固定收益证券FixedIncomeSecurities专家讲座

FixedIncomeSecurities-Lecture10DrHerbertY.T.LamMay2023Today’sLectureMortgageLoansMortgage-BackedSecuritiesMortgagepassthroughsecuritiesCollateralizedMortgageObligationStrippedMortgage-BackedSecuritiesCMOsandSubprimeCrisisMortgagesAmortgageloanisaloansecuredbythecollateralofsomespecificrealestatepropertywhichobligestheborrowertomakeapredeterminedseriesofpayments.Amortgagedesignisaspecificationoftheinterestrate,termofthemortgage,andmannerinwhichtheborrowedfundsarerepaid.Mortgageoriginator(originallender)caneither-holdthemortgageintheirportfolio-sellthemortgagetoaninvestoror-usethemortgageascollateralfortheissuanceofasecurity(mortgagebackedsecurity).Contractrate

(interestrateonamortgageloan) ContractrateisgreaterthantheyieldonaTreasurysecurityofcomparablematurity.Thespreadreflectscostsofcollectioncostsassociatedwithdefault(noteliminateddespitethecollateral)poorerliquidityuncertaintyconcerningthetimingofthecashflow.Fixedrate,levelpayment,fullyamortizedmortgageTheborrowerpaysinterestandrepaysprincipalinequalinstallmentsoveranagreeduponperiodoftime(termofthemortgage).Thefrequencyofpaymentistypicallymonthly.Theservicingfeeisaportionofthemortgagerate.Theinterestratethattheinvestorreceivesiscalledthenetcoupon.GrowingequitymortgagesItisafixed-ratemortgagewhosemonthlymortgagepaymentsincreaseovertime.Amortizationscheduleforalevel-payment

fixed-ratemortgageMortgageloan: $100,000Mortgagerate: 8.125%Monthlypayment:$742.50Termofloan:30years(360months)Examplen=360,mortgagebalance=$100,000,i=0.08125/12.Mortgagepayment=$742.50.monthlypayment=mortgagebalancewhereiisthesimplemonthlyinterestrate.Proofofthemortgageformula…PPP1st2nd

nthextendoneextraperiod:Subtractthetwoterms:sothatExample

MortgagebalanceisreducedwitheachmonthlymortgagepaymentInterestportiondeclinesandrepaymentportionincreases.AdjustableRateMortgagesThemortgagerateisresetperiodicallyinaccordancewithsomechosenreferencerateProtectionclausesagainstoverlylargecouponchangesOthertermsRatecapslimittheamountthatthecontractratemayincreaseordecreaseattheresetdate.Alifetimecapsetsthemaximumcontractrateoverthetermoftheloan.PrepaymentPaymentsmadeinexcessofthescheduledprincipalrepayments.Theamountandtimingofthecashflowsfromtherepaymentsarenotknownwithcertainty.ReasonsSaleofahomeMarketratesfallbelowthecontractrateFailuretomeetthemortgageobligationsFactorsaffectingprepaymentbehaviorsPrevailingmortgagerate -thecurrentlevelofmortgageratesrelativetotheborrower’scontractrate. -Thespreadshouldbewideenoughtocoverthecosts2.Pathhistoryofratespreadisimportant -dependsonwhethertherehavebeenprioropportunitiestorefinancesincetheunderlyingmortgageswereoriginated.Factorsaffectingprepaymentbehaviors3. Presenceofprepaymentpenalty.Macroeconomicfactorse.g.growingeconomyresultsinariseinpersonalincomeandinopportunitiesforworkermigration.Seasonalfactor:HomebuyingincreasesintheSpringandreachesapeakinthelateSummer.Sincetherearedelaysinpassingthroughprepayments,thepeakmaynotbeobserveduntilearlyFall.InterestratepathdependencePrepaymentburnout–Prepaymentsarepathdependentsincethismonth’sprepaymentratedependsonwhethertherehavebeenprioropportunitiestorefinanceoncetheunderlyingmortgageswereoriginated.Example–pathofinterestratesinthepast3yearsFirstpath:11%8%13%8%Secondpath:11%12%13%8%Morerefinancingoccursnowwhentheinterestratesfollowthesecondpath.PrepaymentmodelsDescribestheexpectedprepaymentsontheunderlyingpoolofmortgagesattimetintermsoftheyieldcurveattimetandotherrelevantvariables. predictedfromananalysisofhistoricaldata.ExampleWeeklyreport“SpreadTalk”publishedbythePrudentialSecurities-provides6-month,1-yearandlong-termprepaymentprojections assumingdifferentamountsofshiftininterestrates.Mortgage-backedsecurities(MBS)Mortgage-backedsecuritiesaresecuritiesbackedbyapoolofmortgageloans.1. Mortgagepassthroughsecurities;2. Collateralizedmortgageobligations;3.Strippedmortgage-backedsecurities. Thelasttwotypesarecalledderivativemortgage-backedsecuritiessincetheyarecreatedfromthefirsttype.MBSversusfixedincomeinvestmentsVirtuallynodefaultrisksincethemortgagesinapoolareguaranteedbyagovernmentrelatedagency,suchasGNMA(GovernmentNationalMortgageAssociation)orFNMA(FederalNationalMortgageAssociation).Prepaymentrisk/Reinvestmentrisk Prepaymentprivilegesgiventothehouseholdertoputthemortgagebacktothelenderatitsfacevalue.HowistheOption-adjusted-spread(OAS)determined?OSAanalysisevaluatesthecashflowsforanMBSbasedonthousandsofdifferentinterestratescenarios.Startingwithcertainprepaymentassumptions,eachdifferentinterestratepathisconvertedintoaprepaymentscenario.Forexample,ifmarketratesdrop100bps,whatpercentageofborrowerswillrefinanceinagivenmonth.Avalueforthesecurityisderivedbydiscountingthetheoreticalcashflowstothepresentandaveragingthem.Numericaltechniques:latticetreetogeneratethevariousinterestratescenarios.MortgagePassthroughSecuritiesAmortgagepassthroughsecurityisasecuritycreatedwhenoneormoreholdersofmortgagesformapoolofmortgagesandsellsharesorparticipationcertificatesinthepool.Thecashflowsconsistsofmonthlymortgagepaymentsrepresentinginterest,thescheduledrepaymentofprincipal,andanyprepayments.MortgagePassthroughSecuritiesPaymentsaremadetosecurityholderseachmonth.Themonthlycashflowsforapassthrougharelessthanthemonthlycashflowsoftheunderlyingmortgagesbyanamountequaltoservicingandotherfees.Notallofthemortgagesthatareincludedinthepoolthataresecuritizedhavethesamemortgagerateandthesamematurity.Aweightedaveragecouponrate(WAC)andaweightedaveragematurity(WAM)aredetermined.Senior/subordinatedstructuresThesubordinatedclassisthefirst-losspieceabsorbingalllossesontheunderlyingcollateral,thusprotectingtheseniorclass.Theseniorclassisgivingupyieldtothesubordinatedclassholders.Example $100milliondealdividedinto $92.25millionseniorclass $7.75millionsubordinatedclassSupposethereis$10millionoflosses,thesubordinatedclassexperiences$7.75millionoflosses(100%loss)andtheseniorclassexperiencesalossof$2.25million(2.4%=$2.25/$92.25loss).ContractionriskSupposeaninvestorbuysa10%couponGinnieMaeatatimewhenmortgagesare10%.Whatwouldbetheimpactonprepaymentsifmortgageratesdeclineto6%.

Thepriceofanoptionfreebondwillrise,butinthecaseofpassthroughsecuritytheriseinpriceislessbecausethereisahigherprepayment(refinanceatlowerrate).Theupsidepricepotentialistruncatedduetoprepayments.Thecashflowsfromprepaymentsarereinvestedatalowerrate.

ExpansionriskWhathappenifthemortgageratesriseto15%?Thepriceofthepassthrough,likethepriceofanybond,willdecline.

Itdeclinesmorebecausethehigherrateswilltendtoslowdowntherateofprepayment,ineffectincreasingtheamountinvestedatthecouponrate,whichislowerthanthemarketrate.WhatisaCollateralizedmortgageobligations(CMO)?MortgagesarepooledThe‘pool’issplitintovarioustrancheswithvaryingdegreesofrisk,cashflows,andtimeframes. “tranche”Frenchwordmeaning“slice”InvestorspurchasesecuritiesMortgagesareusedascollateralformortgagepass-throughsecuritiesCollateralizedmortgageobligations(CMO)Acollateralizedmortgageobligationisadebtinstrumentcollateralizedbymortgagepassthroughcertificates.Thecashflows(interestandprincipal)aredirectedtodifferentbondclasses,calledtranchessoastomitigatedifferentformsofprepaymentrisk.Thisisknownas“distributionbasedonthewaterfall”.Collateralizedmortgageobligations(CMO)HistoryofCMOsOriginatedasamortgagepass-throughsecurityGovernment-sponsoredenterpriseswerecreatedtoattractinvestors&createaliquidsecondarymarket.FannieMae,GinnieMae,&FreddieMacwereresponsibleforpurchasingmortgagesandissuingmortgagebackedsecurities1970-GinnieMaeissuedthefirstbondsbackedbypoolsofmortgagestofreeupfundsformorehomeloans1977-Thefirstprivatemortgagebackedsecuritiesaresold1983-FreddieMacissuesthefirstcollateralizedmortgageobligation,whichallowsinvestorstopicktheirlevelofriskAdvantagesofCMOsReducePrepaymentriskAttractawidevarietyofinvestorsbyofferingvarioustranchesRegularmonthlyorquarterlypaymentsGuaranteedbythefinancialinstitutionthatissuestheinvestment.FannieMae&FreddieMacinsurepaymentwhenborrowerdefaultsGinnieMaeinsures“fullfaithandcredit”toinvestorsRemarks-CMOThecreationofaCMOcannoteliminateprepaymentrisk.Itcanonlyredistributeprepaymentriskamongdifferentclassesofbondholders.CMOclasshasadifferentcouponratefromthatfortheunderlyingcollateral,resultingininstrumentsthathavevaryingrisk-returncharacteristicsthatfittheneedsoffixed-incomeinvestors.Supposeinvestorshavedifferentpreferredmaturities,sotheyshouldbewillingtopaydifferentpricesforsecuritiesofdifferentexpectedmaturities.TypesofCMO/TranchePrincipalHandling:Sequential-Pay顺序支付AccrualTrancheorZ-BondPlannedAmortizationClass按计划支付PACTargetedAmortizationClassInterestHanding:Principal-OnlyInterest-OnlyFloatersSequential-paytranchesTotalparvalueof$400millionRulesTrancheAreceivesalltheprincipalpaymentsuntiltheentireprincipalamountowedtothatbondclass,$194,500,000ispaidoff;thentrancheBbeginstoreceiveprincipalandcontinuestodosountilitispaidtheentire$36,000,000.Eachtranchereceiveinterestontherespectiveclass’soutstandingbalanceSequential-paytranchesTranchesmatureinchronologicalorderTranche1receivesprincipalandinterestpaymentswhileTranche2&3receiveinterestonlyuntilTranche1hitsmaturityAfterTranche1ispaidinfull,Tranche2receivesprincipalandinterestpaymentswhileTranche3continuestoreceiveinterestonlypaymentsFinally,Tranche3beginstoreceiveprincipalandinterestpaymentsonceTranche2iscompleteAttractsavarietyofinvestorsbyofferingdifferentlevelsofriskandinvestmentperiodsSequentialCMOAccrualTranchesFive-TrancheSequential-PayStructurewithFloater,InverseFloater,andAccrualBondClasses*

*Theinterestfortheaccrualtranchewouldaccrueandbeaddedtotheprincipalbalance(likezero-couponbond).Theinterestthatwouldhavebeenpaidtotheaccrualbondclassisusedtospeeduppaydownoftheprincipalbalanceofearlierbondclasses.AccrualTranches(Z-bond)alsocalledZ-bondInterestthatwouldhavebeenpaidtotheaccrualtranchesisusedtopayofftheprincipalbalanceofearliertranchesA,B,C’smaturityshortenedNoreinvestmentriskFloating-RateTranches$96,500,000*7.5%=7,237,500Maxinterestforinversefloateris1-monthLIBOR=0Floater’sinterest=$7,237,500*0.5%=$361,875Inversefloater’sinterest=$6,875,625Caprate(K)=$6,875,625/$24,125,000=28.5%Inversefloater=K–L(1-monthLIBOR)0.75(LIBOR+0.5)+0.25(28.5–L*LIBOR)=7.5;L=3Floating-RateTranchesFordisbursementofprincipalpayments:

DisburseprincipalpaymentstotrancheAuntilitispaidoffcompletely.AftertrancheAispaidoffcompletely,disburseprincipalpaymentstotrancheBuntilitispaidoffcompletely.AftertrancheBispaidoffcompletely,disburseprincipalpaymentstotranchesFLandIFLuntiltheyarepaidoffcompletely.TheprincipalpaymentsbetweentranchesFLandIFLshouldbemadeinthefollowingway:75%totrancheFLand25%totrancheIFL.AftertranchesFLandIFLarepaidoffcompletely,disburseprincipalpaymentstotrancheZuntiltheoriginalprincipalbalanceplusaccruedinterestispaidoffcompletely.Floating-RateTranchesForpaymentofperiodiccouponinterest:

DisburseperiodiccouponinteresttotranchesA,B,FL,andIFLonthebasisoftheamountofprincipaloutstandingatthebeginningoftheperiod.FortrancheZ,accruetheinterestbasedontheprincipalplusaccruedinterestintheprecedingperiod.TheinterestfortrancheZistobepaidtotheearliertranchesasaprincipalpaydown.ThereisacaponFLandaflooronIFL.ThemaximumcouponrateforFLis10%;theminimumcouponrateforIFLis0%.Thefactor3inIFLiscalledthecouponleverage.StructuredInterest-OnlyTranchesTheyarecreatedbyalteringthedistributionofprincipalandinterestfromaproratadistributiontoanunequaldistribution.Forexample,alltheinterestisallocatedtotheIOclass(interestonly)andalltheprincipaltothePOclass(principalonly).POsecuritiesarepurchasedatasubstantialdiscountfromparvalue.Thefastertheprepayments,thehighertheyieldtheinvestorwillrealize.IOinvestorswantprepaymentstobeslow.Thisisbecausewhenprepaymentsaremade,theoutstandingprincipaldeclines,andlessdollarinterestisreceived.StructuredInterest-OnlyTranchesFiveTrancheSequentialPaywithanAccrualTrancheandanInterest-OnlyTrancheFortheIOclass,thereisnoparamount.Theamountshownistheamountonwhichtheinterestpaymentswillbedetermined.Thisiscalledthenotionalamount.Notionalamountfor7.5%IOStructuredInterest-OnlyTranchesCreatingaNotionalIOTranchePaymentRules-Interest-onlyForpaymentofperiodiccouponinterest:

DisburseperiodiccouponinteresttotranchesA,B,andConthebasisoftheamountofprincipaloutstandingatthebeginningoftheperiod.FortrancheZ,accruetheinterestbasedontheprincipalplusaccruedinterestintheprecedingperiod.TheinterestfortrancheZistobepaidtotheearliertranchesasaprincipalpaydown.DisburseperiodicinteresttotheIOtranchebasedonthenotionalamountatthebeginningoftheperiod.PaymentRules-Interest-onlyFordisbursementofprincipalpayments:

DisburseprincipalpaymentstotrancheAuntilitispaidoffcompletely.AftertrancheAispaidoffcompletely,disburseprincipalpaymentstotrancheBuntilitispaidoffcompletely.AftertrancheBispaidoffcompletely,disburseprincipalpaymentstotrancheCuntilitispaidoffcompletely.AftertrancheCispaidoffcompletely,disburseprincipalpaymentstotrancheZuntiltheoriginalprincipalbalanceplusaccruedinterestispaidoffcompletely.PlannedAmortizationClass(PAC)MostpopularCMOissuedtodayMakeup50%ofallfirsttimeissuedCMOsMitigateprepaymentriskPrepaymentspeedsetsataspecifiedband(collar)SupporttranchesabsorbtheprepaymentriskPlannedAmortizationClass(PAC)CreatesascheduleoffixedprincipalpaymentsIfprepaymentoccurs,investorreceivesfixedpaymentwhileadditionalfundsareappliedtoacompanion/supporttranche(reduceprepaymentrisk)GuaranteecashflowatgivenintervalsProtectedagainstContraction&ExtensionRiskMinimalRisk=LowerRatesPSAPrepaymentBenchmark(100PSA) 100PSA-startingwithanannualizedprepaymentrateof0%inmonth0,theratewillincreaseby0.2%eachmonth,untilitpeaksat6%after30months,thenconstantannualprepaymentrateof6%125PSA175PSA200PSATargetedAmortizationClass(TAC)SimilartoPlannedAmortizationClassOfferedatafixedrateversusafixedpaymentMinimalRiskExcesscashflowisdistributedtocompaniontrancheCompaniontranchesofferhigherratesNotellinghowfastorslowthetranchewillmatureStrippedMortgage-BackedSecurities(SMBS)本息分离组MBSSMBSarecreatedbyseparating(“stripping”)theinterestandprincipalpaymentsinapass-throughcashflowandthenallocatingspecifiedpercentagesofthesepaymentstoseparateclasses.IO-onlyreceives100%oftheinterestcash-flowsfromtheunderlyingpass-throughsand0%oftheprincipal.PO-onlyreceivesbothscheduledandunscheduledpaymentsofprincipalandnoneoftheinterest.StrippedMortgage-BackedSecuritiesStrippedMortgage-BackedSecuritiesPrincipal-OnlyMortgageStripsReceivesonlyprincipalpaymentsBoughtatdiscountVulnerabletoInterestRateChangesDecreaseininterestratescreateanincreaseinprepaymentThefastertheprepayments,thehighertheinvestor’sreturnStrippedMortgage-BackedSecuritiesInterest-OnlyMortgageStripsNoparvalueReceivesonlyinterestpayments“interestlivesontheprincipal”VulnerabletoInterestRateChangesIncreaseininterestratescreateadecreaseinprepaymentIOwantsprepaymentstobeslow100PSA300PSARelationshipbetweenpriceandmortgageratesforaPassthrough,POandIOMortgageRate<ContractRate(9%)→Prepayment↑→Cashflowdiscountedatalowerrate→POprice↑9%ImpactofmortgageratesIOinstrippedmortgagebacksecuritiesThevalueincreasesmonotonicallywithrateincreasesinceinterestpaymentsincrease.

POinstrippedmortgagebackedsecuritiesThevaluedecreasesmonotonicallywithrateincreasesincefuturecashflowstobereceivedhaslesspresentvalue.WhyIOorPOcashflowsmightbe

ofinteresttoinvestors?PricingandhedgingprepaymentriskIO(negativeduration),hedgeforincreasingratesPO,hedgeforprepaymentrisk,i.e.bymortgageservicersWhyIOorPOcashflowsmightbe

ofinteresttoinvestors?WhyCMOarepopular?TheCMOconvertsalong-termmonthlypaymentinstrumentintoaseriesofsemi-annualpayments,whicharebond-likesecuritieswithshort,intermediateandlongmaturities.

Themultiple-maturitystructurereducesthedegreeofuncertaintyofcashflowsforanyparticularmaturityclass,andprovidesthelongermaturityclasseswithlimitedcallprotection.Thisisbecauseshortertranchesabsorbtheinitialburdenofexcessprincipalrepayments.WhyCMOarepopular?3. InvestorsareattractedbythebroaderrangeofinvestmentmaturitiesmadepossiblebytheCMOstructure.Forexample,insurancecompaniespurchaseheavilyinthe4-6yearlifetranche.Pensionfundshavebeenactiveinthelongertranchesector.

4. Creditquality

Thehighqualityofthecollateral(GNMAetc.)alongwiththeprotectivestructureofthetrust,enablesthesesecuritiestogenerallycarrythehighestinvestmentgradecreditrating.

YieldOfferinvestorsattractiveyieldpremiumsoverTreasuryandevensomecorporatebonds.6. EventriskCMOareessentiallyfreefromdefaultrisk.Theyarealsofreefromeventsthatcausepricefluctuationsinthecorporateworld.ValuationofthetranchesCMOistheunbundlingoftraditionalmortgage-backedsecuritiesintoshorttranchecashflowsandlongtranchecashflows.Themarketyieldofabundledbondistheweightedaverageoftheyieldsforthetwotranches.

Steeperyieldcurves(widerspreadbetweenthelong-termandshort-terminterestrates)andgreaterprepaymentriskenhancethevalueoftheCMOsecurityrelativetothecomparableGNMA(GovernmentNationalMortgageAssociation)pass-through.Each100basispointsincreaseinthesteepnessoftheyieldcurveisfoundtoprovide14basispointsincreaseinCMO’sweightedyield

ValuingMBSusingMonteCarlosimulationGeneraterandominterestratepathsbytakingasinputtoday’stermstructureofinterestratesandavolatilityassumption.Prepaymentsareprojectedbyfeedingtherefinancingrateandloancharacteristicsintoaprepaymentmodel.Giventheprojectedprepayments,thecashflowalonganinterestratepathcanbedetermined.Thesimulationworksbygeneratingmanyscenariosoffutureinterestratepaths.AnestimateofthevalueoftheMBSistheaverageofthesamplevaluesovermanysimulationtrials.SecuritizationMarketActivityHowhaveCMOscontributedtothecurrenteconomicmeltdown?SubprimeLendingBorrowerswhodonotqualifyforprimeloansPredatoryLendingTargetsindividualswithalimitedunderstandingoffinancialtransactionsOfferssubprimeloanstoindividualswhoqualifyforprimeloansConflictsofInterestLackoftrainingorlicensingformortgagebrokersBrokerspaidbyboththeborrowersandloanoriginatorsSomebrokersreceiveda‘yield-spreadpremium’forchargingahigherinterestratethantheborrowerqualifiedforCompaniesratingCMOsPaidbycompanyofferingsecurity,notbuyersofsecuritiesCha