Evaluating the Adequacy of the Deposit Insurance Fund: 

A Credit-Risk Modeling Approach 

December 2001 

Working Paper 2001-02 

Rosalind L. Bennett 

Financial Economist 

Federal Deposit Insurance Corporation 

Washington, D.C. 20429 

(202) 898-7160 

rbennett@fdic.gov 

The views stated here are those of the author and do not necessarily reflect those of the 

Federal Deposit Insurance Corporation. The author would like to thank John O’Keefe, 

Jim Marino, Dan Nuxoll, Fred Carns, Gerald Hanweck, and Peggy Kuhn for their useful 

comments and suggestions. Christine Brickman provided research assistance. 
 

Evaluating the Adequacy of the Deposit Insurance Fund: 

A Credit-Risk Modeling Approach 

Rosalind L. Bennett 

Abstract 

As part of an effort to measure risk effectively, the FDIC hired Oliver, 

Wyman & Company to develop a credit-risk model for the deposit insurance funds. 

I apply their credit-risk model to estimate the FDIC’s loss distribution; and I perform 

sensitivity analysis using different assumptions about the parameters of the model. The 

sensitivity analysis results in a wide range of possible credit ratings associated with the 

deposit insurance funds. Under one set of assumptions, the deposit insurance funds 

would not warrant a BBB rating, whereas under another set of assumptions the funds 

would warrant an A rating. I conclude that the measures of risk derived from the creditrisk model are sensitive to the parameter assumptions, and it is not clear which parameter 

assumptions are most relevant. 

JEL Classification: G21, G28, G11, G33 

Keywords: Deposit insurance, Credit risk, Default risk 
 

 

Introduction 

In recent years, an increasing number of financial institutions in the United States 

and abroad have been using credit-risk models to evaluate the risk of their loan 

portfolios.1 In fact, there have been proposals to reform regulatory capital requirements 

to allow banks to use internal credit-rating models to set capital levels. Banks typically 

use the output from credit-risk models to estimate the risk-adjusted returns on capital 

allocated to various banking activities. Managers of those banking activities are then 

evaluated and compensated on the basis of the profitability of their activities. In addition, 

some managers use credit-risk models for risk-based loan pricing, to measure the riskadjusted profitability of the portfolio and to set concentration limits.2 

Recently the FDIC began to look at credit-risk models similar to those used by 

large financial institutions, as a means of measuring risk to the insurance funds. As part 

of this effort, Oliver, Wyman & Company (OWC) developed an application of credit-risk 

models that explicitly constructs the loss distribution for the FDIC. The OWC model 

uses a bottom-up approach: it builds the cumulative loss distribution from information on 

individual institutions insured by the FDIC. In general, credit-risk models can help the 

1

 Financial institutions also use internal risk-management models, also known as value-at-risk (VaR) 

models, to estimate the value at risk in their trading books. See Nuxoll (1999) for more detail. 

2

 A survey conducted by the Bank for International Settlements (1999) addressed other applications for 

credit-risk models. The survey found that financial institutions were using credit-risk models to set 

concentration and exposure limits, set hold targets on syndicated loans, price loans on a risk basis, improve 

the risk/return profiles of the portfolio, evaluate the risk-adjusted performance of different business lines or 

managers, allocate economic capital, and set and value loan-loss reserves. 
 

FDIC measure and manage risk. In one particular application of credit-risk models, the 

FDIC can use the model developed by OWC to evaluate fund adequacy.3 

The FDIC should perform a validation of the model before fully incorporating any 

credit-risk model into its current risk management practice. There are essentially three 

components of model validation: sensitivity analysis, backtesting, and stress testing. This 

article focuses on the first component—sensitivity analysis.4 

Sensitivity analysis involves analyzing the effect of making different assumptions 

about model parameters on the output from the model. Although by definition 

parameters are fixed in a model, there is still some uncertainty associated with them. 

Sensitivity analysis investigates this parameter uncertainty. 

The accuracy of the parameter estimates as representations of the future, and the 

validity of the model assumptions, determine the overall reliability of a credit-risk model. 

Unfortunately, most financial institutions currently do not conduct sensitivity testing on 

the parameters or assumptions embedded in their credit-risk models. The few 

practitioners who have conducted sensitivity analysis observe that the measurement of 

credit risk in a portfolio typically depends more on the quality of the information used by 

the model than on the details of the modeling approach. In fact, Koyluoglu and Hickman 

(1998a, 1998b) and Gordy (2000) demonstrate that alternative credit-risk modeling 

3

 The FDIC can also potentially use the model developed by OWC to evaluate alternative risk-based 

deposit insurance pricing options. Since the model uses a bottom-up approach, it can be used to measure 

the contribution of an individual institution to the overall risk to the insurance funds, as discussed in 

Hanweck (2000). 

4

 Backtesting entails comparing ex ante estimations with ex post experience. Stress testing involves 

analyzing the effects of alternative economic scenarios (represented by alternative sets of parameters) on 

the model output. In contrast to changing many parameters as in stress testing, sensitivity analysis focuses 

on the effect of changes in one parameter. See BIS (1999) for more information on the validation of creditrisk models. 

2 
 

approaches are essentially equivalent. However, the sensitivity analysis that has been 

conducted indicates that model outputs are sensitive to changes in model parameters, 

especially changes in expected default frequencies (EDFs), severity, and default 

correlations.5 This article focuses on the sensitivity analysis of these three inputs. 

The first section of the article describes credit-risk models and their application to 

risk evaluation. I compare how credit-risk models are used by financial institutions to 

how the FDIC can potentially use credit-risk models to evaluate risk to the deposit 

insurance funds. The next section describes in detail the derivation of the inputs to the 

model (exposure, expected default frequencies, severity, and default correlation 

bucketing) and discusses results from a set of baseline simulations. The following three 

sections discuss the results from the sensitivity analysis performed on three of the inputs: 

expected default frequencies, severity, and default correlation bucketing. The subsequent 

section discusses possible areas for further research, and the final section provides 

concluding remarks. 

The Credit-Risk Model 

There are two types of credit-risk models: default mode and mark to market. The 

default-mode models focus on two outcomes—default or no default. The mark-to-market 

approach models the migration from one credit rating to another. The default mode is the 

most common approach used to analyze the loan portfolio of a bank and is the type of 

model used in this analysis. 

5

 See BIS (1999). 

3 
 

The primary output of a credit-risk model is a probability density function (PDF) 

of credit losses. From the PDF, a financial institution can calculate the expected loss and 

the unexpected loss. The expected loss, which is equivalent to the mean of the PDF, is 

the amount of loss a bank would expect to experience in its portfolio over the chosen time 

horizon. The unexpected loss, or the deviation from the expected loss, measures the 

amount of risk in the portfolio. One measure of risk is the volatility of the potential loss 

around expected loss, or the standard deviation of the PDF.6 

Financial institutions use credit-risk models to estimate the economic capital 

needed to support their credit-risk exposures. The role of loss reserving is to cover 

expected credit losses.7 The role of economic capital is to cover unexpected losses. 

Similarly, the FDIC can look at expected loss generated by a credit-risk model as a 

measure of the amount of reserves needed to cover these losses over the coming year.8 

The FDIC can also use a credit-risk model to evaluate the adequacy of the deposit 

insurance funds to cover unexpected losses—analogous to financial institutions setting 

the appropriate level of economic capital. 

Observed distributions of credit losses on loan portfolios are not normally 

distributed (see Figure 1).9

 The observed distributions are typically skewed toward large 

losses: for a given mean and standard deviation, the probability of incurring large losses 

6

 To be consistent with the terminology used by Oliver, Wyman & Company, I call the standard deviation 

of losses the unexpected loss. 

7

 Generally Accepted Accounting Principles (GAAP) require reserving for probable and estimable losses. 

As discussed in Jones and Mingo (1998), the role of reserving policies is to cover expected losses. In the 

context of this article, expected losses are the product of the probability of incurring a loss multiplied by the 

estimated loss and are thus both probable and estimable. 

8

 The FDIC currently uses an actuarial method to set its contingent loss reserves. 

9

 See Jones and Mingo (1999, 1998). 

4 
 

 

 

is greater than it would be if the distribution were normal. Similarly, the FDIC faces a 

skewed distribution of losses: in any given period, there is a high probability of incurring 

small losses from the failure of a number of small banks but a small probability of 

incurring large losses from the failure of a large bank and/or the failure of a large number 

of banks. Since the distribution is skewed, precise estimation of the high quantiles in the 

distribution is important. The size of the estimation error in this region of the distribution 

can potentially be large and have a large influence on the shape of the distribution. 

Financial institutions typically collapse the estimated PDF into a single measure, 

such as the amount of economic capital required to meet a certain solvency standard. For 

example, if the institution is willing to tolerate a 0.03 percent probability that losses will 

exceed the capital level, or the equivalent of a AA rated corporate bond, it can calculate 

the amount of capital it needs to achieve that solvency standard. Financial institutions 

usually choose a capital standard that is consistent with their desired credit rating.10 

Similarly, the FDIC can use the cumulative loss distribution from a credit-risk model to 

determine what fund balance is required to reach a chosen solvency standard. For 

example, the FDIC may be willing to accept a minimum of 99.68 percent chance that the 

fund will not incur losses larger than the fund balance. The solvency standard can also be 

described in terms of a maximum insolvency probability—0.32 percent in this example. 

Alternatively, the solvency standard can be described in terms of a credit rating for the 

insurance fund. In this example, the 99.68 percent solvency standard is approximately 

10 For more detail, see Jones and Mingo (1999, 1998). 

5 
 

 

 

 

equivalent to a BBB- S&P credit rating or a Baa3 Moody’s credit rating for a one-year 

time horizon.11 

Credit-risk models estimate credit ratings for the deposit insurance funds that are 

equivalent to a credit rating on a corporate bond. Credit ratings for corporate bonds 

reflect the risk that a bond will default. However, the FDIC would never default even if 

the deposit insurance funds became insolvent: the FDIC honors all deposit claims and has 

the full-faith-and-credit backing of the federal government. For this reason, some may 

argue that the potential insolvency of the deposit insurance funds is irrelevant. However, 

funds that are borrowed from the Treasury to cover any insolvency must eventually be 

repaid. In addition, according to the Federal Deposit Insurance Corporation 

Improvement Act of 1991 (FDICIA), the deposit insurance funds must be recapitalized 

through assessments on banks. 

Under current law, the FDIC is required to maintain a target level of funds 

relative to the amount of insured deposits in the industry. The ratio of the size of the fund 

to insured deposits is the reserve ratio. The target level, or designated reserve ratio 

(DRR), is constant and set at 1.25. If the insurance funds are above the 1.25 DRR, the 

FDIC is prohibited from charging insurance premiums to institutions that are well 

capitalized and well managed.12 The DRR explicitly links the level of the insurance 

11 The relationship between bond ratings and default probabilities is discussed below. As shown on Table 

1, the historical one-year default probability is 0.29 for a bond with a Standard and Poor’s rating of BBB-. 

See Brand and Bahar (2000) for the details of this calculation. As shown on Table 2, the historical oneyear default probability is 0.31 for a bond with a Moody’s rating of Baa3. See Keenan et al. (2000) for the 

details of this calculation. 

12 In Section 7(b) of the FDI Act, the FDIC is prohibited from charging assessments in excess of the 

amount needed to maintain the reserve ratio at the DRR unless an insured depository institution exhibits 

“financial, operational, or compliance weaknesses ranging from moderately severe to unsatisfactory, or is 

not well capitalized.” 

6 
 

funds to the amount of exposure, measured by total insured deposits. The level of risk to 

the insurance funds, however, can change even if the reserve ratio is constant. 

Evaluating the risk in the deposit insurance funds differs in significant ways from 

evaluating the risk in a portfolio of loans. Credit-risk models were developed to measure 

risk in a portfolio of individual loans. Applying credit-risk models to evaluate the risk to 

the deposit insurance funds requires viewing the funds as a portfolio of risks. The 

components of the portfolio are not individual loans but exposures to individual insured 

institutions. The FDIC’s exposure to individual banks can be aggregated to arrive at a 

cumulative loss distribution. Each institution has a small, but non-zero, chance of failing 

and thereby causing a possible loss to the deposit insurance funds. In general, there is a 

high probability of a small loss to the insurance fund. There is also a positive probability 

that the insurance funds will incur large losses either from the failure of a large bank or 

from the failure of a large number of banks. 

Although it seems reasonable to make the analogy between the risk associated 

with holding a portfolio of loans and the risk associated with insuring a portfolio of 

banks, clearly the default event is different. The default of a loan means an obligor is 

unable to make scheduled payments. Although defaults of individual loans usually 

contribute to the failure of a bank, typically banks fail because of a combination of a 

wave of individual loan defaults and poor policies, procedures, and management. 

Another distinction between the default on a loan and the failure of a bank is that the 

failure of a bank is a regulatory event: only the regulatory authority can close a bank. 

7 
 

One of the difficulties financial institutions have in estimating parameters for their 

credit-risk models is the lack of data.13 Few financial institutions have historical records 

of default rates on credits within their portfolios. The drawbacks of using internal creditrating systems have been explored extensively in the academic literature.14 The FDIC is 

able to avoid some of these drawbacks because the historical data on the frequency of 

bank failures are much richer than historical data on loan defaults within the portfolio of 

an institution.15 

One of the crucial decisions when a credit-risk model is being constructed is the 

time horizon. There are two approaches to looking at credit risks in the future—through 

the cycle or point in time. Implementing a through-the-cycle credit-rating philosophy 

requires estimating the borrower’s condition at the worst point in an economic or industry 

cycle and grading according to the risk posed at that point. Point-in-time approaches 

base the credit ratings on the current condition of the borrower. Both Moody’s and S&P 

provide through-the-cycle credit ratings.16 Using a through-the-cycle approach to credit 

ratings implies that the credit rating for a particular borrower will change much less 

during an economic cycle than it will if a point-in-time approach is used. Financial 

institutions commonly use a one-year planning horizon, since this is the period over 

which they can take actions that will mitigate the risk. Banks typically do not test their 

13 See Jones and Mingo (1998), BIS (1999), and Carey and Hrycay (2001) for discussions of the 

insufficiency of internal data. 

14 For example, Carey and Hrycay (2001) investigate the methods used to associate a credit-risk rating with 

each borrower in a loan portfolio. They show that small changes in the method cause the results from a 

credit-risk model to vary widely. 

15 Although the FDIC has a rich set of data on bank failures, changes in legislation related to bank closings 

and structural changes in the industry call into question whether the historical data represent default 

probabilities in the future. 

16 Very weak borrowers, however, are rated primarily according to their current condition. 

8 
 

 

 

 

credit models for sensitivity to the chosen time horizon.17 In this analysis I, too, adopt a 

one-year time horizon.18 

In a default-mode model, the expected dollar losses (EL) are the sum over the 

portfolio of the individual exposures (EXPi) times the estimated probability of default 

(EDFi) times the expected loss given default, or severity (SEVi). 

n 

EL  EXP EDF SEV i i i 

i1 

Estimating unexpected losses for the portfolio involves two steps. First, calculate 

a measure of the unexpected losses for an individual asset in the portfolio (ULi). One 

measure of risk is the standard deviation of losses, which I call unexpected losses.19 

UL  EXP EDF 2  SEV2 EDF (1 EDF ) i i iSEVi i i i 

Second, aggregate the volatility of the individual assets into a measure of volatility for 

the portfolio, taking into account the correlation of default between assets ij, and take the 

square root.20 

n n 

UL  ijUL UL i j 

i1 j1 

This simple structure makes it clear that the estimates of all of the parameters 

EDFi, EXPi, SEVi, and ij play an important role when expected and unexpected losses 

for the portfolio are estimated. The quality of these estimates can have a material effect 

on the accuracy of portfolio credit models. 

17 Jones and Mingo (1999, 1998). 

18 BIS (1999) discusses the time horizon typically chosen by financial institutions. The main reason I chose 

a one-year time horizon was for comparability with results provided in Oliver, Wyman & Company 

(2000d) and reported by the FDIC (2000). 

19 This calculation assumes exposure (EXPi) is not stochastic. 

20 For more detail on the derivation of the calculation for unexpected losses, see Ong (1999). 

9 
 

Oliver, Wyman & Company (OWC) developed an application of a credit-risk 

model for the FDIC to evaluate the risks to the deposit insurance funds.21 There are three 

basic types of models that can be used to evaluate either default-mode or mark-to-market 

credit risks: actuarial, Merton based, and econometric. For example, CreditRisk+ is an 

actuarial model, CreditMetrics and Portfolio Manager are Merton-based models, and 

Credit PortfolioView is an econometric model. Koyluoglu and Hickman (1998a, 1998b) 

show that in theory the three types of credit-risk models are not very different. The 

results from the different models, provided the input parameters are equivalent, are 

virtually the same. The model developed by OWC for the FDIC is a combination of the 

actuarial and Merton approaches.22 As in the basic framework above, the expected loss 

for each institution is the product of the expected default frequency (EDFi), the exposure 

(EXPi), and the severity of the loss given default (SEVi). Expected losses measure the 

anticipated average annual loss. The total expected loss for the deposit insurance fund is 

the sum of expected losses for each individual institution insured by the fund. 

Unexpected loss is the anticipated volatility of loss defined as one standard deviation of 

loss. The OWC model uses Monte Carlo simulation techniques to generate an empirical 

distribution of the cumulative losses to the FDIC. 

The inputs to the OWC model are the three elements described above (expected 

default frequency [EDFi], exposure [EXPi], severity [SEVi]) and an additional input: 

bucketing. To simplify the estimation of the correlation coefficients (ij), the model 

21 All discussion of the OWC model is based on OWC (2000a, 2000b, 2000c, 2000d) and meetings with 

OWC held at the FDIC in July through September of 2000. 

22 The discussion of the algorithm used in generating the model is based on the limited information that 

OWC provided to the FDIC. OWC provided a computer model to the FDIC but did not provide 

descriptions of all of the assumptions embedded in the model, nor did OWC provide the uncompiled source 

code used to generate the model. 

10 
 

requires that institutions be grouped into buckets. Rather than estimate a correlation 

coefficient for each combination of individual institutions, the model estimates the 

correlation coefficients between the buckets of institutions. The model assumes that the 

defaults of institutions within a particular bucket move together. 

More specifically, the model uses the method described here to generate the 

empirical distribution of cumulative losses to the FDIC. The model computes the 

average default correlation within the buckets and for the entire portfolio. Given these 

average default correlations, the model generates asset correlations between any two 

buckets and uses this correlation matrix to drive a multivariate normal distribution. As in 

the Merton-based model, the OWC model assumes that asset values follow the 

multivariate normal distribution and that an individual institution defaults when the asset 

value falls below a critical point. The OWC model draws from a multivariate normal 

distribution with the implied asset correlation matrix and determines whether an 

individual institution defaults or not.23 For the banks that fail in the simulation, the 

model calculates the expected loss (ELi) as the product of exposure (EXPi) and severity 

(SEVi).24 Then the model sums these individual expected losses to arrive at the expected 

loss for a simulation. Using Monte Carlo simulation techniques, the model repeats the 

simulation 50,000 times and generates an empirical distribution. The model then 

23 The OWC model uses principal component analysis to drive the simulation of the normal variates from 

the asset correlation matrix. Principal component analysis helps to generate simulations when the 

correlation matrix is known. 

24 The OWC model allows the user to chose whether severity is constant or a random variable. When 

severity is a random variable, the model assumes that it follows a log-normal distribution. Under this 

assumption, for each bank that fails the model draws severity from a log-normal distribution with a given 

mean and standard deviation and uses it to calculate expected losses. 

11 
 

 

 

 

analyzes the sample set of 50,000 cumulative losses to calculate expected and unexpected 

losses and to evaluate fund adequacy. 

Baseline Simulations 

To evaluate the adequacy of the deposit insurance funds, I focus on the credit 

rating that the December 31, 2000, fund balances earn. Since the FDIC does not have a 

desired credit rating in mind, I report the credit rating the funds would earn. If they fall 

short of a BBB rating (the lowest rating available from the model output), I report how 

much additional funding would be required to make the deposit insurance funds the 

equivalent of a BBB rating. 

For all simulations, I investigate fund adequacy for the Bank Insurance Fund 

(BIF) and for a hypothetical merged fund that includes institutions insured by the BIF and 

the Savings Association Insurance Fund (SAIF). Currently the BIF and SAIF are two 

separate insurance funds, and the FDIC calculates and implements separate deposit 

insurance assessments. However, since the FDIC has long held that the two funds should 

be merged, I demonstrate the effect of a merger on fund adequacy. 

In this analysis, I hold a few elements constant across all simulations. All EDFs 

are for a one-year horizon, and severity is assumed to be random. Although the OWC 

model allows for a two-state simulation, I use only the one-state version of the model for 

all simulations.25 I assume there are five factors, an assumption implying that the model 

25 The OWC model allows for simulations using either one or two states. A two-state model allows for the 

definitions of different parameters for a good state and a bad state. The two-state model allows the user to 

set the percentage of states that are good versus bad. 

12 
 

 

 

 

estimates 25 separate correlation coefficients (ij). I ran all simulations for 50,000 

iterations. 

The baseline simulations reported in this article mimic the preliminary 

simulations run by OWC (2000d). Table 3 shows the descriptive statistics for the four 

inputs to the model: exposure, EDFs, severity, and buckets.26 

Exposure 

In the baseline simulations, exposure for each institution is defined as the total 

assets of the institution reported on the December 31, 1999, Call Report.27 One can 

argue that the FDIC’s exposure is significantly less that the total assets of an institution. 

Some have argued that the FDIC’s exposure is limited to the amount of insured deposits. 

However, using the amount of insured deposits presents data problems. First, the amount 

of insured deposits reported on the Call Report is an estimate. Second, the measures of 

severity (discussed below) are available only in terms of total assets. Insured deposits are 

not measured at the time of closure for all institutions that fail, but only for institutions 

that are resolved in such a way that the FDIC is required to determine which deposits are 

insured.28 Defining exposure as total assets does not distort the results of the model since 

severity is measured in terms of losses on total assets.29 

26 Buckets are numbered from 1 to 25. See below for more detail on the definition of the buckets. 

27 The data used in the analysis are from the Call Report and were retrieved in September 2000. Therefore, 

they reflect any revisions made between December 1999 and September 2000. 

28 The FDIC estimates insured deposits before the time of failure but does not make a final insurance 

determination unless such a determination is required for completing the resolution of the failed bank. 

29 The total loss figures measure the loss to the deposit insurance funds and take into account the extent to 

which losses are smaller because the FDIC shares losses with uninsured domestic depositors. 

13 
 

When I evaluate the BIF separately from the SAIF, the exposure of individual 

institutions must take into account that some institutions hold both BIF- and 

SAIF-insured deposits. In all simulations that use an adjustment for this, I allocate 

exposure (total assets) to the appropriate insurance fund on the basis of the BIF- and 

SAIF-insured deposit levels in the institution. If, for example, an institution that has the 

BIF as its primary insurer acquires a SAIF-insured institution, the acquirer must 

separately report the acquired SAIF-insured deposits for insurance assessment purposes 

(along with its own BIF-insured deposits). A parallel reporting is required for acquired 

BIF-insured deposits by SAIF-insured institutions. All acquired deposits are known as 

Oakar deposits, named after the sponsor of the legislation allowing these types of 

acquisitions.30 Under my asset allocation method, if an institution has 25 percent of its 

domestic deposits as SAIF insured and 75 percent as BIF insured, then 25 percent of its 

exposure is allocated to the SAIF and 75 percent to the BIF. The FDIC uses this same 

approach to allocate to the BIF and SAIF the resolution costs that are associated with 

failed banks. 

Expected Default Frequencies 

The expected default frequencies used in the baseline simulations are derived 

from a mix of market information and historical experience. When available, the 

expected default frequencies are translated from the credit rating on long-term debt. 

OWC provided the FDIC with a mapping between individual banks and credit ratings for 

30 See the Federal Deposit Insurance Act (12 U.S.C. 1815 Section 5(d)(3)). 

14 
 

146 publicly traded banks and bank holding companies.31 The source of June 2000 credit 

rating information was Standard and Poor’s (S&P) or, when not available, Moody’s. If 

credit rating information was not available, an unconditional measure of default 

frequency was used. The unconditional measure is the arithmetic average of historical 

defaults of FDIC-insured banks from 1934 to 1997. 

Market Data 

OWC developed a methodology to map S&P and Moody’s credit ratings to 

expected default frequencies (see Table 4).32 This methodology used information from 

all industries, not just the financial industry. 

Since the EDF is an important input into the credit-risk model, it is essential to 

investigate the relationship between credit ratings and EDFs. Additional information 

about this relationship is available from Standard and Poor’s and Moody’s. Both creditratings agencies conduct ongoing research into the default experiences of their rated 

issuers.33 

Brand and Bahar (2000) calculated the historical one-year EDF of corporations by 

Standard and Poor’s credit ratings. Their study uses data from 1981 to 1999 for all U.S. 

and non-U.S. industrials, utilities, insurance companies, banks, other financial 

institutions, and real estate companies. There are some differences between this study 

31 Many of the bank holding companies hold multiple banks. OWC did not provide the FDIC with details 

about how it mapped the credit ratings for institutions to the bank certificate number. 

32 OWC did not provide the FDIC with details regarding the methodology it developed to map credit 

ratings into expected default frequencies. 

33 The definition of default differs slightly across these two rating agencies. Standard and Poor’s defines 

default as the failure to pay any financial obligation. Moody’s definition includes not only these defaults, 

but also the renegotiation of a financial instrument. 

15 
 

 

and the mapping generated by OWC. First, as shown on Table 1, the historical one-year 

EDFs are zero for corporations that have AAA, AA+, or AA ratings. In contrast, 

methodology developed by OWC assigns to institutions with those credit ratings one-year 

EDFs of 0.01, 0.02, and 0.03 percent, respectively.34 The OWC methodology assigned 

significantly higher EDFs for other credit ratings as well: the EDF assigned to institutions 

rated A+ was more than double the historical EDF, and the EDF assigned to institutions 

rated A- was triple the historical EDF. The EDFs assigned by OWC were not 

consistently higher for all of the credit ratings, however. OWC assigned an EDF of 4.46 

percent for institutions rated B, compared with an 8.46 percent historical EDF; and OWC 

assigned an EDF of 7.52 percent for institutions rated B-, compared with a 10.19 percent 

historical EDF. 

Using a proprietary database of ratings and defaults, Moody’s calculates historical 

default rates for industrial and transportation companies, utilities, financial institutions, 

and sovereigns that have issued long-term debt to the public, including non-U.S. issuers. 

At the start of 2000, industrial companies represented 39 percent of rated firms, nonbank 

financials constituted 17 percent of rated firms, and banking institutions were 14 

percent.35 Keenan et al. (2000) calculated the one-year EDFs shown on Table 2 using 

1983–1999 data. There were six categories that had zero EDFs according to the 

historical data; OWC assigned positive EDFs to these categories. As in Table 1, the 

OWC methodology assigned to some of the credit-rating categories EDFs that were 

significantly higher. The EDF assigned by the OWC methodology is more than three 

34 The credit-risk model constructed by OWC does not allow for an EDF of zero. 

35 Keenan et al. (2000), 8. 

16 
times the historical EDF for institutions with a Baa1 credit rating and more than two 

times for institutions with a Baa2 credit rating. Most of the remaining EDFs assigned by 

the OWC methodology were similar to the historical one-year default rates. 

The difference between the mapping methods, historical or OWC, may affect the 

risk measurement and evaluation of fund adequacy generated by the credit-risk model. 

Of the 146 BIF and SAIF institutions that have credit ratings, about half were rated A, 

A+, or A- as of June 2000. Two institutions did not have S&P ratings available; one was 

rated Baa3 and one Ba3 by Moody’s. The highest concentration, 21.62 percent of the 

148 institutions, had A+ credit ratings, and the OWC methodology assigned a 0.05 

percent EDF compared with the historical one-year EDF of 0.02 percent. Similarly for 

other groups with high concentrations of institutions, the OWC methodology either 

assigned higher EDFs or, for one group, the same EDF. Using the higher EDFs causes 

the estimate of the EL to be higher. (See the equation for EL above.) The effect of using 

the higher EDFs on the UL is not clear, since it will also depend on the correlations 

between institutions in the buckets. (See the equation for UL above.) Therefore, using 

the OWC methodology rather than the historical averages from Standard and Poor’s and 

Moody’s will result in higher EL but will have an unknown effect on the UL and on 

overall measures of fund adequacy. 

Although the number of institutions (146) that had market information may seem 

small, the market information represents over one-half of the total for all BIF- and 

SAIF-insured institutions in terms of total assets, total deposits, and insured deposits. 

The 146 BIF and SAIF institutions with S&P or Moody’s ratings account for 

approximately 63 percent of total assets, 61 percent of total deposits, and 53 percent of 

estimated insured deposits of all 9,990 BIF and SAIF institutions in the simulation. 

17 
 

There were 123 BIF-insured institutions that had either S&P or Moody’s credit ratings. 

These 123 institutions account for approximately 65 percent of total assets, 64 percent of 

total deposits, and 56 percent of insured deposits of the 8,638 BIF institutions included in 

the baseline simulation. 

Historical Bank Default Data 

For the institutions that did not have credit ratings available, OWC calculated 

EDFs using the number of failures from 1934 to 1997 as reported in the FDIC’s 1997 

Annual Report. There were 8,515 BIF and 1,329 SAIF institutions that were assigned the 

historical average of 26 basis points.36 

Severity 

When the credit-risk model framework is used to evaluate deposit insurance fund 

adequacy, severity—also known as loss given default—is the loss incurred when an 

institution fails. As mentioned above, total assets are the equivalent of “exposure” for all 

of the simulations. Therefore, severity is expressed as the loss on assets (total losses as a 

percentage of total assets). As also mentioned above, severity is a random variable in the 

model developed by OWC. Since the model assumes that severity follows a log-normal 

distribution, the mean and standard deviation of severity are inputs into the OWC model. 

For the baseline simulation, I constructed the mean and standard deviation of 

severity from a 14-year history of FDIC losses, which is available from the FDIC’s 

36 OWC did not provide the FDIC with details of this calculation. I used information from the Annual 

Reports and the FDIC’s internal Failure Transactions Database and arrived at a historical average of 25.42 

basis points—close to, but not exactly, the 26 basis points. 

18 
 

 

Failed Bank Cost Analysis. I split failures into five size groups and calculated the mean 

and standard deviation of the loss rates on assets. (See Table 5.)37 In the simulations, 

each institution was assigned a mean and standard deviation of loss rates on the basis of 

the size of the institution. Accordingly, the 5,030 BIF-insured institutions in the sample 

with assets less than $100 million (see Table 6) would be assigned a severity mean of 

24.18 percent and a severity standard deviation of 13.78. 

Bucketing 

As mentioned above, another input into the OWC model is bucketing. The model 

treats the stochastic properties of the defaults of institutions within each bucket the same. 

Therefore, it is important to put institutions that are expected to have similar default 

characteristics in the same bucket. I group borrowers into 25 discrete buckets on the 

basis of observable characteristics. 

For the baseline simulations, institutions were sorted by size, and each of the 20 

largest institutions was placed in its own bucket. The remaining institutions were placed 

37 Note that the number of observations in each cell will not match other publicly available data on the 

number of failed banks. To be consistent with calculations performed by the Division of Finance at the 

FDIC, I consolidated 202 of the receiverships into the following 13 groups: 

1. Banktexas, Inc (11 institutions, failed 1987) 

2. First City (59 institutions, failed 1988) 

3. First Republic (41 institutions, failed 1988) 

4. Alliance (2 institutions, failed 1988) 

5. Texas Bank North (2 institutions, failed 1988) 

6. Mcorp (20 institutions, failed 1989) 

7. Texas American Bancshares (24 institutions, failed 1989) 

8. National Bancshares (9 institutions, failed 1990) 

9. Bank of New England (3 institutions, failed 1991) 

10. Southeast Bank (2 institutions, failed 1991) 

11. New Hampshire Banks (7 institutions, failed 1991) 

12. First City (20 institutions, failed 1992) 

13. Merchants Bank (2 institutions, failed 1992) 

19 
 

in five buckets on the basis of size. These five buckets correspond to the five size 

categories used for calculating severity. 

Simulation Results 

Using the baseline assumptions would give the BIF a credit rating worse than 

BBB. Figure 2 presents three separate simulations. The first simulation allocates assets 

to the BIF on the basis of the distribution of Oakar deposits. The second is a baseline 

simulation with all of the assumptions discussed above, except exposure has not been 

adjusted for Oakar deposits. The third simulation is the results that OWC presented to 

the FDIC. The bars in the figure indicate the dollar amount needed in the fund to earn the 

corresponding credit rating. The horizontal line indicates that there was $29.863 billion 

in the BIF as of December 31, 2000. Correspondingly, the distance between the top of 

each bar and the horizontal line measures the additional capital that the insurance fund 

would require in order to earn the corresponding credit rating. 

In the second simulation (baseline), the expected loss to the BIF is approximately 

$1.03 billion and the unexpected loss is $2.96 billion (see Table 7). To obtain an A rating 

for the BIF, the fund would have to grow to $44.73 billion from its balance of $29.863 

billion as of December 31, 2000. The baseline simulation indicates that the BIF and 

SAIF merged fund has an EL of $1.35 billion and a UL of $3.97 billion. There would 

have to be $55.107 billion in a merged BIF and SAIF fund in order to earn an A credit 

rating. The balance of $40.591 that existed in the two funds as of December 31, 2000, 

does earn the merged fund a BBB rating (see Figures 2 and 3). It should be noted that the 

merged fund is rated higher than the BIF alone, as would be expected from the effects of 

diversification. 

20 
 

 

Sensitivity Analysis: Expected Default Frequencies 

The specification of the EDFs is important in the simulations, as is evident in the 

equations for EL and UL.38 I perform sensitivity analysis on the choice of EDFs, using 

three alternative sources of EDFs.39 First, I replace the market information used in the 

baseline simulation with solely the historical EDFs. Second, I use an econometric model 

to generate EDFs. Third, I investigate three different sources of market information other 

than the long-term debt ratings from S&P and Moody’s. 

Historical Expected Default Frequencies 

As mentioned above, the baseline simulation uses two sources of information for 

EDFs. First, when available, credit ratings are used and mapped to EDFs. Second, the 

remaining institutions are assigned an EDF of 26 basis points. In the first attempt to 

measure sensitivity of the model to changes in the EDF, I simply assign the EDF of 26 

basis points to all of the institutions. As a comparison of the first and second columns of 

Table 8 shows, using only the historical EDFs increases both the EL and the UL of the 

distribution of losses. This simulation indicates that the BIF would have to have a 

balance of $76.840 billion to receive an A rating and $52.2 billion to receive even a BBB 

rating (see Figure 4). A BIF and SAIF merged fund would require a balance of $92.763 

billion for an A rating and $60.994 billion for a BBB rating (see Figure 5). By 

performing a rather naive experiment (replacing the market-derived EDFs with the 

38 Carey and Hrycay (2001) emphasize the importance of estimating the default probabilities accurately for 

use in credit-risk models. 

39 All of the sensitivity analysis for the BIF is performed on the baseline simulations with Oakar 

adjustments. 

21 
historical EDFs), I show that the amount of risk to the insurance fund, as measured by the 

OWC credit-risk model, has increased dramatically. 

Expected Default Frequencies from a Logit Model 

A more sophisticated experiment involves generating EDFs from an econometric 

model. The econometric model I use is a logit model that uses financial ratios to predict 

the probability of bank failure (EDF). The model assumes that the probability of bank 

failure takes a logistic functional form and is, by definition, constrained to fall between 

0 and 1. The dependent variable, the log of the odds-ratio, is assumed to be linearly 

related to the explanatory variables (the financial ratios). 

The EDFs for all of the BIF- and SAIF-insured institutions are based upon EDF 

forecasts obtained from a standard “logistic” failure-prediction model. The model states 

that the likelihood of failure over a 12-month period is determined by the institution’s 

financial condition as of the start of the period. Financial condition is measured by 

capital adequacy, asset quality, earnings, and safety-and-soundness examination ratings. 

The data used to estimate the model were year-end condition data and subsequent failures 

between 1984 and 1997 for commercial and savings banks and thrifts. (Thrift data were 

available only between 1991 and 1997.) Table 9 shows the estimated relationships. This 

model is then used to predict EDFs on the basis of December 1999 Call Report and 

examination data. Exposure is adjusted to account for Oakar deposits (as described 

above). 

The first experiment replaces the EDFs in the baseline simulation with the EDFs 

generated by the logit model (see column 3 of Table 8). The average EDF produced by 

the logit model is much lower than the average EDF used in the baseline, but the standard 

22 
 

deviation is much higher. The EL for the BIF is much lower than the baseline—$338 

million compared with $1.081 billion. Similarly, the UL is much lower—$2.3 billion 

compared with $3.1 billion. In fact, when the EDFs generated by the logit model are 

used, the BIF (at the December 31, 2000, balance of $29.863 billion) would earn a rating 

of BBB+. Similarly, the EL and UL for the BIF and SAIF merged fund decrease, and the 

merged BIF and SAIF (at the December 31, 2000, balance of $40.591 billion) would earn 

a rating of BBB+. 

Now, instead of replacing all of the baseline EDFs with the EDFs generated by 

the logit model, I replace only the historical EDFs. The institutions with market 

information have EDFs from the mapping of credit ratings to EDFs provided by OWC. 

Again, the average EDF is much lower than the average EDF in the baseline simulation 

(see Table 8). The mix of market information and EDFs from the logit model shows that 

the BIF (at the December 31, 2000, balance of $29.863 billion) would earn a BBB+ 

rating, and the BIF and SAIF merged fund (at a December 31, 2000, balance of $40.591 

billion) would earn an A- rating (see Figures 4 and 5). 

Overall, using the EDFs generated by a logit model implies that risk to the 

insurance fund (as measured by the OWC credit-risk model) is lower than in the baseline 

simulation. The EDFs generated by the logit model are dependent on the financial 

condition of the insured institution at year-end 1999. Since most insured institutions 

were in very good financial condition relative to historical periods, it is not surprising that 

using this model yields lower measures of risk. 

23 
 

 

Expected Default Frequencies from Market Information 

In the baseline simulation, I mapped S&P and Moody’s ratings of long-term debt 

to EDFs using the OWC mapping. I performed a sensitivity analysis that replaced the 

ratings on long-term debt with ratings on long-term deposits. In addition, I looked to 

another source, KMV, which publishes EDFs and S&P ratings. 

Long-Term Deposit Ratings 

Long-term deposit ratings provided by Moody’s do not take into account the 

benefit of deposit insurance schemes that make payments to depositors.40 When a bank 

fails, the FDIC reimburses insured depositors and then stands in their place in the 

receivership. In contrast, debt holders are low in the priority of claimants on the 

receivership; only stockholders are below them. Thus, the long-term deposit rating 

produced by Moody’s measures risk that more closely mimics the risks incurred by the 

FDIC than debt ratings do. 

I collected credit ratings on long-term deposits from Bloomberg between 

September 14, 2000, and October 4, 2000. I matched the banks first by name to the list 

of S&P and Moody’s ratings provided to the FDIC by OWC.41 The sample contained 91 

BIF and 106 BIF and SAIF institutions with long-term deposit ratings. Although the 

number of institutions with long-term deposit ratings is smaller than the number of 

institutions with ratings in the baseline, institutions in the former group still account for 

40 Long-term deposits are deposits that have a maturity of over one year. 

41 In the data set, I included observations where the names exactly matched, or matches I was able to 

confirm using additional demographic information about the bank. 

24 
 

 

more than half of the total assets, total deposits, and total insured deposits in both the BIF 

alone and the BIF and SAIF merged fund (see Table 10). 

The simulation, which uses a combination of the EDFs from the long-term deposit 

ratings and the historical EDFs, results in slightly higher measured risk. The EL and UL 

both increase (see Table 11). The BIF (at a December 31, 2000, balance of 

$29.863 billion) would not earn a BBB rating. The merged fund (at a December 31, 

2000, balance of $40.591 billion) would earn a BBB rating (see Figures 6 and 7). 

Replacing long-term bond ratings with long-term deposit ratings results in a measure of 

risk that is slightly higher. 

Expected Default Frequencies from KMV 

KMV developed a model of default probability, Credit Monitor, that uses equity 

prices and financial statements. The model relates the market value of a firm’s assets 

(which is the sum of the market value of equity plus the market value of debts) to the 

probability of default.42 The KMV model is based on two theoretical relationships: 

(1) the value of equity can be viewed as a call option on the value of a firm’s assets, and 

(2) a link exists between the observable volatility of a firm’s equity value and the 

unobservable volatility of asset values. The model has three steps: (1) estimate the asset 

value and volatility, (2) calculate the distance to default, and (3) map the distance to 

default into the default probability. The market value of assets and the volatility of assets 

are generated by an option pricing model. Credit Monitor uses option pricing theory to 

derive the asset value and its volatility using the market value of equity, the volatility of 

42 See Crosbie (1997). 

25 
 

equity, and the book value of liabilities. Using the market value of assets, Credit Monitor 

then determines whether the market value of assets is above or below the default point. 

The default point—the asset value at which the firm will default—usually lies between 

total liabilities and short-term liabilities and differs from industry to industry. KMV 

calculates the distance to default (the market net worth which is the market value of the 

firm’s assets minus the firm’s default point divided by the product of the asset value and 

the asset volatility). The distance to default measures the number of standard deviations 

the asset value is away from default. KMV then maps the distance to default to the 

probability of default on the basis of empirical studies of default rates. 

Using a mapping between ticker symbols and bank certificate numbers, I assigned 

KMV EDFs to 119 BIF and SAIF institutions. These institutions account for 

approximately one-half of the total assets, total deposits, and total insured deposits in the 

BIF and in the BIF and SAIF merged (see Table 10). When the KMV EDFs are used in 

combination with the historical average EDF of 26 basis points, the average EDF is not 

much higher than the baseline (see Table 11). The standard deviation of the EDF, 

however, is much higher (over four times higher for BIF and three times higher for BIF 

and SAIF merged). 

The risk to the insurance funds, as measured by the OWC credit-risk model, 

increases dramatically when the KMV EDFs are used. The EL for the BIF increases 

from the baseline of $1.03 billion to $3.24 billion, and the UL increases from the baseline 

of $2.96 billion to $8.53 billion. The EL for the BIF and SAIF merged increases from a 

baseline of $1.35 billion to $4.04 billion; similarly the UL increases from the baseline of 

$3.97 billion to $10.10 billion. The balances in the BIF and in the BIF and SAIF merged 

fund are far below the balance required for a BBB credit rating (see Figures 6 and 7). 

26 
The KMV EDFs are based on equity prices, which tend to be volatile. The higher 

standard deviation of the EDFs had a large influence on the amount of risk measured by 

the OWC model, although the mean of the EDFs was approximately the same. 

Credit Ratings from KMV 

KMV also publishes credit ratings for long-term debt. I used the same mapping 

between ticker symbols and bank certificate numbers using June 2000 published data and 

matched 103 of the BIF and SAIF institutions (see Table 10). Again, these 

103 institutions account for more than one-half of the total assets, deposits, and insured 

deposits in both the BIF and the merged BIF and SAIF. I then mapped these credit 

ratings into EDFs with the OWC methodology that was used for the baseline simulations. 

When the EDFs from the KMV credit ratings and the historical 26 basis point 

EDF are combined, the mean of the EDF is not much different from the baseline; the 

standard deviation is slightly lower. The EL and UL increase slightly for both the BIF 

and the BIF and SAIF merged (see Table 11). The BIF (at the December 31, 2000, 

balance of $29.863 billion) would not earn a BBB rating. The BIF and SAIF merged 

fund (at the December 31, 2000, balance of $40.591 billion) would barely earn a BBB 

rating (see Figures 6 and 7). 

Overall, the sensitivity analysis using different methods of deriving EDFs did 

change the amount of risk measured by the OWC model—in some cases, dramatically. 

Including EDFs derived from a logit model resulted in lower risk than the baseline; it 

resulted in a BBB+ rating for the BIF and a BBB rating for the BIF and SAIF merged. 

When the EDFs from the S&P and Moody’s ratings were combined with the EDFs from 

the logit, the risk measured by the model was even lower—the BIF almost earned a 

27 
 

 

 

BBB+ (almost an A-) rating, and the BIF and SAIF merged earned an A- rating. In 

contrast, measured risk increased slightly when EDFs from long-term deposit ratings 

were used, and increased dramatically when EDFs from KMV were used. 

Sensitivity Analysis: Severity 

In the baseline simulation I defined severity as a 14-year weighted average loss 

rate calculated from the FDIC’s Failed Bank Cost Analysis.

43 However, losses incurred 

by the FDIC varied over time during that 14-year period. I performed sensitivity analysis 

using severity calculated over different time periods. More recently—specifically, 

between 1990 and 1998—losses were lower than over the entire 14-year period (see 

Table 12). The first simulation in the severity sensitivity analysis replaces the 14-year 

average with this more recent loss experience.44 The remaining simulations for the 

sensitivity analysis on severity involve averages over relatively low loss rate periods and 

relatively high loss rate periods. I chose the relatively high loss period, 1986–1989, and 

the relatively low loss period, 1990–1993, by examining the loss data and grouping the 

years accordingly. 

The first simulation run for sensitivity analysis replaces the 14-year average with 

a more recent loss experience: an average over 1990-1998. The mean of severity is lower 

over this period, and the standard deviation is much higher (see Table 13). Using the 

lower severity figures results in a lower EL and UL. The credit rating for the BIF (at the 

December 31, 2000, balance of $29.863) improves from below a BBB rating to an A 

43 The weighted average loss rate is calculated as the sum of losses divided by the sum of assets. Thus, the 

weights used for the average are the total assets of the institution. 

44 The sensitivity analysis for the BIF is performed on the baseline simulation with the Oakar adjustments. 

28 
 

rating (see Figure 8). Similarly, the credit rating for the BIF and SAIF merged fund (at 

the December 31, 2000, balance of $40.591) improves from BBB for the baseline 

simulation to A when the 1990–1998 severity figures are used. 

When the 14-year averages are replaced by the average severity in the relatively 

high-loss period, both the mean and the standard deviation of severity increase (see 

Table 13). The EL and the UL both increase when the 1986–1989 loss rates are used. In 

this high loss rate scenario, the BIF would have to be $43.806 billion to earn a BBB 

credit rating, and the BIF and SAIF merged would have to be $49.431 billion, well above 

the amount currently in the funds (see Figures 8 and 9). 

The simulation using the relatively low loss rates results in a lower EL and UL 

(see Table 13). In this scenario, the mean and standard deviation of severity are both 

lower than the baseline. At the December 31, 2000, balance ($29.863 billion), the BIF 

would earn an A credit rating under the low severity scenario; the BIF and SAIF merged 

($40.591 balance on December 31, 2000) would also earn an A credit rating (see Figures 

8 and 9). 

When the low loss rate period (1990–1993) is combined with the high loss rate 

period (1986–1989), the results are similar to the baseline. The EL and UL are slightly 

lower than the baseline. As in the baseline, the credit rating for the BIF would be below a 

BBB; the credit rating for the BIF and SAIF merged would be BBB (see Figure 8 and 9). 

As one would expect, when an average severity that is calculated from relatively 

high loss rate periods is used, the adequacy of the insurance funds drops. Conversely, 

when an average severity is calculated from a relatively low loss rate period, the 

adequacy of the insurance funds increases. What is important to note is how drastically 

the assessment of the adequacy of the insurance funds changes. Simply replacing 

29 
 

 

 

severity figures that are, on average, only a few percentage points lower, sends both the 

BIF and the BIF and SAIF merged funds from not earning even a BBB rating to earning 

an A rating. 

Sensitivity Analysis: Bucketing 

Bucketing, or grouping institutions into separate buckets, simplifies the estimation 

of the relationship between defaults of different institutions. Rather than estimating the 

relationship between defaults for individual institutions, bucketing the model can 

estimate the relationship between defaults for groups of institutions. This method 

assumes that institutions within the buckets have the same default correlations with 

institutions outside the buckets. Therefore, when one constructs buckets, it is best to 

group institutions that have similar default characteristics. 

In the baseline simulation, the 20 largest institutions were put into individual 

buckets, and five additional buckets group the remaining institutions by size. This 

bucketing scheme places particular emphasis on the largest institutions—the institutions 

that present the risk of high losses to the insurance fund at a low probability of 

occurrence. I conduct sensitivity analysis by grouping institutions, first using a naive 

grouping scheme and then using common characteristics that might cause them to 

weaken and fail together.45 

45 As above, all sensitivity analysis for the BIF is performed on the baseline simulation including the Oakar 

adjustments. 

30 
 

 

 

Equal Number of Institutions in Each Bucket, by Size 

The first simulation takes a naive approach and separates the institutions in the 

sample into 25 buckets, with an equal number of institutions in each bucket. The 

institutions are first sorted by size; so, for example, the 346 largest BIF institutions are in 

the first bucket, the next 346 largest BIF institutions are in the next bucket, and so on. 

This naive bucketing approach causes the measures of risk (EL and UL) to decrease (see 

Table 14). The measures of fund adequacy improves—the December 31, 2000, balance 

of $29.863 billion would earn a BBB rating for the BIF, and the BIF and SAIF merged 

balance of $40.591 billion would earn a BBB+ rating (see Figures 10 and 11). 

Size and Region 

During the banking crisis of the 1980s and early 1990s, bank failures tended to be 

concentrated by region.46 I separate institutions into buckets according to the five size 

categories used for the severity calculations and according to location in five regions of 

the United States: Northeast, Southeast, Central and Midwest, Southwest and West (see 

Table 15). The EL and UL again are smaller than in the baseline simulation (see Table 

14). Under this scenario, fund adequacy improves: at the December 31, 2000, fund 

balances, the BIF is rated BBB, and the BIF and SAIF merged fund is rated BBB+. 

46 Regional concentration may not be the case in the future, since the law now permits interstate banking. 

Thus, institutions may now diversify risk across regions. 

31 
 

 

CAMELS Rating Group and Region 

Institutions with similar supervisory ratings have similar default characteristics. 

In this simulation, I group banks by supervisory rating and by region. Supervisory, or 

CAMELS, ratings range from 1 to 5 (1 being the best). Each of the six components--

capital (C), asset quality (A), management (M), equity (E), liquidity (L), and sensitivity 

to market risk (S)—is rated separately; in addition, supervisors rate the overall health of 

the institution in a composite rating. Regulatory agencies consider institutions with 

composite ratings of 4 or 5 to be problem institutions. A component rating of 4 or 5 

indicates that the institution is having a severe problem in that particular component of its 

business. As of December 1999, most institutions had a composite rating of 1 or 2. 

Since most institutions are concentrated in composite ratings 1 and 2, I am unable 

to place institutions in 25 separate buckets using solely the information from the 

composite rating. Therefore, I create five CAMELS groups using information from the 

composite ratings and from the capital and asset component ratings. The five CAMELS 

groups are 

 CAMELS 1: Institutions with composite CAMELS ratings of 1. 

 Strong 2: Institutions with a composite CAMELS rating of 2 and a capital or asset 

component rating of 1 or 2. 

 Weak 2: Institutions with a composite CAMELS rating of 2 and a capital or asset 

component rating of 3, 4, or 5. 

 Strong 3: Institutions with a composite CAMELS rating of 3 and a capital or asset 

component rating of 1 or 2. 

32 
 

 Weak 3, 4 and 5: Institutions with a composite CAMELS rating of 3 and a capital or 

asset component rating of 3, 4, or 5, and institutions with composite CAMELS ratings 

of 4 or 5. 

Combining the five CAMELS groups with the five regions results in 25 buckets 

(see Table 16). Including CAMELS groups instead of size buckets leads to slightly lower 

measures of risk (a lower EL and a lower UL) (see Table 14). Accordingly, the fund 

adequacy measures improve. The December 31, 2000, balance of the BIF would earn a 

BBB rating, and the merged BIF and SAIF would earn an A- rating (see Figures 10 and 

11). 

CAMELS Rating Group and Size 

If I combine the CAMELS rating groups and size buckets, I am not able to 

populate all 25 buckets required by the OWC model. However, if I modify the two 

largest size categories to be $1 billion to $3 billion and over $3 billion, I am able to 

populate the buckets, but only for the BIF and SAIF merged fund (see Table 17). 

Combining the CAMELS groups with size rather than region results in slightly 

higher measures of risk (the EL and UL are higher) (see Table 14). Accordingly, the 

measures of fund adequacy are lower. The December 31, 2000, balance of the BIF and 

SAIF merged earns an A- rating. 

Specialized Lender and Region 

Banks with exposures to similar types of lending or banks with similar business 

lines are likely to experience difficulties at the same time. For example, if a drought 

33 
 

occurs, I would expect agricultural banks to begin having difficulties. Accordingly, I 

group banks into specialized lending groups, as follows:47 

 Agricultural Bank: Agricultural loans and agricultural real estate loans represent 

more than 25 percent of total loans. 

 Consumer Lender: This category includes both credit-card lenders and other 

consumer lenders. Consumer lenders are lenders whose residential real estate and 

consumer loans are more than 50 percent of total assets. Credit-card lenders are 

lenders whose credit-card loans plus securitized credit-card loans sold are greater than 

50 percent of total loans plus securitized credit-card loans sold and whose total loans 

plus securitized credit-card loans sold are greater than 50 percent of the sum of total 

assets plus securitized credit-card loans sold. 

 Commercial Lender: Commercial and industrial loans, construction loans, multiple 

family real estate loans, and nonresidential real estate loans are greater than 25 

percent of total assets. 

 Mortgage Lender: Residential real estate loans and mortgage-backed securities are 

greater than 50 percent of total assets. 

 Multinational Bank: Total assets are greater than $10 billion, and more than 25 

percent of total assets are held in foreign offices. 

 Other Large: Total assets are greater than $1 billion and the institution is not placed 

in one of the categories above. 

 Other Small Specialized: Total assets are less than or equal to $1 billion, and total 

loans are less than 40 percent of total assets. 

47 Ross Waldrop of the Division of Research and Statistics, FDIC, created these groupings. 

34 
 

 Other Small: Total assets are less than or equal to $1 billion, and the institution is not 

placed in one of the categories above. 

When I combine five of the specialized lenders (agricultural, consumer, 

commercial, mortgage, and multinational) with the regions, three buckets do not have any 

institutions in them (see Table 18). The remaining institutions are put into the three 

remaining groups by type: other large, other small specialized, and other small 

institutions. The measures of risk (EL and UL) are lower than in the simulations that use 

size or CAMELS groups with region groupings (see Table 14). Fund adequacy appears 

slightly worse in this scenario. At the December 31, 2000, balances, the BIF earns an Arating and the BIF and SAIF merged fund earns a BBB+ rating. 

Overall, sensitivity analysis conducted using changes in bucketing results in fund 

adequacy measures that fluctuate less widely than measures when other inputs are 

changed. The December 31, 2000, BIF balance is rated BBB for three of the four 

scenarios and BBB+ for the remaining scenario (specialized lender and region). The 

December 31, 2000, balance of the BIF and SAIF merged fund is rated BBB+ for four of 

the five scenarios and A- for the remaining scenario (region and CAMELS group). 

Further Research 

One area for further research is whether small and large banks should be 

segregated into separate risk portfolios. Small and large banks pose two very different 

types of risk to the FDIC. Small banks as a group pose a high probability of low losses, 

whereas large banks pose a small probability of high losses. In addition, the quality of 

data available to construct inputs that relate to the very large banks is lower than the 

quality of data available for small banks. For example, the historical data on losses 

35 
 

 

 

incurred from failures does not include information for any institution larger than $33 

billion. (The 25 largest institutions as of December 31, 1999, had an average of $159 

billion in total assets.) It may be possible to construct some ad hoc measure of how much 

a large bank would cost the FDIC to close, but such a measure would be just that—ad 

hoc. Another issue is the systemic-risk exception: some of the large banks in the 

portfolio may very well fall under the systemic-risk exception to the Least-Cost Test as 

spelled out by FDICIA. Since this exception has never been invoked, it is difficult to 

figure out how to measure severity in this scenario. 

Another area for future research relates to the application of these mappings 

between credit ratings and EDFs. First, is it appropriate to use the average default rate 

for each credit rating? If it is appropriate, should data from all industries be used to 

calculate the EDFs and then the resulting EDFs applied just to banks? 

The mapping of credit ratings to EDFs makes the implicit assumption that all 

institutions with the same credit rating have the same probability of failing and that this 

probability of failing is equal to the historical average default rate. Kealhofer et al. 

(1998) show that the actual default rate can differ significantly from the historical 

average default rate. Within a rating grade, the range of default rates is substantial, and 

the mean default rate can significantly exceed the median default rate (the mean may be 

almost twice the median). They conclude that the historical average default rate is a 

noisy estimate of the actual mean. As such, the historical EDF is a noisy estimate of the 

probability of default for any given institution. 

If the given institution is a bank, an additional issue arises when historical EDFs 

are used from all industries. Using these mappings of credit ratings to expected default 

frequency may not be appropriate for the banking sector. If banks have systematically 

36 
 

 

different default risks than other corporate borrowers that are assigned the same credit 

rating, the mapping may introduce bias in the assignment of expected default frequencies. 

There is reason to believe that this is the case, since banking is a regulated industry. In 

contrast to most other industries, bank default is a regulatory event: the chartering 

authority closes a bank. And creditors of a bank are given a different priority to receive 

payment from the receivership than creditors of a corporation that goes into bankruptcy. 

Evidence presented by Nickell, Perraudin, and Varotto (2000) shows that banks 

have less stable ratings than industrials. BIS (2000) adds further doubt that the EDFs 

from other industrial sectors should be applied to the banking sector. The BIS study 

suggests that U.S. banks experience a higher default rate than U.S. industrial firms for a 

given Moody’s rating in a given year. Since this suggests that the true relationship 

between credit ratings and expected default frequencies may be different for banks than 

for other corporate entities, it would be useful to construct a mapping for the banking 

industry alone.48 

Certainly I have not exhausted the possibilities for sensitivity analysis. I could 

use more information, such as financial ratios, to form buckets. And, I have conducted 

sensitivity analysis of the OWC model only under the following conditions: random 

severity, one state, with five factors. Any of these assumptions can be changed for a 

more thorough investigation of the model’s sensitivity to inputs. 

I also see some areas in which the model can be extended that may prove useful to 

the FDIC for risk assessment. As it currently stands, the OWC model is a static model 

48 Of course, this study would also encounter problems. The amount of data available is much smaller for 

defaults in an individual industry than for defaults in a group of industries. The lack of data may be so 

severe as to make the study unreliable. Another problem this type of study would face is controlling for 

legislative changes to bank closing procedures, especially the changes made by FDICIA in 1991. 

37 
 

 

 

evaluating fund adequacy for only one period. However, there are dynamic implications 

to fund adequacy (see Sheehan [1998] and Oshinsky [1999]). The model’s response to 

multiyear simulations over the cycle and to stress testing also provides interesting 

research possibilities. 

Another extension would address the issue of large fluctuations in insured 

deposits. Since data limitations allow me to measure exposure only in terms of total 

assets, I ignore this effect. Recently, investment companies have been able to convert 

some of their customer accounts very quickly into FDIC-insured accounts. This implies 

that insured deposits, and thus the exposure of the insurance funds, can change. 

Unfortunately, the OWC model is unable to take this into consideration. However, there 

may be a way to extend the model, using more complicated techniques that are analogous 

to how credit-related optionality (loan commitments and lines of credit) is treated in other 

credit models. 

Another extension of the model that might be useful to the FDIC is to look at 

multistate credit-risk models. These models look at migration of credits across credit 

classes. The analogy for the FDIC would be to look at the migration of banks across 

different risk categories. This would enable the FDIC to track the source of the shifts in 

risk. 

In an early version of documentation for CreditMetrics, J. P. Morgan stated, 

“...almost any risk measurement system is better at stating relative rather than absolute 

risk.”49 Given the amount of uncertainty in the model parameters, it would not be 

prudent to use the models for any application that required an absolute measure. Credit49 J. P. Morgan (1997), 15. This quotation is from an early version of the document and is no longer 

included in the current version available on J. P. Morgan’s web site. 

38 
risk models, however, are useful for measuring both the relative riskiness of portfolios 

under differing circumstances and the contribution of individual credits to the overall 

riskiness of the portfolio. 

Conclusions 

As measured by the OWC credit-risk model, the credit rating of the FDIC is very 

sensitive to different assumptions about the expected default frequencies and the severity 

of losses. Under one set of assumptions the FDIC would not warrant a BBB rating, 

whereas under another set the FDIC would warrant an A rating. 

The OWC model is sensitive to changes in the EDFs. When six different sets of 

EDFs were used, the credit rating for the December 31, 2000, BIF balance ranged from 

requiring $54.163 billion in additional capital to earn a BBB rating to earning an Arating with no additional capital. The credit rating for the December 31, 2000, BIF and 

SAIF balances ranged from requiring $58.862 billion to earn a BBB rating to earning an 

A- rating at current capital levels. 

The model was most sensitive to changes in severity. When average severity 

from recent periods and periods of low loss rates was used, the BIF and the BIF and SAIF 

merged funds were both rated A. When average severity from high loss rate periods was 

used both the BIF and the BIF and SAIF merged funds would not be investment grade. 

In the latter case, the BIF and the BIF and SAIF merged required $13.943 billion and 

$8.841 billion, respectively, to be rated BBB. 

The OWC model was less sensitive to changes in alternative bucketing 

techniques. Fund adequacy measures for the BIF did not change much: the BIF was rated 

BBB in all but one scenario, where it earned BBB- (specialized lender and region 

39 
bucketing). The bucketing scheme had more of an effect on the fund adequacy measures 

for BIF and SAIF merged: the BIF and SAIF merged fund was rated BBB+ under all but 

one scenario, where it was rated ‘A-’ (region and CAMELS group). 

The model developed by OWC for the FDIC provides useful quantitative 

information about the risks faced by the deposit insurance funds and the adequacy of the 

funds. As part of the deposit insurance reform debate, there have been recommendations 

to eliminate the 1.25 designated reserve ratio and replace it with a wider band of accepted 

level of capitalization in the deposit insurance funds. Results from the model may be 

useful information to incorporate into a determination of acceptable levels of 

capitalization. However, this information must be used with caution because, as I have 

demonstrated with the sensitivity analysis, the model results can fluctuate rather 

dramatically under different reasonable assumptions. 

40 
References 

Bank for International Settlements (BIS). 2000. Credit Ratings and Complementary 

Sources of Credit Quality Information. BASEL Committee on Banking 

Supervision Working Papers. 

———. 1999. Credit-Risk Modeling: Current Practices and Applications. BASEL 

Committee on Banking Supervision. 

Brand, Leo, and Reza Bahar. 2000. Ratings Performance 1999. Standard and Poor’s. 

Carey, Mark, and Mark Hrycay. 2001. Parameterizing Credit-Risk Models with Rating 

Data. Journal of Banking and Finance 25, no. 1:197–270. 

Crosbie, Peter. 1997. Modeling Default Risk. KMV Corporation. 

Federal Deposit Insurance Corporation (FDIC). 2000. Options Paper. 

Gordy, Michael B. 2000. A Comparative Anatomy of Credit-Risk Models. Journal of 

Banking and Finance 24, no 1:119–49. 

Hanweck, Gerald. 2000. Interpreting the Model Development and Output Outlined in 

“Modeling the Cumulative Loss Distribution.” FDIC. Unpublished Paper. 

Jones, David, and John Mingo. 1999. Credit-Risk Modeling and Internal Capital 

Allocation Processes: Implications for a Models-Based Regulatory Bank Capital 

Standard. Journal of Economics and Business 51, no 2:79–108. 

———. 1998. Industry Practices in Credit-Risk Modeling and Internal Capital 

Allocations. Federal Reserve Bank of New York. Economic Policy Review 4, no 

3:53–60. 

J. P. Morgan. 1997. CreditMetrics—Technical Document. 

Kealhofer, Stephen, Sherry Kwok, and Wenlong Weng. 1998. Uses and Abuses of Bond 

Default Rates. KMV Corporation. 

Keenan, Sean C., David T. Hamilton, and Alexandra Berthault. 2000. Historical Default 

Rates of Corporate Bond Issuers, 1920–1999. Moody’s Investors Service. 

Koyluoglu, H. Ugur, and Andrew Hickman. 1998a. A Generalized Framework for 

Credit Risk Portfolio Models. 

——. 1998b. Reconcilable Differences. Risk 11, no 10:56–62. 

41 
Nickell, Pamela, William Perraudin, and Simone Varotto. 2000. Stability of Rating 

Transitions. Journal of Banking and Finance no 24:203–27. 

Nuxoll, Daniel A. 1999. Internal Risk-Management Models as a Basis for Capital 

Requirements. FDIC Banking Review 12, no 1:18–29. 

Oliver, Wyman & Company, LLC. 2000a. Modeling the Cumulative Loss Distribution 

Discussion Notes. August 24. Confidential. 

———. 2000b. Modeling the Cumulative Loss Distribution. Discussion Notes. 

August 18. Confidential. 

———. 2000c. Modeling the Cumulative Loss Distribution. August 2. Confidential. 

———. 2000d. Analyzing Policy Options for Deposit Insurance Reform. July 12. 

Confidential. 

Ong, Michael K. 1999. Internal Credit Risk Models: Capital Allocation and 

Performance Measurement. Risk Books. 

Oshinsky, Robert. 1999. Merging the BIF and the SAIF: Would the Merger Improve the 

Funds’ Viability? FDIC Working Paper 99-4. 

Sheehan, Kevin P. 1998. Capitalization of the Bank Insurance Fund. FDIC Working 

Paper 98-1. 

42 
 

Table 1 

Comparison of Rating Calibrations with Standard and Poor’s 

Historical Default Rates 

Historical One-Year Default Rates, Oliver, Wyman & Company OneStandard and Poor’s Rating 1981–1999 Year Default Probability 

AAA 0.00% 0.01% 

AA+ 0.00 0.02 

AA 0.00 0.03 

AA- 0.03 0.04 

A+ 0.02 0.05 

A 0.05 0.07 

A- 0.03 0.09 

BBB+ 0.13 0.13 

BBB 0.22 0.18 

BBB- 0.29 0.31 

BB+ 0.57 0.53 

BB 0.89 0.93 

BB- 1.14 1.57 

B+ 2.66 2.64 

B 8.46 4.46 

B- 10.19 7.52 

Sources: Historical one-year default rates, 1981–1999, are from Brand and Bahar (2000), 15; Oliver, Wyman & 

Company one-year default probabilities from FDIC (2000), 29. 

43 
 

Table 2 

Comparison of Rating Calibrations with Moody’s Historical Default Rates 

Historical One-Year Default Rates, Oliver, Wyman & Company OneMoody’s Rating 1983–1999 Year Default Probability 

Aaa 0.00% 0.01% 

Aa1 0.00 0.02 

Aa2 0.00 0.03 

Aa3 0.07 0.04 

A1 0.00 0.05 

A2 0.00 0.07 

A3 0.00 0.09 

Baa1 0.04 0.13 

Baa2 0.07 0.18 

Baa3 0.31 0.34 

Ba1 0.62 0.63 

Ba2 0.53 1.21 

Ba3 2.52 2.25 

B1 3.46 4.21 

B2 6.88 7.86 

B3 12.23 12.95 

Sources: Historical one-year default rates, 1983-1999, are from Keenan et al. (2000), 27; Oliver, Wyman & Company 

one-year default probabilities from FDIC (2000), 29. 

44 
Table 3 

Descriptive Statistics for Baseline Simulations 

Mean and Standard Deviation 

Simulation Exposure 

Number of (Total Assets) Expected Default 

Institutions (000 omitted) Frequency (EDF) Severity Bucket 

BIF 8,638 $687,856 

(9,207,674) 

BIF with Oakar 8,638 $637,120

 Adjustment (8,625,601) 

BIF and SAIF Merged 9,990 $683,657 

(8,733,580) 

Note: Buckets are numbered 1 through 25. 

0.2575% 

(0.00022) 

0.2575 

(0.00022) 

0.2581 

(0.00031) 

22.67% 

(0.0302) 

22.67 

(0.0302) 

22.57 

(0.0311) 

24.41 

(1.10) 

24.41 

(1.10) 

24.37 

(1.08) 

45 
Table 4 

Rating Calibrations 

Standard & Poor’s Credit One-Year Default One-Year Default 

Rating Probability Moody’s Credit Rating Probability 

AAA 0.01% Aaa 0.01% 

AA+ 0.02 Aa1 0.02 

AA 0.03 Aa2 0.03 

AA- 0.04 Aa3 0.04 

A+ 0.05 A1 0.05 

A 0.07 A2 0.07 

A- 0.09 A3 0.09 

BBB+ 0.13 Baa1 0.13 

BBB 0.18 Baa2 0.18 

BBB- 0.31 Baa3 0.34 

BB+ 0.53 Ba1 0.63 

BB 0.93 Ba2 1.21 

BB- 1.57 Ba3 2.25 

B+ 2.64 B1 4.21 

B 4.46 B2 7.86 

B- 7.52 B3 12.95 

Source: FDIC (2000), 29. 

Note: The one-year default probabilities reflect the methodology of Oliver, Wyman & Company. 

46 
 

 

 

 

 

Table 5 

Severity and the Standard Deviation of Severity 

1986–1998 

Number of Standard Deviation of 

Asset Size Observations Mean of Severitya Severitya 

Less than $100 million 967 24.18% 13.78 

$100 million–$500 million 120 22.39 12.97 

$500 million–$1 billion 15 16.46 10.60 

$1–5 billion 22 12.79 8.45 

Larger than $5 billion 9 8.75 6.93 

Source: FDIC, Failed Bank Cost Analysis, 1986–1998, and consolidation of receiverships as performed by the FDIC Division of 

Finance. 

a

 The mean and standard deviation of the loss as a percentage of assets for individual institutions within the asset size group. 

47 
Table 6 

Size Distribution of BIF and SAIF Institutions in Sample 

as of December 31, 1999 

Asset Size BIF SAIF Total 

Less than $100 million 5,030 584 5,614 

$100 million–$500 million 2,854 567 3,421 

$500 million–$1 billion 334 89 423 

$1–5 billion 283 87 370 

Larger than $5 billion 137 25 162

 Total 8,638 1,352 9,990 

48 
Table 7 

Results from Baseline Simulations 

BIF Only 

(000 omitted) 

Baseline Baseline without Oakar Adjustment Oliver, Wym

Expected Loss (EL) $1,029,281 $1,081,123 

Unexpected Loss (UL) $2,964,964 $3,122,898 Solvency ($30 Billion) 99.82% 99.80% 

Solvency ($40 Billion) 99.91% 99.89% A Rating Solvency $44,730,822 $47,679,389 

A- Rating Solvency $40,281,094 $42,809,475 BBB+ Rating Solvency $33,966,694 $35,607,379 BBB Rating Solvency $30,126,141 $31,343,388 BIF Balance 12/31/2000 $29,863,000 $29,863,000 

BIF and SAIF Merged 

(000 omitted) 

Baseline Oliver, Wym

Expected Loss (EL) $1,348,092 

Unexpected Loss (UL) $3,967,074 

Solvency ($30 Billion) 99.74% Solvency ($40 Billion) 99.85% A Rating Solvency $55,106,919 A- Rating Solvency $50,532,935 

BBB+ Rating Solvency $42,725,025 

BBB Rating Solvency $35,584,250 BIF and SAIF Balance 12/31/2000 $40,591,000 

a Analyzing Policy Options for Deposit Insurance Reform: Phase II (Oliver, Wyman & Company, LLC, September 2000), 16. 

49 
Table 8 

Comparison of Expected Default Frequencies 

BIF Only 

Baseline Historical EDFs Logit EDFs Only S&P and 

Expected Loss (EL) $1,029,281 $1,639,147 $338,418 $3

Unexpected Loss (UL) $2,964,964 $5,130,944 $2,317,682 $2,Solvency ($30 Billion) 99.82% 99.44% 99.87% 9

Solvency ($40 Billion) 99.91% 99.67% 99.92% 9

A Rating Solvency $44,730,823 $76,840,452 $41,828,549 $35A- Rating Solvency $40,281,094 $71,624,047 $36,347,644 $30BBB+ Rating Solvency $33,966,695 $61,482,048 $29,501,005 $25

BBB Rating Solvency $30,126,141 $52,226,188 $25,262,962 $20

BIF Balance 12/31/2000 $29,863,000 $29,863,000 $29,863,000 $29Mean of EDF 0.2575% 0.2600% 0.0589% 0.

Standard Deviation of EDF 0.00022 n.a. 0.000033 0.0

BIF and SAIF Merged 

Baseline Historical EDFs Logit EDFs Only S&P an

Expected Loss (EL) $1,348,092 $2,033,287 $484,328 $

Unexpected Loss (UL) $3,967,074 $6,187,109 $3,214,885 $3Solvency ($30 Billion) 99.74% 99.25% 99.82% 9

Solvency ($40 Billion) 99.85% 99.56% 99.88% 9

A Rating Solvency $55,106,919 $92,763,008 $51,669,367 $43

A- Rating Solvency $50,532,935 $83,345,074 $46,162,110 $38

BBB+ Rating Solvency $42,725,025 $71,136,979 $36,902,057 $32

BBB Rating Solvency $35,584,250 $60,994,320 $29,650,221 $26

BIF and SAIF Balance $40,591,000 $40,591,000 $40,591,000 $40

 12/31/2000 Mean of EDF 0.2581% 0.2600% 0.0708% 0

Standard Deviation of EDF 0.00031 n.a. 0.000125 0

50 
 

Table 9 

Logistic Regression of the Incidence of Failure One Year Following Condition Measurement 

(1984–1997 year-end Call Data) 

Explanatory Variable Coefficient Estimate (Standard Error) 

Intercept -6.6763 (0.2352)* 

Equity plus loss reserves -0.3847 (0.0140)* 

Loans past due 30–89 days 0.1321 (0.0152)* 

Loans past due 90 days or more 0.1224 (0.0070)* 

Gross loan charge-offs -0.0507 (0.0121)* 

Net income -0.1961 (0.0097)* 

Capital rating 0.1814 (0.0670)* 

Asset rating 0.2492 (0.0658)* 

Management rating 0.3406 (0.0558)* 

Earnings rating 0.0084 (0.0587) 

Liquidity rating 0.3802 (0.0463)* 

“Age” of examination data 0.6644 (0.0354)* 

Pseudo R Squared = 57% 

Somers' D = 0.953 

* Significant at the 1% confidence level. 

51 
Table 10 

Coverage of Market Data 

BIF Only 

S

Total 

&P and Moody's 

Baseline 

Long-Term Deposit 

Ratings KMV EDFs 

Number 8,638 123 92 107 Total Oakar Adjusted Assets (000 omitted) $5,941,700,000 

Percent of Total Oakar Adjusted Assets 65.46% 55.13% 55.07% 

Total Deposits (000 omitted) $3,964,400,000 

Percent of Total Deposits 63.99% 53.75% 53.24% 

Total Insured Deposits (000 omitted) $2,361,800,000 

Percent of Total Insured Deposits 55.85% 47.87% 51.15% 

BIF and SAIF Merged 

S&P and Moody's Long-Term Deposit 

Total Baseline Ratings KMV EDFs 

Number 9,990 146 106 119 

Total Assets (000 omitted) $6,829,700,000 

Percent of Total Assets 63.35% 51.23% 51.94% 

Total Deposits (000 omitted) $4,506,300,000 

Percent of Total Deposits 61.36% 50.00% 50.06% 

Total Insured Deposits (000 omitted) $2,849,000,000 

Percent of Total Insured Deposits 53.42% 43.45% 47.00% 

52 
Table 11 

Comparison of Market Information 

BIF Only 

Baseline EDFS from Deposit Ratings EDFs from KMV KM

Expected Loss (EL) $1,029,281 $1,130,759 $3,241,537 Unexpected Loss (UL) $2,964,964 $3,469,460 $8,531,030 Solvency ($30 Billion) 99.82% 99.71% 98.43% Solvency ($40 Billion) 99.91% 99.84% 99.04% A Rating Solvency $44,730,823 $52,669,028 $117,729,928 A- Rating Solvency $40,281,094 $50,391,163 $106,984,102 

BBB+ Rating Solvency $33,966,695 $43,999,126 $93,874,997 BBB Rating Solvency $30,126,141 $37,368,571 $84,026,021 

BIF Balance 12/31/2000 $29,863,000 $29,863,000 $29,863,000 Mean of EDF 0.2575% 0.2581% 0.2680% 

Standard Deviation of EDF 0.00022 0.00019 0.00095 

BIF and SAIF Merged 

Baseline EDFs from Deposit Ratings EDFs from KMV K

Expected Loss (EL) $1,348,092 $1,422,982 $4,036,797 

Unexpected Loss (UL) $3,967,074 $4,216,838 $10,095,162 

Solvency ($30 Billion) 99.74% 99.66% 97.85% 

Solvency ($40 Billion) 99.85% 99.84% 98.66% A Rating Solvency $55,106,919 $57,845,132 $133,540,821.19 A- Rating Solvency $50,532,935 $52,406,777 $127,289,519.36 

BBB+ Rating Solvency $42,725,025 $44,213,931 $111,200,218.98 BBB Rating Solvency $35,584,250 $38,751,914 $99,452,835.69 BIF and SAIF Balance 12/31/2000 $40,591,000 $40,591,000 $40,591,000 Mean of EDF 0.2581% 0.2584% 0.2677% 

Standard Deviation of EDF 0.00031 0.00032 0.00093 

53 
Table 12 

Severity 

Mean, Standard Deviation, and Number of Observations 

1986–1989 and 

Asset Size Group 1986–1998 1990–1998 1986–1989 1990–1993 1990–1993 

Less than $100 Million 24.18% 20.30% 26.28% 20.37% 24.28% 

(13.78) 

n = 967 

(12.17) 

n = 339 

(14.15) 

n = 628 

(12.21) 

n = 322 

(13.81) 

n = 950 

$100 Mil.–$500 Mil. 22.39% 20.23% 26.70% 20.67% 22.89% 

(12.97) 

n = 120 

(12.33) 

n = 80 

(13.29) 

n = 40 

(12.21) 

n = 69 

(12.85) 

n = 109 

$500 Mil.–$1 Bil. 16.46% 17.96% 14.21% 17.96% 16.46% 

(10.59) 

n = 15 

(10.18) 

n = 9 

(11.76) 

n = 6 

(10.18) 

n = 9 

(10.59) 

n = 15 

$1–$5 Billion 12.79% 12.20% 14.81% 12.20% 12.79% 

(8.45) 

n = 22 

(8.19) 

n = 17 

(10.02) 

n = 5 

(8.19) 

n = 17 

(8.45) 

n = 22 

Larger than $5 Billion 8.75% 

(6.93) 

n = 9 

4.43% 

(4.91) 

n = 5 

14.15% 

(5.10) 

n = 4 

4.43% 

(4.91) 

n = 5 

8.75% 

(6.93) 

n = 9 

All Size Groups 23.55% 

(13.71) 

n = 1,133 

19.75% 

(12.15) 

n = 450 

26.05% 

(14.11) 

n = 683 

19.85% 

(12.16) 

n = 422 

23.68% 

(13.73) 

n = 1,105 

Source: FDIC, Failed Bank Cost Analysis, 1986–1998. 

Note: Severity is defined as the loss to the FDIC as a percentage of total assets at failure. 

54 
Table 13 

Comparison of Severity 

Expected Loss (EL) Unexpected Loss (UL) 

Baseline 

$1,029,281 

$2,964,964 

BIF Only 

1990–1998 FBCA Loss 1986–1989 FBCA Loss 

$831,740 $1,304,806 

$2,043,576 $4,097,239 

1990–1993 FBCA Los

$838,6

$2,054,7

Solvency ($30 Billion) Solvency ($40 Billion) 

99.82% 99.91% 

99.94% 99.98% 

99.63% 99.78% 

99.9399.98

A Rating Solvency A- Rating Solvency BBB+ Rating Solvency BBB Rating Solvency 

$44,730,823 

$40,281,094 

$33,966,695 

$30,126,141 

$29,088,866 

$26,273,941 

$22,930,585 

$19,322,538 

$68,411,002 

$61,286,866 

$51,332,350 

$43,805,777 

$29,267,8

$26,469,1

$23,005,9

$19,489,8

BIF Balance 12/31/2000 $29,893,000 $29,893,000 $29,893,000 $29,893,0Mean of Severity Standard Deviation of Severity Expected Loss (EL) Unexpected Loss (UL) 

22.67% 

0.0302 

Baseline 

$1,348,092 

$3,967,074 

19.67% 25.38% 

0.0244 0.0340 

BIF and SAIF Merged 

1990–1998 1986–1989 

FBCA Loss Rates FBCA Loss Rates 

$1,088,398 $1,698,828 

$2,770,582 $5,185,556 

19.86

0.02

1990–1993 

FBCA Loss Rates 

$1,096,96

$2,783,73

Solvency ($30 Billion) Solvency ($40 Billion) 

99.74% 99.85% 

99.89% 99.94% 

99.52% 99.71% 

99.8999.94

A Rating Solvency A- Rating Solvency BBB+ Rating Solvency BBB Rating Solvency 

$55,106,919 $50,532,935 

$42,725,025 

$35,584,250 

$36,864,877 $33,439,131 

$28,069,456 

$24,261,820 

$80,947,302 $67,808,472 

$57,599,839 

$49,431,794 

$37,071,417.3$33,504,511.0

$28,284,784.9

$24,403,095.2

BIF and SAIF Balance 12/31/2000 $40,591,000 $40,591,000 $40,591,000 $40,591,00

Mean of Severity Standard Deviation of Severity 

22.57% 

0.0312 

19.62% 

0.0251 

25.29% 

0.0354 

19.81

0.025

55 
Table 14 

Comparison of Bucketing Techniques 

BIF Only 

Baseline 25 Equal-Sized Buckets Size and Region Buckets Region and CAMELS Group 

Expected Loss (EL) $1,029,281 $1,022,313 $1,021,277 $1,018,609 

Unexpected Loss (UL) $2,964,964 $2,850,705 $2,904,048 $2,672,266 Solvency ($30 Billion) 99.82% 99.85% 99.85% 99.86% 

Solvency ($40 Billion) 99.91% 99.94% 99.92% 99.94% 

A Rating Solvency $44,730,823 $37,928,519 $41,120,109 $38,270,777 

A- Rating Solvency $40,281,094 $34,607,657 $37,073,875 $36,126,245 

BBB+ Rating Solvency $33,966,695 $31,726,703 $32,072,389 $30,502,680 

BBB Rating Solvency $30,126,141 $27,567,381 $28,096,159 $26,438,022 

BIF Balance 12/31/2000 $29,863,000 $29,863,000 $29,863,000 $29,863,000 

BIF and SAIF Merged 

Baseline 25 Equal-Sized Buckets Size and Region Buckets Region and CAMELS Group 

Expected Loss (EL) $1,348,092 $1,358,606 $1,318,140 $1,322,520 

Unexpected Loss (UL) $3,967,074 $4,112,536 $3,332,633 $3,147,276 

Solvency ($30 Billion) 99.74% 99.81% 99.82% 99.83% 

Solvency ($40 Billion) 99.85% 99.90% 99.91% 99.92% 

A Rating Solvency $55,106,919 $50,094,404 $43,968,687 $42,337,006 

A- Rating Solvency $50,532,935 $41,029,174 $41,190,330 $38,340,234 

BBB+ Rating Solvency $42,725,025 $35,556,210 $34,266,907 $33,966,022 

BBB Rating Solvency $35,584,250 $30,349,565 $30,445,176 $29,523,589 BIF and SAIF Balance 12/31/2000 $40,591,000 $40,591,000 $40,591,000 $40,591,000 

56 
Table 14 (continued) 

Comparison of Bucketing Techniques 

BIF Only 

Specialized Lender 

Baseline and Region 

Expected Loss (EL) $1,029,281 $1,011,899 

Unexpected Loss (UL) $2,964,964 $2,669,365 Solvency ($30 Billion) 99.82% 99.88% Solvency ($40 Billion) 99.91% 99.93% A Rating Solvency $44,730,823 $39,197,578 A- Rating Solvency $40,281,094 $33,656,518 BBB+ Rating Solvency $33,966,695 $28,535,282 BBB Rating Solvency $30,126,141 $25,375,685 

BIF Balance 12/31/2000 $29,863,000 $29,863,000 

BIF and SAIF Merged 

Specialized Lender 

Baseline and Region 

Expected Loss (EL) $1,348,092 $1,342,231 

Unexpected Loss (UL) $3,967,074 $3,425,842 

Solvency ($30 Billion) 99.74% 99.79% 

Solvency ($40 Billion) 99.85% 99.89% 

A Rating Solvency $55,106,919 $46,895,982 

A- Rating Solvency $50,532,935 $42,561,018 

BBB+ Rating Solvency $42,725,025 $37,820,884 

BBB Rating Solvency $35,584,250 $33,177,356 BIF and SAIF Balance 12/31/2000 $40,591,000 $40,591,000 

57 
Table 15 

Size and Region Buckets 

BIF Institutions 

Central and 

Northeast Southeast Midwest Southwest West T

Less than $100 Million 213 673 2,757 944 443 

$100–$500 Million 490 565 1,045 422 332 

$500 Mil.–$1 Billion 92 49 111 37 45 

$1–$5 Billion 97 45 65 21 55 More than $5 Billion 45 27 37 10 18  Total 937 1,359 4,015 1,434 893 

BIF and SAIF Institutions 

Central and 

Northeast Southeast Midwest Southwest West T

Less than $100 Million 341 777 3,027 1,003 466 

$100–$500 Million 641 666 1,275 460 379 

$500 Mil.–$1 Billion 115 67 138 42 61 

$1–$5 Billion 120 60 91 29 70 More than $5 Billion 47 29 46 13 27  Total 1,264 1,599 4,577 1,547 1,003 

Note: The Northeast region includes the following states: Connecticut, Delaware, District of Columbia, Maine, Maryland, Massachusetts, New Hampshire, New Jersey, New York, Pennsylvania, Rhode Island, and Vermont. ThSoutheast region includes the following states: Alabama, Florida, Georgia, Mississippi, North Carolina, South CaroTennessee, Virginia, and West Virginia. The Central and Midwest region includes the following states: Illinois, IndIowa, Kansas, Kentucky, Michigan, Minnesota, Missouri, Nebraska, North Dakota, Ohio, South Dakota, and WiscoThe Southwest region includes the following states: Arkansas, Louisiana, New Mexico, Oklahoma, and Texas. The includes the following states: Alaska, Arizona, California, Colorado, Hawaii, Idaho, Montana, Nevada, Oregon, UtaWashington, and Wyoming. 

58 
Table 16 

CAMELS Group and Region Buckets 

BIF Institutions 

Central and 

Northeast Southeast Midwest Southwest West Total 

CAMELS 1s 433 498 1,837 713 280 3,761 

Strong 2s 406 699 1,804 562 470 3,941 

Weak 2s 51 81 214 63 72 481 

Strong 3s 30 56 123 62 50 321 

Weak 3s, 4s and 5s 17 25 37 34 21 134

 Total 937 1,359 4,015 1,434 893 8,638 

BIF and SAIF Institutions 

Central and 

Northeast Southeast Midwest Southwest West Total 

CAMELS 1s 556 584 2,072 754 308 4,274 

Strong 2s 567 814 2,047 617 529 4,574 

Weak 2s 72 97 248 65 78 560 

Strong 3s 47 71 161 70 63 412 

Weak 3s, 4s and 5s 22 33 49 41 25 170

 Total 1,264 1,599 4,577 1,547 1,003 9,990 

59 
Table 17 

CAMELS Group and Size Buckets 

BIF and SAIF Institutions 

Less than $100 Mill– $500 Mill– $1 Bill– More than 

$100 Million $500 Mill $1 Bill $3 Bill $3 Bill Total 

CAMELS 1s 2,208 1,603 219 143 101 4,274 

Strong 2s 2,671 1,482 176 134 111 4,574 

Weak 2s 352 174 15 15 4 560 

Strong 3s 263 124 7 11 7 412 

Weak 3s, 4s and 5s 120 38 6 5 1 170

 Total 5,614 3,421 423 308 224 9,990 

60 
Table 18 

Asset Concentration and Region Buckets 

BIF Institutions 

Central and 

Northeast Southeast Midwest Southwest West 

Agricultural Bank 1 55 1,608 304 125 

Consumer Lender 48 72 139 25 33 Commercial Lender 361 774 1,199 491 588 

Mortgage Lender 246 28 86 26 27 

Multinational Bank 7 n.a. 1 n.a. n.a. 

Other Large Lenders n.a. n.a. n.a. n.a. n.a. 

Other Small Specialized Lenders n.a. n.a. n.a. n.a. n.a. Other Small Institutions n.a. n.a. n.a. n.a. n.a. 

BIF and SAIF Institutions 

Central and 

Northeast Southeast Midwest Southwest West 

Agricultural Bank 1 55 1,613 307 125 

Consumer Lender 54 81 156 32 37 

Commercial Lender 392 845 1,297 512 638 

Mortgage Lender 509 166 493 96 78 Multinational Bank 7 n.a. 1 n.a. n.a. 

Other Large Lenders n.a. n.a. n.a. n.a. n.a. Other Small Specialized Lenders n.a. n.a. n.a. n.a. n.a. Other Small Institutions n.a. n.a. n.a. n.a. n.a. 

61 
Figure 1 

Credit Loss Distribution 

Probability of Loss 

Loss 
Figure 2 

Baseline Simulations 

BIF 

Baseline Baseline without Oakar Adjustment Oliver, Wyman & Co

$0 

$10,000,000 $20,000,000 $30,000,000 $40,000,000 $50,000,000 $60,000,000 

Funds Required for Rating (000 omitted) 

BIF Balance 12/31/2000 

$29.863 billion 
Figure 3 

Baseline Simulations 

BIF and SAIF Merged 

Baseline Oliver, Wyman & Company Resul

$0 

$10,000,000 $20,000,000 $30,000,000 $40,000,000 $50,000,000 $60,000,000 

Funds Required for Rating (000 omitted) 

BIF and SAIF Balance 

12/31/2000 

$40.591 billion 
Figure 4 

Sensitivity Analysis: Expected Default Frequencies 

BIF 

Baseline Historical EDFs Logit EDFs S&P and Logit EDFs 

$0 

$10,000,000 $20,000,000 $30,000,000 $40,000,000 $50,000,000 $60,000,000 $70,000,000 $80,000,000 $90,000,000 

Funds Required for Rating (000 omitted) 

A ABBB+ BBB 

BIF Balance 12/31/2000 

$29.863 billion 
Funds Required for Rating (000 omitted) 

$100,000,000 

$90,000,000 $80,000,000 $70,000,000 $60,000,000 $50,000,000 $40,000,000 $30,000,000 $20,000,000 $10,000,000 

$0 

Figure 5 

Sensitivity Analysis: Expected Default Frequencies 

BIF and SAIF Merged 

BIF and SAIF Balance 

12/31/2000 

$40.591 billion 

Baseline Historical EDFs Logit EDFs Only S&P and L

Alternative EDF Simulations 
Figure 6 

Sensitivity Analysis: EDFs from Market Information 

BIF 

Baseline EDFs from Deposit Ratings EDFs from KMV KMV S&

$0 

$20,000,000 $40,000,000 $60,000,000 $80,000,000 

$100,000,000 $120,000,000 $140,000,000 

Funds Required for Rating (000 omitted) 

BIF Balance 12/31/2000 

$29.863 billion 
Funds Required for Rating (000 omitted) 

$160,000,000 $140,000,000 $120,000,000 $100,000,000 

$80,000,000 $60,000,000 $40,000,000 $20,000,000 

$0 

Figure 7 

Sensitivity Analysis: EDFs from Market Information 

BIF and SAIF Merged 

BIF and SAIF Balance 

12/31/2000 

$40.591 billion 

Baseline EDFs from Deposit Ratings EDFs from KMV KMV S&

Alternative EDF Simulations 
Figure 8 

Sensitivity Analysis: Severity 

BIF 

Baseline 1990–1998 FBCA Loss 1986–1989 FBCA Loss 1990–1993 FBCA Loss 1986–1

Rates Rates Rates FBC

$0.00 

$10,000,000.00 $20,000,000.00 $30,000,000.00 $40,000,000.00 $50,000,000.00 $60,000,000.00 $70,000,000.00 $80,000,000.00 

Funds Required for Rating (000 omitted) 

BIF Balance 12/31/2000 

$29.863 billion 
Funds Required for Rating (000 omitted) 

$90,000,000 $80,000,000 $70,000,000 $60,000,000 $50,000,000 $40,000,000 $30,000,000 $20,000,000 $10,000,000 

$0 

Figure 9 

Sensitivity Analysis: Severity 

BIF and SAIF Merged 

BIF and SAIF Balance 

12/31/2000 

$40.591 billion 

Baseline 1990–1998 FBCA Loss 1986–1989 FBCA Loss 1990–1993 FBCA Loss 1986–19

Rates Rates Rates FBCA 
Figure 10 

Sensitivity Analysis: Bucketing 

BIF 

Baseline 25 Equal-Sized Buckets Size and Region Buckets Region and CAMELS Special

Group 

$0 

$5,000,000 

$10,000,000 $15,000,000 $20,000,000 $25,000,000 $30,000,000 $35,000,000 $40,000,000 $45,000,000 $50,000,000 

Funds Required for Rating (000 omitted) 

BIF Balance 12/31/2000 

$29.863 billion 
Funds Required for Rating (000 omitted) 

$60,000,000 $50,000,000 $40,000,000 $30,000,000 $20,000,000 $10,000,000 

$0 

Baseline 

Figure 11 

Sensitivity Analysis: Bucketing 

BIF and SAIF Merged 

BIF and SAIF Balance 

12/31/2000 

$40.591 billion 

25 Equal-Sized Size and Region Region and Size and CAMELS Spe

Buckets Buckets CAMELS Group Group