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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.