Financial equilibrium with career concerns

27 Pages·2006·0.29 MB·English

TheoreticalEconomics 1 (2006),67–93 1555-7561/20060067
Financialequilibriumwithcareerconcerns
AMILDASGUPTA
DepartmentofAccountingandFinance,LondonSchoolofEconomics
ANDREAPRAT
DepartmentofEconomics,LondonSchoolofEconomics
Whataretheequilibriumfeaturesofafinancialmarketwhereasizeablepropor-
tionoftradersfacereputationalconcerns? Thisquestioniscentraltoourunder-
standingoffinancialmarkets,whichareincreasinglydominatedbyinstitutional
investors. We construct a model of delegated portfolio management that cap-
tureskeyfeaturesoftheUSmutualfundindustryandembeditinanassetpricing
framework. Wethusprovideaformalmodeloffinancialequilibriumwithcareer
concerned agents. Fund managers differ in their ability to understand market
fundamentals,andineveryperiodinvestorschooseafund. Inequilibrium,the
presenceofcareerconcernsinducesuninformedfundmanagerstochurn,i.e.,to
engageintradingevenwhentheyfaceanegativeexpectedreturn. Churnersact
asnoisetradersandenhancetheleveloftradingvolume. Theequilibriumrela-
tionshipbetweenfundreturnandnetfundflowsdisplaysaskewedshapethatis
consistentwithstylizedfacts. Therobustnessofourcoreresultsisprobedfrom
severalangles.
KEYWORDS.Careerconcerns,financialequilibrium,tradevolume.
JELCLASSIFICATION.G0,C7.
1. INTRODUCTION
Therehasbeenasubstantialincreaseintheinstitutionalownershipofcorporateequity
aroundtheworldinrecentdecades. OntheNewYorkStockExchange,forexample,the
percentageofoutstandingcorporateequityheldbyinstitutionalinvestorshasincreased
from7.2%in1950to49.8%in2002(NYSE2003). ForOECDcountriesasawhole,insti-
tutionalownershipnowaccountsforaround30%ofcorporateequity(Nielsen2003).
Institutionaltradersmaybeguidedbyincentivesthatarenotfullycapturedbystan-
dard models in finance (Lakonishok et al. 1992).1 Consider, for example, the case of
AmilDasgupta:[email protected]
AndreaPrat:[email protected]
Wewouldliketothanktheeditor,BartLipman,andtwoanonymousrefereesforinsightfulcomments.We
aregratefultoFranklinAllen,SudiptoBhattacharya,JordiBlanes,JamesDow,DouglasGale,RohitRahi,
DimitriVayanos,andMichelaVerardoforhelpfulconversations. Wearealsogratefultoseminarpartici-
pantsatBerkeley,Bocconi,CarlosIII,CORE,Delta,Duke,Harvard/MIT,Humboldt,LSE,Stanford,Turin,
UCL,ULB,andYale,aswellasconferenceparticipantsatthe2004meetingsoftheSocietyforEconomic
Designfortheircomments.
1Allen(2001)presentspersuasiveargumentsfortheimportanceoffinancialinstitutionstoassetpricing.
Copyright(cid:13)c 2006AmilDasguptaandAndreaPrat. LicensedundertheCreativeCommonsAttribution-
NonCommercialLicense2.5.Availableathttp://econtheory.org.
68 DasguptaandPrat TheoreticalEconomics1(2006)
US mutual funds, which make up a significant proportion of institutional investors in
equitymarkets.2 BecauseofSECregulations,mostmutualfundschargefeesthatarein-
dependentofperformance.3 Theirrevenuedependsonlyontheamountofassetsthat
investorschoosetoentrusttothem. Atthesametime,thereisasubstantialamountof
empiricalevidencethatinvestorsshifttheirmoneytowardsfundsthathaveperformed
well in the recent past creating a “flow-performance” relationship (Ippolito 1992 and
ChevalierandEllison1997).Fundshaveimplicitincentivesto“impressinvestors”inthe
currentperiodinordertoretaintheirinvestorbaseandattractnewbusinessinfuture
periods. Indeed,ChevalierandEllisonpresentevidencethatfundsaltertheirbehavior
inresponsetosuchimplicitincentives.4 Giventhesizeofthemutualfundindustry,such
behaviorislikelytoaffectpricesandquantitiesinfinancialmarkets. Inthispaper,we
consider the theoretical implications of the situation just described. In particular, we
ask:Whataretheequilibriumfeaturesofafinancialmarketinwhichasizeablepropor-
tionoftradersfaceimplicitincentivesofthekindthatdriveUSmutualfunds?
As a starting point, we draw upon the burgeoning theoretical literature on career
concernsforexperts(e.g.HolmströmandRicartiCosta1986,ScharfsteinandStein1990,
Prendergast and Stole 1996, and Ottaviani and Sørensen 2006). An expert is an agent
whosetypedetermineshisabilitytounderstandthestateoftheworld.Thisdiffersfrom
“classicalcareerconcerns”(Holmström1999)inwhichtheagent’stypedetermineshis
abilitytoexerteffort. Expertmodelsareparticularlysuitedtoanalyzeagencyrelation-
ships in financial setups, in which the key driver appears to be the ability to pick the
rightportfolioratherthanpureeffortexertion. Someexpertmodelshavebeenusedto
analyze precisely such settings. For example, Scharfstein and Stein (1990) develop an
agencytheoreticmodelinwhichexpertsmimicthedecisionsofotherexpertsduetoca-
reerconcerns. However,thatpaper,andothersuchapplications,consideronlypartial
equilibriumanalysisinwhichpricesarefixed.
Themaincontributionofthispaperistodevelopafinancialequilibriummodelin
whichpricesaredeterminedendogenouslybythebehaviorofexpertswithreputational
concerns.5 Thisenablesustoexaminetheeffectsofcareerconcernedbehavioronfi-
nancialmarketvariables.6
In our model there are four classes of agents: investors who cannot trade directly,
fundmanagerswhotradeonbehalfofinvestors,noisetraderswhotradeforunmodelled
liquidity reasons, and uninformed traders who act as market makers. It is a dynamic
model:ineveryperiodtheinvestorsselectamongavailablefundmanagers.Fundman-
agersfacecareerconcerns,whicharethedrivingforcebehindourresults.7
2Around37%ofequityheldbyinstitutionsin2002washeldbymutualfunds; thisnumberdoesnot
includestateandprivatepensionfunds(NYSE2003).
3SeeEltonetal.(2003)fordetails.Only1.7%ofUSmutualfundschargedincentivefeesin1999.
4Lakonishok et al. (1991) present evidence of related “window dressing” behavior by pension fund
managers.
5Wesurveytherelatedliteratureonassetpricingandagencyproblemsbelow.
6Italsoenablesustoexaminewhethercareerconcernscanpersistinasettingwherepricesplayboth
informationalandallocationalroles.
7Fortractability,weabstractfromagencyproblemsbetweenthefundcompanyandthefundmanager,
TheoreticalEconomics1(2006) Financialequilibriumwithcareerconcerns 69
Inthebaselinemodel,theformofthepaymentfromtheinvestortothefundman-
agerisexogenouslygivenandplaceslittleornoweightonperformance. Asdiscussed
above,thisassumptionappliesbyandlargetoUSmutualfunds.Thisallowsustomake
ourmainpointsinasimple,tractablemodel.Laterinthepaperweshowthattheresults
arestillvalidinanenvironmentwithendogenouscontracting.
There are two periods. In each period there is a market for a risky asset, which is
liquidatedattheendoftheperiod.Inthebeginningofthefirstperiod,investorsentrust
a fund manager with a sum of money. The fund manager trades on their behalf, and
attheendoftheperiodtheinvestorsobservethereturnobtainedbythemanager. At
thebeginningofthesecondperiodtheinvestorscanchoosetoretainthecurrentfund
managerortoreplacehimwithanewone.Again,thefundmanagertradesonbehalfof
theinvestors.
Fundmanagersarecharacterizedbytheirabilitytoobservemarketfundamentals.
Agoodfundmanagerismorelikelytolearntheliquidationvalueoftheassetbeforethe
assetisliquidated.Inequilibriuminvestorscanattempttoinfertheabilityoftheirfund
managerfromtheoutcomeoftrading.
Therestofthemarketismadeofnoisetraderswhotradeforexogenousliquidityrea-
sons(see,forexample,GrossmanandStiglitz1980)andalargenumberofuninformed
traderswhoactasmarketmakers. Marketmakerspostbidandaskprices. Asmarket
makersarerational,theremaybeanendogenousbid-askspreadtoaccountforadverse
selection.
Themainfindingsareasfollows.
1. Without career concerns, fund managers trade if and only if they possess valu-
able private information. As a benchmark case, suppose that the fund manager
has no career concerns, because the decision to replace or retain him is exoge-
nous.Thenweshowthatinformedmanagerstradebutuninformedmanagersdo
not. Informedmanagerstradebecausetheycanmakeprofitsinthepresenceof
noise traders. Such trade by informed managers leads to a strictly positive bid-
askspread,which,inturn,impliesthattradingwithoutinformationisanegative
expectedutilitygamble.Thus,uninformedmanagersdonottrade.
2. Withcareerconcerns, youngfundmanagerstraderegardlessofwhethertheypos-
sessinformationornot.Ifthedecisiontoreplaceorretainthefundmanagerisen-
dogenous,thereexistsachurningequilibriuminwhichayoungmanageralways
trades. Ifheisinformed,hetradescorrectly. Ifnot,hechurns,thatis,hebuysor
sellsatrandom. Ifanuninformedyoungmanagerdoesnotchurn,hesignalshis
lackofinformationandgetsreplacedinthefollowingperiod.
3. Churningenhancestradingvolume.Thetradingvolumeishigherinthechurning
equilibrium than it is in the equilibrium of the model without career concerns:
suchasthosedocumentedbyChevalierandEllison(1999). Inourset-up,thefundmanagerandthefund
companyarethesameentity:thetermsfundmanagerandmutualfundcanbe(andare)usedinterchange-
ably.
70 DasguptaandPrat TheoreticalEconomics1(2006)
allyoungfundmanagersandallinformedoldmanagersengageintrading. The
effectontradingvolumeishighestwhenthereareveryfewinformedmanagers:
in such a market, trading volume is lowest in the case without career concerns
(because only informed managers trade), leading to the largest relative increase
due to churning. Below, we examine the existing literature and argue that this
findingcontributestowardsapotentialsolutiontothe“tradevolumepuzzle.”
4. Theendogenouscompensationfunctionisskewedagainstaverageperformers. In
thechurningequilibrium,achievinganaveragereturn(asaresultofnon-trading)
isasbadasachievinganegativereturn(asaresultofawrongtrade). Bothout-
comessignalpoorinformationandleadtothemanagerbeingreplaced. Instead
apositiveoutcomeensuresthatthemanageriskept. Theendogenousincentive
structureissuchtheimplicitcompensationofanaverageperformeriscloserto
thatofanunder-performerthantothatofanover-performer.
Whileourmodelisspecial,theintuitionisgeneral. Ifbadagentshavelessuseful
privateinformationthangoodagents,theirexpectationsoffundamentalsareless
likelytodeviatefromthemarketexpectation(thetechnicalconditionsforthisto
be true are examined in Section 3). Hence, bad agents are less likely to benefit
bytrading, andinequilibriumlackoftrademustcarryareputationalcost. This
in turn creates an incentive for fund managers to take excessive risk. An unin-
formedmanagerprefersrandomizingoverperformanceratherthangettingstuck
withanaverageoutcome. Boththeshapeoftheimplicitcompensationfunction
andtherisk-takingbehaviorareconsistentwiththefindingsofChevalierandEl-
lison (1997). Their empirical flow-performance relationship displays convexity,
and,asaconsequence,recentlyestablishedfundsfaceameasurableincentiveto
increasethevarianceofperformance.
It is useful to place the present contribution in the context of the literature on the
tradevolumepuzzle. Anyattempttomodelfinancialtradingfacesthemightyobstacle
of no-trade theorems.8 Under general conditions, the arrival of new private informa-
tioncannotgeneratetradeamongrationaltraders. TheintuitionisrelatedtoAkerlof’s
lemonsproblem. Atraderwhoshowswillingnesstobuy(sell)agivenassetsignalsthat
he has private information indicating that the asset is worth more (less) than its mar-
ketprice. Inequilibrium,thisadverseselectionproblemresultsinzerotrading. Toget
aroundtheno-tradeissue,thefinanceliterature,beginningwithGrossmanandStiglitz
(1980),hasassumedthepresenceofnoisetrading. Noisetradersareagentswhomust
sell or buy because something has changed in their personal situation. For instance
theyarecompelledbyunforeseencircumstancestogenerateorutilizeliquidity(hence,
noisetradersaresometimesreferredtoasliquiditytraders)ortheyneedtobuyparticu-
larsecuritiestohedgeagainstnewrisks. Thepresenceofnoisetradersreducesadverse
selectionandallowsfortradebyinformedspeculators.
However, noise trading theories have come under increasing attack for their per-
ceivedinabilitytoexplaintheorderofmagnitudeoffinancialtrade.Whilenoconclusive
8SeeBrunnermeier(2000)foranoverviewofthetopicandforfurtherreferences.
TheoreticalEconomics1(2006) Financialequilibriumwithcareerconcerns 71
evidence is available, many scholars are reluctant to accept that the trading volumes
observed on modern stock markets (over $10 trillion in 2002 on the New York Stock
Exchange) can be explained by the kind of exogenous events that drive noise trading
(GlaserandWeber2003). (DeBondtandThaler1995,p.392)goasfarastosaythatthe
hightradevolumeobservedinfinancialmarkets“isperhapsthesinglemostembarrass-
ingfacttothestandardfinanceparadigm”. Onesolutiontothetradingvolumepuzzle
is to abandon the rational paradigm, for instance by allowing for overconfidence (e.g.
KyleandWang1997andGlaserandWeber2003). Ourpaperprovidesanalternativeso-
lution. We show that the presence of implicit incentives similar to those faced by US
mutualfundscanleadtoexcessivetradingbyinstitutionsandthusenhancethevolume
oftradeinfinancialmarkets. Moreover, themodelyieldstestableimplications, which
arediscussedintheconclusion.
Ourcoreresultsarederivedinthesimplestpossiblesetting. Weprobetherobust-
nessofourconclusionsbyextendingtheanalysisinseveraldirections. First, weshow
thatanyputativeequilibriaofourgameinwhichchurningdoesnotoccurmustbeper-
verse:intheseequilibria,investorsmustpunishmanagersforobtaininghighreturnson
theirbehalf.
Second, we extend our analysis to incorporate a richer information structure. We
showthatanecessaryandsufficientconditionforchurningtooccuristhatagoodfund
managerismorelikelythanabadfundmanagertoreceiveasignalabouttheliquidation
valueoftheasset. Ifthatmildconditionissatisfied,thereisastrictreputationalcostof
nottrading. Inequilibrium,afundmanagerwhohasreceivedanuninformativesignal
preferschurningtonottrading.
Finally,weincorporateendogenousshort-termcontracts,whichallowforpayment
contingentoncurrentperformancebutnotpaymentcontingentonfutureperformance.
Weshowthat,aslongastheproportionofinformedmanagersissmallenough,theop-
timalcontractisnotcontingentonperformanceandthuschurningpersists.
OurpaperiscloselylinkedtothepioneeringworkofDowandGorton(1997). They
embedamoralhazardproblembetweeninvestorsandtheirfundmanagersintoanasset
pricingmodelandshowthatundertheoptimalcontractfundmanagershaveanincen-
tivetotradeevenwhentheyhavenoprivateinformation, thatis, theychurn. Intheir
model,someuninformedtradersaremotivatedbythedesiretohedgeagainstrisksthat
arise with exogenous probability. In equilibrium, the presence of an agency problem
maygenerateahightradevolumeeveninthepresenceofasmallhedgingcomponent.9
WhileDowandGortonconsiderastaticmodelwithcompletecontracts,wefocusona
dynamicmodelwithincompletecontracts,whichisperhapsabetterrepresentationof
themutualfundindustry. Asaconsequence,weareabletostudyphenomenaofprac-
ticalinterest,suchastheendogenousincentivestructurefacedbyfundmanagers(the
equilibriumflow-performancerelationship)andtherelationshipbetweenchurningand
seniority. Wearealsoabletoshowtheoptimalityofnon-contingentpayforfundman-
agementcompanies,whichisacommonfeatureofthemutualfundindustryintheUS
andelsewhere.
9ForfurtherdiscussionofDowandGorton’sresults,seeBhattacharya(2002).
72 DasguptaandPrat TheoreticalEconomics1(2006)
Inarelatedpaper,AllenandGorton(1993)presentamodelinwhichpricescandi-
verge from fundamentals due to churning by portfolio managers. In their model, bad
fundmanagersbuybubblestocksatpricesabovetheirknownliquidationvalueinthe
hopeofresellingthembeforetheydie—atevenhigherprices—tootherbadfundman-
agers.Theirbehavioristheresultofanoption-likepayoffstructureunderwhichprofits
are shared with managers but losses are not. Churning thus creates the possibility of
short-termspeculativeprofits. Incontrast,inoursetting,churningoccursunderaflat
feestructureduetoreputationalconcernsoverthelifeofthefund.
An earlier paper by Trueman (1988) considers a delegated portfolio management
modelinwhichthefundmanager’sabilityisunknown.Compensationdependsonper-
formanceandontheposteriorbeliefonthefund’smanagerability.Truemanshowsthat
thereisachurningequilibriuminwhichuninformedfundmanagerstrade. Ourpaper
differsintworespects.First,Truemanassumesthatthefundmanager’sfuturecompen-
sationdependsonhisposteriorinanexogenouslygivenway. Insteadinourmodel,fu-
turecompensationdependsontheinvestor’sretentiondecision,whichisendogenous.
Second,Truemanconsidersapartialequilibriummodel(andthereforecannotdiscuss
trade volume) while we take into account the feedback that the fund manager’s trade
hasontheassetmarket.
In a recent study of active management, Berk and Green (2004) present a model
withsymmetricinformation,learning,anddiminishingreturnstofundsizethatrepli-
cates several features of the data, including the flow-performance relationship. Berk
andGreenconsiderapartialequilibriumframework. Hence,unlikeus,theydonotfo-
cusonpricesandvolume. Whileourgoalsaredifferent,ourresultsoverlapwiththeirs
inprovidinganalternativeexplanationfortheflow-performancerelationship(basedon
careerconcerns).Itisworthnotingthat,inexaminingthefinancialequilibriumimpact
ofinstitutionaltrading,wedonotattempttomatchanotheraspectofthedata—thelack
ofperformancepersistence—thatiscapturedbyBerkandGreen. Itwouldbeinterest-
ing,thoughbeyondthescopeofthecurrentexercise,toincorporatediminishingreturns
toscale(asinBerkandGreen(2004))inageneralequilibriumframework(suchasours)
tomatchthedataalongafurtherdimension.
Finally,ourpaperbearsageneralconnectiontoanumberofrecentpapersexamin-
ingtheassetpricingimplicationsofdelegatedportfoliomanagement,someofwhichwe
surveyhere.CuocoandKaniel(2001)showthatexogenouslyspecifiedperformancefees
canhavesignificantassetpricingimplications. Symmetricandasymmetricfeesinduce
different effects. Dasgupta and Prat (2005) show that the presence of career concerns
can diminish the ability of a financial market to aggregate information over time and
canleadtoinformationcascadesandsystematicmispricing.Gümbel(2005)developsa
modelinwhichagencyproblemsarisingoutofdelegatedportfoliomanagementleadto
short-termismbyfundmanagers,whichinturncanhaveimplicationsonassetprices.
Vayanos(2003)considerstheimplicationsofdelegationincentivesonliquiditypremia
infinancialmarkets.
The rest of the paper is organized as follows. The following section develops the
simplestmodelwhichissufficienttogenerateourmainresults. Section3extendsthe
baselinemodelinvariousdirections.Section4concludes.
TheoreticalEconomics1(2006) Financialequilibriumwithcareerconcerns 73
2. THEBASELINECASE
Topresenttheessenceofourresults,webeginbydiscussingasimplebaselinemodel.
Themainassumptionsare:(1)contractsareexogenouslygiven,and(2)agoodmanager
hasperfectinformationwhileabadmanagerhasnoinformation. Theseassumptions
aremadeforanalyticalconvenienceandarerelaxedinSection3.
2.1 Model
Consideraneconomywithtwoperiods,t =1,2. Thereisasinglerisk-neutralprincipal
(investor)andalargepoolofexanteidenticalrisk-neutralagents(fund-managers).One
oftheseishiredatrandomatt =1totradefortheprincipal. Attheendoftheperiod,
theprincipalmayretaintheagentorhireanewoneatrandomfromthepool.Theagent
canbeoftwotypes: θ ∈{b,g}withprobabilities1−γandγrespectively. Thetypeof
anygivenagentisunknowntoboththeprincipalandtheagent,andremainsfixedfor
thedurationofthegame.
At each time period t, there is exactly one risky asset with liquidation value v ∈
t
{0,1};eachvalueoccurswithprobability 1. Thepayoffv isrealizedattheendofeach
2 t
periodandisindependentacrossperiods.Theagent’stypeθ andtheassetpayoffv are
t
independent.10
Ineachperiodt,thefundmanagersubmitsamarketordera ∈A={0,;,1},where
t
0standsfor“selloneunitathighestavailableprice”,1standsfor“buyoneunitatlowest
availableprice”,and;,theemptyset,representslackofactivity.
Attheendofeachperiod,theprincipalandthemarketcanobservethenetreturn
obtainedbytheagent. Aftersuchobservation,theprincipaldecideswhethertoretain
orfirethefundmanager. Theretentiondecisionoftheinvestorisobservedbythemar-
ket.11
Ineachperiod,thereareN ≥1“noisetraders”whotradeforliquidityreasonsunre-
latedtothevalueoftheasset.Eachsuchtraderenters(independentlyofeachotherand
ofassetvalueandmanagertype)withprobabilityη∈(0,1)andbuysorsellsoneunitof
theassetavailableintheperiodwithequalprobability.
TherearealargenumberM ofrisk-neutraluninformedrationaltraderswhoactas
marketmakers.12 Inanyperiod,marketmakerscaneachbuyorsellatmostoneunitof
theassetavailableinthatperiod. Theactionofeachmarketmakerconsistsofsetting
two prices: an ask price pA ∈ (cid:148)1,1(cid:151) for a = 1 and a bid price pB ∈ (cid:148)0,1(cid:151) for a = 0.
t 2 t t 2 t
The fund manager and any noise trader is free to trade with any market maker, and,
10Whilewethusconsideronlyoneshort-termassetperperiod,thespiritofourargumentswouldextend
alsotothecasewheretherearemultiplelongtermassets,aslongastheidentitiesofparticularassetsre-
gardingwhichinformedmanagershaveprivateinformationchangeovertime,andifreturnsandturnovers
areobservable.Wearegratefultoananonymousrefereeforpointingthisout.
11Theprincipalobservesthereturnbutnottheportfoliochoiceortheliquidationvalue.Aswillbeappar-
entlater,thisassumptionisimmaterialtoourresults.Thispropertyisafeatureofthesimplesettingused
here.SeePrat(2005)foramoregeneralanalysisoftheeffectofthestructureoftheprincipal’sinformation
ontheagent’sbehavior.
12WeassumethatM(cid:29)N.
74 DasguptaandPrat TheoreticalEconomics1(2006)
whenindifferentbetweenthem,choosesoneatrandom. Marketmakersarethussub-
jecttoBertrandcompetition(asisnowstandardintheliterature,followingGlostenand
Milgrom(1985)andKyle(1985))andeachsetspricesequaltotheexpectedvalueofthe
assetconditionalontheorder.
The fund manager and noise traders submit their orders to the market makers si-
multaneously.13 Withinaperiod,agivenmarketmakerobservesonlyordersthatarrive
tohim. Tradesareanonymous: amarketmakerwhoreceivesanorderdoesnotknow
whetheritcomesfromthefundmanagerorfromanoisetrader.14
Thefundmanager’sinformationstructureiscommontobothperiodsanddepends
on the fund manager’s type. In each period t, a good fund manager receives a signal
conveying the true liquidation value v , while a bad fund manager receives no signal.
t
Thesignals cantakethreevalues,0,1,and;,anditisdeterminedasfollows:
t
(
v ifθ =g
s (θ,v )= t
t t ; ifθ =b.
Inthepresentsetup,s revealsθ.Whenthefundmanagerlearnshissignalhealsolearns
histype.Theinvestordoesnotobserveeitherthesignalorthetype.
Ineachperiod,thenetreturnoninvestmentis

0 ifa =;
t

χ (a ,pA,pB,v )= v −pA ifa =1
t t t t t t t t

pB−v ifa =0.
t t t
Writeatime-t mixedstrategyforanagentasthemappinga :S→∆A.
t
Inthisbaselineversionofthemodel,thecontractualarrangementbetweenthein-
vestorandthefundmanagerisexogenouslydetermined.Notethatweabstractthrough-
outfromagencyproblemsthatmayarisewithinfundmanagementcompanies. Thus,
mutualfundmanagerscanbeidentifiedwithmutualfundscompanies.Accordingly,we
modelpayoffstomanagersalongthelinesofthefeeschargedbymutualfundcompa-
nies.Givenreturnχ ,thepaymentfromtheinvestortothemanageris
t
π =αχ +β,
t t
whereα∈(0,1)andβ ∈(0,∞). Inmostoftheresultsofthepresentsectionwefocuson
thecaseα→0. However,thefactthatα>0guaranteesthatwhencareerconcernsare
absent,theinterestsofthefundmanagerarealignedwiththoseoftheinvestor.
13SinceM(cid:29)N,weneglectthepossibilitythatanoisetraderandthefundmanagerortwonoisetraders
givetheirorderstothesamemarketmaker.
14WehaveinmindalargeOTCmarket,suchastheNASDAQ,thathasmanydealerswhomakemarkets
simultaneously.Thereisnocentralorderbook,andthusonedealeristypicallyunawareofcontemporane-
ousordersthatarrivetootherdealers.
Thisformulationsimplifiestheanalysissubstantiallywithoutbeingessentialtoourresults. Ourresults
wouldalsoholdinasingledealermarketaslongasthereweresufficientlymanytradingperiodsforeach
asset.SeeDasguptaandPrat(2005)forananalysisofsuchamarket.
TheoreticalEconomics1(2006) Financialequilibriumwithcareerconcerns 75
Forsimplicitythereisnodiscounting.Theinvestor’spayoffisgivenbyχ −π +χ −
1 1 2
π .Thefundmanager’spayoffisπ +π .
2 1 2
Itisclearthatifαandβ wereverylarge(forexample,ifα→1andβ >0),itwould
neverbeintheinvestor’sinteresttoemployafundmanager.Tokeeptheprobleminter-
esting,weassumethatαandβ arenottoolarge.Inparticular,weassumethat
Nη
1(1−α)γ −β ≥0. (1)
2 1+Nη
Weshowbelowthatthisconditionissufficienttoguaranteethattheinvestorwantsto
hirethemanagerratherthantostayoutofthemarket.Furthermore,welatershowthat
the optimal short-term contract between the investor and the fund manager satisfies
thiscondition.
Tosummarize,thetimingisasfollows.
t =1 – Thefundmanagerlearnss andchoosesa .
1 1
– Tradersobservea andsetprices.
1
– Theinvestorandthemarketobservesthenetreturnobtainedbytheman-
ager;v isrevealedtothemarket;paymentstothefundmanageraremade.
1
t =2 – The investor retains the incumbent or hires the challenger. The investor’s
actionisobservedbythemarket.15
– Thefundmanagerlearnss andchoosesa .
2 2
– Tradersobservea andsetprices.
2
– Theinvestorandthemarketobservethenetreturnobtainedbythemanager;
v isrevealedtothemarket;paymentstothefundmanageraremade.
2
2.2 Nochurningwithoutcareerconcerns
We show below that the presence of career concerns can induce bad fund managers
totradewithoutinformation,thatis,tochurn. Beforedoingso,however,weestablish
a benchmark case without career concerns, in order to reassure readers that our core
resultsareindeedduetothepresenceofimplicitincentivesandnottootherfeaturesof
ourdynamicmodel.
Career concerns arise when the fund manager knows that his chance of being re-
placeddependsonhisbehavior.Toeliminatetheimplicitincentivecomponent,assume
thattheprobabilitythatthefirstperiodfundmanagerisretainedisexogenouslygiven
byr ∈[0,1]andisstochasticallyindependentfromanyothervariableinthemodel.
PROPOSITION1. Foranyexogenousr ∈[0,1],fundmanagerstradeifandonlyiftheyhave
privateinformation.Thatis,onlygoodmanagerstrade.
15Wearethusassumingthattheinvestorandthemarketsharethesamebeliefsaboutthefundmanager
att =2.
76 DasguptaandPrat TheoreticalEconomics1(2006)
Theproofofthisresult, andthatofallresultsotherthanthemainresult(Proposi-
tion2),aredetailedintheappendix. Intheabsenceofcareerconcerns,fundmanagers
behaveoptimally. Becauseofthepresenceofnoisetraders,themarketisneverfullyef-
ficient. Thus,itisoptimalformanagerswithperfectprivateinformationtotrade. Mar-
ketmakersrealizethattheymayfaceaninformedfundmanagerandthussetastrictly
positivebid-askspread. This, inturn, impliesthatuninformedfundmanagerslosein
expectationwhentheytradebecauseofadverseselection.Thus,theydonottrade.
2.3 Churningwithcareerconcerns
Wenowreturntotheinitialmodelandlettheretentionchoicebemadebytheinvestor.
What follows is our core result on the existence and characterization of the churning
equilibrium.
PROPOSITION2. If αissmallenough,16thereexistsanequilibriuminwhich:
(i) Theinvestorretainsthefundmanagerat t =2ifhetradescorrectlyat t =1and
replaceshimwithanewfundmanagerifhetradesincorrectlyordoesnottrade.
(ii) Agoodfundmanageralwaystrades.Abadfundmanagerchurnsif t =1anddoes
nottradeif t =2.Formally,
a (s )=s fort =1,2, s 6=;
t t t t
(
0 withprobability 1
a (;)= 2
1 1 withprobability 1
2
a (;)=;.
2
(iii) Marketmakerssetprices:
11+γ+Nη 11−γ+Nη
pA= and pB =
1 2 1+Nη 1 2 1+Nη
12γ+Nη 1 Nη
pA= e and pB =
2 2 γ+Nη 2 2γ+Nη
e e
whereγistheprobabilitythattheperiod2fundmanagerisgood:
e

2γ
γ=1+γ iffirstperiodmanagerwasretained
e
γ otherwise.
PROOF. Fundmanager’sstrategyatt =2:Att =2,abadmanagernevertradesbecause
pA > 1 andpB < 1. Agoodfundmanagerwithsignals =1isstrictlybetteroffbuying
2 2 2 2
because1−pA>0.Agoodfundmanagerwiths =0isbetteroffsellingbecausepB >0.
2 2
16Inparticular,werequirethatα≤(1+Nη)β/γ.