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LEARNING BANKS’ EXPOSURE TO SYSTEMATIC RISK:

EVIDENCE FROM THE FINANCIAL CRISIS OF 2008

ARIEL M. VIALE

Florida Atlantic University, FL 33431

JEFF MADURA Florida Atlantic University, FL 33431

__________________________ *Corresponding author: Ariel M. Viale, Department of Finance, College of Business, Florida

Atlantic University, Boca Raton, FL 33431-0991, E-mail: aviale@fau.edu, Phone: 561.297.2914.

Fax: 561.297.2956. Jeff Madura, Department of Finance, College of Business, Florida Atlantic

University, Boca Raton, FL 33431-0991, E-mail: jeffmadura@belssouth.net, Phone:

561.297.3589. Fax: 561.297.2956. We are especially grateful to the associate editor Ken Cyree

and an anonymous referee whose comments and suggestions help us to improve the article. The

views expressed are those of the authors. All remaining errors are their own responsibility.

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Abstract Using a two-state MRS-ICAPM, we find that the exposure to systematic risk of bank stocks

varies with size and the state of the economy. Across large banks, those with higher net interest

margins and lower capital ratios are the most exposed to unexpected shifts in the term structure

of interest rates. Small banks with higher net interest rate margins and that rely less on non-

interest income are the most exposed to unexpected shifts in the stance of monetary policy. We

apply the asset pricing model out-of-sample to assess its ability to detect troubled banks during a

financial crisis.

JEL Classification: G120, G210.

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I. Introduction

There were various indications that the market pricing of bank risk was overly optimistic

before the financial crisis of 2008 occurred. Commercial banks were aggressively pursuing

expansion into mortgage securitization without recognition that a housing market bubble had

developed. Their diversification of business operations may have reduced their transparency, and

may have created a false perception that their exposure to a weak economy was limited. The

securitization of mortgages and other debt instruments allowed them to reduce their capital, and

may have created a false perception that banks were insulated from mortgage defaults. Banks

increasingly used short-term funding (with asset-backed commercial paper) to finance long-term

investments in mortgages. Credit rating agencies consistently assigned high ratings to pools of

mortgages of questionable quality that were securitized. According to Goodhart (2008), central

banks, the Bank for International Settlements, and the International Monetary Fund expressed

their concerns about how the market was underestimating bank risk before the financial crisis.

The market may have underestimated the risk exposure of banks because of the

presumption that these banks can employ risk management strategies based on derivatives (see

Instefjord, 2005; and Lepetit, Nys, Rous, and Tarazi, 2008). In this regard, Gersbach and

Wenzelburger (2008) develop a model where banks attempt to fully incorporate systematic risk

into the pricing of their loans. Their research shows that the premiums incorporated by banks to

account for systematic risk in the pricing of their loans were too small, and that banks may have

severe exposure if their capital levels are insufficient. Moreover, the risk perception of some

banks before the financial crisis of 2008 may have been clouded by the view that a two-tier (too

big to fail) regulatory policy exists.

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If banks are relatively less transparent than other firms so that investors are unable to

correctly price their exposure to systemic risk, how effective is market discipline? We attempt to

determine whether rational investors equipped with a modified (i.e., regime switching) version of

Merton’s (1973) intertemporal capital asset pricing model (ICAPM) (as implemented by

Petkova, 2006) would have detected the financial distress of banks that failed during the

financial crisis. We apply a four-factor model that accounts for market risk, shocks to the term

structure of interest rates, shocks to the default spread, and shocks to the stance of monetary

policy with a state dependent asset pricing equation conditional on good and bad economic

times.

The first step in our analysis is to estimate an empirical asset pricing model for bank

stock returns. Next, we assess whether the two-state Markov regime-switching (MRS)-ICAPM is

able to correctly detect the ex-ante risk exposure of large and small public banks that failed or

were rescued during the financial crisis of 2008. We calculate the cost of equity out-of-sample

for each of these banks, and compare it with the cost of equity of its corresponding benchmark

portfolio sorted by size. We also allow for a structural break in the data generating process

(DGP) of stock returns during bad economic times and repeat the comparative analysis by

calculating the implied cost of equity of each bank in response to the financial crisis.

Our study is related to that of Fahlenbrach, Prilmeier, and Stulz (2012), who evaluate the

relative performance of banks during the 2008 financial crisis versus their relative performance

during the 1998 period when the Long Term Capital Management (LTCM) fund was rescued

after Russia defaulted on its debt. They also control for bank characteristics and find the

performance is worse during the 2008 financial crisis for banks that were smaller, had high book-

to-market values, and had low betas. Their focus is on the ability to identify ex ante risky banks

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from their past performance based on a previous crisis. According to their hypothesis, bank

managers adapt slowly to the changing economic environment. Fahlenbrach, Prilmeier, and Stulz

(2012) focus on a bank managers’ learning model, which may identify the bank characteristics

that can cause some banks to be persistently exposed to risk. Their assessment of bank

systematic risk is focused on the tail of the distribution of stock returns.

Conversely, our focus is on whether bank failures could have been anticipated by investors during

the financial crisis of 2008 using a standard dynamic asset pricing model in finance. We focus on the

investors’ learning model to identify the risks inherent in the banking function. Our analysis uses the

information contained in the whole (bi-modal) distribution of stock returns. We develop an

intertemporal asset pricing model over a long-term period of time, which explicitly accounts for

low frequency structural breaks in stock returns.

It can be argued that because bank operations constantly change, asset pricing models will not

serve as effective ex ante predictors of a bank’s financial distress. However, our regime switching model

includes a learning mechanism that accounts for time-variation and state dependency. To the extent that

banks maintain a distinct risk profile during good and bad economic times even as bank managers change

their policies, the time-varying state-dependent asset pricing model may effectively anticipate financial

distress in banks. We apply our model out-of-sample in order to determine whether the investors’

learning model can effectively anticipate bank failures during a financial crisis. Thus, our method

offers policy implications for market discipline on bank managers during a crisis.

We find that in the immediate years before the recent financial crisis of 2008, investors

using the MRS-ICAPM would have been able to correctly identify the exposure of large and

small public banks that failed ex-post. The empirical results also suggest that there was a

relatively higher probability of investors experiencing a type I error, i.e., underestimating the

exposure of small banks to a financial crisis. This error may be attributed to the relatively lower

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precision (defined as the inverse of the standard deviation) of small bank stocks as signals of

future business conditions. The probability of experiencing a type II error or receiving a false

signal was relatively lower for small banks than large banks.

An important policy implication of the results is that any equity-based market

information mechanism is heavily dependent on the asset pricing model adopted to identify ex-

ante the risks involved in the banking function. In this regard, we show that when investors

incorporate the chance of an endogenous structural break in the dynamic behavior of the

economy, they have a better assessment of the risks involved in the banking function.

We also find that within the sample of large banks, the sensitivity to unexpected shifts in

the slope of the term structure of interest rates is directly proportional to the net interest margin

and indirectly proportional to the capital ratio. Within the sample of small banks, sensitivity to

unexpected shifts in the stance of monetary policy is directly proportional to the bank’s net

interest margin and inversely proportional to non-interest income.

II. Empirical research design

First, we estimate the two-state MRS-ICAPM for the period from January 1973 to

December 2003. Next, we estimate the cost of equity during good and bad economic times for

banks that failed or were rescued during the financial crisis (from January 2008 to December

2010). For this purpose, we use the regime-switching time-series regressions to estimate in-

sample the state dependent factor loadings, and then calculate out-of-sample expected returns for

the period January 2004 - December 2007 using the market prices of risk of the asset pricing

factors that were significant in-sample.

The comparative analyses of the out-of-sample cost of equity are conducted as follows.

First, we compare each bank’s estimated cost of equity with the average cost of equity of the

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size-ranked benchmark portfolio to which it belongs. Second, we apply two-tailed t-tests and F-

tests of the null hypothesis that the mean and variance of the distributions of the out-of-sample

cost of equity for good and bad economic times are equal. Third, we calculate the probability that

the cost of equity of a typical large and small bank is less than the average cost of equity of its

size-ranked benchmark portfolio during good economic times and during bad economic times.

Fourth, we compare the probabilities that the pricing of the failed (or rescued) bank stocks reflect

a type I error (the signal is too low to anticipate the failure) and type II error (the signal is high

but is giving a false message of failure). Fifth, we identify bank-specific characteristics that may

have influenced the sensitivity of individual bank stock returns to shocks in the slope of term

structure of interest rates and the stance of monetary policy during the crisis. We run OLS cross-

sectional regressions within the sample of large and small banks using the following independent

bank-specific variables: 1) bank sensitivity to implied market volatility (S_VIX), 2) liquidity

proxied by each stock’s turnover ratio (TURNOVER), deposits; net interest margin (NIM), non-

interest income (NOINT); non-performing assets (NONPER), provision for loan losses (PLL),

and capital ratio (CAP). All accounting variables are scaled by total assets (or total revenue in

the case of non-interest income) to account for differences in bank size.

Data

The data are obtained from CRSP, COMPUSTAT, the Fed’s Economic Database (FRED)

at the Federal Reserve Bank of St. Louis’ website: http://research.stlouisfed.org/fred2/, Ben

Bernanke’s website: http://www.princeton.edu/~bernanke/data.htm, Bloomberg, and Banks’ Y-9

financial statements.

In the estimation of the empirical model, we include common stocks of bank holding

companies available on the Center for Research on Security Prices (CRSP) provided by Wharton

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Data Services (WRDS) with SIC codes 6020, 6021, 6022, and 6029. ADRs, REITs, and units of

beneficial interest are excluded. To avoid the survivorship bias inherent in the way

COMPUSTAT adds firms, we only include bank stock returns once they have appeared on

COMPUSTAT for two consecutive years. Without any loss of generality, the in-sample period

begins in January 1973 and ends in December 2003. The asset pricing model is then used to

forecast out-of-sample expected stock returns during good and bad economic times for each

public bank that failed from January 2008 to December 2010.

The total number of banks that failed during this period is 323, from which only 24 banks

had stocks listed in the exchanges and only 17 had entries in the CRSP database. We further

dropped Westernbank from Puerto Rico because its stock only traded for sixty months with no

entry points during any recession period like the rest of the banks. The final number of large

banks that failed is 4, while the sample of small banks that failed is 12.

We expand our definition of failure to include large banks that issued capital during the

financial crisis and received TARP funds from the Federal Reserve. The expanded list includes

the banks that attracted much media attention during the financial crisis: 1) Citigroup, 2) JP

Morgan, 3) Bank of America, 4) Wells Fargo, 5) Bank of New York Mellon, 6) US Bancorp, 7)

Morgan Stanley, and 8) Goldman Sachs. The final number of large banks that failed or were

rescued and therefore qualify for our sample is 12.

Banks are grouped in four benchmark portfolios ranked by size and based on market

capitalization (ME) at the end of June of each year t. 1 Portfolio 1 includes the largest banks in

1 We group stocks in portfolios because since Fama and French (1992, 1993), the asset pricing literature has argued

that creating portfolios reduces idiosyncratic volatility and allows factor loadings and risk premia to be estimated

more precisely, especially if one uses a GRS time-series asset pricing test. The reason we do not sort bank stock

returns by book-to-market (BE/ME), is because it does not help to explain the cross-section of bank stock returns

(see Viale, Kolari, and Fraser, 2009). Moreover, the reason to classify banks in four groups is to obtain a significant

number of banks in each quartile (with a total number of 290 banks per year in average).

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the group and Portfolio 4 includes the smallest banks in the sample. The dependent variable in

the asset pricing regressions is the monthly excess total return per portfolio denoted byetiR , . We

initially use equally weighted returns in our portfolio formation, but then also use value-weighted

returns as a robustness check, and those results (not reported to conserve space) are qualitatively

and quantitatively similar. Given previous asset pricing test results in Petkova (2006) and Viale,

Kolari, and Fraser (2009), and the role that monetary policy should have for the banking

function, the set of risk factors proxying for systematic risk in the asset pricing regressions

includes the value-weighted CRSP excess market total return (MKT), and three tracking

portfolios that have (by construction) maximum correlation with innovations in the slope of the

yield curve (TERM), innovations in the credit spread (DEF), and innovations in the stance of

monetary policy (POL). Consistent with the ICAPM, tracking portfolios capture the effects of

investors’ hedging demands against unexpected shocks in the state variables proxying for both

financial uncertainty (i.e., innovations in TERM and DEF) and monetary policy uncertainty (i.e.,

innovations in POL).

The advantage of using tracking portfolio returns as proxies for innovations in the state

variables is that since portfolio returns are observable and fully tradable, the estimation of the

asset pricing model using maximum likelihood (ML) allows the application of the time-series

asset pricing test (GRS test) of Gibbons, Ross, and Shanken (1989) without the need for a two-

step cross-section asset pricing test [see, e.g., Cochrane (2005, page 272)].

TERM is calculated as the difference between the average yield of a portfolio of long-

term government bonds (with a maturity of more than 10 years) and the one-month Treasury bill

yield. DEF is calculated as the difference between the average yield of a portfolio of long-term

corporate bonds rated Aaa and Baa and the average yield of the portfolio of long-term

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government bonds (with a maturity of more than 10 years). Finally, POL is calculated using the

Bernanke-Mihov index of the stance of monetary policy (Bernanke and Mihov, 1998).2

Innovations in the three state variables were obtained from a first-order vector autoregression

(VAR) that includes the market excess return with causality going from the three state variables

to the market portfolio return as discussed in the empirical ICAPM literature.3

Table 1 provides the summary statistics of the main variables used in the empirical

analyses. Notice that monthly stock returns of relatively small banks are negative on average,

have higher variance than those of relatively large banks, are negatively skewed, and are

autocorrelated. The average shock in the slope of the term structure of interest rates is zero

during the sample period under analysis. Yet, the average shock in the stance of monetary policy

(beyond the targeting of the fed funds rate) has been negative (i.e., expansive) for the period

under analysis.

[INSERT TABLE 1 HERE]

Tracking portfolios

Tracking maximum correlated portfolios (MCPs) are constructed following the general

procedure in Lamont (2001). In brief, the portfolio weights are the result of running an ordinary

least squares (OLS) multiple regression in which the 12-month forecast of the state variable of

interest represents the dependent variable, and the excess returns of 12 stock portfolios ranked by

2 This index has several advantages over other more standard proxies for the stance of monetary policy: 1) it nests

all of them, 2) it is consistent with empirical models used to describe the Fed’s open market operations, and 3) it

allows for possible structural changes in the underlying economy. Bernanke and Mihov use a “semi-structural”

vector autoregression (VAR) model of the market for commercial bank reserves and the Federal Reserve operating

policy. The model includes as variables innovations or surprises in the demand for total reserves, the price of these

reserves (the fed funds rate) , the demand for borrowed reserves at the discount window, the discount rate, and the

demand for non-borrowed reserves. The disturbance term in the equation for non-borrowed reserves constitutes the

shock in monetary policy with the sign determining the stance or bias of the policy shock. A value of zero denotes

no active stance in monetary policy. A negative sign precludes a shift in the stance of monetary policy towards

making credit conditions “easy”. A positive sign signals a shift towards a “tight” stance in monetary policy.

3 Campbell and Shiller (1988) show that any high order VAR can be collapsed to its first order (companion) VAR.

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industry are explanatory variables.4 In each regression, we control for inflation, the market

excess return, and the rest of the factors lagged one period. The resulting tracking portfolio

returns have minimum variance, maximum correlation with the innovations in each state variable

included in the asset pricing model, and the highest R2 among any other alternative portfolio

constructed using univariate OLS regressions (for the proof, see Lamont, 2001).

2.3. Regulatory structural breaks

Our model is intended to derive in-sample estimates of our parameters, which are then

applied out-of-sample. Bank operations have changed substantially over our in-sample period. In

particular, banks began to expand their business across state lines after 1994 due to the Riegle-

Neal Interstate Banking and Branching Efficiency Act. They began to expand their business into

insurance and securities services after 1999 due to the Financial Services Modernization Act

(referred to as Gramm-Leach-Bliley Act). For this reason, we adapt the model to account for

exogenous shifts in the stochastic behavior of returns due to these events. Furthermore, we

differentiate endogenous (real business cycle driven) structural effects from exogenous

(regulatory driven) structural effects by applying Bai and Perron’s (1998, 2003) econometric

tests.

Binder (1985) argues that the use of calendar dummies to proxy for the economic effects

of regulatory changes in security prices is complicated when the announcement might be

partially or totally anticipated in the markets. Consequently, although we have contemplated all

regulation events since 1973, we only include in the asset pricing model those events that have a

statistically significant impact on stock returns. We also assume that the timing of the plausible

4 The source is K. French’s website: http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data_library.html. The

reason to choose portfolios ranked by industry is to follow the standard practice in the asset pricing literature. This

practice minimizes the problem of data mining if one chooses variables that were used in the construction of the

dependent and/or independent variables.

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structural breaks in bank stock returns due to the regulatory change is unknown ex ante and let

the “data speak for itself”. The results of the structural break tests are presented in Table 2. Using

a standard Bayesian information criterion (BIC), we identify two statistically significant common

regulatory-driven structural breaks. The first structural break matches the year of the

implementation of Basel I (D1), while the second break matches the year in which the Gramm-

Leach-Bliley act was implemented (D2).

[INSERT TABLE 2 HERE]

One plausible explanation of the results is the business model hypothesis discussed in

Fahlenbrach, Prilmeier, and Stulz (2012), which suggests that the business model of banks has

changed slowly despite numerous regulatory changes and financial crises in the last decades. We

show that the bank exposure to systematic risk is not only persistent but time-varying and state

dependent, conditioned on the phase of the real business cycle.

The Markov regime-switching intertemporal capital asset pricing model (MRS-ICAPM)

We apply a Markov regime-switching (MRS)-ICAPM to detect the ex-ante risk exposure

of large and small public banks that failed or were rescued during the financial crisis of 2008,

and justify the use of this model here. We assume that the investment opportunity set is time-

varying as in the ICAPM of Merton (1973). Petkova (2006) shows that an empirical ICAPM that

includes the slope of the term structure of interest rates (TERM) as a factor besides the market

return explains the cross-section of stock returns better than the static CAPM and the four factor

model of Fama-French-Carhart. Moreover, Viale, Kolari, and Fraser (2009) show that for the

specific case of bank stocks, an empirical ICAPM that includes TERM and DEF along with the

market return effectively explains bank stock returns. They find that the risk exposure of bank

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stocks varies across size and conclude that this is attributed to the differences in their exposure to

interest rates.

Shifts in the yield curve are driven by shocks in monetary policy (see e.g., Ang and

Piazzesi, 2003, and Evans and Marshall, 2007). In this regard, Bernanke and Gertler (1995) and

Kashyap and Stein (1995) show theoretically and empirically that under the “bank lending

channel view” of monetary policy, the balance sheets of small and large banks respond in

different ways to a shock in monetary policy.5 Kashyap and Stein (2000), Kishan and Opiela

(2000), and Berger and Bouwman (2009) provide additional empirical evidence that the bank

lending channel of monetary policy is stronger for small banks than large banks, regardless of

their capitalization ratios.

Veronesi (1999), Perez-Quiros and Timmerman (2000), and Ozoguz (2009) show

theoretically and empirically that stock returns may be subject to endogenous low frequency

structural breaks. In particular, Perez-Quiros and Timmerman (2000) and Ozoguz (2009) show

that systemic risk and exposure of firms to systematic risk may vary with firm size and the state

of the economy. Ignoring structural breaks in the data generating process (DGP) of stock returns

can affect the forecasting accuracy of any model (see Pesaran and Timmermann, 2004).

Hence, we impose the condition that a common two-state Markov chain drives the data

generating process (DGP) of bank stocks returns mimicking the dynamics of the real business

cycle. Relative to a univariate estimation approach using each portfolio return separately as

dependent variable, the bivariate approach has several advantages. First, the joint estimation

procedure imposes the condition that the bad economic state occurs simultaneously for both

portfolios of small and large banks. It also provides a natural framework to formally test the

5 According to this view, monetary policy affects bank lending and deposits and it may also affect off-balance sheet

activities like loan commitments (Woodford, 1996; and Morgan, 1998).

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hypothesis that exposure to systematic risk is different for small and large banks. One drawback

of this approach is that because the quasi-maximum likelihood (Q-ML) joint estimation

procedure for the four portfolios would be computationally infeasible, we restrict the asset

pricing tests to the largest and smallest portfolios ranked by size (that is Portfolio 1 and Portfolio

4, respectively).6

Formally, bank stock returns follow a two-state Markov regime switching (MRS) –

ICAPM stochastic process:

tititt

e

ti sssR ,, d , with titti GED ,1, ,0~ , for i=1,2 (1)

ttittitiititiiti sEsusua 1,1

2

1,1

2

1,1,, lnln , with titititi su ,

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,, , (2)

where ξλβ ttit

e

it sssREs ˆ is the cross-section regression (CSR) with expected

excess return for stock i as dependent variable conditional on state ts at time t; β is the vector of

risk factor loadings; tt sEs Xλ ˆ denotes the state-dependent vector of market prices of risk

conditional on state ts at time t with tPOLtDEFtTERM

e

tMKTt MCPMCPMCPR ,,,,X the vector of

returns tracking the innovations in the state variables driving the time-varying opportunity set; d

is a vector of calendar dummies proxying the exogenous regulatory changes from Basel I (D1)

and the Gramm-Leach-Bliley act (D2); ti s is the state dependent diffusion parameter

conditional on state ts at time t; the conditional error follows some general distribution (GED)

with mean zero and time-varying variance ti , driven by a Regime-Switching E-GARCH (2,1)

6 The problem arises because the estimation procedure of the regime switching model relies on a non-linear version

of the Kalman filter (the expectation-maximization (EM) algorithm of Dempster, Laird, and Rubin (1977)). The

optimization problem becomes computationally difficult in higher dimensions, what computer scientists call NP-

hard. The solution to the optimization problem cannot be obtained in polynomial time (i.e., reasonable amount of

time). We also estimate the model for each of the four portfolios without imposing the joint restriction. The results

are quantitatively and qualitatively similar so we do not include them to save space. They are available upon request

to the authors.

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process7 with parameters a’s and given the information set at time t – 1 1t , and

1,0...~, Ndiiti s.t. 0, ,, tjtiE , ji and

2

,

0

0,

0

0~

N

t

ti

ξ.

We estimate the MRS-ICAPM using quasi maximum-likelihood (Q-ML) and imposing

the zero mispricing restrictions upfront. Since ts is a latent hidden layer following a two-state

Markov chain we implement Hamilton’s (1989, 1990) nonlinear expectation maximization (EM)

algorithm to estimate the transition probabilities across both economic regimes

2,1,Pr 1 jipisjs ijtt .

As noted before, we use the time-series asset pricing test approach of Gibbons, Ross, and

Shanken (1989) (i.e., GRS test).

III. Empirical results

MRS-ICAPM estimates

Table 3 reports the MRS-ICAPM estimates for good and bad economic times,

respectively. Based on the Gibbons, Ross, and Shanken (GRS) time-series asset pricing test

results, we conclude that the MRS-ICAPM effectively explains bank stock returns with a 95%

confidence level.

[INSERT TABLE 3 HERE]

In this regard, during good economic times for the portfolio of large banks the factor

loadings on MKT and TERM are significant with a 95% confidence level. For the portfolio of

small bank stocks, during good economic times, the factor loadings on TERM and POL are

significant with a 95% confidence level. The regulatory dummy corresponding to Basel I (D1) is

7 As shown by Klaassen (2002), the adopted specification has the advantage over the E-SWARCH model of

Hamilton and Susmel (1994) that it is nested in the general class of GARCH models. Moreover, the exponential

specification for heteroskedasticity allows for asymmetric behavior without imposing non-negative restrictions.

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significant with a 95% confidence level, and the regulatory dummy corresponding to Gramm-

Leach-Bliley (D2) is marginally significant with a 90% confidence level.

During bad economic times, with the explicit inclusion of a monetary policy induced risk

factor POL, we are able to differentiate two types of shocks in the term structure of interest rates.

For the portfolio of large banks in bad economic times, the factor loading on MKT is positive and

significant at the 95% confidence level, while the factor loading on TERM is positive and

significant at the 90% confidence level. The factor loading on TERM is positive and significant

for small banks. During bad economic times, as short term interest rates drop, the yield curve

becomes steeper, benefiting especially small banks as discussed in Viale, Kolari, and Fraser

(2009).

The factor loading on POL is negative and significant at the 95% confidence level for

small banks only in bad economic times. These results are consistent with the bank lending

channel view of monetary policy. In this regard, Berger and Bouwman (2009) analyzed each

financial crisis since 1987 to 2008 and conclude that during regimes of loose monetary policy,

banks adopt lax credit standards increasing credit supply to the point that increases the risk of a

crisis. This effect is most prevalent in small banks. The dummy variable representing the Basel

accord (D1) is significant at the 95% confidence level.

Note that both POL and DEF do not help to explain the behavior of large bank stocks.

This might be because the effects from DEF and POL are captured through the factor loading on

the market return. In this regard, Franke and Krahnen (2005) show that as large banks use

derivatives to shift default risk outside their balance sheets, they increase their exposure to

market risk. A similar argument can be argued if large banks hedge against future shifts in

monetary policy. In this respect, “market beta” during bad times is more pronounced for large

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banks than small banks, while the sensitivity to TERM during bad economic times is more

pronounced for small banks than large banks.

The negative sign of the regulatory dummy D1 reflects the effect of regulation to enforce

risk-driven capital requirements, as Basel I reduced the long-run cost of equity of banks in

general. This effect is more pronounced for small banks than for large banks. D2 is positive and

marginally significant.

The E-GARCH parameters in the variance return equations of small bank stocks are

significantly higher than the corresponding parameters in the variance return equations of large

bank stocks. In particular, the intercept (alpha) in the variance return equation of small bank

stocks is significantly higher than that of large bank stocks during bad economic times. Also,

although returns of both small and large banks are more autocorrelated during bad times, the

stock returns of small banks are more autocorrelated than those of large banks.

Figure I plots the transition probability to the bad economic regime of the two bank

portfolio returns along with the NBER-dated economic recessions. Figure II illustrates the joint

behavior of the conditional variances for small and large bank stocks, respectively. It confirms

how the level of volatility, skewnesss, and persistence of large and small bank stock returns are

different.

[INSERT FIGURE I HERE]

[INSERT FIGURE II HERE]

Robustness checks: Potential model misspecification in the construction of the MCPs

We check for potential (model) misspecification in the construction of the MCPs. For

this purpose, we use the following proposition:

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PROPOSITION 1: If the MCP is specified correctly, then the conditional expected tracking error

should be zero and an integrated conditional moment (ICM) test as in Bierens (1990), and

Bierens and Ploberger (1997) can be used to test the null of no (model) misspecification.

Proof: Is technical and relegated to the Appendix.

The ICM test results are shown in Table 4. Clearly, we cannot reject the null hypothesis

that the MCPs for TERM, DEF, and POL are correctly specified at a 5% level of statistical

significance.

[INSERT TABLE 4 HERE]

Is indirect market discipline feasible?

Table 5 provides the in-sample (January 1973 - December 2003) estimates of the state

dependent factor loadings for the 24 banks that failed from January 2008 to December 2010. The

betas were obtained running univariate two-state Markov regime-switching time-series

regressions in which bank stock excess returns represent the dependent variable, and the risk

factors that were found to explain the behavior of large small and small banks based on the

MRS-ICAPM results (presented in Table 3).

[INSERT TABLE 5 HERE]

After obtaining the in-sample betas for these banks during good and bad economic times,

we forecast the excess returns of the tracking portfolios of the risk factors that were found to

explain the behavior of bank stocks sorted by size for the period from January 2004 to December

2007. With this information, we calculate the out-of-sample expected excess return for each of

these banks, and the cost of equity of each of the two portfolios sorted by size. Note that this

period represents the good economic regime as there were no economic recessions then. To

obtain the out-of-sample cost of equity during a bad economic regime, we repeat the procedure

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for the period 2008 to 2010 using the MRS-ICAPM. Table 6 provides the out-of-sample cost of

equity for each bank, and for both bank portfolios sorted by size.

[INSERT TABLE 6 HERE]

Before the financial crisis of 2008, the monthly cost of equity of large banks was 0.89%,

in line with the historic value of 0.88%. The monthly cost of equity of small banks was 0.31%,

which is well below the historic value of 0.69% and very close to the monthly average yield of

the 1 month Treasury bill of 0.28%. This is consistent with the bank lending channel view of

monetary policy, which shows that a loose monetary policy will have an impact mostly on the

balance sheets of small banks. The loose stance of monetary policy during the period led to very

loose credit standards, an increase of credit supply, and an increase of off-balance sheet

guarantees that might have lowered the investors’ perception of risk for small banks.

Observing the cost of equity of each bank and comparing it with the cost of equity of its

respective benchmark portfolio offers a more complete assessment of the true risk to which these

banks were exposed. The cost of equity of only 4 of the 12 large banks that failed or were

rescued was lower than the portfolio’s average. On the other hand, the cost of equity of 6 of 12

small banks that failed was lower than the benchmark portfolio’s average.

Given the MRS-ICAPM estimates, in the event of an economic crisis, the monthly cost of

equity of both large and small banks was expected to increase to 2.49%. In Figure III, we plot the

prices of a selected number of large and small banks respectively that failed or were rescued

during the financial crisis of 2008. Clearly, investors penalized stocks in the months leading up

to the bank being closed or rescued by the Fed.

[INSERT FIGURE III HERE]

20

Table 7 provides the test results of running two-tail t-tests and F-tests of the null

hypothesis that the distributions of the cost of equity for good and bad economic times are

statistically equal with a 95% confidence level. Panel A shows the test results for large bank

stocks and Panel B for small bank stocks, respectively. We reject the null that the average cost of

equity of both large and small banks that failed during the crisis is the same during good and bad

economic times.

[INSERT TABLE 7 HERE]

Finally, using the cost of equity of each portfolio of failed banks sorted by size we

calculate the probabilities that the cost of equity of a typical bank in the portfolio of ex-post

failed banks would have been less than the out-of-sample portfolio’s cost of equity during good

economic times, greater than the out-of-sample portfolio’s cost of equity during bad economic

times, and somewhere in between. Figures IV and V plot the probabilities for small and large

banks, respectively.

[INSERT FIGURE IV HERE]

[INSERT FIGURE V HERE]

During good times, there is a 17% probability that the cost of equity of a typical large

bank prone to fail will be below its portfolio average ranked by size. That is, the probability of an

investor making a Type I error is 17%. For small banks, this probability is 50%. The difference

may occur because of the relatively lower precision (higher standard deviation) of small bank

stocks. The probability of the stock of a small bank sending a false signal of failure is 8%, versus

16% for large banks. Furthermore, during bad economic times the probability that the cost of

equity of a typical small and large bank prone to failure is above the portfolio’s average cost of

equity is 100%.

21

Cross-sectional analysis of banks’ exposure to shocks in TERM and POL during the crisis

Table 8 shows the estimation results of the two cross-sectional regressions between the

factor loading on TERM for the sample of large banks and sensitivities to market volatility

(S_VIX), turnover ratio (TURNOVER), deposits (DEPOSITS), net interest margin (NIM), non-

interest income (NOINT), amount of non-performing assets (NONPER), provision for loan

losses (PLL), and the bank’s capital ratio (CAP). For the sample of small banks, the regression is

between sensitivities to POL and the same list of regressors.

[INSERT TABLE 8 HERE]

The results lead us to conclude that the sensitivity of large banks to shocks in the slope of

the term structure varies directly with the net interest margin (10% significance level) and

inversely with the bank’s capital ratio (1% significance level). Yet, the sensitivity of small banks

to shocks in the stance of monetary policy varies directly with the net interest margin and

inversely with non-interest income at a 5% significance level.

IV. Conclusion

We investigate whether investors are able to price the banks’ exposure to systematic risk

in the stock market in anticipation of a financial crisis. For this purpose, we estimate a two-state

MRS-ICAPM for the period 1973-2003 to identify the risks that are priced in the cross-section of

large and small banks during good and bad economic times. Then we calculate the out-of-sample

cost of equity for the period 2004 to 2007 for 24 banks that failed or were rescued during the

financial crisis. We compare each bank’s cost of equity with its corresponding size-matched

benchmark bank portfolio cost of equity during good and bad economic times. Our empirical

results provide evidence that investors equipped with an MRS-ICAPM asset pricing model and

22

the bank specific information from public financial statements would have been able to correctly

anticipate the increased exposure to systemic risk of both large and small banks before the crisis.

The empirical results suggest that markets were underestimating the risks of small banks

before the financial crisis. We suspect that the underestimation of bank risk prior to the financial

crisis was due to inflated credit ratings of mortgage pools, the lack of recognition when the

housing price bubble developed, and the false perception that securitization and business

diversification insulated banks from potential mortgage problems. However, we leave the

investigation of the underlying reasons for the underestimation of risk to future research.

Further analyses show that the sensitivity of large banks to shocks in the slope of the term

structure is directly proportional to net interest margin and inversely proportional to the bank’s

capital ratio. On the other hand, the sensitivity of small banks to shocks in the stance of monetary

policy is directly proportional to the net interest margin and inversely proportional to non-

interest income.

One important policy implication of our results is that feasibility of indirect market

discipline is heavily dependent on the asset pricing model used to identify and forecast the risks

in the banking function. In this regard, the empirical results highlight the critical importance of

modeling explicitly endogenous structural breaks or large deviations in the data generating

process of bank stock returns to obtain more accurate forecasts.

23

Appendix

Proof of Proposition 1

Define tx as the variable of interest (e.g., TERM, DEF, POL), R as the vector of stock

returns used to form the tracking portfolio for their innovations, and Z as the vector of control

variables. Following the method in Breeden et al. (1989), Lamont (2001), and Vassalou (2003),

1,111,11 tttttktttt exExEexEx , (A.1)

where k denotes the length of the forecasting period, and e is the innovation in the variable of

interest. Let, ttt xE t1tRa ,1 and 1111 tttt xE zf as

1t1tt, zdR 1tE , with ,

and innovations, and a, d, and f vector of weights. Thus,

11 ttx 1tt ZcRb , (A.2)

where b=a, c=f-ad, and ktttt e 11 . Under the martingale hypothesis, ttt xxE 11

and 11 tttx zf . Making the appropriate substitutions in (A.2) leads to,

11

ttt yx 1tt ZcbR , (A.3)

this is written in a form suitable to be used for the ICM test as described in Bierens (1990), and

Bierens and Ploberger (1997). The null hypothesis of the test is that the specified model (i.e.,

equation (A.3)) represents the conditional expectation of the state variable of interest, i.e.,

0,,1, 1tRkttktt eeE .

Q.E.D.

24

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28

Table 1

Description and summary statistics of main variables

Panel A. Description

etiR , = Monthly excess return on portfolio i ranked by ME at the end of period t.

e

tMKTR , = Monthly excess return of the CRSP value-weighted market index at the end of period t.

tUTERMMCP , = Return on a mimicking portfolio correlated with innovations in the slope of the yield curve

(TERM) at the end of period t.

tUDEFMCP , = Return on a mimicking portfolio correlated with innovations in the default spread (DEF) at the

end of period t.

tUPOLMCP , = Return on a mimicking portfolio correlated with innovations in the monetary policy index (POL)

at the end of period t.

Panel B. Summary Statistics

This table presents the summary statistics of the group of portfolio returns and factors used in the empirical

analysis. The returns of the maximum correlated portfolios track the innovations or unexpected component of each

explanatory variable by construction. Portfolio 1 is the largest and Portfolio 4 the smallest. The sample period is

from January 1973 to December 2003.

Portfolio 1 Portfolio 2 Portfolio 3 Portfolio 4

Mean 0.0506 0.0168 -0.0002 -0.0416

Std.Dev. 0.0495 0.0452 0.0479 0.0548

Minimum -0.0810 -0.1065 -0.1535 -0.2789

Median 0.0493 0.0139 -0.0024 -0.0393

Maximum 0.4235 0.2423 0.2461 0.2042

Skewness 1.9240 0.9528 0.7318 -0.2484

Kurtosis 11.9374 3.3965 2.8345 2.6809

Autocorr. 0.2873 0.3588 0.3700 0.4339

e

tMKTR , tUTERMMCP , tUDEFMCP , tUPOLMCP ,

Mean 0.0046 0.0000 0.0026 -0.0017

Std.Dev. 0.0472 0.0371 0.0239 0.0212

Minimum -0.2313 -0.1300 -0.1159 -0.0597

Median 0.0080 0.0007 0.0028 -0.0024

Maximum 0.1605 0.1274 0.0943 0.0782

Skewness -0.4981 0.0061 0.0407 0.0334

Kurtosis 1.9809 -0.2754 -0.3048 0.3499

T (months) 372 372 372 372

29

Table 2

Regulatory Structural Break Test Results

( titPOLPOLitDEFDEFitTERMTERMiMii MCPMCPMCPRR e

tMKT

e

ti ,,,,,,,, ,, )

Industry / Regressor MKT TERM DEF POL

Portfolio 1

Estimate 0.05 0.52 0.35 0.17 -0.16

Unadj. t-stat / p-value 21.85 [0.00] 3.38 [0.00] 3.77 [0.00] 0.61 [0.54] -0.67 [0.50]

Adj.2R 0.29

BIC # of structural breaks 2

Portfolio 2

Estimate 0.01 0.63 0.36 -0.26 -0.41 Unadj. t-stat / p-value 7.13 [0.00] 4.60 [0.00] 4.30 [0.00] -1.05 [0.30] -2.00 [0.05]

2R 0.33

BIC # of structural breaks 4

Portfolio 3

Estimate -0.00 0.48 0.38 0.27 -0.30

Unadj. t-stat / p-value -1.79 [0.07] 3.40 [0.00] 4.39 [0.00] 1.03 [0.30] -1.42 [0.15] 2R 0.37

BIC # of structural breaks 2

Portfolio 4

Estimate -0.04 0.20 0.51 0.34 -0.83 Unadj. t-stat / p-value -17.61 [0.00] 1.12 [0.26] 4.68 [0.00] 1.02 [0.31] -3.06 [0.00]

2R 0.21

BIC # of structural breaks 4

This table presents the results of the Bai-Perron (1998, 2003) tests for the presence of multiple structural breaks.

The results are robust to the presence of serial correlation and heteroskedasticity. Statistical significance is set at

the 5% level and highlighted in black. Portfolio 1 is the largest and Portfolio 4 the smallest.

30

Table 3

Bivariate MRS-ICAPM

( tititti

e

ti vssR ,, Xβ , titti hGEDv ,1, ,0~ )

Large Small Large Small

Good Economic Times Estimates statt

CONDITIONAL DRIFT EQUATION: ttit

e

i sssRE λβ ˆ

MKT 0.6507** 0.2674 4.5663 1.434

BETA TERMMCP 0.2378** 0.4074** 2.538 3.790

BETA DEFMCP 0.0555 0.0131 0.203 0.038

BETA POLMCP 0.1454 -0.7531** 0.736 -2.609

D1 -0.0815** -0.0678** -6.736 -4.036

D2 0.0955** -0.0079* 7.893 -1.858

MKT = 1.13%, TERM = 0.62%, POL = -0.18%

CONDITIONAL VARIANCE EQUATION: ttittitiititiiti shEsusuah 1,1

2

1,1

2

1,1,, lnln

2.8460** 2.5678** 8.306 8.126

Bad Economic Times

CONDITIONAL DRIFT EQUATION: ttit

e

i sssRE λβ ˆ

MKT 0.5669** 0.3067* 4.101 1.677

BETA TERMMCP 0.1540* 0.4467** 1.713 4.301

BETA DEFMCP -0.0283 0.0523 -0.105 0.152

BETA POLMCP 0.0616 -0.7138** 0.319 -2.504

D1 -0.0023 -0.0285** -0.290 -2.173

D2 0.0117 -0.0079 1.503 -0.594

MKT = 4.55%, TERM = -0.60%, POL = -1.91%

CONDITIONAL VARIANCE EQUATION: ttittitiititiiti shEsusuah 1,1

2

1,1

2

1,1,, lnln

1.1259** 4.1346** 2.020 13.329

E-GARCH – AR1 0.1269** 0.3499** 5.014 3.051

TRANSITION PROBABILITIES

1p 2p

1p 0.01 0.02

2p 0.99 0.98

Large Small

(-) Log Likelihood 1,914.70 -1,702.06

GRS-test 29.00**

This table reports the estimates of the bivariate MRS-ICAPM for the largest and smallest bank portfolios ranked by size.

**denotes statistical significance at the 5% level and * at the 10% level of significance. The E-GARCH autoregressive

parameters are reported as differences from the benchmark regime (good economic times). The sample period is from January 1973

to December 2003. The estimates were obtained using Q-ML assuming a general distribution (GED) for the errors, a non-

linear (EM) algorithm as in Hamilton (1989, 1990), and the restriction that a common Markov chain drives the DGP of

bank stock returns. The parameter is the intercept in the conditional variance equation of bank stock returns.

31

Table 4

Model Misspecification Test Results

( 11

ttt yy 1tt ZcbR )

MCP T(1) T(2) ICM Test CV: 4.26 CV: 3.23

TERM

Result after 1,000 Monte Carlo

Simulations 0.0224 0.0220 1.02

5% significance level Accept Null

10% significance level Accept Null

DEF

Estimate

Unadj. t-stat / p-value 0.0019 0.0017 1.10 2R Accept Null

BIC # of structural breaks Accept Null

POL

Estimate

Unadj. t-stat / p-value 0.0022 0.0020 1.08 2R Accept Null

BIC # of structural breaks Accept Null

This table presents the results of the ICM test in Bierens (1990) and Bierens and Ploberger (1997). The null

hypothesis is equivalent to: H0: E[e(t)|v(t)] = 0 a.s., where e(t) is the regression error and v(t) is the vector of

instrumental variables, i.e., portfolio returns. The ICM test is based on a random function of the form: z(n,x) =

(1/Vn)(e(1)w(x's(t)) +....+e(n)w(x's(t)), where w(.) = cos(.) + sin(.), and s(t) is the vector of standardized and

bounded instruments. T(1) = Integral (z(n,x))^2 dm(x), and T(2) = Integral Fn(x,x)dm(x), where Fn(x1,x2) the

estimated covariance function and m(x) is the uniform measure on K(c), the ICM test statistic is of the form T =

T(1) / T(2). CV denotes critical value.

32

Table 5

In-Sample (January 1973 – December 2003) Factor Loadings

Good Economic Times Bad Economic Times R2 Log-

MKT TERM MKT TERM Bar Likelihood N

Large Banks 0.65 0.24 0.57 0.15

Washington Mutual Bank 0.63 0.25 1.43 0.97 0.35 256.83 248

Indy Mac Bank 0.56 -0.08 0.60 2.10 0.09 211.45 218

Colonial Bank 1.08 0.28 0.61 0.82 0.26 306.82 245

BankUnited FSB 0.01 0.96 1.67 -2.76 0.18 208.06 216

Citigroup 1.42 0.40 6.34 0.81 0.40 408.51 323

JP Morgan 1.21 0.32 1.68 0.71 0.41 459.63 372

Bank of America 1.34 0.82 5.98 0.76 0.54 377.27 295

Wells Fargo 0.95 0.45 1.09 0.49 0.25 486.87 372

Bank of New York 0.63 0.16 2.50 5.63 0.07 396.33 372

US Bancorp 0.83 0.21 0.81 1.30 0.22 455.05 372

Morgan Stanley 0.26 -0.40 1.77 -0.11 0.18 198.62 216

Goldman Sachs 1.13 -0.39 2.40 -0.10 0.67 78.71 55

Good Economic Times Bad Economic Times R2 Log-

TERM POL MKT TERM POL Bar Likelihood N

Small Banks 0.41 -0.75 0.31 0.45 -0.71

Downey Savings and Loan 1.03 -1.15 3.26 1.12 2.50 0.33 295.22 332

First Regional Bank 0.05 -0.72 0.13 1.09 -1.88 0.01 250.26 279

Horizon Bank 0.25 0.30 1.10 4.11 -9.13 0.24 274.40 207

Corus Bank NA 0.05 0.22 0.82 0.72 -0.82 0.24 488.38 371

Imperial Capital Bank 0.88 -0.80 11.10 9.11 -1.28 0.31 123.30 98

Greater Atlantic Bank 0.31 2.02 -7.55 -0.47 -24.66 0.25 37.82 54

Security Bank of Jones County -0.01 0.95 0.06 2.93 -3.53 0.46 92.55 72

Vineyard Bank 2.45 13.04 1,08 1.48 -0.83 0.41 25.01 29

Cooperative Bank 1.06 -2.09 10.63 2.38 10.94 0.48 161.00 148

Shore Bank -0.12 0.15 3.36 1.89 4.63 0.51 109.21 76

The Cowlitz Bank -0.10 0.23 -0.63 2.47 -5.01 0.51 87.98 69

City Bank of Lynnwood WA 0.86 -11.75 0.76 1.17 -0.26 0.55 55.74 54

This table provides the state dependent factor loadings of 24 public banks that failed during the period January 2008 – December

2010. The in-sample factor loadings were obtained running univariate time-series regime-switching regressions between each

bank’s stock excess returns and the portfolio returns tracking the innovations in the factors that were found to be priced in the

period 1973-2003.

33

Table 6

Out-of-Sample (January 2004 – December 2007) Monthly Cost of Equity (%)

Good Economic Times Bad Economic Times

Large Banks 0.89 2.49

Washington Mutual Bank 0.88 5.92

Indy Mac Bank 0.77 1.47

Colonial Bank 1.28 2.28

BankUnited FSB 0.42 9.24

Citigroup 1.60 28.35

JP Morgan 1.40 7.22

Bank of America 1.58 26.75

Wells Fargo 1.19 4.67

Bank of New York 0.86 8.00

US Bancorp 1.05 2.91

Morgan Stanley 0.46 8.12

Goldman Sachs 1.24 10.98

Small Banks 0.31 2.49

Downey Savings and Loan 0.38 9.38

First Regional Bank 0.27 3.52

Horizon Bank 0.32 19.96

Corus Bank NA 0.29 4.85

Imperial Capital Bank 0.37 47.47

Greater Atlantic Bank 0.38 13.05

Security Bank of Jones County 0.30 5.25

Vineyard Bank 2.88 5.60

Cooperative Bank 0.36 26.06

Shore Bank 0.27 5.32

The Cowlitz Bank 0.27 5.20

City Bank of Lynnwood WA 0.06 3.26

This table presents the out-of-sample state dependent cost of equity of 24 public banks that failed

from January 2008 to December 2010. To calculate the cost of equity of each bank during good

economic times we use the in-sample factor loadings from Table 5 and the out-of-sample (January

2004 – December 2007) returns of the tracking portfolios of the innovations in the risk factors that

were found to be priced in Table 3 for the period January 2004 – December 2007. The market price

of risk of MKT is 0.8946% for the period 2004-2007. The market price of risk of TERM is 0.1290%

for the period 2004-2007. And the market price of risk of POL is 0.0277% for the period 2004-2007.

The excess returns of the tracking portfolios for bad economic times are the in-sample historic

values as shown in Table 5. The monthly risk free rate is the average 1 month Treasury yield equal

to 0.2792% for the period January 2004 – December 2007. For comparative purposes, we include the

average cost of equity for the two portfolios sorted by size.

34

Table 7

Distribution Comparison: Good Economic Times versus Bad Economic Times

Panel A: Large Banks Confidence Level: 95%

Test Value

Critical

Value P-Value

Two-tail t-Test -3.36 2.59 0.05

Reject the H0 that the Means are

Equal

F-Test 502.17 2.82 0.00

Reject the H0o that the Variances

are Equal

Panel B: Small Banks Confidence Level: 95%

Test Value

Critical

Value P-Value

Two-tail t-Test -3.13 2.59 0.01

Reject the H0 that the Means are

Equal

F-Test 306.51 2.82 0.00

Reject the H0 that the Variances

are Equal This table presents mean-variance comparison tests between the two distributions of the out-of-sample cost of equity of the banks

that failed during the financial crisis of 2008 for good and bad economic times. We provide the results of a two-tail t-test and F-test

with null hypothesis that the means and variances of the two distributions are equal at a 95% confidence level. We include the

critical values and p-values. Panel A shows the test results for the sample of large bank stocks. Panel B shows the test results for

the sample of small bank stocks.

35

Table 8

OLS Cross-section regressions

𝛽𝑇𝐸𝑅𝑀,𝑖= 𝛼 + 𝜙𝑆_𝑉𝐼𝑋S_VIXi + 𝜙𝑇𝑈𝑅𝑁𝑂𝑉𝐸𝑅TURNOVERi + 𝜙𝐷𝐸𝑃𝑂𝑆𝐼𝑇𝑆DEPOSITSi + 𝜙𝑁𝐼𝑀NIMi +

𝜙𝑁𝑂𝐼𝑁𝑇NOINTi + 𝜙𝑁𝑂𝑁𝑃𝐸𝑅NONPERi + 𝜙𝑃𝐿𝐿PLLi + 𝜙𝐶𝐴𝑃CAPi+ 𝜉, ∀𝑖 = large bank

𝛽𝑃𝑂𝐿,𝑗= 𝛼 + 𝜙𝑆_𝑉𝐼𝑋S_VIXj + 𝜙𝑇𝑈𝑅𝑁𝑂𝑉𝐸𝑅TURNOVERj + 𝜙𝐷𝐸𝑃𝑂𝑆𝐼𝑇𝑆DEPOSITSj + 𝜙𝑁𝐼𝑀NIMj +

𝜙𝑁𝑂𝐼𝑁𝑇NOINTj + 𝜙𝑁𝑂𝑁𝑃𝐸𝑅NONPERj + 𝜙𝑃𝐿𝐿PLLj +𝜙𝐶𝐴𝑃CAPj+ 𝜉, ∀𝑗= small bank

Bank-specific variable Large Banks

𝛽𝑇𝐸𝑅𝑀,𝑖

Small Banks

𝛽𝑃𝑂𝐿,𝑗

𝛼 0.42 0.44

(0.86) (0.11)

𝜙𝑆_𝑉𝐼𝑋 -135.48 0.04

(0.59) (0.63)

𝜙𝑇𝑈𝑅𝑁𝑂𝑉𝐸𝑅 0.64 0.11

(0.31) (0.26)

𝜙𝐷𝐸𝑃𝑂𝑆𝐼𝑇𝑆 -0.59 -0.52

(0.24) (0.17)

𝜙𝑁𝐼𝑀 1.12* 0.08**

(0.06) (0.03)

𝜙𝑁𝑂𝐼𝑁𝑇 -0.31 -0.05

(0.27) (0.04)**

𝜙𝑁𝑂𝑁𝑃𝐸𝑅 1.83 1.70

(0.64) (0.66)

𝜙𝑃𝐿𝐿 2.56 0.02

(0.40) (0.67)

𝜙𝐶𝐴𝑃 -0.55*** -2.95

(0.00) (0.23)

F-test 3.54 1.50

S.E. 4.87 0.40

R2 0.21 0.05

��2 0.15 0.02

This table reports OLS estimates from cross-sectional regressions of large banks sensitivities to shocks in the slope

of the term structure and small banks sensitivities to shocks in the stance of monetary policy. The independent

variables are S_VIX = sensitivity to VIX, TURNOVER, DEPOSITS, NIM = net interest margin, NOINT = non-

interest income, NONPER = non-performance loans, PLL = provision for loan losses, and CAP = capital ratio. P-

values are in parenthesis. ***, ** and * represent significance at 1%, 5% and 10% respectively. The variables are

measured by their means over the financial crisis period .

36

Figure I. This chart plots the transition probabilities of bank stock returns in a bear market regime for

test assets 1 & 4. NBER designated business cycle recessions are represented as grey bars.

Probability of Low Mean and High Variance Regime - Portfolio 1

0

0.1

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b-7

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Probability of Low Mean and High Variance Regime - Portfolio 4

0

0.1

0.2

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37

Figure II. This graph shows the 12-month moving average of the conditional variances of small and

large bank stocks. NBER designated recessions are represented as grey bars.

38

LARGE BANKS

SMALL BANKS

Figure III. This graph shows the stock prices of selected large and small banks that failed during the financial crisis

up to the point in time where they were closed or bailed out with TARP funds.

0

50

100

150

200

250

0

10

20

30

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CNB WFC JPM BK BAC USB MS C GS

0

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Downey Corus City Bank Vineyard Shore Bank

TARP bailout date

TARP bailout date

39

Figure IV. This graph shows the probabilities that the cost of equity of the group of small

failed banks were below (black), between (dark grey), and above (light grey) the average

cost of equity of the portfolio of small bank stocks during good and bad economic times.

Figure V. This graph shows the probabilities that the cost of equity of the group of large failed

banks were below (black), between (dark grey), and above (light grey) the average cost of

equity of the portfolio of large bank stocks during good and bad economic times.

0.50

0.08

1.00

0%

10%

20%

30%

40%

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100%

GOOD BAD

Probability that the cost of equity of small banks

is less than 0.31 and greater than 2.49

0.42

0.17

0.67 1.00

0%

10%

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40%

50%

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100%

Probability that the cost of equity of large banks

is less than 0.89 and greater than 2.49

Good Economic Times Bad Economic Times

Good Economic Times Bad Economic Times

0.16