R. Alton Gilbert

R. NEon Gilbert is an assistant vice president at the FederalReserve Sank of St. Louis. David H. Kelly provided researchassistance.

Market Discipline of BankRisk: Theory and Evidence

ECAUSE of the many failures of banks andthrift institutions in recent years and the highcost of liquidating or reorganizing the bankruptsavings and loan associations, policymakers arenow considering major changes in the way theysupervise and regulate depository institutions inthe United States. The Financial Institutions Re-form, Recovery and Enforcement Act of 1989,which provides the funds for closing bankruptsavings and loan associations (S&.Ls), calls forseveral government agencies to study the issuesinvolved.1 The federal budget document for fis-cal 1991 discusses the basis for reform ofdeposit insurance and the advantages of variousreforms.2

To some extent, the unusually high failurerate of depository institutions (hereafter calledbanks) can be attributed to developments in theeconomy such as declines in the prices of oiland farmland in the early 1980s. Some studiesconclude that fraud and mismanagement ac-count for many of the bank failures.~The gen-eral consensus, however, is that deposit insur-ance creates an incentive for banks to assumehigher risk than they would without it. Suchrisk may be gauged in terms of the variance of

a bank’s return on assets as a percentage of itscapital. The logic that underlies this consensusis that without deposit insurance, banks thatchoose portfolios of assets with higher variancein their rates of return, or lower ratios of capi-tal to total assets, would have to pay higher in-terest rates on deposits. Deposit insuranceblunts this penalty. The relatively high failurerate and losses of the deposit insurance fundsreflect, to some extent, the banks’ response tothe incentives to assume risk created by depositinsurance. Thus, a major issue in the debatesover financial reform is the future role of de-posit insurance.

Some recent proposals to reform deposit in-surance are designed to increase the effective-ness of market forces in reducing the riskassumed by banks. Under these proposals, bankowners and creditors would be exposed tolarger losses if their banks fail. The theory isthat if bank owners and creditors have greaterexposure to losses, they will limit the risk as-sumed by their banks. In some proposals, thisinfluence would complement the efforts of banksupervisors. In others, market discipline wouldreplace government supervision.

‘Title X of the act directs the Secretary of the Treasury andthe Comptroller General, in consultation with variousfederal government agencies and individuals from theprivate sector, to prepare reports on issues related to thereform of deposit insurance, including the implications ofpolicies that would enhance the effectiveness of marketdiscipline.

2Budget (1990), pp. 246-53.3Graham and Homer (1988) and Office of the Comptrollerof the Currency (1988).

This paper describes some of these proposalsfor enhancing the effectiveness of market disci-pline and illustrates how they would affect thebanks incentive to assume risk. The paper alsoexamines the empirical evidence on the effective-ness of market discipline. Proposals for the re-form of deposit insurance that rely on marketdiscipline assume that market participants candifferentiate among banks on the basis of risk,and that market yields on bank debt reflect thatrisk. The paper lists the results of several em-pirical studies and draws conclusions about thepotential effectiveness of these proposals in re-forming deposit insurance.

Various approaches to enhancing the effec-tiveness of market discipline of bank risk arepresented in table 1. choosing one approachover another depends in part on which basicobjective of deposit insurance is considered tobe most important.

The following are the primary objectives ofdeposit insurance:1. To protect depositors with small accounts,2. To prevent widespread runs by depositors on

banks, and3. To protect the insurance fund from losses

that would bankrupt it.~

There are tradeoffs among these objectives.The policy that provides the greatest protectionagainst runs by depositors is complete coverageof all deposit accounts. That policy, however,eliminates any incentive for depositors to exerttheir discipline over the risk assumed by theirbanks, leading perhaps to an increase in the in-surance fund’s losses.

The dollar limit on the amount in each ac-count that is insured, currently $100,000,reflects an attempt to balance these objectives.Total coverage of accounts less than $100,000protects small depositors. The limit on the in-surance coverage per account is designed to in-duce the depositors with large accounts tomonitor their banks and require that riskierbanks pay higher interest rates on their de-posits. Those with relatively large accounts areassumed to be better able to impose such mar-ket discipline. The limit on insurance coverage

Table 1Proposals to Increase theEffectiveness of Market Disciplineof Bank Risk(1) Phase out federal deposit insurance to facilitate the

development and use of private deposit insurance.Short and O’Driscoll (1983). Ely(1985). England (1985~and Smith (1988).

(2) Lower the ceiling on federal ir1suran~ecoverage peraccount. Council of Economic Advisers (1989). pp.203-4

(3) Co-insurance, limit federal deposit insurance to somefraction of each account Boyd and Rolnick (1988)

(4) Place a ceiling on federal deposit insurance per in-dividual at all depository institutions. England (1988)

(5) All institutions must maintain subordinated debtliabilities that are some fraction of their total assets.Cooper and Fraser (1988). Keehn (1989) and Wall(1989).

(6) Early closure: close or reorganize depository institu-tions wnen iheir capital ratios, reflecting the marketvalue of assets and liabilities, are low but still positive.This proposal is designed to enhance the effeotivenossof market discipline by closing or reorganizing bankswhose shareholders have weak incentive to limit rrsks.Benston and Kaufman (1988).

per account, however, tends to undermine theobjective of preventing runs by depositors onthe banking system.

Of course, a run by depositors on an in-dividual bank does not create a serious problemfor the banking system, because these depositorssimply remove their cash from one bank anddeposit it in another in which they have moreconfidence. If the bank subject to the run can-not meet its depositors’ demand for currency, itwill have to close. Its depositors will be paid asthe assets of the failed bank are liquidated. Arun on a bank can serve a useful purpose—amechanism for closing a bank in which deposi-tors have lost confidence.

Runs become a problem for the bankingsystem, however, when depositors withdrawcurrency and, hence, reserves from banks as agroup. Banking history in the United States and

~FederalDeposit Insurance Corporation (1983), pp. viii-xiii.

the United Kingdom prior to their central banksacting as lenders of last resort indicates thatruns on banking systems have occurred, al-though they tended to be separated by manyyears.5

Some argue that deposit insurance is notnecessary to avoid the adverse social effects ofbanking system runs. They maintain that, as longas the central bank acts as an effective lenderof last resort, the liquidity it provides wouldlimit any damage that runs on individual bankscould do.°An alternative view emphasizes thedangers of relying on the central bank tooperate as the lender of last resort to a bankingsystem without deposit insurance. A centralbank might respond inappropriately in a finan-cial crisis, as the Federal Reserve did in the ear-ly 1930s, leading to rapid declines in the assetsof the banking system and widespread bankfailures. Deposit insurance reduces the role ofthe central bank in maintaining stability in theoperation of the banking system. Thus, thechoice among the potential reforms of depositinsurance rests on views about the vulnerabilityof the banking system to runs and the effec-tiveness of a lender of last resort in dealingwith runs.

If the primary objectives of deposit insuranceare to protect small depositors and to protectthe insurance funds from large losses, a logicalchange would be to reduce the insurance cover-age per account. This was proposed by the Pre-sident’s Council of Economic Advisers in 1989.Those who consider the possibility of bankingsystem runs a serious threat to the stability ofthe banking system would oppose a large reduc-tion in the insurance coverage on bank deposits.

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posj~i..,scpj~HAiN}C.IN(.~:.I.1.ISK

The reform proposals are designed to reducethe incentives for banks to assume risk. Inevaluating their effectiveness, it is useful to con-sider three indicators of the banking system’sperformance that reflect this risk: the expectedloss by depositors due to the bank failure, the

expected loss of the Federal Deposit InsuranceCorporation (FDIC), and the probability that abank will fail. The expected loss by depositorsand the FDIC are considered separately sinceproposals that reduce the FDIC’s expected losstend to increase the expected loss by depositors.Focusing on only one of these measures of per-formance misses some of the reform proposals’implications. The third measure, the probabilityof bank failures, is of interest because of evi-dence that bank failures have adverse effects oneconomic activity in addition to the wealthlosses by depositors and owners.7 The studiesthat find adverse effects of bank failures oneconomic activity attribute those effects to theconstraints on the availability of credit createdby bank failures.

The proposals’ implications for the effective-ness of market discipline can best be derived byusing a model of the behavior of banks andtheir creditors.~

The implications of the various reform pro-posals are derived by examining the effects ofproposed changes in deposit insurance on theoptimal choice of risk by a representative bank-er. Several assumptions are made to simplifythe model.

— The only ran-dom variable in the model is the rate of returnon assets of the representative bank, which hasthe same probability distribution under all as-sumptions about the nature of deposit in-surance. Bank regulators are assumed to deter-mine the probability distribution of the rate ofreturn by restricting the types of assets thebank may hold. The only choice for the repre-sentative banker in this model is the level of thebank’s total assets. The capital of the bank isheld constant at $100 in each case. With a givenlevel of capital and a given probability distribu-tion of the rate of return on assets, the proba-bility of failure (losses exceeding capital) is posi-tively related to the total assets of the bank.Management is assumed to choose the level of

5Gitbert and Wood (1986) and Dwyer and Gilbert (1989).6See Kaufman (1988) and Schwartz (1988).7See Bernanke (1983), Calomiris, Hubbard and Stock(1986), Grossman (1989), and Gilbert and Kochin (1989).

8To illustrate the need for such a model, consider a basicreform of eliminating deposit insurance. That changewould increase the interest expense of a bank with a given

portfolio of assets, thereby tending to increase its pro-bability of failure. The penalty of higher interest expenseimposed by depositors on those banks that assume morerisk would induce banks to assume tess risk in theirchoice of assets. The net effect of eliminating deposit in-surance on the probability of bank failure must be derivedfrom a theoretical model that specifies the risk preferencesof depositors and bank managers.

total assets that maximizes the expected profitsof the bank.

With a given level of bank capital, the condi-tions under which the bank fails can be derivedonly with a specific probability distribution ofreturn on assets. This paper uses the discreteprobability distribution presented in table 2.~For each of the seven possible outcomes, therate of return on assets is net of the operatingcost of servicing the assets.

‘rhe rate of return associated with each out-come is assumed to be inversely related to thesize of the bank’s total assets. One reason forthis assumption of an inverse relationship isthat, as the bank increases its total assets, itmust lend to borrowers beyond the local areain which it has some market power. Anotherreason is diseconomies of scale in the operatingcost of servicing assets. For each outcome witha positive return on assets, therefore, the rateof return falls as total assets increase. Thisfeature of the model yields a maximum ex-pected profit for the bank under each assump-tion about deposit insurance.10

— For a given level of totalassets, the bank’s cost depends on the insurancecoverage on its liabilities. This paper considersthe four cases described below. If, as in case A,all deposits are fully insured, the bank can at-tract an unlimited supply of deposits by payingthe risk-free rate of interest. Under each of the

four assumptions about deposit insurance, thecosts of servicing deposit accounts are offset byfees charged to depositors.

For a given level of total assets, the highestexpense occurs in case II, with no deposit in-surance. In this case, the interest rate that thebank must pay on deposits is positively relatedto its total assets. Depositors are assumed to herisk-neutral and to know the probability distri-bution of the bank’s return on assets. Hence,the bank must pay the rate to depositors thatmakes their expected return on deposits equalto the risk-free rate.”

The interest rate that the bank pays deposi-tors is above the risk-free rate if the bank failsin at least one of the seven possible outcomes.If it fails, the depositors receive the liquidationvalue of the bank’s assets. Liquidation value inthose outcomes reflects the probability distribu-tion of the bank’s return on assets. There is noadditional loss to depositors resulting from theelimination of the bank as a going concern.12

The equation for calculating the rate paid todepositors in case B is presented in table 2.

Cases C and D reflect two methods of enhanc-ing the effectiveness of market discipline ofbank risk, while retaining some form of depositinsurance. Co-insurance in case C limits depositinsurance coverage to 90 percent of each de-posit account.” In case D, deposits are fully in-sured, but each bank is required to keep its

9The use of a discrete probability distribution, with a limitednumber of outcomes, makes the presentation simpler thanif a continuous probability distribution was used. In using adiscrete probability distribution, there is a trade-off be-tween simplicity and continuity of the probability of failurewith respect to leverage. The smatter the number of possi-ble outcomes, the larger the jumps in the probability offailure at certain asset levels. Increasing the number ofpossible outcomes, however, increases the difficulty of il-lustrating the calculations. Thus, the probability distributionin table 2 is arbitrary.

‘°Themodel abstracts from possible tosses by our represen-tative bank on the deposits it holds at other banks. If areform proposal increases the probability of losses on in-terbank deposits, the effects of such reform proposals onthe probability of failure at our representative bank wouldbe understated.

This point about possible loss on interbank deposits ismost relevant in comparing the case with no deposit in-surance to the other cases examined below. The model inthis paper is not modified to reflect directly the effects ofpossible losses on interbank deposits.

This model also ignores losses from runs on the bankby its depositors in reaction to the failure of other banks. Ifdeposit insurance coverage is reduced or eliminated, the

failure of some banks may induce depositors to run onother banks to receive currency in exchange for theirdeposits. Several such episodes occurred in the UnitedStates prior to the establishment of deposit insurance inthe 1930s, See Dwyer and Gilbert (1989). To incorporatethe possible effects of runs, the probability distribution ofthe return on assets at the representative bank would haveto be specified as a function of the number of bankfailures.

“The general nature of the comparisons among the fourcases would not be changed if depositors were assumedto be risk averse,

‘2The assumption that a bank’s assets lose no value whenthey are liquidated results in an understatement of the ex-pected loss of depositors and bank creditors in the variouscases. A study by the Federal Deposit Insurance Corpora-tion, Bovenzi and Murton (1988), reports that when theFDIC liquidates the assets of failed banks, their liquidationvalue averages about 70 percent of the book value of theassets of failed banks.

“Boyd and Rolnick (1988) suggest 90 percent coverage ofdeposits in their proposal for a form of co-insurance indeposit insurance.

Table 2A Model of Bank ProfitsNET REVENUERevenue of the bank net of the operating cost of servicing assets, is a :andom var~abIew’th adiscrete probability distribuiron. Lei A be the assets of the bank Tne probability distr~but:onis asfollows

Qutcome Net

number revenue Probabilny

1 04(1 — Alt0.0D0~A 0012 03(1 — Al10.000IA 0 D43 02(1 — Ai10,000)A 0,104 01(1 — Al10.000)A 0705 00(1 Al10.000)A 0,106 —0 1(1 — A,’loOOO$ 0.047 02(1 — A/10.000)A 00)

COSTThe cost of the bank s not a ranoom variable It is the same in each of the seven outcomes Ex-pected orofits are calculateo br four cases, each involving a different assumption about the in-terest expense of the bank In those outcomes in which the bank has a loss, the maximum lossto the snareholders is therr investment of $~00.

Case A: All Liabilities Fully InsuredThe bank pays the risk-free rate of 8 pc-cent on deposits. whicn equal A -- $100

Case B: No Deposit InsuranceAt each level of toial assets of the bank. the interest rate on deposits is set at thelevel that makes the expected return to holders ot uninsur~de~sitsequal to tnerisk-free rate of 8 percent.

The ;nterest rate on deposits in case B. for a given level of assets. can be derived by solving thetollowing equation for R. the interest rate or, deposits To economize on notation., let

= ~1 — Al10.000~A.Then.

1 08(A 100) =

0.01(1 +R)(A-100). or

001(1 4A) it 0.4A — R~A-100)< —100

± 0.04(1 ,.R~(A—10o).or

004~13A’lif03A — R~A—100~< -100

+ 01(1 + R~A-.100). or

0.1(1 2A) ‘f 0,2A’ — R~A--100) c - 100

07(1 — RgA —1001. or

07(1 1A) itO 1A - RfA— 100) < —100

+ 0.1(1 + R)(A 100), or

01(A)1 —R(A—100) < —100

= 0.04(1 +R)(A --100). or

004(09A)if -alA’ — R(A..100) .c —100

~ 0.01(1 — Ri(A— 100), or

0.01(0 8A) if —0,2A R(A— 100) < —‘00

Table 2 continuedA Model of Bank Profits

Case C: ~o-uisuranceThe calculation of the stated interest rate on deposits as in case B is modified by settinq theminimum return to depositors in each outcome at 90 percent of their principal plus statedinterest.

The equation for the interest rate on deposits ‘s the same as that presented for case B exceptthat in each of the seven possible outcomes. the return to the depositors can be no less than09(1+R)tA — 100).

Case D: Subordinated Debt RequirementThe bank :s required to have liabilities that are uninsured and subordinated todeposits. equal to at least 10 percent of its total assets. Deposits are fully insuredThe interest rate on deposits is 8 percent. The ‘nterest rate on subordinated debt.for a given level of assets. can be derived by solving the foltowing equation for R

1.08(0.1)(A) =

0.01(1 +R)0.1A, or

if 0.4A’ - R(0.IA) — 0 08(0.9A— 100) .c —100.

0.01 (the greater of 1 4A — 1 08(0 9A— 100) or zero)

+ 004(1 ~- R)0,1A, or

if 0 3A’ R(0 IA) — 0 08(0,9A-- 100) .c —100,

004 (the greater of 1 3A .- 1 08f0.9A -100) or zero)

01(1 ~R)0 1A, or

if 0 2A — R(0 1A) — 0.08(0 9A— 100) ‘C ‘ 100.

o i (the greater of l,2A’ - 1 08(0.9A ‘100) or zero)

0.7(l--R~0.1A.or

if O,1A - R~0IA) -- 0 08(0.9A - 100) < —100,

07 (the greater ot I 1A — 1.08f0 9A —100) or zero,)

i-C 1fl-i-R)0.1A, or

if —RfO 1A) — 0.0B(0.9A 100) c -.100.

0 1 (the greater of A’ — 1 ,0B~0.9A — 1001 or zero)

+ 0 04(1 -i-R)o 1A or

if 0 1A — R(0.1A) — 008(0 9A —100) < 100,

0.04 (the greater of 0 9A — 1 08(0 9A — 100) or zero)

+ 001(1’-R)OlA or

if —0,2A . RfO 1A,) ‘ 0,08i0 9A --100) < —100

001 ~thcgreater of 0 8A’ — 1 08(0 9A— iorn o~zero)

subordinated debt liabilities equal to 10 percentor more of its total assets.14

In cases C and D, the interest rates on bankliabilities also are set at levels that make ex-pected returns to bank creditors equal to therisk-free rate. Equations for calculating the in-terest rates on bank liabilities are specified intable 2.

Other reform proposals are of interest but aremore difficult to incorporate into this simplemodel. For instance, more detail would be ne-cessary to model the effects of changing thedeposit insurance limit per account or limitingFDIC coverage for each depositor to a givenamount at all insured institutions.

Cáse./L: ~14I .K:.1E.a .~Kas~K,K:~. Ifl.,N:Ufle.:(

The bank maximizes expected profits in thiscase with total assets around $1800 (see figure1). At this level, the bank fails (losses exceed the$100 of capital) in outcomes 5, 6 and 7. ‘I’hus,the probability that the bank will fail is 15 per-cent, based on the probability distribution forthe return on assets in table 2. The FDIC’s ex-pected loss, $14.26, is about 0.84 percent of in-sured deposits. The expected loss of depositors,of course, is zero.

(j~u~:~ .[‘J~ifJ~:it .h1sn.r~.I~n,t

Several reform proposals call for phasing outdeposit insurance (see table 1). With no depositinsurance, depositors lose part of their principalplus interest if the bank fails (if losses exceedthe $100 of capital). The interest rate on de-posits charged by risk-neutral depositors ispositively related to the bank’s total assets (seefigure 2).

The bank maximizes its expected profits withtotal assets equal to $1,000. It fails only in out-comes B and 7. Thus, the probability that thebank will fail is only 5 percent, compared witha 15 percent probability of failure associatedwith maximum profits in case A. Case B illus-trates how a bank that maximizes expected pro-fits can be induced to limit its probability offailure through market discipline imposed by itscreditors.

The FDIC’s expected loss in this case is zero.The expected loss of depositors with total assetsequal to $1000 is $4.21, which is about one-halfof one percent of deposits.

Under the co-insurance option, federal depositinsurance coverage would be limited to a frac-tion of each deposit, with some low level ofeach account fully covered to protect small de-positors. Those who advocate co-insuranceargue that the depositors subject to fractionalcoverage at the margin would monitor the riskassumed by their banks and demand relativelyhigh interest rates on deposits at the banks thatassume relatively high risk.

To simplify the illustration, all deposit ac-counts are subject to the same percentage of in-surance coverage. In those outcomes in whichthe bank fails, payments to depositors under theco-insurance option would be the larger of:

(1) the liquidation value of the bank’s assets,or

(2) 90 percent of the principal plus interest ontheir deposits. The FDIC incurs a loss onlyif the bank fails and the liquidation valueof the bank is less than 90 percent of theprincipal plus interest on deposits.

As in case B, the market interest rate ondeposits is set at the level that makes the ex-pected return on deposits equal to 8 percent.The difference in this case is that depositorshave the option of receiving 90 percent of theirprincipal plus interest from the FDIC if theirbanks fail. Figure 2 indicates that for a givenlevel of total assets, the market interest rate ondeposits is lower in case C than in case B,because in case C the losses of depositors arelimited by deposit insurance.

Under the assumptions of case C, the bankmaximizes expected profits with total assets of$1100. The bank must pay 8.44 percent to at-tract the $1000 in deposits. With assets of$1100, the probability of the bank failing is 5percent. The FDIC’s expected loss is only 0.072percent of insured deposits, about 9 percent of

“Case D involves a higher percentage of subordinated debtto total assets than some of the proposals that call forsubordinated debt requirements. For instance, the recentproposal of the Federal Reserve Bank of Chicago recom-mends that banks be required to maintain a 4 percent

ratio of subordinated debt to total assets. See Keehn(1989). The 10 percent requirement in case D is chosen toindicate that the degree of market discipline that can beimposed through a co-insurance proposal can be matchedwith a subordinated debt proposal.

Figure 1Expected ProfitsDollars

40

30

20

10

0

—100

Figure 2Expected Loss to FDICDollars

40

30

20

10

0

0 500 1000 1500 2000

Dollars

40

30

20

10

0

.—10

2500500 1000 1500 2000Assets

Dollars

40

30

20

10

0

2500Assets

the loss rate for case A, with total assets at$1800. The expected loss to depositors is $5.09,which is about one-half of one percent of totaldeposits.

From the FDIC’s perspective, there are twoadvantages of co-insurance (case C) over fulldeposit insurance (case A). First, the bankchooses a level of assets associated with a lowerprobability of failure. Second, for a given levelof total assets of the bank, the FDIC’s expectedloss is lower under case C.’5

Some proposals for deposit insurance reformwould require banks to issue subordinated debtliabilities that are not federally insured. Theterm “subordinated” refers to the status ofcreditors of a firm in bankruptcy. If a failedbank is liquidated, those who hold subordinateddebt would receive payments only if all deposi-tors are paid in full.

In case D, all deposits are fully insured by theFDIC. The bank, however, must have uninsuredliabilities, which are subordinated to deposits,that equal at least 10 percent of its total assets.The bank would choose to keep subordinateddebt liabilities at the 10 percent minimum since,except at relatively low levels of total assets, theinterest rate on subordinated debt exceeds therisk-free rate paid on insured deposits.

As in cases B and C, those who invest insubordinated debt are assumed to be risk-neutral and know the probability distribution ofthe net return on assets. Figure 3 presents theinterest rate on subordinated debt as a functionof the total assets of the bank.” For most levels

of total assets, the interest rates on subor-dinated debt is higher than the rates ondeposits in the cases analyzed earlier becausethe expected loss is higher for those holdingsubordinated debt. If the bank’s losses exceedthe $100 investment of the shareholders,holders of the subordinated debt receive somepayment only if the liquidation value of thebank exceeds total deposits.

The bank maximizes expected profits withtotal assets equal to $1100. At that level, thebank must pay 12.12 percent on its subordi-nated debt liabilities. The FDIC incurs lossesonly if the loss of the bank exceeds the $100capital of the shareholders plus the subordi-nated debt. The bank has a 5 percent probabili-ty of failure, and the expected loss of the FDICwith total assets equal to $1100 is 0.06 percentof insured deposits. Depositor losses are zero.

/ .~,•.~.~ .~ 2~ ,/ . ., .,. ~. .t~

A comparison of risk in the operation of thebanking system under various assumptionsdepends on one’s assumption about the pro-bability of runs on the banking system. if thisprobability is assumed to be zero, the elimina-tion of deposit insurance (case B) induces banksto assume minimum risk. The FDIC’s expectedloss is zero in this case, and the bank is inducedby market forces to choose the lowest level oftotal assets. One advantage of the subordinateddebt requirement over the other options is that,while the bank is induced to choose a level oftotal assets below that in case A, the subor-dinated debt is not subject to runs. Thus, thecomparison of risk between cases A and D doesnot depend on assumptions about runs on thebanking system.

“Co-insurance, however, has one disadvantage. A changefrom full coverage of insured deposits to co-insurancecreates an incentive for depositors to run on banks inresponse to information (or rumors) about problems atbanks, Even with the FDIC insuring 90 percent of the prin-cipal and interest of deposit accounts, depositors have anincentive to avoid the 10 percent loss by withdrawing theirdeposits from a failing bank. Thus, in comparing cases Aand C, co-insurance reduces the significance of deposit in-surance in preventing runs on the banking system, placinggreater responsibility on the role of the Federal Reserve instabilizing the banking system in a financial crisis, as itfunctions as the lender of last resort. If there is somedoubt that the Federal Reserve will execute its role aslender of last resort, co-insurance may be less advan-tageous than full insurance of deposits.

“The humped pattern of the interest rate on subordinateddebt for case D in figure 3 reflects the particular discreteprobability distribution of returns on the assets used in this

paper. With a continuous probability distribution, or adiscrete distribution with more possible outcomes, the plotof the interest rate as a function of total assets would havea tess humped pattern.The fact that the interest rate on subordinated debt is

higher at higher levels of total assets of the bank might in-dicate a way in which the management of the bank couldtake advantage of those who invest in subordinated debt,The bank could issue some subordinated debt at a lowlevel of total assets, at a relatively low interest rate, andthen increase total assets and issue more subordinateddebt at a higher rate. Investors in subordinated debt canprotect themselves from such actions by insisting oncovenants in the subordinated debt agreements that limitadditional debt. If management of the bank violates such acovenant, the holders of the subordinated debt could go tocourt to make their debt instruments payable on demand.Restrictions on the issuance of additional debt are com-mon in bond covenants. See Smith and Warner (1979).

Figure 3Market Interest Rate on Bank Liabilities

The co-insurance option is not superior underany combination of assumptions. If the possibili-ty of runs on the banking system can be ruledout, there is a subordinated debt requirementthat induces the same degree of market disci-pline of banking risk as co-insurance.

Market forces will be effective in constrainingthe risk assumed by banks only if investors canassess the relative degrees of risk assumed byindividual banks, and then set differential priceson the stock and debt instruments issued by

banks that reflect their information about risk.The results of the studies described in table 3are relevant in evaluating the effectiveness ofmarket discipline. These studies estimate the in-fluence of measures of risk assumed by bankson the stock prices of banks and on the marketinterest rates on uninsured deposits and thesubordinated debt of banks.” These studies donot test the hypothesis that banks adjust theirrisk in response to signals from the markets forbank stocks and debt.”

All but one of these studies report evidencethat is consistent with the hypothesis that stockprices are inversely related to the risk assumed

“The studies described in this section include only thosebased on data for individual banking organizations. Somestudies cited in the literature estimate indices of returns onshare prices or interest rates on bank liabilities for groupsof banks as functions of aggregate data on banking risk,Such results are not relevant in determining whether par-ticipants in the equity and debt markets can distinguishamong the banking organizations, which would benecessary if market discipline of bank risk were to beeffective.

18Gendreau and Humphrey (1980) claim to have developeda model in which there is feedback from adverse signalsin the bank equity market to bank leverage. It is difficult tosee a feedback relationship between the stock price andleverage in this study, since the relationships among stockprices, leverage and other variables are estimated usingcontemporaneous observations. Estimating a feedbackrelationship from market signals to variables under thecontrol of bank management would require dynamicrelationships.

Rate

.20

.16

.12

.08

~042500

Assets

.040 500 1000 1500 2000

Table 3Implications of Empirical Studies for the Effectiveness of Market Disciplineof Bank Risk

Results consistentwith the

effectivenessof market

Authors Relationships estimated Results discipline -

MARKET FOR BANK EQUITY

Beighley. Boyd Share prices of bank stocks estimated Holding constant the influence 0t earn- Yesand Jacobs as a function of (1) capital ratios, ings banks with higher capital rat~osand(1975) (2) earnings and growth of earnings, lower loss rates tend to have higher

(3) asset size, and (4) toss rates, share prices

Pettway (1976) Betas for individual banks (a measure The coefficient on the capital ratio is Yesof risk derived from stock prices) esti- negative for one year but insignrf~cantformated as a function of the capital ratios other years. The negative coefficient onof individual banks. the capital ratio indicates that investors

consider banks with higher capital ratiosto be less risky.

Pettway (1980) For several large banks Ihat failed. On average, returns on the stocks of Yesreturns to shareholders are simulated banks that failed declined relative tofor several years prior to their failure. simulated returns two years beforeSimulations are based on returns from failure.holding stocks of large banks that didnot fail

Brewer and Lee Betas for individual banks are estimated Some of the measures chosen to reflect Yes(1986) as functions of ratios from balance risk have positive, significant regres-

sheets and income statements used sion coefficients.by bank supervisors to reflect risk,

Cornell and Returns to shareholders of 43 large The percentage that Latin American YesShapiro (1986) banks are estimated as functions loans was of total assets had a signi-

of the composition of their assets and ficant, negative impact on returns inliabilities in tne years 1982-83. 1982 Energy loans had a negative

impact in 19B2-83. Loans purchasedfrom Penn Square Bank had a negativeimpact on returns n the month inwhich that bank failed,

Shome, Smith Prices of bank stocks are estimated as a The coefficient on the capital ratio is Yesand Heggestad function of its earnings and capital positive and significant for some years.(1986) ratios, insignificant for other years.

Smirlock and Changes in stock prces of large Coefficient on the ratio of Mexican YesKaufold (1987j banks at the ttme of the announce- debt to equity capital is negative and sig-

ment by Mexico in 1982 of its mora- nificant, Banks were not required totoriurn on debt payments as a function disclose their Mexican debt at the timeof the ‘atro of Mexican debt to equity of the 1982 moratoriumcapital at indivioual banks,

Table 3 continuedImplications of Empirical Studies for the Effectiveness of Market Disciplineof Bank Risk

Results consistentwith the

effectivenessof market

Authors Relationships estimated Results discipline

MARKET FOR BANK EQUITY continued

James (1989) Returns on holding the stock of BHCs The change in the market value of Yesand Cargill estimated as a function of the change loans to less-developed countries has a(1989) in the market value of the BH~s’loans positive, significant coefficient which is

to less-developed countrres and dum- nor significantly different from unity.my variables for individual banks andindividual time penods.

Randall (1989) Tnis is a case study of 40 BHC5 that Stocks prices ot the BHCs that re- Noreported relatively large losses in the ported relatively large losses declined1980s For each BH~.a time period relative to market average stock pricesis destgnated when it began assuming only after the problems became publicrelatively high risk and a time period knowledqe, not during the periodswhen problems became public know- which the banks began assumingledge Stock prices are compared to relatively high rrsk,market averages before and after theproblems oecame puolic knowledge

MARKET FOR UNINSURED DEPOSITSThe interest rale on large denomination certificates of deposit is the dependent

variable in each study

Crane (1976) Identifies the determinants of the CD rhe factor that reflects profit rates and Nora’e us;nq factor analysis. capital ratios is not a significant vari-

able in explaining the CD rate.

Herzig~Marxand Estimates CD rates as a function ot Of bank risk variables, only the liquidi- NoWeaver (1979) variables used by bank supervisors to ty measure has a significant coefficient.

reflect risk, Capital and loss ratios have insignifi-cant coefficients

Baer and Brewer CD rate estimated as a function of ~oofficrentson risk measures used by No(19861 variables used by bank supervisors to bank supervisors are not significant

reflect risk, and separately. as ~unc- Measures of the level and variability oftions of level and variability of the stock prices help explain CD rates.prices of bank stocks

James f1987i The average .nterest ‘ates paid by 58 Each of tnese measures of risk have Yeslarge banks on their iaroe denomina- postive. significant coeffcientstion deposits are estimated as func-eons of leverage, loan loss provisiondivided oy total loans and tne varianceof stock returns

Hannan and CD rate is estimateO as a function of (1) These three va’iahles have significant YesHanweck t1988 the varability of the ratio of ‘ncorne to coeff’cients CD rates tend to be hiqher

assets. (2) the capitai ratio and ~3)bank at banks with more variable income andassets lowe’ capital ratios, holding constant

the influence of total assets

Table 3 continuedImplications of Empirical Studies for the Effectiveness of Market Disciplineof Bank Risk

Results consistentwith the

effectivenessof market

Authors Relationships estimated Results iscipline

MARKET FOR UNINSURED DEPOSITS continued

James (1969) Interest cost on large CDs estimated Interest cost positively related to the Yesas a function of risk measures. domestic ratio of domestic loans to capital andloans/capital, foreign loans/capital and the lean loss provision. The negativethe loan toss provision/total loans, relation between interest cost and the

ratio of foreign loans to capital is inter-preted as evidence of an implicitgovernment guarantee of foreign loans.

MARKET FOR SUBORDINATED DEBT:

In each study the measure of the interest rate on the subordinated debt of banks isthe rate on the subordinated debt minus the rate on long-term U.S. Treasurysecurities, called the rate premium,

Pettway (1976) The rate premium is estimated as a The coefficient on the capital ratio is Nofunction of the capital ratio of banks not significant.and other independent variables,

Beighley (1977) The rate premium is estimated as a The coefficients on the loss and lever- Yesfunction of several measures of risk, age ratios are positive and significantincluding a less ratio and a leverageratio.

Fraser and The rate premium is estimated as a Neither independent variable has a NoMcCormack function of the capital ratio and the significant coefficient(1978) variability of profits divided by total

assets,

Herzig-Marx The rate premium is estimated as a None of the risk measures have signi- No(1979) function of several measures of risk ficant coefficients,

assumed by banks.

Avery. Belton The rate premium is estimated as a Coefficients on the risk measures do- Noand Goldberg function of risk measures derived from rived from balance sheets and income(1988) balance sheets and income statements statements are not significant.

and of the asset size of banks,

Gorton and Use data in Avery, Belton and Goldberq Some of the risk measures derived YesSantemero (1988) to derive a measure of the van- from the balance sheets and income(1988) ance of assets of banks implied by a statements have significant coefficients,

contingent claims valuation model. Themeasure of the variance of assets isestimated as a function of the riskmeasures derived from balance sheetsand income statements,

by banks, holding constant other determinantsof stock prices. The one study that concludesthat stock prices do not reflect the risk assumedby banks, by Randall (1989), examines move-ments in the stock prices of bank holding com-panies that reported relatively large losses inthe 1980s. Randall concludes that these stockprices fell relative to the stock prices at otherbanks after their problems became commonknowledge; however, they did not decline dur-ing the periods when the banks were assumingthe relatively high risk that led to losses. Ran-dall concludes that the stock market does notdiscipline the risk assumed by banks, since therelative declines in bank stock prices did notprecede public information on the consequencesof risk assumed by these banks.

Randall’s study, however, has several weak-nesses. It is a case study, not a statistical studyof the determinants of stock prices. The datingof points at which problems became commonknowledge is arbitrary; the choice of suchdates, however, determines the results. Abouthalf of the cases involve banks in the SouthwestWe would not expect relative declines in thestock prices of these banks before the largedecline in oil prices. We cannot expect the par-ticipants in the market for bank stocks to havegreater foresight in predicting the decline in theprice of oil than the participants in the marketfor oil.

Two studies are particularly interesting interms of investors’ ability to differentiate amongbanks on the basis of risk. Pettway (1980) com-pares stock prices of large banks that failedwith simulated stock prices that were based ondata from banks of comparable size that did notfail. Returns to stockholders of the failed banksdeclined relative to their simulated returnsabout two years before the banks failed. Rela-tive returns of the failed banks also declinedbefore the bank supervisors put them on theproblem bank list. Smirlock and Kaufold (1987)find that, when Mexico announced the morato-rium on its debt payments in 1982, the declinesin the stock prices were proportional to theMexican debt held by banks relative to the book

value of their equity capital. At the time of themoratorium, banks were not required to dis-close their loans to other nations. Nevertheless,investors appeared to have sufficient informa-tion, without such requirements, to make theappropriate adjustments to the prices of bankstocks.

The findings about the relationship betweenrisk and interest rates on uninsured depositsand on subordinated debt are more mixed.‘I’hree of the six studies of bank CD rates reportno evidence that higher CD rates are paid bybanks that assume more risk. Four of the sixstudies of the determinants of rates on the sub-ordinated debt of banks find no significant ef-fects of risk measures on interest rates.

• for the .tt~f(ètth....~tr~.Jtterk.et 1.0 srmffnt.t

In evaluating these results, it is important tonote that, under the procedures followed byfederal bank regulators in recent years, risk hasa more certain implication for bank profits thanfor the returns to the holders of uninsured de-posits or subordinated debt. Losses on bankassets reduce profits, and if losses force a bankto fail, the bank shareholders are likely toreceive nothing after the liquidation or sale ofthe bank,

Uninsured depositors and holders of subor-dinated debt, in contrast, receive less than theprincipal plus contracted interest only if a bankfails. In most cases, the failed bank is mergedwith another bank, and the surviving banksassume all liabilities of the failed banks, in-cluding those in the form of uninsured depositsand subordinated debt, Most of the cases inwhich uninsured depositors and holders ofsubordinated debt absorb some losses involvebanks smaller than those included in the studiesdescribed in this paper)9 These observationsare consistent with the conclusion that interestrates on hank liabilities would be more sensitive

‘~Thiscontrast can be illustrated using some recent studiesand bank failure cases. Avery, Belton and Goldberg (1988)use observations for the 100 largest SHCs, which had totalassets above $3 bUtion in 1985 and 1986. The total assetsof the banks in the sample used by Hannan and Hanweck(1988) average $4 billion. In 1985 and 1986, 69 failedbanks did not have their liabilities assumed by surviving

banks, Of these 69 failed banks. 66 had total assets tessthan $100 million, while the remaining three had totalassets less than $200 million, The failure of some largebanking organizations in the Southwest, in which theBHC’s bondholders absorbed losses, occurred after theperiods covered by these studies.

to the risk assumed by banks if bank creditorslost at least part of their principal plus interestin each bank failure.

The empirical results cannot be used to indicatethe degree of risk that banks would assume ifbank supervisors eliminated various forms ofsupervision and regulation, relying instead onmarket forces to limit bank risk. To illustratesuch a change in policies, suppose bank super-visors eliminate capital requirements and restric-lions on the types of assets that banks may ac-quire, substituting a requirement that banks issuesubordinated debt. The empirical results do nottell us whether the probabifity of bank failureswould increase or decrease under such a changein policies. The only useful information from theempirical studies is that investors in bank stocks,who have the strongest incentives to be sensitiveto the risk assumed by banks, are able to dif-ferentiate among banks on the basis of risk.

This theoretical exercise illustrates howmarket forces could limit the incentives forbanks to assume risk. The incentives for banksto assume relatively high risk are reduced if theinsurance coverage of bank creditors dropsfrom full to partial coverage. One of the impor-tant differences among the various approachesto promoting market discipline of banking riskinvolves the vulnerability of banks to runs.Banks are more vulnerable to runs if depositorsare at risk than if the risks are borne by thoseholding long-term bank debt that is subor-dinated to deposits.

Empirical studies of the effectiveness ofmarket discipline report mixed results. Themost consistent result is that the stock prices ofindividual banks reflect the risk assumed bybanks. Market discipline of such risk wouldtend to be more effective if bank creditors wereforced to absorb losses in a more consistentfashion in hank failure cases.

The empirical studies do not indicate thedegree of r-isk that banks would assume ifdeposit insurance were reformed to enhancethe effectiveness of market discipline. Thus, theempirical studies do not permit us to determinewhether the probability of bank failures wouldrise or fall if the current forms of bank regula-tion were eliminated in favor of market disci-pline by bank shareholders and creditors.

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