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1、FixedIncomeSecurities Lecture10 DrHerbertY T LamMay2013 Today sLecture MortgageLoansMortgage BackedSecuritiesMortgagepassthroughsecuritiesCollateralizedMortgageObligationStrippedMortgage BackedSecuritiesCMOsandSubprimeCrisis Mortgages Amortgageloanisaloansecuredbythecollateralofsomespecificrealestat
2、epropertywhichobligestheborrowertomakeapredeterminedseriesofpayments Amortgagedesignisaspecificationoftheinterestrate termofthemortgage andmannerinwhichtheborrowedfundsarerepaid Mortgageoriginator originallender caneither holdthemortgageintheirportfolio sellthemortgagetoaninvestoror usethemortgageas
3、collateralfortheissuanceofasecurity mortgagebackedsecurity Contractrate interestrateonamortgageloan ContractrateisgreaterthantheyieldonaTreasurysecurityofcomparablematurity Thespreadreflectscostsofcollectioncostsassociatedwithdefault noteliminateddespitethecollateral poorerliquidityuncertaintyconcer
4、ningthetimingofthecashflow Fixedrate levelpayment fullyamortizedmortgage Theborrowerpaysinterestandrepaysprincipalinequalinstallmentsoveranagreeduponperiodoftime termofthemortgage Thefrequencyofpaymentistypicallymonthly Theservicingfeeisaportionofthemortgagerate Theinterestratethattheinvestorreceive
5、siscalledthenetcoupon GrowingequitymortgagesItisafixed ratemortgagewhosemonthlymortgagepaymentsincreaseovertime Amortizationscheduleforalevel paymentfixed ratemortgage Mortgageloan 100 000Mortgagerate 8 125 Monthlypayment 742 50Termofloan 30years 360months Examplen 360 mortgagebalance 100 000 i 0 08
6、125 12 Mortgagepayment 742 50 Proofofthemortgageformula Example MortgagebalanceisreducedwitheachmonthlymortgagepaymentInterestportiondeclinesandrepaymentportionincreases AdjustableRateMortgages ThemortgagerateisresetperiodicallyinaccordancewithsomechosenreferencerateProtectionclausesagainstoverlylar
7、gecouponchangesOthertermsRatecapslimittheamountthatthecontractratemayincreaseordecreaseattheresetdate Alifetimecapsetsthemaximumcontractrateoverthetermoftheloan Prepayment Paymentsmadeinexcessofthescheduledprincipalrepayments Theamountandtimingofthecashflowsfromtherepaymentsarenotknownwithcertainty
8、ReasonsSaleofahomeMarketratesfallbelowthecontractrateFailuretomeetthemortgageobligations Factorsaffectingprepaymentbehaviors Prevailingmortgagerate thecurrentlevelofmortgageratesrelativetotheborrower scontractrate Thespreadshouldbewideenoughtocoverthecosts2 Pathhistoryofratespreadisimportant depends
9、onwhethertherehavebeenprioropportunitiestorefinancesincetheunderlyingmortgageswereoriginated Factorsaffectingprepaymentbehaviors 3 Presenceofprepaymentpenalty Macroeconomicfactorse g growingeconomyresultsinariseinpersonalincomeandinopportunitiesforworkermigration Seasonalfactor Homebuyingincreasesin
10、theSpringandreachesapeakinthelateSummer Sincetherearedelaysinpassingthroughprepayments thepeakmaynotbeobserveduntilearlyFall Interestratepathdependence Prepaymentburnout Prepaymentsarepathdependentsincethismonth sprepaymentratedependsonwhethertherehavebeenprioropportunitiestorefinanceoncetheunderlyi
11、ngmortgageswereoriginated Example pathofinterestratesinthepast3yearsFirstpath 11 8 13 8 Secondpath 11 12 13 8 Morerefinancingoccursnowwhentheinterestratesfollowthesecondpath Prepaymentmodels Describestheexpectedprepaymentsontheunderlyingpoolofmortgagesattimetintermsoftheyieldcurveattimetandotherrele
12、vantvariables predictedfromananalysisofhistoricaldata ExampleWeeklyreport SpreadTalk publishedbythePrudentialSecurities provides6 month 1 yearandlong termprepaymentprojectionsassumingdifferentamountsofshiftininterestrates Mortgage backedsecurities MBS Mortgage backedsecuritiesaresecuritiesbackedbyap
13、oolofmortgageloans 1 Mortgagepassthroughsecurities 2 Collateralizedmortgageobligations 3 Strippedmortgage backedsecurities Thelasttwotypesarecalledderivativemortgage backedsecuritiessincetheyarecreatedfromthefirsttype MBSversusfixedincomeinvestments Virtuallynodefaultrisksincethemortgagesinapoolareg
14、uaranteedbyagovernmentrelatedagency suchasGNMA GovernmentNationalMortgageAssociation orFNMA FederalNationalMortgageAssociation Prepaymentrisk ReinvestmentriskPrepaymentprivilegesgiventothehouseholdertoputthemortgagebacktothelenderatitsfacevalue HowistheOption adjusted spread OAS determined OSAanalys
15、isevaluatesthecashflowsforanMBSbasedonthousandsofdifferentinterestratescenarios Startingwithcertainprepaymentassumptions eachdifferentinterestratepathisconvertedintoaprepaymentscenario Forexample ifmarketratesdrop100bps whatpercentageofborrowerswillrefinanceinagivenmonth Avalueforthesecurityisderive
16、dbydiscountingthetheoreticalcashflowstothepresentandaveragingthem Numericaltechniques latticetreetogeneratethevariousinterestratescenarios MortgagePassthroughSecurities Amortgagepassthroughsecurityisasecuritycreatedwhenoneormoreholdersofmortgagesformapoolofmortgagesandsellsharesorparticipationcertificatesinthepool Thecashflowsconsistsofmonthlymortgagepaymentsrepresentinginterest thescheduledrepaymentofprincipal andanyprepayments MortgagePassthroughSecurities Paymentsaremadetosecurityholderseachm
