Evaluating the Adequacy of the Deposit Insurance Fund:
A Credit-Risk Modeling Approach

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.

³The 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 credit-risk models.

⁵See BIS (1999).

⁶To be consistent with the terminology used by Oliver, Wyman & Company, I call the standard deviation of losses the unexpected loss.

⁷Generally 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.

⁹See Jones and Mingo (1999, 1998).

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

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 one-year 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."

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.

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).

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.

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.

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.

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.

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

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.

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

³⁵ Keenan et al. (2000), 8.

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.

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)<.li>
3. First Republic (41 institutions, failed 1988)
4. Alliance (2 institutions, failed 1988)<.li>
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)

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.

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.

⁴² See Crosbie (1997).

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.

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

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.

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

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.

⁴⁹ 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.