations reduces the chance of costly financial distress
and increases risk-adjusted returns. Therefore, our null and alternative hypotheses are as follows:
Hypothesis 1a. Loan diversification is positively associated with the likelihood of bank insolvency. Hypothesis 1b. Loan diversification is inversely associated with the likelihood of bank insolvency.
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3. Variable estimation
3.1. Measurement of bank insolvency risk
Following the literature, we utilize a Z-score as a proxy measure of the likelihood of bank
insolvency (Hannan and Hanweck, 1988; Stiroh and Rumble, 2006; Laeven and Levine, 2009;
Barry et al., 2011; Shim, 2013). The Z-score of each bank is measured by the return on assets
(ROA) plus the capital to asset ratio divided by the standard deviation of ROA. The standard
deviation of ROA is calculated on a moving average basis over the preceding twelve quarters. The
Z-score is considered as a measure of the bank’s distance-to-default since it presents the number
of standard deviations that profits should fall to push a bank into insolvency. The Z-score is
inversely related to the probability of insolvency. Therefore, a higher Z-score indicates a lower
probability of bank default.
3.2. Loan portfolio diversification
We employ a Herfindahl-Hirschman index (HHI) to construct a loan-based measure of
diversification for each bank. We classify loan scope of the commercial bank into six major sectors:
real estate loans (REA), loans to depository institutions (DEP), commercial and industrial loans
(COM), loans to individuals (IDV), agricultural loans (AGR), and all other loans (OTH).4 The loan
portfolio diversification (Loan HHI) is then calculated by one minus the sum of the squared loan
portfolio shares across all types of loans:
2 2 2 2 2 2
1REA DEP COM IDV AGR OTH
Loan HHITOL TOL TOL TOL TOL TOL
= − + + + + + (1)
4 Because a breakdown of the U.S. commercial banks’ lending into specific industries is not publicly available, our
loan diversity measures rely on sectoral aggregation.
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where TOL denotes total loans and is equal to the sum of the absolute values of REA, DEP, COM,
IDV, AGR, and OTH. A lower value of this diversity index suggests that the bank has a specialized
loan-making, while the higher value indicates that the bank engages in a combination of various
loan-making activities. Loan HHI takes a value of zero if all loans are made to a single sector.
Alternatively, we also define diversified banks in terms of loan activities using a dummy variable
which is equal to one if loan HHI is greater than 90th percentile of HHI distribution and zero
otherwise.
3.3. Other control variables
We include financial statement variables as additional controls, hypothesizing that
characteristics of bank balance sheets and income statements are associated with bank insolvency
risk.
Firm size: The “too big to fail” hypothesis suggests that larger banks may have more
incentives to engage in riskier lending activities due to a government’s safety net. However, the
charter value acts as a restraint against moral hazard (Keeley, 1990). Larger banks may deter
excessive risk-taking behavior to protect their charter or franchise value. Thus, it is difficult to
predict a priori the direction of impact of bank size on its insolvency risk. We measure the natural
logarithm of total assets as a proxy for firm size.
Income diversity: To examine whether the income diversification is associated with the
probability of bank insolvency, we include the income diversity as an additional explanatory
variable in the equation. Our income diversity considers the breakdown of total operating revenue
into two broad categories: net interest income (INT) and total non-interest income (NON). We
follow the basic Herfindahl-Hirschman index (HHI) approach used in the previous studies (Stiroh
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and Rumble, 2006; Shim, 2013). Accordingly, the income diversity is calculated by the sum of the
squares of income share of a bank’s operating revenue across different sources of income:
2 2
1INT NON
Income HHITOI TOI
= − + (2)
where TOI represents total operating income and is equal to the sum of the absolute values of
INT and NON. A higher value of Income HHI signifies that income becomes more diversified.
On the other hand, a lower value of Income HHI indicates that bank income comes from a
specialized source. If the income diversification lowers the volatility of the bank’s profits and
reduces capital requirement, we expect this variable to have a positive sign. However, income
diversity may have a negative impact on the bank’s financial safety if the costs of income
diversification outweigh its benefits.
Non-interest share: DeYoung and Roland (2001) show that replacing traditional lending
activities with non-interest and fee-based activities is associated with higher volatility of bank
earnings. They also find that this shift in product mix is accompanied by an increase in bank
profitability, suggesting a risk premium associated with these activities. Stiroh and Rumble (2006)
find that increased exposure to non-interest activities is relatively volatile but not more profitable
than lending activities. A higher share of non-interest income in total income is expected to be
positively related to bank insolvency risk if increased non-interest income is more exposed to high
volatility. In contrast, a negative relationship between the non-interest share and insolvency risk is
expected if cash flows from banks’ expanded services are more stable and cross-selling
opportunities increase revenues.
Liquidity : The liquidity captures the ability of the bank to meet short-term financial
obligations without having its investments or fixed assets sold quickly at lower prices. During the
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recent financial crisis, some financial institutions failed because they were unable to attain liquidity.
The larger the liquidity, the less likely is the bank to fail. Thus, the liquidity is expected to be
inversely related to bank insolvency risk. The liquidity is calculated by dividing liquid assets (cash
and marketable securities) by total assets.
Asset growth: Banks might achieve fast asset growth due to an effective business practices
and/or strong economic conditions. We expect a positive sign on this variable if banks attain fast
asset growth due to their managerial expertise. Alternatively, banks may attain rapid loan or asset
growth by risk-taking behavior such as relaxing their lending standards (DeYoung, 2003). We
predict a negative coefficient on this variable if fast asset growth is associated with weak
underwriting and credit administration practices that increase the likelihood of the bank’s financial
problems.
Brokered deposits: Banks can acquire deposits directly or indirectly through the mediation
or assistance of deposit brokers rather than from local customers. The brokers market the pooled
deposits to financial institutions for a higher rate and banks often attempt to grow rapidly using
riskier funding sources such as brokered deposits. The acceptance of these brokered deposits may
lead a bank to take greater risk because the bank must earn more to pay high interest costs
(Government Accountability Office, 2013). DeYoung and Torna (2013) and Cole and White (2012)
suggest that brokered deposits tend to be positively associated with the likelihood of bank failure.
Berger and Bouwman (2013) show that small banks are less likely to survive if they have more
brokered deposits. The higher level of brokered deposits is expected to be positively associated
with bank insolvency risk.
Core deposits: Core deposits are typically funds of a bank’s regular customers and viewed
as relatively stable and less costly sources of funding with the lower interest rates. Following the
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Uniform Bank Performance Report (UBPR) User Guide, we define core deposits as the sum of
demand deposits, automatic transfer service (ATS) accounts, money market deposit accounts
(MMDAs), savings deposits and time deposits under $100,000, minus brokered deposits under
$100,000, normalized by total assets.5 Berger and Bouwman (2013) show that more core deposits
help small and medium-sized banks survive. DeYoung and Torna (2013) find that core deposits
are associated with a reduced probability of failure. We expect a positive coefficient on this
variable if banks with larger shares of core deposits face a lower chance of bank failure.
Member of bank holding company: To control for different banking organization, we
include an indicator variable equal to one if the bank is a member of bank holding company (BHC)
and zero otherwise. BHC membership is predicted to be negatively associated with bank
insolvency risk if banks affiliated with BHC have ready access to greater financial resources and
managerial expertise when needed.
Unemployment rate: To examine the impact of local economic conditions on the bank's
insolvency risk, unemployment rate in the state where the bank is headquartered is included as a
proxy for the economic conditions in the bank's home market. The state-level unemployment rate
is a good indicator of where the economy is headed. We expect this variable to be negatively
associated with bank insolvency risk if bank profits rise (fall) in economic upturns (downturns)
and if the volatility of the bank profits increases (decreases) during the economic downturns
(upturns).
5 As of March 31, 2011, the definition was modified to reflect the FDIC’s deposit insurance coverage increase from
$100,000 to $250,000 (Federal Deposit Insurance Corporation, 2011).
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4. Methodology
To examine links between loan portfolio diversification and bank insolvency risk while
controlling for firm-specific, industry and economic characteristics, we initially conduct
multivariate ordinary least squares (OLS) regressions using a series of pooled, cross-sectional, and
time-series data. We use unbalanced panel data to avoid survivor bias and to maximize the number
of observations. Because a bank’s decision to diversify can be affected by bank insolvency risk,
we use the lagged-structure model to mitigate endogeneity concerns. The basic regression model
to test our hypotheses is written as follows:
, 1 0 1 , , , ,i t i t k i t i t i tZ Div X dα α α ν+ = + + + +∑ (3)
where , 1i tZ + denotes the Z-score of bank i at time 1t + , ,i tDiv is a measure of loan portfolio
diversification, ,i tX is a matrix of other control variables, ,i td is a vector of time fixed-effect, ,i tv
is the error term, and 0 1, , and kα α α are vectors of parameters to be estimated. Similar to Laeven
and Levine (2009), we use the natural logarithm of Z-score considering high skewness of Z-score
across our sample banks. The definitions of the variables in equation (3) are presented in Table 1.
To examine the robustness of our results, we employ two different estimation techniques.
One line of recent research argues that the observed diversification discount is attributable to
endogeneity problems (Campa and Kedia, 2002; Villalonga, 2004a). The decision to diversify can
be endogenous if the diversification variable is correlated with other omitted variables such as
management skill, geographic loacation or industry exposure that influences the risk of bank
insolvency. The presence of potential endogeneity problems may lead the standard ordinary least
squares (OLS) approach to produce biased and inconsistent coefficient estimates.
To deal with this potential endogeneity bias, we employ Heckman’s (1979) two-stage
selection correction model. In the first stage, we estimate the predicted values for the bank’s loan
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diversification choice by regressing the observed loan diversification on a vector of explanatory
variables and a range of instrument variables. We use a Probit model in the first stage because the
dependent variable is a binary choice where ,i tDiv is equal to one if loan HHI is greater than 90th
percentile of HHI distribution and zero otherwise. In the second stage, we estimate the equation
(3) by including the predicted values for ,i tDiv and an inverse Mill’s ratio (IMR). The IMR is
produced using the information from the first stage regression and should be added to equation (3)
as an additional explanatory variable to mitigate endogenous problems associated with the bank’s
choice to diversify. We also apply a two-stage least squares (2SLS) estimation method, which
follows the same procedure as the two-stage Heckman approach.
Both two-stage Heckman and 2SLS methods involve the selection of appropriate
instrumental variables. The lagged or historically averaged measures of firm characteristics,
industry growth, and general economic growth are suggested as commonly used instrumental
variables (Campa and Keida, 2002). Therefore, our primary instrumental variable entrants consist
of average firm size for the prior three years, three-year average of loan growth rate, the real GDP
growth rate, firm age and the lagged values of firm and industry characteristics. Among these, we
choose average firm size for the prior three years and three-year average of loan growth rate that
meet the relevance and validity requirements as our instruments.6
5. Data and results
5.1. Data and sample selection
6 We conduct the F-test and Hansen’s J-test to assess the relevance and validity of the instruments. The test results
show that only average firm size for the prior three years and three-year average of loan growth rate meet these
conditions.
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The financial data representing banks' portfolio and operating characteristics are taken
from the FDIC Call Reports. Our sample consists of an unbalanced panel on a quarterly frequency
over the period between 2005: Q1 and 2013: Q3.7 To avoid survivorship bias, our sample contains
both the failed and non-failed FDIC-insured commercial banks operating at any point over the
sample period. We consider the regulator’s decision to close a bank as a bank failure. The list of
closed banks is obtained from the FDIC’s reports. State-level unemployment data are taken from
the Bureau of Labor Statistics’ Employment and Earnings.
Similar to the literature (Laeven and Levine, 2007), we eliminate banks that report missing
values in accounting variables such as assets, equity capital, deposits, total loans, interest income
and non-interest income for both the closed and non-closed banks. There are a number of extreme
values among the observations of financial ratios constructed from raw UBPR data. To ensure that
statistical outcomes are not severely influenced by outliers, we also exclude banks with an unusual
financial ratio, which is defined as the one more than four standard deviations from the sample
mean. Finally, the banks that do not have at least twelve continuous quarterly time series
observations are excluded. This procedure leads to a final sample of approximately 190,300
quarterly observations.
5.2. Estimation results for bank insolvency risk
Table 3 reports estimations of the parameters from the equation (3) using the Z-score as a
measure of bank insolvency risk. Columns 1, 2 and 3 present results for three different estimation
techniques: OLS, 2SLS and Heckman’s two-stage selection correction model, respectively.
7 Because of calculating the standard deviation of ROA based on the preceding twelve-quarter rolling periods, some
variables span the period from 2002: Q1 through 2013: Q3.
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Standard errors in parentheses are adjusted for heteroskedasticity and firm-level clustering
(Petersen, 2009). All models include year indicator variables. However, the coefficient estimates
of year dummies are not reported to conserve space. One generic concern with OLS result is that
some omitted variables like management ability rather than the difference in diversification may
be driving the observed differences in the likelihood of bank insolvency between diversified banks
and focused ones. If this is the case, then treating the bank’s loan diversification as exogenous will
likely produce biased estimates. Thus, our interpretation is based on two-stage estimation
procedures that control for likely endogeneity problems.
The results of the 2SLS and Heckman’s models show that the estimated coefficients of
loan diversity are positive and significant within the 1% significance level, indicating that loan
diversification is inversely associated with bank insolvency risk.8 The results suggest that banks
diversifying their loan portfolio can reduce the probability of their insolvency more efficiently than
banks focusing their loan-making on the specialized area. The pattern of our results on loan
diversity across the various models is somewhat consistent with what has been found by Campa
and Kedia (2002) and Villalonga (2004b) in their studies of examining the impact of the
nonfinancial corporate diversification. They show that the diversification discount disappears
when controlling for the endogenous decision to diversify and find evidence of a diversification
premium.
The results in Table 3 show that the coefficients of bank size are statistically significant
and positive across all models, indicating that large banks tend to have lower insolvency risk. The
result might be consistent with the view that charter or franchise value acts against moral hazard
8 Note that the Z-score is negatively related to the probability of insolvency, with higher Z-score signifying a lower
likelihood of default.
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incentive (Keeley, 1990). The coefficient on the income diversity is positive and significant,
showing that increased income diversification has a positive impact on the bank’s financial
stability. It appears that banks that engage in various income activities may reduce the volatility of
total returns, improving their profitability. Given that omitted firm characteristics may drive both
a bank’s decision to diversify and the likelihood of its insolvency, we use the measure of income
diversity with a lag in this regression. Specifically, we consider the effect of income diversity in
quarter t on bank insolvency risk in quarter t+1. The use of a lag structure helps to partially address
the issue concerning the possible endogeneity of income diversity measure (Acharya, et al., 2006).9
The non-interest income share is negatively related to the Z-score, as expected if the
growing share of non-interest income results in the increased volatility of accounting returns. The
coefficient of liquidity is positive and significant, suggesting that a greater proportion of liquid
assets have a positive effect on the bank’s financial strength. The coefficient of asset growth is
negative and significant only in Heckman’s (1979) two-stage model, indicating that rapid asset
growth is positively related to the likelihood of bank insolvency. The chance of financial problems
may increase if the bank’s loan or asset growth is associated with relaxed lending standards.
The coefficient on the brokered deposits is negative and significant, indicating that greater
reliance on brokered deposits may have a negative impact on the bank’s financial health. In
contrast, core deposits have a positive influence on the bank’s financial strength, as expected if
core deposits are considered to be a stable and less costly source of funding. The results suggest
9 Acharya, et al. (2006) employ two different kinds of Hirschman Herfindahl index (HHI) measures which consist of
industrial sector HHIs (I-HHI) and broad asset sector HHIs (A-HHI) in examining the effect of loan portfolio focus
(diversification) on the bank’s return and risk. They consider one of the two focus measures, I-HHI and A-HHI as
endogenous in year t and the other as its exogenous value in year t-1 to partially control for the possible endogeneity
of focus measures.
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that the use of brokered deposits rather than core deposits is associated with an increased likelihood
of bank insolvency, all else being equal. The significant and positive sign of member of BHC
variable indicates that BHC membership is advantageous for the bank’s financial safety. The
coefficient of the state-level unemployment rate is statistically significant and negative across all
models, indicating that economic conditions in the markets where a bank operates appear to affect
financial health of U.S. commercial banks. The result implies that banks operating in states with
robust economies are likely to have a relatively lower probability of insolvency, while banks in
depressed states are more likely to suffer financial problems.
5.3. Additional tests for bank insolvency risk
5.3.1. Analysis for the breakdown of a bank’s total real estate loans
The existing bank failure and financial distress literature suggests that concentration of
commercial real estate loans is one of the most important determinants in identifying risky banks
(e.g., Cole and Gunther, 1995; Wheelock and Wilson, 2000; Cole and White, 2012; DeYoung and
Torna, 2013). We are interested in closely examining which ones among the components of real
estate loan are more directly correlated with the likelihood of bank insolvency. In the extended
regression analysis, we include a detailed breakdown of a bank’s total real estate loans. Specifically,
real estate constructions and development loans, real estate residential single-family (1–4)
mortgages, real estate multifamily mortgages, and real estate nonfarm nonresidential mortgages
are entered as additional explanatory variables in the regression.
Real estate constructions and development loans: This is a category of loans made to
finance land development preparatory for building new structures or the on-site construction of
industrial, commercial or residential buildings.
20
Real estate residential single-family (1–4) mortgages: This is a category of lending for
1-4 family residential property or nonfarm property containing 1-4 dwelling units. It also includes
the loans for the purchase or holding of the mobile homes or individual condominium dwelling
units.
Real estate multifamily mortgages: This includes loans on nonfarm residential properties
with 5 or more dwelling units used primarily to accommodate households, apartment buildings
containing 5 or more dwelling units, as well as vacant lots in multifamily residential properties.
Real estate nonfarm nonresidential mortgages: This includes loans on business and
industrial properties, association buildings, hotels, hospitals, educational and charitable
institutions and recreational facilities.
These variables are normalized by the bank’s total assets and the category of farm loans is
omitted to avoid the multicollinearity problem. The inclusion of a bank’s isolated total real estate
loans allows us to detect how the shift from the omitted category toward that particular lending
activity influences the likelihood of bank insolvency. We expect residential single-family (1–4)
mortgages to have a positive impact on bank financial health because they are generally considered
to be the safest class of real estate loans. In contrast, constructions and development loans,
multifamily mortgages, and nonfarm nonresidential mortgages are considered to be the riskiest
category of real estate loans due to the long development times of their properties and uncertain
demand from buyers or lessees when the construction phase is completed. The prospect of repaying
these loans depends on selling or leasing the developed properties and lower market demand may
put downward pressure on sales prices or rents, making it difficult for developers to pay the
principal amount to a level acceptable to the lender (Government Accountability Office, 2013).
Hence, we expect a negative sign on latter three categories of loans.
21
Table (4) presents the results that encompass the segmentation of a bank’s total real estate
loans. The significant and positive coefficient on the residential single-family (1–4) mortgages
indicates that if banks have increasingly moved toward offering residential single-family (1–4)
mortgages rather than other types of credit, they are less likely to experience financial problems.
The coefficients of constructions and development loans, multifamily mortgages, and nonfarm
nonresidential mortgages are negative and significant, showing that banks are more likely to face
financial instability, as expected if they shift their focus to this type of real estate loans. The results
suggest that commercial banks may have a comparative advantage by providing more residential
single-family (1–4) mortgages if they know their local single-family residential mortgage markets
better and are well positioned to gather specific information on single-family (1–4) residential
properties.
In this extended regression analysis, we also find strong evidence that increased loan
diversification improves a bank’s financial strength as the coefficients on loan diversity are
positive and statistically significant. The results of other explanatory variables are generally similar
to those presented in Table (3).
5.3.2. Alternative measure of loan and income diversification
In this section, we examine whether our results are robust to alternative measurements of
key variables. First, results in Table (4) show that increased share of residential single-family (1–
4) mortgages is positively associated with bank financial strength, while other type of commercial
real estate loans is inversely related to bank financial health. These results suggest the importance
of isolating the components of a bank’s total real estate loans when examining the effect of loan
portfolio diversification. To reflect different impact of each component of real estate loans, our
alternative loan diversity measure is redefined by including a detailed breakdown of a bank’s total
22
real estate loans. We use a Herfindahl-Hirschman index (HHI) again to measure a bank’s level of
loan diversification. Instead of six major categories as in Section 3.2, we split loan scope into ten
sectors: real estate constructions and development loans, real estate residential single-family (1–4)
mortgages, real estate multifamily mortgages, real estate nonfarm nonresidential mortgages, farm
loans, loans to depository institutions (DEP), commercial and industrial loans (COM), loans to
individuals (IDV), agricultural loans (AGR), and all other loans (OTH). Accordingly, an
alternative measure of loan diversity is computed by one minus the sum of the squared loan
portfolio shares across ten different types of loans described above.
Second, in Section 3.3, income diversity is measured by the breakdown of total operating
income into two broad categories: net interest income and total non-interest income. The sources
of net interest income consist of seven primary components: interest and fee income on loans,
income from leases, interest income on balances due from depository institutions, interest and
dividend income on securities, interest income from assets held in trading accounts, interest
income on federal funds sold, and other interest income. The sources of total non-interest income
are composed of four primary components: fiduciary activities, service charges on deposit
accounts, trading revenue, and other noninterest income.10 To identify an alternative measure of
income diversity, we take into account these eleven breakdowns of total operating income. As in
Section 3.3, we define income diversity as one minus Herfindahl index computed by the sum of
the squares of income share of a bank’s operating revenue across eleven sources of income for
each bank in each quarter. A higher (lower) value of Income HHI indicates that income becomes
more (less) diversified.
10 See Shim (2013) for detailed discussion about the components of net interest income and total non-interest income.
23
Table 5 reports results for these alternative measures of loan/income diversification and
market concentration. Columns 2, 4, and 6 provide results that include the breakdown of a bank’s
total real estate loans. The coefficient of loan portfolio diversification is statistically significant
with a positive sign across all models, reconfirming the inverse relationship between loan diversity
and the likelihood of bank insolvency. The results of the 2SLS and Heckman’s models show that
the coefficients of an alternative measure of income diversity are positive and significant within
the 1% significance level, confirming our preceding findings that income diversity helps banks
improve their financial strength. The results suggest that our inferences are insensitive to different
measures of loan and income diversification. The results of other explanatory variables are
generally similar to those presented in Tables 3 and 4.
5.4. Estimation results for the likelihood of bank failure
In this section, we attempt to provide more information about the important drivers of bank
failures. Our analyses focus on recent bank closures between 2008: Q1 and 2012: Q4 and we
identify 465 failed banks from the list published by FDIC during this period. We use probit
regressions to detect relevant factors contributing to the failure of U.S. commercial banks. We
regress the probability of the bank’s being closed on the loan diversification and a set of control
variables. The binomial probit specification we estimate is the following:
, 0 1 , , , ,Pr( 1)i t i t k i t i t i tFailed Div X dβ β β ε= = Φ( + + + + )∑ (4)
where ,i tFailed is an indicator variable that takes a value of one if the bank fails during the years
2008-2012 and zero otherwise. We employ the same independent variables used in the Z-score
regressions. In addition, equation (4) includes tier 1 capital ratio, profitability, and the ratio of non-
24
performing loans to total loans as important determinants of bank failure.11,12 The level of capital
that banks hold is an essential factor for regulators to determine a bank closure. We use the tier 1
capital ratio defined as the ratio of Tier 1 capital to total risk-weighted assets as a measure of a
bank’s financial strength.13 This is the regulatory capital ratio that assesses a bank’s capital
adequacy. We expect tier 1 capital ratio to be negatively associated with the likelihood of bank
failure because banks with high capital ratio have more flexibility to respond to adverse shocks
(Beltratti and Stulz, 2012) and high capital ratios allow banks to absorb losses without incurring
financial distress. The profitability is measured as the ratio of the earnings before interest and tax
to total assets and predicted to have a negative sign because banks with greater profits are less
likely to fail. The ratio of non-performing loans to total loans is included to control for asset quality.
The sign for this variable is expected to be positive due to the argument that banking problems
arise from a prolonged deterioration in asset quality and a rapid increase in nonperforming loans
ratio would mark the onset of a banking crisis (Reinhart and Rogoff, 2011). All independent
variables are measured two quarters prior to each bank’s failure. Accordingly, we use bank specific
characteristics from 2007:Q3 to 2012:Q2 to predict the probability of bank failure that occurs over
the period 2008: Q1- 2012: Q4.
11 Although tier 1 capital ratio, profitability, and non-performing loans ratio are commonly used as proxies for the
CAMEL ratings (capital adequacy, earnings, and asset quality, respectively), these variables are not included in the
Z-score regressions because Z-score represents bank risk and is measured by capital ratio and profitability. Note that
non-performing loans ratio has been widely used as a measure of bank risk in the banking literature (e.g., Ayuso et al.,
2004; Fiordelisi et al., 2011; Shim, 2013). 12 Other characteristics such as a bank’s underwriting standards, credit administration, and risk management practices
are likely to play a significant role in determining the likelihood of bank failure. We do not control for those variables
because the information is not publicly available. 13 The bulk of Tier-1 capital is represented by paid-in capital and retained earnings.
25
The estimation results of the probit regression for the likelihood of bank failures are
presented in Table (6). The parameters are estimated by the maximum likelihood probit analysis.
Similar to Tables 4 and 5, Columns 2 and 4 include the results for the breakdown of a bank’s total
real estate loans. The coefficient of loan HHI is significant and negative, indicating that the chance
of a bank failure is likely to decrease as banks diversify their loan portfolios. If diversified loan
portfolio is characterized by a low correlation between loan sectors, the reduced volatility from
loan diversity might help banks stabilize their financial conditions. The coefficient of income
diversity is negative and significant, suggesting that diversifying income sources between interest
income and non-interest income activities reduce the riskiness of commercial banks. The negative
relationships between loan and income portfolio diversification and the likelihood of bank failure
are consistent with our earlier findings in Z-score regressions.
The results for other explanatory variables provide interesting insights about important
drivers of recent bank failure. Bank size is negative and significant, indicating that large banks are
less likely to fail. The coefficient of non-interest income share is positive and significant in three
out of four models, implying that banks with high exposure to non-interest income activities are
more likely to be instable. The coefficient of liquidity is negative and significant, showing that
banks with greater liquid assets are less likely to fail. The coefficients of asset growth are not
statistically significant. The significant and positive coefficient of brokered deposits suggest that
the more brokered deposit banks rely on, the greater the likelihood of bank failure, while the
negative and significant coefficient of core deposits implies that the probability of failure is
negatively related to the use of core deposits. The significant and positive signs on BHC indicate
that the probability of bank failure is likely to increase if the bank is a member of bank holding
company.
26
The coefficient of the tier 1 capital ratio is negative and strongly significant, showing that
better capitalized banks are less likely to fail. 14 Capital serves as a financial cushion that banks
use to absorb adverse consequences due to unfavorable asset returns. The more capital a bank
holds, the more losses it can withstand. The result confirms that capital adequacy is an important
factor determining a bank failure, which is consistent with the findings of Jin et al. (2011). The
coefficient on the profitability is negative and significant, implying that high profitability may
facilitate making up capital shortage internally and thus, failure is less likely for banks with greater
earnings. As predicted, the non-performing loans to total loans ratio is positively related to the
likelihood of bank failures. The results is consistent with prior studies indicating that the
deterioration of the quality of bank loan portfolios inevitably increases banks’ risk exposure
(Laeven and Majnoni, 2003) and that bank failures are largely driven by poor loan quality (Cole
and White, 2012). The state-level unemployment rate is significant with a positive sign, showing
that bank failures are positively associated with adverse economic conditions in regions where
banks operate. The result suggests that a bank failure is more likely to occur in states with
deteriorating economies. The coefficients of the residential single-family (1–4) mortgages are
significant and negative, while other components of a bank’s real estate loans show significant and
positive signs. The results indicate that banks with greater proportion of the residential single-
family mortgages than other types of real estate loans are less likely to fail, consistent with prior
findings in Tables 4 and 5.
14 We repeat regressions using the ratio of equity capital to total asset as an alternative measure of capital adequacy.
The results are unaffected and not reported here.
27
6. Conclusion
The question of whether banks should diversify across different sectors or focus on a few
related sectors in their lending operations is an important issue for industry practitioners as well as
regulators who are concerned about the risk of bank insolvency. The literature has not yet achieved
consensus on the relationship between loan diversity and financial stability in the banking industry.
In this paper, we undertake an empirical investigation about how the diversification choice of bank
loan activities is associated with the likelihood of bank insolvency using the data of U.S.
commercial banks over the period 2005:Q1-2013:Q3. The empirical analysis is conducted with
2SLS and Heckman’s (1979) two-stage procedures to address the concern of possible endogenous
diversification variables.
The results show that the choice of bank loan diversification is an important factor
influencing a bank’s financial stability. Specifically, we find that loan diversity is inversely
associated with bank insolvency risk, implying that commercial banks may be able to diminish
financial fragility from diversification of their loan portfolios. The results lend support for the
statement of Government Accountability Office (2013) that a wave of recent bank failures is
largely associated with high concentrations of commercial real estate loans. The statement
indicates that in particular, banks that pursue aggressive growth strategies by relying on
commercial real estate mortgage products are significantly negatively affected because excessive
concentration on real estate loans increases their exposure to the real estate market downturn.
These results hold when using alternative measures of loan diversity.
The regression analysis provides some interesting insights into the influence of bank
specific characteristics on the likelihood of bank insolvency. We find that income diversity is
negatively related to the likelihood of bank insolvency, indicating that banks may pursue income
28
diversification strategy to improve their financial strength. The empirical results suggest that large
bank size, high liquid assets, the use of core deposits, and greater proportion of the residential
single-family (1–4) mortgages are associated with lower probability of insolvency, while growing
share of non-interest income, greater reliance on brokered deposits and high state-level
unemployment rate are associated with an increased likelihood of bank insolvency, all else being
equal. The results of probit regressions that identify important factors for recent bank closures
generally support these findings. In addition, the analysis of probit regression shows that banks
with higher tier 1 capital ratio and/or greater earnings are less likely to fail and failure is more
likely for banks with greater non-performing loans.
29
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Table 1 Definition of variables Variable Description Z-score Return on assets (ROA) plus the capital to asset ratio divided by the standard deviation of ROA Loan HHI(1) 1- Herfindahl index of loan portfolio classified into six major sectors Loan HHI(2) 1- Herfindahl index of loan portfolio classified into 10 sectors Firm size Natural logarithm of total assets Income HHI(1) 1-Herfindahl index based on the sources of total interest income and total non-interest income Income HHI(2) 1-Herfindahl index based on 11 classifications of total operating income Non-interest share Non-interest income / (Net interest income + Non-interest income) Liquidity Liquid assets (cash and marketable securities) / Total assets Asset growth Rate of growth of total asset Brokered deposits Brokered deposits / Total assets Core deposits Sum of demand deposits, automatic transfer, money market deposits, savings deposits and small time deposits divided by total assets BHC member Indicator equal to one if the bank is a member of bank holding company and zero otherwise Tier 1 capital Tier 1 capital / Total risk-weighted assets Profitability Ratio of the earnings before interest and tax to total assets Non-performing loans Non-performing loans / Total loans RE Constructions Real estate constructions and development loans / Total assets RE Single family Real estate residential single-family (1–4) mortgages / Total assets RE Multifamily Real estate multifamily mortgages / Total assets RE Nonresidential Real estate nonfarm nonresidential mortgages / Total assets Unemployment rate State-level unemployment rate Average firm size Average firm size for the prior three years Avg of loan growth Three-year average of loan growth rate
34
Table 2 Summary statistics of regression variables
Variable Mean Std Dev Minimum Maximum Z-score 4.1497 0.9116 -6.5598 5.2983 Loan HHI(1) 0.4234 0.1881 0.0000 1.0000 Loan HHI(2) 0.7149 0.1240 0.0000 1.0000 Firm size 11.8616 1.3583 4.2195 21.4113 Income HHI(1) 0.2428 0.1208 0.0000 1.0000 Income HHI(2) 0.4110 0.1476 0.0000 0.8319 Non-interest share 0.1764 0.1570 0.0000 1.0000 Liquidity 0.2838 0.1686 0.0000 1.0000 Asset growth 1.0249 0.1961 0.0002 14.4854 Brokered deposits 0.0350 0.0806 0.0000 0.9384 Core deposits 0.3092 0.1485 0.0000 0.9409 BHC member 0.8461 0.3609 0.0000 1.0000 Tier 1 capital 0.1573 0.0881 0.0000 1.0000 Profitability 0.0016 0.0110 -1.0430 1.0350 Non-performing loans 0.0242 0.0400 0.0000 1.0000 RE Constructions 0.0616 0.0785 0.0000 0.8309 RE Single family 0.1546 0.1095 0.0000 0.9924 RE Multifamily 0.0152 0.0283 0.0000 0.6697 RE Nonresidential 0.1632 0.1207 0.0000 0.8735 Unemployment rate 0.0657 0.0229 0.0230 0.1410 Average firm size 11.7658 1.3183 7.3310 21.3153 Avg of loan growth 0.0140 0.0613 -1.0499 1.0859
This table presents summary statistics for the variables used in the regressions. The sample consists of 190,358 firm-year observations over the period 2005: Q1-2013: Q3. Z-score is measured by the return on assets (ROA) plus the capital to asset ratio divided by the standard deviation of ROA. Loan HHI(1) is calculated by one minus Herfindahl index of loan portfolio classified into six major sectors, while Loan HHI(2) is one minus Herfindahl index of loan portfolio classified into 10 sectors. Firm size is the natural logarithm of total assets. Income HHI(1) is one minus Herfindahl index based on the sources of total interest income and total non-interest income. Income HHI(2) is one minus Herfindahl index based on 11 classifications of total operating income. Non-interest share is the non-interest income share of the bank’s operating revenue. Liquidity is the ratio of liquid assets to total assets. Asset growth is the rate of growth of total asset. Brokered deposits is the ratio of brokered deposits to total assets. Core deposits is measured by the sum of demand deposits, automatic transfer service account, money market deposits, savings deposits and small time deposits divided by total assets. BHC member is indicator equal to one if the bank is a member of bank holding company and zero otherwise. Tier 1 capital is the ratio of tier 1 capital to total risk-weighted assets. Profitability is the ratio of the earnings before interest and tax to total assets. Non-performing loans is the ratio of non-performing loans to total loans. RE Constructions is the ratio of real estate constructions and development loans to total assets. RE Single family is the ratio of real estate residential single-family (1–4) mortgages to total assets. RE Multifamily is the ratio of real estate multifamily mortgages to total assets. RE Nonresidential is the ratio of real estate nonfarm nonresidential mortgages to total assets. Unemployment rate is the state-level unemployment rate. Average firm size is the average firm size for the prior three years. Avg of loan growth is the three-year average of loan growth rate.
35
Table 3 Regression results for bank insolvency risk
Dependent Variable = Z-score Variable (1) OLS (2) 2SLS (3) Heckman Loan HHI(1) 0.6059*** 0.6183*** 3.6555***
(0.0440) (0.0626) (0.0663) Firm size 0.4827*** 0.4857*** 0.8413***
(0.0533) (0.0550) (0.0178) Income HHI(1) 0.2127*** 0.2141*** 0.3898***
(0.0544) (0.0539) (0.0189) Non-interest share -0.5572*** -0.5596*** -0.7002***
(0.0548) (0.0546) (0.0178) Liquidity 0.5087*** 0.5060*** 0.4878***
(0.0435) (0.0445) (0.0123) Asset growth -0.0007 -0.0007 -0.0010***
(0.0009) (0.0009) (0.0003) Brokered deposits -1.0202*** -1.0184*** -0.9678***
(0.0995) (0.1001) (0.0241) Core deposits 0.6730*** 0.6724*** 0.4367***
(0.0567) (0.0566) (0.0147) BHC member 0.1246*** 0.1241*** 0.1299***
(0.0217) (0.0218) (0.0051) Unemployment rate -6.4155*** -6.3814*** -2.9150***
(0.4709) (0.4891) (0.1192) Constant 0.5162 0.4895 -2.8751***
(0.3417) (0.3609) (0.1274) Inverse Mill’s ratio -0.3995***
(0.0028) Adjusted R-squared 0.1440 0.1440 0.3014
Observations 190,358 190,358 190,358
This table presents the regression results for bank insolvency risk. OLS is an ordinary least squares regression, 2SLS is a two-stage least squares regression and Heckman is Heckman’s (1979) two-stage selection correction model. Z-score (dependent variable) is measured by the return on assets (ROA) plus the capital to asset ratio divided by the standard deviation of ROA. Loan HHI(1) is calculated by one minus Herfindahl index of loan portfolio classified into six major sectors. Firm size is the natural logarithm of total assets. Income HHI(1) is one minus Herfindahl index based on the sources of total interest income and total non-interest income. Non-interest share is the non-interest income share of the bank’s operating revenue. Liquidity is the ratio of liquid assets to total assets. Asset growth is the rate of growth of total asset. Brokered deposits is the ratio of brokered deposits to total assets. Core deposits is measured by the sum of demand deposits, automatic transfer service account, money market deposits, savings deposits and small time deposits divided by total assets. BHC member is indicator equal to one if the bank is a member of bank holding company and zero otherwise. Unemployment rate is the state-level unemployment rate. Inverse Mill’s ratio is a correction term calculated using the information obtained from the first stage regression of Heckman method. The coefficient estimates of year dummies are not reported here to conserve space. Standard errors that adjust for heteroskedasticity and firm-level clustering are presented in parentheses. ***, **, and * indicate significance at the 1%, 5%, and 10% levels, respectively.
36
Table 4 Regression results for the breakdown of a bank’s total real estate loans
Dependent Variable = Z-score Variable (1) OLS (2) 2SLS (3) Heckman Loan HHI(1) 0.4767*** 0.2192** 3.3805***
(0.0558) (0.1169) (0.0664) Firm size 0.6535*** 0.6393*** 0.9799***
(0.0571) (0.0583) (0.0180) Income HHI(1) 0.0487 0.0277 0.2925***
(0.0550) (0.0541) (0.0189) Non-interest share -0.5571*** -0.5247*** -0.7458***
(0.0555) (0.0559) (0.0177) Liquidity 0.3802*** 0.3309*** 0.3296***
(0.0526) (0.0562) (0.0148) Asset growth -0.0008 -0.0008 -0.0010***
(0.0009) (0.0009) (0.0003) Brokered deposits -0.8098*** -0.8528*** -0.8262***
(0.0917) (0.0927) (0.0242) Core deposits 0.5490*** 0.5517*** 0.3792***
(0.0554) (0.0558) (0.0147) BHC member 0.1125*** 0.1203*** 0.1132***
(0.0209) (0.0211) (0.0051) Unemployment rate -6.2088*** -6.3726*** -2.5460***
(0.4707) (0.4746) (0.1248) RE Constructions -1.0738*** -1.2479*** -0.6898***
(0.0975) (0.1167) (0.0267) RE Single family 0.6867*** 0.5006*** 0.4205***
(0.0814) (0.1092) (0.0181) RE Multifamily -0.7847*** -1.0236*** -0.8635***
(0.2938) (0.3096) (0.0659) RE Nonresidential -0.6035*** -0.7634*** -0.5063***
(0.0861) (0.1061) (0.0196) Constant -0.4086 -0.1033 -3.5973***
(0.3566) (0.3839) (0.1273) Inverse Mill’s ratio -0.3856***
(0.0028) Adjusted R-squared 0.1659 0.1647 0.3123
Observations 190,358 190,358 190,358 This table presents the regression results for bank insolvency risk, which include the breakdown of a bank’s total real estate loans. OLS is an ordinary least squares regression, 2SLS is a two-stage least squares regression and Heckman is Heckman’s (1979) two-stage selection correction model. Z-score (dependent variable) is measured by the return on assets (ROA) plus the capital to asset ratio divided by the standard deviation of ROA. Loan HHI(1) is calculated by one minus Herfindahl index of loan portfolio classified into six major sectors. Firm size is the natural logarithm of total assets. Income HHI(1) is one minus Herfindahl index based on the sources of total interest income and total non-interest income. Non-interest share is the non-interest income share of the bank’s operating revenue. Liquidity is the
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ratio of liquid assets to total assets. Asset growth is the rate of growth of total asset. Brokered deposits is the ratio of brokered deposits to total assets. Core deposits is measured by the sum of demand deposits, automatic transfer service account, money market deposits, savings deposits and small time deposits divided by total assets. BHC member is indicator equal to one if the bank is a member of bank holding company and zero otherwise. Unemployment rate is the state-level unemployment rate. RE Constructions is the ratio of real estate constructions and development loans to total assets. RE Single family is the ratio of real estate residential single-family (1–4) mortgages to total assets. RE Multifamily is the ratio of real estate multifamily mortgages to total assets. RE Nonresidential is the ratio of real estate nonfarm nonresidential mortgages to total assets. Inverse Mill’s ratio is a correction term calculated using the information obtained from the first stage regression of Heckman method. The coefficient estimates of year dummies are not reported here to conserve space. Standard errors that adjust for heteroskedasticity and firm-level clustering are presented in parentheses. ***, **, and * indicate significance at the 1%, 5%, and 10% levels, respectively.
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Table 5 Regression results for alternative measures of loan and income diversification
Dependent Variable = Z-score
Variable (1) OLS (2) OLS (3) 2SLS (4) 2SLS (5) Heckman (6) Heckman
Loan HHI(2) 0.3579*** 0.4443*** 0.4552** 1.3742*** 8.4445*** 7.3397***
(0.0633) (0.0625) (0.2317) (0.2558) (0.0838) (0.0846)
Firm size 0.3317*** 0.5557*** 0.3838*** 0.5850*** 0.5877*** 0.8221***
(0.0511) (0.0559) (0.0200) (0.0242) (0.0135) (0.0141)
Income HHI(2) 0.0038 0.0251 0.1109*** 0.0977*** 0.2407*** 0.0684***
(0.0566) (0.0584) (0.0239) (0.0262) (0.0202) (0.0201)
Non-interest share -0.4259*** -0.4999*** -0.5631*** -0.6419*** -0.6191*** -0.6852***
(0.0512) (0.0528) (0.0201) (0.0208) (0.0171) (0.0170)
Liquidity 0.6208*** 0.2281*** 0.5466*** 0.1459*** 0.9133*** 0.6534***
(0.0512) (0.0558) (0.0167) (0.0245) (0.0177) (0.0195)
Asset growth -0.0006 -0.0007 -0.0004 -0.0004 0.0000 -0.0002
(0.0008) (0.0008) (0.0004) (0.0004) (0.0004) (0.0004)
Brokered deposits -1.0218*** -0.7558*** -0.9863*** -0.4922*** -0.9332*** -0.7864***
(0.1030) (0.0914) (0.0589) (0.0727) (0.0260) (0.0260)
Core deposits 0.7391*** 0.4331*** 0.7656*** 0.4390*** 0.3985*** 0.3453***
(0.0586) (0.0543) (0.0181) (0.0204) (0.0160) (0.0159)
BHC member 0.1340*** 0.1049*** 0.1205*** 0.0438*** 0.0431*** 0.0290***
(0.0219) (0.0212) (0.0129) (0.0141) (0.0055) (0.0055)
Unemployment rate -7.8371*** -10.2126*** -7.8539*** -10.3110*** -5.0131*** -4.1030***
(0.4665) (0.2983) (0.2245) (0.0944) (0.1274) (0.1334)
RE Constructions -1.1482*** -1.3236*** -1.0606***
(0.0875) (0.0521) (0.0286)
RE Single family 0.5014*** 0.6279*** 0.3561***
(0.0693) (0.0431) (0.0192)
RE Multifamily -1.4340*** -1.6798*** -0.9017***
(0.2933) (0.0894) (0.0703)
RE Nonresidential -0.7869*** -0.6923*** -0.8063***
(0.0793) (0.0468) (0.0208)
Constant 1.5753*** 0.4263 1.1470*** -0.4729*** -1.2925*** -2.4143***
(0.3218) (0.3446) (0.1143) (0.1106) (0.0920) (0.0932)
Inverse Mill’s ratio -0.0053** -0.0210***
(0.0023) (0.0023)
Adjusted R-squared 0.1356 0.1491 0.1377 0.1389 0.1999 0.2192
Observations 190,358 190,358 190,358 190,358 190,358 190,358 This table presents the regression results for bank insolvency risk using alternative measures of loan and income diversification. OLS is an ordinary least squares regression, 2SLS is a two-stage least squares regression and Heckman is Heckman’s (1979) two-stage selection correction model. Z-score (dependent variable) is measured by the return on assets (ROA) plus the capital to asset ratio divided by the standard deviation of ROA. Loan HHI(2) is one minus Herfindahl index of loan portfolio classified into 10 sectors. Firm size is the natural logarithm of total assets. Income HHI(2) is one minus Herfindahl index based on 11 classifications of total operating income. Non-interest share is the non-interest income share of the bank’s operating revenue. Liquidity is the ratio of liquid assets to total assets. Asset
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growth is the rate of growth of total asset. Brokered deposits is the ratio of brokered deposits to total assets. Core deposits is measured by the sum of demand deposits, automatic transfer service account, money market deposits, savings deposits and small time deposits divided by total assets. BHC member is indicator equal to one if the bank is a member of bank holding company and zero otherwise. Unemployment rate is the state-level unemployment rate. RE Constructions is the ratio of real estate constructions and development loans to total assets. RE Single family is the ratio of real estate residential single-family (1–4) mortgages to total assets. RE Multifamily is the ratio of real estate multifamily mortgages to total assets. RE Nonresidential is the ratio of real estate nonfarm nonresidential mortgages to total assets. Inverse Mill’s ratio is a correction term calculated using the information obtained from the first stage regression of Heckman method. The coefficient estimates of year dummies are not reported here to conserve space. Standard errors that adjust for heteroskedasticity and firm-level clustering are presented in parentheses. ***, **, and * indicate significance at the 1%, 5%, and 10% levels, respectively.
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Table 6 Probit regression results for the likelihood of bank failure
Dependent Variable = Indicator for the bank being closed
Variable (1) (2) (3) (4)
Loan HHI(1) -1.6794*** -0.5045***
(0.0647) (0.1002)
Loan HHI(2) -0.3203*** -0.3552***
(0.0868) (0.1068)
Firm size -0.0260*** -0.0820*** -0.0361*** -0.0820***
(0.0091) (0.0102) (0.0084) (0.0103)
Income HHI(1) -1.1004*** -0.5942***
(0.1221) (0.1259)
Income HHI(2) -1.2377*** -0.2701**
(0.1261) (0.1322)
Non-interest share 0.0057 0.4953*** 0.3139*** 0.2722**
(0.1156) (0.1164) (0.1090) (0.1094)
Liquidity -0.6720*** -0.2385** -0.2583** -0.5724***
(0.0977) (0.1186) (0.1321) (0.1435)
Asset growth -0.0085 -0.0135 -0.0130 -0.0089
(0.0216) (0.0293) (0.0209) (0.0278)
Brokered deposits 1.5891*** 1.3502*** 1.6489*** 1.3549***
(0.0855) (0.0951) (0.0856) (0.0962)
Core deposits -1.4711*** -1.4189*** -1.6355*** -1.4672***
(0.0950) (0.0988) (0.0958) (0.0990)
BHC member 0.2774*** 0.2014*** 0.1934*** 0.1943***
(0.0357) (0.0368) (0.0353) (0.0370)
Tier 1 capital -1.0170*** -0.8454*** -0.8819*** -0.8198***
(0.0428) (0.0455) (0.0432) (0.0459)
Profitability -0.0502*** -0.0620*** -0.0583*** -0.0597***
(0.0110) (0.0114) (0.0109) (0.0114)
Non-performing loans 0.1061*** 0.0996*** 0.1066*** 0.1001***
(0.0075) (0.0078) (0.0074) (0.0078)
Unemployment rate -0.0817 2.7556*** 3.4737*** 2.7341***
(0.8603) (0.9142) (0.8112) (0.9102)
RE Constructions 3.8087*** 4.1946***
(0.1235) (0.0988)
RE Single family -0.7840*** -0.4548***
(0.1372) (0.1169)
RE Multifamily 2.7017*** 3.3359***
(0.2737) (0.2525)
RE Nonresidential 0.5482*** 0.8262***
(0.1194) (0.0995)
Constant -1.9812*** -2.4061*** -2.8137*** -2.5032***
(0.1642) (0.1845) (0.1585) (0.1786)
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Log-likelihood -10314 -9481 -10665 -9495
Pseudo R-squared 0.2850 0.3428 0.2604 0.3416
Observations 136,575 136,575 136,575 136,575 This table presents the regression results for the binomial probit specification. The dependent variable is an indicator that takes a value of one if the bank fails during the years 2008-2012 and zero otherwise. Loan HHI(1) is calculated by one minus Herfindahl index of loan portfolio classified into six major sectors, while Loan HHI(2) is one minus Herfindahl index of loan portfolio classified into 10 sectors. Firm size is the natural logarithm of total assets. Income HHI(1) is one minus Herfindahl index based on the sources of total interest income and total non-interest income. Income HHI(2) is one minus Herfindahl index based on 11 classifications of total operating income. Non-interest share is the non-interest income share of the bank’s operating revenue. Liquidity is the ratio of liquid assets to total assets. Asset growth is the rate of growth of total asset. Brokered deposits is the ratio of brokered deposits to total assets. Core deposits is measured by the sum of demand deposits, automatic transfer service account, money market deposits, savings deposits and small time deposits divided by total assets. BHC member is indicator equal to one if the bank is a member of bank holding company and zero otherwise. Tier 1 capital is the ratio of tier 1 capital to total risk-weighted assets. Profitability is the ratio of the earnings before interest and tax to total assets. Non-performing loans is the ratio of non-performing loans to total loans. Unemployment rate is the state-level unemployment rate. RE Constructions is the ratio of real estate constructions and development loans to total assets. RE Single family is the ratio of real estate residential single-family (1–4) mortgages to total assets. RE Multifamily is the ratio of real estate multifamily mortgages to total assets. RE Nonresidential is the ratio of real estate nonfarm nonresidential mortgages to total assets. The coefficient estimates of year dummies are not reported here to conserve space. Robust standard errors are presented in parentheses. ***, **, and * indicate significance at the 1%, 5%, and 10% levels, respectively.