Interest rate risk propagation: Evidence from the credit crunch

NorthAmericanJournalofEconomicsandFinance28(2014)242–264

ContentslistsavailableatScienceDirect

North

American

Journal

of

Economics

and

Finance

Interest

rate

risk

propagation:

Evidence

from

the

credit

crunch

Hsin-Feng

Yang

_,

_Chih-Liang

_Liu

_,

_Ray

_Yeutien

_Chou

a_{InstituteofBusinessandManagement,NationalChiaoTungUniversity,Hsinchu,Taiwan} b_{DepartmentofFinance,NationalYunlinUniversityofScienceandTechnology,Yunlin,Taiwan} c_{InstituteofEconomics,AcademiaSinica,Taipei,Taiwan}

a

r

t

i

c

l

e

i

n

f

o

a

b

s

t

r

a

c

t

Duringthe2007–2009financialcrisis,USsubprimemortgagerisk

exposuresledtosevereliquidityproblemsinseveralotherforeign

markets.Suchriskcontagionwascausedbyenormouschanges

ininterestrates.Althoughriskcontagionhasbeeninvestigated

byseveralliteratures,themagnitudeofpropagatedinterestrate

riskaroundglobalfinancialmarketsremainsunexplored.

There-fore,thisstudyquantifiesthedegreetowhichtheincreasedcredit

riskwithintheUSfinancialsystempropagatedtotheEuropean

markets’liquidityrisks.Specifically,usingaconditional

value-at-risk(CoVaR)model,wequantitativelymeasureinterestraterisk

ofaEuropeancountry,bylookingattheupsideriskin

distribu-tionofchangesininterestrate.Andsuchpropagationriskmeasure

considersadditionalvalue-at-riskconditionalontheinterestrate

movementsintheUS.Theresultsshowsignificantlypositive

dif-ferencesbetweenEuropeancountry’svalue-at-riskconditionalon

theUSfinancialmarketsbeinginanormalordistressed state.

Thispropagatingeffectincreasedfrom2007,andwasparticularly

pronouncedinthe2008–2009.Inaddition,theinterestraterisk

contagionisespeciallysevereforsomecountriesintheEuroregions

withgreatersovereigndebtproblems.Henceourresultforetellsthe

deteriorationoftheEuropeansovereigndebtcrisiswhichstarted

∗ Correspondingauthorat:DepartmentofFinance,NationalYunlinUniversityofScienceandTechnology,123UniversityRd., Sec.3,Douliu,Yunlin640,Taiwan.Tel.:+88655342601;fax:+88655312079.

E-mailaddresses:Yangsf.bm96g@nctu.edu.tw(H.-F.Yang),chlliu@yuntech.edu.tw(C.-L.Liu),rchou@econ.sinica.edu.tw (R.Y.Chou).

http://dx.doi.org/10.1016/j.najef.2014.03.010 1062-9408/©2014ElsevierInc.Allrightsreserved.

tounfoldin2010.Ourworksupplementstheliteratureby

suc-cessfullyquantifyingthemagnitudeofadditionalinterestraterisk

conditionalonriskexposurefromexternalsectors.

©2014ElsevierInc.Allrightsreserved.

1. Introduction

Inthispaper,wepositthattheinterestrateriskcontagionisthechannelthroughwhichthecredit

riskintheUScausedtheEuropeancountryilliquidityproblemsduringthe2007–2009creditcrunch.

Themoreilliquidfinancialinstitutionsinthebankingindustryare,thelargertheimpactwillbeonrisk

contagionfromanincreaseininterestrate,andsuchcloselinkagescausedinterestrateriskcontagion

(e.g.,Brunnermeier&Pedersen,2009).Therefore,bankssufferinginterbankcreditriskthreatsare

exposedtoilliquidity,andsuchacontagionofsystemicriskleadstosubsequentbankruptcies(see

e.g.,Billio,Gatemansky,Lo,&Pelizzon,2010;Diamond&Rajan,2005;Enenajor,Sebastian,&Witmer,

2012;McAndrews,Sarkar,&Wang,2009;Pais&Stork,2011;Sarkar,2009).Besidestheriskcontagion

amonginstitutions,theincreasedinterestratecanalsoexacerbateinternationalliquidityshortages,

andtheviciouscirclemakesinterestrateriskmoreseverearounddifferentcountries.Thus,fromthe

riskcontagionincountrylevel,wequantifythedegreetowhichthecreditriskinonecountryspread

toothercountriesbyanincreaseininterestrateandresultinliquidityproblems.

TheriskexposuresfromUScreditlossesquicklyspreadandexacerbatedtotheglobalfinancial

marketduringthe2007–2009creditcrunch,andbanks’insolvenciesalsospread rapidlytoother

countriesbywayofanincreaseininterestrates.Thedominoeffectofinterestrateriskpropagation

intheinterbankmarketledtobankinsolvencyandliquidityrisksinmanyEuropeanmarkets(e.g.,

Reinhart&Rogoff,2009;Upper&Worms,2004)andthe2007–2009creditcrunch(e.g.,Melvin&

Taylor,2009;Longstaff,2010).ThefactsofinterestrateriskcontagionareconsistentwithDiamond

andRajan(2005)thatthecontagionofinterestrateriskproblemsoccursallthetime,evenwhen

sectorssharenoexplicitconnection.

Althoughpriorliteraturehasinvestigatedriskcontagionacrossstockmarkets,carry-trademarkets,

realestatesectors,orforeignexchangemarkets.Similarly,riskcontagionduetocounterparty

relation-ships,macroeconomicrisk,orfinanciallinkageshasbeenfullyinvestigated(e.g.,Changa,McAleerc,&

Tansuchat,2013;Forbes&Rigobon,2002;Mandilaras&Bird,2007;Pais&Stork,2011;Pritsker,2001).

However,lessattentionhasbeenpaidtointerestrateriskandbankliquidity,andthemagnitudeof

propagatedinterestrateriskaroundglobalfinancialmarketsremainsunexplored.

Duringthe2007–2009creditcrunch,idiosyncraticcreditproblemsoriginatingfromtheUS

sub-primemortgagemarketspreadrapidlytoothercountriesthroughthechannelsofchangesininterest

rate(e.g.,Reinhart&Rogoff,2009;Tang&Yan,2010)becauseliquidityproblemscorrespondto

coun-terpartyrisk(e.g.,Brunnermeier&Pedersen,2009;Melvin&Taylor,2009).Interestratespread—that

is,thedifferencebetweenlendingandrisklessrates—thereforeprovidesakeytransmissionchannel

forinterestrateriskpropagation,particularlyforeconomicshocks(e.g.,Edwards,1998)andcanbe

takenasaleadingindicatorofdefaultrisk(e.g.,Bernanke,1990;Friedman&Kuttner,1993;Gertler,

Hubbard,&Kashyap,1991;TangandYan,2010).Inthisstudy,weuseamodifiedCoVaRmeasure

toexplorethedegreetowhichtheincreasedcreditriskwithintheUSfinancialsystemduringthe

2007–2009creditcrunchpropagatedtheEuropeanmarkets’liquidityrisks,whichwerecausedbyan

increaseininterestrates.Weexpecttoseethattheinterestrateriskcontagionisparticularlysevere

inseveralspecificilliquidEuroregionsandduringthefinancialcrisis.

Conventionalvalue-at-risk (VaR)modelsare incapableofeffectively addressingthecontagion

effectbecausetheydonotrevealhowtheriskfacedbyonecountryinfluencestheonefacedinother

countries.Therefore,welookattheupsideriskindistributionofchangesininterestrateandconvert

theunconditionalVaRmodeltoaCoVaRmodel,whichallowsustocapturetheadditionalcontagion

interestrateriskbysettingreasonableconditionalfactors(e.g.,Adrian&Brunnermeier,2011;Cakici

&Foster,2003).Specifically,welinktheinterestrateriskcontagiontoboththeliquidityriskinEurope

244 H.-F.Yangetal./NorthAmericanJournalofEconomicsandFinance28(2014)242–264

ThebenefitofCoVaRmodelisthatitcanestimatenotonlythesector’sownriskbutalsorisk

propa-gationbeyondtheinterdependence(e.g.,Adrian&Brunnermeier,2011).Inaddition,theCoVaRmodel

usesaquantileregressionwithoutdistributionalassumptionandallowsforalargerangeof

possi-blequantilesforriskpreferences.We,therefore,explorecountry-levelinterestrateriskcontagionby

measuringthemagnitudeoftheadditionalliquidityriskburdentoEuropeancountriesthatspread

fromtheUScreditmarketduringbothanoncrisis(2003–2006)andcrisis(2007–2009)periods.The

changesintheinterbankofferedrate(IBOR)areusedtoproxytheliquidityriskinEurope,andthe

differencebetweenTreasuryEurodollar(TED)spread—thedifferencebetweeninterestrateson

inter-bankloansandshort-termUSgovernmentdebt—isusedtoproxythecreditriskoftheUSfinancial

system.

Aftercontrollingpotentialproblemsofheteroskedasticityandendogeneitybyusingfitted

Euro-peanliquidityrisks,theresultsshowsignificantlypositivedifferencesbetweenEuropeancountry’s

VaRconditionalontheUSfinancialmarketsbeinginanormalordistressedstate.Theinterestrate

riskpropagatingeffectincreasessince2007andisparticularlysignificantin2008and2009when

liquidityproblemsaremostsevere.OurevidencerevealsthattheCoVaRmodelcansuccessfully

cap-tureEuropeanmarkets’liquidityriskconditionalonthecreditriskofUSfinancialsystem,particularly

duringthecrisis.WealsofindthatliquidityrisksareparticularlylargerinseveralEuroregionswith

smallereconomicscale(Switzerland,Austria,Belgium,Finland,andNetherlands)orseversovereign

debtproblems(Portugal,Ireland,andGreece).

TheempiricalresultssuggestthatwhencalculatinginterestrateVaR,financialsectorsshouldfocus

notonlyontheirownliquidityproblemsbutalsoontheadditionalriskpropagatedfromtheUS.

OurapplicationoftheCoVaRmodelformeasuringinterestrateriskcontagioncontributestothe

literatureinthefollowingways.First,weshowthatthemagnitudeofinterestrateriskcontagion

canbequantitativelymeasured.Althoughpaststudiesusedifferentmethodstoexaminewhether

thepropagationrelationshipbetweendifferentsectorsissignificant,theydonotmeasuretheactual

magnitudeofriskcontagion.Ourstudy,incontrast,resolvestheresearchquestionofquantification

ofthemagnitudeofinterestrateriskpropagation.

Second,wecomplementtheliteraturebyprovidingempiricalevidencetosupportpriortheoretical

viewsthatcreditinsolvencyinonecountryexacerbatesothercountries’liquidityrisks(e.g.,Diamond

&Rajan,2005;Pais&Stork,2011;Zheng&Zuo,2013).ApplicationofCoVaRininterestraterisk

prop-agationprovidespersuasiveevidencethatfinancialinstitutionsshouldevaluatenotonlytheirown

liquidityriskbutalsothecreditspilloverfromothersectors.Finally,ourstudyusesallavailableglobal

datatoidentifythecurrentcontagionrisk.Mostpriorempiricalstudiesaddressonlytheexistenceof

theriskcontagionphenomenon,whileourresultsmeasuretheseverityofriskcontagion.Therefore,

financialinstitutionscanadoptourmodelanduseallavailabledataforexanteanalysisto

evalu-atecurrentinterestrateriskcontagiontounderstandwhethertheircapitalandfinancialstatuscan

preventanyfurthercrisisthreats.

Theremainderofthestudyisorganizedasfollows.Section2developstheCoVaRmodeltocapture

thecontagionofinterestrateriskandintroducesthedata.Section3providesourempiricalresults,

andSection4offersourconcludingremarks.

2. Riskcontagionmodeling

2.1. Interestrateriskcontagion

Theimportantroleofbankingliquidityanditsdeterminantshadbeenraisedfromthecreditcrunch.

Exposuretomarketuncertaintiesandeconomicshockswithinfinancialinstitutionsaremaincausesto

disruptthebalancebetweenliquiditysupplyanddemandinthebankingsystemandexacerbates

fund-ingproblems.Assomefinancialinstitutionsincreasinglyfinancetheirassetholdingsandinvestments

withshortermaturityinstruments,liquidityproblemsbecomemoresevereinthewholefinancial

system(e.g.,Brunnermeier&Pedersen,2009;Pais&Stork,2011;Upper&Worms,2004).Moreover,

duringthe2007–2009creditcrunch,USsubprimemortgageriskexposuresledtosevereliquidity

problemsinseveralotherforeignmarkets,causedbytheenormouschangeininterbankinterestrates

(2009)indicatethatbecausefinancialinstitutionshaveverylargeamountsoftradesacrossvarious

counterparties,creditriskspreadstootherfinancialsectorsandcausessevereliquidityproblems.

Therefore,theliquidityproblemiscausednotonlybythelocalinterbankfundingproblems,butalso

bythecreditriskpropagatedfromexternalsectors.

Theliquidityproblemscausedfromexternalcreditriskcontagionarethroughtheinterbank

link-agesandchangesininterestrate.Firstly,regardingtotheinterbanklinkages,Longstaff(2010)suggests

thataneconomicshockandthesubsequentcrisisleadsfinancialassetstobetransferredtoother

sec-tors,whichisconsistentwithDiamondandRajan(2005),Brunnermeier,Nagel,andPedersen(2008),

andPaisandStork(2011)thatbanks’liquidityproblemsarecloselylinkedwithsystemicrisk.Also,

DiamondandRajan(2005)addressthatwhenonesector’sassetsbecomeilliquid;its

correspond-ingcounterpartiesalsofacesimilarliquidityproblems.Thus,theinterbanklinkagescausebanking

illiquidityandcantriggeraglobalfinancialcrisis.

Secondly,theinterestrateriskpropagatesrapidlyfromonecountrytoanotherevenifthetwo

arenotexplicatedconnected(e.g.,Diamond&Rajan,2005;Longstaff,2010).Literaturessuggestthat

themainreasonforriskcontagionisexcessiveriskexposuresandinterbanklinkages(e.g.,Elsinger,

Lehar,&Summer,2006;Furfine,2003;Johansson,2009;Pais&Stork,2011;Upper&Worms,2004).

Inadditiontothedirectlinkages,othermechanismsalsoallowrisktotransfertodifferent

counter-parties.Forexample,Smith(1991)andAllenandGale(2000)findthatinterest-rateriskpropagation

ismoresevereinbankswithhigherinterbankloans.Althoughpricecomovementandcross-market

interdependencehavebeenfullyexplored(e.g.,Dungey&Martin,2007;Forbes&Rigobon,2002;Pais

&Stork,2011;Pritsker,2001),studiesoninterest-rateriskpropagationinfinancialmarketsarerare.

Inthispaper,wepositthatthechangeininterestrateusethepropagationmechanismsthroughwhich

thecreditriskinonecountryspreadsefficientlytootherfinancialmarketliquidity.

Sincethespilloverrelationbetweenthecreditmarketandliquidityisthroughachannelofchanges

ininterestrate,theinterestratespreadcanbeusedtocapturethiscontagionphenomenon(e.g.,Adrian

&Shin,2010;Borio&Zhu,2012;Brunnermeier&Pedersen,2009;Fong,Valente,&Fung,2010;Gorton

&Metrick,2012).TheTreasuryEurodollar(TED)spreadisameasureofcreditriskcausedbyenterprise

distressesinfinancialmarket(e.g.,Chan-Lau,2010).WhencreditriskismoresevereintheUS,the

TEDspreadincreases,andbankrunscausefinancialinstitutionstoturnfromriskyportfoliostoward

lessriskyinvestments(e.g.,Brunnermeieretal.,2008).Therefore,formeasuringtheUScreditmarket

inthisresearch,weadoptthechangesintheTEDspread,thedifferencebetweentheyieldofthe

three-monthIBORandthethree-monthTreasurybillrate,asthecreditrisk.AsTEDt,thedifference

inTEDspreadbetweentimetandtimet−1,increases,thecostofcapitalriskalsoincreases(e.g.,Billio

etal.,2010;Diamond&Rajan,2005;Sarkar,2009).

Becausethechangesintheinterbankofferedrate(IBOR)canberegardedastheupsideofrisk

exposuretoliquidityrisk(e.g.,Melvin&Taylor,2009;Chan-Lau,2010;Delis&Kouretas,2011;Wong

&Fong,2011),theIBORistakenasopportunitycostofcapitaltransferbetweenfinancialinstitutions

andinvestors(e.g.,Hull,2009).Becauseabankneedstosatisfycertaincreditworthinesscriteriato

quoteanIBOR,sucharateisregardedasanindexforilliquidfundingmarket.We,therefore,take

thechangeintheIBORattimet(IBORt),thedifferenceinone-monthIBORbetweentimetand

timet−1,aseachEuropeancountry’sliquidityrisk.AhigherIBORtisanindicationofadecreased

willingnesstolendbymajorbanks,whilealowerIBORtmeanshigherliquidityinthemarket.As

such,byusingTEDtasanindicationofthebanks’creditworthinessoffinancialmarketandIBORtas

ageneralavailabilityofliquidfundsforbankinglendingactivities,largerinterestratespreadsindicate

anincreaseininterbankilliquidityandinterestrateriskcontagion.

2.2. CoVaRmodel

Theextantliteratureproposesvariousmeasuringapproachesforstudyingthechannelsandcauses

ofriskcontagion,butdistributionassumptionsandmodelinglimitationsconstrainsomeofthe

tradi-tionalapproaches.VaRmodels,forexample,onlyprovidetheirownminimumlossifataileventtakes

place.Suchmodelsdonotrevealthepotentiallosscausedbyriskpropagatedfromothersectors.The

errortermsofthedynamiccorrelationorautoregressiveconditionalheteroscedasticitymodelsneed

estima-246 H.-F.Yangetal./NorthAmericanJournalofEconomicsandFinance28(2014)242–264

tions.Also,thelogitandprobitmodelsonlyfitdiscreteorlimiteddependentvariables.Besides,the

extremevaluemethodologymayignoretheinformationcontentofalargeportionofadatasample,

andtheriskmeasurecouldbeunderestimated(e.g.,Wong&Fong,2011).Inadditiontothedistribution

presumptionsandmodelinglimitations,anotherconcernistimelag.

Differentfrompriorapproachesforestimatingriskcontagioneffectsinfinancialmarkets,some

studiesexaminedthecontagioneffectbymeasuringthedistancetodefault andthen comparing

thedefaultrateamongdifferentbanks.However,theexpecteddefaultfrequencymodelneedsto

beassumedastaticdebtstructure,althoughthevalueofafirm’sassetschanged(e.g.,Saunders&

Allen,2002).Therefore,thesedefault-basedmodelscannotcapturetheex-anteriskcontagioneffect.

Thus,weproposeanalternativeapproachwithoutlimitationstomeasurethecontagionrisk.

To constructa contagion riskmodel in which ex-anterisk propagationcan bequantitatively

measuredwithoutdistributionlimitations,we modifytheCoVaRmodel proposedbyAdrian and

Brunnermeier(2011).Specifically,weemphasizetheadditionalliquidityriskscausedbyrisk

prop-agatedfromexternalcreditmarket.Suchinterestrateriskcontagioneffectconditionalonexternal

sectors’riskcanbeestimatedbyusingquantile regressionofchanges inIBORonthechangesin

TEDspread.Thisapproachisparticularlyusefulforconsideringdifferentriskpreferenceandvaried

percentilesfreefromdistributionassumptions.

Formeasuringsystemicrisk,theCoVaRmeasurementproposedbyAdrianandBrunnermeier

(2011)is definedasthedifferencebetweenVaR conditionalontheinstitutionbeingin anormal

stateandVaRconditionalontheinstitutionbeingindistress.Duringthe2007–2009globalfinancial

crisis,theUSeconomyfacedseverecreditrisk,causingUSfinancialsectorstocomeunderstress;

incontrast,duringanormaltimeperiod,theUSfinancialsystemisliquid,andchangesininterbank

interestratereflectnormalvariationofcreditrisk.Itisexpectedtoseethatduringcrisisperiods,the

valueofCoVaRishighercomparedtotheoneinnormaltimeperiod.Therefore,theCoVaRvalue

canbeusedtoidentifytheriskspillovereffectsandadditionalrisksfacedbyaninstitutioncausedby

interconnectedandsystemicallysignificantinstitutions.Inaddition,itcanbespecificallytakenasan

indextocapturethetoo-interconnected-to-failphenomenon.Inthefollowing,themodelingforthe

CoVaRvaluewillbespecificallyintroduced.

Fordownsiderisk,unconditionalVaRofinstitutioniattheqpercentileisdefinedas

Pr(Xi≤VaRiq)=q. (1)

TheVaRofinstitution,VaRi

q,typicallyanegativenumber,isdeterminedbytheassetreturnvalue

ofinstitutioni(Xi_{)andquantileq.BeyondconventionalunconditionalVaR,weextendtoaconditional}

VaR,whichistheVaRofinstitutionjconditionaloninstitutioni’seventC(Xi_{),saydistressorilliquidity.}

Wheninstitutioni’sasset—returnattainsitsVaRvalue{Xi_=VaR

qi}:

Pr(Xj_≤CoVaRj|C(Xi)

q |C(Xi))=q. (2)

Furthermore,institutioni’scontributiontotheriskofinstitutionjcanbedefinedas

CoVaRj|iq =CoVaR

j|Xi_=VaRi q

q −CoVaRj|X

i_=Mediani

q , (3)

whereCoVaRj|Xq i=MedianidenotestheVaRofinstitutionj’sassetreturnswheninstitutioni’sreturnsare

atitsnormalstateoftheirdistribution(e.g.50%percentile),andCoVaRj|Xq i=VaRiq isinstitutionj’sVaR

wheninstitutioni’sreturnsareatadistressedorextremelypoorstatesuchasduringacrisisperiod.

Moreover,CoVaRj|iq indicatesthedifferencebetweenVaRofinstitutionjconditionalonthedistress

ofanotherinstitutioniandVaRofinstitutionjconditionalonthenormalstateofinstitutioni.Such

CoVaRquantifieshowmuchaninstitutionaddstoanotherinstitution’srisk.

Thevariationinassetreturnvalueofinstitutioni(Xi_{)isestimatedasafunctionofstatevariables:}

whereMdenotesavectorofstatevariables.Also,tocaptureVaRofinstitutionjconditionalonanother

institutioni,thevariationinassetreturnXj_{canalsobeestimatedbyincludingtheinstitutioni’sasset}

returnvariation(Xi_):

Xtj=˛j|i+ˇj|iXti+Mt−1j|i+εj|it , (5)

Theestimationrunsthequantileregressionbyoptimizingamodifiedfunction:

min

˛q,ˇq,q



t



q|X_tj−˛j|iq −ˇj|iqXti−Mt−1qj|i| if(Xjt−˛ j|i

q −ˇj|iqXti−Mt−1qj|i)≥0

(1−q)|X_tj−˛j|iq −ˇj|iqXti−Mt−1qj|i| if(Xjt−˛ j|i

q −ˇj|iqXti−Mt−1qj|i)<0

(6)

Throughoutthestudy,weestimatethepercentilesq=99%and95%casesasmostoftheliteratures

suggest.Withtheestimatedquantileregressionparameters,predictedvaluesofCoVaRare

CoVaRj|it (q)=CoVaR j|Xi_=VaRi

q

q =˛ˆj|i+ ˆˇj|iVaRti(q)+Mt−1ˆj|i. (7)

SuchpredictedCoVaRvalueindicatesunderlyingcompanyj’svalueofriskpropagatedfrom

insti-tutioni.Finally,theCoVaRforeachinstitutioncanbefurthercalculated:

CoVaRj|it(q)=CoVaRj|it (q)−CoVaRj|it (50%)= ˆˇj|i[VaRit(q)−VaRit(50%)]. (8)

CoVaRvaluecanbetakenasthedifferencebetweenVaR,conditionalontheinstitutionbeingin

anormalstate,CoVaRjt(50%)andVaRconditionalontheinstitutionbeingindistress,CoVaRjt(q).It

canalsobetakenastheadditionalVaRcausedfromoutsideinfluences,whichisabovetheordinary

interdependences.

Differentfrompastliteraturesfocusingoninstitutionorcompanylevels,wefocusoncasesinwhich

iandjareatthelevelofdifferentcountriestomeasurethequantityofinterestrateriskcontagions

amongcountriesbecauseduringafinancialcrisis,portfolioreturnsofallfinancialinstitutionsareat

theirVaRlevel.WenextaddressthemodifiedCoVaRmodeltomeasuretheinterestrateriskcontagion.

Becausethecreditriskfacedbyfinancialinstitutionsismoreseverewhentheinterestrateincreases,

theinterestrateriskconcernstheincreaseofinterestratechanges.Therefore,theVaRofinterest

ratefocusesontheupsideriskofthedistributionofchangesininterestrate.FollowingCakiciand

Foster(2003),weconsidertheupsideriskofchangesincountryi’sinterestratebymodifyingthe

conventionalVaRmodelas

Pr(IRi_≥VaRi

q)=q, (9)

whereIRi_{isthechangesininterestrateofcountryi,andVaR}i

qisitsVaRattheqthpercentile,indicating

themarkethasqthpercentageofconfidencethatthechangesininterestratewillnotexceedIRi_.

WefurthermodifytheCoVaRmodelof Adrianand Brunnermeier,(2011)todenoteEuropean

countryj’sinterestrateVaRconditionalontheriskspilloverfromtheUScreditmarketindistress.

ThequantileregressionisadoptedbywhichtheunconditionalVaRcanbeefficientlytransformedas

conditionalVaRunderanyprespecifiedpreferredpercentile:

Pr(IRj_≥CoVaRj|US

q |IRUS=VaRUSq )=q. (10)

ThepredictedvaluefromthequantileregressioncanbetakenastheVaRofEuropeancountryj

conditionalontheVaRoftheUS.Withinthequantileregressionframework,ourCoVaRcanbenow

formallyspecifiedas

CoVaRj|USt (q)=VaRjq,t|VaRUSq,t=˛ˆj|US+ ˆˇj|USVaRUSt (q)+Mt−1ˆj|US, (11)

whereM_t−1isavectorofstatevariablesmadeupofglobalriskinstrumentsattimet−1.Inthisstudy,

weincludeseveralcountrylevelstatevariablesforcontrollingotherpotentialdeterminantsintheUS,

suchaschangesinEuropeancountryj’sinterbankofferedrateattimet−1(IBORt−1),returnsofWest

TexasIntermediatecrudeoilattimet−1(Oilt−1),andreturnsofChicagoBoardOptionsExchangegold

248 H.-F.Yangetal./NorthAmericanJournalofEconomicsandFinance28(2014)242–264

BecausetheinterestrateriskcontagionexploredinourstudyisthespilloverfromtheUSto

Euro-peancountries,weestimate˛, ˆˇ,ˆ andˆ inModel(11)inaquantileregressionbyreplacinginterest

rateincountryi(IRUS_{)withchangesintheTEDspread(TED).Also,theinterestrateincountryj(IR}j₎

inModel(11)isreplacedwithchangesintheEuropeancountryj’sinterestratespreadmeasuredby

theirinterbankofferedrate(IBOR).

Becauseendogeneitycanpotentiallyresultininconsistentresults(e.g.,Forbes&Rigobon,2002),we

includeinstrumentstofitthechangesininterestrates.Firstly,weusethereturnsoftheunderlying

country’sstockindexanditsimpliedvolatilityindexasinstrumentstodeterminethechangesin

interestratebecausethe2007–2009creditcrunchwasaccompaniedbysignificantincreasesinthe

impliedvolatilityindex.Inaddition,foreignexchangeexposureswereoneofthefactorsburdening

banksduringthe2007–2009shock(e.g.,Elsingeretal.,2006;Melvin&Taylor,2009).We,therefore,

includetheunderlyingcountry’sforeignexchangerate(takenasUSdollarstothecountryi’scurrency)

asanotherinstrument.FollowingTangandYan(2010),wereducepotentialendogeneityproblemby

usingtheaboveinstrumentstomeasurethefittedthechangesininterestrates,TEDandIBOR.

Usingthedailydata,theconditionaleventwhereanincreaseinTEDspreadattainstheVaRvalue

{IBORj_≥CoVaRj|US

q |TEDUS=VaRUSq }canbefurtherspecifiedby

CoVaRj|USt (q)=VaRjq,t|VaRUSq,t=˛ˆj|US+ ˆˇj|USVaRUSt (q)+Mt−1ˆj|US (12)

wherethecoefficientsareestimatedbyallofthedailydatainsampleperiods(2003–2009).After

estimatingthecoefficientsofModel(12),thevariableVaRUS

t (q)isthenreplacedwithTEDUSt tohave

fittedCoVaRj|USt (q)inModel(11).TheCoVaRvaluecanbefurthermeasuredbythedifferencebetween

anunderlyingEuropeancountryj’sinterestrateupsideVaRconditionalontheUScreditmarketbeing

inanormal state,CoVaRj|USt (50%), andVaRconditionalontheUS creditmarketbeingindistress,

CoVaRj|USt (q),q=99%or95%.

CoVaR=CoVaRj|US_t (q)−CoVaRj|US_t (50%). (13)

ThisCoVaRmeasurecanthereforesuccessfullyaddressesthemagnitudeofadditionalEuropean

countryj’sliquidityriskconditionaloncreditriskexposurefromtheUS.

Besidesthefactthatinterestrateriskcontagionsareprevalentamongglobalmoneymarkets,the

contagionrisksvarydaily,andsuchvariationsaredependentonthecreditqualityofriskpropagation

sources.TheUScreditriskaffectsEuropeancountry’sliquidityrisk,andthechangesinthisEuropean

country’sriskvarywiththestateoftheUSeconomy.Althoughthefinancialmarketsmayconsider

theirowneverydayinterestraterisk,thecapitalreservesforthecontagionriskmaynotbesufficient

tosatisfytheneedsforthevariationinriskcontagion.Therefore,riskmanagementshouldreflectany

changesinstatesfromtheinterestraterisksources.TheeconomicinferenceoftheCoVaRvalue

indicatesthepercentagechangeininterestrateriskconditionalonanotherfinancialmarket,whichis

theadditionalinterestrateriskchangethattheEuropeanmoneymarketsfacewhencreditrisksinthe

USshiftfromanormalstatetowardamoreseverelyriskystate.Therefore,increasesinCoVaRcan

betakenasadditionalliquidityriskincurredbythemoneymarketwhenitfacesanotherinstitution’s

creditproblem.

TheexplanationoftheCoVaRvalueisthatmanycountriesareburdenedwithadditionalVaR

propagatedfromexternalfinancialmarkets,andthevalueofCoVaRhereisthedifferencebetween

VaRconditionalontheUSfinancialmarketsbeinginanormalstateandVaRconditionalontheUS

systembeingindistress.IftheUSfinancialmarketisunderstress,creditrisksintheUSfinancialsystem

aresevereandsystemicrisksarepropagatedtointernationalmoneymarkets.Suchaphenomenon

causesEuropeanmoneymarketstofacehigherliquidityrisk,leadingtofurtherseverechangesin

interestrates.Assuch,theriskcontagionmakestheCoVaRhigherbecausethedifferencebetween

VaRconditionalontheUSinanormalstateandVaRconditionalontheUSindistressbecomeslarger.

2.3. Preliminaryanalyses

Tocapturetheinterestrateriskcontagion,theEuropeancountry’sliquidityriskshouldreflectthe

0 1 2 3 4 5 6 _%% LIBORR TB TED

Fig.1.TheLondoninterbankofferedrate(LIBOR),Treasurybillrate(TB),andtheUSTreasuryEurodollar(TED)spread.

(TBR),andtheTEDspreadinwhichthedifferencesbetweentheLIBORandtheTBRarelargerwhenthe

TEDspreadincreases.TheTEDspreadincreaseddramaticallyafterAugust2007,andtheLIBOR-TBR

differencebecomeslarger.Thecreditcrunchstartedatthattime,causingfurtherriskcontagionaround

theworld.ThecrisiswasmostsevereinSeptember2008whentheTEDspreadreacheditshighest

andtheLIBOR-TBRdifferencewasthelargest.Theserelationssuggestthattheinterestratespreadcan

reflectthechangeincreditriskoftheUSfinancialmarket.Therefore,theEuropeancountry’sIBOR

andtheUSTEDcouldbefurthertakenasproxyofliquidityriskandcreditrisk,respectively.

TheCoVaRmodelisparticularlyusefulforcapturingthecontagionriskamongdifferentfinancial

sectors(e.g.,Adrian&Brunnermeier,2011).Duringthe2007–2009creditcrunch,systemicriskcaused

manyUSfinancialinstitutionstogobankrupt.TheUSfinancialmarketswerefacedwithlargercredit

risksthatwerepropagatedtoothercountries.Themostsignificantoccurrenceofliquidityproblems

wastheriskcontagionfromtheUStoEuropeanmoneymarkets.WethereforeadopttheCoVaR

modeltomeasuresuchinterestrateriskcontagion.WhentheUSfinancialmarketscameintodistress,

Europeancountryj’sCoVaRduringthefinancialcrisis,CoVaRj_t(q),islargerthanduringordinarytimes,

CoVaRjt(50%),andtheCoVaRvalueissignificantlylargerthanzero.Thus,weexpectthattheCoVaR

valueduringthe2007–2009financialcrisiswillbesignificantlylargerthantheCoVaRbeforethe

creditcrunch.Table1providesthevariablesummariesandcorrelationcoefficients.

Table1,PanelBshowsthatthePearsoncoefficientsofcorrelationbetweenEuropeanIBORand

USTEDarepositiveandlargerfrom2003–2006to2007–2009,suggestingthatthelinkagesbetween

UScreditmarketandEuropeanmoneymarketareincreasinglycrucialduringthecrisisperiods.In

addition,thehigherthecorrelationcoefficientsare,themoreoftenthatEuropeancountry’sinterest

rateriskisaffectedbytheUScreditmarket.However,becausethecorrelationcoefficientsareincapable

ofdescribingtheexactcontagionphenomenon,weusetheIBORandTEDdataandtheCoVaRmodel

tomeasuretheriskcontagion,theresultsofwhicharedescribedinthefollowingdiscussion.

3. Empiricalanalyses

3.1. Mainfindings

WeexplorethedegreetowhichEurope’sliquidityriskswerecausedbypropagationofthecredit

riskinUSfinancialsystemduringthe2007–2009creditcrunchusingaCoVaRmodelinwhichcredit

riskandliquidityriskareestimatedbythedifferenceinTEDspreadandthedifferencebetweenthe

IBOR,respectively.Fig.2AshowstheUSTEDandtheinterbankofferratesinthelargestEuropean

countries(theUnitedKingdom,Germany,andFrance).Fig.2B, incontrast,indicatesthesamefor

Europeancountrieswithmostsevereliquidityproblems(Portugal,Ireland,Italy,Greece,andSpain).

Fig.2CshowsthechangesinIBORofotherEuropeancountries.Thethreepanelsshowthatthetrends

250 H.-F. Yang et al. / North American Journal of Economics and Finance 28 (2014) 242–264 Table1 Summarystatistics.

Europeaninterbankofferedrate(IBOR) USTreasury

Eurodollar(TED) UK Germany France Swiss Austria Belgium Finland Netherlands Portugal Ireland Italy Greece Spain

PanelA:Descriptivesummaries

Mean 4.210 2.614 2.765 1.147 2.764 2.803 2.803 2.773 2.765 2.636 2.615 2.776 2.757 0.575 Median 4.594 2.580 2.630 0.750 2.633 2.670 2.670 2.630 2.633 2.580 2.579 2.640 2.630 0.360 Max 6.750 4.450 5.200 4.620 5.197 5.269 5.270 5.190 5.197 4.421 4.363 5.200 5.250 4.510 Min 0.500 0.240 0.420 0.156 0.422 0.428 0.430 0.320 0.422 0.299 0.250 0.420 0.370 0.103 Std.Dev. 1.479 1.070 1.109 0.851 1.109 1.124 1.125 1.106 1.110 1.056 1.070 1.109 1.088 0.576 Skewness −1.225 −0.438 −0.120 0.665 −0.121 −0.121 −0.120 −0.150 −0.122 −0.386 −0.449 −0.140 −0.082 2.557 Kurtosis 3.974 2.656 2.467 2.251 2.467 2.467 2.465 2.509 2.463 2.577 2.650 2.462 2.558 11.517 Obs. 1724 1724 1724 1724 1724 1724 1724 1724 1724 1724 1724 1724 1724 1724

PanelB:CorrelationcoefficientsbetweenIBORandTED

2003–2006 0.628 0.421 0.478 0.784 0.478 0.478 0.478 0.484 0.478 0.431 0.424 0.458 0.448 2007–2009 0.465 0.452 0.564 0.520 0.564 0.564 0.564 0.569 0.564 0.465 0.452 0.564 0.600 2003–2009 0.304 0.392 0.534 0.642 0.534 0.534 0.534 0.538 0.533 0.413 0.393 0.527 0.555

A B C 0 1 2 3 4 5 6 7

UK Germany France TED

% 0 1 2 3 4 5 6

Portugal Ireland Italy Greece Spain TED

% 0 1 2 3 4 5 6

Austria Belgium Finland Netherlands Swiss TED

%

Fig.2.(A)TheUSTreasuryEurodollar(TED)spreadandtheinterbankofferedrate(IBOR)forthelargestEuropeancountries (UnitedKingdom,Germany,andFrance).(B)USTEDspreadandtheIBORfortheEuropeancountrieswithmostsevereliquidity problems(Portugal,Ireland,Italy,Greece,andSpain).(C)USTEDSpreadandIBORfortheotherEuropeancountries(Austria, Belgium,Finland,theNetherlands,andSwitzerland).

Duringtheyearsoffinancialcrisis,interestratechangespeakseveraltimes.Thefirstpeakisin

August2007.TheAmericanHomeMortgageInvestmentCorporationfiledChapter11bankruptcyon

August6.Inaddition,theMortgageGuarantyInsuranceCorporationannounceddiscontinuationof

cooperationwiththeRadianGrouponAugust8,andthenextday,August9,theFrenchinvestment

252 H.-F.Yangetal./NorthAmericanJournalofEconomicsandFinance28(2014)242–264

wesuggestthattheinterestrateriskcontagioneffectofthesubprimecrisispropagatedrapidlyfrom

theUnitedStatestoEuropeancountriesinAugust2007.

Thesecondpeakofinterestratechangesisattheendof2007.OnNovember1,theFederalReserve

providedmorethanUS$41billionforfinancialinstitutions,indicatingthattheUSfinancialsystemat

thattimefacedsevereliquidityproblems.However,outsideinvestorsandinternationalinstitutions

cannotidentifywhetherthecounterpartieswithwhomtheyweredealingwereindistress.Ifthe

financialinstitutionsareunderstress,theirinvestorsandloanborrowerswouldrunontheirbanks.

Therefore,theFinancialAccountingStandardsBoard’sstandardsonFairValueMeasurementsrequired

financialsectorstoprovidegreatertransparencyof information,furtherprotectingtheinvestors’

rights.

ThethirdpeakisnotseriouslysignificantinEuropeancountriescomparedtothefirsttwopeaksas

theindividualcompanyeventwasreflectedinstockandmoneymarkets.AlthoughBearSternswas

providedwithfundingbytheFederalReserveonMarch14,2008,itwasacquiredbyJPMorganChase

for$2ashareonMarch16,withtheFederalReservebackingtheacquisition.Onemonthlater,Bear

Sternsannouncedthereductionofoperatingcostbylayingoffmorethan5000employees.

Theforthpeakwastheworst:OnSeptember7,2008,theUSfederalgovernmenttookoverFannie

MaeandFreddieMac,andtheUShousemortgagemarketcollapsed.Thetakeovercausedseverepanic,

andtheliquiditypressurerapidlyspreadtoothercountries.Inaddition,theriskcontagioncaused

increasedpressureandmistrustamongfinancialinstitutions,furtherincreasingIBORs.TheBankof

AmericaacquiredMerrillLynchonSeptember14,andthenextdayLehmanBrothersfiledbankruptcy.

ThecrunchwasnotoveruntiltheUSFederalReserveprovidedmorethanUS$85billionfundingtothe

AmericanInternationalGrouponSeptember17.Thesubsequentbankruptciesandbankrunscaused

significantliquidityproblems,andthecreditcrunchfurtherexacerbatedinterestrateriskcontagion.

DuringtheweekofOctober6–10,2008,theUSstockmarketfacedseverelosses.Therepresentatives

ofcentralbankandfinanceministersoftheG7agreedtocooperateindealingwiththeliquidity

problems.However,thedetailsofthefinancialsupportswerenotspecificallyprovidedatthattime,

causingfurthermoneymarketuncertainties.

ThefourpeaksofinterestrateintheEuropeancountries’IBORandtheUSTEDspreadareduetothe

samesourceofrisk:theUSfinancialmarketcreditrisk.Therefore,weexpecttofindapositiverelation

betweentheinterestrateriskcontagionsfromtheUStotheseEuropeancountries.Wefirstadopt

percentileq=99%quantileregressionstoestimatethecoefficientsofchangesinaEuropeancountry’s

IBORonthechangesintheUSTEDspread.Table2showsthattherelationsbetweenEuropeanIBOR

changesandtheUSTEDspreaddifferencesarepositive.Thisresultindicatesthatthecreditriskof

theUSfinancialsystemdeterminetheliquidityrisksinEuropeandsuggestthattheinterestraterisk

contagionfromtheUStotheEuropeanmarketsiscruciallysignificant.Afterexaminingtheinterest

ratecontagioneffect,wenextusetheestimatestomeasuretheEuropeanmoneymarketliquidityrisk

conditionalonthecreditriskoftheUSfinancialsystem.

Afterestimatingthecoefficientsfromthequantileregression,wetaketherealizedvalueofthe

changesinEuropeancountryj’sIBORandtheUSTEDspreadtofitthedependentvariables.The

resultingfittedvaluecanbetakenastheinterestrateVaRofaEuropeancountryjconditionalonthe

creditriskatUSfinancialsystem(CoVaR).ThisCoVaRvaluecapturesnotonlytheinterestrateriskin

theEuropeancountryjbutalsotheadditionalriskpropagatedfromtheUScreditmarket.

Althoughthesystemicbetaˇj|US_{inModel(12)canbetakenasthedegreetowhichEuropeancountry}

j’sliquidityriskisaffectedbytheUScreditrisk,suchcoefficientonlyprovidestheoverallsensitivity

ofthetwointerest ratechanges,andthequantifiedmagnitudeoftheriskcontagioncanonlybe

specificallyaddressedbytheCoVaRvalue.Thehigherthevalueofthesystemicbetaˇj|US,thegreater

theCoVaRis,meaningthattheriskcontagionbecomesmoresevere.Themaindifferencesbetween

systemicbetaandCoVaRvaluesareasfollows.First,thesystemicbetameasuresthesensitivity

ofriskcontagion,whileCoVaRgivesthequantifiedvalueofriskcontagion.CoVaRiscalculated

bymultiplyingthechangesininterestrateriskswiththesystemicbeta.Therefore,theconditional

valueofriskcanonlybeachievedbytheCoVaRvalue.Second,themeasuresdifferincomparability.

CoVaRisthevalueofcontagionrisk,andthevaluesarechangesinpercentages.Incontrast,the

H.-F. Yang et al. / North American Journal of Economics and Finance 28 (2014) 242–264 253

CoVaRandCoVaRforeachEuropeanCountrywithcontemporaneousTEDand99%quantile.

Countryj UK Germany France Swiss Austria Belgium Finland Netherlands Portugal Ireland Italy Greece Spain Quantileestimation:IBORj

t=˛j|US+ˇj|USTEDUSt +Mt−1ˆj|US+εj|USt

Intercept 0.0048*** _0.0046*** _0.0053*** _0.0048*** _0.0041*** _0.0047*** _0.0032*** _0.0033*** _0.0049*** _0.0036*** _0.0046*** _0.0036*** _0.0017*** TEDUS t 0.2401*** 0.0815*** 0.3465*** 0.2566*** 0.3636*** 0.2678*** 0.2268*** 0.2527*** 0.4969*** 0.3495*** 0.3453*** 0.4361*** 0.1795*** IBORj_t−1 −0.0046 −0.0102*** _−0.0093*** _−0.0037*** _−0.0033* _{−0.0006 −0.0001 0.0080}** _{−0.0088 0.0150}*** _{−0.0029 0.0008 −0.0032}*** Oilt-1 0.0001 −0.0001*** _−0.0001*** _−0.0001** _{0.0001 −0.0001}* _−0.0001*** _−0.0002*** _{0.0001 0.0000 −0.0000 −0.0002}*** _0.0001*** Goldt−1 0.0002 0.0002*** _0.0003*** _−0.0001*** _{−0.0000 −0.0001}** _{0.0001 0.0000 −0.0000 0.0000}*** _−0.0002*** _{−0.0001 0.0000} 99%CoVaRvaluesbyindividualyearandaveragesover2003–2006and2007–2009

CoVaR=CoVaRj|US

t (99%)−CoVaRj|USt (50%);CoVaRj|USt (q)=VaRjq,t|VaRUSq,t=˛ˆj|US+ ˆˇj|USTEDUSt +Mt−1ˆj|US

2003 8.20 2.80 11.80 8.70 12.40 9.10 7.70 8.60 16.90 11.90 6.00 14.90 6.10 (16.03) (5.56) (17.25) (23.49) (62.07) (24.79) (33.36) (20.24) (57.81) (40.95) (58.33) (30.58) (23.91) 2004 6.40 2.20 9.30 6.90 9.80 7.20 6.10 6.80 13.30 9.40 4.70 11.70 4.80 (12.22) (5.62) (16.34) (21.29) (62.00) (21.49) (32.81) (20.69) (60.68) (62.23) (67.90) (27.86) (21.73) 2005 6.10 2.20 8.80 6.40 9.20 6.80 5.80 6.40 12.60 8.90 4.50 11.10 4.60 (14.24) (5.80) (16.85) (20.12) (49.88) (20.96) (31.98) (18.97) (48.51) (49.08) (54.68) (26.70) (21.48) 2006 6.40 2.20 9.30 7.00 9.80 7.20 6.10 6.80 13.30 9.40 4.70 11.70 4.80 (9.28) (5.70) (13.60) (15.85) (58.08) (17.29) (35.76) (23.17) (58.52) (41.80) (57.33) (25.73) (20.45) 2007 8.00 2.70 11.50 8.50 12.00 8.90 7.50 8.40 16.50 11.60 5.80 14.40 5.90 (14.36) (5.43) (15.92) (22.50) (53.00) (25.95) (44.45) (19.63) (35.88) (16.87) (35.44) (35.12) (13.30) 2008 13.40 4.50 19.40 14.20 20.10 14.90 12.50 14.00 27.50 19.30 9.80 24.10 9.90 (9.81) (5.65) (12.41) (11.55) (24.49) (15.06) (21.02) (18.65) (23.02) (26.82) (21.49) (18.36) (16.98) 2009 28.20 8.90 40.80 28.10 39.70 31.50 24.80 27.60 54.30 38.20 19.30 47.70 19.60 (27.41) (14.70) (35.51) (29.22) (79.53) (44.14) (65.28) (41.65) (76.53) (82.63) (79.20) (58.18) (40.46) 2003–2006 6.80 2.30 9.80 7.30 10.30 7.60 6.40 7.20 14.10 9.90 5.00 12.30 5.10 (24.61) (11.15) (31.13) (38.87) (100.34) (41.04) (62.92) (40.35) (96.33) (85.80) (98.60) (53.61) (42.76) 2007–2009 14.90 5.40 21.50 17.00 24.00 16.60 15.00 16.70 32.80 23.10 11.70 28.80 11.90 (21.32) (13.78) (25.03) (27.49) (43.21) (29.70) (40.98) (36.09) (41.63) (42.47) (41.16) (38.66) (31.88) Notes:TheyearlyCoVaRmeasuresinthistablearetheaverageofdailyCoVaRvaluesperyear.Theparenthesesarethecorrespondingt-statistics.IBORj

tisthechangesinEuropean countryj’sIBORattimet,andTEDUS

t isthechangeinUSTreasuryEurodollarspreadattimet.Thestatevariablesofglobalriskfactorsattimet−1,Mt−1,includesthechangesinEuropean interbankofferedratesattimet−1(IBORj

t−1),thereturnofWestTexasIntermediatecrudeoilpricesattimet−1(Oilt−1),andreturnsofChicagoBroadOptionsExchangegoldprice indexattimet−1(Goldt−1).

254 H.-F.Yangetal./NorthAmericanJournalofEconomicsandFinance28(2014)242–264

canbecomparedandevaluatedalongsideeachother.Wethereforecalculatethedifferencebetween

VaRconditionalonUSdistressandVaRundernormalstatetoaddresstheroleofcontagionrisk.

BecausethefittedVaRconditionalontheUSindistressislargerthantheVaRconditionalontheUS

inanormalstate,particularlyduringthebeginningofthecreditcrisis,weexpecttoseesignificantly

positivedifferencesbetweenthem.Inaddition,thetradingdaysinwhichtheCoVaRdifferencesare

positiveareprevalentinourdatasettings,thereasonablenessofusingCoVaRasthemeasureofinterest

rateriskcontagioncanbesupported.WethereforetakeCoVaRasthedifferencebetweenEuropean

countryj’sVaRconditionalontheUSindistressanditsVaRconditionalontheUSinthenormalstate,

andaveragethedailyCoVaRvaluestoacquiretheyearlymeasuresofinterestrateriskcontagionfrom

2003to2009.Table2providestheCoVaRresults.Thepositivevaluesofthedifferencesuggestthat

theEuropeanmarketsneedtoaddressnotonlytheirownliquidityproblemscausedbytheincrease

intheirinterestraterisksbutalsotheriskpropagatedfromtheUScreditmarket.

TheeconomicimplicationfortheCoVaRvaluescanbeexplainedbasedonitsmeasurement.The

UK’sCoVaRvaluein2003is8.20(seeTable2).ThispositivevaluesuggeststhattheUKliquidity

marketnotonlyfacesinterestrateriskcontagionfromtheUSinanormalstatebutalsofacesanother

positiveincrementofriskcontagionfromtheUSunderweakcreditmarketconditions.Therefore,the

quantifiedriskvalueof8.20indicatesthatbesidesthevalueofriskcausedbytheUnitedKingdom

itself,anadditional8.2%ofinterestratespreadsexistsabovetheordinaryUK–USinterdependence

thatshouldbeconsideredwhenmeasuringthevalueofinterestraterisk.Thisadditionalincrement

iscausedbythedifferencesintheUScreditmarketbetweenitsnormalanddistressstates.

Usingt-teststatistics,wefurtherexaminewhetherCoVaRdifferencesaresignificant.Table2shows

thatCoVaRdifferencesbyyearand bynoncrisisandcrisisperiodsaresignificantlypositive.It is

expectedtoseethattheadditionalinterestratecontagionriskincreasedsignificantlyfrom2007

to2009whensystemicriskandcreditproblemsbecamemoresevere.Basedonthet-statistics,the

rejectionpowerincreasefrom2007andishighestin2009,theendofthecreditcrisis,suggesting

thatinterestrateriskcontagionwasmostprevalentintheseyearsandsuchex-anteinterestrate

riskcontagionmeasurementprovidesevidenceofeffectivenessofpredictionofthecreditcrisisin

2007–2009.

Besidesthechangesalongthetimehorizonofcrisisandnoncrisisperiods,theCoVaRvaluesvary

acrossdifferentcross-sectionalcountries.Table2showsthatthemagnitudesofCoVaRvalueinthe

largestEuropeannations(UK,GermanandFrance)arelowerduringthenoncrisisperiods.However,

theCoVaRvaluesarelargerinFranceinthecrisisperiodasitfacedalargerpotentialproblemof

sovereigndebtcomparedtotheUnitedKingdomandGerman.Inaddition,theCoVaRvaluesinthe

fivehighlydebt-riddenEurozonenations—Portugal,Ireland,Italy,Greece,andSpain—arerelatively

largerbecauseoftheirliquidityproblems.Amongthesefivenations,theriskcontagioneffectsinthe

twobiggercountries,ItalyandSpain,arelowerastheirsovereigndebtproblemsarenotsignificantly

severebefore2009.

AlthoughtheresultsofinterestrateriskcontagionarefromthesameCoVaRmodel,theCoVaR

valuesarequitedifferentinvariousquantiles.TheCoVaRvaluesfromq=95%shouldbelowerthan

thevaluesfromq=99%.InModel(9),thedifferencesinEuropeancountryj’sCoVaRvaluesbetween

theconditionsofUSfinancialmarketsbeinginanormalstateorindistressshouldbelowerforq=95%,

therebyhavinglowercontagionriskvalues.Incontrast,theCoVaRvaluesfromq=99%isparticularly

highduetotheriskofmoreextremechangesininterestrates.

Table3showstherobustnessoftheCoVaRmodelwithq=95%quantileregression.Comparedto

theresultsinTable2,theyearlyaveragesofthedailyinterestrateriskcontagionarelowerbecause

theq=95%quantileencompasseseventsnotonlyfromtheextremedistresscases(asunderq=99%

quantile)butalsofromotherminoruncertaintiesthatcancauseincreasesininterestratespread.

Therefore,theCoVaRvaluesfrom95%quantilecouldunderestimateriskcontagion,andsuch

evi-denceofCoVaRhighlightsthecrucialroleofinterestrateriskcontagioninextremedistresscases.As

aresult,wesuggestthatselectingtheappropriateupsideriskconfidencelevel(99%vs.95%)shouldbe

dependentontheriskpreferenceandiscruciallyimportanttopreventtheunderestimationofinterest

raterisk.ThelargerCoVaRvaluesfromq=99%(seeTable2)suggestthatwhenconsideringrisk

H.-F. Yang et al. / North American Journal of Economics and Finance 28 (2014) 242–264 255

CoVaRandCoVaRforeachEuropeanCountrywithcontemporaneousTEDand95%quantile.

Countryj UK Germany France Swiss Austria Belgium Finland Netherlands Portugal Ireland Italy Greece Spain Quantileestimation:IBORj

t=˛j|US+ˇj|USTEDUSt +Mt−1ˆj|US+εj|USt

Intercept 0.0018*** _0.0019*** _0.0019*** _0.0032*** _0.0021*** _0.0031*** _0.0014*** _0.0016*** _0.0024*** _0.0013*** _0.0026*** _0.0016*** _0.0001 TEDUS t 0.1716*** 0.1356*** 0.2446*** 0.2452*** 0.3320*** 0.2581*** 0.2771*** 0.2605*** 0.4458*** 0.3592*** 0.2962*** 0.3353*** 0.1548*** IBORj_t−1 0.0010 −0.0061*** _−0.0045*** _{−0.0010 −0.0049}*** _−0.0046*** _{0.0022 −0.0031}* _{−0.0051 −0.0029 −0.0052}*** _{0.0017 0.0011} Oilt−1 0.0001 −0.0000 0.0001** _{0.0000 0.0001}** _{0.0000 −0.0000 −0.0000 0.0000 −0.0000 0.0000 −0.0000 −0.0000} Goldt−1 0.0003*** _{0.0001 0.0001 −0.0001}*** _−0.0001*** _−0.0002*** _−0.0001* _{−0.0000 −0.0000}* _0.0000*** _−0.0002*** _−0.0001*** _−0.0001*** 95%CoVaRvaluesbyindividualyearandaveragesover2003–2006and2007–2009

CoVaR=CoVaRj|US

t (95%)−CoVaRj|USt (50%);CoVaRj|USt (q)=VaRjq,t|VaRUSq,t=˛ˆj|US+ ˆˇj|USTEDUSt +Mt−1ˆj|US

2003 4.50 3.60 6.40 6.40 8.70 6.80 7.30 6.90 11.70 9.50 5.50 8.80 4.10 (7.23) (19.37) (20.63) (22.96) (35.79) (18.86) (40.05) (44.73) (60.06) (82.67) (43.73) (29.36) (15.99) 2004 3.00 2.30 4.20 4.20 5.70 4.50 4.80 4.50 7.70 6.20 3.60 5.80 2.70 (5.05) (16.62) (15.31) (18.03) (32.38) (14.54) (32.13) (39.92) (69.69) (168.44) (38.68) (22.32) (11.43) 2005 2.70 2.30 3.80 3.80 5.20 4.00 4.30 4.10 7.00 5.60 3.30 5.20 2.40 (4.92) (16.52) (14.88) (17.54) (30.91) (14.17) (30.97) (38.51) (64.73) (150.52) (36.90) (21.57) (11.52) 2006 3.10 2.40 4.40 4.40 5.90 4.60 4.90 4.60 7.90 6.40 3.70 6.00 2.80 (3.98) (12.92) (14.04) (14.04) (31.33) (11.66) (24.02) (31.49) (64.10) (94.59) (29.54) (17.17) (9.15) 2007 3.60 2.80 5.10 5.10 6.90 5.40 5.70 5.40 9.20 7.40 4.30 6.90 3.20 (5.68) (9.86) (15.20) (20.62) (26.72) (15.08) (28.91) (32.47) (36.79) (48.50) (32.73) (23.51) (11.81) 2008 5.60 4.40 8.00 8.00 10.80 8.50 9.00 8.50 14.50 11.70 6.80 10.90 5.00 (3.80) (10.70) (12.15) (13.02) (24.29) (11.20) (21.43) (22.99) (31.79) (33.33) (22.69) (15.74) (8.99) 2009 12.60 9.10 18.00 16.40 22.20 19.00 18.50 17.40 29.80 24.00 13.90 22.40 10.40 (10.42) (34.06) (29.31) (36.97) (54.21) (30.94) (54.89) (57.39) (65.80) (70.13) (58.25) (44.82) (27.02) 2003–2006 3.30 2.60 4.70 4.70 6.40 5.00 5.30 5.00 8.60 6.90 4.00 6.50 3.00 (10.35) (30.45) (31.25) (34.39) (56.58) (28.44) (56.03) (63.50) (84.07) (98.81) (61.93) (41.95) (23.26) 2007–2009 6.50 5.40 9.30 9.90 13.30 9.80 11.10 10.40 17.90 14.40 8.30 13.40 6.20 (9.39) (24.59) (23.80) (30.58) (39.31) (23.43) (39.85) (39.80) (43.14) (44.40) (40.09) (34.62) (23.19) Notes:TheyearlyCoVaRmeasuresinthistablearetheaverageofdailyCoVaRvaluesperyear.Theparenthesesarethecorrespondingt-statistics.IBORj

tisthechangesinEuropean countryj’sIBORattimet,andTEDUS

t isthechangeinUSTreasuryEurodollarspreadattimet.Thestatevariablesofglobalriskfactorsattimet−1,Mt−1,includesthechangesinEuropean interbankofferedratesattimet−1(IBORj

t−1),thereturnofWestTexasIntermediatecrudeoilpricesattimet−1(Oilt−1),andreturnsofChicagoBroadOptionsExchangegoldprice indexattimet−1(Goldt−1).

256 H.-F.Yangetal./NorthAmericanJournalofEconomicsandFinance28(2014)242–264

CoVaRvalues.Theymayhavemorecriticalriskburdensiftheytendtosoundlyprotectthemselves

frombeingexposedtomoresevereinterestrateriskcontagion.

3.2. Robustness

Creditconditionsmaynotefficientlyinfluencecurrentdefaultspreadandbondyields(e.g.,Hull,

Predescu,&White,2004;Norden&Weber,2004.).Forreducingpotentialproblemthattheinformation

onUScreditriskcannotbefullyreflectedoncurrentEuropeanliquidity,weexplorethecausaleffect

byadaptingthemodelwithTEDUS

t−1asregressors.Tables4and5providetheevidenceonthelead-lag

relationwith99%and95%quantileregressionestimates.TheempiricalresultsaresimilartoTable2,

namely,thattheUScreditmarketispositivelyrelatedtotheliquidityofcountrieswithinEurope.

Regardingtothechangesininterestrateriskcontagion,theCoVaRmeasuresincreasefrom2007to

2009,itconsistentwiththenotionthattheCoVaRmeasuresreflectthephenomenonthatliquidity

problemspropagatedfromtheUScreditmarketaremoresevereduringthecreditcrunch.

Although thesignificantresultsin Tables 2–5are similar,the CoVaRvalues and the

differ-encebetween2003–2006and2007–2009arelowerforthelead–lagrelationbetweenIBORand

TED.TheseresultssuggestthatalthoughtheinformationonUScreditdistresscannotbecompletely

reflectedonEuropeanliquiditymarketonacurrentday,mostoftheinterestrateriskcontagioneffects

canefficientlyreflected.Thatis,theinterestrateriskinEuropeancountriesispropagatednotonly

mainlyfromthecurrentUScreditmarketbutalsominoredfromyesterday’sUScreditcondition.

However,theeffectsofovernightspilloverarelowercomparedtocurrent-dayriskcontagion.Also,

thechangesinCoVaRvaluesbetween2003–2006and2007–2009arealsolowerforthelead–lag

relationmodels.Therefore,wefindthatusingthelead–lagrelationmodelsforestimatingtheinterest

ratecontagionunderestimatetheriskcontagioneffects.

AnotherconcernisthatthemagnitudeoftheeffectonIBORislargerwhentheTEDincreasesas

theconditionaldistresseventwouldbemoreextreme,whileandthemagnitudeislowerforreducing

TED.ForconsideringthevariedeffectsonIBORduetodifferentdirectionofchangesinTED,

wefollowLopez-Espinosa,Moreno,Rubia,andValderrama(2012)toadopttheasymmetricCoVaR

approachtore-estimatetheCoVaRvalues.

IBORjt=˛j|US+ˇj|US1 TED US t I(TEDUS t ≥0)+ˇ j|US 2 TED US t I(TEDUS t <0)+Mt−1 j|US_+εj|US t (14)

IBORjt=˛j|US+ˇj|US1 TED US t−1I(TEDUS t ≥0)+ˇ j|US 2 TED US t−1I(TEDUS t <0)+Mt−1 j|US_+εj|US t (15) whereI_(TEDUS

t ≥0)isanindicatorfunctionthatequals1ifthechangesinTEDispositive,thatisthe

increaseinTEDspread,andzerootherwise,whileI_(TEDUS

t <0)is,incontrast,isanindicatorfunction

thatequals1ifthechangesinTEDisnegative,thatisthedecreaseinTEDspread,andzerootherwise.

WenexttousethesameapproachtomeasuretheCoVaRvalueswithdifferent99%or95%quintiles.

Tables6and7providetheresultsonModel(14)with99%and95%quintiles,andTables8and9provide

theevidenceonthelead-lagrelationfromModel(15).Similarly,theevidenceisconsistentwithprior

regressionresultsthatinterestrateriskpropagationsturnedincreasinglyseveresince2007andthat

thecontagionwasparticularlysevereduring2008and2009.

TheCoVaRmodelprovidesariskmeasureforevaluatinginterestraterisknotonlyfromthesector

itselfbutalsofromotherexternalinfluences.UnliketraditionalVaRmodelsthatunderestimaterisk

fromothersectors,theCoVaRmodelquantifiesthemagnitudeofadditionalexposuretorisk

propaga-tion.Whenafinancialcrisisisabouttooccur,theinterestrateriskexposureisexacerbatedbecausea

financialsectormustdealnotonlywithitsownliquidityrisksbutalsowiththeriskpropagatedfrom

othercreditmarkets.OurevidencefromtheCoVaRmeasureisconsistentwiththefactthattheinterest

rateriskpropagationsturnedincreasinglyseveresince2007andthatthecontagionwasparticularly

severeduringthecrisisperiodof2008–2009.

Ourquantifiedmeasurecanalsobeappliedtofirm-levelinterestrateriskcontagionbyproviding

themagnitudeofliquidityriskconditionalonexternalinstitutionssubjecttodifferentrisks.Because

theCoVaRmeasureidentifiestheriskimpactdegreeunderexposuretoriskfromanotheroutside

H.-F. Yang et al. / North American Journal of Economics and Finance 28 (2014) 242–264 257

CoVaRandCoVaRforeachEuropeanCountrywithlaggedTEDand99%quantile.

Countryj UK Germany France Swiss Austria Belgium Finland Netherlands Portugal Ireland Italy Greece Spain Quantileestimation:IBORj_t=˛j|US_+ˇj|US_TEDUS

t−1+Mt−1ˆj|US+εj|USt Intercept 0.0037*** _0.0048*** _0.0044*** _0.0039*** _0.0044*** _0.0044*** _0.0042*** _0.0049*** _0.0051*** _0.0045*** _0.0051*** _0.0043*** _0.0052*** TEDUS t−1 0.0572 ** _0.0576*** _0.0424** _0.1337*** _0.1241*** _0.0943*** _0.0653*** _0.0670* _0.0755** _0.1315** _{0.0501 0.1274}*** _0.0706*** IBORj_t−1 −0.0017 −0.0074*** _−0.0067*** _−0.0066*** _−0.0087*** _−0.0071*** _−0.0067*** _−0.0080*** _−0.0114*** _−0.0130*** _−0.0086*** _−0.0075*** _−0.0082*** Oilt−1 −0.0001*** _−0.0001*** _−0.0000* _0.0001*** _0.0002* _{−0.0001 −0.0001 −0.0001 0.0002}* _{0.0001 −0.0001}** _−0.0001** _−0.0000 Goldt−1 0.0002*** _0.0001* _0.0001** _0.0001* _0.0002*** _{0.0001 −0.0000 0.0001 0.0002}** _0.0000** _{0.0000 0.0003}*** _0.0001 99%CoVaRvaluesbyindividualyearandaveragesover2003–2006and2007–2009

CoVaR=CoVaRj|US

t (99%)−CoVaRj|USt (50%);CoVaRj|USt (q)=VaRjq,t|VaRUSq,t=˛ˆj|US+ ˆˇj|USTEDUSt−1+Mt−1ˆj|US

2003 4.50 4.50 3.30 10.50 9.70 7.40 5.10 5.30 5.90 10.30 1.70 10.00 5.50 (10.36) (9.83) (10.22) (25.78) (15.12) (21.72) (20.71) (13.66) (8.29) (28.39) (6.53) (15.92) (16.42) 2004 3.50 3.50 2.60 8.20 7.60 5.70 4.00 4.10 4.60 8.00 1.30 7.80 4.30 (9.07) (9.66) (9.65) (21.13) (12.83) (22.84) (22.22) (14.63) (7.18) (28.76) (7.71) (15.28) (15.13) 2005 3.30 3.50 2.40 7.60 7.10 5.40 3.80 3.90 4.30 7.60 1.30 7.30 4.10 (9.80) (9.90) (9.91) (20.80) (12.89) (22.60) (21.24) (14.39) (7.22) (26.40) (7.55) (15.54) (14.84) 2006 3.50 3.50 2.60 8.20 7.50 5.70 4.00 4.10 4.60 8.00 1.30 7.70 4.30 (8.19) (10.11) (7.62) (23.43) (10.32) (22.75) (22.90) (14.58) (6.24) (29.73) (8.49) (13.20) (9.66) 2007 4.20 4.30 3.10 9.90 9.20 7.00 4.80 5.00 5.60 9.70 1.70 9.40 5.20 (11.99) (10.70) (7.59) (22.44) (12.44) (17.35) (14.37) (12.32) (6.77) (15.23) (4.12) (15.21) (4.77) 2008 7.20 7.20 5.30 16.60 15.40 11.80 8.10 8.30 9.40 16.30 2.80 15.80 8.80 (8.62) (9.38) (7.50) (11.31) (9.60) (15.40) (14.03) (11.52) (5.96) (16.86) (5.92) (11.88) (9.83) 2009 15.50 14.50 11.50 33.70 31.20 25.50 16.40 16.90 19.00 33.10 5.50 32.00 17.80 (20.54) (25.13) (20.72) (21.08) (30.78) (47.87) (49.55) (34.30) (17.92) (54.07) (19.15) (38.14) (20.15) 2003–2006 3.70 3.70 2.70 8.60 8.00 6.10 4.20 4.30 4.90 8.50 1.40 8.20 4.50 (18.52) (19.37) (18.23) (44.41) (25.02) (42.71) (41.19) (27.68) (14.35) (53.02) (14.31) (29.26) (26.16) 2007–2009 8.10 8.70 6.00 20.10 18.60 13.30 9.80 10.10 11.30 19.70 3.30 19.10 10.60 (18.83) (22.37) (16.14) (24.11) (24.01) (28.38) (31.15) (26.31) (15.50) (33.39) (13.88) (28.30) (17.81) Notes:TheyearlyCoVaRmeasuresinthistablearetheaverageofdailyCoVaRvaluesperyear.Theparenthesesarethecorrespondingt-statistics.IBORj

tisthechangesinEuropean countryj’sIBORattimet,andTEDUS

t−1isthechangeinUSTreasuryEurodollarspreadattimet−1.Thestatevariablesofglobalriskfactorsattimet−1,Mt−1,includesthechangesin Europeaninterbankofferedratesattimet−1(IBORj

t−1),thereturnofWestTexasIntermediatecrudeoilpricesattimet−1(Oilt−1),andreturnsofChicagoBroadOptionsExchangegold priceindexattimet−1(Goldt−1).

258 H.-F. Yang et al. / North American Journal of Economics and Finance 28 (2014) 242–264 Table5

CoVaRandCoVaRforeachEuropeanCountrywithlaggedTEDand95%quantile.

Countryj UK Germany France Swiss Austria Belgium Finland Netherlands Portugal Ireland Italy Greece Spain Quantileestimation:IBORjt=˛j|US+ˇj|USTEDUSt−1+Mt−1ˆj|US+εj|USt

Intercept 0.0018*** _0.0026*** _0.0023*** _0.0021*** _0.0022*** _0.0027*** _0.0025*** _0.0027*** _0.0022*** _{0.0003 0.0028*** 0.0020*** 0.0028***} TEDUS t−1 0.0470 0.0300 0.0246 0.0727*** 0.1090** 0.0188 0.0396 0.0186 0.0584* 0.1210*** 0.0252 0.0779*** 0.0286 IBORj_t−1 −0.0029*** _−0.0041*** _−0.0034*** _−0.0032*** _−0.0052*** _−0.0038*** _−0.0039*** _−0.0042*** _−0.0069*** _{−0.0076*** −0.0049*** −0.0037*** −0.0044***} Oilt−1 0.0000 0.0000 0.0001 0.0001** _0.0001* _{−0.0000 −0.0000 0.0000 0.0001}** _{0.0001* 0.0001*** −0.0000 0.0001***} Goldt−1 0.0001** _{−0.0001 −0.0000 −0.0000 0.0002}** _{−0.0000 −0.0000 −0.0001 0.0001}* _{0.0000*** −0.0000 0.0001*** −0.0001*} 95%CoVaRvaluesbyindividualyearandaveragesover2003–2006and2007–2009

CoVaR=CoVaRj|US_t (95%)−CoVaRj|US_t (50%);CoVaRj|US_t (q)=VaRj_q,t|VaRUS

q,t=˛ˆj|US+ ˆˇj|USTEDUSt−1+Mt−1ˆj|US

2003 2.80 1.80 1.50 4.40 6.60 1.10 2.40 1.10 3.50 7.30 0.70 4.70 1.70 (13.28) (11.83) (9.81) (21.04) (17.36) (7.30) (32.10) (8.02) (10.92) (31.96) (3.11) (19.61) (6.59) 2004 1.80 1.20 1.00 2.80 4.20 0.70 1.50 0.70 2.30 4.70 0.40 3.00 1.10 (7.85) (10.27) (8.08) (15.99) (12.23) (5.93) (53.41) (6.43) (7.93) (27.45) (2.55) (14.64) (5.31) 2005 1.60 1.10 0.90 2.50 3.80 0.70 1.40 0.60 2.00 4.20 0.40 2.70 1.00 (9.71) (9.43) (7.54) (15.57) (11.74) (5.60) (40.32) (6.19) (7.56) (25.56) (2.43) (14.15) (5.12) 2006 1.90 1.20 1.00 2.90 4.40 0.80 1.60 0.70 2.30 4.90 0.40 3.10 1.10 (6.12) (10.35) (11.05) (23.75) (9.84) (5.64) (37.40) (5.51) (7.10) (28.92) (3.46) (11.25) (4.96) 2007 2.10 1.40 1.10 3.30 4.90 0.90 1.80 0.80 2.60 5.50 0.50 3.50 1.30 (8.51) (6.28) (6.60) (17.96) (11.21) (4.38) (10.26) (4.43) (6.23) (14.66) (2.13) (12.26) (2.18) 2008 3.50 2.20 1.80 5.30 7.90 1.40 2.90 1.30 4.20 8.80 0.80 5.70 2.10 (6.42) (8.68) (9.53) (8.80) (8.66) (4.60) (17.39) (4.86) (6.03) (18.55) (2.78) (10.01) (4.97) 2009 7.90 4.60 4.20 11.10 16.70 3.20 6.00 2.80 8.90 18.50 1.70 11.90 4.40 (18.07) (24.21) (15.70) (14.92) (27.56) (11.81) (55.48) (16.05) (18.34) (46.96) (6.27) (32.43) (9.10) 2003–2006 2.00 1.30 1.10 3.20 4.70 0.80 1.70 0.80 2.50 5.30 0.50 3.40 1.20 (17.16) (20.44) (17.51) (35.42) (24.58) (12.15) (56.80) (12.87) (16.53) (49.98) (5.63) (28.22) (10.97) 2007–2009 4.00 2.70 2.10 6.60 9.90 1.60 3.60 1.70 5.30 10.90 1.00 7.00 2.60 (15.01) (19.29) (16.21) (18.78) (22.19) (10.25) (30.83) (12.56) (15.53) (33.03) (6.36) (24.81) (8.74) Notes:TheyearlyCoVaRmeasuresinthistablearetheaverageofdailyCoVaRvaluesperyear.Theparenthesesarethecorrespondingt-statistics.IBORj_tisthechangesinEuropean countryj’sIBORattimet,andTEDUS

t−1isthechangeinUSTreasuryEurodollarspreadattimet−1.Thestatevariablesofglobalriskfactorsattimet−1,Mt−1,includesthechangesin Europeaninterbankofferedratesattimet−1(IBORj_t−1),thereturnofWestTexasIntermediatecrudeoilpricesattimet−1(Oilt−1),andreturnsofChicagoBroadOptionsExchangegold priceindexattimet−1(Goldt−1).

H.-F. Yang et al. / North American Journal of Economics and Finance 28 (2014) 242–264 259

CoVaRandCoVaRforeachEuropeanCountrywithasymmetricindicator,contemporaneousTEDand99%quantile.

Countryj UK Germany France Swiss Austria Belgium Finland Netherlands Portugal Ireland Italy Greece Spain Quantileestimation:IBORj

t=˛j|US+ˇ1j|USTEDUSt I(TEDUSt ≥0)+ˇ2j|USTEDUSt I(TEDUSt <0)+Mt−1ˆj|US+εj|USt

Intercept 0.0002 0.0010*** 0.0009*** 0.0007*** 0.0016*** 0.0010*** 0.0010*** 0.0011*** 0.0001 0.0006** 0.0015*** 0.0003 0.0013*** TEDUS t I(TED≥0) 0.7927* 0.5518*** 0.5607*** 0.3891*** 0.7346*** 0.6729*** 0.6422*** 0.7509*** 0.8220*** 1.0563*** 0.4025 0.8237*** 0.5905*** TEDUS t I(TED<0) −0.1936 0.0365 0.0329 0.0027 0.0220 −0.0579 −0.0133 0.1208 0.1195 −0.1392 0.2129 0.1123 0.1076** IBORj_t−1 −0.0013 0.0043 0.0048 0.0052 0.0036 0.0033** 0.0038 0.0024 0.0038 0.0040 −0.0010 −0.0007 0.0042 Oilt−1 −0.0000 −0.0000 −0.0000 0.0000 −0.0001 −0.0001 −0.0001 −0.0000 −0.0000 −0.0001 −0.0000 −0.0002** −0.0000 Goldt−1 0.0002 −0.0002*** −0.0002** −0.0001 −0.0003** −0.0002*** −0.0002*** −0.0002** −0.0002* −0.0004*** −0.0002* −0.0002** −0.0002*** 99%CoVaRvaluesbyindividualyearandaveragesover2003–2006and2007–2009

CoVaR=CoVaRj|USt (99%)−CoVaRj|USt (50%);CoVaRtj|US(q)=VaRjq,t|VaRUSq,t=˛ˆj|US+ ˆˇj|US1 TEDUSt I(TEDUSt ≥0)+ ˆˇ2j|USTEDUSt I(TEDUSt <0)+Mt−1ˆj|US

2003 27.60 18.80 19.10 13.30 25.10 23.20 22.00 25.40 27.80 36.50 13.20 27.90 19.90 (123.48) (79.18) (90.80) (88.44) (77.83) (89.53) (91.30) (97.34) (109.09) (95.99) (78.99) (78.97) (79.48) 2004 19.20 13.20 13.40 9.30 17.60 16.20 15.40 17.90 19.60 25.40 9.40 19.60 14.00 (83.38) (58.48) (67.28) (63.12) (56.01) (62.88) (64.64) (68.41) (76.73) (67.10) (57.92) (57.57) (63.53) 2005 18.90 13.00 13.20 9.20 17.30 16.00 15.20 17.60 19.30 25.10 9.30 19.40 13.90 (109.81) (66.06) (77.41) (74.52) (62.99) (71.77) (74.35) (78.93) (90.24) (76.82) (65.31) (65.77) (71.18) 2006 20.10 13.80 14.10 9.80 18.40 17.00 16.20 18.80 20.60 26.70 9.90 20.60 14.80 (62.51) (44.00) (49.49) (53.05) (42.75) (47.66) (48.61) (51.20) (56.09) (50.21) (45.15) (48.27) (47.04) 2007 20.80 14.40 14.60 10.10 19.10 17.60 16.70 19.50 21.40 27.60 10.40 21.40 15.30 (86.15) (45.72) (47.19) (47.30) (50.45) (55.22) (53.13) (64.09) (64.62) (60.86) (59.29) (59.86) (49.15) 2008 36.00 24.80 25.20 17.50 33.10 30.40 29.00 33.70 36.90 47.80 17.80 37.00 26.50 (37.93) (34.66) (37.52) (34.65) (33.38) (35.61) (36.20) (36.94) (39.26) (36.79) (32.53) (33.21) (36.40) 2009 61.50 42.30 43.00 29.90 56.40 51.90 49.40 57.40 62.80 81.60 30.30 63.00 45.10 (132.04) (106.94) (117.87) (124.20) (103.53) (112.49) (114.39) (118.96) (128.01) (117.73) (104.46) (104.38) (104.62) 2003–2006 21.40 14.70 14.90 10.40 19.60 18.10 17.20 19.90 21.80 28.40 10.50 21.80 15.60 (129.17) (101.42) (111.49) (112.25) (98.69) (107.67) (109.53) (112.81) (121.05) (112.20) (99.23) (102.00) (105.33) 2007–2009 39.60 27.30 27.70 19.30 36.30 33.40 31.80 37.00 40.50 52.50 19.60 40.60 29.10 (54.91) (53.14) (54.44) (53.16) (52.62) (53.93) (54.11) (54.20) (55.18) (54.50) (51.39) (52.27) (53.51) Notes:TheyearlyCoVaRmeasuresinthistablearetheaverageofdailyCoVaRvaluesperyear.Theparenthesesarethecorrespondingt-statistics.IBORjtisthechangesinEuropean countryj’sIBORattimet,andTEDUS

t isthechangeinUSTreasuryEurodollarspreadattimet.I(TEDt>0)isanindicatorfunctionthatequals1ifthechangesinTEDispositive,that istheincreaseinTEDspread,andzerootherwise,whileI(TEDt<0)is,incontrast,isanindicatorfunctionthatequals1ifthechangesinTEDisnegative,thatisthedecreaseinTED spread,andzerootherwise.Thestatevariablesofglobalriskfactorsattimet−1,Mt−1,includesthechangesinEuropeaninterbankofferedratesattimet−1(IBORjt−1),thereturnof WestTexasIntermediatecrudeoilpricesattimet−1(Oilt−1),andreturnsofChicagoBroadOptionsExchangegoldpriceindexattimet−1(Goldt−1).

260 H.-F. Yang et al. / North American Journal of Economics and Finance 28 (2014) 242–264 Table7

CoVaRandCoVaRforeachEuropeanCountrywithasymmetricindicator,contemporaneousTEDand95%quantile.

Countryj UK Germany France Swiss Austria Belgium Finland NetherlandsPortugal Ireland Italy Greece Spain Quantileestimation:IBORj_t=˛j|US_+ˇj|US

1 TEDUSt I(TEDUSt ≥0)+ˇ j|US

2 TEDUSt I(TEDUSt <0)+Mt−1ˆj|US+εj|USt

Intercept −0.0007***0.0006*** 0.0004*** 0.0003*** 0.0009*** 0.0007*** 0.0006*** 0.0005*** −0.0006***−0.0004***0.0005*** −0.0004***0.0007*** TEDUS t I(TED≥0) 0.3553*** 0.3300*** 0.3620*** 0.3511*** 0.5864*** 0.2621*** 0.3067*** 0.3638*** 0.7818*** 0.9672*** 0.5153*** 0.4873*** 0.3379*** TEDUS t I(TED<0)−0.0855 0.1557*** 0.1526*** 0.1191* 0.1238 0.0747 0.1307*** 0.1215* 0.1559** 0.0519 0.0562 0.2590*** 0.1272*** IBORj_t−1 0.0007 −0.0017 0.0006 0.0025 0.0020 −0.0001 −0.0015 −0.0018 −0.0011 0.0005 0.0005 −0.0001 −0.0002 Oilt−1 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0001 0.0000 Goldt−1 0.0002** −0.0002***−0.0002***−0.0001***−0.0003***−0.0001***−0.0001***−0.0002*** −0.0001 −0.0003***−0.0002***−0.0001** −0.0002*** 95%CoVaRvaluesbyindividualyearandaveragesover2003–2006and2007–2009

CoVaR=CoVaRj|US_t (95%)−CoVaRj|US_t (50%);CoVaRj|US_t (q)=VaRj_q,t|VaRUS

q,t=˛ˆj|US+ ˆˇ j|US

1 TEDUSt I(TEDUSt ≥0)+ ˆˇ j|US

2 TEDUSt I(TEDUSt <0)+Mt−1ˆj|US

2003 9.00 7.70 8.50 8.30 14.10 6.30 7.20 8.70 18.90 23.70 12.60 11.30 8.00 (48.02) (42.22) (55.67) (62.02) (52.77) (49.04) (52.33) (43.61) (128.73) (83.75) (65.27) (75.12) (45.31) 2004 5.40 4.80 5.30 5.10 8.60 3.80 4.40 5.30 11.50 14.40 7.70 7.00 4.90 (31.83) (27.95) (36.49) (40.52) (33.94) (31.25) (34.27) (28.59) (77.82) (52.30) (41.95) (51.19) (30.22) 2005 5.40 4.80 5.30 5.20 8.70 3.90 4.50 5.40 11.60 14.50 7.70 7.10 5.00 (35.55) (32.23) (43.66) (49.59) (39.90) (36.41) (40.32) (32.90) (132.48) (67.16) (50.90) (66.88) (35.23) 2006 5.30 4.70 5.20 5.10 8.60 3.80 4.40 5.30 11.40 14.20 7.60 7.00 4.90 (25.34) (22.68) (30.41) (37.61) (27.50) (25.45) (28.49) (23.16) (91.68) (46.93) (35.90) (52.60) (25.12) 2007 5.60 5.10 5.60 5.50 9.20 4.10 4.80 5.70 12.20 15.20 8.10 7.50 5.30 (31.03) (28.53) (38.67) (38.88) (33.45) (33.37) (34.21) (29.05) (94.16) (58.33) (45.42) (63.69) (33.22) 2008 8.70 7.80 8.50 8.30 14.00 6.20 7.20 8.60 18.70 23.30 12.40 11.40 8.00 (20.02) (18.84) (25.62) (27.99) (23.13) (20.88) (22.96) (19.18) (54.15) (37.08) (29.84) (41.53) (21.47) 2009 16.30 14.40 15.90 15.50 26.10 11.60 13.50 16.10 34.80 43.50 23.10 21.20 14.90 (55.15) (52.38) (64.10) (72.48) (60.17) (56.58) (61.88) (53.41) (99.90) (82.45) (71.58) (81.32) (56.14) 2003–2006 6.30 5.50 6.10 5.90 10.00 4.40 5.10 6.10 13.30 16.70 8.90 8.10 5.70 (61.08) (54.41) (68.06) (75.87) (64.79) (60.52) (64.08) (55.66) (105.63) (88.02) (76.14) (85.93) (58.73) 2007–2009 10.20 9.10 10.10 9.80 16.50 7.30 8.50 10.20 22.00 27.40 14.60 13.40 9.40 (41.15) (39.25) (45.62) (47.22) (44.12) (42.07) (43.26) (39.81) (55.00) (51.93) (48.67) (51.47) (42.12) Notes:TheyearlyCoVaRmeasuresinthistablearetheaverageofdailyCoVaRvaluesperyear.Theparenthesesarethecorrespondingt-statistics.IBORj_tisthechangesinEuropean countryj’sIBORattimet,andTEDUS

t isthechangeinUSTreasuryEurodollarspreadattimet.I(TEDt>0)isanindicatorfunctionthatequals1ifthechangesinTEDispositive,thatis theincreaseinTEDspread,andzerootherwise,whileI(TEDt<0)is,incontrast,isanindicatorfunctionthatequals1ifthechangesinTEDisnegative,thatisthedecreaseinTEDspread, andzerootherwise.Thestatevariablesofglobalriskfactorsattimet−1,Mt−1,includesthechangesinEuropeaninterbankofferedratesattimet−1(IBORj_t−1),thereturnofWestTexas Intermediatecrudeoilpricesattimet−1(Oilt−1),andreturnsofChicagoBroadOptionsExchangegoldpriceindexattimet−1(Goldt−1).