evaluating risk-based capital regulation...evaluating risk-based capital regulation thomas l. hogan*...

Evaluating Risk-based Capital Regulation

Thomas L. Hogan* Troy University

151 Bibb Graves Hall

Troy AL, 38061

[email protected]

+1 334-808-6383

Neil R. Meredith West Texas A&M University

2501 4th Avenue

Canyon, TX 79106

[email protected]

+1 806-651-2493

Xuhao (Harry) Pan George Mason University

4400 University Drive

Fairfax, VA 22030

[email protected]

+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.

1

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.

4

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.

5

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).

9

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.

10

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

13

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


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


Loans fully secured by first liens on one to four family residential properties

Other municipal bonds


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


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



28

Table 5. Regressions Testing Risk-Based Capital and Capital Ratios


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



29

Table 6. Regressions Evaluating Risk-Based Capital Ratios


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



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


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


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



Table B.3: Regressions Testing Risk-Based Capital and Capital Ratios


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



Table B.4: Regressions Evaluating Risk-Based Capital Ratios


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



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