Modeling the Banking Firm: A Survey
Author(s): Anthony M. Santomero
Source: Journal of Money, Credit and Banking, Vol. 16, No. 4, Part 2: Bank Market Studies
(Nov., 1984), pp. 576-602
Published by: Ohio State University Press
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ANTHONY
M. SANTOMERO
Modelingthe BankingFirm
A Survey
THISPAPER
REPORTS
on the status of the literatureon micro
bank modeling and assesses our understandingof the banking firm's optimal
behavior. This is no mean task, for much has been written on banking, broadly
defined, over the past couple of decades.
The review is developed in pieces. Each major subproblemis outlined and the
analysisused to deal with the issue explicated. This is not the best way to summarize
the developmentof a field, it should be immediatelyrecognized. One would prefer
to have a smooth continuum of development, moving the frontier of knowledge
evenly throughtime and across subareas.Yet, this is rarelythe way a field develops.
More likely, individualquestions attractattentionand are the subjectsof a substantial numberof contributions.After a time, the field moves on to the new area of
interest. The banking field is no exception.
Before embarkingupon the review, however, a couple of lines shouldbe devoted
to previousattempts.There have been essentially three. First, Pyle (1972) analyzes
the uncertaintyportfolio models at a time when little existed in the literature,and
hence one finds the review a bit vague and sketchy. Baltensperger'scontributions
(1978, 1980) are the next serious and ratherextensive reviews. The qualityof these
This paperwas preparedfor the Eighth Annual Economic Policy Conferenceof the FederalReserve
Bank of St. Louis, held on November 4-5, 1983. The authorwould like to thank Mark J. Flannery,
Stephen M. Goldfeld, Michael L. Smirlock, and Richard Startz for their insights and discussions of
earlierdrafts.
ANTHONY
M. SANTOMERO
is professorof finance, the WhartonSchool, Universityof
Pennsylvania.
Journalof Money,Credit,andBanking,Vol. 16, No. 4 (November 1984, Part 2)
Copyright(C)1984 by the Ohio State University Press
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ANTHONYM. SANTOMERO: 577
comes through after reading the literatureitself. This review, in fact, owes much
to them.
1. WHYDO BANKSEXIST?
Before entering the analysis of the banking firm, it is, perhaps, relevant to ask
why the institutionalbankingstructureexists at all. This questionhas two functions.
First, it allows us to discuss some of the more fundamentalwork in the bankingarea
that centers upon the natureof the financial marketstructurethat is being exploited
by the bankingfirm. Second, it focuses our subsequentdiscussion of the behavioral
models by specifying the natureof the role played by these institutions.
There are basically three approachesto the question of why internal financial
institutionsexist in the financial market. Each approachcenters upon a specific
portionof the bank's activity. The first relatesto the role played by these institutions
as asset transformers.Here, interestcenters upon diversificationpotentialand asset
evaluationas a reason for these financial firms. The second refers to the natureof
the liabilities issued and their centralfunction in a monetaryeconomy. Indeed, the
existence of a mediumof exchange creates an opportunityfor its issuer to gain some
form of seigniorage. Finally, some have emphasizedthe two-sided natureof these
financial firms as critical in any explanationof their behavior. Although each of
these explanations can find its roots in the seminal literatureof financial intermediation, such as Goldsmith (1969) or Gurley and Shaw (1960), all have been
specified more formally in the papers cited here.
A. Asset TransformationFunction
Within this set of explanationsfor financial intermediationthere are two distinct
views, namely, asset diversificationand asset evaluation functions of the financial
firm. The first reason given is presentedin the work of Klein (1973), Benston and
Smith(1976), andKane and Buser (1979). The authorsarguethata fundamentalrole
of intermediationis transformationof large-denominationfinancial assets into
smaller units. Klein (1973) emphasizes the ability of the firm to exploit the suboptimalportfoliochoice of the depositorfaced with unit constraints.The firm offers
a risk-returncombination in its financial assets that dominates the households'
constrainedset, even though economic profit is being earnedby the bank providing
such divisibility services. Benston and Smith (1976) make a similar argument
concerning transactioncost minimization. Kane and Buser (1979) argue, at least
implicitly, that these divisibility problems favor the use of a financial institutionto
diversify for both its depositors and equity holders. The latter authors also offer
evidence to suggest that such diversificationis supportedby the portfolios held by
the banking sector.
The second explanationon the asset side is currentlyreceiving much attention.It
arguesthat the bank is fundamentallyan evaluatorof credit risk for the uninitiated
depositor.These banks function as a filter to evaluate signals in a financialenviron-
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578 : MONEY,CREDIT,AND BANKING
ment with limited information.Financial agents are either pathologicallyhonest or
dishonest, but due to imperfectinformation,participantsfind it difficult to evaluate
the quality of signals or the honesty of agents. This gives rise to financial intermediaries whose primaryrole is the evaluation and purchase of financial assets.
Leland and Pyle (1977) were the first to propose this view of financial intermediation. Much of the recent literaturesprings from their contribution.Starting
with a firm's debt-equity decision, these authors argue that because of imperfect
informationconcerningthe value of the underlyingprojectinvestorscan glean some
informationabout its quality by observing the willingness of the insider to invest
equity capital in the endeavor. Accordingly, the financial structureof the firm adds
informationto the market.Leland and Pyle (1977) extend this approachto financial
intermediation,arguing that this signaling problem could explain financial intermediation. The lack of adequate information on the quality of financial assets
requires a set of firms whose primaryoutput is signal evaluation. However, the
outputfrom such firms is quite fragile. Once resourcesareinvestedin obtainingsuch
information,it becomes available to the marketas a public good. The firm, therefore, has difficulty obtainingthe returnassociatedwith its value. So, it is arguedthat
capturing a return to information can be overcome if the firm that gathers the
informationbecomes an intermediary,holding assets that are found to be of sufficient value.
Campbelland Kracaw(1980), however, counterthatthis solution to the information problemis conditionalupon the assumptionsmade aboutthe natureof information and its lack of general availability. First, they argue that portfolio choice by
knowledgeable firms will be monitored and known in the market, so that honest
intermediariescannot hide portfolio choices. Second, they point out that, in the
absence of prohibition, firms with low quality assets would find it in their best
interestto produce false information. In this case, even honest firms would have
informationcredibilityproblems.Therefore,given the uncertaintyof the value of the
intermediaries'information,the mere observationof the portfolio is not sufficient
to resolve the signaling issue. Campbell and Kracaw's solution to the problem is
similar in tone to the Leland and Pyle (1977) answer to the nonfinancial firm
signaling problem. By dedicating wealth to the firm, the owner-managersof financialintermediariesdemonstratetheir commitmentto the portfolio and signal the
value of the underlyingassets. They also argue that such firms can emerge which
produce information and additional products, such as divisibility or liquidity as
notedabove. Diamond( 1982) subsequentlyexpandson this notion anddemonstrates
that diversification is an importantcharacteristicin the information uncertainty
equilibrium.His results, however, are dependentupon the assumedinformationand
evaluationcost structure.Boyd andPrescott(1983), using a similarframework,note
that financial institutions result in optimal consumption decisions with pathologically honest agents. They also argue that the dishonesty issue, which plays a
relatively importantpart in the solutions of these information models, is overemphasized. Criminal charges make the cost of such dishonesty too high, they
contend.
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ANTHONYM. SANTOMERO: 579
This informationliteratureis still in its formative stages, at least as it relates to
financialintermediation.Yet, it offers some interestinginsights into the existence of
the depository firm. The flow of information is obviously a key element in the
market for financial assets, but, until now, the reasons for intermediationnever
clearly defined a role for it in the financial structure.Many questions remainto be
answered, however. For instance, how importantis honesty in firm information?
Why is it so difficult for investors adequatelyto evaluatethe project'sspecific risk?
Are side paymentsto generate false informationa realistic concern, particularlyin
a multiperiodsetting?
B. TheRoleof theBanksLlabllltles
,
.
...
.
The second reasongiven to explain the existence of the bankingfirm is the central
role played by its demanddeposit liability as the medium of exchange. It has been
many years since Clower's (1967) contributionpointedout the unique functionof a
monetaryunit. The subsequentwork of Niehans (1969, 1971, 1978) formalizedthe
choice of monetaryunit, and exchange patterns.Throughout,the centralfeatureof
a monetaryunit is its ability to minimize the cost of transactionsthatconvertincome
into the optimal consumptionbundle. In fact, Barro and Santomero(1976), in their
model of a monetary exchange economy, derive an effective price level for consumption goods as a direct result of the costs incurredin converting income into
utility-yieldingconsumptiongoods.
Brunnerand Meltzer (1971) take a different approachto the role of money, but
one thatis increasinglyrelevantin light of the recentliteratureon imperfectinformation rational macro models. To these authors, money holdings are part of the
household'sattemptto maximize a utility function in the first and second moments
of consumption.Money allows the economic agent to searchacross the distribution
of prices. As Starr(1972) points out, money balances are acceptedeven if the trade
is not excess demand diminishing.
For whatever reason, money is held by the private sector. These balances, althoughsubjectto standardcost-minimizationanalytics, generateprofitpotentialfor
the issuing institutions. The extent of these gains is dependentupon the characteristics of the money-type liability issued and the explicit pricing structureof the
financial institution. The demand for money literatureis replete with models that
generatepositive money balances. The obvious referenceshere are Baumol (1952),
Tobin(1956), Barroand Santomero(1972), Feige andParkin(1971), Miller and Orr
(1966), and Santomero(1974). Interestedreadersshould refer to Laidler(1977) and
Feige and Pearce (1977) for a thoroughreview.
The common feature of this literatureis the determinationof positive money
holdings that are a function of transactioncosts, uncertainty,and relative rates of
return. The monetary mechanism, along with bank pricing decisions, offers the
financial firm the opportunityto attractdeposits, which may be reinvested at a
positive spread.The extent of this profitwill dependuponthe natureof competition,
as Black (1975) and Fama (1980b) point out, and the nature of the transactions
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580 : MONEY,CREDIT,AND BANKING
network itself. Specific to the latter, the ease of transferbetween accounts, the
developmentof cash dispensingoptions nationwide,andthe adventof home banking
are all centralto the evolution of the banking system's monopoly position.
C. The Two-SidedNature of the Financial Firm
The last line of argumentexplainingthe existence of a bankingfirm centersupon
the conditionsnecessaryfor banksto exist as internalfinancialfirms. Here, the most
quotedreferenceis Pyle (1971), which develops a model of the maximizingfirm in
a financial market with uncertainrates of return. Pyle concludes that covariance
between the returnon loans and deposits fosters intermediationby encouragingthe
risk-aversemaximizerto transformdeposits into loans. Sealey (1980) recently has
extendedthis argumentto considerthe case where rates are set by the intermediary,
ratherthan given by the open market. Here, a correlationbetween profits and the
level of rates is shown to be equally importantas an explanation for financial
intermediation.In both cases, the covariance reduces the uncertaintyaround expectedprofits and, due to concavity, encouragesintermediationactivity. Therefore,
intermediationbecomes possible because the firm can engage in risky arbitrage
acrossmarketsthathave different, thoughuncertain,interestrates. The firm's value
is achieved by the expectationof a positive expected spreadacross markets, and a
sufficiently small variance aroundthis value.
An importantquestionthat is not asked in the Pyle (1971) frameworkis why such
expected spreads exist in the financial markets. Presumably,it is because of the
nature of its asset or liability services, but this is not modeled explicitly. The
literaturecovered in the earliertwo sections, however, offers severalviable explanations for the existence of this positive spreadfor financial intermediaries.In each
case, the reason involves some form of deviation from perfect marketassumptions.
Eitherthereexists nontrivialtransactioncosts, or there are informationproblems,or
bankliabilities have inherentmonopoly potential. In the following sections we deal
with optimal bank behavior to exploit such imperfections.
2. THEOVERALLVIEWOF A BANKINGFIRM'SPROBLEMS
A financial institution is viewed in the literatureas a microeconomic firm that
attemptsto maximize an objective function in terminal wealth. It uses quantity
and/orprice variables, such as asset quantitiesor prices, as control variables. The
extent of such choice is model specific and dependentupon the assumed environment and the degree of regulation. Indeed, regulatoryconstraintsmay constrainthe
opportunityset of assets or liabilities, restrictthe domain of the solution for one or
moreof the endogenousvariables,or increasethe monopolypositionof the industry.
In all of these cases the banking firm is viewed as seeking a mutatis mutandis
solution to its optimization problem. The general form of the problem can be
specified as
max E [V (W[+T)]
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(1)
ANTHONY M. SANTOMERO : 581
subjectto
Wt+T
Wt
( 1
+
Ht+
1)
( 1
ut+2)
+
Ht+T)
***(1 +
(2)
Ei rA,AZ-Ej rD,Dj-C (A', Di)
.
_
Wt+k-
. t+k -
I
o
Wt+k- l
J
where
S 0
> 0 and d2V/dW2+T
V(l) -the objectivefunction,wheredV/8Wt+T
(Wt+T)-thevalueof terminalwealthat the horizontime T
-the stochasticprofitperunitof capitalduringperiodt + k, where
ut+k
O<k
> T
rAa -the stochasticreturnfromasseti
--the assetcategoryi, where1 S i S n
Ai
rD, -the stochasticcost for depositj
-the depositcategoryj, where1 S j S m
DJ
C(@) --the operationscost function,wheredC/dAI ¢ O Vi and
dC/dDy
B O
Vj.
Equation(1) is thegeneralformof theobjectivefunctionto be maximizedby the
bankandas suchallowsfortwo distincttypesof behavior.Fromthefirstderivative,
moreterminalwealthis preferredto less. However,the degreeof marginalutility
dependscruciallyuponthe secondderivative.Thefirmmaybe an expectedvaluemaximizeror a risk-averseinvestor.Bothchoiceshavebeenmadein the literature,
dependinguponthe author'sgoals. Specifically,as will be outlinedbelow, if the
efficientportfolio,as in Parkin(1970),
bankis viewedas selectinga mean-variance
(1980),someformof
Pyle(1971),HartandJaffee(1974),or KoehnandSantomero
efficiencyis not
wealthconcavityis assumed.Onthe otherhand,if mean-variance
betweenrisk
a criterion,or, moregenerally,whenthe marginalrateof substitution
is assumed.
andreturnis not the focus of attention,expectedprofitmaximization
This,of course,is consistentwitha linearobjectivefunctionin terminalwealth,that
= °. Modelsby Klein (1971), Porter(1961), andOrrandMellon
is, 82V/dWt2+T
(1961)aretypicalof this approach.
of the motivationof the firm.
Thechoiceis not irrelevantto ourunderstanding
Somewouldcontendthatit is at the heartof how one views the behaviorof the
financialinstitution.Specifically,when modelingthe optimizationproblem,one
forcebehindbankdecisionsby specifyingtheagent
implicitlydefinesthemotivating
namely,equity
andhis objectivesfor the firm.Two choicesseemreadilyapparent,
Forthe former,a cogentargumentcanbe offered
investors,or bankmanagement.
truein a perfectcapital
in favorof a linearobjectivefunction.This is particularly
neednotexist andthe investor'sopportunity
marketwherefinancialintermediaries
set spansthe institution'schoice. Accordingly,anyefficientbankportfoliocanbe
perfectlyduplicatedor hedgedby the investor.
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582 : MONEY,CREDIT,AND BANKING
In fact, if one views the investor'sobjective function as the relevantone for bank
choice, a more appropriateapproachwould be one in which the bank's portfolio
decisions are determinedby global utility maximizationof the owners. In this case,
equation(1) would be replacedby the risk-averseutility functionof the equity holder
who views the bank's portfolio selection as a subset of his or her overall decisions.
If the investor'sopportunityset completely spannedthat of the bank, nothingwould
be gained by the artificial separationof the portfolio choice problem. On the other
hand, if any of the argumentsof section 1 are correct, the bank's choice set differs
from that of the investor due to its ability to exploit financial marketopportunities
that are not available to the nondepository institution. Yet, even in this case, a
relevant factor in the choice of a bank portfolio is the covariance of the returns
betweenthe bank'sequity with the othercomponentsof the investor'sportfolio. This
idea, however, has never been incorporatedinto bank modeling. Rather,the bank
is viewed as determininga submaximizationconditionalupon an assumptionabout
otherpersonalwealth allocationsbeing fixed. Consistentwith this view, therefore,
it is arguedthat a risk-neutralobjective function should be selected for the banking
firm to assure its investors efficient allocation, without regardto the risk level that
may be hedged elsewhere in the investor's portfolio.
Yet, credible argumentshave been offered in favor of the assumptionof utility
function concavity. The traditionalcorporate finance explanation rests upon the
assumptionthat managementis responsible for decision making and its inabilityto
diversify its humancapital. Fama (1980a) has developed this line of reasoningmost
completely. A similar argumenthas been made concerning the insufficient owner
diversificationby O'Hara (1981). In an industryin which only about 1 percent of
the institutionshave widely tradedequity, the latter appearsat least partiallyvalid.
The agency problemsreportedby Ross (1973) have also been used to motivate the
concavityby Santomero(1983b). Accordingto this view, investorswith linearutility
functionsestablishrewardschedules for managementthatlead to risk-aversebehavior. DraperandHoag (1978) use a similarapproachto intermediationbased uponthe
informationargumentsabove andRoss (1977). Recently, the presenceof bankruptcy
costs, firstmodeled rigorouslyby Stiglitz ( 1972), has addedyet anotherexplanation.
Using this approach, the expected value maximizer behaves as if variance had
negative value due to the probabilityof firm default with its attendantbankruptcy
cost. Whetherany or all of these reasons are sufficient to motivate the assumption
of risk aversion is still open to question. Yet, most of the literatureseems to have
embracedthis approachto the banking problem, at least when necessary.
Acceptingconcavity does not end the problemfor the model builder,as the exact
form of the objective or utility function must be specified. The common approach
here is to rely upon the quadraticor the exponentialforms. Alternatively,a simple
two-termTaylor expansion is taken as indicative of the objective function, with
appropriatecaveats from Pratt(1964).
In equation(2), the general specification above is defined as a multiperiodvaluationproblem.Frequently,independencebetween periods is assumedso as to make
the maximization a single-period analysis. This is clearly the case for portfolio
models, which, to this author'sknowledge, have never been cast in a multiperiod
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ANTHONYM. SANTOMERO: 583
frameworkfor the banking firm. On the other hand, importantcontributionshave
developed from a multiperiodview of the customer, loan, or deposit relationships.
Goldfeldand Jaffee(1970), Flannery (1982), and Blackwell and Santomero(1982)
are symptomatic of intertemporalapproachesthat show that balance sheet constraintsmake single-period problems dependent upon multiperioddecisions. This
will be true, in general, even though those decisions are state variablesat the time
of quantity or pricing decision making. To motivate such models, some intertemporal stickiness must be asserted which is often difficult to model carefully.
Accordingly,these intertemporalmodels frequentlylook like ad hoc specifications
of reasonablea priori intuition.
Equation(3) defines profit per unit of capital invested by the owners of the firm
or their managementrepresentatives.In the second specification, one sees that the
optimizationprocedureinvolves the dual choice of leverage and portfolio components. Each has its own developed literature.The first involves the models to derive
the optimalcapitalstructureof a bankingfirm, for example, TaggartandGreenbaum
(1978) and more recently Orglerand Taggart(1983). The second representsa large
arrayof models of profit maximization,conditionalupon leverage. In fact, most of
the present review will devote itself to profit maximizationor objective function
maximization without reference to capitalization issues. Implicitly, the latter is
assumedto be solved via a submaximizationconditionalupon the given portfolioor
exogenously determinedby regulatorystandards.
Only recently have these two issues been broughttogether. Solving (1), (2), and
(3) results in a joint decision of portfolio structureand leverage, along the lines of
Pringle(1974), Kahane(1977), and Koehn and Santomero(1980). However, this is
accomplishedby using only the most generalasset choice specificationand ignoring
operatingcost considerationstotally.
The issues surroundingoperatingor real resource costs have attractedincreased
attentionlately as the industry itself views these operationalissues of paramount
importance.In fact, it plays a fairly central role in Baltensperger's(1978) review.
This is because there is a large literatureon the trade-offbetween rate spreadsand
productioncost using, traditionally,a single-periodprofit-maximizationframework.
For example, the issue of reserve management,broughtto our attentionby Orrand
Mellon (1961), involves such considerations.Sealey and Lindley (1977) and Towey
(1974), have developed these models to considerappropriateproductmix and scale.
Mitchell(1979), Startz(1983), andothershave recentlybeen analyzingthe interplay
between explicit versus implicit charges for operatingcosts.
Finally, the pricing and quantitydecisions in both the loan and deposit markets
depend crucially upon the nature of market structureassumed, even in a singleperiod case. On the deposit side, there is a long literatureon deposit rate setting
based upon various assumed deposit market structures,for example, competitive,
monopolistic, sticky, and tied-productrelationships.Models by Goldfeld and Jaffee
(1970), Klein (1972), Stigum (1976), Sealey (1980), and Flannery(1982) are representativeof this genre. Likewise, but somewhatbelatedly, the loan marketdecision
has been analyzed. As above, we consider competitive, monopolistic, sticky, and
tied-productrelationships. The portfolio models of Hart and Jaffee (1974) and
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584 : MONEY, CREDIT, AND BANKING
Parkin(1970) are typical of the first; Porter(1961) and Klein (1971) are representative of the second. The sticky price paradigm, also known as the non-marketclearing or rationingliterature,has its roots in Freimerand Gordon (1965), Jaffee
and Modigliani (1969), and, more recently, Jaffee and Russell (1976) and Stiglitz
and Weiss (1981). On the loan side, the pricing issue also includes a treatmentof
the interrelationshipbetween the choice of interestrate and credit risk. This aspect
of lending activity has received increased interest, with Ho and Saunders(1981),
Deshmukh, Greenbaum,and Kanatas(1981), and Santomero(1983b) as examples
of this approach.
To treatthe individualareaslisted above, it is necessaryto concentratemuchmore
heavily on the structureof the problem and its solution technique. For this reason,
the subsequentsections are devoted to the individualissues raisedin bankmodeling.
However, it is importantto recognize that these individualproblems feed directly
into the global maximizationproblem outlined in equations (1), (2), and (3). For
consistency's sake, one would like to have a decompositionprocedurethat results
in an optimal global choice. Although this may be desirable, little academic work
has attemptedsuch a global reconciliation.
MODELS
3. ASSETALLOCATION
The first set of issues treatedhere will be those relatingto asset choice. Models
of asset allocation are primarilyof two types, namely, reserve managementmodels
and portfolio composition models. The first of this set considersthe problemof the
optimalquantityof primaryor secondaryreservesto be held by a bankthatis subject
to stochastic reserve losses due to uncertaindeposit levels. The second is devoted
to the allocationacross risky assets accordingto risk and return.As Patinkin(1965)
points out, the separabilityof these two problems is not in general accurateas the
opportunitycost associated with holding reserves is determinedby the quantityof
risk in the asset portfolio. However, this notion does not play a primaryrole in the
modeling below.
A. ReserveManagementModeling
This literaturehas perhapsthe oldest lineage in bank modeling, tracingits early
roots to Edgeworth(1888). In addition, and perhapsmore relevantly,the modeling
of reserve management was started and largely completed in the two decades
following the Orr and Mellon (1961) contribution.Subsequently,contributionsand
corrections have been made by Poole (1968), Modigliani, Rasche, and Cooper
(1970), Cooper (1971), Frost (1971), Baltensperger(1972a, 1972b, 1974), Brown
(1972), Knobel (1977), and Ratti (1979). Baltensperger(1980) has the most exact
review of this area from which the present section draws.
The basic model of reserve managementcan be outlined as follows. Considera
bank that has two assets: noninterestbearing reserves, R, and earning assets, A,
yielding rA.Its deposits, credit lines, and loan repaymentsare all subjectto random
shifts without notice, with net bank withdrawalsdefined as X, with the density
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ANTHONYM. SANTOMERO: 585
functionf(X). If net withdrawalsexceed reserves, that is, X > R, the bank must
undergoa proportionalcost, c, to obtain the additionalfunds. The bank, therefore,
wishing to maximize expected profit from its deposit balances, must maximize the
following function:
x
c(X-R)f(X)dX,
w17= rA(D -R)-t
(4)
R
where loans are equal to deposits less reserves for expositional simplicity. The
first-orderconditions of this problem result in a reserve quantitythat satisfies the
.
.
cons .ltlon
x
rA
=
f(X)dX,
cJ
(S)
R
that is, the opportunitycost of reserves, on the margin, must equal the expected
reductionin operatingor transactionscosts devoted to reserve adjustments.This is
the essential condition that must be met in reserve managementmodels.
Poole (1968) notes thatfor a symmetricdistributionwith E(X) = 0, this condition
implies thatc > 2rA. Both he and Baltensperger(1980) devote considerabletime to
explainingwhy this might be the case. For example, the cost of reserve deficiency,
c, may not be linear; access to funds may be viewed as uncertain;and, administrativeand regulatoryhassles may ensue for firms with excessive dependenceon the
open marketto adjust reserve positions.
Incorporatingreserve requirements into the analysis further complicates the
matter, but the economics are unaltered. Specifically, the existence of required
reservesundera contemporaneousreserve requirementregime reducesthe effect of
an unexpecteddeposit drain by the amountof reserves held in its support. On the
other hand, lagged reserve requirements,unless carryoverprovisions exist, appear
to leave the analysis unaffected.
The Poole (1968) paperobtains anotherinterestingresult. Analyzing the effect of
a mean preservingspreadoft(X), he concludes that increaseduncertaintydoes not
necessarilyresult in higher reserve positions. The economics of the result are that,
with increaseduncertainty,the bank is more likely to have both excess anddeficient
reserves. Inasmuchas the formerencouragesa reductionin reserves, the net effect
of uncertaintyon reserve assets is ambiguous.
Frost (1971) extends the reserve managementissue to an environmentwhere the
bankinheritsthe previous reserveposition. At any point in time, the ex post reserve
position results from reserve planningand a single drawfrom thef(X) distribution.
The question addressedis whether reserves should be immediatelyadjustedto the
ex ante optimal level for the next period. Here, the authorapplies a Miller and Orr
(1966) approachto adjustmentof reserves, where fixed adjustmentcosts and the
previousperiod's endowmentmust be evaluatedto determineif a movement to the
optimal level is profitable. As is the case with all such models, a range of
"nonoptimal"reserve positions exists where no adjustmentwill take place.
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586 : MONEY,CREDIT,AND BANKING
Baltensperger(1972b, 1974) and Baltenspergerand Hellmuth(1976) extend this
analysisof reserve managementinto its relationshipwith informationand operating
costs. They note that informationon customerhabitsmay reducethe varianceof the
underlyingsubjectivedistributionof stochasticwithdrawals.The lattercould reduce
reserve costs sufficiently to warrantinvestment in such information.Accordingly,
the profit function (4) should be written as
rw
T
= r,,(D -R )-A
cl(X-R)f(X|+)dX-C2+,
(6)
R
where + is an informationunit thatcosts c2to obtain. The ex ante expectationof the
underlyingdeposit risk is dependentupon the quantityof informationinvestment.
The resultantfirst-ordercondition requiresthat the expected marginalreturnfrom
informationproductionbe equal to its constant marginalcost.
In all, this literatureis fairly self-containedand complete. It solves a problemthat
appears central to the banking environment and obtains fairly sensible results.
However, it could be arguedthat, with the adventof a well-developed federalfunds
market,the overall importanceof the problem as a micro banking issue is significantlyreduced.In fact, casual empiricismsuggests thattotal excess reservesamount
to only about 0.1 percent of total bank assets, whereas the proportionof the academic literatureassociated with its determinationis one hundredtimes that figure.
This is, perhaps unfairas the focus of the reservemanagementliteraturetranscends
just excess reservesand includesthe quantityof short-termassets andthe availability
of credit facilities to meet reserve deficiencies. Yet, this feature of the reserve
managementproblem is not partof the model framework.Indeed, the majorshortcoming of this literatureis its implicit assumptionthat all liquidity considerations
can be reducedto the reserve managementproblem. It never squarelyaddressesthe
issues surroundingthe definition of liquidity, its measurementin the balance sheet,
or its optimal quantity. In an environmentwhere liability managementhas gained
increasedimportanceas a liquidity and reserve adjustmenttool, a dependenceupon
reserveitems seems increasinglyless relevant. In addition,given the interdependent
natureof the individualwithdrawalsfrom any particularbank, the lack of considerationof contagion or bank-runphenomenaseems to avoid a significant aspect of
the bank's short-termfunds management.
B. PorMolaoChoaceModels of Asset Allocation
Asset choice modeling in the literaturegenerallytakes two forms. Eitherthe bank
is viewed as possessing some degree of monopoly control over its loan price or the
asset marketis modeled as a perfectly competitive one where the bank must select
appropriatequantitiesof loans of various characteristics.The first set is typified by
Shull (1963), Klein (1971), and Porter(1961), and the second by the contributions
of Pyle (1971), Parkin(1970), Hart and Jaffee (1974), and Sealey (1980).
The first group of papers seeks to obtain an optimal loan and/orasset size from
the maximizationof expected profit of the firm. In virtuallyall cases, the objective
functionis linearin profit. Frequently,uncertaintydoes not even exist, for example,
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ANTHONY M. SANTOMERO : 587
is a ratherstraightforward
Shull(1963)or Stillson(1974).In all cases,theapproach
microeconomicsetup from which the traditionalmarginalconditionsresult. A
controversy
centralto this literatureandperhapsone whichseparatesit fromwork
firmsis the modelingof the mostliquid,or highest
on thebehaviorof nonfinancial
elasticity,market.
In its simplestform, the typicalmodelstructureis a two-sideddiscriminating
monopoly.Marginalrevenueequalsmarginalcost. A variationin anyone market
staticshiftin allmarginalconditions.Shull
feedsthroughthemodelto a comparative
(1963)exhibitssuchbehavior.
Anotherapproach,apparentlyinitiatedby Tobin(1958), has one marketas a
perfectlycompetitiveone. Tobin used the discountwindowfor this purpose,a
positionthatwas laterrejected,at least implicitly,by GoldfeldandKane(1966).
Klein(1971)uses the governmentsecuritymarket.Othershavesuggestedit is the
associatedwitha modelwith
federalfundsmarkets.In anycase, the maximization
one infinitelyelasticsource(use) of fundsresultsin a generalconvergenceof all
asset.Separation
marginalrevenuesandcoststo thisinfinitelysupplied(demanded)
in demandforloans
Variations
existsbetweenassetallocationanddepositstructure.
of one type have no effect on the otherloan decisions.This result,firstpointed
out explicitlyby Klein (1971), causedconsiderabledebate,with commentsby
Pringle(1973) andMiller(1975)questioningthe validityof the infiniteelasticity
assumption.
To formalizethediscussion,one mayview thistypeof modelas theresultof the
process:
followingmaximization
max gT= , rAA '
A,, Dj
z
E
rDD
3
J
'
(7)
where
drAI<
va
0
dAi
Vjim
<>0
dDj
drDm =
O.
dDm
The f1rst-order
condltlonsresult1n
.
.
(gA,)A,
+
rA'
.
.
rDm
(dD ) + rD'
(8)
of the bank'sbehavioron
(1980)takesissue withthis formulation
Baltensperger
assets
thegroundsthatno operatingcostsareincludedin theanalysisanddifferential
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588 : MONEY, CREDIT, AND BANKING
or deposits are indistinguishablewithin the formulation. Although both of these
criticisms are entirely correct, they do not appear to be particularlyrelevant or
fundamental.Stillson (1974) incorporatesservicing costs, as do Towey (1974) and
Sealey and Lindley (1977). In none of these cases does one find resultsthat substantially affect the model's basic conclusions.
To obtain a nonobvious generalizationthrough the use of operating costs or a
productiontechnology, one must go in the direction of Adar, Agmon, and Orgler
(1975). Therethe authorsarguethatthe bankingfirm has a joint productionproblem
so thatoutputmix is a critical determinantof operatingexpense. Withinthis framework, the equilibrium conditions from profit maximization are interdependent.
Separationof loan decisions, as well as asset decisions from liability structure
decisions, becomes impossible. This, of course, makes the operatingcost function
muchmore complex than it is generallyconsideredto be in the theoreticalliterature.
Perhaps it is also more realistic. In an era in which financial intermediariesare
broadeningtheirmenu of financialseries to include activities in both the deposit and
securities areas, this joint productionview of operatingcosts may warrantserious
consideration.
Before turningfrom these simple micromodelsof the firm it is worthnoting what
is not treatedin most of these theoreticalconstructs.Almost withoutexception, these
models representthe bank'sproblemas a single-periodmaximization.Intertemporal
demand considerationsare rarely explicitly modeled, in spite of the fact that the
institutionalliteraturespends much of its time discussing such problems. The customerrelationthat Hodgman(1963) and othershave analyzedis rarelyincorporated
into bankmodels. Whereit is, the treatmenttends to be rathersterile, with the entire
relationshipcapturedby a geometric lag or by cross-productproportionality.Wood
( 1974)or Blackwell and Santomero( 1982) aretypicalof such attempts,but represent
only the most rudimentaryapproachto capture the dynamic effects of customer
relationships.
Multiperiodfirm maximization, too, is only peripherallytreated. Where intertemporalconcerns exist, the objective function is taken to be a multiperioddiscounted valuation function. However, if the literatureon agency costs is relevant,
and there is a conflict between management and investor goals, it would be
interestingto see a betterdevelopmentof this issue in the multiperiodenvironment.
For example, my colleagues have arguedthat front-endfees in the syndicationarea
have caused bank managementto accept risk levels that would have been rejected
if a present value decision rule had been used (see Guttentagand Herring 1980).
Perhapsthis could be due to a conflict between managerand investordiscountrates
or horizons. Unfortunately,without better multiperiodmodeling, theory can say
very little about this subject.
Whereintertemporalmodels do exist (e.g., Wood 1974), the solutionshave some
curious characteristics.For example, consider a simple n period model, such as
n
max X =
rt,rt+l,
*
EX3t-1,7T
t=]
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ANTHONYM. SANTOMERO: 589
subjectto
gr,= r,l,-rD,D,,
conditionsforr,,r,+l, . . . are
/dD, = 0 . Thefirst-order
where1,--I (r,,It l) anddrD,
t77r= o = 1, + (r, - rD,), ' + /3(r+ - rD+l) ,3r +
(10)
as follows.Thebank
Theimplicationof thisoptimalbehaviormaybe characterized
will initiallyaccumulateloansfromperiodto periodas a resultof the buildup of
demandbaseduponpreviousdecisions.Thisincreasedloandemand
intertemporal
impliesthattheinterestratewill riseeachperiodin spiteof a constantcostof funds.
Thisappearsto be anawkwardwayof lookingatthebank'sdynamicbehavior.Yet,
onlyBlackwellandSantomero(1982)considerthe propertiesof theirmodelat the
long-runstationaryequilibrium.
The secondapproachto assetselectionis the portfoliochoicemodelsusingrisk
andreturnas criteria.The most elementaryof these is the workof Pyle (1971),
whichset out to determinethe necessaryconditionsfor financialintermediation
casewherethereis a riskless
Usinga three-asset
framework.
withina mean-variance
he derivesthe optimal
asset, as well as loans and depositsin the intermediary,
behaviorof thefinancialfirm.Necessaryandsufficientconditionsfortheexistence
arealsoderived.Theresultsimplythatcovarianceof ratesacross
of intermediation
the balancesheet is extremelyimportant,and a positiveloan premiumand/or
negativedepositpremiummust exist for the firm to make risky loans and to
deposits.
intermediate
(1980) arguesthatthe
These resultsappearfairlyobvious, and Baltensperger
majorfailingof theworkis its inabilityto motivatethissimpleintuitiveresult.Yet,
becauseit clearlyarticulates
quitea lot of attention,primarily
thepaperhasattracted
the portfoliochoicemodelingof the financialfirm.
Theportfoliomodels,of whichbothParkin(1970),andPyle(1971, 1972)arethe
prototypes,have a ratherstandardset up. The investoror manageris viewed as
maximizinga concavefunctionin end of periodprofit,with a quadraticor exponentialfunctionoftenusedto representthe firm'spreferenceordering.
E(7T)- (b),,2
whereprofitandits variancearedefinedas
X
= E rAAl - E rD,DJ
(J2 =
E[(r-E(7r))2].
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(11)
590 : MONEY, CREDIT, AND BANKING
The solution methodology of these papers is to define the characteristicsof the
feasible set of assets and/orliabilities of the firm. Then, asset choice is restrictedto
the efficient frontier, where additionalreturnis only achievable at the expense of
added variance. The bank, then, selects a point on the efficient frontierwhere the
objective function's marginalrate of substitutionbetween risk and returnis equated
with the market'sopportunityset. Ratherobviously, the determinantsof the optimal
solutionarethe specificationsof the returnsto each asset andliability, andthe choice
of the objective functionof the bank. On the first of these, the returncharacteristics
of the assets are assumed exogenously given and independentof bank decision
making. This view significantlyminimizes the effect of the bank on the asset return
patternsthroughthe manipulationof lending terms and conditions. However, if the
entire set of assets from which the bank constructsits portfolio includes multiple
pricing options for each loan category, this frameworkis theoreticallycorrect. As
far as the second factor determiningthe solution, section 2 notes the difficulty in
determiningthe all-importantobjective function to be maximized.
The above reservationsnotwithstanding,these models lend new insight into the
bank's portfolio selection. Hart and Jaffee (1974) is perhapsthe best of the papers
using this approachto examine the asset structureof the depository intermediary.
Theirresultsshow thatundersome ratherrestrictiveconditions,one can segmentthe
scale of bank operationsfrom its risk-returnchoice. Such a separationtheoremcan
be developed for the bank in an environmentin which no risk-freeasset exists and
a fully liability funded portfolio structureis assumed.
In total, the asset choice models get mixed reviews. One branchof the literature
applies Economics 1 to the bank to obtain results that border on the trivial in
retrospect,that is, marginalrevenue equals marginalcost. It depends, to an excessive extent, on demand and supply curve slopes that are not well motivated or
understood.Alternatively,the Tobin-Markowitzasset portfolio models are used for
quantitychoice in a perfect market. The results follow directly from the finance
literatureand add little more. Their insights, and they are many, come from the
realizationthat the bank asset problem is a special case of the standardportfolio
choice model. As such, thatperceptionof asset managementmust become a partof
the bankingliterature.
4.
LIABILITYCHOICEMODELS
The modeling of the liability side of the balance sheet has taken two separate
paths.For deposits, the modelinghas been akinto the simple monopolisticmodeling
structureoutlined for the asset side. For capital and leverage issues, the literature
has used more sophisticatedtechniques, including bankruptcyconsiderationsand
models from corporatefinancial theory. We consider each in turn.
A. Deposit Modeling
A useful startingpoint for the analysis of liability modeling techniques is the
simple deposit marketform used by Klein (1971). Here, as indicatedabove, there
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ANTHONYM. SANTOMERO: 591
is an infinitely elastic market from which an unlimited quantityof funds may be
obtained. As noted in equation (7), the bank is a deposit rate setter with some
monopolistic control over the deposit market. First-orderconditions from such a
setup indicate that the marginalcost of funds from each deposit source must equal
the marginalcost (use) of funds from the competitive market, as in (7).
This model may be complicated by allowing productioncosts related either to
balancesheld on deposits or to the numberof accounts. Sealey and Lindley (1977),
Klein and Murphy(1971), and Baltensperger(1972b) are typical of this genre. The
solution of this type of model is a fairly obvious extension of the earlierwork; that
is, with productioncosts, the total marginalcosts mustbe equilibrated.The analysis
only becomes interestingwhen differenttypes of productionfunctionsare integrated
into the analysis. For example, Flannery(1982) considers the case of a quasi-fixed
productionprocess whereby the cost functionrelates to changes in deposit balances
ratherthan (or in additionto) the level itself. Assuming that such customer-specific
costs are shared by both the customer and bank, the model demonstratesthat
deposit-rate variation will be reduced relative to open-marketrate movements.
Flanneryargues that such a productionprocess can explain both the long-runcustomer relation and the tendency for deposit rates sometimes to lag behind openmarket rates, both on the up and downside of the market. To Flannery, such
quasi-fixed productiontechnology explains the concept of "core"deposits.
Mitchell (1979) extends the analysis of the productionor operatingcosts to a case
where, due to regulatoryconstraints,explicit interestis incapableof rewardingthe
depositorsufficiently. Implicitpaymentsthen resultfromthe willingness of the bank
to absorbsome of the real productioncosts associated with transactionsin orderto
attractlarger balances. Barro and Santomero (1972) and Santomero (1979), who
treatedthe customerbehaviorwithin such a regime, demonstrateboth the relevance
and importanceof such implicit payments. Mitchell (1979) and Startz(1983) go the
next step to consider the effect of this implicit payment option on the behavior of
the banking firm. Central to their analysis is the ability of the bank to subsidize
bankingactivity, such as check cashing, funds transfers,and account maintenance
costs, to encourage deposit balances. However, their treatmentdepends critically
upon the relationshipbetween such account activities and average balances. The
basic model may be developed as follows. Denote the numberof transactionsusing
the deposit accountas n and the cost and service chargeper transactionas c and k,
respectively. The profit function of (7) may be written more generally as
ST= ,r4,Aa -Ere,Dj
Z
j
-E[(CJ
-kJ)nj(Dj)].
(12)
i
The bank must now consider the return to deposit balances, the cost of deposit
services, and the interrelationshipbetween the two. Mitchell (1979) notes that
increasingthe explicit payments allowed on deposit balances within such a framework may result in either increases or decreases in implicit payments accordingto
the relationshipnj(Dj).Although this work is still in its formative stages, it does
have some interestingimplicationsfor bankdecision makingandpricing. In fact, the
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592
: MONEY, CREDIT, AND BANKING
whole areasurroundingthe relationshipbetween variousforms of payment, deposit
reaction, and, ultimately, profitabilityneeds furtherwork in a real-worldenvironment that is shifting to a greaterextent to rate deregulation.
The movement of deposit rates relative to open-marketinterestrates is another
areaof continualattentionin the literature.A simple neoclassical model of the firm
argues that rates on deposits should move along with market rates. Yet, Weber
(1966) andothershave suggestedthatrateswill move sluggishly for institutionswith
long-lived assets. The general argumentis that due to the inability of the firm to
achieve a satisfactoryincreasein the asset yields from its portfolio, the bankwill be
forced to adjust its deposit rates more slowly to overall marketforces. The Weber
hypothesiselicited a significantnumberof subsequentresponses, of which the major
contributorswere Goldfeld and Jaffee (1970) and Stigum (1976).
The formerauthorsdemonstratethat on a theoreticalplane the phenomenoncan
be explained by boundary conditions forced upon the firm by its balance sheet
constraint.Specifically, considera firm thatmaximizesthe profitfunctioncontained
in equation (7) and attractsassets and liabilities in period one. Optimumprofit is
obtainedfor thatperiodandover the expected horizon, definedby expectedratesand
demand functions. Subsequently, however, assume that there is an unexpected
decline in asset yields. The lower rates imply lower optimal deposit rates given a
fixed liability schedule. However, if the asset portfolio is nonmarketableand relatively fixed in quantity,the bank may find itself in a position thatrequiresit to pay
whateverrate is necessaryto finance its asset portfolio. Laterupwardmovementsin
asset yields will, accordingly, not elicit an appropriaterate increase, as the initial
deposit rate was a nonequilibriumchoice by a constrainedfirm. As Goldfeld and
Jaffee note, such sluggishness is introducedonly because of the possibility that a
corner solution will lead to perverse behavior. In the long run, such behavior is
ruled out.
Stigum returnsto this issue to present a more general treatmentof the problem.
Here, two innovationsare offered. First, she considers the effect of sticky deposits
on the analysis. Assuming thatdeposit balances can be writtenas a functionof both
currentrates of return and the previous deposit balance, she demonstratesthat
deposit inertiawill result in relatively sluggish movementin deposit rateseven if no
boundaryconditionis reached. This is an interestinginsight into the pricingdynamics but the authoroffers little to motivate, in a rigorouseconomic sense, this deposit
inertia.Flannery's(1982) joint cost-sharingframeworkis perhapsone such explanation from the industrialorganizationliterature,as is Adar, et al. (1975). However,
withoutadequateunderstandingof the cause of such sluggish deposit movement, it
is difficult to be convinced that it is a satisfactory answer to the relative rate
movement observed in the deposit markets.
The second generalizationcontained in Stigum (1976) is the additionof deposit
uncertaintyto the analysis of Goldfeld and Jaffee (1970). Consideringboth the case
of risk neutralityand concavity, the authorinvestigates the relative movement of
rates. Not surprisingly,the degree of absoluterisk aversionis a crucial determinant
of bankbehavior.This same factor comes into play in Sealey's ( 1980) slightly more
general treatmentof the deposit rate setting problem. In additionthe latter author
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ANTHONYM. SANTOMERO: 593
considers the correlationof loan and deposit rates as well. This critical feature of
bank modeling will be discussed more fully below when issues related to the
managementof the total bank portfolio are discussed in section 5.
B.
The CapitalDecision
The capital decision of the financial firm is more complicatedthan it may first
appear.This is true because the optimal choice of scale and leverage is determined
by the assumed financial environmentand the raison d'etre of the firm. One must
keep in mind the substantivecontributionof Modiglianiand Miller (1958), illustrating thatin the absence of frictionsandtaxes thereexists no optimalcapitalstructure.
Accordingly, to derive an optimal capital structure,one must determine, first, the
role played by the financial institutionand, second, the extent to which one wishes
to deviate from the perfect market paradigm in explaining its operation. Pringle
(1974) does so by asserting exogenous and fixed deviations from perfect market
behavior, while at the same time assuming a CAPM valuation model. Not surprisingly, his results suggest that an optimal capital is obtained in this model
wherebysuch imperfectionsare appropriatelyexploited. In his framework,there is
a divergencebetween lending and borrowingrates, excess expected returnsexist on
loans, and capitalcost diverges from the risk-adjustedopen-marketrate. The author
shows that optimal capital is attainedwhen the excess marginalrevenue on loans
equals the excess marginalcost of capital.
TaggartandGreenbaum(1978) develop theiranalysisof capitalunderthe assumption thatexcess loan revenues and transactionservice profitscan be exploited by the
value-maximizingfirm. An extension of this approachby Orglerand Taggart(1983)
arguesthat the optimal capital structurefor the bank depends upon its efficiency of
producingsuch intermediaryservices as check processingandrecordkeeping, along
with the interplayof privateand corporatetax rates on profits. An interestingresult
obtainedby the frameworkis its ability to explain variationsin bank capital across
firms by differentialscale and efficiency of bank operations.
Kahane (1977) and Koehn and Santomero (1980) use the portfolio model approach,outlined above, on the bank capitalissue. Startingfrom the general specification of (1), they optimize the bank's rate of return on capital by selecting a
portfolio of assets and leverage position that optimizes shareholders'returns.The
Koehn and Santomeropaper is interestingbecause it analyzes the effect on bank
portfoliobehaviorof a regulatoryshift in capital adequacyregulations.The authors
demonstratethat although capital increases as a fraction of assets, the resultant
portfoliois unambiguouslymorerisky thanbeforethe capitalconstraint.Essentially,
the constrainedfirm attemptsto offset some of the effect of the leverage limit by
absorbinggreaterrisk in its portfoliothanbefore the regulation.Koehn (1979) finds
a similareffect of asset restrictionregulation.These resultslend credenceto the idea
that regulation, if it is to be effective, must be combined with adequate understandingof the behavioralresponse of the banking firm.
Talmor (1980) uses a different approach, employing the gambler's ruin technology to the problem. According to this approach,appropriatecapitalinvolves the
determinationof an acceptable probabilityof bankruptcyand derives an optimal
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594 : MONEY, CREDIT, AND BANKING
structureto achieve this ex ante acceptablelevel. Building on the work by Wilcox
(1971) and Santomeroand Vinso (1977), the paperderives the appropriatelevel of
capital from a continuous time diffusion process whereby the managementdetermines the appropriateex ante probabilityof failure by portfolio choice. An interesting characteristicof the model is that the determinantsof the process are derived
endogenously from the underlyingbalance sheet of the bank.
For all its benefits, however, this approachhas a fundamentalproblem. It is not
clear how one defines the acceptable probabilityof failure. Presumably,the firm
should be managedto optimize firm value for its stockholders.How one links this
objective to an ex ante criterionfor probabilityof failure is not developed in such
models. This could be done by some form of general objective function in which
bankruptcycosts affect shareholders'value, as was discussed in section 2. However,
some would contendthatthe presenceof regulationand deposit insuranceprecludes
this marketresponse mechanism from functioningadequately.
The mantle of regulationhas in and of itself a built-in incentive to increase risk
and leverage. The deposit insurance structureguarantees all depositors up to a
statutorylimit. For these depositors, the liability of the depository institution is
de jure a riskless asset. Accordingly, there is no incentive for these depositors to
respondto bank riskiness per se. The noninsureddepositorswould seem to require
some assuranceof the solvency of the institutionbefore deposits are made. However, regulationhas made their concerns less relevant in terms of the marketdisciplining the depository institution. Over the past several decades, failed institutions
have been dealt with in a mannerthat has protectedall depositors, ratherthanjust
the insuredcategory. Assumptionof the bank location and balance sheets has been
the dominant form of regulatory action. Advances from the discount window to
facilitatethis mannerof resolutionlead KarekenandWallace(1978) to concludethat
such advances are essentially loans to the FDIC.
If one accepts this view that bank liabilities are essentially 100 percent insured,
then the entire issue of bank capital and risk taking should be recast in terms of a
discussion of insurancepricing. The role of the marketto price the riskiness of the
depositoryinstitutionhas been usurpedby the regulatorin its blanketinsuranceof
the industry.
Whatremains,therefore,is to discuss the form and substanceof the insuranceand
the impactit has and can have on the quantityof capitalandrisk held by the banking
firm. Merton (1977) and Sharpe (1978) have made significant contributionsin this
direction. These papers apply the option pricing literatureto the insuranceof bank
liabilities to obtain considerable insight into the deposit insuranceproblem. The
basic approachused is to show thatthe payoff patternof the insurancescheme is like
a put option on the underlying assets of the institution. Then, using the work of
Black and Scholes (1972), one can derive the optimal price for such insuranceand
its functionaldependence.
Following Merton(1977), one may consideressentially threepartiesto the insurance of a liability of the bank: (a) the bank itself, (b) the depositor, and (c) the
insurancecompany (Federal Deposit Insurance Corporation FDIC). The bank
offers the depositora return,B, thatcompensatesthe latterfor the time value of the
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ANTHONYM. SANTOMERO: 595
funds left at the bank. These funds are commingled with the equity suppliedby the
bank's owners in the asset portfolio. After one period, the asset value is given by
V, which is stochastic ex ante. If the ex post value of the asset portfolio is greater
thanB, that is, if V ' B, the bank redeems the depositor'sliability and the insurer
plays no role. The equity holderreceives the differencebetween V andB as a return
on equity, presumablyless the insurancefee chargedby the FDIC. In the event that
V is less thanthe maturityvalue of the liability, that is, if V < B, the depositorstill
receives the insured value, B, but, in this case, the returnis paid partiallyby the
residualvalue of the assets and partiallyfrom the insurancefund. The equity holder
receives nothing, whereas the insurer receives V - B, which is unambiguously
negative. One may rewrite the payoff patternof the insurancefund equivalentlyas
min[O, V - B ] = max[O, B - V] .
( 13)
This is identical to the payoff structureof a put option issued by the FDIC against
the value of the assets at the bank. Using the Black-Scholes option pricing model
to derive the optimal price per dollar, Merton (1977) derives the value of deposit
insurance.
Sharpe (1978) develops this same perspective of the deposit insurance pricing
problemusing a statepreferenceapproach.His main insight is obtainedby reversing
the logic of the optimal deposit insurancepricing scheme. Specifically, the institutional realities in the United States are that FDIC insuranceis grantedundera fixed
net insurance fee. Therefore, there is an inherent tendency for financial firms to
accept higher risk levels than they would in the absence of the insurancesubsidy.
However, note that, given other factors, the value of a fair insurancefee declines as
the capital-asset ratio increases. Sharpe points out that adequate capital is that
quantitywhich would make the currentfixed rate insurancefee the correctprice for
the underlyingput option implicitly issued by the FDIC.
Buser, Chen, and Kane (1981) arguethatappropriatepricingof insurancebenefits
may not be what the regulatorwishes. They argue that the FDIC uses explicit and
implicit costs to offset the inherentbenefits accruingto the insuredliability issuers.
The latter includes capital regulation, safety regulations, communitydevelopment
accountability,and the like. Once acceptingthe benefits of insurancewithoutpaying
the full cost explicitly, the institutioncan be manipulatedby the regulator.However,
the resultantprofit of the firm must at least equal the uninsuredcase to maintain
control.
In all, this literature on optimal bank capital is a bit vague and very model
specific. This has led to a significantdivergencebetween practiceand theory as has
been suggested in Santomero (1983a). Although more work needs to be done, the
field seems to be awaiting a breakthroughin either of two areas. The corporate
finance literatureneeds to develop furtherin orderto aid in the search for a private
determinationof optimal capital. In addition, the interest expressed in variable
pricing of deposit insurance must become much more of an institutionalreality.
Withoutboth of these, the capital area remains murky.
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596 : MONEY, CREDIT, AND BANKING
5.
TWO-51DED MODELING
Thus far, the analysis has been focused upon the modeling of each side of the
balance sheet. Frequently, the models discussed considered the entire portfolio
choice problem, but for expositional convenience a review of the analysis was
placed in either of the two sections above. For example, Klein (1971) considersthe
entireasset-liabilitymanagementproblem. However, the treatmentis separabledue
to the structureof the infinitely elastic market. So, too, Parkin (1970) includes
positive and negative assets within the portfolio choice under uncertainty,but the
main insights gained from the model pertainto its asset choice structure.
Several models have recently appeared,however, which are intimatelyrelatedto
the two-sided natureof the banking problem. The first of these is the recent work
by Deshmukh, et al. (1983), in which they look at the alterationin the financial
intermediationprocess associated with increased interest rate variability. These
authorsargue that the typical bank serves as both an asset-transformerand broker.
The formerborrowsfunds at a fixed ratebefore interestrateuncertaintyon the asset
side is resolved, and the latterborrowsonly afterinterestrates areknown. Increased
ratevolatility shifts the bank's activity more towarda brokeragefunction and away
from the more traditionalasset transformationfunction. The limited upside gain
from higher rates is insufficient to compensatethe bank for the reducedprofit from
asset transformationwhen rates decline. Accordingly, variabilityresults in the shift
to brokerageactivity even for an expected profit-maximizingfirm.
Ho and Saunders (1981) analyze the bank's brokeragefunction in more detail,
using the finance literatureon brokerbid-and-askspreadsto explain bank margins.
Using a diffusion process for rate movementand a concave objective function, they
are able to define the optimum equilibriumspread for the banking firm. As one
might anticipate, this margin is dependentupon the risk aversion of the firm and
interestrate volatility.
One way of sheddinginterestraterisk is to constructa portfolioso as to immunize
it from the effects of rate shifts. There is a whole literatureon this problemand the
method of applicationto the banking firm. Bierwag and Kaufmanhave been the
mainstaysin this durationand immunizationliterature,with theirmost recentwork,
Bierwag, Kaufman, and Toevs (1982). These contributionsdevelop an appropriate
measure of the interest rate exposure of both sides of the balance sheet and a
portfoliostructurethatwill not be adverselyaffectedby interestratemovement.This
is achieved by the use of Macauley's duration measure, among others, and the
two-sided immunizationof the balance sheet throughdurationmatching.
This literatureis interestingand critical to any treatmentof actual bank interest
rate exposure estimation. Its development, use, and limitationsrequiremore space
than can be given here but interestedreaderscan look elsewhere for a critique, for
example, Haley (1982) and Bierwag and Toevs (1982).
Some caveats are in order.First, this techniqueinvolves the matchingof present
value changes associated with an arbitrarilysmall but specific variationin the yield
curve. Rightly or wrongly, bankers worry much more about cash flow than the
academicresearcher.Inasmuchas regulationis frequentlycast in currentbook value
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ANTHONYM. SANTOMERO: 597
terms, this may be rational.By implicationthe bankingfirm may not wish to hedge
its present value position. Second one should keep in mind that there is a distinctionbetween balance sheet hedging and equity-valueimmunization.These two
concepts are in direct conflict inasmuch as a durationhedged balance sheet will
cause the presentvalue of the earnings stream, that is, the bank's equity value, to
vary with rate movement. Third, durationmatchingrequiresactive portfolio management,which may not be practicalin the shortrunor for small institutions.In fact,
Flannery(1981, 1983b) demonstratesthat net currentoperatingincome is not affected by rate movements for large institutions, but is affected for smaller ones.
An allied area which must be discussed in the context of the banking firm is
modeling interest rate risk taking. This area has only recently developed, though
therewas an early work by von Furstenberg(1973). Santomero(1983b) models the
bank'schoice between fixed and variablerate loans to analyze the payoff functions
and to consider the optimal quantity of each in the overall portfolio. Dealing
simultaneouslywith both credit and interest rate risk, it is demonstratedthat both
types of risk arelikely to be presentin the optimalportfoliochoice. The drivingforce
behindthis analysis is the asymmetryof the variablerate payoff function, as noted
by Deshmukh,et al. (1983) in a much differentcontext. The paperdemonstratesthat
creditor defaultrisk is generallyrelatedto interestratefluctuations.Using a concave
utility function, marginal conditions require that the bank accept some nonzero
interestrate exposure in order to minimize the sum of credit and interestrate risk.
In all, these models begin to investigate the financial firm as a true intermediary
that deals simultaneously in both the asset and liability markets and bears both
interestandcreditrisk. Yet much needs to be done before they can purportto explain
bank behavior adequately.First, the credit risk decision must be more adequately
integratedinto the analysis than it has been heretofore. Ratherthan treatingcredit
risk as a simple mean-variance-covariancedecision process, serious consideration
mustbe given to the interdependenceboth between interestrates and defaultprobabilities and between credit risk at one firm precipitatingfailure at others. Second,
the entire area of interestrate risk managementand its optimal level needs further
work. With the adventof a developed futuresmarket,the averageinstitutionhas the
capability of shedding interest rate risk rathereasily. Yet, little has been done to
model this process or characterizethe optimalsolution. This, in particular,is an area
that requires serious modeling and empirical investigation to bring the academic
literatureup to institutionalrealities.
SHEET
6. CREDITLINESAS AN EXAMPLEOF OFF-BALANCE
RISKMANAGEMENT
While the profession has been building models of the banking firm from the
perspectiveof optimal pricing and allocation of balance sheet items, the banking
industryhas been substantiallyexpanding into off-balance sheet activity. Standby
letters of credit, bankers acceptances, and credit lines have grown sufficiently to
cause regulatoryconcern, as the boardstaff study illustrates(Boardof Governorsof
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598 : MONEY,CREDIT,AND BANKING
the FederalReserveSystem1982).In addition,with the erosionof the traditional
securitiesmarket
linesof commercerestrictions,bankshaveenteredsuchstandard
privateplacement,and, mostrecently,disareasas futurestrading,underwriting,
countbrokerage.Yet, little has been done in the academicliteratureto integrate
theseactivitiesintobankingtheory.
The only exceptionis the workon bankcreditlines. Campbell(1978), Thakor
andHons (1981)representsignificantadvances.
(1982),andThakor,Greenbaum
The basic approachtakenby Campbe.ll(1978) is the modelingof pricingwith
uncertainty
in demandandcost. Thishasbeenthe subjectof a numberof papersin
the microtheoryliterature,mostnotablyLeland(1972).TheThakor,et al. (1981)
of a generalmodelof themarketforcredit
papermovesawayfromtheconstruction
The
linesin favorof an in-depthanalysisof the optimalpricingof the instrument.
insightis thatthe bankis issuinga putoptionto the firmsuchthatit
fundamental
standsreadyto purchasea riskyclaim,theloancontract,overa givenhorizon.Then,
CAPMmodelof Merton(1973)to solve the valueof the
usingthe intertemporal
option,an optimalpriceis obtained.
Thereareweaknessesin the applicationof optionpricingto this problem,however. Firstly,partialtake-downsof the creditline makethe pricingissue much
morecomplex.Thakor,et al. arguethathistoricalanalysisandthe decomposition
caneliminatethisdifficult
of thetotalcreditlinesintoa seriesof likelydraw-downs
case. Yet, this is a somewhatheroicassertion.The optionon the timeof usageis
at least as criticalas the valueassociatedwiththe resolutionof priceuncertainty.
Yet, thesemodelsneglectthe formerin favorof the latter.
Secondly,even the price uncertaintyresolutionappearssomewhatartificial.
Creditlineshavetwo pricingconventions,fixedandpegged.Theformeris a minor
to the
partof the marketin whichthe bankspecifiesa fixedrateloancommitment
firmfor a reasonablyshortspaceof time. Fortheselines, the optionpricingmodel
however,thepriceof theloan
Forthelargemajorityof commitments,
is appropriate.
rates.Theoptionin thiscaserelatesto a hedge
is tiedto open-market
commitment
againstthevariabilityof themarkupoverprimeor fundingcost. Thefirmis betting
eitherthatcredittightnesswill increasebankmarginsorthatthefortunesof thefirm
to suchanextentthattheupfrontcostof thecreditline is warranted.
will deteriorate
As the above authorspointout, if the borrowersknew thatthe termswouldbe
identicalat draw-downandat commitmentdates,therewouldbe no incentiveto
purchaseloancommitments.The uncertainavailability,whichcannotbe modeled
of the
very neatlyin these sortsof models,appearscrucialto our understanding
creditline market.
Othershave takenanotherapproachto the creditline literature,whichis more
alongthe lines of availabilitypremiums.Wood(1975), for example,triesto deal
of lackof availablefunds.So, too,
withthe firmreactionto a nonzeroprobability
BlackwellandSantomero(1982)modelthe creditlines as a way for firmsto jump
positionson the queueof acceptableborrowersand thereforeassurethemselves
betweenavailaccessto credit.Thakor(1982)alsorecognizesthisinterrelationship
abilityandcreditlines. James( 1981) goes furtherandarguesthatthedecisionof the
will be paid,thatis, fee or balances,is
firmas to how the cost of the commitment
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ANTHONYM. SANTOMERO: 599
a self-selection process. Firms thatview themselves as more likely to requirefuture
funding will opt for fees over the freezing of needed balances.
7.
CREDIT RATIONING MODELS
In traditionalneoclassical theory of the firm, the lack of available credit is not a
concern. According to the standardparadigm, demand equals supply at the equilibriumprice. Yet, it has long been argued that nonprice rationingof credit is an
integralpartof the market.Althoughdataon this issue is sketchy at best, many have
attemptedto develop models of the credit marketand the bankingfirm thatresult in
some nonprice rationing of credit demands. In fact, this has been somewhat of a
growth area of the literatureover the last decade. Accordingly, before ending a
review of the banking field, an overview of the past and recent literatureon credit
rationingis appropriate.
Before enteringa discussion of the models devoted to explainingthe existence of
creditrationing,a more exact specificationof the phenomenonto be explained is in
order.The traditionalapproachto the problemis to define a situationin which there
is excess demand for credit at the "going interest rate" as a situation of credit
rationing.Subsequentwork by Freimerand Gordon (1965) and Stiglitz and Weiss
(1981) suggests a more exact definition. Credit rationingoccurs when a subset of
firms seeking credit at the going rate are not grantedsuch loans in spite of the fact
thattheirobjective characteristicsare identical, or nearlyso, to those firmsreceiving
credit. This definition recognizes that some borrowers are not worthy of credit
becauseof loan or projectcharacteristicsand are, therefore,formallyrejectedby the
lending institution. Creditrationingsituationshave been furtherdivided into cases
of equilibriumrationinganddynamicrationingby Jaffee andModigliani(1969). The
definition of the former is a case where credit rationing occurs at the long-run
equilibriuminterestrate, whereas the latterexists in the transitoryperiods between
such equilibriums.
A. Rationingand the CustomerRelation
Models devoted to explanationsof credit rationinghave taken three approaches.
The first, and oldest, is the literaturethat attributescredit rationing to the tied
relationshipbetween banks and their customers. Hodgman (1961) was the first to
espouse this view, which arguesthatbecause of the intertemporaland cross-product
relationshipbetween a customer and the bank, preferentialtreatmentis given to
primecustomerswhen credit tighteningoccurs. Accordingly, nonprime,small customers are rationed during periods of interest rate movement. Defining all credit
rationingas dynamic and short-run,he arguedthat the bank was merely behaving
as a multiperiodprofit maximizerby favoring its best customers. In fact, standard
textbooks in the field (e.g., Mason 1979) have made this central to the
bank/customerrelationship.
This line of analysis has some very serious problems. To make the analysis
consistent, it is necessary to arguethatthe bank'sbest customersare ones thatyield
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600
: MONEY, CREDIT, AND BANKING
the banksuper-normalreturnsin a presentvalue sense. Therefore,when a periodof
credit rationing develops, they are given preferentialtreatment. However, it is
unlikely that the bank's best and largest customers can be charged a rate that is
sufficiently high to warrant such preferred treatment. In fact, Blackwell and
Santomero (1982) have demonstratedthat if large firms, with intertemporaldemandsfor creditand multiperiodcommitmentsto the bankinginstitution,arepriced
correctly, they will, on the margin, be no more profitablethan the smaller, lesssophisticatedfirm. Accordingly, if rationingbecomes necessary, there is no reason
to believe that they will be given additional consideration. In fact, the authors
demonstratethat because of the higher elasticity of demand possessed by large
customers with alternativefunding options, these customers are less likely to receive creditpreferenceduringsuch periods of constraintin contrastto the traditional
result. One is left with the feeling that this literatureis of questionableworth.
B. Rationingand Partial Price Discrimination
The second approachto credit rationingargues that there is something about the
transactionscost structurethat leads banks to refuse credit at the going interestrate.
The most well known of these papersis the work of Jaffee and Modigliani (1969).
Accordingto this approach,the bank'soffer curve for creditto any specific customer
or customergroup is defined by the standardprofit-maximizingcriteria.If the bank
could operate as a discriminatingmonopolist, credit would never be rationedand
each customerwould be granteda profit-maximizingrate. However, if the bank is
forced to charge a nonhomogeneous set of customers the same interest rate, then
credit rationingwill result. Such rationingresults because, within the set of nonhomogeneousborrowers,the bank can be shown to charge a rate that lies between
the lowest and highest rates applicableto membersof the group. For the subset of
loans thatshould have been chargeda higherratethanthe optimalratefor the class,
quantityrationingresults. The least risky in the group and the riskless customers,
on the other hand, are never rationed.
The majorproblem with the Jaffee-Modiglianiapproachto rationingis that the
ultimate causes of the rationing are unsubstantiatedassumptions about the loan
market.Specifically, the model asserts that there is only a small set of loan prices
thatcan be chargedto the entirearrayof borrowers.It is, then, assertedthatthe bank
knows the exact customer risk characteristics,even though it does not use such
informationto set loan prices. It can be arguedthat the first assumptionis probably
a reasonable view of the bank trying to deal with a large set of heterogeneous
customers. Transactioncosts presumablyrestrict the extent to which differential
pricing is possible. It is not clear that this reasoning is consistent with the second
assumption.If the bank, for economic reasons, only roughlycategorizesits customers into broadgroups, it is hardto accept the notion that it would find it profitable
to maintainmore explicit knowledge within each group. Yet such additionalinformation is necessary to obtain the results of positive equilibrium and dynamic
creditrationing.
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ANTHONYM. SANTOMERO: 601
Anotherproblemwith this approachto loan sortingis its stability.Any two banks
within such a system will have, presumably,differentgroupingsand group-specific
interestrates. This would seem to imply thatcustomerswho are relativelyless risky
thanthe "average"within a groupmay find it desirableto shift to anotherbank. Their
relative rankingwould improve and borrowingcosts decline as a result of such an
action. In the limit, this type of behaviorshouldresultin adverseor uniqueselection
and in the generalabsence of equilibriumcreditrationingfrom the model. Although
this may not in generalbe the case, theredoes not appearto be anythingin the model
setup to prohibitsuch a degeneratecase.
C. Rationingand InformationProblems
The third approachto credit rationing, and the one that appearsmost promising
at the moment, is the informationasymmetryor adverse selection approach.This
was first suggested by Jaffee and Russell (1976), in which it was argued that
expected value pricing of loan rates hides two differenttypes of borrowers.When
all loans are priced at a single rate, the bank attractsboth honest and dishonest
customers.The formerfully anticipaterepayment,whereasthe latterwill renege in
all states where the implied cost is lower than repayment. An equilibriumcompetitive interestrate will be set so that the marketrate incorporatesthe probability
of defaultby dishonestor unluckyborrowers.They then demonstratethatvariations
in the loan rate from this equilibriumlevel could shift the relative proportionof
honest borrowersso as to improve the expected profit for the financial institution.
Essentially,by restrictingthe percentageof an investmentprojectthatis financedby
the bank, the lender attractsmore honest customersand a smaller loan loss experience. Barro(1976) considers a similarproblemby treatingthe quantityof collateral
as a determinantof the bank offer curve.
In a recent contribution,Stiglitz and Weiss (1981) extend this approach.Dealing
again with customergroupingswith low and high-riskcharacteristics,they demonstratethat as the interestrate chargedto borrowersincreases, the percentageof low
qualityloans may increase. They arguethatwithouta prioriknowledgeof the quality
of each loan applicant, the willingness to pay higher interest rates is a screening
device in identifying high-risk borrowers. Therefore, the bank would prefer to
charge a lower rate than to clear the loan market by discouraging the preferred
borrowinggroup.
Taken as a whole, this credit rationingliteratureis diverse. On one side of the
spectrum,a series of ad hoc assertionsaboutextramarginalpricingis used to explain
rationing.Next, we have an approachthat dominatedthe literaturefor a long period
of time, in which custom or costs mandatea small set of loan categories. These, in
turn,bringaboutboth equilibriumanddynamicrationing,but somehow do not cause
the bank to subdivide its lending classes further.Finally, the recent literatureon
asymmetricinformationhas been used to explain rationing. Here, equilibriumrationing exists by customers self-sorting in response to interestrate signals but not
necessarily dynamic rationing. Although the last approach is clearly the most
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602 : MONEY,CREDIT,AND BANKING
sophisticated,it also raises many questions. Yet, virtually no empirical work has
been done over the past decade to answerthem or to assess the importanceof this
entire set of literature.
8. WHEREDO WE GO FROMHERE?
Therehas been much writtenover the past decadeon the subjectof bankbehavior.
This paper lists and discusses some two hundredcontributions.To conclude my
review of this literature,I offer some thoughts on the futuredirections of work on
bank modeling.
The firstpoint thatspringsfrom this review is thatthereis still much to be learned
about financial institutionsand their place in the economy. We seem to have converged upon a global view of the maximization process that the firm attempts.
Neverthelessthere is little solid work on the natureof the financial firm's product.
The existence question remains vital to our understandingof these institutionsand
why they are capable of achieving their objectives in a relatively efficient capital
market.On the asset side, more work clearly needs to be done along the imperfect
informationline of analysis in our explanationof the financial intermediationprocess. Whetherit will be able to explaiIlthe evolution of banking, broadlydefined,
throughnew productinnovation is an open question. On the liability side, understandingthe evolution of the role and definition of money in a complex payments
system appears central to the explanation of intermediationitself. Liability and
transactionproductinnovationrequiresconsiderablymore attentionthan it is currently receiving in the banking literature.
Within our existing view of bank behavior, the modeling of asset and liability
managementis fairly well formulated.But it is importantto proceed furtheralong
the line of integratingthe two sides of the balance sheet. Issues surroundingcredit
and interest rate risk managementmust be more adequatelymodeled. The recent
workon the interactionof these risk factorsmoves us in the rightdirection,but much
more needs to be done on risk taking, hedging, and diversificationin the financial
firm. Finally,economists must addressthe degree of competitivenessin the financial
markets that surroundthe banking firm. In finance theory virtually no market
imperfectionsare considered.Economists, on the otherhand, have generallytreated
the bank as an imperfectcompetitorin marketsthat exhibit nonequilibriumpricing,
price settingcapability,andprice discrimination.It would be worthwhileif we could
reconcilethese opposing views by incorporatingmodernfinancetheoryin the theory
of the banking firm.
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