Capitalization of the Bank Insurance Fund 

Kevin P. Sheehan 

Financial Economist 

Federal Deposit Insurance Corporation 

Division of Research and Statistics 

550 17th Street, NW 

Washington, DC 20429 

Phone: 202-898-7366 

Fax: 202-898-7149 

E-mail: kesheehan@fdic.gov 

FDIC Working Paper 

98-1 

Abstract: A two-state Markov-switching model is estimated to characterize the time 

series behavior of disbursements from the Bank Insurance Fund (BIF). The estimated 

model is used to project future disbursements, and these projected disbursements are used 

to estimate the likelihood of insolvency as well as the likelihood of the BIF falling below 

two different minimum reserve ratios. The simulation results confirm that the current 

funding arrangement—an assessment rate of 23 basis points with a 1.25 percent required 

reserve ratio—is sufficient to maintain BIF solvency if one assumes that the prior history 

of losses is a good indicator of future losses. 

The comments and suggestions of Barry Kolatch, Steven Seelig, James Marino, Lynn 

Shibut, and Daniel Nuxoll are gratefully acknowledged. The views expressed are those 

of the author and not necessarily those of the Federal Deposit Insurance Corporation. 
1 Introduction 

The FDIC is required to maintain Bank Insurance Fund (BIF) reserves of at least 

1.25 percent of insured deposits; as of year-end 1996 the actual reserve ratio was 1.34 

percent. In light of the BIF’s loss experience in the late 1980s and early 1990s, questions 

have been raised about the adequacy of these levels. At the same time, however, given 

the currently robust financial state of the banking industry, questions have also been 

raised about the need for these levels. 

This study, assuming losses similar to those experienced in the past, simulates the 

BIF’s future reserve levels and examines the implications of different assessment rates 

and required reserve ratios. The results indicate the extent to which the FDIC may have 

to balance two possibly conflicting objectives when it makes decisions affecting its 

ability to sustain funding losses from a future banking crisis. One of the two objectives is 

the desire to minimize assessment rates. The other is the desire to avoid breaching a 

specified minimum fund level. 

Currently assessment rates are to some extent a function of the ratio between BIF 

reserves and insured deposits at any given time. If the ratio drops below 125 basis points, 

the FDIC is required by law either to assess the industry to bring the fund back to this 

minimum level or to adopt a restoration plan whereby the annual assessment rate is at 

least 23 basis points. (The FDIC could ask Congress to relax this requirement and afford 

the agency greater flexibility in setting premium levels of less than 23 basis points.) 

But while the FDIC is required to maintain a fund of at least 125 basis points, a 

crisis may cause the fund to fall below this level. This matters because the FDIC would 

like not only to avoid the possibility of insolvency but also to retain public confidence. 

2 
To help ensure public confidence, it may be desirable for the FDIC to keep the reserve 

ratio above a certain minimum ratio—for example, 50 or 75 basis points. 

These issues are examined by constructing a model (the Markov-switching 

model) that projects future disbursements under certain conditions. The projected 

disbursements are used to estimate the BIF’s likelihood of insolvency as well as the 

likelihood of the BIF falling below two different minimum reserve ratios. These 

probabilities are estimated across a range of assessment rates for a number of different 

required reserve ratios. (Note that the analysis does not explicitly address what effect 

recent bank consolidation will have on the solvency of the BIF.) 

2 Overview of Methodology 

This paper uses a Monte-Carlo simulation to analyze the adequacy of the Bank 

Insurance Fund. I generate sequences of future disbursements and then combine these 

projected disbursements with a recovery rate and an assessment schedule to track the 

level of the bank fund over time. Using these simulated disbursement sequences, I 

quantify the probability of insolvency for alternative funding schemes. More 

specifically, I simulate a thousand sequences of disbursements, and the proportion of 

sequences that exhaust the Bank Insurance Fund determines the probability of 

insolvency. 

When a bank fails, cash is paid out of the insurance fund to cover insured-deposit 

losses. However, this drain on the fund is offset by the sale of failed-bank assets and by 

premium income collected from banks. Historically, annual fund disbursements have 

ranged from 0 basis points (in 1962) to 105 basis points (in 1991), and the recovery rates 

from the sale of the failed-bank assets have averaged about 65 percent. Assume, for 

3 
example, a large annual fund disbursement of 100 basis points. With a recovery rate of 

65 percent, the sale of failed-bank assets would reduce this large gross disbursement to 

35 basis points. Premium income would further offset the gross disbursement. In fact, if 

banks were assessed an average premium of 23 basis points, the drain on the fund would 

be reduced to 12 basis points. 

The simulation approach can be illustrated by drawing on the example above. 

Consider a bank fund balance at the beginning of period t of 100 basis points and assume 

a simulated fund disbursement of 100 basis points, a recovery rate of 65 percent, and an 

assessment of 23 basis points. At the end of the period, the fund balance would be 

reduced by 12 basis points. Given this drain on the fund, the fund balance at the 

beginning of period t +1 would be 88 basis points. After simulating a new fund 

disbursement for period t + 1, one would determine the fund balance for the beginning of 

period t + 2 in the same way. This process would continue, with the simulation algorithm 

tracking the level of the insurance fund across a sequence of simulated disbursements. 

Using this approach, I can quantify the probability of insolvency (and the 

probabilities of falling below different minimum reserve ratios) under the current funding 

arrangement—an assessment rate of 23 basis points with a 1.25 percent required reserve 

ratio—as well as under alternative funding schemes. These probabilities allow me to 

address in a meaningful way the adequacy of different funding arrangements. 

I generate sequences of future fund disbursements and use these projected 

disbursements, along with a recovery rate and an assessment schedule, to track the level 

of the bank fund over time. I argue that the probability of bank failure is higher during a 

banking crisis than during noncrisis periods and capture this difference by using a model 

4 
 

 

that allows for a data-generating process that changes over time. To simulate sequences 

of future disbursements I use a Markov-switching model, whose construction I explain 

below. 

The model projects future disbursements on the basis of two different sets of 

historical data, one for the 63-year period 1934–1996, the other for the more volatile 25-

year period 1972–1996. By projecting disbursements on the basis of these two different 

sets of historical data, I am able to analyze the adequacy of a funding arrangement under 

two very different assumptions. The first simulation, based on disbursements from the 

63-year period 1934–1996, assumes low future losses. In contrast, the second simulation, 

based on disbursements from the 25-year period 1972–1996, assumes high future losses. 

In fact, the average simulated disbursement for the second simulation increases by more 

than 100 percent.1 

3 Markov-Switching Model 

Using data from the 1996 FDIC Annual Report (tables 108 and 110), I began by 

constructing a time series for historical fund disbursements, which is plotted in figure 1. 

Observe that the behavior of disbursements has changed markedly over the history of the 

1

Shaffer (1991) also used a simulation to analyze the adequacy of the Bank Insurance Fund. My analysis 

differs from Shaffer’s work in two important ways. First, Shaffer assumed that disbursements were drawn 

from a stationary distribution. By using a Markov-switching model, I allow for different states of nature 

associated with banking crises. Second, Shaffer investigated some historical assessment rates—e.g., the 

historical assessment rate of 8.33 basis points. I analyze the current statutory framework that requires both 

lower and higher premiums based on the level of the fund, as well as some possible alternative assessment 

rates. 

5 
Figure 1 

0 

20 

40 

60 

80 

100 

120 

1938 1942 1946 1950 1954 1958 1962 1966 1970 1974 1978 1982 1986 1990 1994 

Basis Points 

Fund Disbursements per Insured Dollar 

1934 

 

-201934

Bank Insurance Fund. Before the mid-1970s, disbursements were uniformly small and 

close to zero, whereas since the mid-1970s disbursements have been larger and much 

more variable. The behavior of the series changes quite dramatically, and this change 

may be the result of significant changes in government policy or in the economic 

environment. 

How could one model this dramatic change in the disbursement time series? 

Consider the statistical model 

dt = μ + ε t , (1) 

2 where ε t ~ Nc0,σ ε h. This model characterizes the sample of data as random deviations 

about an average disbursement μ. However, the average disbursement appears to have 

increased some time after the mid-1970s. Indeed, these different time periods may 

represent distinct phases whose features would be more accurately modeled by an 

6 
 

 

 

 

equation representing a data-generating process that changes across time. For the data 

before the mid-1970s, one might specify the model as 

d = μ + ε , (2) t 1 t 

while data after the mid-1970s might be described by 

dt = μ 2 + ε t , (3) 

where μ1 < μ2 . 

Equations (2) and (3) define my statistical model as 

d = μ * + ε . (4) t s t t 

The model assumes two states and these states are specified by the variable st 

*, which 

takes on either the value 1 or 2. When st 

* = 1, the model reduces to the model in equation 

(2). (Setting s* = 1, μ * = μ . ) With the model in equation (2) specifying a small t st 1 

average disbursement, st 

* = 1 identifies the state of small disbursements. When st 

* = 2, 

the model reduces to the model in equation (3). (Setting s* = 2, μ * = μ . ) With the t st 2 

model in equation (3) specifying a large average disbursement, st 

* = 2 identifies the state 

of large disbursements. 

7 
 

 

The model in equation (4) is a plausible description of the data in figure 1. The 

model allows the mean disbursement to vary across states that evolve according to a firstorder Markov transition process, 

p sct = 1st−1 = 1h= p11 

p sct = 2 s = 1h= p (5) t−1 12 

p sct = 1s t−1 = 2h= p21 

p sct = 2 st−1 = 2h= p22 , 

where p + p = p + p = 1. The model maintains the assumption that time series data 11 12 21 22 

may display periodic changes in their observed behavior, and it accounts for such 

changes through switches in states, where the mean disbursement of the state is allowed 

to differ. 

The statistical model characterizes the historical disbursements as the random 

movement between states of small and large disbursements. The state of small 

disbursements appears to have characterized the historical data before the mid-1970s; the 

state of large disbursements appears to have characterized the historical data for some 

time after the mid-1970s; recently there appears to have been a shift back to the state of 

small disbursements. 

I assume that this movement between states is random, and the likelihood of 

moving between states is defined by the transition probabilities in equation (5), where 

pij defines the probability of moving from state i to state j. More specifically, p11 

8 
defines the probability of remaining in the state of small disbursements from one period 

to the next; p12 defines the probability of moving from the state of small disbursements 

to the state of large disbursements; p21 defines the probability of moving from the state 

of large disbursements to the state of small disbursements; and p22 defines the 

probability of remaining in the state of large disbursements from one period to the next. 

The specification (5) is quite general. As Hamilton (1993, pp. 235–36) observes, 

A change in regime [state] could be represented as a permanent 

change in the value of μ, rather than the cycling back and forth 

between states 1 and 2 that seems implicit in [(5)]. However, the 

specification [(5)] allows the possibility of a permanent change as 

a special case if p21 = 0. [That is, once the system moves into the 

state of large disbursements it will never return to the state of small 

disbursements. In other words, p21 = 0 identifies a permanent 

increase in the average disbursement.] Alternatively, we could 

have p21 quite close to zero, with the implication that in a sample 

of given size T we would likely see only a single shift [to the state 

of large disbursements], though at some point in the future we 

should see a return to ... [the state of small disbursements. In this 

case, p21 identifies a temporary increase in the average 

disbursement.] This second parameterization has ... [much] 

appeal—[a temporary increase in the average disbursement 

characterizes the large disbursements of a banking crisis.] 

9 
 

In other words, the model allows for the possibility of a banking crisis; moreover, 

it identifies the crisis and determines the dates associated with its beginning and end. 

Significantly, the statistical features and identification of the crisis are not imposed 

exogenously on the data but, rather, endogenously by the estimation procedure. 

By specifying the probability law rather than imposing particular 

dates a priori, we allow the data to tell us the nature and incidence 

of ... [the crisis]. Thus we view λ ≡ [( σ 2 , μ pp ′ 1, μ 2 , 11, 22 ) ] as a 

vector of population parameters that characterize the probability 

density [( 1 p d d, ,K,d ;λ)] 2 T of the observed data. Our tasks are 

then to find the value of the parameter λ that best describes the 

data, form an inference about when the ... [crisis] occurred, and 

use these parameters and inference to forecast the series and test 

economic hypotheses. (Ibid., p. 236.) 

3.1 Estimates Using Data from 1934–1996 

The two-state Markov-switching model is estimated using historical disbursement 

data for the period 1934–1996. The model specifies a process that moves to and from 

states of small and large disbursements; however, these states are not directly observable. 

Because they are not directly observable, I make an inference about which regime was 

more likely to have been responsible for producing each value of the historical 

disbursements. The upper panel of figure 2 plots the probability of being in state 1 at 

each point in the sample. These probabilities allow us to infer the identities of the states, 

and a probability value close to one identifies the state with near certainty. Observe that 

the probability of state 1 is uniformly close to one for the years before 1984 and the 

10 
Figure 2 

0.0 

0.2 

0.4 

0.6 

0.8 

1.0 

1938 1942 1946 1950 1954 1958 1962 1966 1970 1974 1978 1982 1986 1990 1994 

Probability 

0 

20 

40 

60 

80 

100 

120 

1938 1942 1946 1950 1954 1958 1962 1966 1970 1974 1978 1982 1986 1990 1994 

Basis Points

 1934

 1934 

The Probability of State 1 

Fund Disbursements per Insured Dollar 

 

 

-0.21934

-201934

period 1994–1996; by inference, the probability of state 2 is uniformly close to one 

during the period 1984–1993.2 

State 1 defines the state of small disbursements. With probability of state 1 

uniformly close to one during the periods 1934–1983 and 1994–1996, the model 

2

 The probability of being in a state is referred to in the literature as a smoothed probability. Smoothed 

probabilities are not to be confused with transition probabilities. A smoothed probability is a measure of 

the likelihood of being in a state; in contrast, a transition probability is a measure of the likelihood of 

moving between states. The smoothed probabilities play an important role in estimating the parameters of 

the model. The estimation algorithm weights the observations by the smoothed probabilities; the estimated 

mean disbursement for regime j is then the weighted average of all observations in the sample, where the 

weight for the observation dt is proportional to the probability that date t’s disbursement was generated by 

regime j. The more likely an observation is to have come from regime j, the bigger the weight given that 

observation when one is estimating μ j . The estimated transition probability p$ij is essentially the number 

of times state i seems to have been followed by regime j, where this count is estimated using the smoothed 

probabilities. For a detailed description of the estimation procedure, see Hamilton (1993). 

11 
identifies small disbursements with these two separate periods. For this state of small 

disbursements, the model estimates the mean disbursement to be 6 basis points and the 

average duration to be 43 years. The transition probability of remaining in this state of 

small disbursements from one period to the next is estimated to be p$ = 0 977 . . 11 

State 2 defines the state of large disbursements. With the probability of state 2 

uniformly close to one during the period 1984–1993, the model identifies large 

disbursements with this single period. It estimates the mean disbursement for this state of 

large disbursements to be 49 basis points and the average duration to be 8 years. The 

transition probability of remaining in this state of large disbursements from one period to 

the next is estimated to be p$ = 0877 . . 22 

The results are summarized in table 1. An interpretation of these results is that the 

model is describing the Bank Insurance Fund as either in crisis or not in crisis. More 

specifically, disbursements during the periods associated with state 1 were generally 

small and of no consequence to the solvency of the Bank Insurance Fund. These periods 

identify a fund that is not in crisis, despite the fact that during the years 1939, 1940, and 

1974 disbursements were quite large. 

It is true that disbursements were large during these particular years; nevertheless, 

these isolated large disbursements were not a problem. A long sequence of large 

disbursements, however, does put the insurance fund in jeopardy. The period 1984–1993 

represents ten consecutive years of large disbursements that threatened the solvency of 

the fund. Disbursements during this period were 55, 19, 29, 30, 70, 61, 56, 105, 66, and 9 

basis points, respectively. Given the size of the disbursements and the length of the 

episode, this period identifies an insurance fund in crisis. 

12 
 

Table 1 

Data-Generating Process 

(Data from 1934–1996) 

State 1 State 2 

Time Periods 1934–1983 1984–1993 

1994–1996 

Mean Disbursement 6 49 

Average Duration 43 years 8 years 

To sum up: the model accurately characterizes the 63-year history of the Bank 

Insurance Fund. It identifies most years with small disbursements; the estimated average 

duration of this state corresponds nicely with the long period of small disbursements 

before 1984. It also identifies a single period of stress that corresponds nicely with the 

recent banking crisis. The estimated average duration of this state coincides with the 

length of the crisis; significantly, the model captures the severity of the crisis by 

estimating a mean disbursement that is eight times larger than the average disbursement 

of the noncrisis state. 

3.2 Estimation Using Data from 1972–1996 

The model is now estimated using disbursement data for the subperiod 1972– 

1996. The upper panel of figure 3 plots the probability of being in state 1 at each point in 

the sample. Observe that the probability of state 1 is uniformly close to one for the years 

before 1987 and for the period 1994–1996; by inference, the probability of state 2 is 

uniformly close to one during the period 1988–1993.

 State 1 is again the state of small disbursements. With the probability of state 1 

uniformly close to one during the periods 1972–1987 and 1994–1996, the model 

identifies small disbursements with these two periods. For this state of small 

13 
Figure 3 

0.0 

0.2 

0.4 

0.6 

0.8 

1.0 

1974 1976 1978 1980 1982 1984 1986 1988 1990 1992 1994 1996 

Probability 

0 

20 

40 

60 

80 

100 

120 

1974 1976 1978 1980 1982 1984 1986 1988 1990 1992 1994 1996 

Basis Points 

1972 

1972 

The Probability of State 1 

Fund Disbursements per Insured Dollar 

 

 

 

 -0.21972

-201972

Figure 3: Upper Panel: The Probability of State 1 (1972-1996). Lower Panel: Fund

Disbursements per Insured Dollar, Measured in Basis Points

disbursements, the model estimates the mean disbursement to be 16 basis points and the 

average duration to be 15 years. The transition probability of remaining in this state of 

small disbursements from one period to the next is estimated to be p$ = 0 931 . . 11 

State 2 defines the state of large disbursements. With the probability of state 2 

uniformly close to one during the period 1988–1993, the model identifies large 

disbursements with this single period. It estimates the mean disbursement for this state to 

be 55 basis points and the average duration to be 6 years. The transition probability of 

remaining in this state of large disbursements from one period to the next is estimated to 

be p$ = 0825 . . (See table 2 for a summary of results.) 22 

14 
 

 

 

Table 2 

Data-Generating Process 

(Data from 1972–1996) 

State 1 State 2 

Time Periods 1972–1987 1988–1993 

1994–1996 

Mean Disbursement 16 55 

Average Duration 15 years 6 years 

4 Simulation Model 

We now explore the implications of different funding arrangements for the longterm solvency of the Bank Insurance Fund. For each funding arrangement⎯a funding 

arrangement is defined by the assessment rate and the required reserve ratio⎯I examine 

the fund’s survival properties by using a simulation based on historical disbursement 

data. More specifically, I quantify the probability of insolvency (and the probabilities of 

falling below two different minimum reserve ratios) by generating sequences of future 

fund disbursements. 

4.1 The Simulation Algorithm 

The simulation algorithm is laid out in equation 

i TA = + b1 i TA g + + b1 gc Pr em − − b 1 ) rhD , (6) t t −1 2 t t 

where TAt defines total assets at the end of time t; i defines the net return on assets; 

Pr emt defines assessments during time t; and (1− r Dt ) defines the net disbursements

during time t, with r specifying the recovery rate. Each term of the equation⎯total 

15 
 

 

 

assets, net return on assets, assessments, and net disbursements⎯is elaborated on in the 

pages that follow. 

4.1.1 Total Assets 

The FDIC determines the bank fund balance by reducing total assets by total 

liabilities. The fund balance in the simulation is determined in a similar manner. After 

using the model in equation (6) to simulate future values for total assets, we determine 

the bank fund balance by reducing the simulated total assets by total liabilities, where 

total liabilities are set equal to an amount reserved for troubled banks. More formally, 

the bank fund balance is specified by 

BFt = TAt − Rt , (7) 

where BFt , defines the bank fund balance at the end of time t; TAt defines total assets at 

the end of time t; and 

R t = − r)Dt (1 (7a) 

defines a reserve for troubled banks set up at the end of period t. (Note that since the 

bank fund balance, BFt , is expressed as a percentage of insured deposits, the variables 

TAt and Dt are also expressed as a percentage of insured deposits.) More specifically, 

the amount reserved for the future losses of troubled banks (i.e., losses during period 

t +1) is set equal to the current period’s net disbursement (i.e., losses during period t ). 

16 
At the beginning of each period a number of banks are identified by the regulatory 

process as likely to fail, and an estimated liability for these anticipated failures is 

determined. To illustrate how reserving policy affects the solvency of the Bank 

Insurance Fund, consider the period 1984–1993. This period represents a decade of 

consecutive large insurance losses that threatened the solvency of the BIF. In fact, the 

BIF was technically insolvent at the end of 1991, but insolvency was due only in part to 

this long sequence of large losses. At the end of 1991, the FDIC reserved $15.427 billion 

for the expected losses of those banks identified by the regulatory process as likely to fail 

in the future. With assets depleted at that time, reserving such a large amount drove the 

BIF balance below zero. (That is, TAt was less than Rt = $15.427 billion in equation (7).) 

However, actual losses were $3.7 billion in 1992 and only $677 million in 1993, and if 

the amount reserved had been closer to these actual losses, the BIF would have remained 

in the black. (That is, TAt would have been greater than Rt in equation (7).) 

We capture this sort of phenomenon by including Rt = − r)Dt (1 in equation (7).

This specification assumes adaptive reserving: the reserve for the next period’s expected 

losses is set equal to the current period’s actual losses. Under this specification, the 

model overreserves when a small disbursement follows a large disbursement and 

underreserves when a large disbursement follows a small disbursement. In a typical 

sequence of simulated disbursements, a period of small disbursements follows a period of 

large disbursements. As we move from a period of large disbursements to a period of 

small disbursements, the model incorrectly reserves for future large disbursements. In 

this case, the model overreserves, and this large reserve adversely affects the bank fund 

17 
balance. However, after one period the model identifies the end of a banking crisis and 

then correctly reserves for future small disbursements. 

In other words, in the model the FDIC is initially fooled; but after a short lag the 

FDIC identifies the end of a banking crisis and then reserves for future small losses. 

After one period, the model accurately reserves for future small losses, but since the 

reserve is set equal to the current period’s losses, the amount reserved is never exactly 

equal to the future loss. One could not reasonably expect the FDIC to forecast future 

bank failures with certainty (perfect-foresight reserving), but one would expect these 

forecasts to be somewhat accurate, given the FDIC’s access to Call Report and 

examination information. A reasonable approximation of this reality is an adaptive 

reserving specification. 

4.1.2 Net Return on Assets 

The simulation model assumes that asset earnings are sufficient to cover operating 

expenses and insured-deposit growth in addition to returning 2 percent during periods of 

small disbursements. (Since 1985 operating expenses have ranged from less than 

1 percent to almost 2 percent of total assets. Insured deposits have grown at an annual 

rate of about 2.5 percent over the same period; however, the growth of deposits for 1990– 

1996 was flat, a fact that may reflect a permanent shift away from deposits into other 

financial assets, such as money market mutual funds.) 

Asset earnings in excess of operating expenses and insured-deposit growth 

determine the net return on assets (i), assumed to be 2 percent during periods of small 

disbursements. But since one would anticipate smaller asset earnings during a crisis, a 

zero net return is assumed during periods of large disbursements. In the simulation, a 

18 
period of large disbursements represents a banking crisis. Banking crises often 

correspond with declining values for bank assets. Thus, it is not unreasonable to assume 

that the FDIC may suffer some capital losses on existing assets in liquidation at the onset 

of a crisis and that, as the crisis persists, accretion in the value of assets in liquidation 

may be less than had been anticipated. Nevertheless, a zero net return assumes that the 

smaller asset earnings during a crisis are still sufficient to cover operating expenses and 

the growth of insured deposits. 

In the simulation, only insurance losses can reduce the size of the fund. (The 

fund, measured as a percentage of insured deposits, will decline when money is paid out 

to cover operating expenses and/or when insured deposits increase, but in the simulation 

asset earnings cover these costs.) However, during a period of small disbursements, a 

2 percent net return on assets will cover most insurance losses; in fact, this income will 

generally be greater than insurance losses. With income greater than insurance losses, 

the simulated fund grows during good times. However, during bad times (periods of 

large disbursements), the assumed smaller asset earnings preclude such growth. 

4.1.3 Assessments 

According to the Financial Institutions Reform, Recovery, and Enforcement Act 

of 1989 (FIRREA), if the level of the Bank Insurance Fund falls below 125 basis points 

of insured deposits, banks are assessed a premium. They are assessed rates that are 

sufficient to increase the reserve ratio to the designated reserve ratio within a year. If that 

cannot reasonably be done, they are assessed rates in accordance with a BIF 

recapitalization schedule designed to achieve the designated reserve ratio by the end of a 

19 
15-year period. Assessments over the term of the recapitalization schedule must be at 

least 23 basis points. I model the assessment schedule after this legislation. 

In the model, premiums are assessed at the beginning of the period. Defining RR 

as the required reserve ratio and AR as the maximum assessment rate, 

Pr em = max(0,min( AR, RR − BF )), where BF specifies the beginning fund balance. t t−1 t−1 

(In other words, the beginning fund balance is determined by the fund balance at the end 

of the prior period.) 

The simulation assumes zero premiums when the fund balance is greater than the 

required reserve ratio. To illustrate, consider a required reserve ratio of 1.25 percent, a 

maximum assessment rate of 23 basis points, and a bank fund balance of 150 basis 

points. In this case, Pr emt = max( ,min( 0 23 125 , − 150 )) = 0 basis points. When the fund 

balance is less than the required reserve ratio by an amount smaller than the maximum 

assessment rate, the simulation assumes premiums equal to the deficit. To illustrate, 

consider a required reserve ratio of 1.25 percent, a maximum assessment rate of 23 basis 

points, and a bank fund balance of 120 basis points. In this case, 

Pr emt = max(0,min(23 125 , −120)) = 5 basis points, and the reserve ratio increases to the 

designated ratio within the period. Finally, when the fund balance is less than the 

required reserve ratio by an amount greater than the maximum assessment rate, the 

simulation assumes premiums equal to the maximum assessment. To illustrate, consider 

a required reserve ratio of 1.25 percent, a maximum assessment rate of 23 basis points, 

and a bank fund of 100 basis points. In this case, 

Pr emt = max(0,min(23125 , −100)) = 23 basis points. The premium is set equal to the 

maximum assessment rate; nevertheless, the reserve ratio remains temporarily below the 

20 
designated ratio as we assume the implementation of a recapitalization schedule, where 

assessments over the term of the recapitalization schedule are uniformly set equal to 23 

basis points. 

4.1.4 Net Disbursements 

To simulate gross disbursements ( ), D the estimated transition probabilities are t 

used. Here I illustrate the simulation of gross disbursements using the Markov-switching 

model estimated with data for the period 1934–1996. 

The simulation randomly moves the disbursement process to and from states of 

small and large disbursements, where the estimated transition probabilities specify the 

likelihood of moving between the states. Our two-state Markov-switching model 

identified the final year of the historical disbursement data as a small disbursement. With 

the final year of the historical data identified as a small disbursement, the disbursement 

process either remains in a state of small disbursements during the first simulated year 

with a probability of p11 = 0 977 . , or the disbursement process moves to a state of large 

disbursements with a probability of p12 = 0 023 . .

If the disbursement process remains in a state of small disbursements, then the 

first simulated disbursement is randomly chosen from the set of historical disbursements 

identified as small disbursements. The set of small disbursements contains the historical 

disbursements from the periods 1934–1983 and 1994–1996; each element of the set is 

assumed to be equally likely. (If the disbursement process instead moves to a state of 

large disbursements, then the first simulated disbursement is randomly chosen from the 

set of historical disbursements identified as large disbursements, where each element of 

this set is also assumed to be equally likely.) 

21 
 

Once the first simulated disbursement is generated, the model then determines the 

state of the disbursement process for year two. Assuming that the first simulated 

disbursement is a small disbursement, the disbursement process either remains in a state 

of small disbursements during the second simulated year with a probability of 

p11 = 0 977 . , or it moves to a state of large disbursements with a probability of 

p12 = 0 023 . . Once the state of the process is determined, the second simulated 

disbursement is randomly chosen from the set of historical disbursements identified with 

the state. The algorithm continues until a sequence of 63 future disbursements is 

generated.3 

In practice, some fraction of disbursements is subsequently recovered either 

through the liquidation of assets or by workouts. More generally, we assume that 

r percent of disbursements is recovered; ( ) t 1− rD therefore defines net disbursements in 

the simulation model. These recoveries are assumed to equal 63 percent of gross 

disbursements in any given year—the average recovery rate for the period 1980–1995. 

This is somewhat smaller than the 65 percent average recovery rate over the history of 

the fund; the smaller recovery rate may be explained by the large sales of assets 

associated with the banking crisis of this period.4 

3

 The model is capable of simulating sequences of any length. The number of disbursements in our 

analysis corresponds to the 63-year history of the fund, 1934–1996. That is, we use this history to simulate 

arbitrarily a sequence of equal length. 

4

 The model in equation (6) assumes that all recoveries occur in the first year; however, we also ran the 

simulation assuming that recoveries occurred over a ten-year period, and estimated a recovery schedule 

based on the historical experience since 1986. Our estimates, however, showed that 90 percent was 

recovered in the first two years of the schedule; so not surprisingly, inclusion of this ten-year schedule had 

no effect on the results of the simulation. 

22 
4.1.5 Example of a Simulation 

Assume that the first simulated disbursement is set equal to the small historical 

disbursement of 6 basis points. (With the simulated disbursement identified as a small 

disbursement, the net return on assets (i) is set equal to 2 percent.) We specified that 

63 percent of gross disbursements is recovered either through the liquidation of assets or 

by workouts. Given a gross disbursement of 6 basis points, a recovery rate of 63 percent 

defines a net disbursement of 3.78 basis points. 

In the simulation model, the variable TAt −1 defines prior assets. The algorithm 

begins by setting this variable equal to 136 basis points—total assets as of year-end 1996. 

The bank fund balance as of year-end 1996 was 134 basis points. Assume a required 

reserve ratio of 1.25 percent. Since the bank fund balance is greater than 125 basis 

points, the premium is set equal to 0 basis points. Now, given prior assets equal to 

136 basis points, a net return of 2 percent, assessment income equal to 0 basis points, and 

a net disbursement equal to 3.78 basis points, equation (6) defines total assets at the end 

of the first simulated year as 134.90 basis points. 

Once this value is simulated, one can determine the bank fund balance at the end 

of the first simulated year simply by reducing the simulated total assets (i.e., 134.90 basis 

points) by an amount reserved for troubled banks, where the reserve is set equal to the 

current period’s net disbursement (i.e., 3.78 basis points). Reducing the simulated total 

assets by this amount defines a bank fund balance of 131.12 basis points at the end of the 

first simulated year. This process continues, with the simulation algorithm tracking the 

level of the insurance fund across a sequence of 63 simulated disbursements. 

23 
The simulation generates 1,000 different sequences of 63 disbursements. These 

simulated disbursement sequences are used to quantify a probability of insolvency. A 

single sequence of 63 simulated disbursements defines a simulation trial. If the fund 

balance is positive across an entire sequence of 63 simulated disbursements, then the trial 

is identified with bank fund solvency; if the fund balance falls below zero, the trial is 

identified with insolvency. The proportion of these trials that exhausts the Bank 

Insurance Fund determines a probability of insolvency—the probability that the FDIC 

requires additional funding sometime within a given 63-year period. 

4.2 Simulation Results for a 1.25 Percent Required Reserve Ratio 

This section reports the simulation results for a 1.25 percent required reserve 

ratio. I examine this reserve ratio across a range of different assessment rates by running 

two simulations. The first simulation uses disbursement data for the period 1934–1996; 

the second, disbursement data for the period 1972–1996. 

4.2.1 Probabilities of Insolvency Using Data from 1934–1996 

Solvency of the fund is critically dependent on the size of the maximum 

assessment. The simulation results report that the 1.25 percent required reserve ratio is 

sufficient to maintain FDIC solvency if the maximum assessment rate is 23 basis points.5 

(See table 3.) The Markov-switching model identifies large disbursements with the time 

period 1984–1993. The disbursements for a simulated banking crisis are chosen from 

this set of historical large disbursements, where the average across the set is 49 basis 

points. With an average large disbursement of 49 basis points, a recovery rate of 

24 
 

Table 3 

Probability of Insolvency Using Data from 1934–1996 

Maximum Probability Probability Probability 

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

(Basis Points) (%) (%) (%) 

23.0 0.1 8.2 38.6 

20.0 0.9 16.2 40.0 

17.0 4.0 23.8 44.0 

12.0 16.7 37.3 50.4 

8.33 26.6 44.1 54.9 

63 percent suggests an average net disbursement during a simulated crisis of 18.13 basis 

points. The drain on the fund during a crisis therefore averages about 20 basis points; 

however, this drain is offset by assessments of up to 23 basis points. Because 

assessments are large enough to neutralize the drain on the fund, the probability of 

insolvency is approximately zero. 

This is not true for most of the other assessment rates examined. Although not 

allowed under current law, consider the historical rate of 8.33 basis points. With a 

maximum assessment of 8.33 basis points, premium income is not large enough to 

neutralize the drain on the fund. Assessments in this case cover less than half of the net 

disbursement during a crisis; consequently, a long sequence of large disbursements could 

bankrupt the fund. The probability of this event is found to equal 26.6 percent. 

The simulated disbursements are not independent random draws from some 

specified distribution. Instead, the Markov-switching model randomly moves the 

5

 The assessment rate of 23 basis points is also the current statutory minimum unless the designated reserve 

ratio can be restored within a year. 

25 
disbursement process to and from states of small and large disbursements. States of 

small disbursements tend to follow other small disbursements; states of large 

disbursements tend to follow other large disbursements. Because these states are serially 

correlated, a typical sequence of simulated disbursements consists of a long period of 

small disbursements followed by a shorter period of large disbursements. 

We know the Bank Insurance Fund is vulnerable to a long sequence of large 

disbursements. Recall that the time period 1984–1993 represents ten years of 

consecutive large disbursements that threatened the solvency of the fund. The Markovswitching model estimates the duration of a crisis to be about eight years; therefore, we 

would expect to observe a crisis of this length in almost all of the 1,000 simulation trials. 

In other words, the typical simulated crisis would consist of eight consecutive large 

disbursements averaging 49 basis points. Given the size of these disbursements and the 

length of this episode, it is clear that the simulation provides a strong test for the solvency 

of the fund. (Note that the simulation also allows for the possibility of a much more 

severe crisis—i.e., a crisis longer than eight years with an average disbursement much 

larger than 49 basis points. In fact, a simulated crisis of this magnitude is almost certain 

to occur in at least one of the 1000 simulation trials.) 

4.2.2 Probabilities of Insolvency Using Data from 1972–1996 

The simulation results in table 3 indicate that the current funding arrangement— 

an assessment rate of 23 basis points with a 1.25 percent required reserve ratio—is 

sufficient to maintain FDIC solvency. But the analysis is premised on the assumption 

that the future will be something like the past. The past is the history of the Bank 

Insurance Fund, a history characterized by a long period of stability. Disbursements were 

26 
 

close to zero for the time period 1940–1970. Since the past is dominated by this stability, 

the projections implicitly assume it is likely that the FDIC will again experience another 

thirty years of essentially no bank failures. 

This assumption of stability is relaxed by truncating the data set. I now use 

parameter estimates from the Markov-switching model estimated with disbursement data 

for the subperiod 1972–1996. Since this set of historical data reflects a period of 

generally larger and much more volatile disbursements, the second simulation assumes 

high future losses. In fact, the average disbursement for the second simulation increases 

from 12.04 to 27.49 basis points. Yet despite the fact that simulated disbursements 

increase on average by more than 100 percent, the probability of insolvency remains 

quite close to zero for an assessment rate of 23 basis points. (See table 4.) With a 

probability so close to zero, the results again confirm that the current funding 

arrangement—an assessment rate of 23 basis points with a 1.25 percent required reserve 

ratio—is sufficient to maintain FDIC solvency. 

Reducing assessment rates below 23 basis points would require a change in 

current law; however, if the FDIC were afforded greater flexibility in establishing 

premium levels when the fund drops below 125 basis points, the FDIC’s ability to lower 

assessment levels in a time of crisis would depend on its willingness to assume risk. 

Consider a reduction of the assessment rate from 23 to 20 basis points. If the minimum 

assessment level is reduced slightly to 20 basis points, there is approximately a zero 

probability of the fund becoming insolvent under a low-loss assumption (table 3); 

however, under a high-loss assumption (table 4), a probability of 10.5 percent could not 

rule out the possibility of future FDIC insolvency. 

27 
 

Table 4 

Probability of Insolvency Using Data from 1972–1996 

Maximum Probability Probability Probability 

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

(Basis Points) (%) (%) (%) 

23.0 3.2 48.9 88.2 

20.0 10.5 65.8 91.2 

17.0 27.2 76.9 93.9 

12.0 57.2 87.8 95.7

 8.33 74.2 93.1 97.1 

4.2.3 Probabilities of Low Fund Balances 

Although the current funding arrangement is sufficient to maintain FDIC 

solvency, it cannot guarantee large fund balances. Tables 3 and 4 both report the 

probabilities that the fund balance will fall below either 50 or 75 basis points. These 

probabilities are in general quite large; and in the second simulation, they increase 

substantially. For the current assessment rate of 23 basis points, the probability of a fund 

balance less than 50 basis points increases from 8.2 percent in the first simulation to 

48.9 percent in the second; the probability of a fund balance less than 75 basis points 

increases from 38.6 percent to 88.2 percent. 

4.3 Simulation Results for Alternative Required Reserve Ratios 

Current law mandates a reserve ratio equal to 1.25 percent of insured deposits;6 

however, six alternative required reserve ratios ranging from as low as 100 basis points to 

as high as 150 basis points are examined. I examine each required reserve ratio across a 

6

 If significant risk of substantial losses to the insurance fund is identified, the FDIC Board of Directors 

may raise the required reserve ratio for a particular year. 

28 
 

range of different assessment rates by running two simulations.7 The first simulation uses 

disbursement data for the period 1934–1996; the second, disbursement data for the period 

1972–1996. The results (presented in appendix A) give rise to three conclusions: 

• Substantially reducing the required reserve ratio would depend on the FDIC’s 

willingness to assume risk. Consider a smaller required reserve of 100 basis 

points. For an assessment rate of 23 basis points, the probability of insolvency 

under the lower-loss assumption (table A-1) is close to zero; however, under the 

higher-loss assumption (table A-2), a probability of 12.8 percent could not rule 

out the possibility of future FDIC insolvency. 

• Increasing the required reserve ratio would not allow the FDIC to substantially 

reduce assessment rates. Consider a larger required reserve of 150 basis points 

and a smaller assessment of 12 basis points. The probability of insolvency is 

equal to 11.0 percent under the lower-loss assumption (table A-11); the 

probability of insolvency is equal to 43.4 percent under the higher-loss 

assumption (table A-12). Given these probabilities, a larger fund with smaller 

assessments would not be sufficient to maintain FDIC solvency. 

• But increasing the required reserve ratio while maintaining the current 

assessment rate would substantially reduce the likelihood of small fund balances. 

With a 23 basis points maximum assessment rate, for example, the probability of 

the fund dropping under 50 basis points falls from 8.2 percent to 0.6 percent 

7

 The simulations are run by assuming that total assets are initially equal to the required reserve ratio. To 

illustrate, consider a required reserve ratio of 100 basis points. Total assets and the beginning fund balance 

are both equal to the required reserve ratio of 100 basis points. The beginning bank fund balance is less 

than the 1996 ending fund balance of 134 basis points; however, in this case we assume a one-time rebate 

of 34 basis points. Alternatively, we assume a special assessment is collected if the required ratio is greater 

than the 1996 ending fund balance. 

29 
under the low-loss scenario and from 48.9 percent to 11.5 percent under the 

high-loss scenario. (Compare tables 3 and 4 with tables A-11 and A-12.) 

5 Conclusion 

A model (the Markov-switching model) was constructed that enabled us to project 

future disbursements under certain conditions. I used the projected disbursements to 

estimate the BIF’s likelihood of insolvency as well as the likelihood of the BIF falling 

below two different minimum reserve ratios. These probabilities were estimated across 

a range of assessment rates for a number of different required reserve ratios. 

The simulation results confirm that the current funding arrangement—an 

assessment rate of 23 basis points with a 1.25 percent required reserve ratio—is 

sufficient to maintain FDIC solvency if one assumes that the prior history of losses is a 

good indicator of future losses. More generally, the results indicate that for the current 

funding arrangement 

• The likelihood of the BIF becoming insolvent is very small regardless of the 

loss assumption used. Under the lower-loss assumption, there is only a 

0.1 percent chance of insolvency; under the higher-loss assumption, this 

probability increases slightly to 3.2 percent. 

• But the likelihood of small fund balances is quite large. Under the higher-loss 

assumption, there is a 48.9 percent chance that the fund level will fall below 

50 basis points. Under the lower-loss assumption, there is a 38.6 percent 

chance that the fund level will fall below 75 basis points; this probability 

increases to 88.2 percent under the higher-loss assumption. 

30 
If the FDIC were afforded greater flexibility in establishing premium levels when 

the fund dropped below 125 basis points, the FDIC’s decision whether to lower 

assessment levels in a time of crisis would depend on its willingness to assume risk. 

More generally, the results indicate that 

• If the minimum assessment level is reduced slightly from 23 to 20 basis points, 

there is close to zero probability of the fund becoming insolvent under a low-loss 

assumption; however, under a high-loss assumption, a probability of 10.5 percent 

could not rule out the possibility of future FDIC insolvency. 

• If one of the FDIC’s objectives were to maintain a minimum reserve ratio, 

moving the minimum assessment level below 23 basis points would be 

substantially more difficult. If the minimum assessment level is reduced to 

20 basis points, for example, the probability of the reserve ratio dropping below 

50 basis points almost doubles from 8.2 percent to 16.2 percent under the lowloss assumption and increases to 65.8 percent from 48.9 percent under the highloss assumption. 

With respect to changing the required reserve ratio: on the one hand, substantially 

reducing it would expose the FDIC to the possibility of future FDIC insolvency. On the 

other hand, increasing it would not allow the FDIC to reduce assessment rates 

substantially. However, increasing the required reserve ratio while maintaining the 

current assessment rate would substantially reduce the likelihood of small fund balances. 

Let me conclude with a word of caution. If we assume that the prior history of 

losses is a good indicator of future losses, then the adequacy of the current funding 

arrangement is confirmed by the results. However, the adequacy of the current funding 

31 
 

arrangement is very doubtful when one assumes future losses that are twice as large as 

historical losses. If we double the magnitude of the assumed future losses, the 

probability of insolvency for the current funding arrangement exceeds 50 percent.8 

(The probability of insolvency for the current funding arrangement is unaffected if we 

assume the same magnitude of losses but instead double the length of a crisis.) Running 

the simulation under this assumption of proportionately larger losses illustrates that the 

results in the paper are critically dependent on our assumptions concerning future losses. 

8

 I ran the simulation after first doubling the historical disbursements. The simulation was run twice: once 

employing the revised historical data for the period 1934–1996 and then with the revised historical data for 

the period 1972–1996. Using the revised historical data for the period 1934–1996, the probability of 

insolvency was found to equal 54.7 percent. The probability of insolvency using the revised data for the 

period 1972–1996 was found to equal 94.8 percent. 

32 
APPENDIX 

Required Reserve Ratio of 100 Basis Points 

Table A - 1 

Probability of Insolvency Using Data from 1934–1996 

Maximum Probability Probability Probability 

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

(Basis Points) (%) (%) (%) 

23.0 0.7 42.7 70.5 

20.0 3.7 44.6 70.6 

17.0 10.3 49.3 71.1 

12.0 28.2 56.7 72.2

 8.33 38.5 61.2 73.5 

Table A - 2 

Probability of Insolvency Using Data from 1972–1996 

Maximum Probability Probability Probability 

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

(Basis Points) (%) (%) (%) 

23.0 12.8 88.4 99.9 

20.0 30.2 91.5 99.9 

17.0 51.5 94.5 99.9 

12.0 74.0 96.2 99.9

 8.33 85.4 97.7 100.0 

33 
Required Reserve Ratio of 110 Basis Points 

Table A - 3 

Probability of Insolvency Using Data from 1934–1996 

Maximum Probability Probability Probability 

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

(Basis Points) (%) (%) (%) 

23.0 0.3 37.0 57.5 

20.0 2.0 38.9 59.8 

17.0 7.5 41.7 61.5 

12.0 22.9 49.7 63.7

 8.33 34.0 54.9 65.0 

Table A - 4 

Probability of Insolvency Using Data from 1972–1996 

Maximum Probability Probability Probability 

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

(Basis Points) (%) (%) (%) 

23.0 6.5 86.0 97.0 

20.0 20.4 88.1 97.8 

17.0 40.0 91.2 98.4 

12.0 67.1 94.5 99.4

 8.33 81.4 96.1 99.8 

34 
Required Reserve Ratio of 120 Basis Points 

Table A - 5 

Probability of Insolvency Using Data from 1934–1996 

Maximum Probability Probability Probability 

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

(Basis Points) (%) (%) (%) 

23.0 0.1 19.5 42.6 

20.0 1.2 26.6 46.6 

17.0 5.3 32.5 50.7 

12.0 19.1 43.1 57.4

 8.33 30.1 49.4 60.0 

Table A - 6 

Probability of Insolvency Using Data from 1972–1996 

Maximum Probability Probability Probability 

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

(Basis Points) (%) (%) (%) 

23.0 4.2 68.4 90.3 

20.0 13.4 78.8 94.4 

17.0 32.1 85.1 95.7 

12.0 60.8 91.5 96.8

 8.33 77.4 94.5 98.3 

35 
Required Reserve Ratio of 130 Basis Points 

Table A - 7 

Probability of Insolvency Using Data from 1934–1996 

Maximum Probability Probability Probability 

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

(Basis Points) (%) (%) (%) 

23.0 0.1 6.5 38.4 

20.0 0.7 11.9 39.6 

17.0 3.3 20.1 42.5 

12.0 16.0 36.2 49.6

 8.33 26.1 43.5 54.3 

Table A - 8 

Probability of Insolvency Using Data from 1972–1996 

Maximum Probability Probability Probability 

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

(Basis Points) (%) (%) (%) 

23.0 2.3 41.0 87.4 

20.0 9.3 58.1 89.1 

17.0 24.4 71.9 92.7 

12.0 55.2 85.8 95.2

 8.33 72.4 91.5 96.5 

36 
Required Reserve Ratio of 140 Basis Points 

Table A - 9 

Probability of Insolvency Using Data from 1934–1996 

Maximum Probability Probability Probability 

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

(Basis Points) (%) (%) (%) 

23.0 0.1 1.8 28.6 

20.0 0.4 6.5 31.4 

17.0 2.1 14.2 34.7 

12.0 12.7 28.8 43.4

 8.33 22.5 37.6 48.3 

Table A - 10 

Probability of Insolvency Using Data from 1972–1996 

Maximum Probability Probability Probability 

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

(Basis Points) (%) (%) (%) 

23.0 1.2 21.3 77.2 

20.0 6.5 42.4 84.1 

17.0 18.0 61.1 88.3 

12.0 49.6 79.2 92.9

 8.33 67.0 87.9 95.2 

37 
Required Reserve Ratio of 150 Basis Points 

Table A - 11 

Probability of Insolvency Using Data from 1934–1996 

Maximum Probability Probability Probability 

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

(Basis Points) (%) (%) (%) 

23.0 0 0.6 8.1 

20.0 0.4 3.2 15.9 

17.0 1.6 8.9 23.4 

12.0 11.0 23.6 36.3

 8.33 19.4 33.8 42.9 

Table A - 12 

Probability of Insolvency Using Data from 1972–1996 

Maximum Probability Probability Probability 

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

(Basis Points) (%) (%) (%) 

23.0 0.9 11.5 49.2 

20.0 4.6 27.9 65.1 

17.0 14.2 47.8 76.8 

12.0 43.4 71.7 87.9

 8.33 62.7 83.2 92.7 

38 
 

 

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39