ModelofFinanciallyConstrainedStockReturns

CommentsWelcomeANeoclassicalModelofFinanciallyConstrainedStockReturnsHoracioSaprizaandLuZhangyApril2004AbstractWeusetheq-theoreticalinvestmentmodelaugmentedwithnancialconstraintstoanalyzetheeectsoftheseconstraintsonriskandexpectedreturns.Wendthatnancialconstraintsreducermvalueandinvestmentrates,andtheseadverseeectsaremoreimportantforsmallrmsandrmsinrelativedistress.Morestrikingly,wealsondthatconstrainedrmsarelessriskyandearnlowerexpectedreturnsthanunconstrainedrms,andthatnancialconstraintsaremorebindingingoodtimes.Ourmodelhelpsresolvetheanomaliesregardingtheempiricalrelationsamongnancialconstraints,businesscycle,andexpectedreturns.DepartmentofEconomicsattheUniversityofRochester,email:[e-mail],WilliamE.SimonGraduateSchoolofBusinessAdministrationattheUniversityofRochester,tel:[phone],fax:[phone],email:[e-mail].1IntroductionWeanalyzetheoreticallytheeectsofnancialconstraintsonriskandexpectedreturnsusingtheneoclassicframeworkofoptimalinvestment(e.g.,Abel(1983);AbelandEberly(1994,1996)).Financialconstraintsareparsimoniouslymodeledasadividendnonnegativityconstraint.Wesolvethemodelexplicitlyandexaminethedeterminationoftheshadowpriceofexternalfunds,risk,andexpectedreturnfromstatevariablessuchascapitalstockandaggregateandrm-specicproductivityshocks.Ourmainndingsareeasytosummarize:1.Financialconstraintsreducerms'market-to-bookratiosandinvestmentrates.2.Financialconstraintsaremorelikelytobebindingforrmswithsmallscaleofproductionandforrmsinrelativedistressorwithlowerrm-specicproductivity.Strikingly,theconstraintsaremorelikelytobebindingwhenaggregateeconomicconditionsarerelativelygood.3.Alsostrikingly,nanciallyconstrainedrmsarelessriskyandearnlowerexpectedreturnsthanunconstrainedrms.Themagnitudeoftheseeectsonriskandexpectedreturnsisinverselyrelatedtobothcapitalstockandrm-specicproductivity,butisrelativelyunrelatedtoaggregateeconomicconditions.Ourexplicitlysolvedmodelprovidesrichinsightsintotheeconomicmechanismsunderlyingtheseresults.Sincenancialconstraintsrestrictthefeasiblesetofinvestmentchoices,constrainedrms'market-to-bookratiosandinvestmentratesarelowerthanthoseofunconstrainedrms.Themagnitudeoftheseeectsdependsontowhatextentnancialconstraintsarebinding,i.e.,theshadowpriceofexternalnance.Theshadowpriceisinturn2determinedbythegapbetweentherms'investmentdemandsandtheirinternalfunds.Forsmallrms,theirinternalfundsarelowbutinvestmentratesarehighbecausetheyinvestmoreandgrowfasterinthemodel.Thussmallrmsaremoreconstrainednancially,consistentwiththeevidenceinGertlerandGilchrist(1994).Productivityshocks,bothaggregateandrm-specic,havetwoosettingeectsontheshadowpriceofexternalfunds.Apositiveshockraisestheinternalfunds,decreasingtheshadowprice,buttheshockalsoraisesinvestmentdemands,increasingtheshadowprice.Forrm-specicshocks,theformerforcedominates;thusrmswithlowrm-specicproductivityaremorelikelytobeconstrained.However,foraggregateshocks,thelatterforcedominates;thusrmsinboomsaremorelikelytobeconstrained.Weshowthatthisasymmetricresponseoftheshadowpriceofexternalfundstoaggregateandrm-specicshocksisdrivenbythestochasticdiscountfactor.1Aggregateshocksaectthestochasticdiscountfactor,butrm-specicshocksdonot.Withtime-varyingdiscountrates,aggregateshocksaectcapitalinvestmentthroughtwochannels.Inthepresenceofpositiveaggregateshocks,rmswillincreaseinvestmentbecausetheircapitalstocksbecomemoreproductive(theproductivitychannel).Further,becausediscountratesfallwithpositiveaggregateshocks,rms'expectedcontinuationvaluesgoup,stimulatinginvestmentevenfurther(thediscountratechannel).Incontrast,rm-specicshocksimpactinvestmentonlythroughtheproductivitychannel.Asaresult,investmentratesaremuchmoresensitivetoaggregateshocksthantorm-specicshocks.Ourresultsexplainwhypartialequilibriuminvestmentmodelscannotgeneratethepatternofasymmetricresponse.Thesemodelsroutinelyassumeaconstantdiscountrate,1Whiletime-varyingexpectedreturnhasbeenwellestablishedinassetpricingliterature(e.g.,Cochrane(2001)),itsimplicationsforcorporateinvestmentseemtohavebeenlargelyunderexplored.OnenotableexceptionisLettauandLudvigson(2002).3implyingthataggregateandrm-specicshocksentersymmetricallyintorms'decisions.Inthesemodels,rmsaremoreconstrainedinbadtimes,justlikermswithlowerrm-specicproductivityaremoreconstrainedinourmodel.Ourresultsalsosuggeststhattheasymmetricresponseislikelytoshowupingeneralequilibriummodelsbecausetheirimplieddiscountratesarelinkedtoaggregateconsumptionandarethusstochastic.Indeed,Gomes,Yaron,andZhang(2003a)showthattheimpliedshadowpriceofexternalfundsisprocyclicalinseveralgeneralequilibriummodels(e.g.,BernankeandGertler(1989);CarlstromandFuerst(1997);andBernanke,Gertler,andGilchrist(1999)).Whatdrivesourmodel'spredictionthatconstrainedrmsarelessriskyandearnlowerexpectedreturnsthanunconstrainedrms?Firmsareconstrainedbecausetheirinvestmentdemandsarehigherthantheirinternalfunds.Investmentdemandsareinturndeterminedbymarginalq,thenet