美联储-数量和覆盖利息平价（英）

FinanceandEconomicsDiscussionSeries

FederalReserveBoard,Washington,D.C.

ISSN1936-2854(Print)

ISSN2767-3898(Online)

QuantitiesandCovered-InterestParity

TobiasJ.Moskowitz,ChaseP.Ross,SharonY.Ross,KaushikVasudevan

2024-061

Pleasecitethispaperas:

Moskowitz,TobiasJ.,ChaseP.Ross,SharonY.Ross,andKaushikVasudevan(2024).“QuantitiesandCovered-InterestParity,”FinanceandEconomicsDiscussionSeries2024-061.Washington:BoardofGovernorsoftheFederalReserveSystem,

/10.17016/FEDS.2024.061

.

NOTE:StafworkingpapersintheFinanceandEconomicsDiscussionSeries(FEDS)arepreliminarymaterialscirculatedtostimulatediscussionandcriticalcomment.TheanalysisandconclusionssetfortharethoseoftheauthorsanddonotindicateconcurrencebyothermembersoftheresearchstafortheBoardofGovernors.ReferencesinpublicationstotheFinanceandEconomicsDiscussionSeries(otherthanacknowledgement)shouldbeclearedwiththeauthor(s)toprotectthetentativecharacterofthesepapers.

QuantitiesandCovered-InterestParity

TobiasJ.Moskowitz,ChaseP.Ross,SharonY.Ross,KaushikVasudevan*July11,2024

Abstract

Studiesofintermediatedarbitragearguethatbankbalancesheetsareanimportantconsideration,yetlittleevidenceexistsonbanks’positioninginthiscontext.Usingconfidentialsupervisorydata(covering$25trillionindailynotionalexposures)weexaminebanks’positionsinconnectionwithcovered-interestparity(CIP)deviations.Exploitingcross-sectionalvariationinCIPdeviationsthathavelargelychallengedexistingtheories,wedocumentthreenovelforcesthatdrivebases:1)foreignsafeassetscarcity,2)marketpowerandsegmentationofbanksspecializingindifferentmarkets,and3)concentrationofdemand.Ourfindingsshedempiricallightontheinterplayoffrictionsinfluencingbanks’provisionofdollarfunding.

JELCodes:F3,F31,F65,G1,G13,G15,G2,G23

Keywords:basis,covered-interestparitydeviation,foreignexchange,safeassets

*T.MoskowitzisattheYaleSchoolofManagement,YaleUniversity,NBER,andAQRCapitalManagement,email:

tobias.moskowitz@.

C.RossisattheBoardofGovernorsoftheFederalReserveSystem,email:

chase.p.ross@.

S.RossisattheBoardofGovernorsoftheFederalReserveSystem,email:

sharon.y.ross@.

K.VasudevanisattheDanielsSchoolofBusiness,PurdueUniversity,email:

kvasude@.

WethankTristanD’Orsaneoforexcellentresearchassistance.Forcommentsandsuggestions,wethankourdiscussantsRashadAhmed,WillDiamond,BenGolez,PiotrOrłowski,StephenSzaura,andMengboZhang,aswellasRicardoCorrea,WenxinDu,NathanFoley-Fisher,PeterHansen,ToomasLaarits,JinsookLee,BorghanNarajabad,StasNikolova,JunkoOguri,DavidRappoport,BryanRicketts,MattSeay,AlexVardoulakis,XiaochuanXing,ChenziXu,EmreYoldas,seminarparticipantsattheUniversityofNebraskaandFedBoard,andconferenceparticipantsattheWabashRiverConference,2024ASSA,2024MFA,theSpring2024NBERFinancialMarketFrictionsandSystemicRisksmeeting,the2024EasternFinanceAssociationmeeting,andthe2024UCLAFinkCenterConference.AQRCapitalisaglobalassetmanagerwhomayormaynotusetheinsightsandmethodsinthispaper.TheanalysisandconclusionssetfortharethoseoftheauthorsanddonotindicateconcurrencybymembersoftheBoardofGovernorsoftheFederalReserveSystem,AQR,ortheirstaffs.

1

1Introduction

Spreadsonbank-intermediatedarbitragetrades,calledbases,havepersistedsincethe2008financialcrisis,attractingsubstantialattentionfromacademicsandpractitioners.Theexistenceofbasesisoftencitedasevidencethatfinancialintermediariesarenotsimplyaveil,asassumedinclassicaltheories.Thelitanyoffrictionsfacedbyintermediaries,therefore,mayhaveimportonassetpricesand,byextension,thebroadereconomy.Priorworkfocusesprimarilyonassetpricingdata.Inthispaper,weusenovelquantitydata,togainabetterunderstandingofintermediaries’basistradingactivityandofhowintermediaryconstraintsaffectassetprices.

Wefocusoncovered-interestparity(CIP)asasimpleandcleararbitragetradeinter-mediatedbybanks

.1

CIPdeviationshavebeenusedasaprimaryempiricallaboratorytodescribetheimportanceofintermediationfrictions.ACIParbitragetradeconsistsofthefollowing:tomeetforeigncustomerdemandtoborrowdollars,anintermediaryborrowsdollars,entersintoaforeignexchangeswapwiththecustomertoexchangethedollarsforforeigncurrency,andinveststheproceedsinforeignsafeassets.Atmaturity,theintermediaryreceivesdollarsfromthecustomerandrepaystheinitialdollarloan.CIPimpliesthatthereturnonthistransactionshouldbezero.DeviationsfromCIPareimportantbecausetheyreflectfrictionsintheglobalprovisionofdollarfunding,whichoccurslargelyviacurrencyswapsandforwards.MoststudiestestandrejectthatCIPbasesarezeroandrelatenon-zero

basestomeasuresofintermediaryfrictions(Duetal.

(2018),

Iidaetal.

(2018),

Cenedese

etal.

(2021),

Wallen

(2022),

DuandSchreger

(2022),

Augustinetal.

(2022))

.

Tobetterunderstandtheroleofintermediariesinassetpricesand,specifically,theglobalprovisionofdollarfunding,weusegranularconfidentialsupervisorydata.Wealsoexploitcross-sectionalvariationinCIPbases,whoseexistenceisapuzzleforexistingintermediarytheoriesforthebasis.Ouruniquequantitydataprovidebankpositionsinthesemarkets,whichwhenmergedwithprices,shedsubstantiallightonwhatdrivesbases,including

explainingtheirpuzzlingcross-sectionalheterogeneity.

1Thereareseveraltypesofbasistradesbeyondcovered-interestparity,includingtheequityindex

futures/cashbasis(Hazelkornetal.,

2023),theTreasuryon-the-run/off-the-runspread(Krishnamurthy,

2002),theTreasurycash/futuresbasis(BarthandKahn,

2021),theTreasurycash/swapbasis(JJermann,

2020;

Boyarchenkoetal.,

2018b),thebond/CDSbasis(BaiandCollin-Dufresne,

2019),andtheCDX/CDS

basis(Boyarchenkoetal.,

2018c)

.WefocusonCIPbasesbecauseourdataprovidedetailedbankexposureinformationtospecificcountryinterestratesandcurrencies,allowingagranularexamination.

2

Wefindthatthreenovelforcesareimportantfordrivingbases.First,intermediariespurchaseforeignriskyassets,ratherthansafeassets,correspondingwiththeirsyntheticdollarlendingtocustomers.SinceCIParbitragerequiresapositioninsafeassets,banksonlyimperfectlyexecuteCIParbitrageandtakeonmeaningfulrisk.Second,marketsaresegmented,withbanksspecializingindifferentcurrenciesandtenors,sobasesreflectbank-specificconstraints.Segmentationalsoreducestheelasticityofbasestodemandviareducedrisksharingandmarketpower.Third,intermediariesfaceconcentrateddemandinsomemarketsfromcertaincounterpartiesandrequirecompensationassociatedwithcounterpartyrisk.Webreakdownandquantifyhoweachofthesechannelsgeneratestime-seriesandcross-sectionalvariationinCIPdeviations.Ourresultshighlightthepresenceandimportanceofsegmentationandsearchfrictionsineventhelargestandmostliquidmarkets.

Tobetterinterpretourfindingsandguideourempiricalinvestigation,webuildastylizedmodelwhererisk-averseintermediariesmeetcustomers’demandfordollarsinexchangeforforeigncurrencybyengaginginbasistradesbutfaceseveralfrictions:coststoexpandtheirbalancesheets,foreignsafeassetscarcity(difficultyinlocatingscarceforeignsafebondswithlowyields),heterogeneousexpertiseinriskyassets,andcounterpartylimits.

Themodelshowcaseshoweachfrictioncontributestobases.Balancesheetcostsdriveacommoncomponentofbasesacrossallcurrencies,whichistheprimaryfocusoftheliterature.However,theotherfrictionswemodelhaveanimpact,too,and,importantly,cancapturethecross-sectionalheterogeneityinthedata.Forexample,scarceforeignsafebondsthatarehardtofindandhavelowyieldsleadintermediariestoholdriskybonds.Inturn,weobservedifferencesinbasesacrosscurrenciesbasedontheamountofsyntheticdollarborrowingdemandfromthosecurrencies.Heterogeneousexpertiseleadsintermediariestospecializeincertainmarkets.Thissegmentationcreatesmarketpowerandimpedesrisksharing,whichaffectstheelasticityofthebasisdifferentiallyacrosscurrencies.Counterpartylimitsalsoimplythattheconcentrationofdemandcontributestotheinelasticityofbases.Thesefrictionsvaryacrossbanksandmarkets,generatingcross-sectionalvariationinbases.

Totestthemodel’simplicationsandwhetherthesechannelscancapturethevariationinbases,weusetheFederalReserve’sFR2052aComplexInstitutionLiquidityMonitoringReport,whichprovidesgranular,high-frequencydataonthebalancesheetsofthelargestbanksintheUS.Thedatacover$25trillionofdailynotionalexposureonaverage.Becausethereportprovidesdetailedsnapshotsofderivativeexposuresaswellastheassetsandliabilities

3

sideofbanks’balancesheets,weobtainanovelviewoftheotherwiseopaquepositioningofintermediariesincurrencymarkets.Analyzingthedata,wefindthatbanksnetlendabout$100billiononaveragethroughswapsinthemarketswestudy,indicatingtheirimportanceinmeetingglobaldemandfordollarfunding.Moreover,weshowthatbankssyntheticallylendthemostdollarsinthesamemarketswherethebasisindicatesdollarfundingisthemostexpensive.Thisfactisconsistentwiththebankingsectorfacingincreasingmarginalcoststomeetdollardemandfromeachcurrency.Guidedbyourmodel,weempiricallyinvestigatehowtheoutlinedfrictionscontributetotheseincreasingmarginalcosts.

First,wefindforeignsafeassetscarcityisanimportantdriverofCIPbases.ToexecuteCIPbasisarbitrage,anintermediarymustholdtheequivalentof$1ofmaturity-matchedforeignsafeassetsforevery$1itlendsinordertoearntheforeignrisk-freerate.Inpractice,however,bankshold$0.05perdollarlentwhenmatchingmaturitiesperfectly.Evenwhenemployingagenerousdefinitionofmaturity-matchedsafeassetsthatignorescounterpartyriskandpermitssmallmaturitymismatches,banksholdonly$0.48offoreign“safe”assetsper$1lent.Asignificantcomponentofintermediaries’currencyexposureis,therefore,hedgedwithmaturity-mismatchedsafeassetsandwithriskyassets.ThechoiceorconstrainttoexecuteimperfectCIParbitrageexplainswhydollarfundingismostexpensiveinmarketswherebanksaredoingthemostdollarlendingsincethosearethemarketswhereintermediariesaretakingthemostrisk.

Intermsofmagnitudes,wefindthataonestandarddeviationchangeindollarborrowingdemandincreasesthemagnitudeofthebasisby4to9bps,withoutaccountingforanycross-currencydifferencesinbanks’abilitiestoaccess(maturity-matched)foreignsafeassets.Inaddition,therearedifferencesinthecostoflocatingmaturity-matchedsafeassetsacrosscurrencies.Wecapturethiscostusingcross-currencyvariationinthenumberofdollarsofforeignsafeassetsheldperdollarofswapexposure,whichwecallthesafeassetratio.Wefindthataonestandarddeviationdifferenceinthesafeassetratiocorrespondstoafurtherincreaseinthebasisof7to9bps.

Second,wefindthatcurrencymarketsegmentationcontributestoCIPbases.Wedefineamarketasatenor×currencypair,sothe1-monthEURUSD,1-yearEURUSD,and1-yearJPYUSDarealldistinctmarkets.Foreachmarket,wecalculateaHerfindahl-HirschmanIndex(HHI)ofbankexposureandfindastrongrelationshipbetweenmoreconcentratedmarketsandlargerbases:aonestandarddeviationmoresegmentedmarkethasa10to14

4

bpslargerbasis.Combinedwithourresultsonsafeassetscarcity,therelationshipbetweensegmentationandbaseshighlightstheimportanceofrisk—andintermediariesimperfectlysharingit—asdriversofCIPdeviations,whichmayalsobeamplifiedbymarketpower.

Wealsoidentifysegmentationbyexaminingtheextenttowhichbank-specificconstraintsarereflectedinbases.WeusetheMarch2023bankingturmoilasanaturalexperimenttotesttherelationshipbetweenbank-specificshocksandthebasis.Therewasanotableshiftof

depositstowardthelargestUSbanksfollowingtheSiliconValleyBank(SVB)turmoil.We

showthatcurrencymarketsintermediatedbybankswithcomparativelylargerdepositinflowshadcomparativelysmallerbasisdislocations.Thisresultisconsistentwiththemodel’spredictionthatconstraintsfacingbankswhospecializeincertainmarketswilltransmittopricesinthosemarkets,consistentwithmarketsegmentationonthesupplyside.

Thepresenceandimportanceofsegmentationaresurprisinginoursettingsinceglobalcurrencymarketsareamongthelargestandmostliquidmarketsintheworld.Weshowthatsegmentationispersistent,withmarketsharesdisplayingpersistenceandmoresegmentedcurrencymarketsremainingsoovertime.Ourmodelascribessegmentationtoheterogeneousexpertiseinexecutingarbitrageacrossmarkets,wherebanksspecializeinmarketswheretheyhavethemostexpertise.Weprovidesupportforthismechanismbyshowingthatbanksspecializeincounterpartysegments.Forexample,abankmightspecializeinCanadianinsurancecounterparties,whileanothermaycatertoAsiansovereignwealthfunds.WefurthershowthatbanksholdmoreloansinthecurrenciesinwhichtheyhavelargecurrencymarketsharesinFXswapmarkets,suggestingthatbankshavemarket-specificexpertiseandamorereadilyavailablesetofcounterpartiesinthemarketstheyspecializein.

Third,wefindthatsomecurrencymarketshaveconcentrateddemand.Marketswithalessdiversemixofcounterpartiesalsohavelargerbasisdislocations,controllingforforeignsafeassetscarcityandsegmentation.Moreconcentrateddemandisassociatedwithlargerbases,consistentwithbanksmanagingcounterpartyrisk.Aonestandarddeviationincreaseindemandconcentrationhasa7bpslargerbasis.

Analysisofthecross-sectionofCIPdeviationsrevealsseveralnovelandimportantfrictionsaffectingprices:scarcityofforeignsafeassetsandsupplyanddemandsegmentation.Thesefrictionsmatterforarbitrageactivityeveninglobalcurrencymarkets,whicharesomeofthelargestandmostliquidmarkets.

5

RelatedLiterature

OurworkismostcloselyrelatedtoworkonCIPdeviations(Duetal.

(2018),

Iidaetal.

(2018),

Cenedeseetal.

(2021),

Wallen

(2022),

DuandSchreger

(2022),

Augustinetal.

(2022))andbank-intermediatedarbitragespreads(e.g

.,

GarleanuandPedersen

(2011),

Pasquariello

(2014),

Boyarchenkoetal.

(2018a),

Andersenetal.

(2019),

Anderson

etal.

(2021),

Foley-Fisheretal.

(2020))

.PreviousworkfocusesprimarilyonincreasedbankfundingcoststhatgiverisetoCIPdeviationsfollowingthe2008financialcrisis,forexample,

duetobankregulation(Duetal.

(2018))ordebtoverhangfrictionsassociatedwiththe

expansionofbankbalancesheets(Andersenetal.

(2019))

.

Incontrast,ourworkshinesalightontheassetsideofintermediaries’basistradesusinguniquedataonquantities.OurfindingsindicatethateitherthedifficultyinlocatingforeignsafeassetsforuseinCIPtradesorthechoicetoinvestinhigher-yieldingassetsresultsinintermediariesholdingriskiersecuritiesintheforeignlegsoftheirbasistrades,thusmakingCIParbitrageactivityrisky.Thisconclusioncomplementsthefindingsof

Diamondand

VanTassel

(2021),whosuggestthatconvenienceyieldsonforeignsafeassetsmayhelp

explainCIPbases;andthoseof

Liao

(2020),whodocumentsastrongrelationshipbetween

CIPdeviationsanddifferencesincorporatecreditspreadsacrosscurrencies.Ourresultsarealsorelatedto

Duetal.

(2023a),whofindthatthesecurityholdingsofthebanking

andinsurancesectorsintheEuro-areafarexceedtheamountofgovernmentdebt,withinstitutionstiltingtheirportfoliostowardsriskycorporatedebt.Furthermore,giventhereal

costsofCIPdeviations(DuandHuber

(2023)),ourresultthatsafeassetscarcitymayhelp

driveCIPdeviationshighlightstherealeffectsofsafeassetscarcityconsistent(e.g.,

Caballero

(2006),

Caballeroetal.

(2017),

CaballeroandFarhi

(2018))

.

Uniquely,wefocusoncross-sectionalvariationinbases.Weconcludethatintermediary

heterogeneity(Kargar

(2021))andtheaccompanyingsegmentationofintermediariesinto

differentmarketsareimportantdriversofbases

.2

Usingsupervisoryregulatorydata,weprovidedirectevidenceofsegmentation’simpactintransmittingidiosyncratic,bank-specificconstraintsintoassetprices.Thisresultisconsistentwithotherwork(e.g.,

Rimeetal.

(2022);

Siriwardaneetal.

(2022);

Kloksetal.

(2023))

.However,ourempiricalevidenceuniquelysheds

lightonthesourceofsegmentation.BecausewefindthatCIParbitrageisrisky,ourresults

2Anecessaryingredientisthattherearedifferencesindollardemandviacurrencyforwards,which,forexample,mayarisefromdifferencesincurrencyhedgingdemandacrosscurrencies(e.g.,

LiaoandZhang

(2021)and

DuandHuber

(2023))

.Similarheterogeneityindemandalsoexistsinothermarkets,forexample,

equityindexfuturesmarkets(Hazelkornetal.

(2023))

.

6

highlightanotherchannelthroughwhichsegmentationaffectsbases—reducedrisksharing.Theevidencesupportstheideathatinvestorsspecializein“complexassetmarkets”duetomarket-specificexpertise(e.g.,

GlodeandOpp

(2020),

Eisfeldtetal.

(2023),

Bryzgalova

etal.

(2023)),emphasizingthattheriskinessofarbitrage—anddifferencesinintermediaries’

abilitiestoreducethatrisk—arekeytounderstandingsegmentedarbitrage.

Lastly,ourworkcontributestotheliteratureonintermediaryassetpricing(Brunnermeier

andPedersen

(2009),

HeandKrishnamurthy

(2013),

Adrianetal.

(2014),

Gabaixand

Maggiori

(2015),

Heetal.

(2017),and

Duetal.

(2023b))thatemphasizestheintermediary

sector’smarginalutilityasastatevariabledeterminingassetriskpremia,duetohouseholds’limitedparticipationinassetmarkets.Ourfindingsindicatethatlimitedparticipationispresentevenwithintheintermediarysectoritselfandsuggestthatthemarginalutilityofspecializingintermediariescontributestomarketriskpremiaandnotjusttheintermediarysectorinaggregate.

2Model

Wepresentastylizedmodeltoorganizeandinterpretourempiricalinvestigation.Themodelyieldsasetofpredictionsonthecross-sectionaldriversofCIPbasesandillustrateshowdifferentfrictionsgiverisetovariationinbases.

2.1Setup

ThereareNkforeigncurrencies(againsttheUSD),indexedbyk={1,...,Nk}.Forsimplicity,eachcurrencyfacesaunitaryexchangerateversustheUSD.Therearetwotypesofinvestors:Nifinancialintermediaries,indexedbyi={1,2,...,Ni}andNccustomers,indexedbyc={1,2,...,Nc}.Therearetwoperiods,t=1,2.Allinvestorsinvestinperiod1andrealizepayoffsinperiod2.

TheU.S.offerssafebondsinperfectlyelasticsupply,withreturnsnormalizedtozero.Eachforeigncurrencyfeaturesthreetypesofassets:one-periodcurrencyforwards,safebonds,and‘risky’bonds,whichareimperfectsubstitutesforsafebondsandwhichinvestorsfaceidiosyncraticrisktoinvestin,asdetailedbelow.Allriskyforeignbondsofferareturnofr.Safeforeignbondsincurrencykofferexpectedreturnsofrk≤r.Currencyforwardsarein

7

zeronetsupply,andtheirpriceisendogenouslydetermined.

CustomerDemandforCurrencyForwardsandtheBasis.Customersonlytransactincurrencyforwards.Inperiod1,customercexogenouslydemandstosyntheticallyswapXc,kdollarsfromcurrencykintoUSDviaforwards.Inaggregate,syntheticdollardemandtoswapcurrencykfordollarsisgivenbyXk=ε1Xc,k.Forsimplicity,weassumethatcustomers’tradesarenettedout,suchthatsign(Xk)=sign(Xc,k),∀c,k.ThepriceofcurrencyforwardsforcurrencykisgivenasPf,k.

ThebasisforcurrencykisthepriceoftheforwardcontractminustheexpectedreturnfromborrowinginUSDandinvestinginforeignsafeassets:

Basisk三Pf,k−rk.

Withexogenousrisk-freerates,thebasisisdeterminedbytheforwardprice.

ForeignBondsandSafeAssetScarcity.Thereisasufficientsupplyofsafebondsto

hedgeallcurrencytrades,buteachintermediaryifacesatotalsearchcostofs,ks,kto

locatesafebondsincurrencyk,wheresi,kisthesafebondpositionofintermediaryiincurrencykandλs,kisacoefficientthatcaptureshowquicklysearchcostsincreaseincurrencyk.Thatis,safebondsincurrencykbecomeincreasinglydifficulttolocateasdemandforthemincreases.

Intermediariesmayalsotakepositionsinriskybondsofeachcurrency,inperfectlyelastic

supply.Intermediaryifacesanidiosyncraticpayoffvarianceofσ,kwhenpurchasingrisky

bondsincurrencyk.Intermediarieswithlowerσ,kforagivenmarketfacelessriskintheir

basistradeswhensubstitutingawayfromsafebondsinthecashlegsoftheirbasistrades.Thisfeaturecanbeinterpretedasintermediarieshaving“market-specificexpertise”insubstitutingawayfromsafeassets.Theheterogeneityinriskfacedbydifferentintermediariesmayreflect,forexample,differencesintechnologiesacrossintermediariesinproducinginformationaboutissuersinagivenmarket,differencesinaccesstocounterparties,oralternativelydifferences

intradeexecution(GlodeandOpp

(2020),

Eisfeldtetal.

(2023))

.

IntermediaryHedgingandSafeAssetChoice.Eachintermediaryimaximizesamean-varianceobjectivefunction,E(Wi,2)−i,2),whereWi,2istheterminalwealthofintermediaryi,E(·)andV(·)aretheexpectationsandvarianceoperators,andγiisa

8

coefficientthatcapturestherisk-bearingcapacityofintermediaryi.Intermediariestakethe

othersideofcustomerdemandinsyntheticfundingmarkets.IntermediaryitakesapositionofZi,kincurrencyforwardk.ForwardmarketclearingisgivenbyΣiZi,k+ΣcXc,k=0,∀k.

Intermediariesareconstrainedtofullyhedgetheircurrencyexposurefrommeetingforwarddemandviacashbonds.Tosatisfytheirfirst-orderconditions,intermediaries’allocationstosafeandriskybondsincurrencykmustmakethemindifferenttoobtainingmarginal

hedgepositionsineither.Thismeansthatgiventheirtotalpositionof−Zi,kincashbondsofcurrencyk,intermediaryiallocatesaproportionαi,k三toriskybondsandallocates

theremainderoftheirhedgepositiontothesafebond.Giventheirpositions,intermediaryi’sprofitsincurrencykaregivenby−(αi,kr+(1−αi,k)rk−Pf,k)Zi,k.

Eachintermediaryalsofacesasetofconstraintsthatwedetailbelow.

BalanceSheetCost:Intermediaryifacesincreasingmarginalcoststoexpanditsbalancesheet(e.g.,becauseofregulationordebtoverhang).Thisiscapturedbyeachintermediaryfacingacostoftheform

(1)

Weassumequadraticcostsformathematicalease,butconceptually,ourresultsdependonlyonthefactthatconstraintsare(weakly)convex.

CounterpartyConstraints:Intermediaryipaysincreasingmarginalcoststomeetdemandfromspecificcounterparties.Allelseequal,intermediariesprefertoequalizepositionsacrossdifferentcounterpartiesfordiversificationpurposes.

Here,weassumethatforeachcurrencykandcustomerc,intermediaries’counterpartypositionisdirectlyproportionaltotheirholdingincurrencyk,i.e.,

Zi,k,c=Zi,k(2)

whereZi,k,cisdefinedasintermediaryi’spositionincurrencykoppositecustomerc.Foreachcounterpartyc,intermediaryifacesacostoftheform

(3)

9

FixedParticipationCosts:EachintermediarypaysafixedparticipationcostofλPC,ktotradeincurrencyk.Thiscanbethoughtof,forexample,asthecostofsettingupatradingdeskforcurrencyk.

2.2ModelPredictions

Wecanwritefinancialintermediaryi’sproblemas

(Risk)

λs,k(SafeAssetScarcity)

λPC,k1(FixedParticipationCosts)

(BalanceSheetCosts)

(CounterpartyCosts)

Ourfirstsetofpredictionsdoesnotrelyonintermediaryheterogeneity,soforclarityof

exposition,we(1)setfixedparticipationcoststozeroand(2)assumethereisnoheterogeneityacrossintermediariesinrisk-bearingcapacityorinriskfaced(i.e.,σi,k=σkforsomevalueσkandγi=γforsomevalueγ,∀i,and∀k)

.3

3Intheappendix,wepresentanexpressionforthebasiswithoutthissimplification,whichresultsinamorecomplicatedexpressionthatyieldsthesamepredictionsaspresentedhere.

10

TakingthefirstorderconditionwithrespecttoZi,k,andaveragingacrossintermediaries,

Basisk=(SafeAssetScarcity)+λBS|Xk,|(BalanceSheetCosts)+λCP|Xc,k,|

Thisexpressionforthebasisyieldsthefollowingpredictions:

Prediction1(SignoftheBasis).Thedirectionofsyntheticdemandfordollarsfromcurrencykdeterminesthesignofthebasis.

Prediction2(BalanceSheetCosts)