FYI: An Update on Emerging Issues in Banking

A Portfolio Perspective for Evaluating the Adequacy of the Insurance Funds

December 10, 2003

FDIC economists have teamed up with prominent members of the academic community to 

develop a state-of-the art approach to measure risks posed to the bank (BIF) and savings 

association (SAIF) insurance funds.1 This approach, referred to hereafter as the Loss Distribution 

Model or LDM, employs many of the same techniques and methods used in credit risk and 

economic capital models employed by large financial companies to measure and manage risk. 

The LDM not only introduces a greater degree of rigor and precision to determining the potential 

for BIF and SAIF losses due to failures, but it also represents a critical step toward developing an 

integrated fund model that accounts for all factors relevant to managing the insurance funds.

Background: Loss Expectations and Potential Loss Distributions are Basic Measures of the 

Insurance Fund Exposures to Bank and Thrift Failures

The LDM provides FDIC managers with a systematic and quantitative means of measuring 

potential losses to the BIF and SAIF resulting from potential bank and thrift failures. These 

measures include not only estimates of failure-related losses that are most likely given current 

industry conditions (i.e., expected losses) but also failure-related losses that might result from 

changes in the condition of the economy and the industry (i.e., unanticipated losses).

A rudimentary measure of expected losses to the insurance funds considers expected BIF and 

SAIF outlays associated only with institutions whose failure appears likely. Such measures, 

which satisfy the FAS 5 accounting definition of probable and reasonably estimable losses, form 

the basis for the contingent loss reserves recorded by the FDIC in its financial statements. A 

more precise statistical measure of expected loss also considers the failure probabilities of 

institutions where failure is not likely but nevertheless possible. In this case, the relevant 

expected loss equation, summed across all insured institutions, is expressed as follows:

Expected Loss = (Probability of Failure) x (Loss Rate Given Failure) x (Deposits)

Note the similarity between components in this equation and the components used to determine 

capital levels for credit exposures of banks under the advanced internal ratings-based approach 

contained in the Basel II Capital Accord. Specifically, Probability of Failure is analogous to 

Probability of Default (PD), the Loss Rate Given Failure is analogous to Loss Given Default 

(LGD), and Deposit levels are analogous to Exposures at Default (EAD). In this sense, the 

Expected Loss equation above can be thought of as representing the credit risk elements inherent 

in insured depositories. Measures of expected losses are one output of the LDM.

Expected loss measures produce useful estimates to managers of the FDIC insurance funds for 

planning purposes. However, prudent funds management can not rely solely on single "point" 

estimates. Because of the uncertainty surrounding future events, actual results can and often do 

deviate from expectations. Accordingly, the FDIC must take into account potential events that 

could result in higher-than-anticipated losses to the insurance funds. Planning for these 
"unanticipated" events requires consideration of the entire range of reasonably possible loss 

outcomes as well as the numerical probability of each outcome's occurrence.

Chart 1 further illustrates the idea behind measuring unanticipated losses. The chart shows two 

different distributions: a normal distribution and a skewed distribution. Normal distributions are 

used to describe processes where possible outcomes are distributed symmetrically about the 

expected value or mean (that is, the likelihood of exceeding the expected value or mean is equal 

to the likelihood of falling below this expectation). Normal distributions, however, are not the 

best representation of potential insurance fund losses. Rather, the FDIC's experience with bank 

and thrift failures suggests that estimates of possible loss outcomes should more closely resemble 

the skewed distribution pattern shown in Chart 1. In other words, while most outcomes (or 

scenarios) will produce a low rate of failures (and resulting losses), there are a small number of 

scenario outcomes, such as the failure of a large bank, that produce large losses to the funds.2

D

Why are such loss distributions relevant to the management of the FDIC insurance funds? Given 

the uncertainties surrounding expected loss projections, it is important to build fund balances to 

levels sufficient to absorb a large percentage of the potential outcomes suggested by the loss 

distribution.3 The percentage of potential outcomes covered is often referred to as a "solvency 

standard," which in turn is typically related to the average default experience of corporate 

obligations.4 The LDM gives FDIC management a systematic way to evaluate the range of 

potential or unanticipated losses stemming from bank and thrift failures as well as the 

probabilities associated with these outcomes. With this information, the FDIC is then able to 

determine the adequacy of the insurance funds relative to a given solvency standard.

How the Loss Default Model Works: A Nontechnical Description5
Figure 1 illustrates the basic structural components of the LDM. The approach can be broken 

down into three steps. As a first step, three separate models produce the key underlying "credit 

risk" parameters for bank and thrift failures:

• A failure model produces estimates of failure probabilities (PDs) for each insured 

institution. These PDs are determined using a statistically-based model that is based on 

highly predictive variables such as examination ratings, problem asset ratios, capital 

levels, and profitability measures.6

• A model of FDIC loss experience produces loss or LGD estimates based on historical 

loss experience and the types of assets held and the liability structure (priority of 

receivership claims) of each individual institution.

• A deposit growth model uses statistically-based methods to predict estimated deposit 

levels in each insured institution (EAD). The model is driven by a variety of factors 

including previous deposit growth rates, examination ratings, and quarters-in-existence.

In the LDM approach, the above three models produce initial period estimates of PDs, LGDs, 

and EADs. The next step in the process uses an economic model to determine changes in these 

initial parameter estimates. Underlying this economic model are statistically-based relationships 

between the key parameters (PD, LGD, and EAD) and changes in the economic variables. The 

economic variables used are the term structure of interest rates (3 month and 3 year rates), 9 

regional and 1 national bank stock price indices, and 9 regional house price indices.

The final step in the process is to use a computer simulation to consider a wide variety of 

different economic scenarios and the possible effects on banks and thrifts. This simulation 

produces a distribution of possible bank and thrift failures and related insurance fund losses. 7 All 

losses produced in the simulations are discounted back from the time of failure to the present 

time. The appropriate rate of interest to use in the discounting process is determined by a 

separate interest rate model. The key outputs of the simulation model include information 

relating to the identity of failed banks, the time of failure, the level of deposits at failure, and the 

losses produced by the failed institution (discounted back to the present).
D

How the Loss Default Model Improves Funds Management Practices at the FDIC

The LDM represents a significant advancement in FDIC processes for both quantifying risk 

exposures and formulating strategic plans and policies to respond to these risks. The nature of 

these improvements is detailed below.

LDM Can Add Precision to Informed Judgment:

By introducing rigorous and unbiased estimates of expected and unanticipated failure-related 

losses, the LDM provides a greater degree of precision to decision makers when it comes to 

establishing contingent loss reserves and developing funds management policies.

To illustrate how the LDM adds precision to the process, consider a situation where managers 

are tasked with determining the likelihood that a particular institution will fail during the next 12 

months. Using informed judgment alone, the managers may initially equate the prospects of 

failure to the flip of a coin (implying a 50 percent probability of failure). If the LDM, which by 

design incorporates an unbiased view of historical experiences related to institutions with similar 

characteristics, produces a default probability closer to 30 percent, managers may decide to 

refine their estimates accordingly. In this purely hypothetical case, informed judgment alone was 

not able to discern the difference between a 30 percent probability of failure and a coin-toss. 

However, such differences in estimates can make a substantial difference in setting reserves for 

potential failures, particularly if the institution in question is large.

The Accuracy of LDM Estimates Can Be Verified Over Time:

Since the LDM model produces quantitative outputs, it is possible to evaluate the accuracy of 

these estimates by comparing them with actual results. If the model is found to produce biased 

estimates of potential losses over time, it can be recalibrated to improve its accuracy.
LDM Incorporates Consideration of Economic Conditions:

A major innovation of the LDM is the inclusion of macroeconomic variables. Past bank and 

thrift failures have certainly been heavily influenced by changes in economic factors such as 

interest rates and real estate values. The LDM uses information about the historical relationships 

between these economic factors and key risk parameters (PD, LGD, and EAD) to produce more 

informed estimates of potential failures and the ultimate loss produced by these failures. 

Incorporating macroeconomic variables into the model also lays the foundation for considering 

the impact of potential stress events (regional recessions, sharp rises in interest rates, or the 

bursting of a housing bubble, to name a few) on the insurance funds.

LDM Provides a Portfolio Perspective to FDIC Decision Makers:

A principal tenet of portfolio theory is that the total risk in a portfolio of investments (as 

measured by the standard deviation of portfolio returns) is not equal to a simple weighted 

average of individual investment risks. Rather, a manager can reduce or diversify risk in the total 

portfolio by adding investments whose returns are not perfectly correlated (the returns do not 

move up and down in a one-to-one relationship) with the returns of the existing portfolio. While 

the FDIC can not "select" the institutions it insures in the same sense as a portfolio manager 

selects among alternative investments, this concept of diversification nevertheless illustrates the 

importance of considering the degree to which bank failures, for example, are correlated across 

the entire spectrum of insured institutions in estimating portfolio-wide failure probabilities. The 

LDM is a true portfolio model because it implicitly accounts for correlations such as those 

between failure probabilities of individual institutions.

LDM Provides a Barometer of Overall Industry Conditions:

Because the LDM produces portfolio estimates of expected and unanticipated failure-related 

losses, it can serve as a general barometer of the health of overall industry conditions. If, for 

example, the LDM were to show a substantial rise in expected losses relative to past estimations 

(or a substantial increase in variation of potential losses - a widening in the loss distribution 

curve), FDIC managers could reasonably conclude that conditions in the industry are 

deteriorating and formulate appropriate policy decisions to respond to these deteriorating 

conditions.

LDM is a Critical Component of an Integrated Approach to Managing the Insurance Funds:

By dynamically considering the exposure of the funds to bank and thrift failures, the LDM 

provides a critical component in the design of an integrated funds management model. Over 

time, the LDM will be integrated with models that account for other fund considerations such as 

income related to investments and premiums, cash flow considerations, and insured deposit 

balances.

An Integrated Fund Model Will Facilitate the Evaluation of the Impact of Policy Decisions:

Once the LDM is incorporated into an integrated fund model, managers will have a powerful tool 

to evaluate the impact of policy decisions related to the deposit insurance funds. As an example, 

managers will be better able to quantify and evaluate how the funds would respond to different 

deposit insurance pricing schemes.
Conclusion

LDM represents a substantial advancement in the analytical capabilities the FDIC has at its 

disposal to assess risk to the BIF and SAIF deposit insurance funds. Of course, even with the 

most sophisticated of models, estimation errors can and do occur. Accordingly, management of 

the FDIC does not view the outputs of the LDM as a substitute for informed judgment. Rather, 

the LDM will be used as another important input into the funds management process and as a 

tool that will facilitate more informed decisions related to evaluating and maintaining the 

solvency of the insurance funds.

1 Developers are Robert A. Jarrow of Cornell University's Johnson School of Management, 

Michael Fu and Huiji Zhang of the University of Maryland's Robert H. Smith School of 

Business, and Rosalind L. Bennett and Daniel A. Nuxoll from the FDIC.

2 The skewed distribution in Chart 1 illustrates an additional point related to reserving policies. 

Note that the mean of the skewed distribution falls above the median of the distribution. The 

mean loss is the expected loss and is the appropriate benchmark for reserving policy. In contrast, 

by definition of median, realized losses would exceed the median loss half the time and be less 

than the median loss half the time. The two differ because mean loss (and expected loss) reflects 

the large losses that could result from one or more large bank failures. 

3 It is not feasible to have fund balances cover all potential losses since this would entail holding 

balances roughly equivalent to total insured deposits.

4 For instance, a "triple-B" solvency standard suggests coverage of roughly 99.60 percent of 

possible losses (the average historical default rate of 'BBB' rated firms is roughly 40 basis 

points), while a "single-A" solvency standard suggests coverage of roughly 99.95 percent of 

possible losses. While the differences between these two solvency standards seem small, the 

resulting implied fund balances are significantly (billions of dollars) different.

5 For technical specifications of the model, refer to A General Martingale Approach to 

Measuring and Valuing the Risk to the FDIC Deposit Insurance Fund" by Jarrow, Bennett, Fu, 

Nuxoll, and Zhang. For a copy of this paper, please contact the FDIC's Public Information 

Center at 801 17th Street, NW, Washington, DC 20434, telephone 800-276-6003, or e-mail 

publicinfo@fdic.gov.

6 Examination ratings are supervisory-based assessments of insured institution risk. Composite 

ratings of '1' are accorded to institutions with little perceived risk, while composite ratings of '5' 

are accorded to institutions deemed likely to fail in the near-term.

7 This process is commonly referred to as a Monte Carlo simulation, which determines the 

outcomes of literally thousands of different scenarios. These different scenarios can be 

determined empirically by drawing from historical information (note that such an approach 

determines the inherent correlation between model inputs and outputs) or more explicitly by the 

user (e.g., when considering a potential stress event such as a recession).

About the Author
Steven Burton is a Senior Financial Analyst in the Financial Risk Management Branch of the 

Division of Insurance and Research, FDIC. 

About FYI

FYI is an electronic bulletin summarizing current information about the trends that are driving 

change in the banking industry, plus links to the wide array of other FDIC publications and data 

tools. 

Disclaimer 

The views expressed in FYI are those of the authors and do not necessarily reflect official 

positions of the Federal Deposit Insurance Corporation. Some of the information used in the 

preparation of this publication was obtained from publicly available sources that are considered 

reliable. However, the use of this information does not constitute an endorsement of its accuracy 

by the Federal Deposit Insurance Corporation. 
Chart 1 - Two Hypothetical 

Loss Distributions

Normal Skewed

0.000000 0.000000 

0.000000 0.033825 

0.000000 0.386696 

0.000000 1.120568 

0.000000 1.994828 

0.000000 2.806988 

0.000000 3.459680 

0.000000 3.928295 

0.000000 4.225348 

0.000000 4.378081 

0.000001 4.416758 

0.000001 4.369349 

0.000003 4.259573 

0.000006 4.106579 

0.000013 3.925333 

0.000027 3.727250 

0.000054 3.520863 

0.000105 3.312423 

0.000201 3.106412 

0.000378 2.905956 

0.000696 2.713157 

0.001256 2.529349 

0.002221 2.355300 

0.003850 2.191358 

0.006540 2.037578 

0.010891 1.893799 

0.017778 1.759716 

0.028445 1.634927 

0.044611 1.518974 

0.068578 1.411360 

0.103335 1.311581 

0.152624 1.219129 

0.220959 1.133508 

0.313555 1.054240 

0.436145 0.980867 

0.594651 0.912957 
0.794709 0.850101 

1.041040 0.791916 

1.336722 0.738048 

1.682398 0.688163 

2.075537 0.641956 

2.509843 0.599140 

2.974929 0.559454 

3.456374 0.522655 

3.936217 0.488518 

4.393913 0.456838 

4.807706 0.427425 

5.156305 0.400105 

5.420674 0.374717 

5.585758 0.351113 

5.641896 0.329157 

5.585758 0.308724 

5.420674 0.289700 

5.156305 0.271979 

4.807706 0.255462 

4.393913 0.240062 

3.936217 0.225695 

3.456374 0.212286 

2.974929 0.199764 

2.509843 0.188065 

2.075537 0.177131 

1.682398 0.166905 

1.336722 0.157338 

1.041040 0.148383 

0.794709 0.139997 

0.594651 0.132140 

0.436145 0.124775 

0.313555 0.117869 

0.220959 0.111389 

0.152624 0.105308 

0.103335 0.099597 

0.068578 0.094233 

0.044611 0.089191 

0.028445 0.084451 
0.017778 0.079992 

0.010891 0.075797 

0.006540 0.071847 

0.003850 0.068127 

0.002221 0.064623 

0.001256 0.061320 

0.000696 0.058206 

0.000378 0.055268 

0.000201 0.052497 

0.000105 0.049880 

0.000054 0.047410 

0.000027 0.045076 

0.000013 0.042870 

0.000006 0.040785 

0.000003 0.038814 

0.000001 0.036949 

0.000001 0.035184 

0.000000 0.033513 

0.000000 0.031931 

0.000000 0.030432 

0.000000 0.029012 

0.000000 0.027666 

0.000000 0.026390 

0.000000 0.025179 

0.000000 0.024031 

0.000000 0.022941 

0.000000 0.021906 

Source: FDIC 

Figure 1 is a schematic diagram that shows the structure of the Loss Distribution Model (LDM), the 

various component models and parameters that feed into the LDM model, and the main outputs of the 

LDM model. Starting at the top of the diagram, there are three separate boxes with the following labels: 

Bank Failure or PD Model, Loss Rate or LGD Model, and Deposit Growth or EAD Model. These three 

boxes represent the three initial LDM model parameters. Arrows from each of these three boxes point 

both to the right toward a box titled Economic Model and directly downward to another box titled 

Simulations. The arrows pointing toward the Economic Model box indicate that the LDM model 

parameters PD, LGD, and EAD are fed into an economic model, which estimates subsequent changes in 

these initial parameters. The Economic Model box also has an arrow pointing leftward toward the 
Simulation box to indicate that the output of the economic model feed into the simulation. To the right 

of the diagram is another box titled Interest Rate Model, which also has an arrow pointing to the 

Simulation box. This interest rate model is needed in the simulations to calculate a discounted value for 

loss estimates. In summary, the simulations depend on initial parameter values from the PD, LGD, and 

EAD models, outputs of the economic model, and outputs of the Interest Rate Model. Finally, the 

Simulation box has an arrow pointing to a box titled Model Outputs, which lists the following output 

elements produced by the simulations: Identity of the Failed Institution, Time of Failure, Deposits at 

Failure, Losses at Failure, and Discounted Losses at Failure.