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THE USE OF MARKET INFORMATION I N PRICING
DEPOSIT INSURANCE
by James B. Thomson

James B. Thomson i s an economist a t t h e Federal
Reserve Bank o f Cleveland.
The a u t h o r thanks
Ed Kane, Andy Chen, E r i c Rosengren, and t h e
r e f e r e e s of t h e Journal o f Money, C r e d i t and
Banking f o r h e l p f u l comments on an e a r l i e r
v e r s i o n of t h i s paper.
Working papers o f t h e Federal Reserve Bank o f
Cleveland are p r e l i m i n a r y m a t e r i a l s , c i r c u l a t e d
t o s t i m u l a t e d i s c u s s i o n and c r i t i c a l comment.
The views s t a t e d h e r e i n a r e t h e a u t h o r ' s and
n o t n e c e s s a r i l y those o f t h e Federal Reserve
Bank of Cleveland o r o f t h e Board o f Governors
o f t h e Federal Reserve System.

August 1986
Federal Reserve Bank o f C l e v e l a n d

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The Use o f Market I n f o r m a t i o n i n P r i c i n g D e p o s i t I n s u r a n c e

Abstract

This

paper

argues

that

d e p o s i t - i n s u r a n c e guarantee i s

information

about

the

value

of

a v a i l a b l e f r o m market- generated d a t a .

the
Under

c e r t a i n assumptions, an unbiased e s t i m a t e o f t h e market v a l u e o f t h e d e p o s i t
I n p r a c t i c e , however, i t i s o n l y p o s s i b l e t o

guarantee i s r e a d i l y a v a i l a b l e .

observe a lower bound a g a i n s t which e s t i m a t e s o f deposi t - i n s u r a n c e premia can
be compared.
In

the

associated

absence
with

deposit- insurance

of

federal

deposit

insurance

reforms,

the

includes:

1)

total
the

guarantee

guarantee on

i n s u r e d d e p o s i t s , 2 ) a c o n d i t i o n a l guarantee on u n i n s u r e d d e p o s i t s ,
conditional

guarantee

of

the

stockholders'

residual

c l a i m on

and 3) a
the

future

e a r n i n g s o f t h e bank.
Introduction

The

debate

on

pricing

deposit

insurance

concern t o a p u b l i c p o l i c y concern.
(19831,

the

Federal

Home

has

gone f r o m a p u r e l y academic

The Federal D e p o s i t I n s u r a n c e C o r p o r a t i o n

Loan Bank

Board

(1983>,

and

t h e U.S.

Treasury

Department (The Working Group o f t h e Cabinet C o u n c i l on Economic A f f a i r s 1985)
have a l l i s s u e d r e p o r t s on r i s k - b a s e d d e p o s i t - i n s u r a n c e p r i c i n g .

These execu-

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tive- agency

studies

accompany

deposit- insurance p r i c i n g (see,

a

large

body

of

academic

research

on

f o r example, A v e r y , Kawst, and Hanweck 119851;

H o r v i t z [19831; Kane [1983, 1985, and 19861; Merton [1977, 19781; P y l e 11983,
19861; R o c h e s t e r and Walker [19851; and Ronn and Verma C19851).
If

the

Federal

Deposit

d e p o s i t - i n s u r a n c e premium e q u a l

Insurance

Corporation

charges

a

t o t h e r i s k premium t h e m a r k e t would r e q u i r e

t o p r o v i d e t h e same l e v e l o f r i s k - b e a r i n g s e r v i c e s ,
appropriately priced.'

(FDIC)

The p u r p o s e o f t h i s paper

u n c o n d i t i o n a l l y uninsured depositors e x i s t ,

then the
is

the market's

insurance

t o show ( 1 )

ex

is

that if

ante estimate o f

t h e f a i r v a l u e o f d e p o s i t i n s u r a n c e can be observed; and ( 2 ) i n t h e absence o f
deposit- insurance reforms,

t h e d e p o s i t insurance guarantee c o n s i s t s o f

the

d e p o s i t i n s u r a n c e p u t on t h e i n s u r e d d e p o s i t s , a c o n d i t i o n a l g u a r a n t e e o n t h e
u n i n s u r e d d e p o s i t s , and a c o n d i t i o n a l g u a r a n t e e of t h e s t o c k h o l d e r s ' r e s i d u a l
c l a i m o n t h e f u t u r e e a r n i n g s o f t h e bank.
Section

I o f t h i s paper,

which o u t l i n e s

the

assumptions

used

a n a l y s i s , shows t h a t i f banks a r e c l o s e d when t h e y a r e f o u n d t o be

in

the

insolvent,

and u n i n s u r e d d e p o s i t o r s and s t o c k h o l d e r s b e a r t h e i r f u l l s h a r e o f t h e l o s s e s ,
t h e n t h e f a i r v a l u e o f t h e d e p o s i t g u a r a n t e e on $1 o f i n s u r e d d e p o s i t s i s t h e
r i s k premium p a i d on $1

of

uninsured deposits.

Section

I1 relaxes

the

a s s u m p t i o n t h a t t h e FDIC a l w a y s c l o s e s banks t h a t a r e f o u n d t o be i n s o l v e n t a t
t h e time o f examination.

'

W i t h FDIC f o r b e a r a n c e s ,

t h e o b s e r v e d r i s k p r e m i um

o n $1 o f u n i n s u r e d d e p o s i t s i s a l o w e r bound e s t i m a t e o f t h e f a i r v a l u e o f t h e

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d e p o s i t guarantee on $1 o f insured deposits.

Section I11 presents a numerical

example showing how market i n f o r m a t i o n could be used i n c a l c u l a t i n g t h e f a i r
value o f the d e p o s i t guarantee.

The paper's

conclusions a r e presented i n

section IV.

I.

The Market Value o f Deposit Guarantees w i t h o u t FDIC Forbearances

The f o l l o w i n g assumptions are used i n t h i s a n a l y s i s :
Market

1)

efficiency.

This

assumption

is

necessary

the

if

market

p a r t i c i p a n t s are t o p r o v i d e an accurate estimate o f the r i s k o f the
The semi- strong form o f t h e e f f i c i ent- markets hypothesi s and

bank.

dissemination
.

2>

of

adverse

information

regarding

insured

banks

is

r e q u i r e d f o r the a n a l y s i s t o hold.
The absence o f e x t e r n a l s o c i a l benef i t s associated w i t h t h e p r o v i s i o n
o f f e d e r a l d e p o s i t insurance a t the margin.

I f the s o c i a l b e n e f i t s

associated w i t h the l a s t d o l l a r o f deposit- insurance coverage exceed
the

private

benefits

deposit- insurance

associated

coverage,

then

the

with

the

market

last

premium

dollar
is

of

not

the

s o c i a l l y optimal deposi t- insurance premi um (see M e r r i ck and Saunders
[19851>.
3>

A1 1 bank 1 i a b i 1it i e s are homogeneous d e p o s i t 1 i a b i 1i t i e s .

The bank i s

assumed t o issue one type o f deposit t h a t matures on the same day t h e
bank

is

examined

and

the

assumed f o r e x p o s i t i o n a l
analysis

to

liabilities

hold
that

n e g o t i a b l e CDs).

is

simplicity.

that

mature

d e p o s i t guarantee i s r e p r i c e d .

on

the
the

bank

All

This

that i s required for

issue

examination

some
date

is
the

uninsured. d e p o s i t
(possibly

large

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Frictionless

4)
.

markets.

The

absence

of

transaction

costs

and

indivisibilities in the deposit and insurance markets ensures that
arbitrage can remove pricing errors when they occur.
transaction costs and the indivisibilities

The size of the

limits the degree of

pricing error that cannot be removed by arbitrage.
No FDIC forbearances.

51

The F.DIC closes all banks that are insolvent.

Stockholders of banks with a positive net worth that falls below the
statutory (or regulatory) minimum capital requirements are given the
option of increasing the capital in the bank or a1 lowing the deposit
guarantor to close the bank.

Banks with positive net worth that

exceeds the statutory (or regulatory) minimum capital requirements are
allowed to pay out the excess net worth to their stockholders.

This

is a counterfactual assumption. It assumes that the FDIC is capable
of and wi 1 1 ing to close banks when they are found to be insolvent.
Negative net worth is a necessary, but not a sufficient, condition for
the forced closing of a bank by the FDIC.'
The following notation is used throughout the paper:
A

=

value of the bank's assets,

B,

=

value of a $1 risk-free discount bond at time t,

Dt

=

value of the bank's deposits at time t,

C(*>

=

American call option,

c(*)

=

European call option,

D

=

the face value of D, at t=T,

p(*)

=

European put option.

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When 100 p e r c e n t

of

a bank's deposits

deposi t - i n s u r a n c e guarantee equal s t h e t o t a l
provided

in

t h e v a l u e of

the

v a l u e o f r i sk-bear! ng s e r v i c e s

t h e market by u n i n s u r e d d e p o s i t o r s when t h e bank i s s u e s o n l y

uninsured d e p o s i t s .
value o f

are insured,

Merton (1977) shows t h a t w i t h 100 p e r c e n t i n s u r a n c e t h e

t h e d e p o s i t guarantee equals

which a l l o w s

the

stockholders

t o sell

t h e European p u t o p t i o n p(A,T-t;D1,
the assets o f

t h e bank,

d e p o s i t o r s f o r t h e f a c e v a l u e o f t h e i r d e p o s i t s , D, a t t i m e t=T.
Merton (19741,

i n t h e absence o f t h e d e p o s i t guarantee,

to

A,

the

Following

the t o t a l value o f

r i s k - b e a r i n g s e r v i c e s p r o v i d e d by t h e u n i n s u r e d d e p o s i t o r s i s ,

By M e r t o n ' s
value

of

(1973)

the

Theorem 6,

deposit

and by l e t t i n g Do/D = d o and AID

guarantee

(risk- bearing

services)

on $1

a,

=

the

o f - insured

(uninsured) deposits a t t=O i s :

The r e s u l t i n e q u a t i o n ( 2 ) has l i t t l e p r a c t i c a l use i n p r i c i n g d e p o s i t
guarantees i f i t o n l y h o l d s when a1 1 o f t h e b a n k ' s d e p o s i t s a r e e i t h e r i n s u r e d
or

If

uninsured.

Bo-do cannot

be

100

percent

observed.

If

of
the

g u a r a n t o r have t h e same p r i o r i t y of

the

banks

uninsured

deposits

are

depositors

and

insured,
the

then

deposit

c l a i m a g a i n s t t h e assets o f t h e bank,

r e l a x i n g t h e assumption o f f u l l o r no insurance t o a l l o w f o r p a r t i a l i n s u r a n c e
o f t h e b a n k ' s d e p o s i t s does n o t a f f e c t e q u a t i o n ( 2 ) . 4

To see t h i s ,

l e t w,

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be
The

the

percentage

stockholders

of
now

the
hold

p(w,,A,T-t;w,,D>

FDIC and

bank's
two

deposits

that

put options:

issued

by

the

are

uninsured

p(w,A,T-t;w,D>

uninsured

(~,+w,~=l).

i s s u e d by t h e

depositors.

By M e r t o n ' s

(1973) Theorem 6 , t h e t o t a l v a l u e o f t h e s t o c k h o l d e r s ' p u t o p t i o n s a t t = O i s :

(3)

p(w,A,T;w,,D)

By d e f i n i t i o n ,
risk- bearing
dollar

w,+w,,

=

services

of

uninsured

uninsured)

deposits.

+ p(w,A,T;w,D>
1.

T h e r e f o r e , a bank does n o t a f f e c t t h e v a l u e o f

provided

by t h e u n i n s u r e d d e p o s i t o r s

(insured)
The

(w,+w,)p(A,T;D).

=

deposits

by

issuing

value

of

the

total

(FDIC)

w,D

on each

insured

deposit

guarantee

(w,,D
is

w,D(Bo-do).

111.

The A n a l y s i s w i t h Federal B a i l o u t s of I n s o l v e n t Banks

T h i s s e c t i o n r e l a x e s assumption 5 o f s e c t i o n I by assuming t h a t a s e t o f
constraints,
banks.

z,

exists

that affects

t h e FDIC's a b i l i t y t o c l o s e i n s o l v e n t -

The a n a l y s i s shows t h a t w i t h FDIC forbearances,

t h e r i s k premium

p a i d on t h e e x p l i c i t l y u n i n s u r e d d e p o s i t s i s t h e lower bound o f t h e m a r k e t ' s
v a l u a t i o n o f t h e d e p o s i t guarantee.

Furthermore, t h e c o s t o f t h e guarantee i s

shown t o i n c r e a s e when t h e s t o c k h o l d e r s '

p o s i t i o n i n t h e bank i s n o t c l o s e d

o u t when t h e bank i s found t o be i n s o l v e n t .
L e t q ( z ) be t h e p r o b a b i l i t y t h a t a t t h e n e x t examination d a t e t h e bank i s
i n s o l v e n t and t h e FDIC i s unable t o c l o s e i t .
assumed

to

be

a

single

index

function,

F o l l o w i n g Kane (1986>, z i s

which

consist

of

information

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constraints, staff constraints, the reserve position of the insurance fund,
and political and legal constraints on the FDIC's ability to close insolvent
banks.

If the insolvent bank is allowed to operate, the FDIC may choose to

operate it as a mutual institution (that is, close out the position of the
existing shareholders) or a1 low the equity holders to retain their position.
Initially, it is assumed that the equity holders are closed out.
If a bank is found to be ins~lvent, both the FDIC and the uninsured
depositors have the right to force the closing of the bank.

If the FDIC

wishes to a1 low the bank to operate until the next examination day, it must
buy out the position of the uninsured depositors or guarantee value of the
uninsured depositors' claim against the bank.

The FDIC must provide a

guarantee of at least the market value of the uninsured depositors' claim on
the bank at the time of examination to keep the uninsured depositors from
forcing a liquidation of the bank.6

It is assumed that the same set o f

constraints, z, that prevents the FDIC from closing the bank, forces it to
guarantee the face val ue of the uni nsured depos i ts. '
The value of the guarantee on $1 of conditionally uninsured deposits at
t=O is q(z)p(a,T;l>.

The risk-bearing services provided by the conditionally

uninsured depositors on $1 of deposits at t=O is:

The observed risk premium on $1 of conditional ly uninsured deposits is shown
below in equation ( 5 ) :

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The f a i r v a l u e o f t h e d e p o s i t guarantee on $1 o f i n s u r e d d e p o s i t s i s now t h e
observed r i s k premium on t h e c o n d i t i o n a l l y u n i n s u r e d d e p o s i t s

scaled by 1,

minus t h e p r o b a b i l i t y t h a t t h e FDIC w i l l p r o t e c t t h e c o n d i t i o n a l l y u n i n s u r e d
d e p o s i t o r i f t h e bank i s

found t o be i n s o l v e n t .

The t o t a l

value o f

the

d e p o s i t - i n s u r a n c e s u b s i d i e s and guarantees i s :

G = w i D ( B ~ - d o ) + q(z>~,D(Bo-do).

(6)

Because q ( z ) i s n o t observed, t h e m a r k e t ' s e s t i m a t e o f t h e f a i r v a l u e of
t h e d e p o s i t guarantee cannot be observed.
equal t o 1,

However, s i n c e q ( z ) i s l e s s t h a n o r

t h e r i s k premium p a i d on t h e c o n d i t i o n a l l y u n i n s u r e d d e p o s i t s

r e p r e s e n t s t h e minimum v a l u e o f

t h e d e p o s i t - i n s u r a n c e guarantee.

It i s a

lower bound t h a t can be used t o e v a l u a t e e m p i r i c a l e s t i m a t e s o f t h e f a i r v a l u e
of

t h e d e p o s i t guarantee.

The upper bound o f t h e f a i r v a l u e o f t h e d e p o s i t

guarantee would be r e f l e c t e d

i n t h e r i s k premium o f

the subordinated debt

i s s u e d b y t h e bank.
E q u a t i o n (6) assumes t h a t t h e s t o c k h o l d e r s '
t h e bank i s found

t o be i n s o l v e n t .

p o s i t i o n i s c l o s e d o u t when

L e t y ( z ) be t h e p r o b a b i l i t y t h a t on t h e

n e x t examination day t h e bank i s i n s o l v e n t , and t h e s t o c k h o l d e r s r e t a i n t h e i r
position

in

position

i n i n s o l v e n t banks,

option,

C,,

the

bank.

By

which r e p r e s e n t s

Max[y(z)C,,A-Dl.

failing

t o always c l o s e o u t t h e

t h e FDIC has changed t h e
the equity o f

stockholders'

value o f

the

call

t h e bank and i s now equal

The v a l u e o f t h e c a l l o p t i o n C,,

to

can be broken down i n t o

two components:

t h e value o f t h e e q u i t y w i t h o u t the deposit- insurance subsidy

C,

and t h e d e p o s i t - i n s u r a n c e s u b s i d y x

=

Max(0,A-D>

=

Max[y(z)C,,OI.

t o t a l v a l u e o f t h e d e p o s i t - i n s u r a n c e s u b s i d i e s and guarantees a t t=O i s now:

The

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Therefore,

a l l o w i n g the stockholders t o r e t a i n th.eir r e s i d u a l

c l a i m on t h e

a s s e t s and f u t u r e e a r n i n g s o f t h e bank i n c r e a s e s t h e v a l u e of

the deposit

guarantee.

111. Market Estimates of t h e D e p o s i t Guarantee

To demonstrate how market i n f o r m a t i o n can be used i n p r i c i n g t h e d e p o s i t
guarantee,

t h e y i e l d s on six- month (secondary market)

certificates
collected.'

of

deposit

(CDs),

and

prime

Treasury b i l l s ,

commercial

paper

(CP)

bank
are

The y i e l d s a r e t h e d a i l y quoted ones r e p o r t e d i n t h e Federal

Reserve B o a r d ' s s t a t i s t i c a l r e l e a s e H.15,

" Selected I n t e r e s t Rates,"

f o r the

t r a d i n g day c l o s e s t t o January 1 and J u l y 1 f o r each year 1980 t h r o u g h 1985.
A l l r e p o r t e d y i e l d s a r e c o n v e r t e d t o bond- equivalent ones.

An annual y i e l d i s

computed f o r each i n s t r u m e n t by t a k i n g t h e geometric average o f i t s six- month
y i e l d i n January and J u l y f o r t h a t year.
The r i s k premium on CDs (CP) i s c a l c u l a t e d as t h e d i f f e r e n c e between t h e
annual y i e l d on CDs ' ( c P ) and T - b i l l s .

Assuming 10 p e r c e n t i n s u r a n c e and

' O

d i f f e r e n t v a l u e s o f q ( z > , t h e v a l u e of t h e d e p o s i t guarantee i s e s t i m a t e d f r o m
t h e r i s k premium on t h e CDs.
on $1 of

"

insured deposits i s R

By e q u a t i o n ( 5 ) ,
-

q

.

t h e v a l u e o f t h e guarantee

The v a l u e o f t h e guarantee on $1

o f c o n d i t i o n a l l y u n i n s u r e d d e p o s i t s i s q(z)R,,/(1-q(z)).
T a b l e 1 p r e s e n t s numerical e s t i m a t e s of t h e v a l u e o f t h e d e p o s i t guarantee
on $1 o f i n s u r e d and c o n d i t i o n a l l y u n i n s u r e d d e p o s i t s f o r 1980 t o 1985.
p o i n t s are brought out i n the table.

Two

F i r s t , t h e v a l u e o f t h e guarantee on t h e

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c o n d i t i o n a l l y uninsured deposits i s a p o s i t i v e f u n c t i o n o f q(z).

Second,

the

v a l u e o f t h e d e p o s i t guarantee on i n s u r e d and c o n d i t i o n a l l y u n i n s u r e d d e p o s i t s
v a r i e s across y e a r s .
the

conditionally

If q ( z > i s n o t known, t h e n t h e observed r i s k premium on

uninsured d e p o s i t s

can o n l y be used as

the lower

a g a i n s t which e s t i m a t e s o f t h e d e p o s i t guarantee can be compared.

bound

As seen i n

t a b l e 1, t h e degree t o which t h e observed l o w e r bound can be used t o f i n e - t u n e
r i s k - b a s e d models o f d e p o s i t guarantees decreases as q ( z > i n c r e a s e s .
One way o f making q ( z )

o b s e r v a b l e i s t o f o r c e banks t o i s s u e d i s c o u n t

bonds

that

can

be

insulated

would

have

the

same m a t u r i t y

from
as

the
the

deposit
deposit

p r i o r i t y o f c l a i m on t h e bank as d e p o s i t s .
debt

is

deposits

Rb

=

Bo-do.

The

value

(BO-do) i s now o b s e r v a b l e .

of
In

guarantees.
insurance

These

"

bonds

p u t and t h e

same

The r i s k premium on $1 o f t h i s

the

deposit

addition,

t h e guarantee on c o n d i t i o n a l l y u n i n s u r e d d e p o s i t s

guarantee
q ( z > and

on

the

(q(z)(Bo-do)>

insured
value

of

can now be

computed as:

IV.

Conclusion

The market p r o v i d e s i n f o r m a t i o n on t h e v a l u e o f d e p o s i t guarantees.

Under

r e s t r i c t i v e assumptions, t h e v a l u e o f t h e d e p o s i t guarantee i s o b s e r v a b l e .
p r a c t i c e , however,

o n l y a lower bound can be observed.

system o f f e d e r a l d e p o s i t insurance,

Under

In

the current

t h e d e p o s i t guarantee c o n s i s t s o f ( 1 ) t h e

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guarantee of the insured deposits, ( 2 ) a conditional guarantee of the bank's
uninsured deposits, and (3) a guarantee of the stockholders' residual o n the
future earnings of the bank.

Because the guarantee has real value t o the

banks' stockholders, insolvent banks should always be reorganized in a manner
that closes o u t the position of the stockholders.

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Notes
1.
For purposes o f e x p o s i t i o n , t h i s paper c o n c e n t r a t e s on t h e v a l u e o f FDIC
guarantees. The a n a l y s i s i s v a l i d f o r a l l t h r e e f e d e r a l d e p o s i t g u a r a n t o r s :
t h e FDIC, t h e Federal Savings and Loan I n s u r a n c e C o r p o r a t i o n (FSLIC), and t h e
N a t i o n a l C r e d i t Union Share I n s u r a n c e Fund (NCUSIF).
2. L e g a l l y , t h e FDIC does n o t have t h e power t o c l o s e i n s o l v e n t banks.
The
FDIC must p e t i t i o n t h e b a n k ' s c h a r t e r i n g agency t o c l o s e t h e bank. However,
t h i s process i s g e n e r a l l y a f o r m a l i t y , and, i n p r a c t i c e , t h e FDIC i s a b l e t o
f o r c e t h e c l o s i n g o f i n s o l v e n t banks.

3. See Kane (1986) f o r a d i s c u s s i o n o f t h e c o n s t r a i n t s f a c e d by t h e FDIC t h a t
may p r e v e n t i t f r o m c l o s i n g i n s o l v e n t banks.
4.
C u r r e n t l y , t h e d e p o s i t guarantee i s e x p l i c i t l y extended t o t h e f i r s t
$100,000 o f each d e p o s i t account ( t h i s 1i m i t i s p e r person, p e r account t y p e ,
a t each i n s u r e d i n s t i t u t i o n ) . I f t h e d e p o s i t guarantee i s n o t extended t o t h e
e x p l i c i t l y u n i n s u r e d d e p o s i t s , t h e s t a t u t o r y guarantee o f o n l y t h e f i r s t
$100,000 o f any d e p o s i t does n o t a f f e c t t h e v a l u a t i o n o f t h e p o r t i o n o f t h e
A proof o f t h i s i s available from the author.
d e p o s i t i n excess o f $100,000.

5. T h i s i s assumed f o r e x p o s i t i o n a l s i m p l i c i t y . The a n a l y s i s i s s t i l l v a l i d
i n cases where t h e purchase- and- assumption method i s used t o d i s p o s e o f t h e
bank (and any o t h e r t e c h n i q u e used t o h a n d l e a f a i 1i n g bank t h a t l e a v e s
u n i n s u r e d d e p o s i t o r s whole).
6. I t does n o t m a t t e r whether t h e FDIC buys o u t t h e u n i n s u r e d d e p o s i t o r s and
i s s u e s i n s u r e d d e p o s i t s t o r e p l a c e them, o r guarantees t h e market v a l u e o f t h e
uninsured deposits.

7. T h i s assumption seems t o h o l d i n p r a c t i c e . H i s t o r i c a l l y , t h e m a j o r i t y o f
f a i l e d banks have been disposed o f u s i n g t h e purchase- and- assumption t e c h n i q u e
(see B a r n e t t , H o r v i t z , and S i l v e r b e r g [19771>.
8. I f t h e bank i s n o t r e q u i r e d t o pay f o r t h e c o n d i t i o n a l guarantee on i t s
u n i n s u r e d d e p o s i t s , i t r e c e i v e s a subsidy from t h e FDIC o f q ( z ) ( B o - d o > on
each d o l l a r o f c o n d i t i o n a l l y u n i n s u r e d d e p o s i t s i t i s s u e s . C o m p e t i t i o n among
banks f o r c o n d i t i o n a l l y u n i n s u r e d d e p o s i t s m i g h t r e s u l t i n a f r a c t i o n , v,,
o f t h e subsidy b e i n g p a i d t o t h e c o n d i t i o n a l l y u n i n s u r e d d e p o s i t o r s .
The
observed r i s k premium on $1 o f c o n d i t i o n a l l y uninsured d e p o s i t s i s R, =
(l-q(z>(l-~~))(Bo-do>.
9.

For e x p o s i t i o n a l purposes, i t is,assumed t h a t x=O.

10. The spread between t h e T - b i l l r a t e and t h e CD and CP r a t e s i n c l u d e s a t a x
d i f f e r e n t i a l because T - b i l l s a r e n o t s u b j e c t t o s t a t e and l o c a l taxes, w h i l e
CDs and CP are.
This makes t h e spreads w i d e r than t h e t r u e r i s k - i n d u c e d
spread and biases t h e d e p o s i t guarantee e s t i m a t e s upward.

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11. The CDs are assumed t o be 10 percent insured because the c u r r e n t c e i 1 i n g
on insurance coverage i s $100,000, and the m a j o r i t y o f widely traded CDs are
o f a $1,000,000 denomination (see Stigum [19781).
12. This, o f course, assumes t h a t y(z)=O.

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