动态地Hedcing抵押保证的安全的一个新的战略（PDF30）(1)

ANewStrategyforDynamicallyHedgingMortgage-BackedSecuritiesJacobBoudoukh,MatthewRichardson,RichardStantonandRobertF.WhitelawMay1995AbstractThispaperdevelopsanewstrategyfordynamicallyhedgingmortgage-backedsecurities(MBSs).TheapproachinvolvesestimatingthejointdistributionofreturnsonMBSsandT-notefutures,condi-tionaloncurrenteconomicconditions.WeshowthatourapproachhasasimpleintuitiveinterpretationofformingahedgeratiobydierentiallyweightingpastpairsofMBSandT-notefuturesreturns.Anout-of-samplehedgingexerciseisperformedfor8%,9%and10%GNMAsoverthe1990-1994periodforweeklyandmonthlyreturnhorizons.Thedynamicapproachisverysuccessfulathedgingoutthein-terestrateriskinherentinalloftheGNMAs.Forexample,inhedgingweeklyreturnson10%GNMAs,ourdynamicmethodreducesthevolatilityoftheGNMAreturnfrom41to24basispoints,whereasastaticmethodmanagesonly29basispointsofresidualvolatility.Moreover,only1basispointofthevolatilityofthedynamicallyhedgedreturncanbeattributedtoriskassociatedwithU.S.Treasuries,whichisincontrastto14basispointsofinterestrateriskinthestaticallyhedgedreturn.SternSchoolofBusiness,NYU;WhartonSchool,UniversityofPennsylvania;HaasSchoolofBusiness,UCBerkeley;andSternSchoolofBusiness,NYU.WewouldliketothanktheQGroupfornancialsupport.IntroductionInstitutionsholdsignicantpositionsinmortgage-backedsecurities(MBSs)foravarietyofrea-sons.Whetherthesepositionsreflecttradesonrelativevalueorinvolveinventoryholdingsduetocorebusinesses,hedgingtheinterestrateriskofthesesecuritiesisanimportantconcern.Thisisespeciallytruegiventhewell-documentedcasesofhugemonetarylossesincurredbynancialinstitutionsandinvestmentgroupswithrespecttotheirMBSportfolios.MBSvaluation,andbyextensionhedging,isnotastraightforwardexercise.Whilexed-rateMBSsissuedbygovernmentagenciesrepresentdefault-freeclaimstotheinterestandprincipaloftheunderlyingmortgages,thetimingofthesecashflowsdependsontheprepaymentbehaviorofthepool.Inparticular,asinterestratesfall,individualshaveanincentivetorenanceexistingmortgagesatthenewlowerrates.Thus,xed-rateMBSinvestorsareimplicitlywritingacalloptiononthecorrespondingxed-ratebond.Eventhoughprepaymentscanoccurforreasonsnotassociatedwithinterestratemovements,interestratesarethepredominantfactorinvaluingMBSs.Becauseofthispredominance,U.S.Treasurysecurities,or,morespecically,Treasurynote(T-note)futures,areoftenusedtohedgeMBSs.Thereasonsaretwofold:(i)T-notefuturesareveryliquidderivatives,and(ii)thepricesoftheseinstrumentsaredeterminedbytheunderlyingtermstructureofinterestratesandthusrelatedirectlytothevalueofMBSs.TherearetwocommonapproachestohedgingMBSsusingT-notefutures.TherstispurelyempiricalandinvolvestheregressionofpastreturnsonMBSsagainstpastreturnsonT-notefutures.TheresultingrelationcanthenbeusedtohedgetheinterestrateriskofMBSsusingtheriskinT-notes.Theadvantageofthismethodisthatitdoesnotinvolvestrongassumptionsregardingtheunderlyingmodelfortheevolutionofinterestratesorprepayments.Thedisadvantage,however,issevere.Thismethodisstaticinnature.Itdoesnotexplicitlyadjustthehedgeratioforchangesininterestratesandmortgageprepayments.1Thatis,theobservationsusedintheregressionrepresentanaverageoftherelationbetweenMBSsandT-notefuturesonlyoverthesampleperiod,whichmayormaynotrepresentativeofthecurrentperiod.Asanalternative,thesecondapproachismodel-based.Itinvolvesspecicationoftheinterestrateprocessandaprepaymentmodel.TheseassumptionsthenhelpmapanMBSpricingfunc-tionaltointerestratesandpossiblyotherfactors.2TheapproachrepresentsadynamicmethodfordeterminingcomovementsbetweenMBSpricesandT-notefuturesprices.Conditionaloncurrentvaluesoftherelevanteconomicvariablesandonparticularparametervalues,thesecomovementsarecompletelyspecied.Theproblemswiththisapproacharetwofold.First,thereisnoconsensusregardingwhatisareasonablespecicationofhowthetermstructuremovesthroughtime,andhowthesemovementsrelatetoprepaymentbehavior.Anymodelpriceisgoingtobetieddowncloselytothesepossiblyadhocassumptions.3Second,andmoresubtle,istherecognitionthat1theparametervaluesthemselvesmayoftenbe\chosenorestimatedfromastaticviewpoint.Forexample,empiricalprepaymentmodelsoftenreflectadhocprojectionsofprepaymentratesonsetsofhousingandinterestratefactors.Dotheresultingcoecients,whichrepresentanaverageoftherelationinthepast,havethesamelinktothevariablesdescribingthecurrentperiod?Manyofthewell-documentedMBS-hedgingascoeswouldimplythatthisisnotthecase.Inthispaper,weprovidearstpassatbridgingthegapbetweentheregressionandthemodel-basedapproaches.Ourgoalistomaintainsomeofthedistribution-freepropertiesofthepurelyempiricalmethod,whilerecognizingtheimportantdynamicpropertiesofMBSsandotherxedincomeinstruments.Inparticular,weproposeamethodbasedonestimatingtheconditionalproba-bilitydensityofMBSreturns,T-notefuturesreturns,andrelevantcurrentinformation(suchasthelevel,slopeandcurvatureofthetermstructure,interestratevolatility,andprepaymenthistory).ThismethodallowsustohedgeMBSswithT-notefutures,conditionaloncurrentinformation.Thus,thehedgeratioisderivedinasimilarwaytoonesfromexistingempiricalmethods,buti