IMF -有戰(zhàn)略投資者的債務(wù)危機 A Debt Crisis with Strategic Investors - Changes in Demand and the Role of Market Power

ADebtCrisiswith

StrategicInvestors:

ChangesinDemandandtheRoleofMarketPower

RicardoAlvesMonteiro

WP/25/19

IMFWorkingPapersdescriberesearchin

progressbytheauthor(s)andarepublishedtoelicitcommentsandtoencouragedebate.

TheviewsexpressedinIMFWorkingPapersare

thoseoftheauthor(s)anddonotnecessarily

representtheviewsoftheIMF,itsExecutiveBoard,orIMFmanagement.

2025

JAN

NATn

?2025InternationalMonetaryFundWP/25/19

IMFWorkingPaper

InstituteforCapacityDevelopment

ADebtCrisiswithStrategicInvestors:ChangesinDemandandtheRoleofMarketPowerPreparedbyRicardoAlvesMonteiro*

AuthorizedfordistributionbyAliAlichiJanuary2025

IMFWorkingPapersdescriberesearchinprogressbytheauthor(s)andarepublishedtoelicit

commentsandtoencouragedebate.TheviewsexpressedinIMFWorkingPapersarethoseofthe

author(s)anddonotnecessarilyrepresenttheviewsoftheIMF,itsExecutiveBoard,orIMFmanagement.

ABSTRACT:Thispaperdocumentschangesininvestors'demandforsovereigndebtduringadebtcrisis.UsingadatasetcontainingindividualbidsonPortuguesedebtauctions,Idocumentthatbidfunctionsbecomemoreinelasticduringthecrisis.Thatis,investorsrequirebiggerdropsinpricetobuyadditionalunitsofdebt,increasingthegovernment’smarginalcostofissuingdebt.Ithendecomposethesechangesindemandintotwo

components:afundamentalcomponent,duetochangesinthevaluationofthesecurity,andastrategiccomponent,thatarisesfrominvestors'marketpower.Ifindthat,althoughtheroleofmarketpowerisnegligibleinnormaltimes,itgetsmorepronouncedleadinguptoandduringthecrisis.Thegovernmentisnotabletoextractthefullsurplusfromstrategicinvestors,and,asaresult,theauctionmechanismlosesefficiencyduringthatperiod.Finally,Idiscussapossiblemitigationstrategy.Everythingelseconstant,theuseofshortermaturitiescouldavoidhigherinefficiencycosts.

JELClassificationNumbers:

D44,E43,F34,G12,H63

Keywords:

Debtauctions;defaultrisk;demandelasticity;marketpower

Author’sE-MailAddress:

ralvesmonteiro@

*IthankAgênciadeGest?odaTesourariaedaDívidaPública-IGCP,E.P.E.foraccesstothedataset.IamgratefultomyadvisorsManuelAmadorandTimKehoefortheirsupportandinsightfuldiscussions.IthankCristinaArellano,MarcoBassetto,TamonAsonuma,DanielBelchior,JoséCardosodaCosta,CristinaCasalinho,DoireannFitzgerald,SteliosFourakis,WilliamJungerman,LeonardoMartinez,FranciscoRoldan,andparticipantsattheMinnesota-WisconsinInternationalMacroWorkshop,andattheInternationalMonetaryFundInstituteforCapacityDevelopmentforexcellentcomments.Allremainingerrorsaremyown.

3

WORKINGPAPERS

ADebtCrisiswithStrategic

Investors:ChangesinDemandandtheRoleofMarketPower

PreparedbyRicardoAlvesMonteiro1

1IthankAgênciadeGest?odaTesourariaedaDívidaPública-IGCP,E.P.E.foraccesstothedataset.IamgratefultomyadvisorsManuelAmadorandTimKehoefortheirsupportandinsightfuldiscussions..IthankCristinaArellano,MarcoBassetto,TamonAsonuma,DanielBelchior,JoséCardosodaCosta,CristinaCasalinho,DoireannFitzgerald,SteliosFourakis,WilliamJungerman,LeonardoMartinez,FranciscoRoldan,andparticipantsattheMinnesota-WisconsinInternationalMacroWorkshop,andattheInternationalMonetaryFundInstituteforCapacityDevelopmentforexcellentcomments.Allremainingerrorsaremyown.

1

1Introduction

Governmentsaroundtheworldmaintainenormousstocksofsovereigndebt.Mostofthisdebtisissuedinauc-tionsandonlythentradedinthesecondarymarket.Insovereigndebtauctions,investorssubmitbidsconsistingofthehighestpricetheyarewillingtopaytopurchaseaunitofdebt,andhowmuchtheyarewillingtobuy.Then,thegovernmentchooseswhichbidstoaccept.Itfollowsthatthegovernmenteffectivelytakesinvestor’saggregatebidfunctionasgivenandchoosesitspreferredpricequantitypair.Thegovernmentisamonopolistinsovereigndebtauctions.

Theelasticityofdemandisakeystatisticforamonopolistasitpinsdownitsoptimaldecision.Demand,however,israrelyobservedbytheresearcher,letaloneitselasticity.Inthispaper,IuseaproprietarydatasetcontainingallindividualbidssubmittedonPortuguesesovereigndebtauctionsfrom2003to2020toestimatetheelasticityofdemand.Thetime-seriesincludestheEuropeansovereigndebtcrisisof2010-2014,providingauniqueopportunitytoassesshowdemandandthepriceelasticityofdemandchangeduringhighdefaultriskevents.Thecrisisperiodstartsin2010,afterthenewlyelectedGreekgovernmentdisclosedthatitsbudgetde?citswerefarhigherthanpreviouslythough,thisledtothedowngradeofGreekdebtandtoasharpincreaseinspreads.ThefocussoonfollowedtoPortugalthatbyApril2011,afterabailoutfromtheInternationalMonetaryFundandEuropeaninstitutions,lostpartofitsmarketaccess.Thisperiodlastedthrough2013,andby2014Portugalhadafullreturntonormal,pre-crisis,procedures.

ThePortugueseagencythatissuessovereigndebtmentionschangesindemandaroundthedebtcrisisastheexplanationforloweramountsbeingissuedduringtheperiod.Analyzingthedifference,attheauctionlevel,betweentheaveragepriceandthemarginalprice,thelowestpriceaccepted,isinformative.Figure

1

depictsthisdifferenceasthespreadbetweenthemarginalyield

1

,themaximumyieldacceptedbythegovernment,andtheaverageoftheyieldsbidintheauction,weightedbytheamountbid,for12monthTreasuryBills.Innormaltimes,theaverageandmarginalpricesareveryclose,andspreadsareessentiallyzero.Duringthecrisis,however,themarginalpriceoftheauctionislowerthantheaverageprice.Conversely,marginalyieldsarehigherthanaverageyields.Thisdifferencebetweenpriceshighlightswhyitismisleadingtouseaverageyieldsasatooltoassessthecostofissuinganadditionalunitofdebt.Aspointedby

AguiarandAmador

(2021),theyieldcurvedoesnot

re?ectthemarginalcostofborrowing,itistheelasticityofthebondpricewithrespecttothegovernmentpolicy–theinverseoftheelasticityofdemand–thatdeterminesthemarginalcostofissuingagivensecurity.Ittellsushowbigofadropinprice(jumpinyield)investorsrequireforthegovernmenttoissuealargeramountofdebt.

I?ndthatthebidfunctionsforbothshortandlongmaturitysecuritiesgetsigni?cantlymoreinelasticleadinguptoandduringthesovereigndebtcrisis.Thatis,toincreasetheamountofdebtissuedby1%,thepriceneedstodecrease,inpercentageterms,bymorethanithadbeforethecrisis.Particularly,I?ndthattheinverseprice

elasticityforTreasuryBillsis,onaverage,thirteentimeshigherleadinguptoandduringthecrisis,from0.012to

1Ayieldistheinterestraterequiredbyinvestors,suchthatthepresentvalueoftheclaim–oneunitpromisestopay1euroatmaturity–isconsistentwiththepricesubmittedintheinvestor’sbid.

2

0.15basispoints.AsforTreasuryBonds,I?ndthatthesamemeasureofelasticityis,onaverage,26%higherintheleaduptothecrisisperiod

2

,from0.29to0.36basispoints.

20

Legend

12M3M

15

Spread(b.p.)

10

5

0

2005201020152020

Figure1:SpreadbetweenMarginalandAverageYieldsofTreasuryBills

Primarydealershipmodelsarewidelyusedbydebtmanagementof?ces.Inthese,onlyalimitednumberofauthorizeddealers–theprimarydealers–participatesintheauctions,andthenactasmarketmakersbysellingthosesecuritiesinthesecondarymarket.Asanexample,inEurope,accordingto

AFME

(2020),atleast20

countriesuseaprimarydealershipmodel.

Asmallnumberofparticipantssuggeststheexistenceofstrategicbehaviorfrominvestors.Inparticular,asinglebidin?uencesthepricethatclearstheauctionandinvestorsinternalizethateffect.Asaresult,bidssubmittedmightdifferfromthedealers’willingnesstopay.Thiswedge,betweenbidsandvaluations,isadirectconsequenceofdealer’smarketpower.Thisisincontrastwiththecompetitivenatureofsecondarymarketsfordebt,opentoamuchlargernumberofinvestors.

Thenon-competitivenatureofthemarketandinvestors’strategicbiddingmotivatesthedecompositionexer-cisethatfollows.Howmuchoftheobservedshiftsinbidfunctionsareduetoshiftsinthevaluationoftheassetandhowmuchoftheseshiftsareduetothemarketpowerofinvestorsandtheirstrategicdecisions?Isthisdecompositionofbidsconstantacrossmaturities?

Thegoaloftheexerciseistohaveabetterunderstandingofhowinvestors’demandforsovereigndebtwithdifferentmaturitiesevolvesaroundhighdefaultriskevents,whileconsideringthenon-competitivenatureofthemarket.Withthisdecomposition,itispossibletoestimatewhatistheelasticityoftheactualinvestors’willingnesstopay.

2NotethatTreasuryBondsstoppedbeingissuedinmid2011aroundthebailout.ThisexplainswhytheincreaseisnotasnoticeableforTreasuryBonds.

3

To?lterthedata,Iintroduceanenvironmentbasedon

Wilson

(1979)framework,andmorespeci?callyon

Hortac?suandMcAdams

(2010)and

Kastl

(2011b)

.Theauctionmodelusesadiscriminatorypriceprotocol–pay-as-bid–andtreatsallinvestorsasidenticalex-ante.Investorsdifferex-postontherealizationoftheidiosyncraticprivatesignalsregardingthesecuritybeingauctioned.Giventheprivaterealizationoftheirsignal,aswellastheirsubjectiveexpectationoftheaggregatestate,eachinvestorthensubmitsadiscretebidfunctionthatmaximizestheirexpectedutility.

Inthedataset,Iobservetheequilibriumobject,thediscretebidfunctions.Throughanecessaryequilibriumcondition,Ithenbackouttheprimitive,investors’truevaluations.Withbothinvestor’svaluationsandbids,Iassesshowthewedgebetweenthetwoevolvesaroundthecrisis.Thiswedgerepresentsinvestor’smarketpower:biddingbelowthevaluationispossibleasinvestorsinternalizethatasinglebidcanin?uencetheclearingprice.

I?ndthatmarketpowerplaysalimitedroleduringnormaltimes.However,leadinguptoandduringthecrisisthewedgebetweenbidsandvaluationgetsmorepronounced.Themechanismfollows.Innormaltimes,thebidscheduleismostly?atandassuch,investorshavenoroomtoexercisemarketpowerandarepricetakersforallintentsandpurposes.Leadinguptoandduringthecrisis,bidsgetmoredispersedandbidschedulesbecomesteeper.Theincreaseddispersionofbidsimpliesthatthesubjectivedistributionsofthepricethatclearstheauctionarelessprecisethanbeforethecrisis.Particularly,thelikelihoodratioofbidk+1inabidfunctionbeingawinningbid,relativeto,bidkbeingthelastwinningbid,increases.Thisleadstoalargerwedgebetweenbidsandvaluationsasinvestorsbidbelowvaluetoavoidthewinner’scurse.

Aconsequenceofthelargerwedgebetweenbidsandvaluationsisthattheauctionmechanismbecomeslessef?cientduringthecrisis.Thatis,thegovernmentisnotabletoextractthefullsurplusfrominvestorsastheyarebidingbelowtheirwillingnesstopay.Lettheinef?ciencybemeasuredastheratiooftheaggregatewedgeovertheamountissuedineachauction.I?ndthat,attheirpeak,inef?ciencycostsgoupto0.6%oftheissuedamount,duringthecrisis.

Finally,amorenormativeanalysisshouldfollow.Particularly,whatcanthegovernmentdotomitigatetheseinef?ciencycostswhenissuingdebtduringacrisis?Ibrie?ylookatmaturitychoiceasamitigationdevice,asdifferentsecuritiesfacedifferentwedgesbutalsoneedtoberolledoveratdifferentfrequencies.Amorethoroughanalysisofoptimalmaturitychoiceaccountingfortheinef?ciencycostsofthemechanismisleftasfutureresearch.

Theremainderofthepaperisorganizedasfollows:section2presentsaliteraturereview;section3introduces

thedatawhileprovidingrelevantinstitutionalbackgroundandevidenceforchangesindemandleadinguptoand

duringthecrisis;section4presentsthemodelusedto?lterthedataandbackoutinvestors’valuationsofthesecuritiesbeingauctioned;section5discussestheestimationprocedure;section6discussestheroleofmarketpowerandpresentstheriseofinef?ciencycostsleadinguptoandduringthecrisis;section7discussesapossiblemitigationstrategyfromthegovernmentthroughmaturitychoice;section8concludes.

4

2LiteratureReview

Thispaperbuildsonthesovereigndebtanddefaultliterature,withanemphasisontheauctionframeworkusedtoissuedebtandinvestors’marketpower.Relatedpapershereinclude

Coleetal.

(2021)and

Bigioetal.

(2021)

.Eachusesdataforsovereigndebtauctionsforothercountries.Themotivationof

Coleetal.

(2021)issimilar,

theauthorspresentamodelthatfocusoninvestors’choicesinanauctionsettingwithinformationheterogeneity.However,intheirsampletherearenomeaningfulhighdefaultriskepisodes,andwhiletheauthorsfocusonmatchingmomentsandpatternsinmicrodataforMexico,theydonottacklethechangesindemandduringahighdefaultriskeventandtherolethatmarketpowerplaysontheevolutionofbids.

Bigioetal.

(2021)usesmicro

dataonsovereigndebtauctionsfromSpaintoassessliquiditycosts.Theirfocusisonoptimaldebt-maturitymanagementinthepresenceofsuchcosts.Ialsodiscussmaturitychoicebutasamitigationstrategytotheinef?ciencycostscreatedbyinvestors’marketpower.Importantly,withthisdataencompassingthehighdefaultriskevent,Icantopresentestimatesforthepriceelasticityoftheaggregatebidfunctionsandevaluatehowthiselasticityevolvesaroundthecrisis.

Thispaperalsorelatestothoseestimatingelasticitiesofdemandforsovereigndebt.Relatedpapersinclude

Albuquerqueetal.

(2022)and

Morettietal.

(2024)

.

Albuquerqueetal.

(2022)usesbidleveldataforPortuguese

sovereigndebtauctionstoestimatetheelasticityofdemandandassessitspredictivepowerforsame-bondpost-auctionreturnsinthesecondarymarket.Todosotheyfocusonuniformpriceauctionsafterthesovereigndebtcrisis.Thispaperestimateselasticityandanalysisitsevolutionaroundthesovereigndebtcrisis.Itthenusesthisinformationtobetterunderstandtheimplicationsofdefaultriskforstrategicbidding.

Morettietal.

(2024)

estimatestheelasticityofdemandforsovereigndebtinthesecondarymarket.Itthenincorporatestheinelasticdemandintoasovereigndebtmodeltoassessitsimpactongovernment’ssupplyofbondsanddefaultrisk.Incontrast,thispaperestimatestheelasticityofdemandforsovereigndebtintheprimarymarkets.Asnotedbefore,thesecondarymarketpricedenotestheaveragepriceofdebt,whichcandiffersubstantiallyfromthemarginalpriceofdebtattheauction.Thelatteriswhatdetermineshowmuchdebtthegovernmentissuesattheauction.

Intermsofmethodology,theauctionmodelusedto?lterthedataisbasedon

Hortac?su

(2002),and

Kastl

(2011b)

.

Hortac?su

(2002)presentsamodelbasedon

Wilson

(1979)ofamulti-unitdiscriminatorypriceauction

witha?nitenumberofsymmetricrisk-neutralbidderswithindependentprivatevalues.Inthismodel,asinglebidaffectsthebidfunctionsthroughchangesinthedistributionofthepricethatclearstheauction.Theyconstructanon-parametricestimatorofthedistributionexploitingare-samplingtechnique.

Kastl

(2011a)buildsonthis

frameworkbyallowingfordiscrete-stepbidfunctions.

Kastl

(2020)providesareviewoftheliteratureandmethods

appliedto?nancialauctionsandparticularlytotreasurybondauctions.Thispaperusesthetoolsdevelopedbytheauthorsmentionedandfocusinsteadontheimpactthatahighdefaultriskeventhasondealers’biddingpatternsand,particularly,tobidshadingovertime.

Thispaperalsorelatestothequantitativesovereigndebtliterature.Theworkthatstartedwith

Aguiarand

Gopinath

(2006)and

Arellano

(2008),basedontheclassicsettingof

EatonandGersovitz

(1981),focuson

5

sovereigndefaultastheoutcomeofthegovernment’s?nancingproblemprovidedtherearecompetitiveinvestorsthatarewillingtolendaslongastheybreakeven

3.

Sincethoseinitialquantitativemodels,therehasbeensubstantialdevelopmentsintheliteraturewiththestudyofmaturitychoiceandself-ful?llingcrisis,tonameafew.Examplesofsuchare

ArellanoandRamanarayanan

(2012)andquantitativemodelsbasedon

Coleand

Kehoe

(2000),suchas

BocolaandDovis

(2019)

.Finally,

Aguiaretal.

(2019)pointsoutthatthepriceelasticity

ofdemandisthecrucialelementthatdetermineshowmuchthegovernmentborrowsandwhetheritpreferstoborrowlong-termdebtorshort-termdebt.Thispaperprovidesestimatesforthepriceelasticityofdemandandaimstoofferabroaderunderstandingofinvestors’strategicconsiderationsinthecontextoftheprimarymarketforsovereigndebtanditsinteractionwithdefaultrisk.

Thispaperalsorelatestothestrandofliteratureonsovereigndebtmanagementandmaturitychoice.Previ-ousworkonthetopicinclude

ArellanoandRamanarayanan

(2012),

Broneretal.

(2013),

Snchezetal.

(2018)

and

Aguiaretal.

(2019)

.Inthispaper,Ipresenttheinef?ciencycostsinducedbytheauctionmechanismfordif-ferentmaturities.Thefactthatinef?ciencycostsvaryacrossmaturitiesintroducesanewmargintobeconsideredformaturitychoice.

Finally,thepaperisrelatedto

AlvesMonteiroandFourakis

(2023)inthatitsharesthesamedatasetand

studiesthecrisisperiodinPortugal.Thisotherpaperhowever,hasadifferentgoal.Insteadoffocusingonthegamebetweeninvestorsinanauctionwhentheyexercisemarketpowergivenarandombondsupply,itfocusonthestrategicinteractionbetweenthesetofinvestorsandagovernmentthatalsooptimizes.

3Data:BackgroundandEvidence

AuctiondatawasprovidedbythePortugueseTreasuryandDebtManagementAgency(IGCP,Portugueseacronym).ThedatacomprisesallauctionsofTreasuryBills(shortmaturities)andTreasuryBonds(longma-turities)heldfrom2003and2004,respectively,andupto2020.Assuch,thetimeseriesincludesthesovereigndebtcrisisof2010-2014,whichenablestheanalysisofchangesindemandduringthatperiod.Importantly,thedatacomprisesallindividualbids(priceandamount)thatwereplacedineachauction,eveniftheywerenotexecuted.

IssuanceofTreasuryBillsintheprimarymarketisdonethroughauctions.TreasuryBondsarelaunchedforthe?rsttimeinsyndicatedoperations

4.

Newissuancesofalinethathasalreadybeenlaunchedaredonethroughauctions.Bothtypesofsecuritieswereauctionedusingadiscriminatorypriceprotocol,whereinvestorspay-as-bid,upto2011.From2014onward,TreasuryBondswereauctionedusingauniformpriceprotocol,wherebidsareexecutedatthemarginalpriceoftheauction.Forathoroughanalysisoftheimpactoftheauctionprotocolontheoutcomesoftheauctionsreferto

AlvesMonteiroandFourakis

(2023)

.

TheIGCPusesaprimarydealershipmodeltoissuebillsandbonds.Onlyprimarydealers,agroupof?nancial

3See

AguiarandAmador

(2014)forasurvey.

4Asyndicateisagroupofbanksthatisgiventhemandatetoplaceaspeci?camountofgovernmentbonds.ItfollowsabookbuildingprocessthatallowsforpermanentlymonitoringofordersandinterventionintheallocationofsuchordersbytheIGCP.

6

intermediaries,participateintheauctions.Dealersarepermittedtosubmitmultiplebids

5

providedthatthetotalvaluedoesnotexceedtheupperlimitoftheoverallamountannouncedfortheauction.

Anauctionisasfollows:i)thegovernmentannouncesanauctionandthecharacteristicsofthesecuritybeingauctioned,aswellasatargetforthesizeoftheissuance;ii)theauctiontakesplaceandinvestorssubmitbidsthatconsistofapriceandamountpair;iii)theauctionclosesandthegovernmentordersbidsindescendingorderofprice;iv)thegovernmentchoosestheminimumpriceitiswillingtoaccept,determiningthesizeoftheissuance;v)bidsabovetheminimumpriceareexecutedandinvestorspayeithertheminimumprice(inauniformpriceauction)orthepricetheybid(inadiscriminatorypriceauction).

Table

1

presentssomesummarydataforthemostcommonbillandbondauctions.Onecanobserve400TreasuryBillauctionsand161TreasuryBondauctions.Themostcommonmaturitiesare12and3monthsforthebillsand10and5yearsforbonds.Inbillauctionsthenumberofbidsaverages39andinbondauctionsitaverages56.Dealers(mean)refertotheaveragenumberofdealerspresentintheauctionsofeachsecurity.Steps(mean)refertotheaveragenumberofbidssubmittedbyasingledealer.Issued(mean,MC)refertotheaverageamountissuedbytheIGCPinauctionsofeachtypeofsecurity.

Table1:SummaryDataonTreasuryBondandBillauctions

Security

Auctions

Bids(mean)

Dealers(mean)

Steps(mean)

Issued

(mean,MC)

3Months

101

35.2

14.5

2.4

471.0

6Months

88

36.4

14.7

2.4

505.6

12Months

101

44.0

15.4

2.8

1,037.5

AllBills

400

38.7

14.8

2.5

703.1

5Years

21

55.9

18.9

2.8

732.3

6Years

14

56.5

18.2

3.0

754.1

10Years

52

59.1

17.9

3.2

805.8

AllBonds

161

56.4

17.9

3.0

756.0

3.1ChangesinDemand

BelowIshowevidencethatmotivatestheshiftininvestors’demandforPortuguesesovereigndebtwhileap-proachingandduringthesovereigndebtcrisis.Figures

2

and

3

,respectively,presenttheaggregatebidfunctions(downwardstepfunctions)andtheamountsissued(dashedline)bythePortugueseGovernmentin3-monthand12-monthtreasurybillauctionsovertime.Inpanel(a),theaggregatebidfunctionsarepresentedaspriceandamountpairs:theamountthatthegovernmentisabletoraiseateachgivenprice.Panel(b)presentsanalter-nativerepresentationoftheaggregatebidfunction:theyieldrequiredbyinvestorsforborrowingeachamountto

thegovernment.Theaggregatebidfunctionisobtainedbyaggregatingindividualbids.

5ForTreasuryBillauctionseachdealermaysubmitupto?vebidsperauction,forTreasuryBondauctionsalimitisnotspeci?ed.

7

Theanalysisfocusonthecrisisevent.The?gurespresentarepresentativeauctionbefore,duringandafterthesovereigndebtcrisis

6.

AdjustedPrice

1.010

1.005

1.000

0.995

0.990

Feb21,2007Apr20,2011Feb18,2015

050010000500100005001000

Amount(millionEUR)

(a)ChangesinDemand(Prices)

Differencefrommaximumyield(b.p.)

0

-100

-200

-300

-400

Feb21,2007Apr20,2011Feb18,2015

05001000

0500100005001000

Amount(MillionEUR)

(b)ChangesinDemand(Yields)

Figure2:Aggregatebidfunctionsfor3monthtreasurybills

6IntheappendixIpresentasequenceofallauctionsfrom2007to2016.Exactdatesdifferdependingonthematuritybeingissued.

8

AdjustedPrice

1.010

1.005

1.000

0.995

0.990

May16,2007Mar16,2011Mar18,2015

050010001500200005001000150020000500100015002000

Amount(millionEUR)

(a)ChangesinDemand(Prices)

Differencefrommaximumyield(b.p.)

50

0

-50

-100

May16,2007Mar16,2011Mar18,2015

0500100015002000

05001000150020000500100015002000

Amount(MillionEUR)

(b)ChangesinDemand(Yields)

Figure3:Aggregatebidfunctionsfor12monthtreasurybills

9

Inpanel(a),pricesarenormalizedbythemarginalpriceoftheauction,i.e.theminimumpriceacceptedbythegovernment.Thatis,bidswithanadjustedpriceabove1areexecutedandthosewithanadjustedpricebelow1arenotexecuted.Panel(b)depictsthedifference,inbasispoints,betweenthemaximumannualizedyieldacceptedbythegovernmentintheauctionandtheannualizedyieldsassociatedwitheachsubmittedbid.Itfollowsthatbidswithapositivedifferenceinyieldsareexecutedandthosewithyieldsabovethemaximumyieldaccepted(andso,anegativedifference)arenotexecuted.Finally,themaroondashedlineidenti?estheamountofdebtissuedineachauction.

Duringtheperiodbeforethecrisis,representedbytheauctionsin2007,thereisalmostnodispersionacrossthepricesofindividualbids.Thatis,investorssubmitsimilarly?atbidfunctions.Duringthecrisisperiod,rep-resentedbytheauctionsin2011,thisisnolongerthecase.Particularly,thereareseveralbidswithpricessigni?cantlybelowtheauctionprice,and,consequently,requiringyieldsfarabovethemaximumacceptedyield.Notethatabidwithaprice1%belowthemarginalpriceintheauction,requiresanannualyield400basispointsor100basispointsabovethemaximumacceptedyield,for3monthand12monthbills,respectively.Thesearemeaningfuldifferences.Afterthecrisisperiod,representedbytheauctionsin2015,thereisarecoveryoftheaggregatebidfunct