Effects of Bank Consolidation on the Bank Insurance Fund 

Robert Oshinsky 

Financial Economist 

Division of Research and Statistics 

Federal Deposit Insurance Corporation 

550 17th Street, N.W. 

Washington, D.C. 20429 

Phone: 202-898-3813 

Fax: 202-898-7149 

E-mail: roshinsky@fdic.gov 

The author gratefully acknowledges the comments and suggestions of William R. 

Watson, Barry Kolatch, Steven Seelig, James Marino, Lynn Shibut, and Kevin Sheehan. 

The views expressed are those of the author and not necessarily those of the Federal 

Deposit Insurance Corporation. 
1. Introduction 

Consolidation in the banking industry has increased at record levels during recent 

years. At year-end 1990, the 25 largest banking organizations held approximately 22 

percent of industry assets; by year-end 1998, this figure had increased by more than twothirds to approximately 54 percent. 

This study examines the implications of this consolidation for the Bank Insurance 

Fund (BIF). The results show that, based on historical loss and failure rates, the 

consolidation that took place between 1990 and 1997 increased the risk of BIF 

insolvency by approximately 50 percent, and that megamergers that took place or were 

announced during the 18 months between year-end 1997 and midyear 1999 increased the 

risk of insolvency further. Moreover, unlike the BIF of 1990, the solvency of the BIF of 

today is inseparably tied to the health of the largest banking organizations. 

Section 2 (“Background”) of this study provides background information on 

trends in the industry, differences between large and small institutions, and historical loss 

and failure rates. Section 3 (“Simulation Model”) describes the Monte Carlo model used 

to simulate the financial condition of the BIF. Section 4 (“Results”) discusses the results, 

and section 5 (“Conclusion”) contains some concluding remarks. 

2. Background 

Two studies were conducted in the 1990s predicting the probability of insolvency 

of the BIF, but major changes in the banking industry since the mid-1980s have raised 

critical issues not addressed by the authors of those studies, Sherrill Shaffer in 1991 and 

Kevin Sheehan in 1998. Shaffer employed a Markov process to study the probability of 

2 
insolvency of the BIF. On the basis of the FDIC’s funding mechanism before the 

Financial Institutions Reform, Recovery, and Enforcement Act of 1989 (FIRREA), he 

found the BIF to be underfunded. Sheehan used a Markov-switching model, coupled 

with more up-to-date assumptions about the FDIC’s assessment rates, to project the 

probability of insolvency under today’s funding arrangements. He found that the BIF 

would be able to weather most crises without becoming insolvent. But both Shaffer and 

Sheehan implicitly assumed that future disbursements and losses would fall into a pattern 

similar to that of past FDIC disbursements and losses. Given the structural changes 

alluded to above, however, and particularly the consolidation initiated in 1998 when the 

first U.S. megabank was formed (Bank of America, with $619 billion in banking assets), 

the question of probable BIF insolvency needs to be studied anew. 

In addressing consolidation, one cannot merely assume that large banks are big 

replicas of small banks. Large banks differ from small banks not only in size but also in 

liability structure, failure rates, and loss rates. To capture the effects of consolidation on 

the BIF, one must take all of these differences into account. 

2.1 Size: Consolidation within the Industry 

When a bank fails, the FDIC is authorized to bill the cost of the failure to affiliate 

or sister banks. Therefore, the model assumed that the failure of one institution 

simultaneously caused the failure of affiliate institutions in a holding company. To proxy 

the failure of all affiliate institutions at one time, the model aggregated institutions by 

3 
 

bank holding company. Therefore, the discussion of concentration is on the basis of bank 

holding companies or banking organizations.1 

Until 1977, the 100 largest banking organizations held approximately 51 percent 

of industry assets (table 1). This level decreased to approximately 48 percent as of 

Table 1 

Industry Consolidation 

Percentage of Banking Assets Held by the Largest Banking Organizations 

1998 1977 1986 1990 1998 Pro forma 

25 largest 38.2% 27.9% 31.8% 53.9% 54.5% 

100 largesta 51.5 48.4 54.6 72.6 72.7 

All others 48.5 51.6 55.4 27.4 27.3 a

 Included in the 100 largest banking companies are the 25 largest banking companies. 

year-end 1986. By year-end 1990, however, the level was 54.6 percent and rising. With 

the acceleration of large-bank mergers in the early 1990s, the 100 largest banking 

organizations held 72.6 percent of industry assets as of year-end 1998. After adjusting 

for announced mergers as of June 30, 1999,2

 the new 100 largest banking organizations 

on a pro forma basis will hold 72.7 percent of the industry assets. As for the 25 largest 

banking organizations, throughout the 1980s they held approximately 30 percent of 

industry assets, but merger activity in the 1990s rocketed this level from 31.8 percent at 

year-end 1990 to 53.9 percent by year-end 1998. In addition, after adjustments are made 

for the announced mergers, the 25 largest banking organizations held 54.5 percent of 

industry assets on a pro forma basis. This level of consolidation is unprecedented in the 

United States. 

1

 Throughout this paper, the terms “banking organization,” “bank holding company,” and “banking 

company” will be used interchangeably. The term “institution” refers to individual banks and not to the 

banking organization.

2

 These mergers include, but are not limited to, Fleet Financial Group, Inc.’s acquisition of BankBoston 

Corporation and Union Planters Corporation’s acquisition of First Mutual Bancorp, Inc. 

4 
 

2.2 Liability Structure 

The liability structure of banks is significantly different today than in years past. 

Although banks continue to rely primarily on domestic deposits for funding, the level of 

deposit funding has decreased significantly, falling from a high of nearly 94 percent of 

total assets in 1945 to a low of 66 percent of total assets in 1998. The shortfall in deposit 

funding has been replaced by an increased reliance on other borrowed funds, other 

liabilities, and capital. In addition, funding structure varies significantly with bank size. 

The 25 largest banking organizations depend less on domestic deposits than the smallest 

organizations. After the decline in deposit funding in the early 1990s, the 25 largest 

institutions used domestic deposits to fund 56.9 percent of domestic assets as of 1998, 

whereas the institutions outside of the 100 largest used domestic deposits to fund 

81.0 percent of their domestic assets. 

The decline in reliance on domestic deposits is a two-edged sword. On the one 

hand, as discussed in the next section, a reduction in a reliance on deposits may lead to 

lower losses if an institution fails. On the other hand, since domestic deposits make up 

virtually the entire BIF assessment base, a decrease in domestic deposits means that, if 

the BIF suffers losses, it will be more difficult for it to replenish itself than it would have 

been in the past. 

2.3 Failure Probabilities and Loss Rates 

Large and small banks also exhibit different failure probabilities and loss rates. 

Among BIF-member banks, large banks have historically experienced much lower loss 

rates, and very large banks have experienced lower failure rates. Table 2 summarizes 

5 
 

failure rates and table 3 summarizes loss rates, by asset-size class. 

Table 2 

Failure Rates, 1934–1997 

(Percentage of Institutions per Year) 

Low High Average 

Top 25 0.0% 4.0% 0.1% 

26–100 0.0 4.0 0.3 

All others 0.0 3.5 0.3 

During the first 64 years of the FDIC’s existence (1934–1997), there were 

2 failures of top 25 banking organizations, 12 failures of top 26–100 banking 

organizations, and 1,372 failures of smaller institutions. But although the range of annual 

failure rates is similar across institution sizes, the average number of failures per year for 

top 25 organizations is significantly lower. 

Table 3 

Loss Rates, 1934–1997 

Low High Simple 

Average 

Weighted 

Average 

Top 50 –0.9% 10.2% 3.2% 5.3% 

51–100 0.0 18.3 6.6 6.8 

All others 4.8 bp 60.1 11.9 16.0 

As seen in table 3, loss rates follow a similar pattern. Historical loss rates for top 

100 failures (calculated as a percentage of each failed bank’s assets) ranged from a small 

gain to a loss of 18.3 percent, averaging 5.4 percent. The loss rates for the remaining 

institutions (calculated as an annual aggregate percentage of small-bank failed assets) 

ranged from a low of 4.8 basis points to a high of 60.1 percent, averaging 11.9 percent. 

Economists have several explanations for the differences in failure and loss rates between 

large and small institutions: large banks enjoy economies of scale, more flexibility in 

funding sources, better diversification of risk, and a smaller likelihood of fraud of 

sufficient size to cause failure.3 

3

 Another explanation may relate to systemic-risk concerns. When the LDC (less-developed-country) debt 

crisis caused several large banks to become troubled in the early 1980s, regulators practiced forbearance 

6 
 

The model explicitly takes into account the differences between large and small 

institutions by incorporating the data underlying tables 2 and 3.4 That is, it explicitly 

assumes that past failure and loss rates are indicative of future failures and losses. There 

are a number of reasons to question this assumption. Very few failures have taken place 

in recent years and the banking industry has changed significantly over time. As barriers 

to interstate banking have fallen, there has been significant geographic diversification. 

This has no doubt lowered the probability of failure, although the very low failure rates of 

the largest banking companies probably already reflect the fact that they have diversified 

balance sheets. The risks faced by banks have also changed as more sophisticated 

hedging techniques have given banks the tools to better manage risk— and to take on 

more risk. Increased competition from non-bank financial-service companies has also 

affected the risk profile of the industry. 

In addition, there have been a number of legislative changes over the last decade 

that were designed to limit FDIC exposure. The Federal Deposit Insurance Corporation 

Improvement Act of 1991 (FDICIA) introduced prompt corrective action (PCA). PCA 

requires closure of a bank— with certain exceptions— 90 days after its capital ratio falls 

below 2 percent. In theory, this should lead to lower losses, although in practice by the 

time a bank falls below 2 percent capital additional losses are often already imbedded in 

its balance sheet. Moreover, PCA may lead to more bank closings than would have 

otherwise been the case. A study of bank closings between 1980 and 1992 found that, 

rather than allowing multiple large banks to fail. Forbearance has been used to assist smaller banks, as 

well. 

4

 See section 3 below and the Appendix for details. 

7 
 

had PCA been in effect during that period, 143 banks that did not fail might have been 

closed.5 

FDICIA also introduced the least-cost test, and the Omnibus Budget 

Reconciliation Act of 1993 (OBRA) introduced national depositor preference. Before 

these acts, the FDIC was obliged only to resolution strategies that were less costly than a 

payoff and liquidation. This resulted in all depositors and general creditors being made 

whole in all but the smallest bank failures. With one exception (discussed below), the 

least-cost test effectively prevents the FDIC from covering uninsured depositors in full 

unless an acquirer is willing to pay a sufficient premium for the uninsured deposits to 

make it cheaper to pay uninsured depositors in full than to leave them behind in a 

receivership. Depositor preference gives domestic deposits a preference over other 

general creditors in a receivership. Thus, no general creditor gets paid if the FDIC 

suffers a loss. In theory, the least-cost test and depositor preference should lead to lower 

losses. In certain cases, this is probably true. For example, it is hard to see how a large 

money-center bank that has very few insured deposits could cause the FDIC a loss.6 

However, it is probably unrealistic to believe that, as a bank gets into trouble, its creditors 

would not move to protect themselves by withdrawing their funds or by securing their 

lending. Thus, the least-cost test and depositor preference may mitigate losses by less 

than it would appear at first glance.7 Indeed, since they will encourage uninsured 

depositors and unsecured creditors to withdraw funds from a troubled bank, they may 

serve to cause a liquidity problem and hasten a failure. 

5 FDIC (1997b), p. 460.

6

 This is absent a systemic-risk determination, which is discussed below.

7

 For a full discussion of this point, see Marino and Bennett (1999). 

8 
 

FDICIA allows an exception to the least-cost test only when a least-cost 

resolution would lead to systemic risk. Because of their sheer size, regulators would 

probably consider using this exception were a megabank to fail. After meeting several 

technical requirements,8 the FDIC may select a more costly resolution method in such a 

case. If a systemic-risk determination is made and a bank is resolved in a more costly 

manner, then the incremental cost (that is, the difference between the resolution cost and 

the least-cost option) is funded by one or more special assessments rather than the 

insurance funds. However, because the FDIC would be responsible for carrying out the 

resolution, and because the special assessment(s) would not be made until sometime after 

the resolution, the full resolution cost would likely be charged to the BIF (and possibly 

the SAIF) for some period of time. 

In short, the legislative changes of recent years have not been tested, and a priori 

it is unclear what effect they will have on future loss and failure rates. 

3. Simulation Model 

Because the number of banking failures generally ebbs and flows, the model was 

designed to simulate periods of small, medium, and large disbursements. This was 

accomplished by employing a Markov-switching model, which used historical patterns of 

BIF disbursements to define the probability of switching among the three levels of 

disbursements. 

8

 To use the systemic-risk exception, the Secretary of the Treasury, upon the recommendation of a twothirds majority of the FDIC and Federal Reserve Boards, and after consultation with the President, must 

find that to follow the least-cost test would lead to systemic risk. 

9 
 

The model then projected the financial condition of the BIF for 50 years. For 

each year, bank failures (and losses from failures) were projected on the basis of the state 

of the banking industry and random variations within each state. To capture the effects of 

industry consolidation that are most likely to influence the solvency of the BIF, the 

top 100 banking organizations were simulated individually. The rest of the industry was 

simulated on an aggregate basis. Premium assessments were based on the BIF’s financial 

condition and the minimum assessment schedule mandated by FIRREA.9 The simulation 

was performed 1,000 times using a Monte Carlo simulation. 

3.1 Markov-switching Model 

The Markov-switching model defined movements among the small-, medium-, 

and large-disbursement states on the basis of historical data.10 The process identified 

30 years in the small-disbursement state, 19 years in the medium-disbursement state, and 

15 years in the large-disbursement state. The transition probabilities resulting from the 

Markov-switching model are listed in table 4. It shows that the probability of 

Table 4 

Probabilities of Movement between Disbursement States 

To 

From 

Small state Medium state Large state 

Small state 0.883 0.117 0.000 

Medium state 0.170 0.676 0.154 

Large state 0.000 0.196 0.804 

staying in a small-disbursement state, State 1, from one period to the next is high, 

p$11 = 0883 . , and the probability of staying in a large-disbursement state is high, 

p$33 = 0. . 804 However, the probability of staying in a medium-disbursement state, while 

9

 Once again, this assumed no systemic-risk determinations. 10 For a detailed description of the Markov-switching model, see Hamilton (1993). 

10 
 

large, is much smaller than the other two, thereby implying that it is easier to move out of 

a medium-disbursement state than out of either a small- or a large-disbursement state. 

Also of note, the data do not support direct movement between the small- and 

large-disbursement states. 

These probabilities imply that the average length of a high-stress period for the 

fund was approximately 4.4 years, the average length of a moderate-stress period is 

approximately 3.1 years, and the average length of a low-stress period is approximately 

8.7 years. 

3.2 Industry Stratification 

The industry was separated into three groups: top 25, top 26–100, and all other 

institutions. Financial data were gathered from the Call Reports for each insured 

commercial and savings bank.11 For institutions that were subsidiaries of bank holding 

companies (BHCs), all banks under a common BHC were aggregated to proxy the 

banking assets in the banking family.12 The banking families were then separated into 

the top 25, top 26–100, and all others. The group of “all others” was summed, and small 

percentages of the total were removed each year to proxy small-bank failures. As 

banking companies within the top 100 failed, failed organizations were not replaced with 

other companies, since the cutoffs that define the asset-size classes were based on asset 

size in 1997 rather than the number of organizations. 

11 After separation into asset-size classes, adjustments to the data were made to remove the deposits insured 

by the Savings Association Insurance Fund (SAIF) from Oakar institutions. Oakar institutions hold 

deposits insured by both the BIF and the SAIF. When an Oakar institution fails, the cost of the resolution 

is split between the BIF and the SAIF on the basis of the portion of deposits insured by each fund.

12 Although aggregation can overstate the banking assets of the banking family by not removing 

intercompany transactions, information about intercompany transactions is not readily available. 

11 
3.3 The Simulation Algorithm 

The model calculated the balance of the BIF each year on the basis of the prior 

year’s asset balance, losses from failures, insurance premiums, net income (after 

expenses) of the fund, and reserves for future failures. This section describes the 

calculation of each of these items and how they are combined to produce the scenarios. 

The Appendix describes the equations in more detail. 

Losses from failures were calculated by estimating failed-bank assets and then 

applying loss rates. For the top 100 banking companies, specific banks were randomly 

selected to fail, based on the historical failure rates for each stratum (top 25 or 26–100) 

during each historical disbursement state (small, medium, or large). For the remaining 

banks, a similar procedure was used to project the portion of bank assets that would fail. 

For the top 100 banking companies, loss rates were randomly selected from specific 

historical failures, with the top 25 drawing from the five top 50 failures experienced to 

date and 26–100 drawing from the nine remaining failures of top 100 organizations. For 

the remaining banks, a random selection from historical experience for small banks was 

used. 

Insurance premiums were calculated based on the requirements of FIRREA. 

Thus, a premium of 23 basis points was assessed on domestic deposits during periods 

when the fund balance fell below 103 basis points. If the fund balance exceeded 125 

12 
 

basis points, no premiums were collected. Otherwise, sufficient premiums were collected 

to bring the fund balance to 125 basis points.13 

Net income (investment income less expenses) was assumed to vary according to 

the state of the banking industry. During the large-disbursement state (that is, periods of 

stress), the fund would yield no income. Net income was projected to be 2 percent of the 

BIF’s asset balance per year during periods of medium disbursements and 4 percent per 

year during periods of small disbursements. 

The BIF balance was calculated as BIF assets minus a reserve for future losses. 

Reserves are estimated to equal the losses in the current year, excluding losses for top 25 

banking companies. Consistent with historical experience, this implicitly assumes that 

the FDIC would be unable to predict changes accurately in the condition of the industry, 

but that the FDIC would not reserve for very large organizations because the probability 

of failure is very low. 

Throughout the simulation, both assets and deposits of insured institutions were 

assumed to grow by 3 percent per year. 

3.4 Monte Carlo Simulation 

The 50-year simulation was repeated 1,000 times, and the number of runs 

resulting in BIF insolvency determined the probability of insolvency. To ensure that the 

only differences in the results were attributable to changes in the assumptions for each 

scenario, the same series of random numbers (that is, the periods of stress, the failures, 

13 Note that the FDIC is also required to charge higher premiums to banks that pose more risk to the fund. 

Thus, this formula slightly understates premium assessments. Moreover, the understatement is higher 

during periods of stress when more banks are in trouble. 

13 
and the loss rates) was used for each scenario. To ensure consistency across the 

scenarios, the initial fund balance was set to the 1997 level for every simulation. 

4. Results 

The model was run several times— each with some of its assumptions changed. 

4.1 December 1990 and December 1997 Structures 

The model was initially run using the December 1990 and December 1997 

industry structures. The results, shown in table 5, suggest that recent consolidation in 

Table 5 

Simulation Results— December 1990 and 1997 Structures 

Probability Probability Probability Model of Fund < 0 bp of Fund < 50 bp of Fund < 75 bp 

1990 structure 3.9% 17.8% 43.7% 

1997 structure 6.0 17.1 34.0 

the industry has increased the insolvency risk to the BIF while ameliorating the risk of 

the reserve ratio falling below 75 basis points. During the 1990s, concentration within 

the top 25 banking organizations increased significantly, from 39.2 percent of industry 

assets to 53.6 percent. With such a large percentage of the industry’s assets spread 

among so few organizations, the probability that the failure of one of these organizations 

would cause BIF insolvency increased significantly. In addition, the probability of a 

severely insolvent BIF— defined as more than 100 basis points insolvent— increased from 

0.3 percent in 1990 to 1.3 percent in 1997. Although a top 25 failure would be 

devastating to the BIF, companies in the top 25 fail less often compared with other banks, 

and when they fail, the loss rates are lower. Therefore, a large percentage of the industry 

moved from higher failure probabilities to lower failure probabilities during the 1990s. 

14 
 

This movement partially offset the increased risk attributable to the growth of the largest 

insured banking companies. It also influenced the probability of the fund reserve ratio 

falling below 50 basis points and 75 basis points. Compared to 1990, a series of small 

bank failures is now less likely to reduce the fund balance significantly. 

Also of note, as stated in section 2.2 (“Liability Structure”), the funding structure 

of banks changed significantly during the 1990s. From 1990 to 1997, total assets grew 

by almost 35 percent while the BIF assessment base grew by barely 11 percent. Since the 

model projected BIF losses based on assets, the slower-growing assessment base resulted 

in a fund that was unable to replenish itself as fast as it once could. The net result of the 

increased consolidation, reduced failure probability, and reduced assessment base as a 

percent of assets was a higher probability of BIF insolvency.14 

4.2 Pro forma Structure 

Next, the model was run using the December 1998 industry structure adjusted for 

several large recent and pending mergers, as noted in section 2.1 (“Size: Consolidation 

within the Industry”).15 Compared with the December 1997 structure, the consolidation 

during 1998 and adjustments for the pending mergers effectively moved $68.3 billion in 

14 The liability structure can also have a significant effect on the losses incurred by the BIF. It appears that 

some of the change in the industry’s liability structure may reduce the BIF’s losses as banks shift toward 

funding sources that would typically incur losses were the institution to fail. When a bank becomes 

troubled, however, the composition of its liabilities tends to shift toward secured and FDIC-insured funding 

sources (thus shifting losses to the BIF). Therefore, it is difficult to predict how the changes in the 

industry’s funding composition will affect future loss rates. 15 The assets and liabilities of the institutions were merely summed. As of year-end 1998, the funding 

structure of large banks is different from that of smaller banks, with larger banks holding proportionally 

fewer deposits. It is unknown, however, if the difference in funding is based on the banks’ desire to have 

fewer deposits or on an inefficiency of deposits to fund the desired level of bank size. Therefore, the 

liability structures of the merged institutions were not adjusted. 

15 
 

assets from smaller institutions into the top 25 (where failures occur less often).16 

However, this only increased the concentration within the top 25 from 53.6 percent of 

industry assets to 55.2 percent. More importantly, the top 25 organizations fell to only 

20 companies in the pro forma scenario. In December 1997, the average top 25 

organization held $103.4 billion in assets; in the pro forma structure, the average top 25 

organization held $145.0 billion in assets— an increase of 40 percent. While there were 

fewer large companies and therefore a lower probability that a large company would fail, 

the mergers increased the likelihood that the failure of one very large organization would 

bring down the BIF. Put differently, before the mergers, the probability that two top 25 

companies would fail during the same year was extremely low. But, if these two top 25 

companies merged, the resultant combined banking organization had a far greater 

probability of failing than both of the formerly separate companies would fail in the same 

year. When top 25 organizations merged, therefore, the risk of BIF insolvency increased. 

Since the top 25 companies fail so infrequently, most years in the simulation had 

fewer failed assets and lower losses. Therefore, the probability of falling below other 

minimum reserve ratios decreased. The net result, shown in table 6, was a slight increase 

in the probability of insolvency and a slight decrease in the probability of falling below 

other minimum ratios. 

Table 6 

Simulation Results— Pro forma Scenario 

Probability Probability Probability Model of Fund < 0 bp of Fund < 50 bp Of Fund < 75 bp 

1997 structure 6.0% 17.1% 34.0% 

Pro forma 6.5 16.6 32.1 

16 The top 25 organizations in the pro forma simulation hold $314.5 billion more than the top 25 in the 

1997 structure simulation. Of this, $246.2 billion is considered banking industry growth during 1998. 

Therefore, the mergers only moved $68.3 billion into the top 25. 

16 
Another important result was that the level of insolvency deepened materially. 

For the 1997 simulation, 13 insolvent runs (21.7 percent) had a minimum BIF level 

below negative 100 basis points. But the pro forma simulation projected 25 insolvent 

runs (38.5 percent) below negative 100 basis points. Whereas the number of insolvencies 

increased only from 60 to 65, the average level of insolvency deepened from 70.8 basis 

points to 101.0 basis points. 

4.4 Profiles of Simulated Insolvencies 

As industry concentration has increased, the nature of the BIF’s risks has 

changed. To better understand these changes, the years that triggered insolvency were 

examined. More specifically, for each of the years that caused insolvency, the largest 

bank failure was flagged. Table 7 presents the results. Although the simulation using the 

Table 7 

Number of Years When BIF Became Insolvent (1,000 runs) 

Largest Failure 1990 Industry 1997 Industry Pro forma 

Top 25 27 (69.2%) 55 (91.7%) 64 (98.5%) 

Top 26— 100 12 (30.8%) 5 (8.3%) 1 (1.5%) 

All others 0 (0.0%) 0 (0.0%) 0 (0.0%) 

Total 39 60 65 

1990 industry structure had the fewest number of insolvent years, it had the largest 

percentage of the BIF insolvencies that occurred with no top 25 failures. In the 

simulation for the 1997 industry structure, the number of BIF insolvencies increased but, 

more noticeably, the percentage of insolvencies that included top 25 failures increased far 

more— from 69.2 percent to 91.7 percent. In the 1998 pro forma scenario, an even higher 

percentage of insolvencies occurred in years with a top 25 failure (98.5 percent). This 

result suggests that the risk to the BIF is becoming inseparable from the health of the 

top 25 organizations. If a top 10 organization fails, there is a 12.5 percent chance that the 

17 
 

failure will cause the BIF to become insolvent.17 To clarify the implications for the BIF, 

the model was constrained to prevent any top 10 organization from failing.18 The results 

are shown in table 8. Without any top 10 failures, the probability of insolvency was 

Table 8 

Probability of Insolvency— Pro forma Scenario 

Probability Probability Probability Model of Fund < 0 bp of Fund < 50 bp of Fund < 75 bp 

With top 10 failures 6.5% 16.6% 32.1% 

Without top 10 failures 0.5 7.9 22.6 

0.5 percent, and the probability of the reserve ratio falling below 50 and 75 basis points 

decreased significantly. The top 10 organizations in the pro forma structure held 

44.0 percent of industry assets. When the model was altered to prevent top 10 failures, 

nearly half of the industry could never fail but the associated insurance assessments 

would continue to be collected. Since the remaining industry assets were spread among 

many institutions, the probability of BIF insolvency became minuscule. In the rare cases 

of insolvency, the BIF became solvent again within one or two years.19 

4.6 Simulation Results for Alternative Assessment Schemes 

Two ways to lower the probability of insolvency are to raise the designated 

reserve ratio (DRR) or to raise assessment rates when the BIF falls below the DRR. This 

section examines the BIF’s sensitivity to the DRR and to the maximum assessment rate 

charged to banks. Using the pro forma simulation as the base line, the model was run 

17 This statement is based on the results of the pro forma scenario. 18 This change can also be interpreted as an assumption that: all top 10 failures would be deemed systemic 

failures; the full cost of resolution would be borne by the industry in the form of a special assessment; the 

BIF would not temporarily incur the loss until the special assessment is collected; and the special 

assessment would not cause additional bank failures. It is highly unlikely that all of these conditions would 

prevail absent legislative changes.

19 Of the five insolvent years, the largest insolvency was negative 26.4 basis points. All others would have 

returned to solvency within one year. 

18 
 

under several alternatives. Table 9 provides the results with various DRRs, and table 10 

provides the results with various maximum assessment rates.20 

Table 9 

Simulation Results— Pro forma Scenario 

Various Designated Reserve Ratios 

Designated Reserve Probability Probability Probability 

Ratio of Fund < 0 bp of Fund < 50 bp of Fund < 75 bp 

145 5.0% 11.2% 18.5% 

135 5.9 14.2 25.2 

125 6.5 16.6 32.1 

115 7.8 20.2 42.0 

105 8.9 25.5 53.4 

Table 10 

Simulation Results— Pro forma Scenario 

Various Maximum Assessment Rates 

Maximum Probability Probability Probability 

Assessment Rate of Fund < 0 bp of Fund < 50 bp of Fund < 75 bp 

33 5.3% 10.5% 18.9% 

28 5.6 13.5 25.1 

23 6.5 16.6 32.1 

18 8.5 21.8 44.2 

13 12.9 33.5 57.8 

The results show that small changes to the assessment rate or the DRR would 

bring about only minor changes to the risk profile of the BIF. In other words, the FDIC 

could not materially improve the risk profile of the BIF by making minor adjustments to 

either the DRR or the assessment rate. Even a significant increase in the DRR or the 

assessment rate would still leave the BIF vulnerable to insolvency risk. This is consistent 

with the finding that the risk of severe insolvency has increased with the advent of 

megamergers. 

Note that a large reduction in the assessment rate is more damaging to the BIF 

than a large reduction in the DRR. If the maximum assessment level was decreased, the 

fund could not build up as fast as before, and even with a high DRR, the probability of 

20 The model implicitly assumes that an increase in the maximum assessment rate does not provoke 

additional bank failures. If this assumption does not hold true, then the results will be less sensitive to 

19 
 

insolvency increased. For example, when the reserve ratio was increased to 145 basis 

points and the maximum assessment rate was decreased to 13 basis points, the probability 

of insolvency increased from 6.5 percent to 9.7 percent. However, when the reserve ratio 

was decreased to 105 basis points and the maximum assessment rate was increased to 33 

basis points, the probability of insolvency decreased to 6.0 percent. 

5. Conclusion 

Merger activity in the 1990s appears to have increased the risk to the BIF. 

Moreover, the health of the BIF has become more and more dependent on the health of 

the top 25 banking organizations, and future insolvency may be deeper, and harder to 

emerge from, than in the past. Thus, it would appear to be incumbent on the FDIC to 

seek ways to mitigate this risk, by carefully monitoring the health of the nation’s largest 

banking organizations, or perhaps by exploring other risk-reduction strategies. 

changes in the maximum assessment rate. 

20 
Appendix 

The Simulation Algorithm 

The model determined BIF assets using the algorithm in the equation 

TA = (1+ i)TA + (1+ i )(Prem - (LR )FBA ) (1) t t - 1 2 t t t 

where TAt defines the total assets of the insurance fund at the end of time t; i defines the 

net return on assets of the insurance fund; Premt defines assessments during time t; LRt 

defines the loss rate on failed-bank assets during time t; and FBAt defines the failed-bank 

assets during time t. Each of these terms is explained in the following pages. 

Assessments 

The model calculated assessments according to the requirements in FIRREA. 

FIRREA requires that if the level of the insurance fund drops below 125 basis points of 

insured deposits, the industry shall be assessed a premium to increase the level of the 

fund. If one year’s assessments do not bring the fund balance to 125 basis points, the 

assessment rates must accord with a recapitalization schedule that will return the fund to 

the proper level within 15 years. While this schedule is in force, the assessment rate must 

be at least 23 basis points. 

The premiums assessed during a period were based on the formula 

Prem = max(0,min(AR *AB ,RR - (BIF -(LR )FBA - R + R + E ))) (2) t t t - 1 t t t t - 1 t 

where AR is the maximum assessment rate, ABt is the assessment base at the end of 

time t after failed institutions are removed, RR is the required reserve level, BIFt – 1 is the 

beginning fund balance, Rt is the reserves for future bank failures, Rt – 1 is the reserves 

from the prior year, and Et is an adjustment for earnings expected during the period 

21 
 

(assuming a half year’s earnings for assets spent on resolutions and a full year’s earnings 

on the remaining assets). 

To illustrate the formula, table A-1 shows three examples of premiums when the 

minimum required level (RR) is 125 basis points and the maximum assessment rate 

(AR * ABt) is 23 basis points. For the sake of clarity, all values in the table have been 

adjusted to be a percentage of insured deposits, and the earnings adjustment (Et) is 

assumed to be 0. For periods when the BIF level was equal to or greater than 125 basis 

Table A-1 

Examples of Premium Formula 

BIF 

Balance Losses Change in Reserves Formula Premium 

(BIFt – 1) ((LRt)FBAt) (Rt

 – Rt – 1) (Premt) 

150 30 25 Premt = max(0, min(23, 125 – (150 – 30 – 25)) 23 

150 20 15 Premt = max(0, min(23, 125 – (150 – 20 – 15)) 10 

150 10 5 Premt = max(0, min(23, 125 – (150 – 10 – 5)) 0 

points, no assessments were made. For periods when the BIF level is equal to or less 

than 102 basis points, the premium was equal to 23 basis points. For BIF levels less than 

125 basis points but greater than 102 basis points, the premium was equal to the amount 

necessary to bring the BIF up to 125 basis points.21 

Failure and Loss Rates 

For each year from 1934 through 1997, the percentage of failed institutions within 

each size class was calculated. Failure rates that fell into the small-, medium-, and 

large-disbursement years were grouped separately. These failure rates were used to 

randomly determine specific failures of top 100 companies during the simulation for each 

given year. For the smaller banks, the proportion of bank assets that fail varied 

randomly, depending on the disbursement state. 

21 The Federal Deposit Insurance Corporation Improvement Act of 1991 requires that high-risk institutions 

pay higher premiums, even when the fund is fully capitalized. Therefore, the model slightly underestimates 

22 
 

More specifically, the model determined failures on the basis of the formula 

25 100 

t i,t - 1 FBA = å (Fail (3) i,t *Asset ) + å (Faili,t *Asset ) + SFail t *SAssets i,t - 1 t - 1

i=1 i=26 

where FBAt defines the total assets failed during year t; Faili,t is assigned a value of 0 if 

the specific company’s probability of survival is greater than its probability of failure for 

year t— otherwise it is assigned the value of 1;22 Asseti,t-1, for i between 1 and 25, is the 

asset balance for the i

th top 25 organization in existence at the beginning of year t, and for 

i between 26 and 100, it is the asset balance for the i

th top 26–100 organization in 

existence at the beginning of year t; SFailt is the percentage of “all other” institutions that 

will fail during year t; and SAssett-1 is the total assets of “all other” institutions in 

existence at the beginning of year t. For simplicity, further references to Faili,t*Asseti,t-1 

will be called FAsseti,t and further references to SFailt*SAssett-1 will be called FSAssett. 

The application of failure rates differed between the top 100 and the “all other” 

institutions. For the top 100 organizations for a given disbursement state, the model 

randomly selected a year from the period that defined the disbursement state. That year’s 

experience determined the probability of a bank’s failure. From a uniform distribution, 

each company was assigned a random number between 0 and 1, which is defined as that 

company’s probability of survival. If an institution’s probability of survival was less than 

or equal to the probability of failure, that company failed. For example, if three 

companies had probabilities of survival equal to 0.02, 0.10, and 0.85 and the year’s 

experience was a 4 percent probability of failure, the company with a probability of 

survival of 0.02 failed, while the other two survived. 

assessment premiums. The underestimation is somewhat larger during periods of stress, when more banks 

are troubled. 

23 
 

 

For “all other” institutions for a given disbursement state, the model randomly 

selected a year from the period that defined the disbursement state. For an estimate of 

failures, that year’s percentage of banking assets failed was then applied to “all other” 

banking assets. 

The projected failures of the top 100 organizations are summarized in table A-2. 

Table A-2 

Bank Failures during the Simulation (1,000 runs of 50 years) 

Disbursement 

State 

Number 

of Years 

Number 

of 

Top 25 

Failures 

Prob. of 

Top 25 

Failure 

Average 

Number of 

Top 25 

Orgs. 

Number of 

Top 26–100 

Failures 

Prob. of 

Top 26–100 

Failure 

Average 

Number of 

Top 26–100 

Orgs. 

Low 25,341 0 0.00 24.7 726 2.86 72.4 

Medium 14,566 0 0.00 24.4 1,508 10.35 71.0 

High 10,093 1,270 12.58 23.9 6,868 68.05 68.8 

Total 50,000 1,270 2.54 24.4 9,102 18.20 71.3 

During any given simulation run, the probability of a top 25 banking company failure 

during a specific year was 2.54 percent, while the probability of a top 26–100 

organization failure during a specific year was 18.20 percent.23 

Once the failed assets had been determined, the model determined losses to the 

BIF using the equation 

25 100 

(LR )FBA = å (FAsset * LRate ) + å (FAsset *LRate ) + FSAsset *SLRate (4) t t i,t t i,t t t t 

i=1 i=26 

where (LRt)FBAt defines the net losses to the insurance fund during year t; LRatet is the 

loss rate for top 100 organizations during year t;24 and SLRatet is the loss rate for “all 

other” institutions during year t. 

22 For each year, the probability of failure for the top 25 organizations differed from the probability for the 

top 26–100 organizations. 23 These probabilities are slightly lower than expected, given the inputted probabilities. This difference is 

due to the nonreplacement of failed companies. As top 100 companies fail, they are not replaced and the 

top 100 are left with fewer than 100 members, as shown in the columns “Average Number Top 25 Orgs.” 

and “Average Number Top 26–100 Orgs.”. 24 For each year, the loss rate is different for the top 25 and the top 26–100 organizations, but it is the same 

for each member within each size group. 

24 
 

 

The methodology for determining loss rates differed only slightly between the 

top 100 and “all other” institutions. Once the failed banking assets were determined, the 

model randomly selected loss rates to determine the charge to the BIF. For top 25 

failures, the model selected one of the historical top 50 bank failure loss rates.25 For the 

top 26–100 failures, the model selected one of the historical top 51–100 bank failure loss 

rates.26 (The reason for segmenting at 50 instead of 25 is that only two top 25 companies 

have ever failed, so a segmentation at 25 would have too few options from which the 

model would pick.) For “all other” failed assets, the model used the historical loss rate 

for all small bank failures during the same year that determined the proportion of “all 

other” bank assets that failed. 

BIF Reserves 

The only substantive liabilities of the BIF are reserves for future bank failures, 27 

which were determined by 

R = å

100 

(FAsset * LRate ) + FSAsset *SLRate . (5) t i,t t t t 

i=26 

Note that equation (5) is similar to equation (4), which was used to determine the losses 

to the BIF for the given year, as defined in the previous section. The difference is the 

exclusion of top 25 failures. The model did not reserve for any top 25 failures, since the 

probability of a top 25 failure is very low. Thus, the balance of the bank fund was 

25 A top 25 failure, if determined to be a systemic-risk failure, would be completely or partially funded 

through a special assessment. This is taken into account in the model by the possibility of a low or 0 loss 

rate. 

26 Since failing banks experience asset runoff during the years before failure, the loss rates were calculated 

using total assets two years before failure. For example, if a bank failed with $100 million in assets, if the 

cost to the BIF was $12 million, and if two years before failure the bank had $120 million in assets, the loss 

rate used in the model would be 10 percent and not 12 percent.

27 Another liability that could become material is borrowing for working cash. However, this is offset by 

the value of assets held in receivership. Because the FDIC passes a large portion of assets at resolution 

25 
 

determined by 

BIFt = TA t - Rt (6) 

where BIFt defines the fund net balance at the end of time t; TAt defines total assets in the 

fund at the end of time t; and Rt defines the reserves for troubled banks that are set aside 

in time t. 

By using losses to the BIF from one year as the loss reserves for the next year, the 

model implicitly assumed that the FDIC will not be able to accurately predict changes in 

its environment right away. This method of adaptive reserving over-reserves when a 

small disbursement follows a large disbursement and under-reserves when a large 

disbursement follows a small disbursement, a pattern that matches recent history. For 

example, at the end of 1991 the FDIC reserved $15.4 billion to cover expected losses of 

the banks that were identified as likely to fail. At that time insurance fund assets were 

depleted, and reserving the large amount caused the BIF to become insolvent. However, 

actual losses were $3.7 billion in 1992 and $677 million in 1993. 

In addition, the model’s adaptive reserving corrected itself within one year of the 

change from one disbursement state to the other. For example, as the disbursement state 

moved from a period of large losses to a period of moderate losses, the model reserved 

for a future large loss. Since the next period had a moderate loss, the model overreserved and adversely affected the insurance fund. After this first period of moderate 

losses, the model correctly reserved for the next moderate loss. Therefore, initially the 

model did not properly foresee the change of disbursement states, but it corrected itself 

after one period. Since the probability that disbursement states will change is relatively 

(particularly for large institutions), the effects of working cash on the solvency of the BIF are assumed to 

be de minimis. 

26 
 

low, the chance of a series of successive periods alternating among the disbursement 

states, with the consequent repetitive improper reserving, is low. 

Return on Assets 

In equation (1), the net return on assets (i) was defined as insurance fund asset 

earnings in excess of operating expenses. Since 1995, the assets in the BIF have earned 

between 5.0 percent and 6.1 percent, averaging 5.6 percent. Expenses as a percentage of 

BIF assets during this period have been between 2.2 percent and 2.5 percent, averaging 

2.3 percent. Hence, the net yield on BIF assets during this period has ranged from 2.8 

percent to 3.8 percent, averaging 3.3 percent.28 Therefore, the model assumed that the 

net yield on the BIF’s assets would be 4 percent during periods of low disbursements, 

2 percent during periods of medium disbursements, and 0 percent during periods of large 

disbursements. 

The model assumed the premiums are assessed throughout the year and proxied 

this by collecting all the premiums in the middle of the year. Therefore, the premiums 

earned one-half of the yield that was earned by the accumulated BIF assets. In addition, 

the model assumed that bank failures occur throughout the year and proxies this by 

removing assets from the BIF in the middle of the year. Therefore, the assets removed 

earned one-half of the yield that was earned by the accumulated BIF assets. 

Asset and Deposit Growth 

The model assumed that banking assets and deposits grew at 3 percent per year. 

Both grew at the same rate to proxy a constant funding structure. If assets were to grow 

at a rate different from the rate for deposits, there would have been a de facto change in 

28 One would expect the fund’s yield to drop during periods of stress because BIF expenses would increase 

and the fund balance would drop. 

27 
banks’ funding structure. The 3 percent level assumes that future industry growth will be 

a little slower than the current 5 percent growth. Since earnings on the fund in periods of 

minimal bank failure and losses are assumed to exceed the growth of deposits, the BIF 

would be self-sustaining without a need to assess premiums. 

28 
 

 

Bibliography 

Federal Deposit Insurance Corporation (FDIC). 1997. Annual Report. FDIC. 

——— . 1997. History of the Eighties— Lessons for the Future: An Examination of the 

Banking Crises of the 1980s and Early 1990s. 2 vols. FDIC. 

——— . 1998. A Brief History of Deposit Insurance in the United States. FDIC. 

Hamilton, James D. 1993. Estimating, Inference, and Forecasting of Time Series 

Subject to Changes in Regime. In Handbook of Statistics, edited by G. S. Maddala, C. R. 

Rao, and H. D. Vinod. Vol. 11. Elsevier Science Publishers. 

Marino, James A., and Rosalind L. Bennett. Forthcoming. The Consequences of 

National Depositor Preference. FDIC Banking Review 12, no. 2:19-38. 

Shaffer, Sherrill. 1991. Aggregate Deposit Insurance Funding and Taxpayer Bailout. 

Journal of Banking and Finance 15:1019–37. 

Sheehan, Kevin P. 1998. Capitalization of the Bank Insurance Fund. Working Paper 

98-1. FDIC. 

29