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
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
VarðDÞ¼ðxÀxÞTRðxÀxÞ;where1isaunitvector.
IfwerewritethematrixBjas
Bj¼ð1ÀqÞIþq11T;
nikXk
1X1X2
ðxijÀxÞþqn2xiÀxÞ2:VarðDÞffið1ÀqÞiðNiNij
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.
References
Calem,P.S.,LaCour-Little,M.,2001.Risk-basedcapitalrequirementsformortgageloans.WorkingPaper2001–60.TheFederalReserveBoard,FinancialandEconomicsDiscussionSeries,November.Carey,M.,1998.Creditriskinprivatedebtportfolios.JournalofFinance53,1363–1387.
Carey,M.,2000.Dimensionsofcreditriskandtheirrelationshiptoeconomiccapitalrequirements.WorkingPaper7629,NationalBureauofEconomicResearch,March.
Crouhy,M.,Galai,D.,Mark,R.,2000.Acomparativeanalysisofcurrentcreditriskmodels.JournalofBankingandFinance24,59–117.
Frey,R.,McNeil,A.,2002.VaRandexpectedshortfallinportfoliosofdependentcreditrisks:Conceptualandpracticalinsights.JournalofBankingandFinance26,1317–1334.
Gordy,M.,2000.Acomparativeanatomyofcreditriskmodels.JournalofBankingandFinance24,119–149.
Jarrow,R.A.,Turnbull,S.M.,2000.Theintersectionofmarketandcreditrisk.JournalofBankingandFinance24,271–299.
Loffler,G.,2003.Theeffectsofestimationerroronmeasuresofportfoliocreditrisk.JournalofBankingandFinance27,1427–1453.
Lucas,A.,Klaassen,P.,Spreij,P.,Straetmans,S.,2001.Ananalyticapproachtocreditriskoflargecorporatebondandloanportfolios.JournalofBankingandFinance25,1635–16.
Morgan,J.P.,1997.CreditMetricsTM–TechnicalDocument.J.P.Morgan&Co.Incorporated,NewYork.
A.M.Cowan,C.D.Cowan/JournalofBanking&Finance28(2004)753–771771
Nagpal,K.,Bahar,R.,2001.Measuringdefaultcorrelation.Risk14,129–132.
Scheessele,R.,2002.Blackandwhitedisparitiesinsubprimemortgagerefinancelending.WorkingPaperHF-014,USDepartmentofHousingandUrbanDevelopment,HousingFinance,April.
Vandell,K.,1995.Howruthlessismortgagedefault?Areviewandsynthesisoftheevidence.JournalofHousingResearch6,245–2.
Zhou,C.,1997.Defaultcorrelation:Ananalyticalresult.WorkingPaper,FederalReserveBoard,Washington,DC.
因篇幅问题不能全部显示，请点此查看更多更全内容
Copyright © 2019- howto234.com 版权所有 湘ICP备2022005869号-3
违法及侵权请联系：TEL:199 1889 7713 E-MAIL:2724546146@qq.com
本站由北京市万商天勤律师事务所王兴未律师提供法律服务