Duisenberg school of finance - Tinbergen Institute Discussion Paper TI 15-036/ IV/ DSF - PDF document

Duisenberg school of finance - Tinbergen Institute Discussion Paper TI 15-036/ IV/ DSF 89Faculty of Economics and Business, University of Amsterdam, and Tinbergen Institute, Bank of Canada, Canada. Tinbergen Institute is the graduate school and research institute in economics of Erasmus University Rotterdam, the University of Amsterdam and VU University Amsterdam. More TI discussion papers can be downloaded at http://www.tinbergen.nl Tinbergen Institute has two locations: Tinbergen Institute Amsterdam Gustav Mahlerplein 117 1082 MS Amsterdam The Netherlands Tel.: +31(0)20 525 1600 Tinbergen Institute Rotterdam Burg. Oudlaan 50 3062 PA Rotterdam The Netherlands Tel.: +31(0)10 408 8900 Fax: +31(0)10 408 9031 Duisenberg school of finance is a collaboration of the Dutch financial sector and universities, with the ambition to support innovative research and offer top quality academic education in core areas of finance. DSF research papers can be downloaded at: http://www.dsf.nl/ Duisenberg school of finance Gustav Mahlerplein 117 1082 MS Amsterdam The Netherlands Tel.: +31(0)20 525 8579 Cheapbut ighty:howglobalimbalancescreatenancialfragilityToniAhnertyandEnricoPerottizMarch2015AbstractCanawealthshifttoemergingcountriesexplaininstabilityindevelopedcountries?Investorsexposedtopoliticalriskseeksafetyincountrieswithbetterpropertyrightprotection.Thisinducesprivateintermediariestooersafetyviainexpensivedemand-abledebt,andincreaseslendingintomarginalprojects.Becausesafetyconsciousfor-eignersescapeanyriskbyrunningalsoinsomegoodstates,cheapforeignfundingleadstolargerandmorefrequentruns.Beyondsomescale,foreignrunsalsoinducedomesticrunsinordertoavoiddilution.Whenexcessliquidationcausessociallosses,adomesticplannermaylimitthescaleofforeignin owsorcreditvolume.Keywords:capital ows,unstablefunding,safehaven,absolutesafety.JELclassications:F3,G2. WethankFernandoBroner,NicolaGennaioli,OlivierJeanne,AlbertoMartin,JavierSuarez,researchersattheNewYorkFedandseminarparticipantsatBankofCanada,CEMFI,theCEPR-IESEConferenceonFinancialStabilityandRegulation,theCEPR-CREIWorkshoponMacroeconomicsofGlobalInterdepen-dence,IMF,andNYUforusefulcomments.Theviewsexpressedaresolelytheresponsibilityoftheauthorsandshouldnotbeinterpretedasre ectingtheviewsoftheBankofCanada.yFinancialStudiesDivision,BankofCanada,234LaurierAveW,Ottawa,Ontario,K1A0G9,Canada.E-mail:tahnert@bankofcanada.ca.zUniversityofAmsterdam,CEPR,andTinbergenInstitute.AmsterdamBusinessSchool,Roetersstraat18,Amsterdam1018WB,Netherlands.E-Mail:E.C.Perotti@uva.nl 1IntroductionThescaleoftherecentcrisishasledtoasearchforglobalexplanations.Aleadingviewisthatexcesscreditwasdrivenbylowinterestrates,associatedwiththerecyclingoflargeglobalimbalancesintosafeUSassets.1AtatimeofdecliningUSsavingrates,thecreditboomwaslargelyfundedbyin owsseekingsafeassets,thusreducinginterestrates.PrivateliabilitiescreatedbynancialintermediarieshelpedtosatisfyademandforsafetyinexcessofthesupplyofTreasurysecurities.TheeectwasaportfolioreallocationthatincreasedtheriskconcentrationinholdingsbyUSresidents,whobecamemoreexposedtoshocks.2ThisnarrativeexplainswellhowglobalimbalancesmayleadtolargerriskbearingforUSinvestors.Itdoesnotsuggestaneectonnancialfragility,asforeignin owsareassumedverystable.Thispapershowshowsafety-seekingforeignfundingmaycreateriskbyincreasingthefrequencyofruns.Thisresultoccursunderoptimalcontractinginasimplesetupwithoutdepositinsuranceorbailouts,whenintermediariesbearallriskcreatedbytheirchoices.Itisdrivenbyspecicfeaturesofmostcapitalin owsintodevelopedmarkets,namelytheirsafety-seekingnature.Historically,capitalmovedfromdevelopedtoemergingcountries,thoughlessthanim-pliedbyneoclassicaltheory(Lucas,1990).Developingcountrieshadtoborrowinforeigncurrencybecauseofexpropriationriskassociatedwithaweakinstitutionalframework,whichcausedsuddenreversalsandnancialcrises.Incontrast,foreignershavefordecadesaccu-mulatedclaimsinreservecurrencies(GourinchasandRey,2007).Netcapital owshaveinfactreversedsince1998,withdevelopingcountriesnowfundingthedevelopedworld(Prasadetal.,2007).Estimatesonin owsintotheUSare$7:8trillionoverthe2002-2007creditboom.Inadditiontowell-recordedin owsofocialreserves,81%oftheseUSexternallia-bilitieswereheldbytheprivatesector(Forbes,2010).Thesein owsoftenseekanonymity,andarechanneledvialegalentitiesinoshorecenters. 1Bernanke(2005)discusseda\savingsglut"abroadasanexplanationforUStradedecits.2CaballeroandKrishnamurthy(2009):\[


]theUSsellsrisklessassetstoforeignersandinsodoingraisestheeectiveleverageofitsnancialinstitutions."(p.584).1 Figure1:Leftpanel:Netin owsintotheUSfromoshorecenters.AssetsownedbyoshorecenterbankinvestedintheUS(solidblue)andassetsownedbyUSbankinvestedinoshorecenters(dashedgreen).Rightpanel:CompositionofoshorecenterbankassetsinvestedintheUS.TotalinvestmentinUS(solidblueagain)andinvestmentinUSbanks(dottedred).Source:BISlocationalbankingstatistics.AllvaluesinbillionUSD.Figure1showstheremarkablegrowthofnetprivatein owsintheUSfromoshorecentersduringthecreditboom(leftpanel),andhowtheytargetedprivatelyintermediatedsafeassets(rightpanel).Thissuggeststhatastrongcomponentofforeignin owscomesfrominvestorsforwhichlegalanonymityisaformofsafety,andinvestthroughprivateinter-mediariesratherthanholdingassetsintheirownname.IdenticationrulesonUSinsureddepositsorUSTreasurypurchasesmayunderminestrictanonymity,sodirectholdingsofsafeassetsmaybeavoided.Thispaperanalyzestheconsequencesofsuchawealthshifttodevelopingcountryresidentsseekingtoinvestinmarketswithbetterprotectedpropertyrights.Largerforeignin owsarebenecial,astheysupporthigherdomesticlending.Theyaretraditionallyseenasverystable(CaballeroandKrishnamurthy,2009).Eveninthedepthofthecrisis,theUSdollarappreciated(Maggiori,2013).Ourcontributionistoshowthatdemandabledebtistheoptimalprivatecontracttoattractforeigninvestors,andhowsatisfyingtheirdemandforsafetyincreasesthefragilityofnancialintermediaries(Shin,2011).Intuitively,providingsafetytosaversunderuncertaintyrequiresoeringalessstableformoffunding.2 1980198519901995200020052010 centerbankinvested centers 1980198519901995200020052010 centerbankinvested centerbankinvested Becauserunsleadtocostlyearlyliquidation,long-termdebtwouldbedesirable.How-ever,foreignersseekingabsolutesafetywouldnotacceptsuchclaims,astheyaresometimesworthless.Thus,intermediariesneedtocarveoutanabsolutelysafeclaimfromtheirassetstoattractforeignin ows.3Theoptimalfundingarrangementisthenacombinationofsafedemandabledebtandalong-termclaimthatbearslossesinarun.Sincedomesticsaversareabletosatisfytheirsafetyneedsotherwise,theyoerinsurancebyacceptingthehighreturnriskyclaim.Thisenablesintermediariestocapturesomesafetyrents,bytargetingcheapdemandabledebttosafetyseekingforeigners.Sinceintermediariesneedenoughstablefundingtoinsuresuchinvestors,lendingmaybeconstrainedbyavailabledomesticfunding.Weshowthatundertheoptimalcontract,riskintolerantforeignerswithdrawwheneverinformationonassetvalueisimprecise,causingcostlyliquidationinsomegoodstates.Thusforeignfundingmaybecheap,butitislessstable.Theprivatefundingchoicewillacceptgreaterinstabilityinexchangeforahigherreturningoodstates.Wealsoshowthattheremaybeinsucientincentivesforarbitrageurstocounterinecientearlyliquidation.Theframeworkenablestoassesstheeectofanincreasingsupplyofforeignfundingonthescaleandriskproleofdomesticcredit.First,itleadstoaversionofexcesslending,asthemarginalprojecthasanegativeNPVatthediscountratedemandedbysavers.Second,itcreatesincreasinglylargerunsingoodstates.Thenalresultisanincreaseinrisknotjustforotherclaims,butalsointheaggregate.Theeectisnotdrivenbyanincreaseinassetriskascreditincreases,butinacombinationofalargerscaleoflendingandlessstablefunding.Theprivatechoiceissociallyinecientinthepresenceofsocialcostsofdefault.Animportanteectofincreasedcreditisthatitrealisticallyinvolveslendingagainstassetswhosevalueisincreasinglyopaque,holdingconstanttheirrisk.(Forevidenceontheroleofhousingnanceincreditbooms,seeforexampleJordaetal.,2014.)Weshowhowinoursettingthisresultsinahigherfrequencyofruns.Thusultimatelyboththescaleandfrequencyofnancialfragilityarerelatedtothescaleofnon-speculativeforeignin ows. 3Gourinchasetal.(2010)showthattheUSprovidesinsurancetotherestoftheworld,intheformofaloweryieldduringnormaltimes,andatransferofwealthtoforeigninvestorsincrises.3 Wenextconsiderthecasewhensomedomesticinvestorsholddemandabledebt,e.g.forliquidityneeds.Asthesesaversarenotriskintolerant,theywouldnotrunsimplybecauseofinnitesimaluncertainty(thatis,whentheimprecisesignalsuggestsahighstate).How-ever,weshowthatonceforeignfundingreachesacertainscale,itwillinducealsodomesticdepositorstoruninthesecircumstances.Thisresultarisesnotoutorriskavoidance,butinordertoavoiddilutionoftheirclaim.Finally,weconsiderwhether\safe"domesticintermediaries(suchasmoneymarketfunds)mayinvestonbehalfofforeignersindomesticsafeassetstoavoidruns.Aslongasthemonitoringofassetchoiceisimperfect,leveragedintermediariesalwayshaveanincentivetoinvestinriskyassets,andcannotcrediblyprovideabsolutesafetyviatheirassetsholdings.KacperczykandSchnabl(2013)documenttherisk-takingbehaviorofmoneymarketfundsduringthenancialcrisisof2007{2010.Thesimplesetupallowsalimitedwelfareanalysis.CheapforeignfundinginducesahighercreditvolumeintomarginalprojectswithanegativeNPVatdomesticrates,subsi-dizedbytheinsurancepremiaearnedfromforeigners.Thisisecientunderlinearprefer-ences,unlesstherearesocialcostsofexcessliquidation.Weshowhowasociallyoptimalbalancebetweenstabilityandaggregatecreditwilldierfromtheprivatechoice.Thenourapproachmayrationalizemacroprudentialpoliciestargetingshort-termforeignin ows,suchasasystemicrisktaxonnon-corefunding(Hahmetal.,2013),tocomplementthecapitalandliquidityrequirementsproposedinBaselIII.Inthiscontext,publicguaranteesmaybedamaging,astheincreasedriskabsorptioncapacitywouldallowbankstoattractmoreunstablefunding.Thiswouldshiftbothexogenousandendogenousrisktopublicinsurance.Themodeldoesnotseektooerafullanalysisofportfoliochoice.Weassumethatforeignerswhogainedsafetyviadomesticclaimsinvestanyresidualwealthintheirowncountry.Thismayre ectsomeadvantageinlocalinformation,whichensuresthemahigherreturnevenundersomeexpropriationrisk.4 LiteratureDemandforabsolutesafetyinourapproachisrationalizedbyaminimumsubsistenceconstraint.Uptothisthreshold,agentsactasinnitelyrisk-averseastheyneedtosecuresomeessentialneeds.Suchpreferencesareconsistentwithrecentevidenceonthestrengthandstabilityofdemandforsafeassets(KrishnamurthyandVissing-Jorgensen(2012);Gortonetal.,2012).Recentworkhasmodeledsuchdemandasarisingfrominnitelyrisk-averseagents(CaballeroandFarhi,2013).Inthepresenceofneglectedrisk,theycancauselargeshocks(Gennaiolietal.,2013).Gennaiolietal.(2013)pioneeredthenotionoflowprobabilityriskdrivingrunsbyinnitelyriskaverseinvestors.Inoursimpleversionthisriskisalwayssalient,butconsiderednegligiblebysomesetofagents.AstrictsegmentationbetweensavingsandinvestmentmarketsismodeledinAllenetal.(2014).Segmenteddemandmayarisefromnon-contingentpreferenceforliquiditytobackpayments,theclassic\moneyintheutilityfunction".Asmoney-likeclaimsoertransactionservices,theyarecheapertoissue(Stein,2012).Thisprivateincentivetooerliquidclaimsneedstobebalancedagainstanyilliquidityexternality,suchasresales(PerottiandSuarez(2011);Stein,2012).Inourapproach,demandabledebtarisefromriskintoleranceratherthantransactionorliquidityservices,thoughabriefextensionconsiderstheinteractionbetweenthetwomotives.OurapproachisconsistentwiththeempiricalresultsinKrishnamurthyandVissing-Jorgensen(2013)ontheeectofchangesinthesupplyofgovernmentsafeassets.Adecreaseleadsnotjusttoanincreaseinnetshort-termnancialdebt,butalsoanincreaseinlong-terminvestmentsnetoflong-termfundingbynancialintermediaries.Here,thecreditexpansionisboostedbyabundant,lessexpensivefundingsupply,andisassociatedwithanincreaseinmaturitytransformation.Ourpapercomplementsarichinternationalnanceliteratureonthe\originalsin".Mostcapitalin owsindevelopingcountriestaketheformofshort-termforeignloansbecauseofpoliticalrisk(EichengreenandHausmann,1999).Tirole(2003)explainssuchdemandableclaimsasadisciplinarydevice,re ectinggreateragencycostinacontextofpoliticalrisk.Ourresultsderivedirectlyfromthenatureofforeigninvestmentintosafehavens,inacontext5 ofsymmetricbutimpreciseinformation.Acriticalassumptionintheliteratureisthatforeignersneedanintermediarytoaccessdomesticassets(CaballeroandKrishnamurthy,2009).Inoursettingthismaybejustiedbytheneedforsafe-keeping,orfortheanonymitygainedbyinvesting(possiblyviaanoshorecenter)intoadomesticlegalentity.4OcialdatasuggeststhatthecompositionofUSnetexternalassetsisskewedtowardsriskyassets,whileforeignersinvestinsafedollarassets.Thereisabundantevidencethatforeignersseekingsafetyacceptalowerratesofreturn(Caballeroetal.,2008).Forbes(2010)ndsthatforeigninvestorsintheUSearnlessthanUSinvestorsearnabroad,evenafteradjustingforexchangeratemovementsandroughmeasuresofrisk.ForeignerswithlessdevelopeddomesticbondmarketsinvestcomparativelymoreintheUS,conrminganeedforsafety.ThehistoricalaccumulationofUSdecitsnetofocialreservessuggestsasubstantialbuild-upinthestockofforeigncapital,thoughgranularevidenceisimpairedbyapreferenceforanonymity.However,newevidencelinkspoliticalriskinspeciccountriestocapital ightintosafehavens(BadarinzaandRamodorai,2014).Mendozaetal.(2009)showhowcountrieswithbetterprivatecontractualenforcementbenetbyattractingforeigninvestmentin ows,andareabletoexplaintheirdecliningnetassetholdings.Ourapproachiscomplementaryaswehighlightdierencesinprotectionfrompublicexpropriation,andthusdescribenonspeculativecapital ows.Ourassumptionofasubsistencelevelinpreferencesmaybeseenasanextremeversionofhabitformationmodels,whicharewellsupportedbyevidenceinassetpricingandmacroe-conomics.5Intuitively,asagentsbecomewealthier,theyadjusttheirlifestylerequirementsorincreasetheirobligations,requiringahigher\safe"componentofwealth.ThismayalsoexplainthestableshareofUSsafeassets(Gortonetal.,2012).Underthisinterpretation,thedemandforsafetyfromemergingcountrieswillincreaseastheybecomewealthier.Hence,bothcreditvolumeandinstabilityincountrieswithgoodpropertyrightswouldrise. 4Secrecyisahallmarkofcapital ight.In2011,a$32bndiscrepancywasreportedinAngola'snationalaccounts,widelyattributedtorentextractionfromitspoliticalelite.Estimatesofannualcapital ightfromRussiaareamultipleofthisamount.Taxevasionandmoneylaunderingareotherreasonsforanonymity.5HabitformationinAbel(1990)andCampbellandCochrane(1999)oeranexplanationfortimeseriesanomalies,suchasthesizeoftheequitypremium.Fuhrer(2000)usesittoexplainthe`hump-shaped'gradualresponseofspendingandin ationtoshocks.6 Oursettingderivesdemandabledebtasanoptimalcontracttosatisfysaversseekingabsolutesafety.Traditionally,demandabledebtisexplainedbycontingentliquiditydemand(DiamondandDybvig,1983),alsoessentialfortheadverseselectionapproachinGortonandPennacchi(1990).Inatwo-periodsetting,demandforliquidityisindistinguishablefromsafetydemandforearlywithdrawals.6Alsointhisapproachinvestorpreferencesareextreme,assomesaversvalueconsumptiononlyattheinterimdate.However,latewithdrawingsaversmaysuerdefault,whichisincompatiblewithabsolutesafetypreferences.Suchpreferencesalsocreatelargescaleinstabilityundersalientbeliefsonrisk(Gennaiolietal.,2013).Demandabledebtisalsorationalizedasanoptimalcontracttoresolveagencycon icts(DiamondandRajan(2001);CalomirisandKahn,1991).InDiamondandRajan(2001),demandabledebtrunsactasathreattocontrolagency.Thepresenceofjitteryinvestorsmakesthisthreatcostlysincerunsmayoccurinsolventstates.2ModelTheeconomyextendsoverthreedatest2f0;1;2g.Itispopulatedbydomesticandforeignsaversandacontinuumofdomesticintermediariesi2[0;1]thatraisefundingfromsavers.EachintermediaryhasaccesstoaspecicpoolofriskyinvestmentIi0thatyieldsR(I)withprobability 2(0;1)atthenaldate(highstate)andzerootherwise(lowstate).Liquidationattheinterimdateyields2(0;1)inallstates,soliquidationisecientinthelowstate.Investmenthasdecreasingreturnstoscale,whereR0(I)0andR00(I)0.Thus,marginalrevenueinthehighstate,MR(I)IR0(I)+R(I),decreasesininvestment.Attheinterimdatethereisalwaysanimprecisepublicsignalabouttheinvestmentreturn.Inaddition,inthehighstate,thereisaprecisesignalwithprobability2(0;1)(contingencyG).Ifthereisnoprecisesignal,someresidualuncertaintyremains.Theimpre-cisesignalmaycorrectlysuggestthatthestateishigh(contingencyM)orlow(contingencyB),butisincorrectwithprobability&#x]TJ/;༗ ;.9;Ւ ;&#xTf 1;.93; 0 ;&#xTd [;0(contingenciesXandE).Figure2summarizes. 6Inadynamicconsumptionsmoothingsetup,liquidityneedscannoteasilyexplainthehugestockofdemandabledebtheldbyhouseholds.7 Figure2:Theinformationsstructureofthemodel.Forsimplicity,henceforthweassumethatuncertaintypersistsonlyaftertheimprecisesig-nalsuggeststhehighstate(soweeliminatecontingencyX).7Therefore,conditionalonnoprecisesignal,theBayesianprobabilityofthehighstateis (1�)(1�) (1�)(1�)+(1� )1.AllsaversneedabsolutesafetyforaminimumamountS2(0;1)oftotalconsumption,anamountrequiredforsubsistence.Oncethislevelisattainedineitherperiod,saversactasrisk-neutralinvestorswithnotimediscounting,wherectdenotesconsumptionatdatet:U(c1;c2)=8&#x]TJ/;༗ ;.9;Ւ ;&#xTf 1;.42; 0 ;&#xTd [;&#x]TJ/;༗ ;.9;Ւ ;&#xTf 1;.42; 0 ;&#xTd [;&#x]TJ/;༗ ;.9;Ւ ;&#xTf 1;.42; 0 ;&#xTd [;&#x]TJ ;� -2;
.51; Td;&#x [00;&#x]TJ ;� -2;
.51; Td;&#x [00;&#x]TJ ;� -2;
.51; Td;&#x [00;:c1+c2c1+c2Sif�1c1+c2S(1)Foreignsavershaveworseaccesstoasafestoreofvalue,re ectingalowerdegreeofpropertyrightprotectionintheircountry.Domesticsavershaveaccesstosafeshort-termstoragewithunitreturnattheinterimdate,andtolong-termstoragewithreturnT&#x-278;1atthenaldatethatcannotbeliquidatedearly.Incontrast,thereturnon(short-orlong-term)foreignstorageisx2[S;T).Therefore,foreignsaverscansatisfytheirabsolutesafety 7Whileasymmetricallyimprecisesignalismoregeneral,ourresultsareinvarianttothissimplication.8 StatesignalContingency needsviaforeignstorageorbyinvestinginadomesticintermediary.AsinCaballeroandKrishnamurthy(2009),weabstractfromforeigners'riskyinvestmentbyassumingittakesplaceintheirowncountryandfrominvestmentabroadbydomesticsavers.Table1summarizestheendowmentsattheinitialdate.Foreignsavershaveaunitendowment,sotheirmassWmeasurestotalforeignwealth.Asanormalization,theunitmassofdomesticsaversisendowedwith1+S=T.AsdomesticsaverssatisfytheirabsolutesafetyneedslocallybyinvestingS=Tinlong-termdomesticstorage,oneunitofdomesticwealthisavailabletoinvestinriskyclaims.ItsrequiredreturnistheopportunitycostT. Agents Mass Endowment Foreignsaver W 1 Domesticsaver 1 1+S=T Banker 1 0 Table1:Agentsandendowments.Theexpectedmarginalrevenueofinvestmentis MR(I)+(1� )(1�).Weassumethatinvestmentinitiallydominateslong-termstoragebut,becauseofdecreasingreturns,domesticfundingsucesforecientinvestmentinautarky: MR(0)+(1� )(1�)�T� MR(1)+(1� )(1�)(2)Theresidualdomesticendowmentisstoredlong-termtoequalizetheexpectedmarginalrevenue,soautarkyinvestmentIAut2(0;1)satises MR(IAut)+(1� )(1�)=T.Attractingcheaperfundingfromabroadenablesalargerscaleofecientinvestment.Intermediariesaresubjecttolimitedliabilityandmaximizetheexpectedvalueofeq-uity,equaltoinvestmentproceedsafterdebtpayments.Investmentreturnsarepubliclyobservableatthenaldatebutnon-veriable,sowerestrictattentiontodebtcontracts(HartandMoore,1998).Whenfundedwithdemandabledebt(sothatintermediariesarebanks),weabstractfromrunsbasedonpurecoordinationfailure(AllenandGale,1998).Wenextconsidertheoptimalfundingarrangement.Eachintermediaryhasuniqueaccesstooneunitofdomesticfundingdi1,providedtheexpectedreturnoeredisno9 smallerthanT.(Thiscouldariseinamodelofspatialcompetitionwithsomedis-utilityofdistance.)IntermediariescompeteforforeignfundinginaWalrasianmarket.Attheinitialdate,eachintermediarymayoerclaimstoraisedomesticfundingdi0andforeignfundingfi0inordertoinvestIidi+fi.Weclosethedescriptionofthemodelwithanobservationsabouttheintermediaries'abilitytooerabsolutesafety.Inordertoattractforeignfunding,anintermediaryhastoensurefullrepaymentalsointhelowstate.Ifforeignsavershadverypoorownstorageoptions,x,theirrequiredreturnissatisedwithoutinsurancefromotherlendersevenincaseofearlyliquidation.Inthisextremecase,foreignsaversactuallyprovideinsurancetodomesticsavers.Wehenceforthexcludethiscasebyassumingx.BenchmarkWeestablishrstthebenchmarkwhenagentsareperfectlyinformedinallstates(!0).Banksalwaysterminateinvestmentecientlyinthelowstate,ensuringareturnof.Lemma1summarizestheoptimalfundingarrangementinthiscase.Lemma1Debtseniorityunderecientliquidation.Underperfectinformation(!0),theoptimalfundingcontractisamenuofseniorlong-termdebtandjuniorlong-termdebt.Foreignsaversselectseniordebt,whiledomesticsaversselectjuniordebt.ProofSeeAppendixA.Thebenchmarkoptimalfundingcontractusessenioritytoensuretheabsolutesafetyofforeignfunding.Domesticsaversreceiveahigheryieldtocompensatefortheirsubordination.Incentivecompatibilityholdssincedomesticsaverspreferthehigherexpectedreturnofthesubordinateddebtcontract,whileforeignsaversseektheabsolutesafetyofseniordebt.Long-termdebtprecludesthepossibilityofinecientliquidationattheinterimdate,triggeredbysafety-seekingforeignsaverswhentheprecisesignalisnotobserved.10 3Unstablein owsandendogenousriskWeturntothemainmodel,whereagentsmakeraremistakesinthelowstate.Asaresult,seniorlong-termdebtleadstoacompletelossincontingencyE,violatingtheabsolutesafetyneedsofforeignsavers.Thisalterstheoptimalfundingcontractradically.Proposition1Optimalfundingcontracts.Supposeinvestmentisnotalwaystermi-natedinthelowstate(�0).Domesticfundingisattractedwithlong-termdebt.Foreignfundingcanonlybeattractedwithdemandabledebt,providedasucientamountofloss-absorbingdomesticfundingisattractedtooerabsolutesafetyinthelowstate.Foreignsaverswithdrawearlyunlesstheprecisesignalisobserved.Theoptimalcontractingproblemisfairlysimpleinthisenvironment.Foreignsaversneveracceptthelong-termdebtcontractwithfacevalueLasitdoesnotprovideabsolutesafety.However,theyacceptdemandabledebt,providedthereabsolutesafetyneedsaremetinallcontingencies.Therefore,thebank'sabilitytooerabsolutesafetyrequirestheliquidationvaluetobehighenoughtocoverthedemandabledebtclaim:Iixfi;(3)whichrequiresasucientamountofloss-absorbingdomesticfunding,dix� fi.Underthiscondition,theintermediarycanoerabsolutesafetytoforeignsaversinallcontingen-cies.However,thesafety-seekingnatureofforeignfundingcreatesnancialfragilityundertheoptimalfundingcontract.ToavoidthecompletelossincontingencyE,foreignsaverswithdrawwhenevertheprecisesignalisnotobserved.Corollary1Ifforeignfundingisattracted,therearesometimesrunsinthehighstate,leadingtotheliquidationofinvestment.Whileliquidationisecientinthelowstate,thesewithdrawalscreateaneciencylossincontingencyM,whichincreasesinthescaleofforeignfunding.Undertheoptimalfundingcontract,thepromisedamountforearlywithdrawalsissetaslowasconsistentwithabsolutesafety.11 Whileattractingforeignfundingundertheoptimalcontractingenablestoexpandin-vestment,italsocausesearlywithdrawalswheneverthereisuncertaintyaboutthehighstate.Thisdenesabasictrade-obetweencostandstabilityofforeignfunding.Theresultindicatesthatdomesticintermediariesattractforeignfundingonlyifitslowcostcompensateforthelossescausedbysafety-seekingrunsincontingencyM.WhiledemandabledebtrunsalsoforceecientliquidationincontingencyE,thisexpectedbenecialeectisinnitesimalrelativetoitsaveragecost.Table2summarizesallpayoswhenforeignfundingisattracted. State Probability Return F D Bi G  R(Ii) X L RIi�Ldi�Xfi M (1�) R(Ii) x minL;RIi�R xfi di maxfRIi�R xfi�Ldi;0g B (1� )(1�)  x minL;Ii�xfi di maxfIi�xfi�Ldi;0g E (1� ) 0 x 0 0 Table2:Payoswhenforeigncapitalisattracted.DandFarethepayostodomesticandforeignsavers,respectively,whileBiisthepayotobanki.Weconsidernowthesupplyanddemandforforeignin ows.ForeignsaverscansatisfytheirabsolutesafetyneedsbyinvestingS xinself-storage,orinademandabledebtcontract(X1;X2)withreturnofatleastxinallcontingencies.ThefacevalueofdemandabledebtatthenaldateX2XmayexceedX1xifthereisstrongcompetitionforforeignfunding.Lemma2Supplyofforeignfunding.Foreignfundingissuppliedundertheconditionthattheintermediarycanoerabsolutesafety.Underthiscircumstance,foreignfundingcanbeattractedwithdemandabledebtoffacevalues(x;X).Theaggregatesupplyis:f(X)=8���&#x]TJ ;� -2;
.52;&#x Td ;&#x[000;&#x]TJ ;� -2;
.52;&#x Td ;&#x[000;&#x]TJ ;� -2;
.52;&#x Td ;&#x[000;:0Xx0;WS xifX=xWS xX�x(4)Bank'sfundingchoiceTheprivatelyoptimalfundingchoicemaximizesthebank'sex-pectedprot,equaltoexpectedinvestmentreturnnetoffundingcosts.DomesticfundinghasanaveragecostofT.ForeignfundingcostsXincontingencyG,R(Ii) xincontingencyMduetocostlyliquidation,andxincontingencyB.(IncontingencyE,thebankisbankrupt).12 Lemma3Demandforfunding.Theintermediarychoosesonlydomesticfunding(au-tarky)ifuncertaintyistoohigh.Incontrast,if� 2(0;1),thereexistsauniquethreshold XT �(1� )(1�) x�1� x R(IAut)suchthat:Ifforeignfundingisexpensive,X X,autarkyisoptimal:fi=0anddi=IAut.If X�XX x MR�x x�
�x� T ,thesafetyconstraintbinds:di=�x� 
fi.Bothdomesticandforeignfundingisattracted,wherefiisuniquelydenedby: MRx fi=T+ xh X�Ti:(5)Inthisinteriorsolution,theexpectedmarginalrevenueofinvestmentequalstheexpectedmarginalcostofbothdomesticandforeignfunding.Ifforeignfundingischeap,XX ,thecornersolutiondi=1andfi= x�obtains.Theintermediaryraisesthemaximumamountofforeignfundingconsistentwithabso-lutesafety,giventhelimitedamountofdomesticfunding.ProofSeeAppendixB,whichalsocontainsthedenitionof .Uniquenessfollowsfromthedecreasingmarginalrevenueofinvestment.Aggregationisstraightforwardunderacontinuumofidenticalintermediaries,sofRi2[0;1]fidianddRi2[0;1]didi.Wenowstatetheequilibrium.Proposition2Uniqueequilibrium.Considerthecaseofsmallmistakes�0andsucientlylowuncertainty,� .Thereexistsauniqueequilibriumifforeignwealthisabundant,W�W 2(0;1),wherethislowerboundisimplicitlydenedby: MRS W + (1�)R(IAut)+(1� )(1�)=T:(6)ProofSeeAppendixC.13 Figure3:Equilibriuminthemarketforforeignfunding:supply(straightblue)anddemand(dashedgreen).Theleftpaneldepictstheunconstrainedcase,whilethelimitedsupplyofdomesticfundingmaybindintherightpanel(X �x).Corollary2summarizesthetwopossiblecases,illustratedinFigure3.Corollary2UndertheconditionsofProposition3,theamountofsafetyseekingforeignwealthdeterminestheequilibriuminthemarketforforeignfunding.IfX �x,therearetwocases:IfW W W Sx x�,theequilibriumisinterior:foreignfundingisfi=f=WS xanddomesticfundingisdi=d=x� xWS2(0;1).Theequilibriumfacevalueofdemandabledebtis:X=x MRS W�x� T (7)IfforeignwealthisabundantW W,thecornersolutiond=1andf= x�occurs.Inthiscase,theamountofinexpensiveforeignfundingthatcanbeattractedislimitedbytherisk-absorptioncapacityofdomesticfunding.IfX x,thereisaninteriorequilibriumwithadierentupperboundonforeignwealth:MRS  W=x� xT +:(8)14 f f Wecannowassesstheriskcreatedbysafety-seekingforeigncapital.Proposition3Financialfragility.Whenforeignfundingisattracted,withdrawalsbyforeignsaversleadtofullliquidationofinvestment.Theresultingeciencylossincontin-gencyMequalstoS R�S W
WforW2(W ; W)andtoR�x x�
x x�forW W.ProofSeeAppendixD.Corollary3ForeignwealthandnegativeNPV.Wheneverforeignfundingisattracted,thevolumeofdomesticinvestmentincreasesinforeignwealth,whileitsnetpresentvalueatdomesticdiscountratesdecreasesinforeignwealth.IfX xand R�x x�
+(1� )(1�)T,thenthereexistsauniquewealththresholdW2�W ; W
suchthatthenetpresentvalueofinvestmentisnegativeatdomesticdiscountratesforallW�W.ProofSeeAppendixE.Wecannowsummarizetheaggregateeectofcapitalin ows.Underourinitialassump-tion,condition(2),theNPVofinvestmentinautarkyispositive,NPVAut IAut(�R0(IAut) T�0.Whilenotanessentialassumption,itensuresthatsomecapitalin owsareecient.Ifforeignwealthisabundantandthusforeignfundingcheap,investmentexpandsuntilitearnsanegativeNPVatdomesticdiscountrates.Notethatthisinducedexpansionincreditisecientunderlinearpreferences:foreigncapitalinducesmorecreditnotjustbecauseitexpandsavailablefunding,butbecauseitreducesitsmarginalcost.Asinvestorswhosupplycheapforeignfundingaresatised,theirmarginalrequiredrateofreturnbecomestheappropriatediscountratefordomesticbanks.15 4Extensions4.1UncertaintyoverassetreturnInoursetup,impreciseinformationmayleadtorunsbyriskintolerantinvestors,sointerme-diarieshaveanincentivetoprioritizemore\transparent"assets.Westudyheretherealisticcasewhenlendingmorerequiresinvestinginmore\uncertain"assets.Tokeepourfocusdistinctfromthetraditionalriskshiftingincentiveinbanking,weassumethatmorelendingdoesnotinvolveinherentlyriskierassets,butassetsthataremoreopaque.Thisnotionisconsistentwithevidencethatcreditboomstendtofundrealestateinvestment.Specically,assumethatuncertaintyoverassetvaluesatt=1increasesinthecreditvolume,asthechanceofaprecisesignalfalls.Thisimplies=(Ij)withd dIj0.Itiseasytoshowthatthisleadstoagreaterfrequencyofruns,sincecontingencyMoccursmoreoften.Astheintermediarybearsallcost,theimpactofmoreopaqueinvestmentisfullyinternalized,anditisstraightforwardtogeneralizetheresultsofLemma3.Theautarkyallocationisnotaected,giventhatonlylong-termdebtisoeredtodomesticsavers.AutarkyisnowoptimalwheneverXXT�(1� )(1�)x� (1�(IAut))x R(IAut) (IAut):(9)Ifforeignfundingischeap,XX,theintermediarywouldstillattractasmuchforeignfundingaspossible,constrainedbytheabsolutesafetyconditionfi= x�di.Thenewlevelofforeignfundingraisedfi(X)isimplicitlygivenby: (Ii)MR(Ii)=T+ xh X�T� 0(Ii)x R(Ii)�Xi:(10)Relativetothebaselinecase,nowamarginalincreaseinforeignfundedinvestmentleadstomorefrequentliquidationinthehighstate.Sincethebankernowincursmorefrequentcostlyliquidationduetoforeignruns,itschoiceofthescaleofforeignfundingislower.16 Thisnaturalextensionshowshowrisk-intolerantforeignfundingislikelytoincreasethefrequencyofruns,inadditiontotheirscale.4.2SocialcostofexcessiveliquidationOurcontractingresultwithitstrade-obetweenthecostandstabilityoffundingistheoptimalchoiceforriskneutralintermediaries.Aproperwelfareanalysismustconsiderthepossibilitythatthisprivatechoicehassocialconsequences.Asidefromriskaversion,anaturalcaseinoursetupisthatexcessliquidationmaycausesomesocialcostsassociatedwithearlytermination.Runsmayinvolvebankruptcycosts.Largerrunswillaecttheliquidationpriceofassets,orunderminecondenceindomesticintermediaries,bothcausinganegativeexternalityeect(Stein,2012).Weconsiderherethesimplecaseofasocialcostofexcessliquidation�0perunitofassetsterminatedearly,inthegeneralcasewithendogenousuncertaintyoverassets(asinthepreviousextension).Recallthatinthecaseofautarky,therearenosuchcostsasfundingislongterm.Weexcludeanycostinthecasewhenliquidationisecient,namelyinthelowstate.Considerrsttheinvestmentandfundingchoiceofaconstrainedplanner.Theplanner(P)internalizesthesocialcostofexcessliquidation,takingthesupplyofforeignanddomesticfundingasgiven(thatis,itisawareoftheabsolutesafetyconstraintofforeignsavers).Forsucientlycheapforeignfunding,thesocialoptimumofinvestmentIP(andthusthevolumeofforeignfunding,fP)isgivenby: (IP)MR(IP)=T+ xh X�T� 0(IP)x R(IP)�Xi+socialcostz }| {h (1�(IP))� x 0(IP)fPi:(11)Relativetotheprivatechoice,theplanner'sproblemincorporatesthesocialcostofexcessiveliquidation.Itiseasytoseethatthisimpliesalowervolumeofcredit,andagreaterdegreeofstability.Inparticular,thesocialdemandforforeignfundingislowerthantheprivate17 demand,sincethesocialcostofinvestmentexceedstheprivatecostbythehighlightedamountinequation(11).Supposeloss-absorbingdomesticisnotconstrained(sodP1)andforeignwealthisabundant(sothecostofforeignfundingisX=xevenintheprivateequilibrium).Theplannerthenchoosestoattractlessforeignwealthinordertoreduceliquidationvolumesinthehighstate.8Thesecondbenetfromareducedintermediationvolumeisalowerfrequencyofruns,asassetuncertaintyislower(contingencyMoccurslessoften).Figure4showsthiscase. Figure4:Thesocialandprivateoptimumofforeignfunding.ThecostXversusthevolumeofforeignfundingf.Thesupplyofforeignfundingisagainthestraightblueline,whereastheprivateandsocialdemandforfundingarethedashedgreenanddashedredlines,respectively.ThecaseofX xisdepicted.Theimplicationisthatmoreforeignfundedcredithasadirecteectnotjustontheamountbutalsothefrequencyofexcessliquidation,bothcontributingtosystemicrisk.Thuscapitalrequirementshouldbecomplementedbystablefundingnorms(asenvisionedintheBaselIIIrecommendations,sofarnotintroduced),thatrecognizethelowerstabilityassociatedwithsafety-seekingforeignin ows.Inaddition,thecalibrationofliquidityrisk 8Ifforeignwealthisscarce,thedownwardshiftinthedemandforforeignfundingdoesnotaecttheallocation,butreducesthecostofforeignfunding(verticalsupplycurve).Ifaccessofforeignsaverstosafestoragewereheterogeneous,theresultwouldagainbelesscredit,aswellaslowerforeignfunding.18 f weightsshouldrecognizethesensitivityofout owstoassetopaqueness,asdistinctfromassetliquidity.4.3PrivatearbitrageWeconsidernextwhetherdomesticinvestorscouldresolvetheinecientliquidationbyactingasarbitrageurs,relyingontheirsuperiorriskabsorptioncapacityrelativetoforeigners.Thisentailsstoringsomeresourcesuntiltheinterimdate,whichhasanopportunitycostofthetermpremiumT�1.Thesearbitrageurscouldbuyclaimsfromwithdrawingforeignsaverswhentheimprecisesignalindicatesahighstate,andnegotiatewiththebanktoappropriatetheprotfromavoidingliquidationincontingencyM.Considerthemaximumpossiblebenetfromthisposition,namelywhenthearbitrageurhasallthebargainingpower.Anarbitrageurwithaunitofcapitalatt=1canbuy1=xunitsofrunningdemandableclaimsincontingenciesMandE(recallthatthereremainssomeresidualuncertaintywhentheimprecisesignalispositive).Next,theseclaimsmaybetradedforalong-termclaimworthatmostR(I) xperclaim.ThisstrategygeneratesR(I) incontingencyM,whichoccurswithprobability (1�),andacompletelossincontingencyE,wherethestateislow.ForanygivenI,asucientconditiontoexcludethepossibilityofdomesticarbitrageursis:T�1� (1�)R(I) :(12)Insum,aprivatesolutiontotheineciencyalwaysfailswhenitsopportunitycost(thetermpremium)exceedsthemaximumexpectedgainincontingencyM.Formoregeneralbargaininggames,orinthepresenceofspeciccosts,theconditionwillbelessstringent.Notethatitisimpossibleforthearbitrageurtoleverupinordertoincreaseitsexpectedprots.First,foreignfundingcannotbeattractedasthearbitrageurmakesomeinnitesimalerrors.Second,otherdomesticsavershavethesameopportunitycostT�1.19 4.4Moneymarketmutualfundsandrisk-takingincentivesWehavesofarassumedthatdomesticintermediariescannotinvestdirectlyinsafestorage,becausetheyseekanonymity,orbecausedomesticsafestoragerequiressomelocaleort(e.g.forsafekeepingormaintenanceofarealasset).Alternatively,safetydemandbydomesticorforeignsaversmayhaveuseduptheavailablestock.Inthiscase,safeassetsmustbecarvedoutofriskyinvestmentbyintermediaries.Considerthecasewhenthereisnoexcessdemandforsafety,inthesensethatsomeamountofliquidsafeassetsisavailableforinvestment.Thiscreatestheoptionfordomesticintermediaries,suchasmoneymarketmutualfunds,toinvestingovernmentdebttosatisfysomesafetydemand.Supposetheseintermediariescaninvestinlong-termstorage,withasafereturnofT.Competitionamongsuchintermediarieswillimprovereturnsforforeignsaversuntilthesupplyofsuchsafeassetsisfullyexhausted.Beyondthispoint,theoutcomewillbeasinourmodel.However,thissolutionisfragileinacontextofextremeriskaversion.Supposethereisatinychancethattheassetchoiceisnotfullyobserved(governancerisk),andthattheseintermediariescanaccessthesameinvestmentopportunitiesasbanks.Becauseoftheirleverage,theseintermediarieshaveanincentivetomakesomeriskyinvestment,sinceitsreturnexceedsT.Asaresult,suchintermediariescouldnotattractsafety-seekingforeignfunding.KacperczykandSchnabl(2013)documenttherisk-takingbehaviorofmoneymarketfundsduringthenancialcrisisof2007{2010.4.5InducedrunsWeconsidernowtheeectofforeignfundingondomesticsaversholdingdemandabledebt.Supposeamass!�0ofdomesticsaverschoosesademandableclaim,duetoexogenousreasonssuchaseaseofpaymentortimingofliquidityneeds.Let betheliquiditydis-countthatdomesticsaversarewillingtoaccept,where1� x,sothattheyacceptthedemandabledebtcontracttargetedatforeignin ows.Forsimplicity,theavailableamount20 ofrisk-absorbingdomesticfundingisunchanged,ensuringanunchangedcapacitytoinsuresafety.Asaresult,somedemandabledebtisheldbyrisktolerantdomesticsavers,whomaychoosetorollovertheclaimevenwhenthereisonlysomesmalluncertaintyoverthehighstate(thatis,whentheimprecisesignalsuggestsassetvaluesarehigh).Thosedomesticsaversoptimallychoosetorolloverif: (1�)(1�) (1�)(1�)+(1� )minnX;R(I)I�R(I)x fX !X+Lox:(13)wherethersttermistheprobabilityofthehighstateconditionalonafavorableimprecisesignal;thesecondisthepromisedreturnXatthenaldate,ortheirexpectedshareoftheresidualprojectreturnincaseofdefault.(Aunitmassofdomesticsaverswithlong-termdebtoffacevalueLandamass!ofdomesticsaverswithdemandabledebtoffacevalueXreceiveanequalshareoftheproceeds,netofliquidationrequiredtoserveforeignsavers.)Thisallowstostudythecomparativestaticofanincreaseinthesupplyofunstableforeignfunding.Inequilibriumthishasseveraleects.First,moreforeignfundingreducestheequilibriumfacevalueofdemandabledebtatthenaldate,X.Second,itincreasestheamountofforeignfundingfattractedinequilibrium,whichleadstolargerrunsandthusmorecostlyliquidationincontingencyM.Third,therewillbeamarginaleectoninvestmentvaluebecauseofdiminishingreturns.Itisimmediatetoseethatalltheseeectsincreasetheincentivesofdomesticsaverstowithdrawattheinterimdate.Itiseasytoshowthatthereisathresholdlevelofforeignfundingsuchthatinequilibriumdomesticsaverswithdrawtheirdemandabledebtwheneverthereisuncertainty,andthusevenwhenassetvalueisalmostcertainlyhigh.Inconclusion,anincreasingrelianceonunstableforeignfundingmayfeedintogreaterinstabilityofdomesticfundingeveninthegoodstate,astheyanticipatelargelossesduetoaforeignrun.Herethelocalsaversarenotdrivenbyriskintoleranceastheforeignsavers,butbytheincentivetoavoiddilutionoftheirclaim.21 5ConclusionThispaperhassoughtafoundationforthewidespreadviewthatglobalimbalancesshapedthecreditboomandultimatelythenancialcrisis(CaballeroandKrishnamurthy,2009).Weshowhowtheaccumulationofwealthincountrieswithaweakprotectionofpropertyrightscreateademandforabsolutesafetytobeprovidedbyintermediariesinsafecountries.Theoptimalcontractualarrangementshapesthefundingstructureofdomesticintermediaries,creatingaclearlinkbetweeninexpensivefunding,creditexpansionandinstability.Ourmainresultisthatpressuretoprovideabsolutesafetydoesnotjustredistributeriskamongsavers,butincreasesriskvialargerandmorefrequentruns.Thisresulthasclearpolicyimplications,asthesociallypreferredfundingstructurewouldinvolvelesscreditvolumeandlowerinstabilitythantheprivatechoice.Whilelargeglobalimbalancesre ectmajorshiftsinwealthawayfromdevelopedcoun-tries,alargefractionhas ownbackasinexpensiveliabilitiesofdomesticintermediaries,enablingtoexpandcreditattimesofdecliningsavings.Weshowthatthesafetyseekingnatureofthese owsmakesthemjittery,drivenbyaheightenedintoleranceforrisk.Thusthefundingshiftleadstogreatervulnerabilityeveninsolventstates,andmayinducerunsevenbyrisktolerantinvestorsseekingtoavoiddilution.Studyingin owsintodevelopedcountriesisspeculartotheliteratureonsuddencapitalout owsinemergingeconomies.Ourcontributionistoderiveoptimalcontractualformsshapedbyanunderlyingdemandforsafety,andtoshowhowitmaycreateendogenousruns,asinrecentworkbyGennaiolietal.(2013).Adistinctcontributionistoshowhowinecientrunsmaybetriggeredbyriskintoleranceevenwhenatinyprobabilityoflossesisfullyanticipated.Infuturework,weplantobroadenthesimpleframeworkadoptedheretoaccommodateamoregeneralviewofportfolio owsacrosscountrieswithdierentinstitutionalquality.22 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AProofofLemma1Considerthesupplyoffundingrst.Domesticsaverssatisfytheirabsolutesafetyneedslocally,sodomesticfundingdi2[0;1]canbeattractedbyintermediaryiwithaclaimthatyieldsatleastTinexpectation(asdoeslong-termdomesticstorage).Thisisbestachievedwithlong-termdebt,sincedomesticsaverswhoseekexpectedreturnhavenoincentivetowithdrawprematurely.EachforeignsaverinvestsS xinforeignstorageinautarkytosatisfytheabsolutesafetyneeds.Therefore,foreignfundingissuppliedtodomesticintermediariesifaminimalreturnofxisensuredinallcontingencies.ForanintermediarytosatisfythisabsolutesafetyconstraintincontingencyMandB,it(i)oersaseniorclaimtoforeignsaversand(ii)attractsasucientamountofrisk-absorbingdomesticfunding,(di+fi)xfi.Thisrequireseitherfi=0ordi�x� 
fi�0.Sincesafety-seekingforeignsaverswouldcauseinecientliquidationofinvestmentincontingencyM,itisoptimalfortheintermediarytooerlong-termdebtcontractsonly.Se-niorityensuresthesafetyneedsofforeigners,providedenoughdomesticfundingisattracted.LetLSxdenotethefacevalueofseniorlong-termdebtandLJTdenotethefacevalueofjuniorlong-termdebt,wherethelowerboundsarisefromtheparticipationconstraintsofsavers.Furthermore,theincentivecompatibilityconstraintofforeignsaversismet,sincejuniorlong-termdebtcontractdoesnotguaranteeabsolutesafety,Ii�LSfixdi.ThereisaWalrasianmarketforforeignfunding,soallintermediariesandforeignsaverstakeLSasgiven.Hence,theaggregatesupplyofforeignfundingis:f(LS)=8&#x]TJ ;&#x-458;&#x.895;&#x -21;&#x.669;&#x Td ;&#x[000;&#x]TJ ;&#x-458;&#x.895;&#x -21;&#x.669;&#x Td ;&#x[000;&#x]TJ ;&#x-458;&#x.895;&#x -21;&#x.669;&#x Td ;&#x[000;&#x]TJ ;&#x-458;&#x.895;&#x -21;&#x.669;&#x Td ;&#x[000;&#x]TJ ;&#x-458;&#x.895;&#x -21;&#x.669;&#x Td ;&#x[000;&#x]TJ ;� -2;
.52;&#x Td ;&#x[000;&#x]TJ ;� -2;
.52;&#x Td ;&#x[000;&#x]TJ ;� -2;
.52;&#x Td ;&#x[000;&#x]TJ ;� -2;
.52;&#x Td ;&#x[000;&#x]TJ ;� -2;
.52;&#x Td ;&#x[000;:0LSx0;WS xifLS=xWS xLS�x(14)Increasesinforeignwealthshiftsoutthesupplycurveofforeignfunding.26 Conditionalonattractingforeignfunding,Table3summarizesthepayostothein-termediaryandsaversinallcontingencies.TheintermediaryalwaysdefaultsincontingencyB,leadingtoatleastpartialdefaultonjuniorclaims,whichareheldbydomesticsavers. State Probability Return F D Bi G  R(
) LS LJ R(Ii)Ii�LJdi�LSfi M (1�) R(
) LS LJ R(Ii)Ii�LJdi�LSfi B 1�  minLS;Ii fi max0;Ii�LSfi di 0 Table3:PayoswhenforeigncapitalisattractedIntermediaryimaximizesitsexpectedequityvaluebychoosingtheamountofforeignanddomesticfundingandthefacevalueofjuniorlong-termdebt.SinceahigherfacevalueLJreducesexpectedprotsbutmakestheparticipationconstraintofdomesticsaversslacker,itisalwaysoptimalfortheintermediarytosetitatthelowestvalueconsistentwithparticipationofdomesticsavers:LJ=T �1� max0;Ii�LSfi di (15)Therearetwocases.Case(I)describescompletedefaultondomesticsaversincontingencyM,LSfiIixfi,whilecase(II)describespartialdefaultincontingencyM,LSfiIi.Itisalwaysoptimaltoattractsomedomesticfunding,di&#x-278;0.Proofbycontradiction:ifdi=0,thenfi=0fromtheabsolutesafetyconstraint.Hence,theexpectedprotsarezero,whichisdominatedbytheautarkyallocationwithstrictlypositiveprots,AutIAut[ R(IAut)+(1� )�T]&#x-278;0.Thisestablishestheclaim.Weshowedthattheoptimalfundingcontractwhenagentsareperfectlyinformedislong-termdebt.Seniorityisgiventoforeignsaverstosatisfytheirabsolutesafetyconstraint.Sinceforeignfundingisweaklycheaperthandomesticfunding,someofwhichisattractedinequilibrium.Specicexpressionsforthefacevaluesofdebtcontractandthecompositionoffundingcanbeobtainedbysolvingtheconstrainedoptimizationproblemdescribedabove.27 BProofofLemma3Westartbyshowingthatthebank'sproblemsimpliesasstatedbelow.Domesticfundingisexpensive,asimpliedbytheparticipationconstraintofdomesticsavers:E[D]= L+ (1�)min(L;R(Ii)Ii�R(Ii) xfi di)+(1� )(1�)minL;Ii�xfi diT:Theexpectedprotofbankiis:E[i]= [R(Ii)Ii�Ldi�Xfi]+ (1�)maxR(Ii)Ii�R(Ii) xfi�Ldi;0+(1� )(1�)maxfIi�xfi�Ldi;0g:EachintermediaryimaximizesitsexpectedprotsE[Bi]bychoosingitsfundingprole(di,fi)andthefacevalueoflong-termdebtL,takingthefacevalueofdemandabledebtXasgiven.Thesechoicesareconstrainedbytheparticipationconstraintofdomesticsaversandtheabsolutesafetyconstraint.Thefacevalueoflong-termdebtreducesthebank'sexpectedprotsbutmakestheparticipationconstraintofdomesticsaverslessbinding(withoutaect-ingtheabsolutesafetyconstraint).Hence,thebanksetsLfortheparticipationconstraintofdomesticsaverstobind.Thus,thebank'sproblemcanbereducedtothefollowingproblem:maxfi2[0;1);di2[0;1]^i=Ii[ R(Ii)+(1� )(1�)]�diT(16)�fi X+x (1�)R(Ii) +(1� )(1�)s.t.IixfiIi=di+fiTheobjectivefunctionistheexpectedrevenuefrominvestmentnetofthecostofdomesticandforeignfunding.Wenowsolvethisstandardconstrainedoptimizationproblem.LetLitheLagrangianoftheproblemandibetheLagrangemultiplierassociatedwiththeabsolutesafetyconstraintofbanki.Therst-orderconditionsare:28 dLi ddi= MR(Ii)+(1� )(1�)�T� (1�)xR0(Ii) fi+idLi dfi= MR(Ii)+(1� )(1�)(�x)� X� (1�)x [R0fi+R]�x �1iandi0anddix� fiwithcomplementaryslackness.B.1SlackabsolutesafetyconstraintConsiderthecaseinwhichtheconstrainttoprovideabsolutesafetydoesnotbind(i=0).Therearetwosubcases:(A)foreignfundingismoreexpensive,(B)foreignfundingischeaperthandomesticfunding.(A)moreexpensiveforeignfundingSupposethatforeignfundingisexpensiverelativetodomesticfunding,XT �(1� )(1�) x�1� x R(Ii).Then,noforeignfundingisattracted,fi=0,andtheautarkylevelofinvestmentoccurs,di=IAut.TheprotlevelisAutIAut[ R(IAut)+(1� )(1�)�T].Weneedtoconrmtwosuppositions.First,theabsolutesafetyconstraintistriviallyslack,i=0.Second,forforeignfundingtobe(prohibitively)expensive,werequire:X XT �(1� )(1�) x�1� x R(IAut):(17)Autarkyistheuniqueequilibriumif Xx.However,weimposealowerboundonuncer-taintyinordertoallowforanequilibriuminwhichforeignfundingisattracted.Inshort:� 0 R(IAut)+(1� )(1�)� xT [R(IAut)�]2(0;1)(18)(B)foreignfundingischeaperthandomesticfundingIfforeignfundingischeaprelativetodomesticfunding,XT �(1� )(1�) x�1� x R(Ii),thentheintermediarywould29 wishtoattractonlyforeignfunding,fi�0,andnodomesticfunding,di=0.Thisallocationviolatestheabsolutesafetyconstraint,however.Contradiction.B.2BindingabsolutesafetyconstraintConsidernowthecaseinwhichtheconstrainttoprovideabsolutesafetybinds(i�0).Hence,di=�x �1
fiandIi=x fi.Optimalityrequiresfi�0,sowehavedLi dfi=0.SolvingthisequationfortheLagrangemultiplieryields:i= x� MR(Ii)�(1� )(1�)�  x�X� (1�)x x�[R(Ii)+R0(Ii)fi]:(19)InsertingthemultiplierindLi ddiyields:dLi ddi= x x�MRx fi�T�  x�X:(20)First,ifdi2(0;1],thendLi ddi=0,sotheoptimalamountofforeign(anddomestic)fundingisimplicitlydenedby:MRx fi=x� xT + xX:(21)Theleft-handsidestrictlydecreasesintheamountofforeignfundingsinceMR0(
)0.Theright-handsideisapositiveconstant.Notethattheleft-handsideatzerostrictlyexceedstheright-handsideforallX X.Therefore,thereexistsauniqueinteriorsolutionfi(X)�0forallX X.9Thedemandforforeignfundingindownward-sloping,dfi(X) dX0,sincetheright-handsideincreasesinthepriceofforeignfunding.Sincedomesticfundingisbounded,di1,werequirealowerboundonthepriceofforeignfundingtoguaranteeaninteriorsolution:XX x MRx x��x� T :(22) 9Thatis,R(0)x� xT + xXforallX Xbecauseoftherstboundaryconditionandthedenitionoftheautarkyinvestmentlevel.30 IfXX ,thentherethecornersolutiondi=1andfi= x�prevails.Foraninteriorsolutiondi1toexist,werequireX Xthatimposesalowerboundontheinformativenessofforeignfunding:� 1 R(IAut)+(1� )(1�)�T R(IAut)�MR�x x�
2(0;1):(23)Finally,weneedtoestablishthati�0assupposed.Insertingtheoptimalitycon-ditionintheexpressionfortheLagrangemultiplieryieldsanupperboundonthepriceofforeignfundingX~X,whichisimplicitlydenedby:~XT �(1� )(1�) x�1� x RIi(~X):(24)NotethatlimX!~XIi(X)�IAutandlimX!~Xfi(X)�0.Thisfollowsfromrst-ordercondition,equation(21),andthedenitionofautarkyinvestment: RIi(~X)+ Ii(~X)R0Ii(~X)+(1� )(1�)=T:(25)NotethatlimX! XIi(X)�IAutandlimX! Xfi(X)�0.Thisfollowsfromrst-ordercondition,equation(21),andthedenitionofautarkyinvestment: R�Ii( X)
+(1�)R�IAut
+Ii� X
R0�Ii( X)
+(1� )(1�)=T:(26)Hence,Ii( X)�Ii(~X).Sinceinvestmentdecreasesinthefacevalueofforeignfunding,wealsohave X~X.B.3Whenisautarkyoptimal?Theexpectedequityvalueoftheintermediarythatchoosesautarkyis:AutIAut[ R(IAut)+(1� )(1�)�T]= �IAut
2(�R0(IAut)):(27)31 ForX2[X ;~X],abank'sexpectedequityifchoosingtoattractforeignfundingis:i(X)= x fi(X)Rx fi(X)� Xfi(X)�Tx� fi(X);(28)wherefi(X)2(0; x�]isdeterminedasdescribedabove.Bytheenvelopetheorem,theexpectedprotstrictlydecreasesinthefacevalueofforeignfunding,di dX0.SupposeaswitchingthresholdofforeignfundingXSexists.ThisimpliesthatautarkyispreferredforXXSandattractingforeignfundingispreferredforXXS.Twoconditionsarerequired:atthelowerboundX ,attractingforeignfundingmustbepreferable,whileautarkyispreferableattheupperbound X.Onecanshowthattherstconditionismorerestrictiveandimposesanotherlowerboundontheinformativenessofforeignsavers.Specically,theexpectedprotattheupperbound X{wheretheforeignfundinglevelisfi( X)denedabove{is:i( X)=Ii( X) R�Ii( X)
+ (1�)R(IAut)+(1� )(1�)�T(29)Hence,i( X)Autisimpliedbyalowerboundontheinformativenessofforeignsavers:&#x-278; 2Ii( X)�IAut Ii( X) R(IAut)+(1� )(1�)�T R(IAut)�R(Ii( X))2(0;1)(30)Then,theeectivelowerboundis maxf 0; 1; 2g.CollectingthevariouscasesyieldsthedemandforfundingstatedinLemma3.CProofofProposition2ThisproofsbuildsonLemma2andLemma3.Toensureexistenceofequilibrium,werequirealowerboundonforeignwealth.ThislowerboundW isgivenbytheinteractionbetweenthesupplyofforeignfunding,f=WS x,andthedemandforforeignfundingasimpliedbythesolutiontotheintermediary'sproblem.ThedenitionstatedinthePropositionfollows32 immediately.Toensureaninteriorequilibrium,werequire X�x.Thisconditioncanbeexpressedasalowerboundontheinformativenessofforeignsaversthatwederivedbefore.Thiscompletestheproof.DProofofProposition3ThisproofbuildsonLemma2,Lemma3,andProposition2.Foreignfundingisattractedwheneverforeignwealthissucientlyabundant,W�W .Fortheseequilibria,theabsolutesafetyconstraintbinds,Ii=rfiforeachintermediaryi.Hence,therearenoresourcesleftafterforeignsaverswithdrewattheinterimdateincontingencyM(seeTable2).Thus,thebankmakeszeroprotsandfullydefaultsondomesticsavers.ThetotaleciencylossisR(I) xf.FocusingonthemoregeneralcaseofX �x,wehavetworelevantrangesofforeignwealth.First,forW2(W ; W),wehavethatI=S Wandf=S xW,whichyieldsaneciencylossofR�S W
S W.Second,forW W,wehavethatI=x x�Wandf= x�W,whichyieldsaneciencylossofR�x x�
x x�.Thiscompletestheproof.EProofofCorollary3IrrespectiveofwhetherX �xornot,thenetpresentvalueofinvestmentatdomesticdiscountratesforalevelofforeignwealthbelowtheupperbound Wis:NPV= R�WS 
+(1� )(1�) T�1:(31)33 Hence,thenetpresentvaluesdecreasesinforeignwealth:NPV0(W)= R0�WS 
S  T0:(32)IfX �x{whichisimpliedbyx� T [MR(x x�)�]{thenthecornersolutionwithI=x x�occursforsucientlyabundantforeignwealth.Thus,thegrosspresentvalueofinvestmentneversmallerthan R(x x�)+(1� )(1�) T.Bycontinuity,theresultinCorollary3follows.34