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Evaluating Risk-based Capital Regulation
Thomas L. Hogan* Troy University
151 Bibb Graves Hall
Troy AL, 38061
tlhogan@troy.edu
+1 334-808-6383
Neil R. Meredith West Texas A&M University
2501 4th Avenue
Canyon, TX 79106
nmeredith@wtamu.edu
+1 806-651-2493
Xuhao (Harry) Pan George Mason University
4400 University Drive
Fairfax, VA 22030
xpan3@masonlive.gmu.edu
+1 806-401-1930
* Corresponding author
JEL Codes: G21, G28, G32
Key Words: Bank, Capital, Risk-based capital, Regulation
Last revision: August, 2013
The authors would like to thank the Mercatus Center
at George Mason University for financial assistance.
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Evaluating Risk-based Capital Regulation
Abstract
Risk-based capital (RBC) ratios are an important component of US banking regulation,
yet empirical evidence on the effectiveness of RBC regulation has been mixed. Although several
studies find that RBC regulations actually increase risk in the banking system, supporters of
RBC regulation maintain that these rules can better identify at-risk banks. This paper evaluates
the capital and RBC ratios of US commercial banks from 2001 through 2011. We find the
standard capital ratio to be a significantly better predictor of bank performance than the RBC
ratio. Using the capital and RBC ratios together performs no better than the capital ratio alone.
These results suggest that the standard capital ratio is a superior metric for evaluating bank risk.
JEL Codes
G21, G28, G32
Keywords
bank, capital, risk-based capital, regulation
2
1. Introduction
The standard capital ratio of equity over assets has long been used as an important
indicator of bank risk. Banks with more equity are less affected by asset depreciation than are
other banks because a drop in the value of their assets affects only their equity and not their
liabilities. In response to the savings and loan crisis of the 1980s, the Federal Reserve adopted
risk-based capital (RBC) regulations in 1991 based on the Basel Committee on Bank Supervision
(1988, hereafter “Basel Accords”) to improve the effectiveness of US banking regulation and to
standardize the US banking system with other systems around the world.1 The Fed is currently in
the process of adopting more complex RBC standards based on Basel II and Basel III.2
RBC regulations are intended to improve the Fed's measurement of bank risk, provide an
incentive for banks to limit their risk-taking activities, and thereby decrease risk in the banking
system. The RBC ratio measures equity as a percentage of risk-weighted assets (RWA); each
category of assets is assigned a weight appropriate to its perceived level of risk. Banks with
riskier assets must maintain more capital, while banks with safer assets require less capital.
However, if this method of assessing risk is flawed, its use may increase, rather than decrease,
systemic risk in the banking system.
Critics of the Basel system have pointed out several ways in which RBC regulation has
increased risk in the banking system.3 First, RBC can encourage risk-taking by individual banks,
especially if regulators have not properly identified the riskiness of a particular class of assets.
Jablecki (2009, p.16) shows that the misrating of risky assets in the risk-weighting system of the
1 A preliminary RBC framework was introduced in June 1988. Banks were given a grace period through December
31, 1990 to become compliant with the new regulations. For further detail, see “Banks and Banking” (2011, p.21). 2 Basel II and Basel III refer to the Basel Committee on Banking Supervision (2004; 2010).
3 This paper deals mostly with empirical studies of RBC regulation. In terms of theory, VanHoose (2007, p.3694)
finds that “the literature offers widely divergent conclusions about . . . whether risk-based capital regulation truly
makes individual banks and the banking system as whole ‘safer.’”
3
Basel Accords has encouraged US banks to adopt “regulatory capital arbitrage techniques, in
particular securitization.”4 Second, risk-weighting systems can create systemic risk by
encouraging many banks to invest heavily in the same class of assets. Friedman (2011) explains
how RBC regulations give banks an incentive to hold certain classes of risky assets, such as
MBS and Greek government bonds, and that this approach has increased systemic risk in the
United States and the European Union respectively.5
It is possible, however, that the benefits of RBC regulation might outweigh the potential
costs. If the RBC ratio is, in fact, an effective predictor of bank risk, then the RBC ratio might
help regulators identify particularly risky banks, and this advantage might offset the
disadvantage of increased systemic risk. Some studies, such as Estrella, Park, and Peristiani’s
(2000), have proposed that optimal banking regulation might utilize some combination of capital
and RBC regulations. The Fed currently employs such a system (discussed further in the next
section), which is based on the Basel Accords. However, if the RBC ratio does not improve the
predictive power of the capital ratio, then RBC regulation may cause significant harm without
providing any added benefit. Therefore, we must turn to the empirical question of whether or not
the RBC ratio is better than the capital ratio as a predictor of bank performance.
To evaluate the effectiveness of the capital and RBC ratios as predictors of bank
performance, we use a method similar to that of Avery and Berger (1991). Avery and Berger
(1991) is among the first empirical studies to validate the use of RBC as a measure of bank
4 Unfortunately, this problem cannot be resolved simply by periodically reevaluating the assets’ risk weightings,
because regulators themselves cannot be certain of all potential risks. For example, regulators seriously
underestimated the riskiness of mortgage-backed securities (MBS), which were viewed in the 1980s as safe, low-
risk assets but are now recognized as very high in risk. 5 In particular, see chapters “How Securitization Concentrated Risk in the Financial Sector” (pp.183–99) by Acharya
and “A Regulated Meltdown: The Basel Rules and Banks’ Leverage” (pp.200–27) by Richardson, Jablecki, and
Machaj, and well as the introductory chapter by Friedman himself.
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performance.6 The authors find that a bank's RWA (the denominator of the RBC ratio) is
correlated with several indicators of its performance such as income, nonperforming loans, and
bank failures. Our study improves on Avery and Berger (1991) in three important ways. First,
we use more recent data covering the period 2001-2011. Second, our dataset allows us to use
actual RBC ratios reported by commercial banks rather than estimate each bank's RWA as in
Avery and Berger (1991). Third, we use a more accurate econometric model to test for
differences between the predictive powers of the capital and RBC ratios.
Contrary to Avery and Berger (1991), we find evidence that the capital ratio is a better
indicator of bank performance than the RBC ratio. This finding is consistent with other recent
empirical studies. Estrella et al. (2000, p.33) find that “the risk-weighted ratio does not
consistently outperform the simpler ratios, particularly with short horizons.” Demirgüҫ-Kunt et
al. (2011, p.1) write that “the relationship between stock returns and capital is stronger when
capital is measured by the leverage ratio rather than the risk-adjusted capital ratio.” Acharya et
al. (2013) finds that higher RBC is correlated to worse performance on "stress tests" of
commercial banks similar to those administered by the Federal Reserve.
This paper contributes to the debate on bank regulation by comparing the capital and
RBC ratios reported by US commercial banks in their Call Reports as indicators of performance.
It is broken into five sections. Section 2 discusses our sample of bank income and balance-sheet
data as well as the calculation and use of bank RBC ratios. Section 3 introduces our econometric
model for analyzing and comparing the capital and RBC ratios. Section 4 provides the results of
our analysis, which indicate that the standard capital ratio is a significant predictor of bank
6 Avery and Berger (1991) is a well-known empirical study of RBC regulation. It is widely cited and often
described as providing empirical evidence for the effectiveness of RBC regulations, sometimes with the caveat that
the risk weights used by regulators may not be properly calibrated.
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performance. In contrast, the RBC ratio is not a significant predictor of performance, even when
used in conjunction with the capital ratio. Section 5 concludes our study.
2. Data
Data for our study are taken from the FDIC’s Consolidated Reports of Condition and
Income (Call Reports) administered by Federal Financial Institutions Examination Council
(FFIEC) using annual reports from 2001 through 2011 (Federal Deposit, 2013).7 While the time
period we cover encompasses unusual turmoil in the banking sector, we argue that our analysis is
pertinent because the effectiveness of bank capital regulation is likely to matter most during
times of crisis. In addition, volatility during this period is likely to increase the differences
between the performance of safe banks and risky banks, thus improving the identification of
risky banks and accuracy of our analysis.
To provide a basic understanding of RBC ratios and how they are calculated, we discuss
the RBC ratio as described by Avery and Berger (1991) and the changes that have occurred since
that time. Beginning in 1991, the Fed adopted RBC ratios as measures of bank risk. The RBC
ratio is calculated as the bank's adjusted equity divided by its RWA, which are the sum of all
categories of bank assets multiplied by their respective risk weights. The new standards,
estimated by Avery and Berger (1991) from Fed press releases, included three capital
requirements, two of which were based on RWA. As shown in table 1, each bank must maintain
7 Call Report data are only freely available back to 2001. Similar data are available on bank holding companies from
the Fed's Consolidated Financial Statements for Bank Holding Companies (FR Y-9C) reports dating back to 1986.
We use Call Report data to be consistent with Avery and Berger (1991).
6
Tier 1 capital of 4% of RWA, Tier 1 plus Tier 2 capital of 8% of RWA, and Tier 1 capital of 3%
of total assets.8
Table 1 shows definitions for the estimated RWA standards from Avery and Berger
(1991). The table is divided into two parts: risk categories and capital requirements. Bank assets
are sorted into four risk categories (A1–A4). Each category has a different risk weight ranging
from 0% to 100%, based on the perceived riskiness of the assets in that category. The A1
category has a 0% risk weight because it contains safe assets, such as cash and US Treasuries.
Category A2 has a 20% risk weight. It includes riskier assets, such as interbank deposit and
claims, non-OECD deposits and securities, and some MBS.9 Category A3 has a 50% weight and
contains loans secured by properties and municipal bonds. The most risky category, A4, has a
100% risk weight and consists of loans to private entities and individuals, some real estate assets,
investments in subsidiaries, and claims against non-OECD governments and banks. Category A4
is critical in measuring RWA because its high-risk assets are likely to have a disproportionately
large impact on bank performance.
Banks’ off-balance activities are also considered in the RBC standards. Avery and Berger
(1991) group such activities into two categories: counterparty guarantees (category B1) and
market-risk contracts (category B2). In category B1, the main assets are bank guarantees of
counterparty risk, such as letters of credit and loan comments. The B2 category assets are
primarily market-risk contracts that fluctuate with market prices—swaps, forward contracts, and
other derivative products.
8 This final requirement of Tier 1 capital as a percentage of total assets is similar to the pre-1991 requirements of
primary and total capital as percentages of total assets. 9 The term “non-OECD deposits” refers to those held in any country other than the 34 countries of the Organization
for Economic Co-operation and Development.
7
After defining each subcategory, total RWA can be calculated as the sum of all assets in
the subcategory from A1 to B2 multiplied by their respective risk weights:
RWA = 0.0 × A1 + 0.2 × A2 + 0.5 × A3 + 1.0 × A4 + B1 + B2.
RWA is used as a tool for monitoring the relationship between a bank’s investing activities and
its level of capital. All commercial banks regulated by the FDIC are required to hold minimum
capital level (K) as a percentage (α) of RWA:
K = α × (RWA).
As previously described, the Fed’s current RBC regulations, based on the Basel Accords, require
each bank to maintain minimum standards regarding several measures of capital. Table 1 shows
that banks are required to maintain Tier 1 plus Tier 2 as 8% of RWA.10
Because these capital
requirements are measured as percentages of RWA, higher levels of RWA imply that more
capital is necessary to meet the required minimum percentage.
There have been many proposals to revise and update the Fed's RBC regulation since
their implementation in 1991, but few of these proposed changes have been enacted into law.11
However, a revised system of RBC standards has recently been adopted that attempts to combine
important elements of Basel II, Basel III, and the Dodd-Frank Wall Street Reform and Consumer
Protection Act of 2010 (Dodd-Frank Act).12
The current revisions were slated to take effect on
10
As mentioned earlier, banks must also maintain Tier 1 capital as 4% of RWA and 3% of total assets. 11
For a summary of these changes, see “Risk-Based Capital” (2012, pp.53060-53061). 12
These revisions were proposed, amended, and finalized in “Risk-Based Capital” (2008; 2010; 2012).
8
January 1, 2013, and banks will have up to one year to become compliant with the updated
regulations (“Risk-Based Capital” 2012, p.53070).
Under the new requirements, every bank with total assets of $1 billion or more must
calculate its RBC ratio according to three specifications: 1) the existing risk-weighting system, 2)
an "advanced" risk-weighting system calculated by the bank itself based on its own internal
models,13
and 3) a value-at-risk (VaR) measure based on the bank's trading exposure.14
Of these
three measures of RBC, only the general RBC ratio can be calculated using publicly available
data. The advanced RBC ratio is based on proprietary risk models that are specific to each bank,
and the VaR measure of RBC is based on each bank's recent trading expose. Furthermore, even
if the proprietary models for bank risk and trading exposure are currently known, the past data
required to estimate these metrics for previous years of our sample is not available since banks
were not required to record these data over the years of our sample. For these reasons, our
analysis will focus on the general RBC ratio reported by each bank on its end-of-year Call
Report. The formula currently used in calculating the RBC ratio is very similar to the original
formulation used in Avery and Berger (1991) and has changed only slightly over our sample.15
In addition to regulating banks' capital and risk-taking activities, the Fed has now adopted
several new methods of evaluating banks' crisis response processes. One such provision,
mandated by the Dodd-Frank Act, is the requirement that banks with assets of $50 billion or
13
"Advanced internal ratings-based (IRB) systems means a bank holding company’s internal risk rating and
segmentation system; risk parameter quantification system; data management and maintenance system; and control,
oversight, and validation system for credit risk of wholesale and retail exposures" (“Risk-Based Capital” 2012,
Pt.225, Appendix G, p.334) 14
"[T]he final rule requires a bank, each quarter, to compare each of its most recent 250 business days of trading
losses (excluding fees, commissions, reserves, net interest income, and intraday trading) with the corresponding
daily VaR-based measure calibrated to a one-day holding period and at a one-tail, 99.0 percent confidence level"
(“Risk-Based Capital” 2012, p.53069). 15
The similarity between the RBC weighting system in 2001 and 2011 is evident in comparing "Schedule RC-R:
Regulatory Capital" in Federal Financial (2001, pp.29-32) and Federal Financial (2010, pp.50-55).
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more submit to the Fed a "living will" that must "describe the company's strategy for rapid and
orderly resolution under the Bankruptcy Code in the event of material financial distress or failure
of the company."16
The Dodd-Frank Act also mandates the Fed undertake "stress tests" of large
banks to determine their exposure to changing market conditions. The tests are intended to be
forward-looking examinations that include sensitivity analysis of bank capital and
creditworthiness under various conditions given the future capital planning and management
processes of each bank. The first round of stress tests, known as Supervisory Capital
Assessment Program (SCAP), was performed in 2009. The Fed has since introduced a new
stress test, the Comprehensive Capital Analysis and Review (CCAR) which "significantly
expands upon more traditional approaches to assessing capital adequacy" (Board of Governors of
the Federal Reserve 2011, p.3).17
Although living wills and stress tests have become important components of bank capital
regulations, they are omitted from our quantitative analysis for several reasons. First, these
analyses are only applicable for large banks while our study applies to all U.S. commercial
banks.18
Second, these analyses require data that is not available for our time period. Living
wills and CCAR analyses require planning documents created by each firm's board of directors,
and these documentation requirements were not in place prior to the financial crisis of 2008.
Third, the analyses of living wills and capital plans are subjective in nature because Fed officials
must assess the practicality and reasonableness of assumptions inherent in each bank’s planning
process. Fourth, living wills and capital plans are of secondary importance relative to bank
16
These are publicly available on the Federal Reserve. The quotation above is taken from their website.
http://www.federalreserve.gov/bankinforeg/resolution-plans.htm 17
Other stress tests include CAMELS (Asset quality; Management; Earnings; Liquidity; and Sensitivity to market
risk). Cole and White (2012) finds that proxies for CAMELS components are strong predictors of bank failures. 18
We discuss in section 4 the robustness of our results on separate subsamples of large and small banks.
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capital regulation. If capital regulation can effectively maintain bank solvency, then no
emergency capital plan or living will is necessary. It is, therefore, primarily important to
evaluate the effectiveness of the Fed's RBC regulation before concerning ourselves with other
regulatory procedures.19
Following Avery and Berger (1991) we use five measures of bank performance as
dependent variables in our regression analysis. These variables are listed in table 2.20
We
calculate INCOME as the bank’s net income for the year as a percentage of adjusted assets. We
compute NONPERFORM as the value of nonperforming loans and CHARGEOFF as the value of
loan charge-offs during the year, with both variables given as percentages of adjusted assets. We
include FAILURE as a dummy variable that is set to 1 if the bank failed within two years of the
end-of-year Call Report or 0 otherwise. One other performance measure, INCOMESTD,
represents the standard deviation of each bank’s INCOME over the 10 years of our sample.
Because this variable has only one entry for each bank, the regressions using INCOMESTD as
the dependent variable are cross-sectional. Consequently, the number of observations in the
INCOMESTD regressions is much lower than the number of observations in the other regressions
we estimate. For the independent variables in the regressions on INCOMESTD, we take the
averages of the categories of bank assets for each bank over all years of the sample.
Because bank assets at the start of the year should predict performance at the end of the
year, we lag independent variables one year relative to performance variables, as in Avery and
Berger’s study (1991). Data for independent variables (of risk categories, dummies for failing the
19
For example, Acharya et al. (2013) argue that the use of RBC regulations causes banks to hold inadequate capital,
which in turn causes banks to perform poorly in stress testing. The authors find that "…the continued reliance on
regulatory risk weights in stress tests appears to have left financial sectors under-capitalized, especially during the
European sovereign debt crisis, and likely also provided perverse incentives to build up exposures to low risk-weight
assets" (p. 1). 20
Appendix A, table A.1 provides the exact Call Report fields used to define each variable.
11
old and new standards, and time dummies for each year) run from 2001 to 2010, while data for
dependent variables run from 2002 to 2011. The one-year lag structure measures whether the
independent variables predict future bank performance. Like Avery and Berger (1991), we
exclude banks from the NONPERFORM and CHARGEOFF regressions if a bank failed in the
year preceding a measurement date; unlike Avery and Berger,21
we also eliminate banks from the
INCOME regressions if a bank failed in the previous year. We exclude very small banks (those
with less than $10 million in assets in 1989 inflation-adjusted dollars) from the sample as done
by Avery and Berger (1991). Our sample contains a total of 61,591 small-bank and 10,635 large-
bank observations, respectively, for the INCOME and FAILURE regressions, and 61,300 small-
bank and 10,537 large-bank observations, respectively, for the NONPERFORM and
CHARGEOFF regressions. For the INCOMESTD regression, we have 8,034 small-bank
observations and 1,051 large-bank observations.
Table 2 also lists four control variables that will be used in section 4 to test the robustness
of our base-case analysis: REALEST, C&I, CONSUMER, and COMMIT. REALEST is the value
of real estate loans as a percentage of a bank’s adjusted assets (total assets plus loan loss
reserves). C&I refers to commercial and industrial loans, CONSUMER to consumer loans, and
COMMIT to loan commitments. Each of these variables represents a specific class of bank assets
that might significantly affect RWA. For example, REALEST refers to one to four family real
estate loans, which may have carried significant risk during the recent recession and housing bust.
Avery and Berger (1991) include these four variables in their regressions to account for
misassignment of risk weights in the event that the riskiness of these assets was not properly
classified in the RWA categories.
21
For failed banks, Avery and Berger (1991, p.855) estimate income in the year of failure as “the negative of
existing capital at the end of the previous year minus the FDIC’s estimated net outlay for the bank.”
12
Table 2 provides descriptive statistics for the sample including the mean, minimum,
maximum, and standard deviation of each variable. Appendix A shows each category of bank
assets as a percentage of total assets charted by year over the period of our sample. For the full
sample, most of the means and standard deviations reported in table 2 are similar to those in
Avery and Berger (1991), with a few exceptions. The variables CAP and RBC both have
negative minimum values. This is because our sample contains a few banks with negative equity
during the period. The RBC variable has a maximum value over 160, which may seem quite
high considering the maximum for CAP is less than 1. This is a consequence of the structure of
the RBC formula. Since safe assets are assigned low risk weights of 0 percent, a bank with
mostly safe assets may have total RWA that is less than its total equity, causing the RBC ratio of
a few banks (about 0.5 percent of the sample) to be greater, in some cases much greater, than 1.
INCOMESTD is higher in our sample, which reflects the 2008 bust in the banking sector (see
figure A.1). Real estate loans averaged only 8.86% of bank assets in Avery and Berger’s study
but are higher throughout our sample (see figure A.3). This is consistent with the work of
Blaško and Sinkey (2006), which describes how regulatory incentives caused US banks to
increase their real estate exposure through the 1990s.
One variable, MKTRISK, has mean and maximum values that are orders of magnitude
larger in our sample than in Avery and Berger (1991). However, the primary reason for the
increase in MKTRISK is that one extreme outlier bank, Goldman Sachs, reported 2008 off-
balance-sheet assets of more than 100 times the value of the total assets of the bank itself.
(Figure A.4 shows the resulting spike in MKTRISK in 2008.) Excluding this outlier, average
MKTRISK grew from 0.17% to 0.74% over the period, with a mean of 0.37%. This is higher than
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the mean of 0.17% from Avery and Berger (1991) and illustrates increased use of off-balance-
sheet activities over the period.
To summarize, our data set is similar to the sample used by Avery and Berger (1991), and
the differences are mostly attributable to unusual conditions during the recession and financial
crisis of 2007 to 2009. In addition, banks have increased their holdings of real estate loans and
off-balance-sheet activities, partly because of incentives created by the deficiencies in the new
RBC standards described by Blaško and Sinkey (2006), Jablecki (2009), and Friedman (2011).
These factors appear to account for all notable discrepancies between our data set and that of
Avery and Berger (1991).
3. Model
Our econometric analysis is similar to Avery and Berger (1991) but with an added step to
better identify differences between the capital and RBC ratios. Five bank performance
measurements (INCOME, INCOMESTD, NONPERFORM, CHARGEOFF, and FAILURE) are
regressed against the risk and failure variables shown in table 2.22
In the following regression
equations, we use Πit to represent performance variable of bank i in year t. We let Ωt represent
year dummies over the period. Equation 1 shows the regression of the performance variable Πit
on the RBC ratio and dummy variables Ωt for each year of our sample.
(1) Πit = β0 + β1RBCit−1 + Ωt + εit.
22
We use the linear probability model for the failure regressions to follow Avery and Berger (1991) as closely as
possible. Because the linear probability model is inherently heteroskedastic, we employ robust standard errors as in
Wooldridge (2010, pp. 563-564).
14
Equation 2 replaces RBCit with the banks’ capital ratios (CAPit) as an independent variable.
(2) Πit = β0 + β1CAPit−1 + Ωt + εit.
The coefficient estimates from our analysis of equations 1 and 2 can tell us whether CAPit
and RBCit are individually related to our measures of bank performance. Avery and Berger
(1991, p.857) predicts that higher levels of capital and RBC should lead to better bank
performance, demonstrated by higher income and lower standard deviation of income, fewer
nonperforming loans, fewer charge-offs, and fewer bank failures. While it is clear that capital
should be negatively related to nonperforming loans, loan charge-offs, and bank failures, the
relationships between capital and income and between capital and the standard deviation of
income are not as obvious. It may be the case that banks with more capital are safer, which
suggests lower net income and lower standard deviation of income. Conversely, the relationship
between capital and income or between capital and the standard deviation of income may be
positive if banks are committing regulatory arbitrage. Banks may have an incentive to buy mis-
rated assets such as MBS that will effectively increase their net income and standard deviation of
income while simultaneously increasing their capital and RBC ratios. If this is the case, then we
may find that higher capital and RBC ratios are related to higher income and higher standard
deviation of income.
The second step of the analysis is to directly compare capital and RBC ratios as
indicators of bank performance. Assuming that both variables are individually significant
indicators of performance, we want to know which of the two is the better indicator. We begin
by estimating equation 3, which includes both CAPit and RBCit:
15
(3) Πit = β0 + β1RBCit−1 + β2CAPit−1 + Ωt + εit.
Regression equation 3 reveals the effects of CAPit and RBCit on bank performance when
included in the same regression. However, equation 3 cannot be used to accurately test for
significant differences between coefficient estimate β1 of the RBC ratio and the coefficient
estimate β2 of the capital ratio. Testing the difference in the coefficient estimates for CAPit and
RBCit produced by equations 3 requires accounting for the covariation between CAPit and RBCit
(as in Wooldridge 2003, p.141). Because equations 3 does not account for covariance between
CAPit and RBCit, it does not statistically measure the difference between these variables. This
problem can be corrected in one of two ways. One option is to measure the covariance between
variables and include it in the analysis. However, a simpler way is to follow Wooldridge’s (2003,
pp.141–142) method. We begin by defining a new coefficient, θ1 = β1 − β2, where β1 and β2 are
from equations 3, and we create a new variable, TOTCAPit, that is the sum of CAPit and RBCit as
seen in equation 4.
(4) TOTCAPit = CAPit + RBCit.
Because our purpose here is to establish whether or not the RBC ratio provides new and useful
information, we will include TOTCAPit and θ1 in the regressions with RBCit:23
(5) Πit = β0 + θ1RBCit−1 + β2TOTCAPit−1 + Ωt + εit.
23
We could, alternatively, include TOTCAPit and CAPit (but not RBCit) in equations 8 and 9. The resulting
coefficient estimate θ1 would be the same but with the opposite sign.
16
As previously described, this method is more effective than including both CAPit and RBCit,
because it accounts for the covariance between variables when statistically assessing whether
there is a difference between β1 and β2 in equation 3.24
If the estimated coefficient θ1 of RBCit in regression 5 is significant, this indicates that
CAPit and RBCit are significantly different from each other. In this case, the sign of the RBCit
coefficient indicates whether RBCit is significantly better or significantly worse than CAPit as a
predictor of performance. As previously discussed, higher levels of capital and RBC should lead
to better bank performance. Thus, if the coefficient of RBCit is significant in predicting better
performance (positive for income and negative for the other dependent variables), then the RBC
ratio is a significantly better predictor of bank performance than the capital ratio. If the
coefficient of RBCit is significant in indicating worse performance (negative for income and
positive for the other dependent variables), then the capital ratio is a better indicator of bank
performance than the RBC ratio.
4. Results
This section presents the results of our regressions comparing the actual capital and RBC
ratios of commercial banks as predictors of bank performance. Tables 3 through 6 give the
coefficients estimated in equations 1, 2, 3, and 5, respectively. Heteroskedastic robust standard
errors are reported in all tables.
Tables 3 and 4 display results for RBC and CAP separately. Both tables show positive
coefficients of CAP and RBC for dependent variables INCOME and INCOMESTD. The positive
24
For a more detailed explanation of the method we employ here, please see Wooldridge (2003, p.141).
17
coefficients for CAP are statistically significant at the 5% threshold and below. The findings
suggest that banks that hold more capital tend to have more income and that the income level
varies considerably. The positive coefficients for RBC are statistically insignificant. This result
is consistent with evidence from Friedman (2011) that banks committed regulatory arbitrage by
buying mis-rated assets such as MBS in order to increase both capital and income.
Looking at the dependent variables CHARGEOFF, NONPERFORM, and FAILURE,
coefficients of CAP and RBC are negative in tables 3 and 4. The CAP coefficients are
statistically significant at the 1% level, while the RBC coefficients are statistically insignificant.
The evidence suggests that banks that hold more capital tend to have fewer charge-offs, fewer
nonperforming loans, and a lower likelihood of failure. Since none of the coefficient estimates
for RBC are significant, we cannot reject the null hypothesis that the RBC ratio is not a
significant predictor of bank performance.
The results show that for every variable of bank performance, CAP is statistically
significant with the expected sign. By contrast, the coefficient estimate of RBC is not significant
in any case. From this evidence alone, we can conclude that the capital ratio is a better predictor
of bank performance than the RBC ratio. However, we would like to know if CAP is a
significantly better predictor or if the difference is only marginal. We would also like to test
whether a combination of CAP and RBC in our regression analysis improves the accuracy of our
estimation process. To test these hypotheses, we compare CAP and RBC directly in equation 3.
Table 5 provides results of equation 3 with RBC and CAP estimated jointly. The results
are noticeably similar to those of tables 3 and 4, where RBC and CAP are estimated separately:
Coefficients for CAP maintain similar statistical significance levels and the same signs as in table
4, with positive coefficients for INCOME and INCOMESTD and negative coefficients for
18
CHARGEOFF, NONPERFORM, and FAILURE. As in table 3, coefficients for RBC are
statistically insignificant for INCOME, INCOMESTD, NONPERFORM, and CHARGEOFF. The
RBC coefficient for FAILURE is positive and statistically significant at 5%. However, the size of
the coefficient is only 0.0003, which is two orders of magnitude lower than the coefficient for
CAP. This suggests that RBC is not an important or economically significant predictor of bank
failure.
Comparing tables 3, 4, and 5, we see that CAP is always statistically significant, usually
at the 1% level, while RBC is almost never statistically significant. This holds true even when
both CAP and RBC are included in the same regression. Furthermore, RBC is more statistically
significant when CAP is included as a regressor. Contrary to the hypothesis that optimal capital
regulation will be some combination of the capital and RBC ratios, our data indicates that use of
the RBC ratio will not improve the effectiveness of bank capital regulation. In addition, the R-
Squared statistics in table 5 are exactly the same as those in table 4, again indicating that
inclusion of the RBC ratio does not improve the accuracy of the estimation process. Thus, the
combination of capital and RBC ratios is no better than the use of the capital ratio alone in
predicting bank performance.
Table 6 shows the results of equation 5 comparing RBC with TOTCAP as indicators of
bank performance. The coefficients for RBC have a statistically significant negative correlation
at the 1% level with INCOME and INCOMESTD, after controlling for TOTCAP. For the other
dependent variables—NONPERFORM, CHARGEOFF, and FAILURE—RBC has positive
coefficients with statistical significance at the 1% threshold for NONPERFORM and FAILURE
and no statistical significance for CHARGEOFF, after controlling for TOTCAP.25
The results
25
The P-value for CHARGEOFF is 0.108, which is very close to being significant at the 10% level.
19
suggest that the standard capital ratio is more reliable than the RBC ratio as an indicator of bank
performance because of the statistically significant negative coefficient on INCOME and the
statistically significant positive coefficients on NONPERFORM and FAILURE. Our results are
consistent with those of Estrella et al. (2000), who found that RBC ratios do not consistently
outperform simple standard capital ratios as measures of bank performance.
Equations 3 and 5 each include multiple variables that are based on measures of bank
capital. They are, therefore, likely to be highly correlated. We perform some simple tests to
assess the risk of multicollinearity that might cause our coefficient estimates to be less precise.
Excluding the RBC coefficient for FAILURE, standard errors in table 5 for RBC and CAP
coefficients do not appear significantly different from standard errors in tables 3 and 4 for RBC
and CAP coefficients, indicating that multicollinearity is not likely a significant problem. To test
more formally, we conduct a variance inflation factor (VIF) analysis based on equation 3 to test
for multicollinearity between RBC and the other variables, including CAP. The VIF statistic is
1.28, indicating that RBC is over 94% independent of the other variables. Because
multicollinearity is not considered a significant problem until VIF statistics approach the range
of 5 to 10, we argue that multicollinearity is not a significant issue.
To check the robustness of our results, we make several alterations to our base-case
analysis. First, to account for any misweighting of asset categories, we include the specific asset
categories of real estate loans (REALEST), consumer loans (CONSUMER), commercial and
industrial loans (C&I), and loan commitments (COMMIT) as additional determinants in
equations 1, 2, 3 and 5. For example, the addition of these determinants to equation 1 yields
equation 6.
20
(6) Πit = β0 + β1RBCit−1 + β2COUNTERit−1
+ β3MKTRISKit−1 + β4REALESTit−1 + β5C&Iit−1
+ β6CONSUMERit−1 + β7COMMITit−1 + Ωt + εit.
Results of the regressions with these control variables are presented in Appendix B tables B.1
through B.4. The results are consistent with results for equations 1, 2, 3, and 5. The magnitudes of the
coefficients for TOTCAP, CAP, and RBC fluctuate marginally, but their signs and statistical significance,
with the exception of statistical significance for the coefficient of TOTCAP on CHARGEOFF, remain
consistent regardless of whether extra controls for COUNTER, MKTRISK, REALEST, C&I, CONSUMER,
and COMMIT are included or not.26
Second, there is a danger that the significance of our coefficients is related to the
structure of our variables and that using the leverage ratios (assets over equity) rather than the
capital ratio (equity over assets) might lead to different results.27
To test this possibility, we
invert the capital and RBC ratios with the expectation that coefficient signs and statistical
significance resembling tables 3 through 6 will result, but with opposite signs. Indeed, similar to
Avery and Berger (1991), we find this to be the case. In essence, we confirm that the differences
between the capital and RBC ratios result from the use of the actual RBC ratios reported in
banks’ Call Reports instead of the structure of the capital or RBC formulas.
Third, we examine whether our results are ascribed to bank size. Following Avery and
Berger (1991), we divide our sample into small bank and large bank subsamples because bank
risk and performance may differ substantially according to size. Our small-bank subsample
26
We repeat the VIF test on our regression equation including CAP, RBC, and control variables. The low VIF score
again confirms that multicollinearity is not a problem, 27
Due to the large quantity of data created by these many alternative tests, results of the following analyses are
described in words, but numerical results are not included. Data tables are available from the authors upon request.
21
includes all banks with total adjusted assets (gross assets plus loan loss reserves) of less than
$250 million, measured in 1989 dollars, during the entire sample period. Our large-bank
subsample, meanwhile, consists of banks with real adjusted assets of more than $250 million in
at least one year. The significance of our coefficient estimates for each subsample is nearly
identical to our base case, indicating that our results are robust to bank size.
Fourth, we test robustness by using a Tier 1 capital ratio in place of the total capital ratio,
CAP. Current Fed regulations include capital requirements both as a percentage of RWA and of
total assets. Unlike table 5, however, the current requirement is measured by Tier 1 capital as a
percentage of total assets. To replicate the results of table 5 using Tier 1 capital rather than total
capital, we replace our variable CAP, representing total capital, with the variable T1CAP,
representing Tier 1 capital. We find that results using T1CAP are similar to our base-case results.
The Tier 1 capital ratio is a significantly better predictor of bank performance than the RBC ratio.
Additionally, using the Tier 1 capital ratio and the RBC ratio together does not improve the
accuracy of estimation compared to the Tier 1 capital ratio alone. This casts some doubt on the
argument made by Estrella et al. (2000, p.33) that optimal capital regulation should include both
a RBC requirement and a Tier 1 capital requirement.
5. Conclusion
The RBC ratio is a fundamental component of US commercial bank regulation. However,
recent evidence suggests that this new metric may cause more harm than good. As discussed
earlier, several studies show that banks are able to circumvent the RBC risk-weighting system
and that RBC standards encourage banks to buy risky assets, such as MBS. Not only do RBC
standards increase the individual bank’s level of risk, but they also increase systemic risk in the
22
banking system by reducing diversification and increasing fragility. No individual or group can
expect to know, much less quantify, the complete set of factors affecting risk in the banking
system. The RBC system has the general defect of presupposing that a centralized group of
regulators is able to predict ex ante risk when, in fact, many risks can only be identified ex post.
Despite the dangers endemic to RBC regulation, some economists argue that the RBC
ratio is a superior metric for predicting bank performance and should, therefore, continue to be
used in banking regulation. Avery and Berger (1991) is among the first studies to empirically test
the effectiveness of RBC regulation. Although their study does expose some potential
shortcomings of the new methodology, the authors conclude that the new RBC standards
“constitute an improvement over the current flat-rate deposit insurance scheme” (1991, 872).
Their work is widely cited as proof of the effectiveness of RBC standards.
This study reevaluates the hypothesis that the RBC ratio is a better predictor of bank
performance than the capital ratio of equity over assets. We base our methods on Avery and
Berger (1991), but we attempt to improve on their analysis by using the actual RBC ratios
reported by commercial banks in their Call Reports and by comparing the capital and RBC ratios
directly in the same regression. In contrast with Avery and Berger (1991), we find that the RBC
ratio is significantly less accurate than the capital ratio as a predictor of bank performance.
Regressing bank performance on the capital and RBC ratios together, we find that capital is a
statistically significant indicator of performance even after accounting for RBC. The RBC ratio,
on the other hand, is almost never statistically significant regardless of whether capital is
included in the regression. When we regressed bank performance on the RBC ratio and the sum
of capital and RBC ratios, we find the RBC ratio to have statistically significant negative
coefficients for income and for the standard deviation of income, and statistically significant
23
positive coefficients for nonperforming loans and bank failures. This indicates that the capital
ratio is a significantly better indicator of bank performance than the RBC ratio.
Our results have important implications for US banking regulation. The Federal Reserve
has adopted the RBC ratio as its primary indicator of bank risk and intends to increase its
reliance on the RBC system through further implementation of the Basel Accords. However, the
evidence from this study suggests that the Fed should move in exactly the opposite direction. The
risk-based weighting system is inherently flawed and easily exploitable. Other studies have
shown that the capital ratio is less subject than the RBC ratio to the danger of regulatory
arbitrage, which creates harm to individual banks and the entire banking system. This paper
shows that the standard capital ratio is a superior metric for evaluating bank risk.
Although some economists recommend that regulators employ a combination of RBC
and capital ratios, as the Fed does, we find that using capital and RBC ratios together does not
improve the accuracy of our estimations of bank performance. Whether used alone or in
conjunction with the capital ratio, the RBC ratio is almost never a significant predictor of
performance. We therefore conclude that RBC regulation has the potential to create significant
harm with little or no added benefit. The Fed should abandon its use of the RBC ratio and return
to the simple and effective capital ratio as a measure of bank risk.
24
Table 1. Summary of the Risk-Based Capital Standards
Risk categories
– Category A1 (0% weight)
Cash, Federal Reserve Bank balance
Securities of the US Treasury, OECD governments, and some US agencies
– Category A2 (20% weight)
Cash items in the process of collection
US and OECD interbank deposits and guaranteed claims
Some non-OECD bank and government deposits and securities
General obligation municipal bonds
Some mortgage-backed securities
Claims collateralized by the US Treasury and some other government securities
– Category A3 (50% weight)
Loans fully secured by first liens on one to four family residential properties
Other municipal bonds
– Category A4 (100% weight)
All other on-balance sheet assets not listed above, including
loans to private entities and individuals, some claims on non-OECD governments and banks, real
assets and investment in subsidiaries
– Category B1 (off-balance sheet counterparty guarantees; weights in parentheses)
Direct-credit-substitute standby letters of credit (mainly 100%)
Performance-related standby letters of credit (mainly 50%)
Unused portion of loan commitments with original maturity of more than 1 year (mainly 50%); other
loan commitments (0%)
Commercial letters of credit (20%)
Bankers’ acceptances conveyed (20%)
– Category B2 (off-balance sheet market risk contracts; weights in parentheses)
Interest rate swaps, forward commitments to purchase foreign exchange and other items (between 0 and
5% of the notional value, plus the market-to-market value of the contract, capped at 50%)
Capital requirements
– Tier 1
Common equity, some preferred stock, minority interest in consolidated subsidiaries less goodwill
Tier 1 capital must be at least 4% of risk-weighted asset
– Tier 2
Loan loss reserve (limited to 1.25% of risk-weighted asset), subordinated debt (limited to 50% of Tier
1), and other preferred and convertible stock
Tier 2 capital cannot be larger than Tier 1 capital
Tier 1 plus Tier 2 capital must be at least 8% of risk-weighted assets
– Leverage requirement
Tier 1 capital must be at least 3% of total on-balance sheet assets
Source: Avery and Berger (1991, p.853).
25
Table 2: Descriptive Statistics
Mean SD Min Max
RBC 0.1825 0.6763 -0.0236 160.8951
CAP 0.1097 0.0667 -0.0150 0.9999
INCOME 0.0080 0.0257 -1.3561 3.6171
INCOMESTD 0.0096 0.0802 0.0000 7.2689
NONPERFORM 0.0191 0.0231 0.0000 0.4143
CHARGEOFF 0.0038 0.0089 0.0000 0.6541
FAILURE 0.0054 0.0732 0.0000 1.0000
COUNTER 0.0107 0.0143 0.0000 0.4536
MKTRISK 0.0051 0.4564 0.0000 121.7247
RWA 0.6329 0.1949 0.0000 12.8077
REALEST 0.0888 0.0633 0.0000 0.4810
C&I 0.0212 0.0549 0.0000 0.9555
CONSUMER 0.0527 0.0692 0.0000 1.0097
COMMIT 0.0072 0.0118 0.0000 0.4536
Source: Federal Reserve Reports of Condition and Income.
26
Table 3. Regressions Testing Risk-Based Capital Ratios
INCOME INCOMESTD NONPERFORM CHARGEOFF FAILURE
RBC 0.0029 0.0126 -0.0011 -0.0003 -0.0009
(0.0024) (0.0118) (0.0007) (0.0002) (0.0007)
2003 -0.0000 -0.0015*** -0.0001 0.0001
(0.0003) (0.0002) (0.0001) (0.0003)
2004 0.0004 -0.0032*** -0.0007*** -0.0003
(0.0003) (0.0002) (0.0001) (0.0002)
2005 0.0007** -0.0034*** -0.0011*** -0.0003
(0.0003) (0.0002) (0.0001) (0.0002)
2006 0.0006 -0.0022*** -0.0012*** -0.0001
(0.0004) (0.0002) (0.0001) (0.0002)
2007 -0.0009 0.0022*** -0.0007*** 0.0024***
(0.0006) (0.0003) (0.0001) (0.0006)
2008 -0.0074*** 0.0093*** 0.0012*** 0.0164***
(0.0003) (0.0003) (0.0001) (0.0015)
2009 -0.0106*** 0.0132*** 0.0042*** 0.0193***
(0.0003) (0.0004) (0.0002) (0.0017)
2010 -0.0078*** 0.0119*** 0.0038*** 0.0126***
(0.0003) (0.0004) (0.0002) (0.0014)
2011 -0.0048*** 0.0078*** 0.0026*** 0.0035***
(0.0003) (0.0004) (0.0002) (0.0008)
Constant 0.0102*** 0.0071*** 0.0156*** 0.0030*** 0.0004*
(0.0004) (0.0019) (0.0002) (0.0001) (0.0002)
R-Squared 0.03 0.01 0.08 0.05 0.01
Observations 72,226 9,085 71,837 71,837 72,226
Note: Robust standard errors are in parentheses.
* significant at 10%; ** significant at 5%; *** significant at 1%
27
Table 4. Regressions Testing Capital Ratios
INCOME INCOMESTD NONPERFORM CHARGEOFF FAILURE
CAP 0.0598*** 0.1825** -0.0220*** -0.0028*** -0.0375***
(0.0111) (0.0778) (0.0011) (0.0010) (0.0030)
2003 -0.0002 -0.0014*** -0.0001 0.0002
(0.0003) (0.0002) (0.0001) (0.0003)
2004 0.0002 -0.0032*** -0.0007*** -0.0001
(0.0003) (0.0002) (0.0001) (0.0002)
2005 0.0005 -0.0033*** -0.0011*** -0.0001
(0.0003) (0.0002) (0.0001) (0.0002)
2006 0.0002 -0.0021*** -0.0012*** 0.0001
(0.0004) (0.0002) (0.0001) (0.0002)
2007 -0.0015*** 0.0025*** -0.0007*** 0.0028***
(0.0005) (0.0003) (0.0001) (0.0006)
2008 -0.0082*** 0.0096*** 0.0013*** 0.0170***
(0.0003) (0.0003) (0.0001) (0.0015)
2009 -0.0110*** 0.0134*** 0.0043*** 0.0196***
(0.0003) (0.0004) (0.0002) (0.0017)
2010 -0.0080*** 0.0120*** 0.0038*** 0.0128***
(0.0003) (0.0004) (0.0002) (0.0014)
2011 -0.0049*** 0.0078*** 0.0026*** 0.0036***
(0.0003) (0.0004) (0.0002) (0.0008)
Constant 0.0045*** -0.0113 0.0177*** 0.0032*** 0.0041***
(0.0011) (0.0081) (0.0002) (0.0001) (0.0004)
R-Squared 0.05 0.03 0.09 0.05 0.01
Observations 72,226 9,085 71,837 71,837 72,226
Note: Robust standard errors are in parentheses.
* significant at 10%; ** significant at 5%; *** significant at 1%
28
Table 5. Regressions Testing Risk-Based Capital and Capital Ratios
INCOME INCOMESTD NONPERFORM CHARGEOFF FAILURE
RBC 0.0011 0.0034 -0.0004 -0.0002 0.0003**
(0.0013) (0.0060) (0.0003) (0.0002) (0.0001)
CAP 0.0561*** 0.1703*** -0.0207*** -0.0022* -0.0385***
(0.0109) (0.0659) (0.0014) (0.0011) (0.0032)
2003 -0.0002 -0.0014*** -0.0001 0.0002
(0.0003) (0.0002) (0.0001) (0.0003)
2004 0.0002 -0.0032*** -0.0007*** -0.0001
(0.0003) (0.0002) (0.0001) (0.0002)
2005 0.0005 -0.0033*** -0.0011*** -0.0001
(0.0003) (0.0002) (0.0001) (0.0002)
2006 0.0002 -0.0021*** -0.0012*** 0.0001
(0.0004) (0.0002) (0.0001) (0.0002)
2007 -0.0015*** 0.0025*** -0.0007*** 0.0028***
(0.0005) (0.0003) (0.0001) (0.0006)
2008 -0.0082*** 0.0096*** 0.0013*** 0.0170***
(0.0003) (0.0003) (0.0001) (0.0015)
2009 -0.0110*** 0.0134*** 0.0043*** 0.0196***
(0.0003) (0.0004) (0.0002) (0.0017)
2010 -0.0080*** 0.0119*** 0.0038*** 0.0128***
(0.0003) (0.0004) (0.0002) (0.0014)
2011 -0.0049*** 0.0078*** 0.0026*** 0.0036***
(0.0003) (0.0004) (0.0002) (0.0008)
Constant 0.0047*** -0.0105 0.0176*** 0.0032*** 0.0042***
(0.0011) (0.0073) (0.0002) (0.0001) (0.0004)
R-Squared 0.05 0.03 0.09 0.05 0.01
Observations 72,226 9,085 71,837 71,837 72,226
Note: Robust standard errors are in parentheses.
* significant at 10%; ** significant at 5%; *** significant at 1%
29
Table 6. Regressions Evaluating Risk-Based Capital Ratios
INCOME INCOMESTD NONPERFORM CHARGEOFF FAILURE
RBC -0.0550*** -0.1669*** 0.0203*** 0.0020 0.0388***
(0.0112) (0.0635) (0.0016) (0.0012) (0.0033)
TOTCAP 0.0561*** 0.1703*** -0.0207*** -0.0022* -0.0385***
(0.0109) (0.0659) (0.0014) (0.0011) (0.0032)
2003 -0.0002 -0.0014*** -0.0001 0.0002
(0.0003) (0.0002) (0.0001) (0.0003)
2004 0.0002 -0.0032*** -0.0007*** -0.0001
(0.0003) (0.0002) (0.0001) (0.0002)
2005 0.0005 -0.0033*** -0.0011*** -0.0001
(0.0003) (0.0002) (0.0001) (0.0002)
2006 0.0002 -0.0021*** -0.0012*** 0.0001
(0.0004) (0.0002) (0.0001) (0.0002)
2007 -0.0015*** 0.0025*** -0.0007*** 0.0028***
(0.0005) (0.0003) (0.0001) (0.0006)
2008 -0.0082*** 0.0096*** 0.0013*** 0.0170***
(0.0003) (0.0003) (0.0001) (0.0015)
2009 -0.0110*** 0.0134*** 0.0043*** 0.0196***
(0.0003) (0.0004) (0.0002) (0.0017)
2010 -0.0080*** 0.0119*** 0.0038*** 0.0128***
(0.0003) (0.0004) (0.0002) (0.0014)
2011 -0.0049*** 0.0078*** 0.0026*** 0.0036***
(0.0003) (0.0004) (0.0002) (0.0008)
Constant 0.0047*** -0.0105 0.0176*** 0.0032*** 0.0042***
(0.0011) (0.0073) (0.0002) (0.0001) (0.0004)
R-Squared 0.05 0.03 0.09 0.05 0.01
Observations 72,226 9,085 71,837 71,837 72,226
Note: Robust standard errors are in parentheses.
* significant at 10%; ** significant at 5%; *** significant at 1%
30
Appendix A. Summary Statistics
Table A.1. Variable Definitionsa
Capital Variables
CAP Total equity (rcon3210) divided by total assets (rcon2170)
RBC Total risk-based capital (rcon3792) divided by total risk-based assets (rcona223)
Performance Variablesb
INCOME Net income (raid4340)
INCOMESTD Sample standard deviation of INCOME for each bank
NONPERFORM Sum of all 30-day and 90-day past due loans and nonaccrual loans and leases
(rcon2759 + rcon2769 + rcon3492 + rcon3493 + rcon3494 + rcon3495 + rcon5398
+ rcon5399 + rcon5400 + rcon5401 + rcon5402 + rcon5403 + rcon3499 + rcon3500
+ rcon3501 + rcon3502 + rcon3503 + rcon3504 + rconb834 + rconb835 + rconb836
+ rcon1606 + rcon1607 + rcon1608 + rconb575 + rconb576 + rconb577 + rconb578
+ rconb579 + rconb580 + rcon5389 + rcon5390 + rcon5391 + rcon5459 + rcon5460
+ rcon5461 + rcon1226 + rcon1227 + rcon1228 + rcon3505 + rcon3506 + rcon3507)
CHARGEOFF Loan charge-offs (riad4635)
FAILUREc Dummy; equals one if the bank fails within 2 years
Control Variablesb
REALEST Sum of all 1-4 family residential real estate (rcon1797 + rcon5367 + rcon5368)
C&I Sum of commercial and industrial loans (rcon1763 + rcon1764)
CONSUMER Sum of all consumer loans (rconb538 + rconb539 + rcon2011)
COMMIT Unused loan commitments on 1-4 family residential real estate (rcon3814) a This table lists Call Report fields as of 2001. Some Call Report field names are changed in later years.
b All performance and control variables are calculated as percentages of adjusted assets which equals total
assets (rcon2170) plus loan loss reserves (rcon3123). c A list of failed banks is available from the FDIC at
http://www.fdic.gov/bank/individual/failed/banklist.html
31
Figure A.1. Income as a percentage of adjusted assets.
0.0%
0.2%
0.4%
0.6%
0.8%
1.0%
1.2%
1.4%
200
1
200
2
200
3
200
4
200
5
200
6
200
7
200
8
200
9
201
0
201
1
INCOME
32
Figure A.2. Nonperforming loans and loan charge-offs as percentages of adjusted assets.
0.0%
0.5%
1.0%
1.5%
2.0%
2.5%
3.0%
3.5%
200
1
200
2
200
3
200
4
200
5
200
6
200
7
200
8
200
9
201
0
201
1
NONPERFORM
CHARGEOFF
33
Figure A.3. Real estate loans, commercial and industrial loans, consumer loans, and loan commitments as
percentages of adjusted assets.
0.0%
2.0%
4.0%
6.0%
8.0%
10.0%
200
1
200
2
200
3
200
4
200
5
200
6
200
7
200
8
200
9
201
0
201
1
REALEST
C&I
CONSUMER
COMMIT
34
Figure A.4. Assets representing counterparty risk and market risk as percentages of adjusted assets.
0.0%
0.5%
1.0%
1.5%
2.0%
2.5%
200
1
200
2
200
3
200
4
200
5
200
6
200
7
200
8
200
9
201
0
201
1
COUNTER
MKTRISK
35
Appendix B. Regression Results
Table B.1: Regressions Testing Risk-Based Capital Ratios
INCOME INCOMESTD NONPERFORM CHARGEOFF FAILURE
RBC 0.0029 0.0121 -0.0009 -0.0002 -0.0010
(0.0024) (0.0115) (0.0006) (0.0001) (0.0008)
COUNTER 0.0053 -0.1556** 0.0074 -0.0169*** -0.0913**
(0.0112) (0.0704) (0.0098) (0.0039) (0.0407)
MKTRISK 0.0003*** 0.0003 -0.0002*** -0.0000 -0.0002***
(0.0001) (0.0002) (0.0000) (0.0000) (0.0000)
REALEST -0.0066*** -0.0629*** 0.0326*** -0.0085*** -0.0274***
(0.0020) (0.0160) (0.0014) (0.0005) (0.0041)
C&I 0.0065*** 0.0014 0.0061*** 0.0160*** 0.0193***
(0.0021) (0.0089) (0.0015) (0.0009) (0.0065)
CONSUMER 0.0207*** -0.0122 0.0177*** 0.0355*** -0.0313***
(0.0029) (0.0094) (0.0017) (0.0025) (0.0022)
COMMIT -0.0940*** 0.2249*** -0.1256*** 0.0342*** 0.1093**
(0.0118) (0.0673) (0.0120) (0.0046) (0.0485)
2003 0.0002 -0.0012*** 0.0001 -0.0001
(0.0003) (0.0002) (0.0001) (0.0003)
2004 0.0008*** -0.0026*** -0.0003*** -0.0008***
(0.0003) (0.0002) (0.0001) (0.0002)
2005 0.0012*** -0.0027*** -0.0006*** -0.0010***
(0.0003) (0.0002) (0.0001) (0.0002)
2006 0.0011*** -0.0014*** -0.0007*** -0.0010***
(0.0004) (0.0002) (0.0001) (0.0003)
2007 -0.0002 0.0032*** -0.0001 0.0014**
(0.0006) (0.0003) (0.0001) (0.0006)
2008 -0.0067*** 0.0102*** 0.0019*** 0.0153***
(0.0003) (0.0003) (0.0001) (0.0015)
2009 -0.0099*** 0.0140*** 0.0050*** 0.0181***
(0.0003) (0.0004) (0.0002) (0.0016)
2010 -0.0071*** 0.0126*** 0.0047*** 0.0113***
(0.0003) (0.0004) (0.0002) (0.0014)
2011 -0.0041*** 0.0087*** 0.0036*** 0.0021***
(0.0003) (0.0004) (0.0002) (0.0008)
Constant 0.0098*** 0.0133*** 0.0118*** 0.0009*** 0.0051***
(0.0006) (0.0028) (0.0003) (0.0002) (0.0005)
R-Squared 0.04 0.01 0.10 0.14 0.01
Observations 72,226 9,085 71,837 71,837 72,226
Note: Robust standard errors are in parentheses. * significant at 10%; ** significant at 5%; *** significant at 1%
36
Table B.2: Regressions Testing Capital Ratios
INCOME INCOMESTD NONPERFORM CHARGEOFF FAILURE
CAP 0.0608*** 0.1806** -0.0187*** -0.0017* -0.0415***
(0.0111) (0.0779) (0.0011) (0.0009) (0.0032)
COUNTER 0.0127 -0.1212** 0.0052 -0.0170*** -0.0981**
(0.0098) (0.0592) (0.0098) (0.0039) (0.0407)
MKTRISK 0.0003*** 0.0006*** -0.0002*** -0.0000 -0.0002***
(0.0001) (0.0002) (0.0000) (0.0000) (0.0000)
REALEST 0.0020** -0.0274*** 0.0300*** -0.0087*** -0.0337***
(0.0010) (0.0034) (0.0014) (0.0005) (0.0042)
C&I 0.0143*** 0.0310** 0.0037** 0.0158*** 0.0135**
(0.0021) (0.0129) (0.0016) (0.0009) (0.0065)
CONSUMER 0.0217*** -0.0044 0.0174*** 0.0355*** -0.0323***
(0.0028) (0.0070) (0.0017) (0.0025) (0.0023)
COMMIT -0.1045*** 0.1658*** -0.1224*** 0.0344*** 0.1175**
(0.0108) (0.0477) (0.0120) (0.0046) (0.0486)
2003 0.0000 -0.0012*** 0.0001 -0.0001
(0.0003) (0.0002) (0.0001) (0.0003)
2004 0.0006** -0.0026*** -0.0003*** -0.0007***
(0.0003) (0.0002) (0.0001) (0.0002)
2005 0.0010*** -0.0026*** -0.0006*** -0.0008***
(0.0003) (0.0002) (0.0001) (0.0002)
2006 0.0008** -0.0013*** -0.0007*** -0.0007***
(0.0004) (0.0002) (0.0001) (0.0003)
2007 -0.0009* 0.0034*** -0.0001 0.0018***
(0.0005) (0.0003) (0.0001) (0.0006)
2008 -0.0076*** 0.0105*** 0.0019*** 0.0158***
(0.0003) (0.0003) (0.0001) (0.0015)
2009 -0.0104*** 0.0142*** 0.0051*** 0.0185***
(0.0003) (0.0004) (0.0002) (0.0016)
2010 -0.0073*** 0.0127*** 0.0047*** 0.0115***
(0.0003) (0.0004) (0.0002) (0.0014)
2011 -0.0042*** 0.0087*** 0.0036*** 0.0021***
(0.0003) (0.0004) (0.0002) (0.0008)
Constant 0.0029** -0.0090 0.0139*** 0.0010*** 0.0100***
(0.0012) (0.0077) (0.0003) (0.0002) (0.0007)
R-Squared 0.05 0.03 0.10 0.14 0.01
Observations 72,226 9,085 71,837 71,837 72,226
Note: Robust standard errors are in parentheses.
* significant at 10%; ** significant at 5%; *** significant at 1%
Table B.3: Regressions Testing Risk-Based Capital and Capital Ratios
INCOME INCOMESTD NONPERFORM CHARGEOFF FAILURE
RBC 0.0011 0.0097 -0.0004 -0.0001 0.0003**
(0.0013) (0.0112) (0.0003) (0.0001) (0.0001)
CAP 0.0571*** 0.0418*** -0.0173*** -0.0013 -0.0423***
(0.0110) (0.0158) (0.0014) (0.0010) (0.0033)
COUNTER 0.0141 -0.1463** 0.0047 -0.0171*** -0.0978**
(0.0098) (0.0704) (0.0097) (0.0039) (0.0407)
MKTRISK 0.0003*** 0.0003* -0.0002*** -0.0000 -0.0002***
(0.0001) (0.0002) (0.0000) (0.0000) (0.0000)
REALEST 0.0019* -0.0480*** 0.0300*** -0.0087*** -0.0338***
(0.0010) (0.0182) (0.0014) (0.0005) (0.0042)
C&I 0.0143*** 0.0135 0.0037** 0.0158*** 0.0135**
(0.0021) (0.0090) (0.0015) (0.0009) (0.0065)
CONSUMER 0.0219*** -0.0060 0.0174*** 0.0355*** -0.0322***
(0.0028) (0.0100) (0.0017) (0.0025) (0.0023)
COMMIT -0.1049*** 0.1822** -0.1222*** 0.0345*** 0.1174**
(0.0108) (0.0723) (0.0120) (0.0046) (0.0486)
2003 0.0001 -0.0012*** 0.0001 -0.0001
(0.0003) (0.0002) (0.0001) (0.0003)
2004 0.0006** -0.0026*** -0.0003*** -0.0007***
(0.0003) (0.0002) (0.0001) (0.0002)
2005 0.0010*** -0.0027*** -0.0006*** -0.0008***
(0.0003) (0.0002) (0.0001) (0.0002)
2006 0.0008** -0.0013*** -0.0007*** -0.0007***
(0.0004) (0.0002) (0.0001) (0.0003)
2007 -0.0008* 0.0034*** -0.0001 0.0018***
(0.0005) (0.0003) (0.0001) (0.0006)
2008 -0.0075*** 0.0105*** 0.0019*** 0.0158***
(0.0003) (0.0003) (0.0001) (0.0015)
2009 -0.0104*** 0.0142*** 0.0051*** 0.0185***
(0.0003) (0.0004) (0.0002) (0.0016)
2010 -0.0073*** 0.0127*** 0.0047*** 0.0115***
(0.0003) (0.0004) (0.0002) (0.0014)
2011 -0.0042*** 0.0087*** 0.0036*** 0.0021***
(0.0003) (0.0004) (0.0002) (0.0008)
Constant 0.0031*** 0.0068** 0.0138*** 0.0010*** 0.0101***
(0.0011) (0.0029) (0.0003) (0.0002) (0.0007)
R-Squared 0.05 0.01 0.10 0.15 0.01
Observations 72,226 9,085 71,837 71,837 72,226
Note: Robust standard errors are in parentheses.
* significant at 10%; ** significant at 5%; *** significant at 1%
Table B.4: Regressions Evaluating Risk-Based Capital Ratios
INCOME INCOMESTD NONPERFORM CHARGEOFF FAILURE
RBC -0.0559*** -0.1648*** 0.0169*** 0.0011 0.0426***
(0.0113) (0.0637) (0.0017) (0.0011) (0.0034)
TOTCAP 0.0571*** 0.1682** -0.0173*** -0.0013 -0.0423***
(0.0110) (0.0660) (0.0014) (0.0010) (0.0033)
COUNTER 0.0141 -0.1165** 0.0047 -0.0171*** -0.0978**
(0.0098) (0.0552) (0.0097) (0.0039) (0.0407)
MKTRISK 0.0003*** 0.0006*** -0.0002*** -0.0000 -0.0002***
(0.0001) (0.0002) (0.0000) (0.0000) (0.0000)
REALEST 0.0019* -0.0281*** 0.0300*** -0.0087*** -0.0338***
(0.0010) (0.0039) (0.0014) (0.0005) (0.0042)
C&I 0.0143*** 0.0303** 0.0037** 0.0158*** 0.0135**
(0.0021) (0.0124) (0.0015) (0.0009) (0.0065)
CONSUMER 0.0219*** -0.0041 0.0174*** 0.0355*** -0.0322***
(0.0028) (0.0068) (0.0017) (0.0025) (0.0023)
COMMIT -0.1049*** 0.1639*** -0.1222*** 0.0345*** 0.1174**
(0.0108) (0.0460) (0.0120) (0.0046) (0.0486)
2003 0.0001 -0.0012*** 0.0001 -0.0001
(0.0003) (0.0002) (0.0001) (0.0003)
2004 0.0006** -0.0026*** -0.0003*** -0.0007***
(0.0003) (0.0002) (0.0001) (0.0002)
2005 0.0010*** -0.0027*** -0.0006*** -0.0008***
(0.0003) (0.0002) (0.0001) (0.0002)
2006 0.0008** -0.0013*** -0.0007*** -0.0007***
(0.0004) (0.0002) (0.0001) (0.0003)
2007 -0.0008* 0.0034*** -0.0001 0.0018***
(0.0005) (0.0003) (0.0001) (0.0006)
2008 -0.0075*** 0.0105*** 0.0019*** 0.0158***
(0.0003) (0.0003) (0.0001) (0.0015)
2009 -0.0104*** 0.0142*** 0.0051*** 0.0185***
(0.0003) (0.0004) (0.0002) (0.0016)
2010 -0.0073*** 0.0127*** 0.0047*** 0.0115***
(0.0003) (0.0004) (0.0002) (0.0014)
2011 -0.0042*** 0.0087*** 0.0036*** 0.0021***
(0.0003) (0.0004) (0.0002) (0.0008)
Constant 0.0031*** -0.0082 0.0138*** 0.0010*** 0.0101***
(0.0011) (0.0070) (0.0003) (0.0002) (0.0007)
R-Squared 0.05 0.03 0.10 0.15 0.01
Observations 72,226 9,085 71,837 71,837 72,226
Note: Robust standard errors are in parentheses.
* significant at 10%; ** significant at 5%; *** significant at 1%
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