WORKING PAPER SERIES

Determining the Target Deposit Insurance 

Fund: Practical Approaches for Data-Poor 

Deposit Insurers

John P. O’Keefe

Federal Deposit Insurance Corporation

and

Alexander B. Ufier

Federal Deposit Insurance Corporation

May 2017

FDIC CFR WP 2017-04

fdic.gov/cfr

NOTE: Staff working papers are preliminary materials circulated to stimulate discussion and critical 

comment. The analysis, conclusions, and opinions set forth here are those of the author(s) alone and do not 

necessarily reflect the views of the Federal Deposit Insurance Corporation. References in publications to this 

paper (other than acknowledgement) should be cleared with the author(s) to protect the tentative character 

of these papers.
Determining the Target Deposit Insurance Fund:

Practical Approaches for Data-Poor Deposit Insurers

John P. O’Keefe

Federal Deposit Insurance Corporation

550 17th Street, NW

Washington, DC 20429

Jokeefe@fdic.gov

And 

Alexander B. Ufier 

Federal Deposit Insurance Corporation

550 17th Street, NW

Washington, DC 20429

Aufier@fdic.gov

May 2017

Key words: Deposit Insurance, Bank Failure Prediction

JEL classification code: G21, G28

_____________________

* Disclaimer—This paper is based on World Bank executed technical assistance projects with 

the financial support from the FIRST initiative. The authors would like to thank Julian Casal and 

Jan Nolte of the World Bank for their advice and assistance as well as Chris Martin and Chacko 

George of the FDIC, who provided feedback during the peer review process for entry of the 

paper into the working paper series. The analysis, conclusions, and opinions here are those of 

the author(s) alone and do not necessarily reflect the views of the Federal Deposit Insurance 

Corporation, the International Bank for Reconstruction and Development/World Bank and its 

affiliated organizations, or the Executive Directors of the World Bank or the governments they 

represent.
1

ABBREVIATIONS AND ACRONYMS

DIF Deposit Insurance Fund

EAD Exposure at Default

FDIC U.S. Federal Deposit Insurance Corporation

FIRST Financial Sector Reform and Strengthening Initiative

GDP Gross Domestic Product

IADI International Association of Deposit Insurers

LGD Loss Given Default

PCA Principal Component Analysis

PD Probability of Default
2

Table of Contents

1. Introduction ..........................................................................................................................................4

1.1. Deposit Insurance Funding ...........................................................................................................4

1.2. Determining the Target Deposit Insurance Fund..........................................................................5

2. Proposed Target Fund Framework .......................................................................................................7

2.1. Identifying States of the World.....................................................................................................7

2.1.1. Constructing Principal Components .....................................................................................7

2.1.2. Identifying Crisis Periods.......................................................................................................8

2.1.3. Calibrating to Other Periods .................................................................................................9

3. Probability of Bank Failure..................................................................................................................10

3.1. Types of Failures in Simulation Study .........................................................................................10

3.1.1. Credit Failures.....................................................................................................................10

3.1.2. Monte Carlo Simulations of Credit Failures........................................................................11

3.1.3. Liquidity Failures.................................................................................................................12

3.1.4. Systemic Failures.................................................................................................................13

3.2. Estimating Probabilities of Failure ..............................................................................................13

3.2.1. Statistical Models of Bank Failure.......................................................................................13

3.2.2. Rating Agency-based Forecasts of Bank Failure .................................................................16

3.2.3. Actuarial Bank Failure Rates ...............................................................................................18

4. Loss Given Default...............................................................................................................................19

4.1. Failure Resolutions......................................................................................................................19

4.1.1. Priority of Claimants............................................................................................................19

4.1.2. Structure of Losses..............................................................................................................19

4.2. Deposit Insurance Losses............................................................................................................20

4.3. FDIC Loss Rates ...........................................................................................................................20

5. Exposure at Default.............................................................................................................................21

5.1. The U.S. Case...............................................................................................................................21

6. Correlation of Bank Failures................................................................................................................22

6.1. Stock Return Data .......................................................................................................................22

6.2. Book Equity .................................................................................................................................23

7. Model Calibration ...............................................................................................................................23
3

7.1. Probability of Default (PD)..........................................................................................................23

7.1.1. Statistical Predictions..........................................................................................................23

7.1.2. Issuer Default Ratings .........................................................................................................23

7.1.3. Industry Failure Rates .........................................................................................................23

7.2. Loss Given Default (LGD):............................................................................................................24

7.3. Exposure at Default (EAD)...........................................................................................................24

7.4. Correlation of Default.................................................................................................................24

8. Model Results .....................................................................................................................................24

8.1 Desired Fund Size........................................................................................................................25

8.2 Longer Horizons..........................................................................................................................26

9 Inherent Weaknesses of Model Assumptions....................................................................................27

10 Conclusion.......................................................................................................................................28

References ..................................................................................................................................................29

Appendix A—Principal Components Analysis used for Macroeconomic Crisis Periods.............................32
4

1. Introduction

The main public policy objectives of a deposit insurer are to reimburse depositors after bank failure, act 

as receiver for failed banks, and contribute to the stability of a financial system. To achieve these 

objectives and build public confidence in a deposit insurance system, deposit insurers must be ready to 

act quickly after a bank failure. Sound funding arrangements are essential aspects of such readiness, as 

they ensure prompt reimbursement of insured depositors and sufficient funds for the deposit insurer to 

unwind the institution. Depositor confidence depends, in part, on knowing that adequate funds for 

deposit insurance would always be available to ensure the prompt reimbursement of their claims. It is 

therefore considered a best practice to build credible ex-ante funding mechanisms that have the 

financial capacity to ensure that these obligations are met.

According to internationally accepted best practice by the International Association of Deposit Insurers 

(IADI), the appropriate measure of adequacy of a Deposit Insurance Fund (DIF) is the Target Fund Ratio

(or Reserve Ratio). 1 The Target Fund Ratio is the ratio of the balance in the DIF to estimated insured

deposits in the banking system. Each country is encouraged develop its own target level and funding 

path to achieve said target based on its financial obligations using relevant data and a transparent 

methodology. Each national target fund is likely to differ based on the level of financial development, 

banking concentration, and regulatory environment, in addition to meeting minimum demands placed 

on the country by other voluntary agreements such as European Union’s Directive on Deposit Guarantee 

Schemes.

2 This target fund level should be reviewed regularly and the method to calculate it subject to 

validation in accordance with changing financial conditions.

3

This paper presents a framework to help deposit insurers determine a Target Fund Ratio. The framework 

takes into consideration the role that credit and liquidity risks play in a bank failure. The goal of the 

paper is to show how deposit insurers might adapt the Target Fund Ratio framework to their economies 

and overcome the data limitations many jurisdictions face when attempting to determine deposit 

insurance losses. We have previously applied this framework to determining the Target Fund Ratio for 

deposit insurers in Nigeria, Zimbabwe, and the United States (O’Keefe and Ufier 2016a, O’Keefe and 

Ufier 2016b.) We use data for the U.S. Federal Deposit Insurance Corporation (FDIC) in this paper.

4

1.1. Deposit Insurance Funding

There exists a vast literature on deposit insurance that examines all elements of deposit insurance 

schemes, with the most consequential question addressed by this literature being “how should the 

deposit insurer pay for bank-failure resolution and related insurance costs?” IADI has synthesized much 

of this literature and discusses (IADI, 2009) three funding options: 1) funding used to resolve a bank 

failure that is received prior to the bank’s failure (ex-ante funding), 2) funding received after the bank’s 

 

1 See IADI (2009, 2014).

2 Art. 10 (2) of Directive 2014/49/EU. 3 See “IADI Core Principles for Effective Deposit Insurance Systems,” November 2014, p.29. 4 We do not present target fund model results for the Nigeria Deposit Insurance Corporation (NDIC) and Zimbabwe 

Deposit Protection Corporation (DPC) in this paper.
5

failure (ex-post funding); and 3) hybrid approaches that combine ex-ante and ex-post funding. There are 

pros and cons to each option. Ex-ante funding can help avert delays compared with ex-post funding, 

with delays often being potentially expensive. Presence of a fund can improve public confidence. It is 

arguably fairer to fund ex-ante as failed banks contribute to the fund prior to failure as opposed to only 

collecting taxes from survivors. Risk-based premiums can be used to discourage risky behavior easily in 

ex-ante settings but less so in ex-post ones, and premiums can be adjusted to reduce pro-cyclicality in 

bank profits to spread resolution costs but cannot in ex-post regimes. However, ex-ante funding

regimens come at the cost of lost capital to banks that may otherwise could have put it to better use 

outside the insurance fund, high burdens on individual banks if there are few banks compared with expost funding, administrative costs from managing the fund that would not exist were it collected expost, and moral hazard problems on both the banks and fund managers of having a large standing 

resolution fund (IADI 2009). 

On a net, IADI (2009) concludes that the benefits of ex-ante funding outweigh the costs and that ex-ante

funding of deposit insurance is preferred to ex-post, especially for recently established deposit insurance 

systems.5 IADI (2009) states that most deposit insurance funding schemes combine elements of ex-ante

and ex-post funding, as it is likely beneficial from a social welfare perspective to spread failureresolution cost recovery over a long period before, during, and after a severe crisis. IADI (2009) states 

that the target deposit insurance fund should, at a minimum, be adequate to absorb insurance losses 

the insurer might incur under “normal” circumstances. As a result, this paper seeks to estimate the 

necessary size of an ex-ante deposit insurance fund and leaves ex-post deposit insurance schemes for 

future work. 

1.2. Determining the Target Deposit Insurance Fund

IADI (2009) states that the majority of countries use their experience with bank-failure losses to 

determine the target deposit insurance fund. Given sufficient data on failure costs, a deposit insurer can 

estimate the empirical frequency distribution of losses and use that distribution to determine the level 

of losses the insurance fund should be able to absorb. This approach to determining the target deposit 

insurance fund is known as the Loss Distribution Approach. However, countries with limited experience 

closing failed banks will lack sufficient data to develop an accurate empirical loss distribution and may 

have difficulty estimating the likelihood of low-probability, high-loss events. As a result, practitioners 

must calibrate observed losses to an assumed probability distribution of losses, and results are highly 

sensitive to assumptions made in estimating the likelihood and size of low probability, high loss events.

This approach is inherently backward-looking and cannot take into consideration recent changes in the 

banking industry profile as well as regulatory environment.

6

A more forward-looking alternative to the Loss Distribution Approach is the Credit Portfolio Approach, 

which allows one to incorporate the effects of current economic conditions into deposit insurance 

 

5 IADI (2009) states that 80 percent of deposit insurance schemes at that time used ex-ante funding. 6 Potential concerns include deregulation, changes in depositor preference, changes in deposit insurance 

assessment schemes, or any number of banking rule changes. 
6

losses. This approach to modeling the target deposit insurance fund is based on the model of bond 

pricing by Merton (1974) and the loan portfolio model of Vasicek (1987, 1991, and 2002), hereafter the 

Merton-Vasicek Model. Merton (1974) develops a model for the pricing of corporate bonds that takes 

into account the possibility the issuing firm might default on payments. Merton (1974) presents the 

simple case of a corporation financed by a single bond and equity. In the model, bondholders have a 

claim on all of the corporation’s assets should the corporation default on bond payments while equity 

holders receive nothing. Merton recognizes that since bond holders have a call option of the value of the 

firm’s assets, bonds can be priced using the Black and Scholes (1973) option pricing framework. Under 

Merton’s approach, a firm fails when the market value of firm’s assets (call option value of the bond) 

falls below the nominal value of the firm’s obligations to bond holders. Merton recognized this default 

model generalizes to failures occurring when the market value of a corporation’s assets falls below the 

nominal value of the corporation’s liabilities and all of the corporation’s creditors can be viewed as 

having call options on the corporation’s assets.

Vasicek (1987, 1991, and 2002) generalizes the Merton (1973) framework to model losses on loan 

portfolios. Vasicek assumes that obligors’ asset value changes are determined by idiosyncratic and 

systemic risk factors. The systemic risk factor is common to all obligors (that is, the state of the 

economy). In the Vasicek model, changes in the value an obligor’s assets are correlated with those of 

other obligors through the common risk factor. Finally, the correlation among obligors’ asset value 

changes determines the correlation among obligor defaults. The possibility of correlated default is 

particularly important to models of the target deposit insurance fund.

The Credit Portfolio Approach assumes that the features of the financial safety net that can influence 

deposit insurance costs are captured in historical data and do not change over the forecast horizon. This 

approach has been used to model the target deposit insurance fund for many countries, including 

Colombia (Fogafin, 2013), Canada (CDIC, 2011), Singapore (Oliver, Wyman & Company, 2002), Nigeria 

(Katata and Ogunleye, 2014), (O’Keefe and Ufier, 2016a), and Zimbabwe (O’Keefe and Ufier, 2016b), 

supporting its use in a similar setting in this paper. As we shall show in the Section 2, The Credit 

Portfolio Approach allows for a forward-looking view of banking industry risk through separate 

estimates of bank probability of failure, correlation in failures, insurer exposure and losses given failure.

This will provide estimates superior to the Loss Distribution Approach, with lower data prerequisites 

that can easily be applied and customized for numerous national settings.

The remainder of the paper is organized as follows. Section 2 presents the proposed Target Fund Ratio

framework in various states of the world. Section 3 discusses estimation of the probability of bank 

failure, followed by estimation of losses given default in Section 4. Section 5 provides a brief discussion 

of exposure at default and Section 6 similarly considers failure correlations. Section 7 provides 

information on model calibration and execution, and Section 8 discusses results. Section 9 discusses the 

framework’s assumptions and inherent weaknesses, and Section 10 concludes.
7

2. Proposed Target Fund Framework

This model employs a Merton-Vasicek based model, the Credit Portfolio Approach, to estimate deposit 

insurance losses. The model will allow deposit insurers to revise the target fund estimate as industry 

conditions change. This approach does not attempt to model the indirect influences of the financial 

sector safety net on deposit insurance costs; rather, it assumes that these effects are reflected in model 

input data. Default models, such as this model, describe expected losses as expressed by equation 1.

EEEEEEEEEEEEEEEE LLLLLLLL LL iiii ss oo ww wwww = PPPPtt ∗ LLLL tt ∗ EEEE tt (1)

Where EEEE tt is the overall exposure at default in state of the world , LLLL tt is the loss rate per default in 

state of the world , and PPPPtt is the probability of default in state of the world . This model will generate

failures PPPPtt based on measures of default probabilities as well as correlations of defaults, and use rules 

developed from data on loss given default LLLL tt and exposure at default EEEE tt in a simulation to yield 

total expected losses and, as a result, a necessary fund level given a certain level of risk tolerance. 

Before discussing each component that together generates losses, we shall discuss differing states of the 

world which may affect all the components and how we estimate each of these components of the 

default model. 

2.1. Identifying States of the World 

In order to develop a robust estimate of deposit insurance fund adequacy, we consider how deposit 

insurance losses vary under different macroeconomic conditions as denoted by subscript . Specifically, 

we consider three states of the economy—a severe economic downturn (crisis period), the average 

conditions over a business cycle (through the cycle), and current (normal) conditions—and calibrate the 

target fund simulation model to these states. In each of these states, we generate defaults from 

observed defaults and correlations of returns that contribute to PPPP as well as to select different 

parameters for LLLL and EEEE .

7 In order to identify these periods, we analyzed U.S. macroeconomic 

economic data over the period 1983:Q4–2016:Q1 and identified quarters of the worst economic 

performance, employing general macro-economic indicators and measures of bank condition in this 

analysis. Our approach is to first identify the combination of economic indicators, for example, civilian 

unemployment rate, gross domestic product, that best explain variation in the economic data for the 

United States and subsequently study how the economy, as characterized by these indicators, changes 

over time. Specifically, we use Principal Component Analysis (PCA) to reduce analysis to a single 

composite variable—the first principal component. Further information about principal components 

analysis and extensions to this approach that can refine period selection can be found in appendix A.

2.1.1. Constructing Principal Components

We used the following measures to differentiate U.S. crisis from non-crisis periods: GDP growth, Civilian 

Unemployment Rate, Labor Force Participation Rate, Net Exports as a share of GDP, Inflation as 

 

7 These three views of the economy are designed to show variation in potential deposit insurance losses and are 

similar in spirit to the views of the economy used in mandatory capital stress-tests for U.S. banks. 
8

measured by the Consumer Price Index, and Nonperforming Bank Loans as a share of total loans. We use 

principal components analysis to create six principal components from these six variables. We focus on 

the first principal component in this analysis, PC1, which explained 39 percent of the overall variation in 

the chosen economic data. Table 1 presents the variable weights for six key economic indicators for the 

period 1983:Q4–2016:Q1. These factor weights suggest that higher (lower) values of PC1 imply worse 

(better) economic conditions.8

Table 1

Macroeconomic Variables Used to Explain U.S. Economic Conditions

(1983:Q4–2016:Q1)

Variable Variable Weight for First Component9

GDP Growth -0.24

Labor Force Participation Rate -0.50

Net Exports, % of GDP -0.03

Civilian Unemployment Rate 0.57

Consumer Price Index 0.27

Nonperforming Bank Loans, % of Loans 0.54

We recover the values for the first principal component for the United States between 1983:Q4 and 

2016:Q1 using the weights as illustrated by equation 2, and then sort years from best to worst using the 

principal component.

PPPP1,2009:Q1 = (−0.24) ∗ h2009:Q1 + ⋯ + (0.54) ∗ NN /LLLL LL 2009:Q1 (2) 

2.1.2. Identifying Crisis Periods 

After sorting years by relative level of economic stress, the second step in crisis period identification is to 

determine a cutoff value of the first principal component to distinguish between crisis and non-crisis

periods. For this, we use a Bai and Perron break test to find a single break in the data series for PC1

when arranged from highest (here, the worst) to lowest (here, the best) PC1. Note that we are not 

 

8 A country may see a reversed scale from what is shown here, with higher values meaning better performance 

and lower values meaning worse performance. It will cause more interpretation problems if signs were mixed—

for example, unemployment rate and GDP growth having the same direction of weights—and require deeper 

investigation of variables included in the principal components. 

9 If each of these weights is squared, then each column will add up to 1. 
9

arranging quarters chronologically, but by value of their principal component. We identified a break 

point in the PC1 series at size-ranked observation 104 of 130, which corresponds to a PC1 value of 0.44. 

We identify values with higher PC1 values than the cutoff as crisis periods. We observe that the crisis 

period quarters happen to be in two distinct bands, as shown in Figure 1. As additional support for the 

PC1 approach, we find the worst PC1 (2.03) occurred in 2009:Q3, which corresponds closely to the 

height of the most recent U.S. financial crisis. 

Figure 1

Based on our analysis of U.S. economic data for the period 1983:Q4–2016:Q1, there are two distinct 

crisis periods. The first occurred during 1990:Q3–1991:Q4, which largely coincides with the New England 

banking crisis. The second occurred during 2008:Q1–2014:Q1, which generally coincides with the recent 

U.S. and global financial crisis and slow economic growth thereafter. The start of these crisis periods 

roughly correspond to those identified by the National Bureau of Economic Research (NBER), a private 

nonprofit research group with expertise in identifying U.S. business cycles that U.S. academic and 

government economists cite widely. The first NBER period is July 1990–March 1991 and the second 

period is December 2007–June 2009. It is important to point out that the NBER methodology differs 

from ours and is focused on “peak-to-trough” business cycles while ours is focused on the severely 

adverse economic downturn periods.10 Our periods likely last considerably longer as our model includes 

nonperforming loans and unemployment, which tend to lag general measures of economic performance

such as the GDP. We will use the data from both of these periods to form our estimates for crisis period

parameters.

2.1.3. Calibrating to Other Periods

In addition to identifying crises periods, we wish to calibrate the Target Fund Model to conditions over a 

full business cycle, as well as current economic conditions. The NBER states that of the 11 business 

 

10 Business cycle dates are available at the NBER website, http://www.nber.org/cycles/cyclesmain.html

-1.50

-1.00

-0.50

0.00

0.50

1.00

1.50

2.00

2.50

1983198819931998200320082013

First Principal Component

Quarter

First Principal Component: U.S. Macroeconomic Indicators 

(1983:Q4 - 2016:Q1)

U.S. Financial Crisis: 2008:Q1 - 2014:Q1

New England Banking Crisis:

1990:Q3 - 1991:Q4 

PC1 Break Point 0.44
10

cycles it identified for the period 1945–2009, the average time from one trough to the next was 70 

months, or just under six years, and the longest cycle from previous trough to peak was 120 months, or 

10 years. To ensure that we capture as much of a full business cycle as possible, we use the most recent 

10-year period 2006:Q1– 2016:Q1 as our through-the-cycle period. Finally, we use the two-year period, 

2014:Q1–2016:Q1 as our current period. Table 2 combines our findings for U.S. economic state 

identification.

Table 2. Crisis Period and Business Cycle Identification

Economic State Periods

Crisis 1990:Q3–1991:Q4

2008:Q1–2014:Q1

Through-the-Cycle 2006:Q1– 2016:Q1

Current 2014:Q1–2016:Q1

This model explicitly treats each of these periods as different data generating processes, as opposed to 

assuming that there is a single data-generating process and crises, for example, are particularly low 

draws from the asset returns process. The crisis parameters would be assuming a distribution of returns 

calibrated only on the worst years, current times calibrated on average years at the center of a single 

distribution, and through the cycle calibrated on all years. Differing approaches to generating default 

probabilities and segmenting data-generating processes can produce different results, and regulators 

should carefully consider their calibrations to match their own business cycle experiences. 

3. Probability of Bank Failure

This section focuses on the PPPP element of the default model, here the probability of bank failure, which 

Section 6 builds on by considering the correlation of returns and thus failures among different financial 

institutions. This PPPP constitutes the most heavily modeled portion of the target fund framework, and 

will encompass credit failures PPPPCC, liquidity failures PPPPll, and systemic failuresPPPPss, each coming from 

asset return simulations: 

PPPP = PPPPCC + PPPPll + PPPPss (3)

3.1. Types of Failures in Simulation Study

The 2007–2009 global financial crisis showed that the interaction of credit and liquidity risks, coupled 

with systemic market shutdowns, could lead to catastrophic deposit insurance losses. We begin by 

discussing our conceptual approach to simulating bank failures caused by credit risk PPPPCC, followed by 

descriptions of the interaction of credit and other risks, liquidity and systemic risk, through the 

simulation.

3.1.1. Credit Failures

For the purpose of this discussion, obligor default is synonymous with bank insolvency or failure. As 

stated previously, in a Merton-Vasicek Model, obligors are assumed to default when their wealth or 

total asset value falls below that of their outstanding liabilities. Equation 4 expresses an asset’s one-
11

period gross return as a weighted average of systemic and idiosyncratic risk measures. In equation 4, RRii

is the one-period asset return, wwii is the weight placed on a single systemic risk factor, XX, and ii is the 

weight placed on idiosyncratic risk factor, EEii. The systemic risk factor is something faced by all actors—

high unemployment, asset price collapses, or changes in a government policy that affect bankruptcies 

may affect the credit quality of loans held by all banks, for example. The idiosyncratic risk factor is 

specific to the bank—several of its lines of business may be doing particularly well or poorly. All obligors 

face the same systemic risk. While XX can be a set of several risk measures, Gordy (2000) shows that 

these risks can be reduced to one systemic risk factor. Conversely, each obligor ii has different 

idiosyncratic risk, EEii.

11

RRii = wwii ∗ XX + ii ∗ EEii (4)

Without loss of generality, the Merton-Vasicek Model assumes that XX and EEii are standard normal 

random variables. Hence, asset returns, RRii R

, are also distributed as standard normal random variables.12

As we shall see in subsequent sections, the use of standard normal random variables greatly simplifies 

quantification of insurance losses.

13 Obligor default occurs when the change in the value of their assets 

is less than or equal to some critical value, ii:

wwii ∗ XX + ii ∗ EEii ≤ ii (5)

A more common representation of the asset return model is shown in equation 6.

RRii = �ρρ ∗ XX + �1 − ρρ ∗ EEii (6)

In equation 6, the term ρρR is the correlation between firms’ asset returns and is assumed to be identical 

across any two firms. We next describe the asset return and failure simulation process in general terms.

Specifics on model calibration are presented in sections 6 and 7.

3.1.2. Monte Carlo Simulations of Credit Failures

To create a loss distribution for a nation’s banking sector, we must first create a frequency distribution 

of bank failures using a Monte Carlo simulation of asset returns. Rather than comparing simulated bank 

asset returns and ending asset values to those of liabilities, the Monte Carlo simulation takes a more 

straightforward approach to simulating failure events. Failures are assumed to occur whenever a 

randomly chosen asset return is more negative than that implied by the bank’s expected failure

probability.

 

11 This discussion of the asset return process is based largely on Gordy (2000). Gordy shows that one can view the 

asset return generation process as being driven by a latent variable that is also determined by systemic and 

idiosyncratic risks.

12 Standard normal random variables are normalized by subtracting the mean value of the variable and dividing 

this difference by the standard deviation. Hence, a standard normal random variable has a mean of zero and 

standard deviation of one. 

13 Note that equation 4 does not include a time subscript since the default model is a one period model.
12

Using the assumptions of the Merton-Vasicek Model, the asset return associated with an expected

failure probability can be obtained by taking the inverse of the cumulative standard normal density 

function, evaluated at that failure probability, as shown is equation 7:

RRii = Φ−1(EEEEEEEEEEEEEEEE FF FF PP PP PP PPii) (7)

Using this approach, we are assured that the simulated failure rate for each bank out of a large number 

of random draws of asset returns equals the expected failure probability. We use three sources of 

information on expected failure probabilities—a logistic regression model of bank failure, bank failure

rates associated with banks’ issuer default ratings, and actuarial failure rates.

We use the Merton-Vasicek Model assumptions to randomly sample asset returns. Specifically, we 

generate asset returns by taking random draws of values of the idiosyncratic and systemic risk factors in 

equation 6. Next, we use an estimate of the correlation in bank failures based on bank stock return 

correlations to weight the risk factors and sum the weighted terms to get a single random draw of the 

asset return. As shown in equation 8, bank failure is assumed to occur whenever the simulated asset 

return is more negative than that implied by the failure probability estimate (worse than the stated 

critical value ii.) As stated at the beginning of this section, equation 8 only refers to credit failure 

events. 

II RRii < Φ−1(EEEEEEEEEEEEEEEE FF FF PP PP PP PPii) h BB BB ii FF (8)

We calibrate the systemic risk factor to an economy using the mean and standard deviation of the 

annual GDP growth rate. Since the idiosyncratic risk factors are standard normal random variables, we 

generate failure events by random draws from the weighted sum of a normal random variable and a 

standard normal random variable and using expected failure probabilities to determine the failure 

threshold for asset returns. 

3.1.3. Liquidity Failures

Banks rely on a variety of short-term funding sources, and interruption in funding can make it impossible 

for banks to continue operations. This was the case during the 2007–2009 U.S. financial crisis, when 

interbank lending and loan securitization markets froze as a result of heightened uncertainty about 

banks’ conditions. Without the immediate provision of liquidity from the central bank and other support 

programs, many of the largest banks in the United States and other countries faced failure.

Because of the existence of these liquidity programs, observed failure rates during this crisis were lower 

than they otherwise would have been. Had these institutions failed, higher costs would have 

accumulated to the deposit insurer. Additionally, if the deposit insurer were funding some of these

emergency programs, they would have incurred additional costs. Ignoring these near-failures due to 

liquidity would potentially underestimate the liability that could accumulate to the deposit insurer in 

financial distress. Thus, we expand failures beyond just credit defaults to include the possibility of 

liquidity defaults, PPPPll. We consider the possibility of liquidity failures by assuming that banks will lose a 

significant portion of uninsured deposits and other short-term funding if their asset returns place them 

“near” credit failure status and no further government guarantees are forthcoming. At this point, fire 
13

sales of assets to meet liquidity demands may drive the bank to failure. The near-credit-failure threshold 

is admittedly subjective and regulators can consider conditions for their country, but this provides a 

useful overlay to increase bank default risk. We assume a near-credit-failure event occurs whenever the 

asset loss is 90 percent or more of that which would cause a credit failure, excluding the previously 

discussed credit failures, as shown in equation 9.

II 0.90 ≤ RRii

Φ−1(PPPPii) < 1.0 RR < 0 h ii ll (9)

In simpler terms, equation 9 increases bank failure rates via directly tightening the default threshold to 

account for the possibility that liquidity failures may occur in weakly capitalized banks, such as selffulfilling runs and asset fire sales.

3.1.4. Systemic Failures

In addition to the credit and liquidity risks banks face, there is the possibility of a systemic event that 

disrupts the operations of all banks. One might model systemic risk as arising from a loss of confidence 

in short- and long-term interbank lending for all banks, including lending by banks outside the country to 

banks in-country. All interbank lending might cease at the point where borrowing lost due to all 

individual credit and liquidity failures exceeds a critical threshold. Taking into consideration the 

importance of interbank borrowing to each bank, if the lost funding exceeds an assumed threshold,

banks that rely significantly on interbank funds might all fail due to the shutdown of that market. An 

example of how one might model systemic failures follows:

We wish to model the systemic risk arising from a loss of confidence in short- and long-term 

interbank lending for all U.S. banks, including lending by non-U.S. banks to U.S. banks. We 

assume all interbank lending ceases at the point where borrowing lost due to all individual credit 

and liquidity failures is at least 30 percent of total interbank borrowing. We also consider the 

importance of interbank borrowing to each bank. If the lost funding is at least 10 percent of the 

bank’s assets, the bank is assumed to fail due to the market wide loss of interbank funds.

Unfortunately, U.S. banks do not report sufficiently detailed information on lending to and borrowing 

from other banks in the United States and elsewhere to include systemic failures in our Target Fund 

Ratio analysis. This is not necessarily the case for other jurisdictions, however, and we recommend 

incorporating systemic risk in the Target Fund Ratio framework.

3.2. Estimating Probabilities of Failure

Moving beyond the distinct components that will compose default probabilities, we next consider data 

sources for those probabilities of defaults. We enumerate three approaches to estimating bank failure 

probabilities below: statistical models (usually logistic regressions), credit rating agency studies, and 

actuarial failure rates.

3.2.1. Statistical Models of Bank Failure

Deposit insurers that have extensive experience closing insolvent banks can use this information to 

develop statistical models of bank-failure prediction. The most commonly used approach to modeling 
14

bank failure is logistic regression, in which the dependent variable is a binary (0, 1) indicator of the 

occurrence of bank failure within a specific time period, usually one year. The most informative 

explanatory variables for bank failure prediction will vary across countries. However, the bank-failure 

prediction literature finds bank financial measures of capital adequacy, asset quality, management 

quality, earnings strength, liquidity and sensitivity to market prices (hereafter, CAMELS attributes) are 

frequently informative explanatory variables. For example, we estimated a stepwise logistic regression 

of the determinants of bank failure within a given one-year period, using the CAMELS attributes as 

explanatory variables. Specifically, we used measures of the CAMELS attributes as of quarter-ends 

2014:Q1, 2015:Q1 and 2016:Q1 as explanatory variables in the logit model and related these covariates 

to the incidence of failure in the year following each of these quarter-ends. The potential explanatory 

variables were those used by the FDIC’s off-site bank monitoring model, SCOR.14

 

14 See Collier, Charles, Sean Forbush, Daniel Nuxoll, and John O’Keefe (2003).
15

Table 3. Stepwise Logistic Regression of Determinants of U.S. Bank Failures

(Forecast Horizon is One Year)

Table 3 shows the estimated coefficient signs for the explanatory variables are as expected. Increases in 

loans past due 30 to 89 days, loan-loss reserves, and loan charge-offs increase the likelihood of failure 

while increases in equity capital, income before taxes, loans and long-term securities, liquid assets and 

loan-loss provisions decrease the likelihood of failure. 

A deposit insurer can select the appropriate period over which to estimate the logistic regression to 

provide estimates of default that reflect different periods of economic conditions—current period, 

through-the-cycle and crisis period conditions—and apply these coefficient estimates to subsequent 

period financial data to obtain out-of-sample predictions of banks’ failure probabilities. For example, in 

this study we used the above logit model estimates (Table 3) and year-end 2016 financial data to predict 

bank failure probabilities for 2017. 

2014:Q1 to 2016:Q1

Independent Variables* Estimated Coefficient (Standard Error) 

Equity -0.6958*** 

(0.1166)

Loans Past due 30 Days or More 0.4448***

(0.1160)

Loan Loss Reserves 0.5919** 

(0.2212)

Income Before Taxes -0.8811*

(0.3541)

Loans and Long-term Securities -0.1083*** 

(0.0300)

Liqud Assets -0.0736**

(0.0261)

Provisions for Loan Losses -2.2281*

(1.0077)

Gross Charge-offs 1.7021* 

(0.7495)

Intercept 6.7699**

(2.4539)

Pseudo R-squared 0.6358

N 19,105

* p<0.05, ** p<0.01, *** p<0.001

*Note: All variables are measured as a percentage of gross assets.
16

If a country has too few explicit bank closings with which to estimate a logistic regression, it may still be 

possible to model the likelihood that banks become critically undercapitalized. Models considering 

capitalization levels can use a variety of capital adequacy measures such as equity plus reserves-to-book 

assets and tier 1 plus tier 2 capital-to-risk weighted assets and observe when a threshold is breached, 

although the exact measure and capital level are up to the individual deposit insurer. Thresholds for 

determining when a bank becomes critically undercapitalized can be based on regulatory capital 

requirements or expert judgment. For example, a 2 percent threshold for equity capital-to-book assets 

that is in line with U.S. prompt corrective action bank closure policies. An “in-substance” failure could be

said to occur when the aforementioned capital measure drop below 2 percent, but the regression 

remains the same.

There are two limitations to the statistical bank-failure prediction model. First, government support—

such as credit guarantee or liquidity programs that affect the profit and indirectly capital position of 

banks—to the industry during crisis periods may make industry condition appear better than would be 

the case without government support. Second, government capital injections will improve bank capital 

adequacy and reduce the occurrence of observed failures, directly improving the capital position of 

banks.

3.2.2. Rating Agency-based Forecasts of Bank Failure

To counter the aforementioned weakness in the statistical bank-failure model, one could alternatively 

estimate failure probabilities with forecasts based on banks’ credit ratings. Banks that issue publicly 

traded debt receive credit ratings from rating agencies. Fitch, Moody’s, and Standard and Poor are the 

three best-known credit rating agencies that rate both the default risk of individual securities and 

issuers.

According to FitchRatings (2014, 2013b, 2011), Fitch credit ratings are designed to rate debt issues and 

issuers vulnerability to default, where default refers to failure to meet interest and principal payments 

on securities. Since we are primarily interested in banks versus all securities, we focus on Fitch Issuer 

Default Ratings (IDRs) for banks. Fitch IDRs rate banks’ ability to service outstanding debt and are credit 

risk ratings. IDRs do not take into consideration market, liquidity, and other risks except to the extent 

that these risks affect the ability of the bank to make debt payments.

Fitch bank IDRs have two components: 1) the default vulnerability of the issuer assuming “ordinary 

support” from internal and external sources, and 2) the likelihood of receiving extraordinary support.

Ordinary support includes support from parent organizations, shareholder support, as well as external 

support, such as regular access to a central bank for liquidity. Extraordinary support includes support 

from external sources that one would expect to be forthcoming should the bank become in danger of 

default, such as the possibility of a collapse of the financial system. Extraordinary support includes 

liquidity, guarantees, and capital injections. Fitch states that extraordinary support that was forthcoming 

in the past is not necessarily assumed to be available in the future. Hence, not all the government 

programs used to manage the 2007–2009 global financial crisis are assumed by Fitch analysts to be 

available in future when they rate banks’ likelihood of receiving extraordinary support. Since Fitch IDRs 
17

are measures of default risk, regardless of the source of a bank’s financial support, IDRs are the higher of 

a bank’s individual rating and support rating.15 Fitch states that IDRs are not designed to be predictors of 

the numeric probability of default, but rather are ordinal risk measures. As a consequence, the observed 

default rates for across all IDR ratings bands vary over economic cycles. As with other measures of 

default, regulators must choose available data carefully to assign default probabilities to differing 

periods. 

FitchRatings (2013a) reviews the experience of bank issuers of debt globally and presents cumulative 

failure rates for one- to three-year horizons by IDR. Fitch points out that issuer default and issuer failure 

are not the same. An issuer may be able to make debt payments; but if that ability is contingent on the 

bank receiving extraordinary support, Fitch classifies the bank as “failed” even though it’s not in default.

More generally, when computing historical issuer failure rates, Fitch includes banks that were non-viable 

without external support among the failed banks. Table 4 lists the current, average long-term, and 

global financial crisis period one-year bank failure rates from the 2013 Fitch study. 

Table 4. Fitch Credit Ratings and Global Bank Failure Rates16

Individual 

Rating Long-term IDR Most Current Available

Long-term 

Average

Crisis Period 

Average

Fitch IR 

Bands Fitch LT IDR Bands 2011 failure 

rate (%)

1990–2011 

average annual 

failure rate (%)

2008–2009 

average annual 

failure rate (%)

A AAA, AA+, AA 0 1.05 30.0

A/B AA+, AA,AA-,A+,A 0 1.03 9.60

B AA-, A+,A, A- 0 0.77 6.26

B/C A, A-, BBB+, BBB 0 0.90 4.55

C BBB+,BBB, BBB-, BB+ 0.42 1.59 3.58

C/D BBB-, BB+, BB, BB- 1.16 2.03 2.01

D BB, BB-,B+,B,B- 4.60 2.96 2.09

D/E B+,B,B-,CCC 1.72 3.93 7.93

E CCC,CC, C 13.33 7.38 18.16

All Banks 1.82 1.71 4.92

Note that the average bank failure rates in Table 4 do not always increase the poorer the Fitch individual 

ratings (IRs). Specifically, Table 4 shows that average failure rate for A-rated banks exceeds that for Brated banks for the 1990–2011 period and the average failure rate for A, B, and C-rated banks exceeds 

that for D-rated banks for the 2008–2009 period. The non-monotonic relationship between Fitch IRs and 

bank failure rates is consistent with the definitions of IRs and bank failures in the Fitch 2013 study, as 

Fitch classified some banks as failed due to reliance on extraordinary support even though these same 

 

15 Fitch ratings of issuer default risk have evolved over time; however, there has not been any fundamental change 

of the way Fitch sets IDRs. Specifically, Fitch replaced its Individual Ratings (IRs) with Vulnerability Ratings (VRs) in 

2011. The VRs consider the same core risks as IRs, but use a more granular rating scale than did IRs. 16 See “Global Bank Rating Performance Study: 1990–2012”, FitchRatings, November 27, 2013, p. 9.
18

banks made debt payments. The largest banks, therefore, were most likely to receive assistance as they 

were systemically important and also likely to have the best credit rating, generating this pattern. 

3.2.3. Actuarial Bank Failure Rates

Countries can estimate directly bank failure rates based on the global banking industry or on their 

domestic industry. This will require a calculation of actuarial tables. To accommodate short-term and 

long-term perspectives in target fund design, we include three bank-failure forecast horizons in the 

target fund framework—one-, two-, and three-year cumulative failure rates.17 As an example, we 

obtained historical failure rates from the FitchRatings (2013a) study on global bank failure rates

between 1990 and 2011. Sources may also include the central bank or other regulators tracking business 

activity. Table 5 presents historical cumulative failure rates from the study.18 

Table 5. Cumulative Bank Failure Rates From the FitchRatings (2013) Study 

Economic State Period One Year Two Year Three Year

Crisis Period 2008-2009 4.92% 7.29% 7.70%

Through-the-Cycle 1990-2011 1.77% 3.66% 5.61%

Current Period 2011 1.82% 2.61% 8.59%

Table 6 presents one- , two-, and three-year cumulative failure rates for U.S. FDIC-insured banks for the 

three economic states we identified. Clearly, if a country has a significant history of bank closings, 

country failure rates are preferred to external failure rates. A shortfall of industry average failure rates is 

that one cannot differentiate banks in terms of failure risk and one failure rate is applied to all banks. 

Table 6. Cumulative Bank Failure Rates for the U.S.

Economic State Periods One Year Two Year Three Year

Crisis Period 1990:Q3–1991:Q4

2008:Q1–2014:Q1 1.10% 1.93% 2.38%

Through-the-Cycle 2006:Q1– 2016:Q1 0.65% 1.27% 1.87%

Current Period 2014:Q1–2016:Q1 0.13% 0.18%* 0.20%*

*Rates truncated since failure data only exist through 2017:Q1.

 

17 In the event of three years of failure versus one year of failure, we are not taking three-versus-one draws from 

the distribution, but a “total” three-year result with a certain cumulative failure rate versus a one- year result with 

a certain failure rate. 

18 See “Global Bank Rating Performance Study: 1990-2012,” Special Report, FitchRatings (November 27, 2013).
19

4. Loss Given Default

This section discusses the determinants of Deposit Insurance Fund (DIF) loss rates as a percentage of 

failed-bank assets.19 Sections 4.1 and 4.2 discuss the features of a deposit insurer that influence DIF 

losses. Section 4.3 describes the key cash inflows and outflows that determine DIF losses, and Section 

4.4 presents information on U.S. FDIC losses on bank closings between 1984 and 2016. While the 

examples of insurance loss determinants given in this section may not apply to all insurers, the section

provides information on how deposit insurers generally should approach the task of determining loss 

given default. The model here will use data to create a rule for loss given default, and does not model or 

simulate explicitly in the calculation of losses as it does default events. Regulators may choose a single 

value for loss given default or select differing values to reflect all current conditions in the country.

4.1. Failure Resolutions

The bank failure-resolution process has three main elements. First, the deposit insurer makes payments 

to insured depositors using the resources of the DIF. Assuming that depositors are paid fully and 

promptly—sensible performance goals on their own—this payout process should not vary much across 

deposit insurers. Second, the insurer is entitled to receive reimbursement from asset liquidations based 

on the subrogated rights of insured depositors. Third, the deposit insurer reimburses all other bank 

creditors using the proceeds (recoveries) from failed-bank asset liquidations and/or proceeds from other 

forms of failure resolution. These last two can be significant sources of variation in loss rates across 

deposit insurers.

4.1.1. Priority of Claimants

The primary determinant of deposit insurance losses lies in how asset recoveries are disbursed. The FDIC 

Act states that the FDIC’s subrogated claim has priority over that of uninsured depositors and other 

creditors. Among claimants, deposits have preference over all other non-secured, non-preferred 

claimants. If a deposit insurer has first claim on assets, even a relatively low recovery rate will mean very 

few losses for the insurer. Not all deposit insurers have the same claim structure, however. If the 

deposit insurer is pari passu with other claimants, losses are likely to be high even with a relatively high 

recovery rate.

4.1.2. Structure of Losses

Table 7 summarizes the key cash flows associated with bank-failure resolutions for the DIF. Note that all 

recoveries, including recoveries from appointed agents and the courts, are included in the recoveries 

listed in Table 7. Deposit Insurers often record recoveries from failed-bank resolutions by bank asset 

type. In Table 7 we use three broad categories of bank assets—Risk (for example,, loans), Physical (for 

example, fixed assets), and Investment (for example,, securities)—to illustrate this point.

 

19 Failed-bank assets are measured the quarter-end prior to failure. This loss rate base was chosen since one will 

only know reported bank assets prior to closing for the purpose of projecting losses. 
20

Table 7. Failed-bank Recoveries and Claims Payment

Cash Inflows: 

Recoveries on Risk Assets, 

Physical Assets and 

Investments

After Bank Closure

Recoveries made by DIF

- Risk asset repayments/collateral sales

- Physical asset sales

- Investment asset sales

Recoveries made by appointed agents

Recoveries from court cases/litigation

Cash Outflows: 

Disbursements for creditor 

claims and liquidation 

expenses

Insured Depositor Claims 

Receivership Expenses

- Liquidation Expenses 

- Asset Management 

- Appointed Agent Expenses 

Uninsured Creditor Claims

Secured Claims Are paid directly from collateral 

4.2. Deposit Insurance Losses

Equation 10 shows net recoveries on assets for an individual failed bank, j, as the sum of recoveries over 

the life of the receivership (periods 0 to T) minus receivership expenses. 

Net Recoveriesjj = ∑ RR RR tt

TT

tt=0 − ∑ LL LL EEEEEEEE tt

TT

tt=0 (10)

After receivership expenses and preferred claims, the FDIC has the next claim on recoveries equal to the 

subrogated claim of insured depositors. Hence the FDIC’s net cash flow is always less than or equal to 

zero, that is, never a profit. 

NN h FF jj = NN RR RR jj − PP CC jj − II jj (11)

Should net recoveries exceed insured deposits and preferred claims, the FDIC would distribute the 

excess to uninsured claimants.

4.3. FDIC Loss Rates

Tables 8 and 9 present information on FDIC net loss rates as a percentage of failed-bank assets for the 

crisis, through-the-cycle, and current periods identified previously. Insurance losses take into 

consideration recoveries from asset liquidations and/or bidder payments for failed banks, receivership 

expenses, preferred and secured liabilities, and FDIC’s subrogated claim. These rule-based values are 

then used with failure simulations to determine net losses for each simulated year. We computed loss 

rates on failed-bank assets for five bank asset-size groups to control for the historical relationship 

between bank size and deposit insurance loss rates—loss rates tend to decline as bank size increases.20

 

20 Possible reasons for the inverse relationship between bank size and failure-resolution costs are the market 

monitoring of large, publicly traded banks, continuous on-site supervisory presence at the largest banks, and 

greater portfolio diversification and franchise value of large compared with small, community banks. An 
21

An alternative approach would be to compute loss rates by asset types, for example, risk assets, physical 

assets, and investments. However, these types of loss rates were not available for this study.

Table 8. FDIC Loss Rates on Failed-Bank Assets

Asset Size Crisis Period Through-the-Cycle Current Period

<= $100 M 23.8% 29.1% 20.1%

$100 M to $500 M 24.4% 24.7% 16.0%

$500 M to $1 B 22.5% 22.3% 7.0%

$1 B to $10 B 18.4% 18.8% 12.0%

Over $10 B 13.1% 15.4% ---

Table 9. Number of Failed Banks by Asset Size Group

Asset Size Crisis Period Through-the-Cycle Current Period

<= $100 M 250 129 16

$100 M to $500 M 292 262 9

$500 M to $1 B 69 63 1

$1 B to $10 B 65 56 1

Over $10 B 11 9 ---

5. Exposure at Default

Estimating deposit insurance exposure at default is relatively straightforward compared with other 

parameters necessary to estimate a deposit insurance fund target. Data on deposits and bank liabilities 

should be available from quarterly bank financial statements that banks file with their regulators. 

Estimates of insured deposits are often reported by banks as well, sometimes directly to the deposit 

insurer and other times to the central bank. The accuracy of self-reported insured deposits varies with 

the complexity of deposit insurance coverage rules, with more complex rules yielding less reliable 

estimates. The percentage of deposits that are insured will vary with bank type within the country, and 

insurance exposures depend heavily on the deposit insurance thresholds relative to average depositor 

wealth levels as well as wealth distributions. Thus, the resulting exposure at default parameter will not 

be explicitly modeled in the simulation, but rather determined as a rule from available data. 

5.1. The U.S. Case

U.S. insured banks with assets over $1 billion are required to report an estimate of insured deposits 

quarterly to their primary federal regulator. Based on U.S. bank data as of December 2016, insured 

deposits as a percentage of domestic deposits decrease as bank asset size increases. Among banks with 

assets over $10 billion, insured deposits as a percentage of domestic deposits were 61 percent, and 

among banks with assets between $10 billion and $1 billion, the percentage of insured deposits was 74

percent. While we do not have self-reported insured deposits for banks with assets under $1 billion, the 

 

examination of the determinants of large versus small-bank failure-resolution costs, however, is beyond the scope 

of this paper. 
22

FDIC does have information on insured deposits at closing for 161 banks that failed between January 

1984 and December 2016. This sample is a small selected fraction of the 1,859 banks that failed during 

this period. However, as the purpose of this exercise is to bound the cost of the deposit insurer, we find 

insured deposits were an average of 97 percent of total deposits for these 161 failed banks. In the U.S. 

Target Fund Ratio estimates, we use the self-reported insured deposit shares for banks with assets over 

$1 billion and assume the percentage of deposits that are insured is 97 percent for banks with assets 

under $1 billion. Countries with higher income inequality usually have a higher proportion of uninsured 

deposits, and regulators may elect to segment exposure at default by institution size or economic 

conditions as they see fit, or may instead choose to use only a single proportion for exposure given 

default across all banks and periods. 

6. Correlation of Bank Failures

A major contribution of this paper is going beyond default probabilities discussed in Section 3 to model 

the correlation of defaults through the correlation in asset returns, ρρ. Obtaining correlations of bank 

failures to combine with overall probabilities of bank failure allows regulators to simulate a more

realistic distribution of defaults. We discuss two primary approaches that can be used to obtain 

correlations in the movement of bank values and thus their proximity to failure. 

6.1. Stock Return Data

Pricing data for publicly traded banks will incorporate all publically available information and possibly

some private information as well about the valuation of the company. Correlations obtained from these

data can be aggregated based on desired periods to generate correlation inputs for the simulation 

model. Regulators could estimate pairwise Pearson correlations for each pair of bank stock returns, and 

then take the average of these correlations to get an overall industry average correlation. 

Table 10 shows the mean pairwise correlation in quarterly stock returns for all publicly traded U.S. 

insured banks for the three economic periods previously identified. Overall, return correlations are low,

but do increase with economic stress, as expected. This is potentially due to the U.S. banking sector 

having numerous banks of varying size, product mix, geographic coverage, and complexity.21

Table 10. Bank Quarterly Stock Return Correlation

Period Mean Correlation

Crisis 0.094

Through-the-Cycle 0.090

Current 0.049

 

21 An alternative approach to using mean pairwise stock return correlations for all bank stocks is to compute 

average pairwise average correlations by industry segments, based on asset size, business orientation (for 

example, wholesale versus retail banking) or other bank characteristics. For simplicity, we use the overall pairwise 

average correlations in this paper.
23

6.2. Book Equity

Alternatively, one could derive correlation using book equity in a similar process. Banks that are 

required to report financial statements to the central bank would report returns on equity, and 

regulators could estimate pairwise Pearson correlations for each pair of bank returns on equity, and 

then average these correlations for an overall correlation in returns on equity. While every bank will 

have a value using this approach—even smaller private banks—they will not be subject to the same 

amount of public scrutiny and information gathering that stock return data are subject to, and thus this 

measure of asset correlation is generally of worse quality. Regulators should choose carefully between a 

larger number of low-quality equity measures from book equity data and a smaller number of higherquality equity measures from common stock data. 

7. Model Calibration

Estimating the national level bank-failure loss distribution using the Monte Carlo simulation model 

requires estimates of four parameters as discussed above—probability of default, loss given default, 

exposure at default, and correlation of default. For this example, we lay out the simulation options again 

in brief and note the selections we made.

7.1. Probability of Default (PD)

Deposit insurers should keep records on the number of bank closings during their history to use as a 

basis for simulating defaults. However, countries that lack long-term data must use other methods for 

estimating the probability of default. Options for all these data environments are presented below: 

7.1.1. Statistical Predictions

Statistical predictions of undercapitalization may be used as when failure information is sparse. In this 

approach, regulators estimate the likelihood of banks becoming critically undercapitalized (for example, 

less than 2 percent equity and reserves-to-assets ratio in the U.S. case) using available bank financial 

data, usually with a logistic model. This is discussed in section 3.2.1.

7.1.2. Issuer Default Ratings

Credit ratings have been used to model bank failure risk in many jurisdictions where actual closings are 

infrequent or when data are unavailable to make statistical predictions of undercapitalization or closing. 

This is discussed in section 3.2.2.

7.1.3. Industry Failure Rates 

Failure rates based on actual closings may be available for some periods but not others. Records may be 

missing in some cases, and in other cases the variance in closures may be artificially high if banks are 

closed periodically as part of major government consolidation initiatives rather than when they become 

insolvent. This is discussed in Section 3.2.3. This is the measure used for this U.S. simulation, with 
24

differing values for each of the three economic periods and from one- to three-year horizons, shown in 

Table 6, and contributes to the credit as well as liquidity probabilities of failure.

7.2. Loss Given Default (LGD):

Estimating loss given default requires access to information about recoveries from past asset 

liquidations among differing economic conditions as discussed in Section 4. Losses given default are 

not explicitly modeled in the simulation, but rather are determined by a rule from historical experience.

Each country must choose these values based on its experience and institutional background. This 

simulation uses differing values of LGD for each of the three economic periods and by bank asset size, as 

shown in Table 8.

7.3. Exposure at Default (EAD)

Countries should have access to estimates of share of insured deposits as well as overall asset size from 

their bank’s reporting as discussed in Section 5. This will allow regulators to create a rule-based value for 

the share of insured deposits in each bank, and regulators can elect to have it vary by period or across 

banks at their discretion. Exposure at default varies by individual bank in this simulation, but is constant 

across all three economic periods. In the U.S. Target Fund Ratio estimates, we use the self-reported 

insured deposit shares for banks with assets over $1 billion and assume the percentage of deposits that 

are insured is 97 percent for banks with assets under $1 billion.

7.4. Correlation of Default

Regulators can either use publicly available stock returns or figures reported to the regulators on book 

equity to generate a measure of default correlation as discussed in Section 6. For this simulation, we use 

stock market data and overall pairwise return correlations by economic period, as shown in Table 10.

8. Model Results

Using the above inputs across the three differing sets of economic conditions—current, through-thecycle, and crisis period—regulators can estimate losses from bank failures. Crisis conditions are likely to 

generate the highest required reserve ratio, and are likely to be the binding target for deposit insurers. 

We used 500 random joint draws of systemic and idiosyncratic risk factors in the Monte Carlo 

simulations to generate failure events across each of these three periods of conditions over one-, twoand three-year horizons. The greater the number of simulations, the greater the ability of the model to 

detect high-loss, low-probability events. Since there were about 5,857 FDIC-insured banks as of 

December 2016, we limited the number of random draws of the risk factors to 500. The simulations 

resulted in over 2.9 million bank-simulation failure-loss results, from which we derive the FDIC’s 

cumulative loss distribution.

22

 

22 The Excel simulation model execution time for bank-simulation events will vary with the capacity of the 

computer used to run the simulations. Our simulation run times was about five hours. Countries with vastly 
25

It is common in these scenarios to have the vast majority of simulations result in few or no failures, with

a few simulations yielding large numbers of failures. After identifying the failure events, each failed bank 

will impose costs to the insurer equal to the product of the loss given default rule and the exposure at 

default of that bank. These losses per bank are then summed to estimate total losses to the deposit 

insurer for that particular random draw. 

8.1 Desired Fund Size

The aggregate amount of deposit insurance losses an insurer wishes to be able to absorb over a specific 

time horizon is a public policy choice. As a benchmark, over the past 40 years U.S. Aaa and Aa rated 

municipal bonds have made payments of interest and principal 99.97 percent of the time.23 The 99.97 

percent confidence level is also commonly used as a benchmark for U.S. banks’ economic capital models 

and the Basel II capital requirements.24 The 99.97 percent confidence level implies a loss level that is 

exceeded once in every 3,333 Monte Carlo simulations. The 99.97 percent loss threshold is, however, at 

odds with the U.S. experience with deposit insurance. The Federal Savings and Loan Insurance 

Corporation became insolvent, the National Credit Union Share Insurance Fund narrowly avoided 

bankruptcy by capitalizing a portion of member credit unions’ capital and the FDIC twice became bookequity insolvent due to high failure-loss reserves that were not needed thanks to improvements in the 

economy as well as government support programs during previous banking crises. For these reasons, we 

chose a confidence level more in line with the experience for the U.S. Target Fund Ratio estimate—a 

99.8 percentile confidence level—that ensures the target fund is exceeded only once in 500 trials. The 

confidence level we selected is consistent with previous research on the adequacy of the FDIC’s 

insurance fund in non-crisis periods.25 

Table 11 presents the results for estimates of the Target Fund Ratio necessary to absorb insurance 

losses at the 99.8 percent confidence level for three economic states where all results are based on U.S. 

historical bank failure for PD in section 7.1, insurance loss rates for the LGD rule as mentioned in in 7.2, 

bank balance sheets to summarize exposure as in section 7.3, and average pairwise correlation in stock 

returns as a measure of failure correlation mentioned in 7.4. We assume rigorous enforcement of FDIC’s 

 

smaller numbers of banks than the United States, for example, 20 to 30 banks, can run 50,000 simulations in 

minutes.

23 See “Safety of Investment Grade Bonds - Examining Credit Ratings and Default Rates of Municipal and Corporate 

Bonds” by Stephen J. Huxley and Brent Burns, Asset Dedication White Paper Series (February 2011). 24 There is inherently a tradeoff between selecting periods of the economy to use to calibrate default probabilities 

and the confidence level. Assuming that the economy uses only one data generating process, one would need to 

look at a higher confidence level than if one were to consider the economy uses multiple data generating 

processes instead and looking at the data generating process for the bad states of the economy, to get the same 

level of safety. 25 Schuermann and Kuritzkes (2005) use a Merton credit loss model of the FDIC’s Bank Insurance Fund (BIF), 

estimated as of year-end 2000 and find that the BIF was adequate to cover losses up to the 99.85 percentile level 

but note that under different, stressed market conditions the confidence level was 96 percent. See Til 

Schuermann and Andrew Kuritzkes, Deposit Insurance and Risk Management of the U.S. Banking System: What is 

the Loss Distribution Faced by the FDIC?” Journal of Financial Services Research 27:3 217–242, 2005.
26

least costly resolution rule by assuming losses cannot exceed the value of insured deposits. To avoid 

false precision, we round Target Fund Ratio estimates to the nearest full percentage point. Using a oneyear bank failure horizon and limiting insurance losses to insured deposits, the Target Fund Ratio

estimates under current, through-the-cycle and crisis period conditions are 3, 4 and 5 percent of insured 

deposits respectively. 

Table 11. Target Fund Ratio as a Percentage of Insured Deposits 

(Target for 99.8% Confidence Level)

Cumulative Failure Rate Current Period Through-the-Cycle Crisis Period

One Year 3% 4% 5%

Two Year 3% 4% 5%

Three Year 4% 7% 7%

The FDIC’s current Target Fund Ratio is 2 percent of estimated insured deposits, a target which has been 

reaffirmed annually. The FDIC did not arrive at its Target Fund Ratio using a credit risk modeling 

approach as was used here; rather, the FDIC based its Target Fund Ratio choice in part on an analysis of 

historical FDIC losses, income and insurance fund levels. In addition to historical analysis, the FDIC must 

consider specific statutory factors when selecting the Target Fund Ratio—the risk to the DIF in current 

and future years, economic conditions, the potential for sharp swings in insurance assessment rates and 

other factors the FDIC’s Board of Directors deem appropriate. The FDIC published a historical analysis by 

Davison and Carreon (2010) which used data from the period 1950 to 2010 and a different model from 

this one that was based on aggregate data in an income and expense simulation model that reviewed 

the FDIC’s historical losses and simulated insurance fund levels under alternative insurance premium 

and fund maintenance strategies, arriving around a 2% minimum fund estimate.

26

It is thus difficult to directly compare our credit loss model estimates of the Target Fund Ratio with the 

FDIC’s historical insurance fund analysis. The credit loss model in this paper uses a point in time 

estimate of potential insurance losses over one-, two- and three-year failure horizons and does not 

incorporate funding from insurance assessments and FDIC investment income over a long horizon that 

Davison and Carreon (2010) take into consideration. Other countries may not have as much flexibility in 

directing investments for their deposit insurance funds or making special or prepaid assessments of the 

banking sector as the FDIC has, which would necessitate a more conservative fund target. Finally, the 

credit loss model cannot take into consideration certain statutory factors the FDIC must consider when 

setting the Target Fund Ratio, such as potential future changes in regulatory legislation.

8.2 Longer Horizons

The Target Fund Ratio estimates increase as we increase the bank failure horizon to allow the deposit 

insurer to weather longer crises, with the three year failure horizon Target Fund Ratio estimate reaching 

7 percent under crisis period conditions. Table 11 shows the sensitivity of the Target Fund Ratio 

 

26 See FDIC (2010). 
27

estimates to the bank failure horizon and the economic conditions FDIC operates under when 

liquidating failed-bank assets.27

9 Inherent Weaknesses of Model Assumptions

All approaches to estimating the target deposit insurance fund require one to make assumptions about 

which factors influence the target fund (i.e., drivers of insurance losses) and the manner in which these 

factors combine to influence the target fund. The Loss Distribution Approach relies on historical data on 

deposit insurance losses and is entirely a data-driven approach. Implicit in the Loss Distribution 

Approach is the broad assumption that past drivers of deposit insurance losses remain relevant in the 

future and that the manner in which these drivers combine to influence insurance losses remains much 

the same in the future. The Credit Portfolio Approach relies on less data than the Loss Distribution 

Approach and, therefore, the Credit Portfolio Approach must use explicit assumptions about the drivers 

of insurance losses and how these drivers combine to influence insurance losses. While it is still reliant 

on historical data, it can be used to generate simulations based on new conditions and incorporate data 

from sources other than the historical experiences of the host country. 

As discussed previously, the Credit Portfolio Approach does not model the influence of the legal and 

regulatory environment on insurance losses and assumes the structure of the financial safety net, and 

deposit insurance regime in particular, remain unchanged from that reflected in the model input data. 

The Credit Portfolio Approach also makes strong assumptions about the process that generates bank 

asset value changes and, therefore, bank failures. The specific assumptions for asset returns are:

a. assets value changes are driven by a linear combination of systemic and idiosyncratic risk factors

(Merton-Vasicek Model),

b. both risk factors are transformed to standard normal random variables (mean zero and standard 

deviation of one),

c. idiosyncratic risk and systemic risk are distributed independently of one another,

d. the idiosyncratic risk of any two obligors is distributed independently of one another,

e. Idiosyncratic risk of all obligors in not serially correlated.

It is generally acknowledged by economists that firms’ profitability, liquidity and capitalization are 

influenced by firm-specific factors and events (e.g., hiring of new corporate executives), as well as by 

general macroeconomic conditions, i.e., systemic factors. There is less agreement, however, on how to 

measure idiosyncratic and systemic risk factors and on the manner in which these factors combine to 

determine asset returns. 

The strongest assumption of Merton-Vasicek Models is that asset returns are normally distributed. 

Financial securities returns are typically non-normally distributed and have return distribution with “fat 

tails” that allow for higher probabilities of large losses. While the normal return distribution assumption 

might lead to some underestimation of low probability, high loss events, we feel the calibration of the 

 

27 We recommend deposit insurers also conduct sensitivity analysis around the sensitivity of Target Fund Ratio 

estimate to changes in the Monte Carlo simulation model parameters—PD, EAD, LGD and failure correlation.
28

loss distribution to three states of the economy—current, through-the-cycle and crisis period—and the 

use of a high threshold for the loss confidence level, 99.8 percent, helps ensure the adequacy of target 

fund estimates.

10 Conclusion

Deposit insurers need not restrict themselves to one methodology for determining the target deposit 

insurance fund. Further, the target fund estimation has been the subject of many academic studies. For 

these reasons, deposit insurers can choose a Target Fund Ratio by drawing upon several sources of 

information. For example, the FDIC has studied the target fund question using a wide variety of sources 

of information—FDIC historical experience, simulations based on past FDIC losses, credit risk models 

developed by outside experts and academic literature on deposit insurance. The target fund framework 

presented herein describes a transparent process that can be undertaken by regulators to estimate the 

Target Fund Ratio even when faced by significant data challenges.
29

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32

Appendix A—Principal Components Analysis used for Macroeconomic Crisis Periods

1. Principal Component Analysis

Principal component analysis can most easily be explained through an example of its application to, for 

example, risk measurement. Suppose one has year-end 2015 data on bank-level observations for several 

bank profitability and efficiency measures—return on assets, net interest income-to-assets, expenses on 

fixed assets-to-total revenue, and noninterest expense-to-total revenue. Principal component analysis 

finds that linear combination of the underlying variables that best explains the total variation in the data 

and is orthogonal (uncorrelated) with the original variables. 

More formally, let X be a matrix containing data on the bank financial ratios we wish to summarize in an 

index. The columns of X are different bank observations and the rows are the different financial ratios. If

we measure our variables as deviations from means, the matrix product X’X becomes the variancecovariance matrix of X. In addition, if we normalize the deviations from means by the standard 

deviations, then X’X becomes a matrix of pairwise correlation coefficients for the different financial 

ratios.

PCA transforms a dataset of correlated variables into a dataset of uncorrelated variables, the principal 

components. There are as many principal components as there are variables in the original dataset. 

PCA, however, selects that orthogonal row vector C (aka, eigenvector) that maximizes the amount of 

variance in the original dataset explained by the principal components. The product of the data row 

vector X’

and column eigenvector C is the first principal component:28

PC1 = X’C (1A.)

PCA assumes the underlying data are quantitative measures or ordinal measures. PCA is scale 

dependent. Hence, unless all variables are measured in the same units (for example, percentages, 

dollars), the data should be normalized as described previously. In equation 2A, PC1 is the first principal 

component and is the sum of the products of the variable weights or factor loadings 1, 2, ... , NN based 

on the eigenvector and the value for the corresponding underlying economic variables 1, 2, ... , NN for 

that observation, here quarter t.29

PPPP1,t = ( 1) ∗ 1,tt + ⋯ + ( NN) ∗ NN,tt (2A.) 

Principal component analysis ranks these transformed variables based on the amount of variance in the 

entire dataset the principal component explains, hence the first principal component explains more 

variance than the second principal component and so on for the remaining principal components.

Another property of principal components is that they are all independent (uncorrelated) of one 

another, with the result that each principal component explains different characteristics of the dataset. 

 

28 More specifically, to find the first principal component, one solves the constrained maximization problem of 

finding that eigenvector, C, that maximizes the variance-covariance matrix (C’X’XC) such that C’C = I, where I is the 

identity matrix. 

29 The sum of the squared factor loadings will equal one.
33

While there are as many principal components as there are underlying raw variables, the first one or 

two principal components usually explain a majority of the variance of the dataset. This latter result

means one can obtain a great deal of the information in a dataset using just the first one or two 

principal components (dimension reduction). 

To know how to interpret the principal component values across banks, one can estimate the Spearman 

rank order correlation coefficient between the principal component and the underlying variables. 

Typically one will find some variables to be more highly correlated with the principal component than

are other variables and that the correlations change as one uses the second, third, and remaining 

principal components. These correlations also provide a way to validate the informational content of the 

principal component.

2. Two-Stage Principal Component Analysis

If one has, for example, five measures of a single bank attribute, such as asset quality, one can replace 

these variables with an average value. However, it is not clear how to weight the individual variables 

used by this average. One way to determine the weights for the individual asset quality measures is to 

find the first principal component for the five asset quality measures and then use this principal 

component as a variable in a second principal component analysis, which we next describe.30 

In the two-stage PCA, each of the key desired attributes, for example, the six CAMELS attributes, is

individually modeled with separate principal components analyses. Next, all first principal components 

from the first stage PCA are used as variables in a second-stage PCA. Equation 3A shows the secondstage PCA in which the weights, ai, for the six CAMELS PC1 are determined by the principal components

procedure discussed previously. The resulting first principal component is a composite CAMELS attribute 

index. 

 PPPP1 composite ,t = ( 1) ∗ PPPP1,cccccc cc ,tt + ⋯ + ( 6) ∗ PPPP1,ssssssss ss ss tttt mm mmmm ,tt (3A.) 

The advantage of the two-stage PCA is that there is no intermediate variable selection step required and 

all key variable types, for example, CAMELS attributes, are maintained through the final step. 

The two-stage principal component analysis of banks’ CAMELS attributes is one way in which analysts 

can measure banks’ condition using the widely used CAMELS attributes even when supervisory ratings 

of banks based on onsite safety and soundness exams are not available. The first-stage PCA provides 

principal components (indexes) for each of the six CAMELS attributes (that is, substitutes for CAMELS 

component ratings) and the second-stage PCA provides a first principal component for bank overall 

condition (that is, substitutes for the composite CAMELS ratings).

 

30 Vincent and Sutherland (2013) discuss the use of the two-stage PCA in the construction of socioeconomic 

indexes. Two-stage PCA is also used in pattern recognition models as a way to further reduce the noise in the video 

signals as discussed in Zhang, Dong and Shi (2010).
34

To evaluate the potential of the first principal component to measure bank riskiness, we compare the 

predictive accuracy of two bank-failure prediction models. The first model is a standard logit regression 

of the determinants of bank failure during a one-year period as a function of prior year-end bank 

financial condition. We measure bank financial condition using 12 financial ratios that are used by the 

FDIC’s Statistical CAMELS Offsite Rating (SCOR) model.31 The 12 ratios capture each of the six CAMELS 

attributes and are heavily weighted toward asset quality measures since asset quality is a primary driver

of bank safety and soundness. We estimate stepwise logit regressions annually to determine the most 

predictive variables, and use parameter estimates to estimate out-of-sample failure probabilities for 

banks in the following year. The second model is a one-stage PCA of all 12 SCOR financial ratios using 

the same year-end data used in the logit model out-of-sample forecasts. We estimate models annually 

using data on all U.S. insured banks and thrifts between 2008 and 2014, a period that includes the most 

recent U.S. financial crisis. For brevity we do not present all logit model estimates and results here.

However, representative results for the 2009 logit model estimates and 2010 PCA factor loadings used 

in risk rankings are shown in tables 1A and 2A. In table 1A the logit model coefficient estimates show 

increases in equity capital and liquid assets reduce the likelihood of failure, while increases in other real 

estate owned and nonaccrual assets increase the likelihood of failure, as expected. Table 2A shows the 

factor loadings for the SCOR model ratios also have an intuitive relationship with the risk index, PC1. The 

factor loadings for equity capital, liquid assets and income before taxes are negatively related to PC1, 

while all remaining SCOR ratios (primarily asset quality measures, loan loss measures and noncore 

funding) are positively related to PC1. These factor loading signs suggested bank riskiness increases with

PC1. 

In terms of in-sample explanatory power of the two models, the first principal component explained 34 

percent of total variance in the data and the first three principal components explain 58 percent of total 

variance. These results suggest the logit model should outperform PCA in short-term failure prediction. 

 

31 The 12 SCOR model financial variables are equity capital, loan-loss reserves, loans past due 30-89 days, loans 

past due 90 days or more, nonaccrual loans, other real estate owned (includes repossessed real estate), loan and 

lease charge-offs, provisions for loan losses, income before taxes, noncore funding, loans and long-term securities 

(maturities over 5 years). Liquid assets are the sum of cash balances, securities, federal funds and repurchase 

agreements sold. Noncore funding is the sum of time deposits over $100,000, foreign deposits, federal fund and 

repurchase agreements purchased, demand notes issued to U.S. Treasury, and other borrowed money. All financial 

variables are measured as a percent of the bank’s gross assets (assets plus loan-loss reserves). For further details 

see Collier, Forbush, Nuxoll, and O’Keefe (2003). 
35

Table 1A. Stepwise Logit Regression of the Determinants of Bank Failure

Table 2A. Factor Loading (Eigenvector) for First Principal Component 

Figure 1A shows comparative model results for out-of-sample bank failure prediction for 2011.

32 In 

Figure 1A, we compare the percentage of 2011 bank failures that are correctly identified by the ranked 

indexes—logit model failure probability and first principal component. The logit model correctly 

identifies 82 percent of failed banks in the first 1.56 percent of all 7,490 risk-ranked banks while the first 

 

32 All model estimates and forecasts are available from the authors upon request.

Year-end 2010

Independent Variables* Estimated Coefficient (Standard Error) 

Equity -1.0792***

(0.1168)

Liquid Assets -0.0580* 

(0.0258)

Other Real Estate Owned 0.1122*

(0.0486)

Nonaccrual Loans and Leases 0.1018* 

(0.0421)

Intercept 2.4547*

(0.9877)

Pseudo R-squared 0.7199

N 7,490

* p<0.05, ** p<0.01, *** p<0.001

*Note: All variables are measured as a percentage of gross assets.

First Principal Component

SCOR Ratios Factor Loading

Equity Capital -0.1859

Loans PD 30-89 0.2035

Loans PD 90+ 0.0554

Nonaccrual Loans and Leases 0.3804

Other Real Estate Owned 0.3059

Liquid Assets -0.2604

Noncore Funding 0.1650

Charge-offs 0.3589

Income Before Taxes -0.3273

Loan Loss Reserves 0.3878

Loan Loss Provisions 0.4156

Loans and long-term Securities 0.1689
36

principal component correctly identifies 58 percent of failed banks.33 We obtained similar results for 

2012 through 2015. While we expected the logit model to be more accurate than PCA in risk ranking 

banks, deposit insurers in many jurisdictions do not have a sufficient number of historical bank failures 

with which to estimate a logit model of bank-failure prediction.34 We believe PCA can provide a useful 

alternative to empirical risk measures that are based on probability distributions, require significant 

historical data on failure events, or rely on bank risk ratings from credit rating agencies or government 

safety and soundness examinations of banks. All deposit insurers should have access to bank financial 

statements and have a sufficient understanding of bank risk drivers, for example, SCOR model variables, 

with which to use PCA, however. 

Figure 1A.

3. Interpretation of First Principal Component

Section 2 demonstrated the ability of the first principal component to risk-rank banks. If one normalizes 

the financial data used in PCA, that is, subtract the mean and divide the difference by the standard 

 

33 There were 92 bank failures in 2011. Banks file quarterly financial reports with their primary federal regulators 

that are used to obtain the SCOR financial ratios. Since 26 banks failed in the first quarter of 2011, prior to filing 

financial reports for year-end 2010, our sample includes 66 of the 2011 bank failures. 34 Our tests of PCA’s relative predictive power is obviously biased toward the logit model since we obtained a best 

fit logit model based on the FDIC’s long-standing early warning system SCOR. While we did not conduct an 

exhaustive search for the “best” failure prediction model, the SCOR model contains explanatory variables common 

to published literature on the determinants of bank failures. Further, we did not conduct a second-stage PCA in the

interests of simplicity; however, we anticipate a second-stage PCA would further enhance the predictive accuracy 

of the approach. 

0.0%

10.0%

20.0%

30.0%

40.0%

50.0%

60.0%

70.0%

80.0%

90.0%

100.0%

0.0%3.0%5.9%8.9%

11.8%14.8%17.7%20.7%23.6%26.6%29.5%32.5%35.4%38.4%41.3%44.3%47.2%50.2%53.1%56.1%59.0%62.0%64.9%67.9%70.8%73.8%76.7%79.7%82.6%85.6%88.5%91.5%94.4%97.4%

Percent of Failed Banks

Percent of All Banks Ranked by Risk Index (logit & PC1)

Failure Prediction: Logit Model vs First Principal Component

(Out-of-Sample Forecasts for U.S. Banks in 2011)

Logit Model PC1
37

deviation, one obtains a standard normal variable that has a mean of zero and standard deviation of 

one. If normality can be reasonably assumed, most statistical textbooks contain the information on the 

distributions of standard normal random variables (aka, Z scores) that can be used to determine the 

likelihood of various values. For example, the Z score distribution indicates that 95 percent of scores will 

fall between +/- 1.96 and 99.7 percent of scores between +/- 3. The Z score distribution is also assumed 

constant over time, and implicitly this assumes one can compare first principal components not only 

across banks, but also over time. 

Like an issuer default rating, the default frequency for any PC1 range (bucket) will vary with economic 

conditions, and in general rise with economic stress. Where deposit insurers lack information on issuer 

default ratings, CAMELS ratings, and other formal ordinal risk rankings, it might be possible to determine 

the default frequencies for banks in several comparable jurisdictions over time and map these to a

countries PC1 buckets. These default rates could serve as a means to calibrate a bank’s PC1 to the failure 

risk they present to the deposit insurer.