Risk-Based Capital, Portfolio Risk, and Bank Capital:

	A Simultaneous Equations Approach

	Kevin Jacques and Peter Nigro

	Office of the Comptroller of the Currency

	Economic & Policy Analysis

	Working Paper 94-6

	September 1994

The opinions expressed in this paper are those of the author and do not necessarily reflect

those of the Office of the Comptroller of the Currency or the Department of the Treasury. 

Any whole or partial reproduction of material in this paper should include the following citation:  Jacques, Kevin and Peter Nigro, “Risk-Based Capital, Portfolio Risk, and Bank Capital: A Simultaneous Equations Approach," Office of the Comptroller of the Currency,

E&PA Working Paper 94-6, September 1994.

Abstract:  This paper examines the impact the recently implemented risk-based standards have had on both bank capital and portfolio risk.  To date, little if any attention has focused

on how the risk-based capital standards have impacted bank risk and capital levels.  Building

on previous research, this paper uses a three-stage least squares (3SLS) model to analyze the

relationship between bank capital, portfolio risk, and the risk-based capital standards.  The

results suggest that the risk-based capital standards had a significant impact on capital and

risk levels in well-capitalized banks, but little impact on undercapitalized banks.  	

The authors thank Philip Bartholomew, Mike Carhill, Robert DeYoung, David Nebhut, Thomas Lutton, Louis

Raffis, Robert Skinkle, and Gary Whalen for helpful comments, Kari Falkenborg for research support, and

Claire Emory for editorial assistance.  All errors are the responsibility of the authors.

Please address questions to Kevin Jacques, Senior Financial Economist, Economics and Evaluation Division,

Office of the Comptroller of the Currency, 250 E Street SW, Washington, DC 20219, (202) 874-4816.

Questions regarding subscriptions to the OCC Economic and Policy Analysis Working Paper Series should be

addressed to Communications Division, Comptroller of the Currency, Washington, DC 20219.

I. Introduction

     Throughout the 1970s, the capital position of many banking institutions declined

significantly.  To address this decline, in December 1981, the bank regulators issued explicit

minimum capital standards for banks and bank holding companies.  These standards required

banks to hold capital at least equal in amount to a fixed percentage of their assets.  While

these standards have been given credit for increasing bank capital ratios, the 1980s saw an

increase in both the number and cost of bank failures.  A weakness of the minimum capital

standards is that they failed to take into account the risk in a bank's portfolio of assets; high-

risk assets required the same amount of capital as low-risk assets.           

     In July 1988, the bank regulators, as part of the international Basle Committee on

Banking Regulation and Supervisory Practices, announced the adoption of the risk-based

capital standards.1  The purpose of the risk-based standards was to make bank capital requirements sensitive to the risk in a bank's portfolio of assets and off-balance sheet

activities.  To date, the risk-based capital standards appear to have been at least partially

effective in increasing bank capital ratios.  Since 1991, the equity-asset ratio for all

commercial banks increased from 6.75 percent to 8.01 percent in 1993, while the risk-based

capital ratio increased from 10.67 percent to 13.17 percent over the same period.  

     Although adoption of the risk-based standards has focused attention on capital levels,

little if any attention has been given to the corresponding level of risk in bank portfolios and

how the adoption of the risk-based capital standards may have impacted bank risk levels.  To

date, some theoretical and empirical research suggests that increasing regulatory capital standards might cause banks to increase, rather than decrease, portfolio risk.  Furthermore,

higher bank capital levels do not, by themselves, guarantee that banks are adequately

capitalized.  From a public policy perspective, what is important is the amount of capital a

bank holds relative to its level of risk.       

     This paper contributes to the literature by examining the impact that the recently

implemented risk-based standards have had on not only bank capital, but also portfolio risk. 

Modifying recent work by Shrieves and Dahl (1992), this paper uses a three-stage least

squares (3SLS) model to recognize the relationship between bank capital, portfolio risk, and

the risk-based capital standards.  By using the 3SLS technique, the model explicitly

recognizes the endogeneity of changes in capital and risk, and as such, is preferable to single

equation OLS models that assume either capital or risk is exogenous to the bank.

II. Previous Literature

     In recent years, a number of theoretical and empirical studies have examined the relationship between bank capital levels and portfolio risk.  For example, using the mean-

variance framework, Kahane (1977), Koehn and Santomero (1980), and Kim and Santomero

(1988), have shown that regulatory capital standards may have the unintended effect of

causing utility maximizing banks to engage in increasingly risky behavior.  In contrast,

Furlong and Keeley (1989) and Keeley and Furlong (1990), argue that the mean-variance

approach is inappropriate because it ignores the effect of deposit insurance.  Using a

contingent-claims model, their results suggest that increased capital standards will not cause

banks to increase portfolio risk.  But Gennottee and Pyle (1991) find that even if the impact of deposit insurance is accounted for, increased stringency in capital standards may lead

banks to incur greater portfolio risk if the bank is not restricted to zero net present value

investments. 

     With regard to risk-based capital regulation, Kim and Santomero (1988) and Kendall and

Levonian (1992) have examined how the design of risk-based capital standards influences

bank risk taking.  The results of Kendall and Levonian are particularly interesting, because

they find that a risk-based rule designed to minimize the probability of bank failure will lead

banks to choose high-risk assets.  Recent empirical work by Haubrich and Wachtel (1993)

suggests that implementation of the Basle risk-based capital standards caused significant

changes in the composition of bank portfolios, but does not address the impact of these

changes on overall portfolio risk.          

III. Risk-Based Capital Standards

     In July 1988, the Basle Committee on Banking Regulation and Supervisory Practices,

composed of representatives from 12 major industrialized countries, approved the adoption of

a risk-based capital standard for banks in members' respective countries.2  Prior to the implementation of the risk-based standards, U.S. banks were subject to a requirement that

they hold a minimum fixed percentage of their assets in the form of capital, regardless of the

level of risk in their portfolio. 

     Beginning on December 31, 1990, the risk-based capital standards supplemented the existing capital requirement.  The primary purpose of the risk-based standards was to require

banks to hold capital in accordance with the perceived credit risk in their portfolio.  As such,

the risk-based standards link capital to risk by assigning risk weights to broad categories of

assets.  Currently, the risk-based standards contain four risk-weight categories:  0 percent,

20 percent, 50 percent, and 100 percent.  Low credit risk assets, such as cash and U.S.

government securities, are considered to have no default risk and are assigned to the 0

percent risk category.  At the other extreme, higher credit risk assets such as commercial

loans, are assigned to the 100 percent risk weight category.  Having assigned individual

assets to the appropriate risk-weight category, the bank computes its total risk-adjusted assets

by summing its risk-weighted assets (the dollar volume of each asset multiplied by the

corresponding risk weight).3  As a final step, capital must be held as a percentage of the total risk-weighted assets.  Effective December 31, 1990, banks were required to hold a minimum

7.25 percent of their risk-weighted assets in the form of capital; beginning at the end of

1992, the minimum risk-based standard increased to 8 percent.  Other things being equal, the

greater the credit risk in a bank's portfolio, the greater the total risk-weighted assets, and the

greater the level of capital that the bank must hold against its portfolio.  

IV. Limitations of the Risk-Based Capital Standards 

     Under an ideal risk-based capital system, any increase in a bank's portfolio risk would be accompanied by an increase in capital to act as buffer against possible losses arising from the

additional risk.  This implies that the risk-based capital standards should explicitly link

changes in required bank capital with changes in portfolio risk.  However, as currently

written, conceptual weaknesses in the risk-based standards may undermine the relationship

between changes in portfolio risk and changes in required capital.  One reason for this is that

the current risk-based capital standards account primarily for credit risk.  As Benston (1991)

notes, the risk-based standards do not explicitly incorporate capital charges tied to interest

rate risk.4  Thus, a capital-deficient bank can meet the minimum risk-based standards by substituting interest-sensitive, low credit risk assets, such as long-term Treasury bonds, for

shorter-term, higher credit risk assets such as commercial loans.  By substituting assets in

this manner, a bank's portfolio risk may actually increase while the dollars of capital

required under the risk-based standards will decrease.  

     In addition, as Keeton (1989), Avery and Berger (1991), and Kaufman (1991) observe, if

the risk weights used in the risk-based capital standards do not accurately reflect the true risk

of an asset, then banks may actually have an incentive to increase portfolio risk.  This

situation occurs, in part, because the risk-based standards use simplified risk classifications

that create an incentive for banks to arbitrage both between and within risk categories. 

Evidence that the risk weights used in risk-based capital differ from the actual risk of the

asset is provided by Bradley, Wambeke, and Whidbee (1991) and Avery and Berger (1991).  Furthermore, by ignoring the variance-covariance relationship between assets, the risk-based

capital standards may not accurately differentiate between changes in asset composition that

hedge portfolio risk and those that increase portfolio risk.

     Finally, it must be recognized that the minimum risk-based  capital standards, by

themselves, do not limit the amount of risk in a bank's portfolio.  Rather, the risk-based

standards dictate how much capital a bank must hold, conditional upon the estimated level of

credit risk in a bank's portfolio.  In fact, as discussed above, the risk-based capital standards

may actually cause banks to increase portfolio risk. 

V. Model Specification

     The preceding sections suggest that a relationship exists between bank capital and

portfolio risk.  Recent empirical work by Shrieves and Dahl (1992) finds that bank capital

levels and portfolio risk are simultaneously and positively related: increases in capital

standards lead to increasing levels of portfolio risk, and increases in portfolio risk lead to

increases in bank capital levels.  In general, a positive correlation between portfolio risk and

capital may occur when leverage and portfolio risk are substitutes while a negative

correlation may result from the mispricing of deposit insurance.  Our interest is not only in

how portfolio risk and capital may be related, but also what impact the risk-based capital

standards may have had on them.  

     To examine these issues, the simultaneous equation model developed by Shrieves and

Dahl (1992) is modified to incorporate the risk-based capital standards.  In the Shrieves and

Dahl model, observed changes in bank capital and risk levels are decomposed into two components, a discretionary adjustment and a change caused by factors exogenous to the

bank such that:   

(1)	ΔCAPj,t  = ΔdCAPj,t + Ej,t 

(2)	ΔRISKj,t = ΔdRISKj,t + Sj,t

where ΔCAPj,t and ΔRISKj,t are the observed changes in capital and risk levels, respectively, for bank j in period t.  ΔdCAPj,t and ΔdRISKj,t represent the discretionary adjustments in capital and risk, and Ej,t and Sj,t are exogenously determined factors.  In any period, banks may not be able to adjust their desired capital and risk levels instantaneously.  Thus,

Shrieves and Dahl model the discretionary changes in capital and risk using the partial

adjustment framework such that:

(3)	ΔdCAPj,t  = α(CAP*j,t - CAPj,t-1) 

(4)	ΔdRISKj,t = β(RISK*j,t - RISKj,t-1) 

where CAP*j,t and RISK*j,t are bank j's target capital and risk levels, respectively.  In the partial adjustment framework, the discretionary changes in capital and risk are proportional

to difference between the target level and the level existing in period t-1.  Substituting

equations (3) and (4) into equations (1) and (2), the changes in capital and risk can be

written:

(5)	ΔCAPj,t  = α(CAP*j,t - CAPj,t-1) +  Ej,t

(6)	ΔRISKj,t = β(RISK*j,t - RISKj,t-1) + Sj,t. 

Thus, the observed changes in capital and risk in period t are a function of the target capital

and risk levels, the lagged capital and risk levels, and any exogenous factors.  The target

levels of capital and risk are not observable, but are assumed to depend upon some set of

observable variables.  Examples of factors exogenous to the bank that could influence capital

or risk levels include changes in regulatory capital standards or  macroeconomic conditions.  

     Specifying variables to explain changes in capital and risk, the model is written:

(7)	ΔCAPj,t = Γ0 + Γ1SIZEj,t + Γ2BHCj,t + Γ3LEVDj,t + Γ4ΔRISKj,t 

		 + Γ5INCj,t + Γ6DEPj,t - Γ7CAPj,t-1 + Γ8RPGj,t + Γ9RPLj,t + μj,t

(8)	ΔRISKj,t = θ0 + θ1SIZEj,t + θ2BHCj,t + θ3LEVDj,t + θ4ΔCAPj,t 

		 + θ5DEPj,t - θ6RISKj,t-1 + θ7RPGj,t + θ8RPLj,t + ωj,t    

where μj,t and ωj,t are disturbance terms.  In this study, changes in capital and risk are influenced by a number of explanatory variables including:  the size of the bank (SIZE),

whether the bank is affliated with a multibank holding company (BHC), changes in risk

(ΔRISKj,t) and capital (ΔCAPj,t), lagged levels of capital (CAPt-1) and risk (RISKt-1), and the degree of regulatory pressure.  These variables are taken from Shrieves and Dahl (1992),

where SIZE is measured as the natural log of a bank's total assets and BHC is a dummy variable that equals unity for banks belonging to a multibank holding company.   ΔRISKj,t and ΔCAPj,t are included to recognize the possible simultaneous relationship between changes in capital and changes in risk.  In addition, the ratio of income to total assets (INC) in period

t-1 is taken from Dahl and Shrieves (1990) as a proxy for profitability in period t and the

change in the deposit to asset ratio (DEP) is used to measure the impact of changes in

deposits on capital and risk.    

     The leverage ratio is also included as a variable to explain changes in capital and risk. 

As Baer and McElravey (1993a) note, concurrent with the adoption of the risk-based capital

standards came changes in the calculation of the leverage ratio. Specifically, U.S. banks with

a CAMEL rating of 1 were required to hold a minimum of 3 percent of their balance sheet

assets in the form of Tier 1 capital.5  Banks not rated CAMEL 1, or those with significant credit or other types of risk were required to meet even higher leverage ratios, these being at

least 100 to 200 basis points above the minimum.  Thus, a dummy variable for banks with

less than a 5 percent leverage ratio (LEVD) is included, because if a bank is constrained by

the leverage ratio, it would be expected to increase its total capital-asset ratio, independent of

the risk-based standards.6 

     Empirical estimation of equations (7) and (8) requires measures of both bank capital and

portfolio risk.  Following previous research, capital was measured as the ratio of equity capital to total assets.  Measurement of portfolio risk is more difficult, and the literature on

risk measurement suggests a number of different ways, all of which are subject to some

criticism.  Avery and Berger (1991), McManus and Rosen (1991), and Berger (1992), use

total risk-weighted assets as a percentage of total assets (RWARAT) in measuring portfolio

risk.  Avery and Berger have shown that this ratio correlates with risky behavior while

McManus and Rosen argue that it is superior to nonperforming loans, which reflect the ex-

post outcome of lending decisions.  Other studies, such as those by Berger (1992), Berger

and Udell (1992), and Shrieves and Dahl (1992), use nonperforming loans, because that

measure is less subject to criticisms of being a lagging indicator than are other measures,

such as net charge-offs.  Thus, nonperforming loans as a percentage of total assets, NONP,

is used as an alternative measure of portfolio risk.

     Of particular interest in this study are the regulatory pressure variables, RPG and RPL. 

Previous studies have tended to use a dummy variable to signify the degree of regulatory

pressure a bank is under.  Unfortunately, this definition of regulatory pressure implicitly

assumes that there is no response from banks above the minimum regulatory capital

standards.  Other authors, such as Peltzman (1970), Mingo (1975), Dietrich and James

(1983), and McManus and Rosen (1991), use ratios involving a bank's capital level and the

regulatory minimum standards as a way of calculating the degree of regulatory pressure. 

These methods allow banks above the minimum regulatory standards to respond and have the

added benefit of recognizing the nonlinear relationship between the regulatory capital

standards and either portfolio risk or changes in capital ratios.    

     In this paper, RPG and RPL signal the degree of regulatory pressure brought about by the risk-based capital standards.  In order to recognize the nonlinear relationship between

regulatory standards and the dependent variables, the regulatory pressure variable is defined

as the difference between the inverse of bank j's risk-based capital ratio (RBCj) and the inverse of the regulatory minimum risk-based ratio of 7.25 percent.7  Because banks with risk-based capital ratios above and below the 7.25 percent threshold may react to the

standards differently, this study partitions the regulatory pressure variable into two variables,

RPG and RPL.  RPL equals (1/RBCj - 1/7.25) for all banks whose risk-based capital ratio is less than 7.25 percent and 0 for all banks with risk-based ratios above the minimum.  These

banks are under considerable regulatory pressure to increase their capital ratios since they did

not meet the minimum risk-based capital standard at the end of 1990.  Therefore, RPL

should have a positive effect on capital (Γ9 > 0) or a negative effect on portfolio risk (θ8 < 0), because banks can meet the minimum risk-based standards by either raising capital or

reducing risk-weighted assets.8  

     A second regulatory pressure variable, RPG, equals (1/RBCj - 1/7.25) for all banks whose risk-based ratio is greater than or equal to 7.25 percent, 0 otherwise.  While banks

with risk-based capital ratios in excess of 7.25 percent were not explicitly capital constrained,

implementation of the risk-based standards may have significantly affected their level of

capital or portfolio risk.  Since these banks already meet the minimum risk-based standards,

they may choose to reduce capital (Γ8 > 0) or increase their level of portfolio risk (θ7 < 0).9  Alternatively, as Hancock and Wilcox (1992), Furlong (1992), and Baer and McElravey

(1993b) note, banks may increase their capital position as a buffer against shocks to equity.10  Because banks must meet the risk-based capital standards on a continuous basis,

implementation of the risk-based standards may cause these banks to increase their capital (Γ8 < 0) or reduce risk (θ7 > 0) as insulation against any uncertainty regarding whether the bank meets the regulatory minimum.  

     The partitioned definition of regulatory pressure has two advantages over those used in

previous research.  First, unlike many previous studies, this specification of regulatory

pressure allows banks that are not explicitly capital deficient to also respond to the

introduction of new regulatory standards.  Second, partitioning the data set by whether or not

a bank meets the minimum risk-based threshold allows banks that are undercapitalized to

respond differently than those banks that are not explicitly undercapitalized.  Previous models

have tended to assume there is no regulatory response by well-capitalized banks or that their response is the same as that of undercapitalized institutions.

VI. Data and Empirical Estimation  

     Effective December 31, 1990, banks were required to hold 7.25 percent of their risk-

weighted assets in the form of capital.  This study covers the first year the risk-based capital 

standards were in effect (1991), using call report data on 2,570 FDIC-insured commercial

banks with assets greater than $100 million, from year end 1990 (period t-1) and year end

1991 (period t).  The model is estimated using the 3SLS procedure, which recognizes the

endogeneity of both bank capital ratios and risk levels in a simultaneous equation framework. 

Unlike ordinary least squares, the 3SLS technique provides consistent estimates of the

parameters.    

     The results of estimating equations (7) and (8), using the various measures of portfolio

risk, are presented in Tables 1 and 2.11  The size of the bank (SIZE) appears to significantly increase both capital and risk levels, whereas the multibank holding company variable (BHC)

was found to have a negative and signficant impact on risk.  The parameter estimates on the

lagged levels of capital and risk in Tables 1 and 2 range between 0.248 and 0.305, thus

implying slow adjustment of both capital and risk to a bank's desired levels.  The income-

asset ratio variable yielded mixed results, and the negative coefficient on DEP suggests that

banks with more stable deposit bases tended to hold less capital.  Finally, the results suggest

	Table 1

	Three-Stage Least Squares Estimates of Risk-Based Capital

	on Portfolio Risk (RWARAT) and Bank Capital

  Variable  

 INTERCEPT

 SIZE

 BHC

 LEVD

 CAPt-1

 RWARATt-1

 ΔRWARAT

 ΔCAP

 INC

 DEP

 RPL

 RPG

   ΔCAPt   

  -2.285* 

 (-2.59) 

   0.260*

  (4.03)

  -0.113

 (-0.74)

   0.319

  (1.22)

  -0.296*

(-11.21)

  ------ 

  -0.115* 

 (-5.03) 

  ------

  -0.012

 (-0.23)

  -0.096*

 (-6.87)

  -1.364

 (-0.58)

 -17.685*

 (-5.11)

ΔRWARATt  

  -1.602

 (-0.67)

   1.563*

  (9.92)

  -0.823*

 (-1.96)

  -0.692   

 (-0.96)

   ------

  -0.251*

(-16.59)

   ------

  -0.911*

 (-3.66)

   ------ 

  -0.144*

 (-3.32)

   3.987

  (0.61)

 104.308*  

 (10.60)

		Number of banks:		2,570

		System weighted R2		0.108

t-statistics in parentheses; * indicates significance at the 5 percent level; ** indicates significance at the 10

percent level.

	Table 2

	Three-Stage Least Squares Estimates of Risk-Based Capital

	on Portfolio Risk (NONP) and Bank Capital

  Variable  

 INTERCEPT

 SIZE

 BHC

 LEVD 

 CAPt-1

 NONPt-1

 ΔNONP

 ΔCAP

 INC

 DEP

 RPL

 RPG

   ΔCAPt   

   0.300

  (0.42)

   0.096**

  (1.79)

  -0.061

 (-0.41)

   0.089

  (0.36)

  -0.248* 

(-10.52)

  ------

  -0.254**

 (-1.69)

  ------    

   0.119**

  (1.77)

  -0.077*

 (-5.59)

  -1.706

 (-0.76)

 -10.550*

 (-2.88)

   ΔNONPt  

   0.821*

  (2.45)

   0.046**

  (1.82)

  -0.245*

  (-3.60)

  -0.005

 (-0.05)

  ------

  -0.305*

(-15.96)

   ------

  -0.180*

 (-4.20)

   ------

   0.015*

  (2.08)

   1.936**

  (1.82)

  13.148* 

 (10.24)

		Number of banks:		2,570

		System weighted R2		0.103    

t-statistics in parentheses; * indicates significance at the 5 percent level; ** indicates significance at the 10

percent level.

	Table 3

	Summary Statistics for Sample Banks

	(1990 - 1991)

  Variable  

Number of banks

Median RBC ratio 1990

Median income-asset ratio 1991

Equity and Assets 

Median equity-asset ratio  (K/TA) 1990

Median (K/TA) 1991

Median change 1990-91

% change equity capital   

% change total assets(TA)

% change risk-weighted assets(RWA)

  Risk ratios  

Median (RWA/TA) 1990

Median (RWA/TA) 1991

Median change (RWA/TA)

Median nonperforming loans-total assets    

   (NONP) 1990

Median NONP 1991

Median change NONP

Banks with RBC

 ratio < 7.25% 

      67

     6.71%

    -0.94%

     3.68%

     4.18%

    +0.50

     2.02%

    -7.26%

   -14.84% 

    77.11%

    72.15%

    -4.96

     4.27%

     4.05%

    -0.22

Banks with RBC

ratio >= 7.25%

    2,503

    11.59%

    +0.95%

     7.41%

     7.47%

    +0.06

     6.61%

     4.14%

    -5.35%

    69.95%

    63.43%

    -6.52

     0.82%

     0.85%

    +0.03

that changes in risk and changes in capital are negatively related.  Changes in risk have a negative impact on changes in capital when risk is measured using RWARAT (-0.115 in

Table 1) and NONP (-0.254 in Table 2).  In addition, changes in capital have a negative

influence on risk in both risk equations (-0.911 in Table 1 and -0.180 in Table 2). 

Consistent with previous research, this result suggests that banks may have exploited the

mispricing of deposit insurance.

     Of primary interest in this study is what impact the risk-based capital standards had on

changes in bank capital and portfolio risk.  An examination of the capital and risk equations

in Tables 1 and 2 suggests some rather surprising results.  First, banks that were not

explicitly constrained by risk-based capital responded to implementation of the standards by

increasing their capital-asset ratios and reducing their  portfolio risk.  To see this, note that

the parameter estimate for regulatory pressure (RPG) is significant in both Tables 1 and 2

and equals -17.685 using RWARAT (Table 1) as the measure of risk.  For the median bank

in this group, with a risk-based capital ratio of 11.59 percent (Table 3), this equals an

increase in its capital-asset ratio by 92.0 basis points as a result of the risk-based standards.12  Coupled with an increase in median bank equity capital of 6.61 percent (Table 3), these

findings suggest that risk-based capital was effective in raising capital and is consistent with

the theory that well-capitalized banks increased capital to provide a buffer against shocks to

equity.

     In addition, banks with risk-based capital in excess of 7.25 percent responded to the new

capital standards by significantly decreasing their level of portfolio risk.  The parameter

estimate on RPG is positive and significant in both risk equations.  Using θ7 = 104.308 from Table 1, the median bank reduced its portfolio risk by 5.42 percentage points (-0.052 *

104.308) from its year-end 1990 value of 69.95 percent.  This result suggests that regulatory

pressure led to a reduction in portfolio risk even for banks that were not capital constrained.  

        On the other hand, the results in Tables 1 and 2 suggest that banks that were explicitly

constrained by the risk-based standards did not significantly increase their equity-asset ratios

in response to implementation of the risk-based capital standards.  While the median

constrained bank raised its equity-asset ratio by 50 basis points during this period (Table 3),

the parameter estimates on RPL in Tables 1 and 2 are not significantly different from zero.13 Given that these banks had a median return on assets of -0.94 percent in 1991, and that

raising capital from external sources is costly, constrained banks may have been extremely

limited in their ability to meet the risk-based standards by raising capital.14  Rather, the increase in the equity-asset ratios for constrained banks appears to be explained by a decrease

in total assets and portfolio risk.  An examination of Table 3 shows that the median bank in

this group decreased total assets by 7.26 percent and total risk-weighted assets by 14.84

percent, thereby shifting the composition of their portfolios toward lower risk-weighted assets.  This result is confirmed by noting that the parameter estimate on ΔRWARAT equals -0.115 (Table 1) and is significant at the 5 percent level.  Multiplying this estimate by the

change in RWARAT (-4.96) for the median constrained bank results in an increase in the

equity-asset ratio equal to 57.0 basis points.  Thus, the increase in capitalization of

constrained banks appears to be the direct result of changes in the size and composition of

bank portfolios, and not the introduction of the risk-based capital standards.  

     Although it appears that implementation of the risk-based standards had no direct effect

on the capital levels of constrained banks, it is possible that the risk-based standards

indirectly affected capital ratios by causing a reduction in portfolio risk.  However, the

results of the portfolio risk equations are mixed.  The parameter estimate on the regulatory

pressure variable (RPL) in the risk equations is not significant using RWARAT as a measure

of risk but is significant when NONP is utilized as the risk measure.  The parameter estimate

of 1.936 on RPL in Table 2 is significant at the 10 percent level, but of the wrong sign.  For

the median constrained bank, with risk-based capital of 6.71 percent, this result suggests an

increase in NONP of 0.02 percentage points (0.011 * 1.936).15  While extremely small, this result implies that implementation of the risk-based capital standards may have had the

unintended result of increasing, rather than decreasing, portfolio risk.  

VII. Conclusion 

     This study examines the impact of the risk-based capital standards during the first year of implementation.  Modifying the 3SLS model developed by Shrieves and Dahl (1992), the

results suggest that the risk-based capital standards brought about significant increases in

capital and decreases in portfolio risk of well-capitalized banks.  Risk-based capital

constrained banks also showed increases in the equity-asset ratio, but these increases appear

to be primarily the result of decreasing portfolio risk and a reduction in total assets.  Finally,

while the overall level of portfolio risk in constrained banks decreased, implementation of the

risk-based standards appears to have had little effect on the portfolio risk of these banks.

	References

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Avery, Robert B., and Allen N. Berger, "Risk-Based Capital and Deposit Insurance

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	Appendix 1

	Three-Stage Least Squares With Minimum RBC at 8%

  Variable  

 Intercept

 SIZE

 BHC

 LEVD

 CAPt-1

 RWARATt-1

 ΔRWARAT

 ΔCAP

 INC

 DEP

 RPL

 RPG

   ΔCAPt   

  -2.044* 

 (-2.35) 

   0.258*

  (4.00)

  -0.109

 (-0.71)

   0.254

  (0.98)

  -0.298*

(-11.19)

  ------ 

  -0.114* 

 (-4.99) 

  ------

   0.003

  (0.061)

  -0.095*

 (-6.84)

  -1.624

 (-0.70)

 -17.955*

 (-5.04)

   ΔRWARAT   

  -2.630

 (-1.12)

   1.561*

  (9.85)

  -0.859*

 (-2.03)

  -0.219   

 (-0.31)

   ------

  -0.252*

(-16.58)

   ------

  -0.955*

 (-3.80)

   ------ 

  -0.149*

 (-3.41)

   4.764

  (0.73)

 108.241*  

 (10.65)

		Number of banks:		2,570

		System weighted R2		0.109

t-statistics in parentheses; * indicates significance at the 5 percent level; ** indicates significance at the 10

percent level.

	Appendix 2

	Three-Stage Least Squares Estimates With Minimum RBC at 8%

  Variable  

 Intercept

 Size

 BHC

 LEVD 

 CAPt-1

 NONPt-1

 ΔNONP

 ΔCAP

 INC

 DEP

 RPL

 RPG

   ΔCAPt   

   0.423

  (0.60)

   0.097**

  (1.79)

  -0.060

 (-0.40)

   0.057

  (0.23)

  -0.249* 

(-10.50)

  ------

  -0.257**

 (-1.70)

  ------    

   0.129**

  (1.91)

  -0.076*

 (-5.57)

  -1.765

 (-0.80)

 -10.785*

 (-2.88)

   ΔNONP   

   0.629**

  (1.91)

   0.047**

  (1.87)

  -0.246*

  (-3.62)

   0.048

  (0.43)

  ------

  -0.302*

(-15.86)

   ------

  -0.174*

 (-4.05)

   ------

   0.015*

  (2.14)

   2.342*

  (2.23)

  12.946* 

  (9.87)

	Number of banks:		2,570

	System weighted R2		0.102    

t-statistics in parentheses; * indicates significance at the 5 percent level; ** indicates significance at the 10

percent level.