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Default correlation An empirical investigation of a subprime lender

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JournalofBanking&Finance28(2004)753–771

www.elsevier.com/locate/econbase

Defaultcorrelation:Anempiricalinvestigation

ofasubprimelender

AdrianM.Cowan

aa,*,CharlesD.Cowan

b,cDepartmentofFinance,EconomicsandQuantitativeMethods,SchoolofBusiness,UniversityofAlabamaatBirmingham,115010thAve.South,Birmingham,AL35294,USA

bAnalyticFocusLLC,Birmingham,AL35203,USA

cUniversityofAlabamaatBirmingham,Birmingham,AL35294,USA

Abstract

Inrecentyears,subprimelendinghasgrownsubstantiallyasanimportantsectorofthecreditmarkets.Thispaperisconcernedwiththeriskmanagementofsubprimeloanportfoliosandtheimportanceofdefaultcorrelationinmeasuringthatrisk.Usingalargeportfolioofresidentialsubprimeloansfromananonymoussubprimelender,weshowthatdefaultcorre-lationissubstantialforthislender.Inparticular,thesignificanceofdefaultcorrelationin-creasesastheinternalcreditratingdeclines.Ourresultssuggestthatlendersandregulatorswouldbewellservedinvestingintheunderstandingofdefaultcorrelationinsubprimeport-folios.

Ó2003ElsevierB.V.Allrightsreserved.

JELclassification:G21;C10

Keywords:Creditrisk;Defaultcorrelation;Mortgage;Subprimelending

1.Introduction

Subprimelendersincludebothlargefinancialinstitutionsthatoffersubprimeloansasasubsetoftheirportfoliosandinstitutionsthatrestricttheirlendingactivitiestosuchloans.Subprimeloanportfoliosgenerallyhavegreaterrisksofdefaultwithhighercreditspreadstocompensatelendersforthehigherrisk.Thesubprimelend-ingmarkethasgrownsubstantiallyinrecentyears.AsnotedbyScheessele(2002),

*Correspondingauthor.Tel.:+1-205-975-90;fax:+1-205-672-74.E-mailaddress:acowan@business.uab.edu(A.M.Cowan).

0378-4266/$-seefrontmatterÓ2003ElsevierB.V.Allrightsreserved.doi:10.1016/j.jbankfin.2003.10.005

7A.M.Cowan,C.D.Cowan/JournalofBanking&Finance28(2004)753–771

totalsubprimelendinggrewfrom$90billionin1996to$173billionin2001.In2001,subprimeloansrepresentedaconsiderable8.3%oftheoverallmortgagemarket.Giventhegrowthofthismarketsectorcombinedwiththehigherrisksrelativetoothermortgageportfolios,understandingthecreditriskoftheseportfoliosisofcrit-icalimportancebothtothelendersthemselvesandtotheregulatorsoftheselenders.Thispaperfocusesononeaspectofcreditriskanalysis;i.e.,theimportanceofdefaultcorrelationinmeasuringcreditriskinsubprimeportfolios.

Significantadvancesarebeingmadeinthemeasurementandmodelingofcreditriskinlendingportfolios.However,giveninherentdifficultiesinnecessarydataacquisition,feweradvanceshavebeenmadewithrespecttoretailcreditportfoliosingeneral.Thispaperrepresentsthefirstempiricalinvestigationofdefaultcorrela-tionwithinatotallysubprimeloanportfolio.WhereasCalemandLaCour-Little(2001)studymortgageportfoliosofwhichsubprimeloansrepresentasubset,weareconcernedwithportfoliosthatconsistexclusivelyofsubprimeloans.ThisisanimportantdistinctionastherearemanylendersthroughouttheUSwhoservethesubprimemarketexclusively.Usingaproprietarydatasetofresidential,subprimeloansasasinglecasestudy,weareabletoprovideadditionalinsightintotheimpor-tanceofdefaultcorrelationinsuchportfolios.

Subprimelendershavehistoricallyusedspecifiedlimitstomanagecreditriskexposure,suchasadollarlimitestablishedbyborroweroradollarlimitestablishedbygeographicregion.Infact,Carey(2000)observesthatthemonitoringofestab-lishedcreditlimitshaslongbeenapartofexaminationsintheUnitedStates.Ourresultssuggestthatsubprimelenderswouldbewellservedtodevelopmoresophis-ticatedcreditmeasurementtechniques.Despitethesmallerexposuresfromsubprimeloansascomparedwithcommercialportfolios,wefindsubstantiallylargerdefaultcorrelationsthanreportedforcommercialbondsandloans.Thisalsohasimplica-tionsforcapitalrequirements,asGordy(2000)findsthatcapitalrequirementsbasedonindustrycreditriskmodelsvaryconsiderablybasedonaveragedefaultcorrela-tionsintheportfolio.Despitethefactthatweanalyzetheportfolioofasinglelender,ourresultsstronglysupporttheinvestmentinfurtherunderstandingofdefaultcor-relationbothbyregulatorsthatevaluateinternalriskmodelsandbyfinancialinsti-tutionsdevelopingmodelstomanagerisks.

Theremainderofthepaperisorganizedasfollows.Section2discussestheprevi-ousliteratureassociatedwithdefaultcorrelation.Section3describesthedataandmethodology.WepresentourempiricalresultsinSection4.Section5concludesthepaper.

2.Defaultcorrelation

Defaultcorrelationisameasureofthedependenceamongrisks.Alongwithdefaultratesandrecoveryrates,itisanecessaryinputintheestimationofthevalueoftheportfolioatriskduetocredit.Ingeneral,theconceptofdefaultcorrelationincorpo-ratesthefactthatsystemiceventscausethedefaulteventtocluster.Coincidentmove-mentsindefaultamongborrowersmaybetriggeredbycommonunderlyingfactors.

A.M.Cowan,C.D.Cowan/JournalofBanking&Finance28(2004)753–771755

Withinthecontextofretailportfolios,systemiceventsmightincludethemacroeco-nomiceventsofchangesintherateofunemploymentorgeographicallyspecificeventssuchasthosemodeledbyCalemandLaCour-Little(2001).Defaultcorrelationisde-finedbyNagpalandBahar(2001)astherelationshipbetweendefaultprobabilitiesandjointdefaultprobabilities.Theynotethathistoricalratesofdefaultsupporttheideathatcrediteventsarecorrelated.Thiscorrelationisacriticalfactorintheestima-tionofthetailsoftheoverallcreditlossdistributions.Failuretorecognizetheimpactofshockstotheportfoliothroughdefaultcorrelationwillultimatelyunder-estimatethemeasuresofriskandeconomiccapitalrequiredtomanagethatrisk.Incontrastwithotherresidentialloanportfoliosinwhichonewouldanticipatethatdefaultcorrelationcanbeverylow,understandingdefaultcorrelationiscriticalforlowercreditqualitysubprimeportfolios.Severalauthorshavedocumentedtherelationshipbetweentheinitialcreditqualityoftheportfolioanddefaultcorrelationincommercialportfolios.Generally,ascreditqualitydeclines,theimportanceofde-faultcorrelationincreases.Forexample,Zhou(1997)showsimplieddefaultcorrela-tionsbasedonZ-valuesthatarealmostzeroforhighlyratedfirmsbutsubstantialforlowlyratedfirmsevenovershorttimehorizons.Usingcorporatebondandloanportfolios,Lucasetal.(2001)providenumericalresultsshowingthatforagivencor-relation,ahigherportfolioqualitylowersextremecreditlossquantiles.Similarly,Loffler(2003)findsthatcorrelationuncertaintyisamoresignificantfactorforport-foliosratedBascomparedwithportfoliosratedBBBforuncertaintyinthe1%value-at-risk(VaR).Althoughthesestudiesdealwithcommercialloanandbondportfolios,themanagementofasubprimeloanportfolioisanalogoustotheman-agementofanon-investment-gradebondportfolio.Ourresultsareconsistentwiththesepreviousstudies.Thesignificanceofdefaultcorrelationincreasesastheinternalratingsofthelenderdecline.Thus,itislikelythatignoringdefaultcorrelationinthedevelopmentofcreditriskmodelsforsubprimeportfolioswouldleadtoconsider-ablemodelrisk.

ThereareseveralmethodologiescurrentlyemployedinthedevelopmentofdefaultcorrelationswithinportfoliosasdiscussedinZhou(1997).Forexample,Loffler(2003)estimatesdefaultcorrelationsbasedonthejointdistributionofassetvalues.AsdiscussedinCrouhyetal.(2000),equitypricesareoftenusedasaproxytoesti-mateassetcorrelations,giventhatassetvaluesarenotdirectlyobservable.Onecom-monlyemployedmethodistheidentificationofabenchmarkforthepurposeofdevelopingassetreturncorrelationsandthenmappingtheseintodefaultcorrela-tions.Theapproachrequiresmakingassumptionsabouttherelationshipbetweenas-setpricesanddefault.However,thisapproachisnotapplicablewithinaretailcontextasthereisnoassetpricefortheindividualborrower.Alternatively,defaultcorrelationscanbeinferredfromhistoricaldefaultvolatilitiesasdescribedgenerallywithinAppendixFofJ.P.Morgan’sCreditMetricsTechnicalDocument(1997).Weadoptasimilarapproachinthispaper.Adefaultcorrelationcoefficientisestimatedbasedontheassumptionthatallloanswithintheriskclasshaveidenticaldefaultrates.Theapplicationofsuchanapproachtosubprimeportfoliosassumesthatinternalcreditratingassignmentsareconsistent.Specifically,wefollowtheexchangeablemodelsframeworkofFreyandMcNeil(2002).

756A.M.Cowan,C.D.Cowan/JournalofBanking&Finance28(2004)753–771

3.Dataandmethodology

Thedataforthispaperarethedetailedloanhistoryfileofalargesubprimelender.ThislenderidentifiesitselfasasubprimelenderandisidentifiedassuchonthemostrecentannuallistofsubprimelendersbytheDepartmentofHousingandUrbanDevelopment.1Theprotectionoftheanonymityofthelenderprecludestheprovi-sionofdetaileddescriptivestatisticsofthedata.

OursampleconsistsofmonthlydataonresidentialloansfromJuly1995throughDecember2001.Werestrictouranalysistothe30-yearfixed-rateloanportfolio,andtheanalyzedportfolioconsistsexclusivelyofloansonone-tofour-familyresidentialproperties.2Althoughmultiplefactorscontributetotheclassificationofaloanassubprime,thesubprimenatureoftheanalyzedportfolioisclearlyreflectedinthelowFairIsaacCorporation(FICO)creditscoresatthetimeoforigination.ThelowertheFICOscore,thelowerthecreditworthinessoftheborrower.AmedianFICOscoreof587inoursampleissignificantlybelowthenationalmedianscoreof725,asreportedbyCalemandLaCour-Little(2001).

AsnotedbyJarrowandTurnbull(2000),creditrisktimehorizonsarecommonlyoneyear.Initially,weconsideredexaminingalloftheseloansonanannualbasis,butthisgaveusonlysixfullyearsworthofdata.Becausecrediteventsaretypicallylessrareeventsforsubprimelendersascomparedwithprimelenders,wetakeadvantageofthischaracteristictoreducethecredittimehorizon.Monthlyratesarevolatileandnotgenerallyreflectiveofoveralleconomicactivity.Thus,wecalculateratesonasemiannualbasis,breakingeachyearintoJanuarythroughJuneandJulythroughDecember.Usinga6-montheventhorizonallowsustobenefitfromamorereason-ablenumberoftimeperiodswhileatthesametimeguardingagainstspuriousvola-tilitythatmaydisguiseanyrealcorrelationwithexternaleconomicfactors.

Weusetwoseparatemeasuresofthedefaulteventforcomparativepurposes.First,wedefinedefaulttooccuratforeclosurewhenthelendertakesthecollateralasrealestateowned(REO).Second,weemployalessstringentmeasureof90daysormoredelinquenttodefinedefault.Thisservestoexpandoureventsample,sinceapproximatelytwiceasmanyloansare90daysormoredelinquentascomparedtoforeclosed.Thisdifferencereflectsthefactthatnotalldelinquenciesultimatelyleadtoforeclosure.Manydelinquentloanseventually‘‘cure’’andreturntocurrentstatusorprepaybecauseofsales.

Usingtheloanhistoriesfromthislender,wesummarizetheloansbycharacteris-ticsoftheborrowerandwithin6-monthtimeperiods.Wethencompute,foreachtimeperiod,therateofdefaultfortheoverallpoolofloansandalsoforsubgroupsofloansdefinedbytheborrowercharacteristics.Anumberofdiscretevariablesare

1TheDepartmentofHousingandUrbanDevelopment(HUD)annuallyidentifiesalistoflenderswhospecializeineithersubprimeormanufacturedhomelending.Thelistingsfor1993–2001areavailablefromtheHUDwebsiteatwww.huduser.org/datasets/manu.html.2Weretainthetwo-tofour-unitpropertyloansintheanalysisasthisisconsistentwiththepermittedBaselIIdefinitionofresidentialmortgageloansandconsistentwiththecurrentcategorizationsofresidentialloansonbankandthriftregulatoryreports.

A.M.Cowan,C.D.Cowan/JournalofBanking&Finance28(2004)753–771757

usedtodefinesubgroups,includingpaymenttoborrowerincomeratio,occupancy,andinternalriskgroup.3Weusedecilestoidentifysubgroupswhendealingwithsequentialvariables,suchascreditscore.Forsequentialvariables,weplaceloansinorderfromsmallesttohighestvalueandcreatedeciles.Asaresult,eachcategoryinthetabulationcontains10%oftheborrowers.Forthelowend(10thdecile)andthehighend(90thdecile)ofthedeciles,wefurthersubdivideby5%cutoffs;i.e.,0–5%,5±10%,90–95%,95±100%.Thisyields12categoriesinall,asseeninthetablesinSection4.Thisseg-regationoftheportfolioisconductedforallnumericallysequentialvariablesrele-vanttotheborrower,loan,andproperty.

AgeneralmodelofdefaultcorrelationcanbesummarizedbythinkingaboutthecorrelationbetweeneventsonaloanbyloanANDhalf-yearbyhalf-yearbasis.Ifwelookateachloan-timecombination,wecanconsiderloansheldbythesubprimelen-derinthesametimeperiodandalsoloanperformanceacrosstimeperiods.Toexam-inedefault,weassumethatdefaulteventsareindependentacrosstimeperiods.Inotherwords,notdefaultinginanyonetimeperiodisnotpredictiveofwhethertheloandefaultsinthenexttimeperiod.Thisisnecessarybecauseloansthatdefaultareimmediatelyremovedfromtheloanset.Thisallowsustoconsiderloan-timeblocks.Thecorrelationmatrixisblockdiagonalandhasonlythreepossibleentries:1,0,and,qthecorrelationcoefficient.Theblockdiagonalmatrixtakestheform

B16066R¼60

00

2

0B2000

00B300

ÁÁÁÁÁÁÁÁÁ...ÁÁÁ

7777705BkNÂN0003

16q66

whereBj¼6q

qq

2

q1qqq

qq1qq

ÁÁÁÁÁÁÁÁÁ...ÁÁÁ

3qq77q7:77q51njÂnj

ð1Þ

Ablockisthesetofallloansthatareheldbythelenderinanyonetimeperiod(inthiscase,a6-monthperiod).ThecorrelationrhoðqÞisassumedtobethesameinallblocks.Thenumberofblocks,k,isthenumberoftimeperiodsduringwhichaloancouldexist.Naturally,inanytimeperiodsomenewloansenterthepoolasneworig-inationsaremadeandsomeloansleavethepoolasaresultofeitherbeingpaidofforbeingforeclosed.Thismeansthattheblocksaredifferentsizes,dependingonthenumberofloansthatexistinanyonetimeperiod.

Acrosstimeperiodsthedefaulteventisconsideredtobeindependentsothatoff-diagonalblocksinthematrixRarefilledwithzeros.Thedefaultcorrelationismea-suredasthevariabilityofthedefaultevents(indicatedaszero/onedummyvariables)fromtimeperiodtotimeperiodrelativetothevariabilityofthedefaulteventiftherewerenovariabilityfromtimeblocktotimeblock.

Wealsolookedatthesourceoftheloan(wholesaleorretail)andwhetherthedocumentationwasfullorlimited.Thesefactorsaddednosignificantdiscriminationintermsofdefaultcorrelationandthereforewedonotpresenttheresults.

3758A.M.Cowan,C.D.Cowan/JournalofBanking&Finance28(2004)753–771

Aricherbutmuchmoredifficultmodeltoexaminewouldhaveoff-diagonalblocksinthematrixRbemeasuresofautocorrelationforlagsof1,2,3,...timeperi-ods.Itisdifficulttoknowthefullimpactofconsiderationofpotentialautocorrela-tion.Ontheonehand,theautocorrelationmaybepositive,indicatingthatiftherearealargenumberofdefaulteventsintimeperiodj,itislikelytherewillbealargenumberofdefaulteventsintimeperiodjþ1,andsotheoverallvariabilityofdefaulteventsmaybeevenlarger.Thiswouldindicatethattheeffectsofchangesineco-nomicconditionsbothpredominateandlinger.Iftheautocorrelationwerenegative,thiswouldsuggestthattheborrowersrespondtoandrecoverfromchangesineco-nomicconditionssothatalargenumberofdefaultsinonetimeperiodwouldlikelybefollowedbyasmallernumberthenextperiod.Thismayalsoreflectactivitiesonthepartoflenderstorespondtoincreasesinthenumberofdefaultsbyredoublingeffortsatworkoutsandothersuchremedies.Asubsequentpaperconsidersbothcon-temporaneousandlaggedcorrelationsindefaultanddelinquency.

Ifweassumenocorrelationwithinatimeblock,wewouldexpectthelikelihoodofdefaulttobesimplytheaveragerateofdefault.However,underthedefaultcorrela-tionmodel,theratewillappeartovaryfromtimeperiodtotimeperiod,sinceitdoes,conditionalonchangingeconomicconditions.Wecannotobservethechangingcon-ditions–wemaynotevenknowwhichvariablesareimportanttoconsider.Butwecanmodelthesituationbyallowingthedefaulteventstobecorrelatedwithintimeperiodswhileindependentbetweentimeperiods.

Oneespeciallycompellingresultofthisformulationistoconsiderthevarianceofthetotalnumberofdefaultsunderthismodel.Ifxisavectorwhoseentriesarezerooroneindicatingdefault,withanxvalueforeachloan-timeperiod,thenthesum-marystatisticsforthetotalnumberofdefaults,D,anditsvariance,observedoverakperiodtermis

D¼1Txand

VarðDÞ¼ðxÀ󰀂xÞTRðxÀ󰀂xÞ;where1isaunitvector.

IfwerewritethematrixBjas

Bj¼ð1ÀqÞIþq11T;

nikXk

1X1X2

ðxijÀ󰀂xÞþqn2xiÀ󰀂xÞ2:VarðDÞffið1ÀqÞið󰀂NiNij

ð2Þ

ð3Þ

ð4Þ

thenthevarianceofthetotalnumberofdefaults,VarðDÞ,reducestoapproximately

ð5Þ

Whenqequalszero(nocorrelationbetweendefaultevents),thenthevarianceissimplytheusualvariancemeasuredfromeachobservationtotheoverallmeanacrossalltimeperiods.Whenqisone,inanyblockifanyloandefaults,theyallde-fault.Thuswhenqisone,thecontributiontothevarianceofthetotalnumberofdefaultsisonlythevariabilitybetween(butnotwithin)theblocks.Thisrepresenta-

A.M.Cowan,C.D.Cowan/JournalofBanking&Finance28(2004)753–771759

tionmakesiteasytoseethatthedefaultcorrelationissimplytherelationofthevar-iabilityofthedefaultrateovertimeperiodsrelativetothevariabilityonewouldseeiftherewerenodefaultcorrelation.

4.Empiricalresults

Themagnitudeofdefaultcorrelationforthetotalpoolofloansislow,butanexaminationofsubgroupsshowsthatdefaultcorrelationcanbeasignificantprob-lemforasubprimelender.Thisistrueevenforastableportfolioofloanslikefixed-rate30-yearloans.Wepresentourresultsandshowhowtheyvarybysubgroupandalsopresentsomeofthedefaultanddelinquencyratesdiscovered.

AscanbeseeninTable1andtheaccompanyingFig.1,thereissomevariationfortheentiresampleinthedefaultrateasmeasuredbyforeclosurebutmuchmorevar-iationovertimeinthedelinquencyrate.However,itisrelativelylargecomparedwiththeincidenceofforeclosuresreflectedintheCalemandLaCour-Little(2001)sample.Wefind3.5%oftheloansforeclosedoverasix-and-a-half-yearobservationperiodcomparedwithonly0.8%overa5-yearperiodexhibitedinthesampleofCalemandLaCour-Little(2001).Thisdifferenceprimarilyreflectsthemixofprimeandsubprimeloansintheirportfolio.Inaddition,itmayreflectdifferencesinsampleperiods,althoughtheCalemandLaCour-Little(2001)periodoverlapsoursample

Table1

Overalldefaultanddelinquencyratesforall30-yearfixed-ratesubprimeloansregardlessofinternalriskclassification,July1995throughDecember2001

ForeclosedREO

1995:21996:11996:21997:11997:21998:11998:21999:11999:22000:12000:22001:12001:2Total

Defaultcorrelation

0.28%1.15%1.83%2.57%3.56%1.25%0.65%0.69%0.58%0.86%0.85%1.23%0.98%0.98%0.0079

90ormoredaysdelinquent4.61%4.84%6.66%6.07%6.%2.17%1.43%2.34%2.21%2.60%3.45%2.91%3.12%2.95%0.0109

Thesecondcolumninthistablepresentstheforeclosureratesfor6-monthperiodsbetweenthelatterhalfof1995throughthelatterhalfof2001,whilethethirdcolumnpresentstheratesatwhichloansbecame90ormoredaysdelinquentatleastonceduringthelifeoftheloan.Thevariationoftheratesisanindicationofincreaseordecreaseinthefrequencyoftheeventscausedbyevents’beingcorrelatedwithoneanotherwithinatimeperiod.Theratesdisplayedinbothcolumnsareforallloansintheloanportfolio.

760A.M.Cowan,C.D.Cowan/JournalofBanking&Finance28(2004)753–771

Fig.1.Defaultanddelinquencybasedontotal30-yearfixed-ratesubprimeloanportfolio.Thisgraphshowsthesteadyincreaseinthedelinquencyandforeclosureratesfrom1995through1997,followedbyadeclineinbothratestolowerlevelsuntiltheendof2001.REOisRealEstateOwned,theforeclosureontheloan,while90+Del.is90ormoredaysDelinquent.periodduringtheincidenceofhighestforeclosuresanddelinquencies.However,regardlessofthehigherincidenceofdefaultinouroverallportfolio,defaultcorrela-tionisaminimal0.0079forforeclosuresandaslightlyhigher0.011fordelinquentloans.Neitheroutcomereallydemonstratesaverylargedefaultcorrelation.

Moreinsightisavailableregardingdefaultcorrelationonceweinvestigatesubsetsofborrowers.Whenweexaminetheborrowersbysubgroupasdefinedintheprevi-oussection,wefindthatsomesubgroupsaresubjecttosignificantdefaultcorrela-tion.

Thefirstandmostobviousvariabletoconsideristheinternalriskgradeassignedtotheborrowerbythesubprimelender.Thisratingwouldbecomparabletothebondratingdiscussedaboveforcommercialbonds.However,inthecaseofbonds,thebondratingsareindependentlyassignedbyratingagencies,theychangeovertime,andtheyaretracked.Agreatdealofliteratureisdevotedtotheanalysisandinterpretationoftheseratingchanges,andtransitionmatricescanbeusedtobetterestimatethelikelihoodofdefaultinthebondmarket.Formortgageloans,weobserveonlytheriskgradeatthetimeoforigination,andwemustassumethatthisisasufficientindicatorfortheborrower.Whilewecannotmeasurehowtheriskgrademightchangeovertimefortheborrower,thefactthattheborrowerstartedinaparticularriskgradeisstillveryindicativeofthelikelihoodofdefaultordelin-quency.DefaultanddelinquencybyinternalriskclassificationispresentedinTable2.Therearetwointerestingresultsinthistable.First,thecreditratingcategoriesappeartoberelativelyconsistentasariskmeasure.Second,defaultcorrelationre-vealsborrowerdifferenceswhenmeasuredbyforeclosureascomparedwithdelin-quency.

Internalriskclassificationsappeartoaccuratelycapturecreditrisk.Thelikeli-hoodofdelinquencyandforeclosuremonotonicallyincreasesastheriskcategory

Table2

Defaultanddelinquencyratesof30-yearfixed-rateloansbyinternalriskclassificationRiskgradeForeclosedREO90ormoredaysdelinquentAAABCCCAAABCCC1995:20.00%0.00%0.27%0.99%0.00%0.00%1.69%3.23%9.85%11.70%1996:10.00%0.87%0.76%2.33%2.42%2.17%1.92%4.39%9.73%12.10%1996:20.00%0.34%2.50%3.%5.00%0.65%4.24%6.%14.57%10.00%1997:10.00%2.10%3.06%4.78%7.29%0.28%3.30%6.97%15.65%18.75%1997:20.22%2.07%4.35%11.19%21.43%1.09%4.82%8.70%23.13%21.43%1998:10.00%0.69%2.06%9.32%7.27%0.44%2.33%2.52%9.32%14.55%1998:20.04%0.66%0.93%5.15%4.55%0.42%1.27%2.05%7.73%13.%1999:10.30%0.78%0.70%3.%2.63%0.%2.15%3.26%8.86%18.42%1999:20.28%0.50%0.81%2.92%0.00%1.14%1.79%2.96%8.10%11.11%2000:10.32%1.01%0.99%3.15%4.93%1.25%2.10%3.79%9.73%9.85%2000:20.41%0.74%1.38%2.61%3.06%1.87%2.40%5.39%12.48%15.31%2001:10.75%0.92%2.07%4.06%4.97%1.41%3.08%4.71%10.39%9.39%2001:20.50%0.83%1.67%5.27%6.98%1.77%3.37%5.48%10.19%11.05%Total0.41%0.83%1.42%3.90%4.53%1.36%2.51%4.33%10.74%12.79%Default

0.0013

0.0040

0.0086

0.0197

0.0620

0.0030

0.0042

0.0084

0.0170

0.0123

correlation

Columns2–6(panel1)inthistablepresenttheforeclosureratesfor6-monthperiodsbetweenthelatterhalfof1995throughthelatterhalfof2001,whilethecolumns7–12(panel2)presenttheratesatwhichloansbecame90ormoredaysdelinquentatleastonceduringthelifeoftheloan.Thevariationoftheratesisanindicationofincreaseordecreaseinthefrequencyoftheeventscausedbyevents’beingcorrelatedwithoneanotherwithinatimeperiod.Theratesdisplayedinapanelarraytheloansbytheinternalriskratingassignedbythelender(AAthroughCC).

A.M.Cowan,C.D.Cowan/JournalofBanking&Finance28(2004)753–771761762A.M.Cowan,C.D.Cowan/JournalofBanking&Finance28(2004)753–771

decreases.Inaddition,thedefaultcorrelationmonotonicallyincreasesastheinternalriskclassificationdecreases.Thissuggests,aswouldbeexpected,thatlowerriskratedborrowersaremorevulnerabletosystemicevents;i.e.,theseborrowershavemoredifficultyrecoveringfromsevereincidents.Thus,boththelikelihoodmeasuresandthedefaultcorrelationindicatethattheinternalriskclassificationsdesignedbythelenderappeartocapturetheinherentriskcharacteristicsoftheloans.

Thedefaultcorrelationrevealsanunexpectedpatternbyinternalriskclassifica-tion.Thedefaultcorrelationclimbsfromnearzerotoq¼0:06asriskgradedeclines.Thesamemeasureappliedtodelinquenciesshowsthesametrend,fromverysmalltomeasurable,butfordelinquenciesthecorrelationisnotaspronounced.Webelievethatthissuggeststhatthelesscreditworthyborrowersreflectapatternofhabitualdelinquency.Forsomeborrowers,delinquencyisarecurringstate,andpaymenthis-toriesrevealacycleofdelinquencyandrecovery.Althoughthisgroupofborrowersismorevolatilerelativetooveralldelinquency,thedelinquencymaynotnecessarilyreflectsomeunderlyingsystemiceventfortheseindividuals.Suchaconsistentpat-ternwouldreducethecorrelationofdefaultfordelinquencies.Atthesametime,extraordinaryeventswilltendtopushlowergradeborrowersintoforeclosureinclustersasrevealedinthehighermeasureofdefaultcorrelationbasedonforeclo-sures.Thus,aswouldbeexpected,iftheexternaleventthatoccursissufficientlyse-vere,itwillleadtodelinquencyfollowedbydefault.

Thelikelihoodofdefault,whethermeasuredbyforeclosureordelinquency,ismuchgreaterforpropertieswheretheownerisnottheoccupant,asshowninTable3.Thelikelihoodofdefaultbasedonforeclosureisnearlythreetimeslargerforloanssecuredbynon-owner-occupiedpropertiesascomparedwithowner-occupied.Thisisconsistentwithagreatdealofthemortgageliterature,whichsuggeststhatborrow-erswillnotruthlesslyexercisethedefaultoption(e.g.,Vandell,1995).Borrowerswillcontinuetoremaincurrentontheirmortgagesevenafterthevalueofthehomefallsbelowtheoutstandingmortgagebalance.Althoughthisfailuretoexercisethedefaultoptionisattributedtomanysourcesintheliterature,ourresultsareconsistentwithautilityexplanationofbehavior.Thissuggeststhatborrowersderiveutilityfromremainingintheirhomesevenafterdeclinesinmarketvalue.Incontrast,nosuchutilitywouldbefoundinnon-owner-occupieddwellings.

Defaultcorrelationishighestformortgagescollateralizedwithsecondhomes,which,ingeneral,representhighercreditworthyborrowersasmeasuredbyinitialFICOscoreorinternalriskweighting.Thedefaultcorrelationforforeclosedsecondhomesis0.087comparedwithonly0.026fornon-owner-occupiedandanegligible0.005forloansonowner-occupiedproperties.ThisisconsistentwiththefindingsofCalemandLaCour-Little(2001)thatthehighercreditworthyborrowersex-antedefaultprimarilybasedonunusualcircumstances.However,ourresultsalsosuggestthatitisnotnecessarilyaneventuniquetotheborrower.

DefaultratesbypropertytypearedepictedinTable4.TheresultsareconsistentwiththoseinTable3,andthesimilarresultsaremostlikelyduetothesubstantialoverlapinthenon-owner-occupiedand2–4unitcategories.Theoveralldefaultandthedefaultcorrelationarelowestforsingle-familydetachedresidencesandsig-nificantlyhigherforotherpropertytypes.Forpropertieswith2–4units,thedefault

A.M.Cowan,C.D.Cowan/JournalofBanking&Finance28(2004)753–771

Table3

DefaultanddelinquencyratesbytypeofoccupancyOccupancy1995:21996:11996:21997:11997:21998:11998:21999:11999:22000:12000:22001:12001:2TotalDefault

correlation

ForeclosedREONon-owner0.00%1.53%2.94%5.05%10.23%1.81%0.95%2.57%1.70%2.70%1.40%2.97%2.23%2.37%0.0258

Owner0.33%1.03%1.%2.30%2.72%1.21%0.63%0.55%0.50%0.73%0.82%1.12%0.91%0.87%0.00

Secondhome0.00%5.88%3.85%0.00%6.90%0.00%0.00%0.00%0.61%1.09%0.51%0.00%0.35%0.63%0.0874

90ormoredaysdelinquentNon-owner5.52%5.61%8.82%7.80%10.23%3.63%4.95%4.00%4.36%4.50%6.70%5.20%3.80%5.09%0.0080

Owner4.43%4.79%6.33%5.77%6.57%2.05%1.15%2.21%2.03%2.49%3.23%2.77%3.10%2.80%0.0108

763

Secondhome7.14%0.00%7.69%11.11%3.45%0.00%0.00%2.34%3.07%0.55%2.53%1.73%1.40%2.02%0.0556

Columns2–4(panel1)inthistablepresenttheforeclosureratesfor6-monthperiodsbetweenthelatterhalfof1995throughthelatterhalfof2001,whilethecolumns5–7(panel2)presenttheratesatwhichloansbecame90ormoredaysdelinquentatleastonceduringthelifeoftheloan.Thevariationoftheratesisanindicationofincreaseordecreaseinthefrequencyoftheeventscausedbyevents’beingcorrelatedwithoneanotherwithinatimeperiod.Theratesdisplayedinapanelarraytheloansbytheuseoftheproperty,asdefinedbywhetherthepropertyisowneroccupiedornot,orifthepropertyisasecondhome.

correlationisquitesubstantial,reflectingaverylargeincreaseinthedefaultrateinbothhalvesof1997.

WenextcomputethedefaultcorrelationsbasedongroupingsbycreditscoreandpresentthesensitivityofdefaultcorrelationtoinitialborrowerFICOscoresinTable5.Aswouldbeexpected,ourresultsaresimilartothosereportedbyinternalriskcat-egory,giventhatthecreditscoreisaninputtothefinalinternalclassification.ThetendencyfordefaultcorrelationtobehigherforforeclosuresthandelinquenciesasexhibitedforinternalriskclassificationsinTable2iseliminatedwiththefinerclas-sificationsprovidedbyFICOscoredeciles.Whereastheuseofdecilesmaintainsaconsistentnumberofloansacrossdeciles,thisisnotthecaseforinternalriskclas-sifications.Whiledefaultcorrelation,whethermeasuredbyforeclosureordelin-quency,increasessteadilyastheinternalriskclassificationdeclines,thesameresultdoesnotholdwhentheloansaresegregatedbyFICOscoredeciles.Itisthere-foreinterestingtonotethatthislatterclassificationprovidesthegreatestdifferencesindefaultcorrelation.Thisfindingoffersapromisingavenueforfutureresearchinevaluatingtheefficiencyofinternalversusexternalratings.

Weevaluatedefaultcorrelationbymortgagepaymenttoborrowerincomeratio.Similartopreviouscategories,thisratioismeasuredattimeoforigination.Decilesarecreatedfromthepaymenttoincomeratio,andborrowersaregroupedfrom

7A.M.Cowan,C.D.Cowan/JournalofBanking&Finance28(2004)753–771

Table4

DefaultanddelinquencyratesbypropertytypePropertytypeForeclosedREO1995:21996:11996:21997:11997:21998:11998:21999:11999:22000:12000:22001:12001:2Total

Defaultcorrelation

SFR

Manufacturedhousing0.00%0.00%0.00%3.23%3.70%0.00%0.45%0.56%0.18%0.45%1.63%1.45%1.48%1.04%0.0138

2–4Units

Condo

PUD

0.34%1.26%1.77%2.39%3.39%1.38%0.72%0.68%0.56%0.91%0.84%1.21%0.98%0.98%0.0067

0.00%0.93%3.30%6.48%10.71%1.49%0.%1.04%1.52%1.23%1.04%2.52%1.80%1.76%0.0461

0.00%0.00%3.28%0.00%0.00%0.00%0.00%1.18%0.51%0.61%0.29%0.52%0.24%0.46%0.01

0.00%0.00%0.00%3.77%1.79%0.56%0.00%0.22%0.33%0.30%0.55%0.49%0.31%0.40%0.0258

90ormoredaysdelinquent1995:24.93%1996:14.68%1996:26.37%1997:16.16%1997:26.78%1998:12.28%1998:21.33%1999:12.32%1999:22.19%2000:12.56%2000:23.44%2001:12.92%2001:23.21%Total

Defaultcorrelation

2.96%0.0105

0.00%

5.26%9.52%0.00%7.41%0.00%1.35%2.25%2.87%2.69%4.08%3.75%3.80%3.26%0.0240

4.60%8.41%14.29%10.19%8.33%2.49%4.44%4.57%4.43%5.04%5.52%3.77%3.42%4.71%0.0225

0.00%3.85%1.%2.53%7.14%2.37%0.96%1.18%1.03%1.37%1.87%1.17%1.90%1.58%0.01

3.45%2.22%6.00%3.77%7.14%0.56%0.57%1.51%0.33%1.50%1.94%2.55%1.74%1.70%0.0237

Columns2–6(panel1)inthistablepresenttheforeclosureratesfor6-monthperiodsbetweenthelatterhalfof1995throughthelatterhalfof2001,whilethecolumns8–12(panel2)presenttheratesatwhichloansbecame90ormoredaysdelinquentatleastonceduringthelifeoftheloan.Thevariationoftheratesisanindicationofincreaseordecreaseinthefrequencyoftheeventscausedbyevents’beingcorrelatedwithoneanotherwithinatimeperiod.Theratesdisplayedinapanelarraytheloansbytheinternalriskratingassignedbythelender(AAthroughCC).

lowesttohighest.TheseresultsarepresentedinTable6.Mortgagesubgroupsdelin-eatedbythisratioandcreditscoreshowthegreatestdifferencesoverallindefaultcorrelation.Onealsofindsthatloanswithhigherratiosofmortgagepaymenttobor-rowerincomearemorelikelytodefaultandthedefaultcorrelationislarger.This

A.M.Cowan,C.D.Cowan/JournalofBanking&Finance28(2004)753–771765

suggeststhatanydisruptioninhouseholdincomeflowwillmorelikelyleadtoade-faultordelinquencyasalargerportionoftheborrower’sincomeisgoingtothemortgagepayment(andpresumablylessintosavings).Thus,asexpected,economicdistresswillleadtogreaterdefaultcorrelationforthesegroups.

Finally,itisimportanttorecognizethatourlimitedsampleperiodfromJuly1995throughDecember2001introducespotentialselectionbias.Defaultcorrelationcap-turessystemicevents,andthus,thetimeperiodoverwhichitismeasurednaturallyimpactstheestimates.AsnotedbyCarey(1998),datacoveringaverylongperiodmitigatebutdonoteliminatethisproblem.Thereisanissueofhowrepresentativethistimeperiodisofgeneralactivityfoundinthesubprimemarket.Ingeneral,theeconomywasenjoyingexpansionduringmuchofoursampleperiod,buttherewereunderlyingeconomicweaknessesaswell.SimilartotheCalemandLaCour-Little(2001)timeframe,oursampleperiodincludesaperiodofprimarilyrisingorstablehousepricesinmostgeographicmarkets,evensubsequenttothebeginningofthe2001recessioninMarch4ofthatyear.AccordingtotheFederalHomeLoanMortgageCorporation’s(FreddieMac’s)monthlymortgageratesurvey,thesampleperiodincludesbothperiodsofdecliningandrising30-yearmortgagerates,withapeakof8.5%duringtheperiodinMayof2000andalowof6.6%inOctoberof2001.Despitethedeclininginterestrateenvironmentformuchof1997and1998,subprimeborrowersarelargelyprecludedfromprepaymentbecauseoflockoutperi-odsandsignificantprepaymentpenalties.Itisclearfrombothouroverallportfolioandthecategorizedsubsamplesthatsurgesoccurredindefaultsanddelinquenciesinthe1996–97period.Thesesurgescoincidewiththetremendousincreaseinpersonalbankruptciesoverthissameperiod.Personalbankruptciesincreased29%and20%in1996and1997,respectively,fromprioryears.Overall,oursampleperiodrepresentsaverymixedeconomicpicture.Nevertheless,foranylimitedtimeperiodexamined,therearealwaysissuesofselectionbiastobeconsidered.

5.Conclusion

Thispaperpresentsthefirstformalstudyofdefaultcorrelationwithinanexclu-sivelysubprimemortgageloanportfolio.Wefindthatdefaultcorrelationsforthespecificportfoliostudiedareinsignificantuntiltheportfolioissegregatedintoappro-priateriskgroups.Weanalyze6-monthdefaultcorrelationusingbothactualdefault(foreclosure)andabroaderdefinitionofdelinquencythatisconsistentwithpreviousliterature(e.g.,CalemandLaCour-Little,2001).Contrarytoourexpectations,ac-tualdefaultsgenerallyresultinhigherdefaultcorrelationsthandelinquencies.Asanticipated,themagnitudeofdefaultcorrelationincreasesastheinternallyassignedriskgradedeclines.

TheNationalBureauofEconomicResearch(NBER)identifiesMarch2001asthebeginningofthe2001recession.

4Table5

Defaultanddelinquencyratesbycreditscore:ForeclosedREO(panelA)and90ormoredaysdelinquent(panelB)Credit0–5%6–10%11–20%21–30%31–40%41–50%51–60%61–70%71–80%81–90%91–95%96–100%PanelA1995:20.00%7.69%2.04%0.00%0.40%0.00%0.00%0.00%0.00%0.00%0.00%0.00%1996:10.00%21.43%3.33%1.80%1.42%0.51%0.00%0.00%0.00%0.00%0.00%0.00%1996:20.00%26.09%3.08%2.14%2.45%1.75%0.38%0.00%1.59%0.00%0.00%0.00%1997:10.00%16.67%18.06%3.59%3.51%0.74%0.91%0.32%0.00%0.00%0.00%0.00%1997:250.00%38.46%14.52%11.61%4.40%2.43%1.72%0.30%0.48%0.00%0.00%0.00%1998:10.00%27.27%26.42%7.59%2.94%0.37%0.50%0.00%0.14%0.00%0.00%0.00%1998:20.56%2.94%3.%4.%1.51%0.27%0.11%0.09%0.09%0.00%0.00%0.00%1999:10.%2.11%1.36%0.84%1.73%1.58%0.27%0.44%0.15%0.17%0.00%0.00%1999:20.17%0.99%1.07%1.47%1.22%0.58%0.73%0.50%0.23%0.06%0.00%0.15%2000:10.93%0.79%1.41%1.72%0.72%1.27%1.14%0.31%0.75%0.55%0.92%0.13%2000:21.65%1.43%1.72%1.56%1.09%0.90%0.79%0.65%0.41%0.28%0.68%0.00%2001:12.62%2.18%1.79%1.94%2.18%1.37%1.12%0.78%0.%0.71%0.66%0.37%2001:21.66%1.93%1.97%1.81%1.%1.34%0.68%0.%0.69%0.35%0.32%0.14%Total1.32%2.14%2.27%2.11%1.66%1.06%0.74%0.47%0.46%0.34%0.44%0.14%Default

0.0110

0.0567

0.0435

0.0128

0.0027

0.0013

0.0009

0.0003

0.0006

0.0006

0.0027

0.0010

correlation

766A.M.Cowan,C.D.Cowan/JournalofBanking&Finance28(2004)753–771PanelB1995:20.00%46.15%18.37%4.79%4.78%1.55%2.94%0.%0.00%0.00%0.00%0.00%1996:10.00%57.14%20.00%7.66%3.99%3.06%1.53%0.53%2.27%0.00%0.00%0.00%1996:2100.00%43.48%36.92%13.68%5.52%3.26%1.88%1.40%0.00%0.00%0.00%0.00%1997:1100.00%.17%26.39%10.31%5.56%5.17%3.93%0.96%0.00%0.00%0.00%0.00%1997:2100.00%30.77%37.10%20.65%7.60%5.47%2.41%2.09%0.95%0.00%0.00%0.00%1998:10.00%36.36%20.75%13.10%3.53%2.43%1.16%0.68%0.42%0.00%0.00%0.00%1998:20.00%2.94%1.77%4.35%4.87%2.26%1.46%0.46%0.47%0.12%0.00%0.00%1999:13.76%3.51%5.23%5.39%4.50%2.96%1.87%1.45%1.35%0.69%0.77%0.00%1999:23.28%3.95%4.14%4.21%2.76%2.96%2.20%1.88%1.15%0.77%0.90%0.30%2000:14.41%4.74%5.20%3.99%3.95%2.81%2.92%1.63%1.35%0.73%1.53%0.%2000:28.38%6.99%5.53%6.22%5.10%4.72%2.20%1.70%2.10%1.17%1.22%0.81%2001:14.78%5.39%5.37%5.05%4.83%3.94%2.30%1.84%1.%1.53%0.66%0.65%2001:25.97%5.55%4.77%5.58%5.79%3.85%3.51%2.35%1.59%1.28%1.37%1.02%Total5.12%6.19%6.25%5.98%4.67%3.49%2.40%1.%1.37%0.98%1.05%0.65%Delinquent0.0244

0.0701

0.0520

0.0138

0.0011

0.0013

0.0010

0.0009

0.0009

0.0009

0.0033

0.0023

correlation

Columns2–13(panelA)inthistablepresenttheforeclosureratesfor6-monthperiodsbetweenthelatterhalfof1995throughthelatterhalfof2001.Thevariationoftheratesisanindicationofincreaseordecreaseinthefrequencyoftheeventscausedbyevents’beingcorrelatedwithoneanotherwithinatimeperiod.TheratesdisplayedinapanelarraytheloansbytheexternalriskratingdeterminedbyuseofFICOscores.ThecreditscoreistheFairIsaacFICOscoreobtainedbythelenderpriortoloanorigination.Eachcreditpercentageindicatesthedecileorhalf-decilecategorycreatedusingcreditscore.Theleftmostgroup(0–5%)hasthelowestcreditscoresatthetimetheloanismade.

Columns2–13(panelB)inthistablepresentthedelinquencyrates,90ormoredaysatleastonceduringthelifeoftheloan,for6-monthperiodsbetweenthelatterhalfof1995throughthelatterhalfof2001.Thevariationoftheratesisanindicationofincreaseordecreaseinthefrequencyoftheeventscausedbyevents’beingcorrelatedwithoneanotherwithinatimeperiod.TheratesdisplayedinapanelarraytheloansbytheexternalriskratingdeterminedbyuseofFICOscores.ThecreditscoreistheFairIsaacFICOscoreobtainedbythelenderpriortoloanorigination.Eachcreditpercentageindicatesthedecileorhalf-decilecategorycreatedusingcreditscore.Theleftmostgroup(0–5%)hasthelowestcreditscoresatthetimetheloanismade.

A.M.Cowan,C.D.Cowan/JournalofBanking&Finance28(2004)753–771767Table6

DefaultratesbyP&Itoincomeratio:ForeclosedREO(panelA)and90ormoredaysdelinquent(panelB)P&Ito0–5%

6–10%

11–20%

21–30%

31–40%

41–50%

51–60%

61–70%

71–80%

81–90%

91–95%

96–100%

incomePanelA1995:20.00%0.00%0.00%0.00%0.00%0.00%1.12%0.00%1.00%0.00%1.72%0.00%1996:11.46%1.19%1.36%0.60%1.44%0.00%3.17%0.69%0.71%1.23%2.63%0.00%1996:21.32%3.23%0.00%2.16%0.00%3.60%3.31%0.74%1.39%2.33%2.20%3.49%1997:11.70%0.00%3.23%1.96%1.65%2.99%3.38%2.86%4.27%2.31%2.11%5.13%1997:24.85%3.%2.00%4.12%2.94%3.25%3.08%5.19%2.13%2.56%5.26%10.53%1998:10.66%1.24%0.72%1.48%1.42%0.30%1.55%1.17%1.67%1.66%1.68%3.06%1998:20.00%1.21%0.26%0.82%0.%0.77%0.16%0.33%0.51%0.77%1.65%1.75%1999:11.94%0.71%0.36%0.39%1.14%0.32%0.69%0.58%0.72%0.55%0.26%0.85%1999:21.06%0.26%0.81%0.71%0.15%0.31%0.65%0.65%0.67%0.48%0.70%0.74%2000:11.38%0.95%1.06%1.03%0.67%0.49%1.02%0.57%0.66%0.94%0.91%0.95%2000:20.84%0.80%0.71%0.68%0.50%1.24%0.82%1.06%0.95%0.60%0.68%1.68%2001:11.37%1.03%1.24%1.08%1.15%1.32%1.51%0.61%1.59%1.05%1.83%1.24%2001:21.63%1.07%0.77%0.45%0.76%0.98%1.31%1.30%1.02%0.%1.04%0.95%Total1.31%0.94%0.86%0.86%0.80%0.91%1.13%0.90%1.04%0.90%1.17%1.31%Default

0.0103

0.0114

0.0084

0.0124

0.0075

0.01

0.0108

0.0196

0.0090

0.0066

0.0127

0.0583

correlation

768A.M.Cowan,C.D.Cowan/JournalofBanking&Finance28(2004)753–771PanelB1995:23.23%5.36%4.21%4.67%4.49%2.11%5.62%4.44%3.00%5.71%8.62%5.88%1996:13.65%1.19%2.04%3.57%5.76%1.40%4.76%7.59%5.00%8.02%7.%7.77%1996:26.62%5.38%4.07%4.32%4.83%10.79%6.61%4.41%6.94%7.56%8.79%13.95%1997:13.98%5.00%4.61%7.84%6.59%3.59%7.43%6.86%7.93%4.63%3.16%15.38%1997:24.85%3.%5.00%8.76%5.88%6.49%9.23%7.14%4.96%8.21%12.28%13.16%1998:10.66%1.24%2.63%0.74%2.55%1.18%3.11%2.33%2.67%3.05%4.20%4.08%1998:23.13%0.97%1.28%1.23%2.08%0.77%1.47%1.47%1.02%1.08%1.23%2.18%1999:14.04%3.02%1.81%1.96%1.56%2.16%2.87%1.97%2.38%2.22%3.17%2.56%1999:22.47%2.61%1.61%2.28%1.62%2.45%2.03%1.69%2.26%2.63%2.%3.49%2000:11.49%2.38%2.05%1.87%2.40%3.14%2.92%2.48%3.37%3.18%2.72%3.47%2000:24.10%3.33%2.70%2.%2.69%3.14%4.15%3.98%3.27%2.88%5.19%5.31%2001:14.02%2.78%2.90%2.22%2.25%1.93%3.07%3.52%2.61%2.79%4.03%4.70%2001:23.61%2.33%2.76%2.31%2.39%2.76%3.11%4.17%2.95%4.60%3.03%3.58%Total3.29%2.65%2.44%2.44%2.45%2.62%3.21%3.24%2.95%3.34%3.75%4.47%Delinquent0.0063

0.0081

0.0056

0.0230

0.0122

0.0261

0.0156

0.0129

0.0124

0.0159

0.0268

0.04

correlation

Columns2–13(panelA)inthistablepresenttheforeclosureratesfor6-monthperiodsbetweenthelatterhalfof1995throughthelatterhalfof2001.Thevariationoftheratesisanindicationofincreaseordecreaseinthefrequencyoftheeventscausedbyevents’beingcorrelatedwithoneanotherwithinatimeperiod.Theratesdisplayedinapanelarraytheloansbytheorderedprincipalandinteresttoincomeratio.TheP&Itoincomeratioisameasureofabilitytopay.EachP&Itoincomeratiopercentagereportedasheadersindicatesthedecileorhalf-decilecategorycreatedusingthisratio.Theleftmostgroup(0–5%)hasthehighestabilitytopayatthetimetheloanismade.

Columns2–13(panelB)inthistablepresentthedelinquencyrates,90ormoredaysatleastonceduringthelifeoftheloan,for6-monthperiodsbetweenthelatterhalfof1995throughthelatterhalfof2001.Thevariationoftheratesisanindicationofincreaseordecreaseinthefrequencyoftheeventscausedbyevents’beingcorrelatedwithoneanotherwithinatimeperiod.Theratesdisplayedinapanelarraytheloansbytheorderedprincipalandinteresttoincomeratio.TheP&Itoincomeratioisameasureofabilitytopay.EachP&Itoincomeratiopercentagereportedasheadersindicatesthedecileorhalf-decilecategorycreatedusingthisratio.Theleftmostgroup(0–5%)hasthehighestabilitytopayatthetimetheloanismade.

A.M.Cowan,C.D.Cowan/JournalofBanking&Finance28(2004)753–771769770A.M.Cowan,C.D.Cowan/JournalofBanking&Finance28(2004)753–771

Brieflyreviewingtheresultsfromactualdefaults,weobtaina6-monthdefaultcorrelationof0.062forCC-ratedborrowersascomparedwithaminuscule0.001forAA-ratedborrowers.Whengroupedbyoccupancytype,thedefaultcorrelationincreasesto0.087forsecond-homeloansand0.026fornon-owner-occupiedhomes.Incontrast,classificationbypropertytyperesultsinamaximumdefaultcorrelationof0.046fortwo-tofour-unitproperties.

Ifdefaultcorrelationsareverylowwithinsubprimeportfolios,anexpensiveinves-tigationofdefaultcorrelationsisnotanefficientuseofresources.However,ourfind-ings,combinedwiththefindingsofLoffler(2003)thatlowergradeportfoliosaremoresensitivetochangesindefaultcorrelations,suggestthattheindustryshouldfocusonthisissue.Althoughourfindingsrepresentbutonelender,theyclearlypro-videsufficientinsighttosuggestdirectionsforfurtherinvestigation.If,asCarey(2000)suggests,badtaillossratesareunderstatedbyestimatingportfoliolossdistri-butionsbyequallyweightingeventsineachdatabaseyear,thenourresultsshouldcompelbothsubprimelendersandregulatorstofurtherinvestigatetheimpactofde-faultcorrelation.

Acknowledgements

WearegratefulforthehelpfulcommentsreceivedfromparticipantsattheRetailCreditRiskConferenceattheFederalReserveBankinPhiladelphia,April2003,andfromLanceNail.Wearealsogratefultotheeditors,LorettaMesterandMitchellBerlin.Andwewouldespeciallyliketothankananonymousrefereeforconstructivecriticismsandcomments.

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