固定收益证-券Analysis-of-Residential-Mortgage-Backed-Securities课件

Chapter19

AnalysisofResidentialMortgage-BackedSecurities

LearningObjectivesAfterreadingthischapter,youwillunderstandthecashflowyieldmethodologyforanalyzingresidentialmortgage-backedsecuritiesthelimitationsofthecashflowyieldmethodologyhowtheeffectivedurationandconvexityarecalculatedforthecashflowyieldmethodologyonemeasureforestimatingprepaymentsensitivitywhytheMonteCarlosimulationmethodologyisusedtovalueresidentialmortgage-backedsecuritieshowinterest-ratepathsaresimulatedinaMonteCarlosimulationmethodologyhowtheMonteCarlosimulationmethodologycanbeusedtodeterminethetheoreticalvalueofaresidentialmortgage-backedsecurityLearningObjectives(continued)Afterreadingthischapter,youwillunderstandhowtheoption-adjustedspread,effectiveduration,andeffectiveconvexityarecomputedusingtheMonteCarlosimulationmethodologythecomplexitiesofmodelingcollateralizedmortgageobligationsthelimitationsofoption-adjustedspreadmodelingriskandhowitcanbestresstestedhowthetotalreturniscalculatedforaresidentialmortgage-backedsecuritythedifficultiesofapplyingthetotalreturnframeworktoresidentialmortgage-backedsecuritiesStaticCashFlowYieldMethodologyThestaticcashflowyieldmethodologyisthesimplesttouse,althoughweshallseethatitofferslittleinsightintotherelativevalueofaresidentialmortgage-backedsecurity(RMBS).Exhibit19-1summarizescashflowyieldsaccordingtovariousPSAprepaymentassumptionsforthefourtranchesassumingdifferentpurchaseprices.(SeetruncatedversionofExhibit19-1inOverheads19-5,19-6and19-7.)Noticethatthegreaterthediscountassumedtobepaidforthetranche,themoreatranchewillbenefitfromfasterprepayments.Theconverseistrueforatrancheforwhichapremiumispaid.Thefastertheprepayments,thelowerthecashflowyield.Exhibit19-1PriceCashFlowYieldTablefortheFourTranchesinFJF-06TrancheA:Orig.par:$194,500,000;type:sequential;coupon:6.00%(fixed)IfPricePaidIs:50.00PSA100.00PSA165.00PSA250.00PSA400.00PSA400.00PSA700.00PSA1000.00PSA90–2408.3709.0109.7610.6111.8712.5913.8815.6391–248.098.669.3210.0711.1711.8112.9414.4792–247.828.318.889.5310.4911.0312.0113.3393–247.567.978.459.009.8110.2711.1012.22….….….….….….….….….106–244.423.963.422.811.921.410.52-0.68107–244.213.693.072.381.370.80-0.21-1.57108–243.993.412.731.960.830.20-0.93-2.44109–243.783.142.391.540.30-0.40-1.64-3.29Averagelife:5.093.802.932.331.791.581.311.07Mod.duration:4.123.222.572.091.641.461.221.00Exp.maturity:9.407.155.404.153.072.652.241.82Exhibit19-1PriceCashFlowYield

TablefortheFourTranchesinFJF-06TrancheB:Orig.par:$36,000,000;type:sequential;coupon:6.50%(fixed)IfPricePaidIs:50.00PSA100.00PSA165.00PSA250.00PSA400.00PSA400.00PSA700.00PSA1000.00PSA90–317.858.128.498.959.6910.1310.8911.8391–317.697.938.258.669.319.7010.3611.1892–317.547.758.028.378.949.279.8410.5593–317.397.577.808.098.578.859.339.92….….….….….….….….….106–315.615.395.104.744.163.823.232.51107–315.485.244.914.503.853.462.801.99108–315.365.084.724.273.543.112.381.48109–315.244.934.544.043.242.761.960.97Averagelife:10.177.765.934.583.352.892.351.90Mod.duration:7.235.924.783.842.922.562.111.74Exp.maturity:7.235.924.783.842.922.562.111.74Exhibit19-1PriceCashFlowYieldTablefortheFourTranchesinFJF-06TrancheZ:Orig.par:$73,000,000;type:sequential;coupon:7.35%(fixed)IfPricePaidIs:50.00PSA100.00PSA165.00PSA250.00PSA400.00PSA400.00PSA700.00PSA1000.00PSA90–017.877.968.098.278.618.849.3310.1091–017.827.898.008.168.478.689.119.7992–017.767.837.938.078.338.518.899.4993–017.717.767.857.978.208.358.689.20….….….….….….….….….106–017.046.986.906.796.586.436.135.65107–016.996.936.846.716.466.295.945.39108–016.946.876.776.626.356.165.775.15109–016.896.826.706.546.246.035.594.90Averagelife:22.3919.5716.2112.789.017.465.493.88Mod.duration:19.4216.6813.8111.088.066.785.113.67Exp.maturity:29.7429.7429.7429.7429.7429.7429.7424.24StaticCashFlowYieldMethodology(continued)VectorAnalysisOnepracticethatmarketparticipantsusetoovercomethedrawbackofthePSAbenchmarkistoassumethatthePSAspeedcanchangeovertime.Thistechniqueisreferredtoasvectoranalysis.Avectorissimplyasetofnumbers.Inthecaseofprepayments,itisavectorofprepaymentspeeds.VectoranalysisisparticularlyusefulforCMOtranchesthataredramaticallyaffectedbytheinitialslowingdownofprepayments,andthenspeedingupofprepayments,orviceversa.StaticCashFlowYieldMethodology(continued)LimitationsoftheCashFlowYieldThesameshortcomingsfoundintheyieldtomaturityapproacharealsopresentinapplicationofthecashflowyieldmeasure:theprojectedcashflowsareassumedtobereinvestedatthecashflowyieldtheRMBSisassumedtobehelduntilthefinalpayoutbasedonsomeprepaymentassumptionThecashflowyieldisdependentonrealizationoftheprojectedcashflowaccordingtosomeprepaymentrate.Ifactualprepaymentsvaryfromtheprepaymentrateassumed,thecashflowyieldwillnotberealized.StaticCashFlowYieldMethodology(continued)YieldSpreadtoTreasuriesTheyieldforaRMBSwilldependontheactualprepaymentexperienceofthemortgagesinthepool.Nevertheless,theconventioninallfixed-incomemarketsistomeasuretheyieldonanon-Treasurysecuritytothatofa“comparable”Treasurysecurity.TherepaymentofprincipalovertimemakesitinappropriatetocomparetheyieldofaRMBStoaTreasuryofastatedmaturity.Instead,marketparticipantshaveusedtwomeasures:Macaulaydurationandaveragelife.StaticCashFlowYieldMethodology(continued)StaticSpreadThestaticspreadistheyieldspreadinastaticscenario(i.e.,novolatilityofinterestrates)ofthebondovertheentiretheoreticalTreasuryspotratecurve,notasinglepointontheTreasuryyieldcurve.Inarelativelyflatinterest-rateenvironment,thedifferencebetweenthetraditionalyieldspreadandthestaticspreadwillbesmall.StaticCashFlowYieldMethodology(continued)StaticSpreadTherearetwowaystocomputethestaticspreadforRMBS.Onewayistousetoday’syieldcurvetodiscountfuturecashflowsandkeepthemortgagerefinancingratefixedattoday’smortgagerate.Useofthisapproachtocalculatethestaticspreadrecognizesdifferentpricestodayofdollarstobedeliveredatfuturedates.Thesecondwaytocalculatethestaticspreadallowsthemortgageratetogoupthecurveasimpliedbytheforwardinterestrates.Thisprocedureissometimescalledthezero-volatilityOAS.Inthiscaseaprepaymentmodelisneededtodeterminethevectoroffutureprepaymentratesimpliedbythevectoroffuturerefinancingrates.StaticCashFlowYieldMethodology(continued)EffectiveDurationModifieddurationisameasureofthesensitivityofabond’spricetointerest-ratechanges,assumingthattheexpectedcashflowdoesnotchangewithinterestrates.Modifieddurationisconsequentlynotanappropriatemeasureformortgage-backedsecurities,becauseprepaymentsinfluencetheprojectedcashflowasinterestrateschange.Wheninterestratesfall(rise),prepaymentsareexpectedtorise(fall).Asaresult,wheninterestratesfall(rise),durationmaydecrease(increase)ratherthanincrease(decrease).Thispropertyisreferredtoasnegativeconvexity.StaticCashFlowYieldMethodology(continued)EffectiveDurationNegativeconvexityhasthesameimpactonthepriceperformanceofaRMBSasitdoesontheperformanceofacallablebond.Wheninterestratesdecline,abondwithanembeddedcalloption,whichiswhataRMBSis,willnotperformaswellasanoption-freebond.Althoughmodifieddurationisaninappropriatemeasureofinterest-ratesensitivity,thereisawaytoallowforchangingprepaymentratesoncashflowasinterestrateschange.Thisisachievedbycalculatingtheeffectiveduration,whichallowsforchangingcashflowwheninterestrateschange.StaticCashFlowYieldMethodology(continued)ModifiedDurationExample.Toillustratetheeffectivedurationcalculation,considertranchedata:P_=102.1875;P+=98.4063;P0(initialprice)=100.2813;Δy

=0.0025.Substitutingintothedurationformulayields:StaticCashFlowYieldMethodology(continued)EffectiveDurationExample.Toillustratetheeffectivedurationcalculation,considertranchedata:P_=101.9063(at200PSA;basispointsdecrease);P+

=98.3438(at150PSA;basispointincrease);P0=100.2813;Δy

=0.0025.Substitutingintothedurationformulayields:StaticCashFlowYieldMethodology(continued)EffectiveDurationNoticethattheeffectiveduration(whichallowsforchangingcashflowwheninterestrateschange)islessthanthemodifiedduration(7.11versus7.54).Thedivergencebetweenmodifieddurationandeffectivedurationismuchmoredramaticforbondclassestradingatasubstantialdiscountfromparoratasubstantialpremiumoverpar.StaticCashFlowYieldMethodology(continued)StandardConvexityExample.Toillustratetheconvexityformula,considertheabovetranchedata:P+=98.4063;P_=102.1875;P0(initialprice)=100.2813;Δy

=0.0025.Thestandardconvexityisapproximatedasfollows:StaticCashFlowYieldMethodology(continued)EffectiveConvexityExample.Toillustratetheeffectiveconvexitycalculation(whichallowsforchangingcashflowwheninterestrateschangesothat

P_changes),considertheotherabovetranchedata:P+

=98.3438(at150PSA;basispointincrease);P_=101.9063(at200PSA;basispointsdecrease);P0=100.2813;Δy

=0.0025.Substitutingintothedurationformulayields:StaticCashFlowYieldMethodology(continued)EffectiveConvexityThestandardconvexityindicatespositiveconvexity(24.930),whereastheeffectiveconvexityindicatestheyhavenegativeconvexity(–249.299)Thedifferenceisevenmoredramaticforbondsnottradingnearpar.ForaPOcreatedfromatranche,thestandardconvexitycanbeclosetozerowhereastheeffectiveconvexitycanbeverylarge.Forexample,iftheeffectiveconvexityis2,000,andtheyieldschangeby100basispoints,thepercentagechangeinpriceduetoconvexityis:

(effectiveconvexity)(Δy)2=2,000(0.01)2=0.2000or20.00%StaticCashFlowYieldMethodology(continued)PrepaymentSensitivityMeasureThevalueofaRMBSwilldependonprepayments.Toassessprepaymentsensitivity,marketparticipantshaveusedthefollowingmeasure:thebasispointchangeinthepriceofanRMBSfora1%increaseinprepayments.Specifically,wehave:

prepaymentsensitivity=(Ps

–P0)100where

Ps

=price(per$100parvalue)assuminga1%increaseinprepaymentspeedand

P0=initialprice(per$100parvalue)atassumedprepaymentspeed.Noticethatasecuritythatisadverselyaffectedbyanincreaseinprepaymentspeedswillhaveanegativeprepaymentsensitivitywhileasecuritythatbenefitsfromanincreaseinprepaymentspeedwillhaveapositiveprepaymentsensitivity.MonteCarloSimulationMethodologyForsomefixed-incomesecuritiesandderivativeinstruments,theperiodiccashflowsarepathdependent.Thismeansthatthecashflowsreceivedinoneperiodaredeterminednotonlybythecurrentandfutureinterest-ratelevelsbutalsobythepaththatinterestratestooktogettothecurrentlevel.Poolsofpass-throughsareusedascollateralforthecreationofcollateralizedmortgageobligations(CMOs).Consequently,forCMOstherearetypicallytwosourcesofpathdependencyinaCMOtranche’scashflows.First,thecollateralprepaymentsarepathdependent.Second,thecashflowtobereceivedinthecurrentmonthbyaCMOtranchedependsontheoutstandingbalancesoftheothertranchesinthedeal.Thusweneedthehistoryofprepaymentstocalculatethesebalances.MonteCarloSimulationMethodology(continued)BecauseofthepathdependencyofaRMBS’scashflow,theMonteCarlosimulationmethodisusedforthesesecuritiesratherthanthebinomialmethod.Conceptually,thevaluationofpass-throughsusingtheMonteCarlomethodissimplebut,inpractice,itisverycomplex.Thesimulationinvolvesgeneratingasetofcashflowsbasedonsimulatedfuturemortgagerefinancingrates,whichinturnimplysimulatedprepaymentrates.ValuationmodelingforCMOsissimilartovaluationmodelingforpass-throughs,althoughthedifficultiesareamplifiedbecausetheissuerhasslicedanddicedboththeprepaymentriskandtheinterest-rateriskintosmallerpiecescalledtranches.Thesensitivityofthepass-throughscomposingthecollateraltothesetworisksisnottransmittedequallytoeverytranche.Someofthetrancheswindupmoresensitivetoprepaymentriskandinterest-rateriskthanthecollateral,whereassomeofthemaremuchlesssensitive.MonteCarloSimulationMethodology(continued)UsingSimulationtoGenerateInterest-RatePathsandCashFlowsThetypicalmodelthatWallStreetfirmsandcommercialvendorsusetogeneraterandominterest-ratepathstakesasinputstoday’stermstructureofinterestratesandavolatilityassumption.Thetermstructureofinterestratesisthetheoreticalspotrate(orzero-coupon)curveimpliedbytoday’sTreasurysecurities.Thevolatilityassumptiondeterminesthedispersionoffutureinterestratesinthesimulation.Thesimulationsshouldbenormalizedsothattheaveragesimulatedpriceofazero-couponTreasurybondequalstoday’sactualprice.MonteCarloSimulationMethodology(continued)UsingSimulationtoGenerateInterest-RatePathsandCashFlowsThesimulationworksbygeneratingmanyscenariosoffutureinterest-ratepaths.Ineachmonthofthescenario,amonthlyinterestrateandamortgagerefinancingratearegenerated.Themonthlyinterestratesareusedtodiscounttheprojectedcashflowsinthescenario.Themortgagerefinancingrateisneededtodeterminethecashflowbecauseitrepresentstheopportunitycostthemortgagorisfacingatthattime.Prepaymentsareprojectedbyfeedingtherefinancingrateandloancharacteristics,suchasage,intoaprepaymentmodel.Giventheprojectedprepayments(voluntaryandinvoluntary),thecashflowalonganinterest-ratepathcanbedetermined.MonteCarloSimulationMethodology(continued)UsingSimulationtoGenerateInterest-RatePathsandCashFlowsTomakethismoreconcrete,consideranewlyissuedmortgagepass-throughsecuritywithamaturityof360months.Exhibit19-4(seeOverhead19-27)showsN

simulatedinterest-ratepathscenarios.Eachscenarioconsistsofapathof360simulatedone-monthfutureinterestrates.Justhowmanypathsshouldbegeneratedisexplainedlater.Exhibit19-5(seeOverhead19-28)showsthepathsofsimulatedmortgagerefinancingratescorrespondingtothescenariosshowninExhibit19-4(seeOverhead19-27).Assumingthesemortgagerefinancingrates,thecashflowforeachscenariopathisshowninExhibit19-6(seeOverhead19-29).Exhibit19-4SimulatedPathsofOne-MonthFutureInterestRatesInterest-RatePathNumberaMonth123…n…N1f1(1)f1(2)f1(3)f1(n)f1(N)2f2(1)f2(2)f2(3)f2(n)f2(N)3f3(1)f3(2)f3(3)f3(n)f3(N)4f4(1)f4(2)f4(3)f4(n)f4(N)…tft(1)ft(2)ft(3)ft(n)ft(N)…358f358(1)f358(2)f358(3)f358(n)f358(N)359f359(1)f359(2)f359(3)f359(n)f359(N)360f360(1)f360(2)f360(3)f360(n)f360(N)aNotation:ft(n),one-monthfutureinterestrateformontht

onpathn;N,totalnumberofinterest-ratepaths.Exhibit19-5SimulatedPathsofMortgageFinancingRatesInterest-RatePathNumberaMonth123…n…N1r1(1)r1(2)r1(3)r1(n)r1(N)2r2(1)r2(2)r2(3)r2(n)r2(N)3r3(1)r3(2)r3(3)r3(n)r3(N)4r4(1)r4(2)r4(3)r4(n)r4(N)….….….….….….trt(1)rt(2)rt(3)rt(n)rt(N)….….….….….….358r358(1)r358(2)r358(3)r358(n)r358(N)359r359(1)r359(2)r359(3)r359(n)r359(N)360r360(1)r360(2)r360(3)r360(n)r360(N)aNotation:rt(n),mortgagerefinancingrateformontht

onpathn;N,totalnumberofinterest-ratepaths.Exhibit19-6SimulatedCashFlowonEachoftheInterest-RatePathsInterest-RatePathNumberaMonth123…n…N1C1(1)C1(2)C1(3)C1(n)C1(N)2C2(1)C2(2)C2(3)C2(n)C2(N)3C3(1)C3(2)C3(3)C3(n)C3(N)4C4(1)C4(2)C4(3)C4(n)C4(N)….tCt(1)Ct(2)Ct(3)Ct(n)Ct(N)….358C358(1)C358(2)C358(3)C358(n)C358(N)359C359(1)C359(2)C359(3)C359(n)C359(N)360C360(1)C360(2)C360(3)C360(n)C360(N)aNotation:Ct(n)cashflowformontht

onpathn;N,totalnumberofinterest-ratepaths.MonteCarloSimulationMethodology

(continued)CalculatingthePresentValueforaScenarioInterest-RatePathGiventhecashflowonaninterest-ratepath,itspresentvaluecanbecalculated.Thediscountratefordeterminingtheresentvalueisthesimulatedspotrateforeachmonthontheinterest-ratepathplusanappropriatespread.Thespotrateonapathcanbedeterminedfromthesimulatedfuturemonthlyrates.TherelationshipthatholdsbetweenthesimulatedspotrateformonthTonpathnandthesimulatedfutureone-monthratesiszT(n)=simulatedspotrateformonthT

onpathn

fj(n)=simulatedfutureone-monthrateformonthjonpathnConsequently,theinterest-ratepathforthesimulatedfutureone-monthratescanbeconvertedtotheinterest-ratepathforthesimulatedmonthlyspotratesasshowninExhibit19-7(seeOverhead19-31).Exhibit19-7SimulatedPathsofMonthlySpotRatesInterest-RatePathNumberaMonth123…n…N1z1(1)z1(2)z1(3)z1(n)z1(N)2z2(1)z2(2)z2(3)z2(n)z2(N)3z3(1)z3(2)z3(3)z3(n)z3(N)4z4(1)z4(2)z4(3)z4(n)z4(N)…tzt(1)zt(2)zt(3)zt(n)zt(N)…358z358(1)z358(2)z358(3)z358(n)z358(N)359z359(1)z359(2)z359(3)z359(n)z359(N)360z360(1)z360(2)z360(3)z360(n)z360(N)aNotation:zt(n)

spotrateformontht

onpathn;N,totalnumberofinterest-ratepaths.MonteCarloSimulationMethodology(continued)CalculatingthePresentValueforaScenarioInterest-RatePathThepresentvalueofthecashflowformonthToninterest-ratepathndiscountedatthesimulatedspotrateformonthTplussomespreadisPV[CT(n)]=presentvalueofcashflowformonthTonpathnCT(n)=cashflowformonthTonpathnzT(n)=spotrateformonthTonpathnK

=appropriaterisk-adjustedspreadThepresentvalueforpathn

isthesumofthepresentvalueofthecashflowforeachmonthonpathn.MonteCarloSimulationMethodology(continued)DeterminingtheTheoreticalValueThepresentvalueofagiveninterest-ratepathcanbethoughtofasthetheoreticalvalueofapass-throughassumingthatthepathwasactuallyrealized.Thetheoreticalvalueofthepass-throughcanbedeterminedbycalculatingtheaverageofthetheoreticalvalueofalltheinterest-ratepaths.LookingattheDistributionofthePathValuesThetheoreticalvaluegeneratedbytheMonteCarlosimulationmethodistheaverageofthepathvalues.Thereisvaluableinformationinthedistributionofthepathvalues.Ifthereissubstantialdispersionofthepathvaluesthentheinvestoriswarnedaboutthepotentialvariabilityofthemodel’svalue.MonteCarloSimulationMethodology(continued)SimulatedAverageLifeTheaveragelifereportedinaMonteCarloanalysisistheaverageoftheaveragelivesalongtheinterest-ratepaths.Thegreatertherangeandstandarddeviationoftheaveragelife,themoreuncertaintythereisaboutthesecurity’saveragelife.Option-AdjustedSpreadTheoption-adjustedspreadisameasureoftheyieldspreadthatcanbeusedtoconvertdollardifferencesbetweenvalueandprice.Itrepresentsaspreadovertheissuer’sspotratecurveorbenchmark.IntheMonteCarlomodel,theOASisthespreadKthatwhenaddedtoallthespotratesonallinterest-ratepathswillmaketheaveragepresentvalueofthepathsequaltotheobservedmarketprice(plusaccruedinterest).MonteCarloSimulationMethodology(continued)OptionCostTheimpliedcostoftheoptionembeddedinanyRMBScanbeobtainedbycalculatingthedifferencebetweentheOASattheassumedvolatilityofinterestratesandthestaticspread:optioncost=staticspread–option-adjustedspread.EffectiveDurationandConvexityEffectivedurationandeffectiveconvexitycanbecalculatedusingtheMonteCarlomethodasfollows.Thebond’sOASisfoundusingthecurrenttermstructureofinterestrates.ThebondisrepricedholdingOASconstantbutshiftingthetermstructure.Twoshiftsareusedtogetthepricesneededtoapplytheeffectivedurationandeffectiveconvexityformulas:yieldsareincreasedyieldsaredecreasedMonteCarloSimulationMethodology(continued)SelectingtheNumberofInterest-RatePathsLet’snowaddressthequestionofthenumberofscenariopathsorrepetitions,N,neededtovalueaRMBS.AtypicalOASrunwillbedonefor512to1,024interest-ratepaths.Thenumberofinterest-ratepathsdetermineshow“good”theestimateis,notrelativetothetruthbutrelativetothemodel.Themorepaths,themoreaveragespreadtendstosettledown.Itisastatisticalsamplingproblem.MostMonteCarlosimulationmodelsemploysomefromofvariancereductiontocutdownonthenumberofsamplepathsnecessarytogetagoodstatisticalsample.Variancereductiontechniquesallowustoobtainpriceestimateswithinatick.MonteCarloSimulationMethodology(continued)LimitationsoftheOASMeasuresTheOASisaproductofthevaluationmodel.Thevaluationmodelmaybepoorlyconstructedbecauseitfailstocapturethetruefactorsthataffectthevalueofparticularsecurities.InMonteCarlosimulationtheinterest-ratepathsmustbeadjustedsothaton-the-runTreasuriesarevaluedproperly.AnotherproblemwiththeOASisthatitassumesaconstantOASforeachinterestratepathandovertimeforagiveninterest-ratepath.Finally,theOASisdependentonthevolatilityassumption,theprepaymentassumptioninthecaseofRMBS,andtherulesforrefundinginthecaseofcorporatebonds.MonteCarloSimulationMethodology(continued)IllustrationWecanuseaplainvanilladeal(i.e.,relativelysimplederivativeinstrumentwithstandardfeatures)toshowhowCMOscanbeanalyzedusingtheMonteCarlosimulationmethod.Theplainvanillasequential-payCMObondstructureinourillustrationisFNMA89-97.AdiagramoftheprincipalallocationstructureisgiveninExhibit19-8(seeOverhead19-39).UsingtheOASfromtheMonteCarlosimulationmethodology,afairconclusioncanbemadeaboutthissimpleplainvanillastructure:whatyouseeiswhatyouget.Ingeneral,however,amoneymanagerwillingtoextenddurationgetspaidforthatrisk.Exhibit19-8

PrincipalAllocationStructureofFNMA89–97RD97A97B97C97ZTime

HighLowStructuralPriorityTotalReturnAnalysisNeitherthestaticcashflowmethodologynortheMonteCarlosimulationmethodologywilltellamoneymanagerwhetherinvestmentobjectivescanbesatisfied.TheperformanceevaluationofanindividualRMBSrequiresspecificationofaninvestmenthorizon,whoselengthformostfinancialinstitutionsisdictatedbythenatureofitsliabilities.Themeasurethatshouldbeusedtoassesstheperformanceofasecurityoraportfoliooversomeinvestmenthorizonisthetotalreturn.TotalReturnAnalysis(continued)HorizonPriceforCMOTranchesThemostdifficultpartofestimatingtotalreturnisprojectingthepriceatthehorizondate.InthecaseofaCMOtranchethepricedependsonthecharacteristicsofthetrancheandthespreadtoTreasuriesattheterminationdate.Thekeydeterminantsarethe“quality”ofthetranche,itsaveragelife(orduration),anditsconvexity.QualityreferstothetypeofCMOtranche.TotalReturnAnalysis(continued)OASTotalReturnThetotalreturnandOASframeworkscanbecombinedtodeterminetheprojectedpriceatthehorizondate.Attheendoftheinvestmenthorizon,itisnecessarytospecifyhowtheOASisexpectedtochange.Thehorizonpricecanbe“backedout”oftheMonteCarlosimulationmodel.AssumptionsabouttheOASvalueattheinvestmenthorizonreflecttheexpectationsofthemoneymanager.ItiscommontoassumethattheOASatthehorizondatewillbethesameastheOASatthetimeofpurchase.Atotalreturncalculatedusingthisassumptionissometimesreferredtoasaconstant-OAStotalreturn.Allrightsreserved.Nopartofthispublicationmaybereproduced,storedinaretrievalsystem,ortransmitted,inanyformorbyanymeans,electronic,mechanical,photocopying,recording,orotherwise,withoutthepriorwrittenpermissionofthepublisher.PrintedintheUnitedStatesofAmerica.

Chapter20

AnalysisofConvertibleBonds

LearningObjectivesAfterreadingthischapter,youwillunderstandwhataconvertiblebondiswhatanexchangeablebondisthebasicfeaturesofaconvertiblesecuritythetypesofconvertiblesecuritiesconversionvalue,marketconversionprice,conversionpremiumpershare,conversionpremiumratio,andpremiumoverstraightvalueofaconvertiblebondtheinvestmentfeaturesofaconvertiblesecuritywhattheminimumvalueofaconvertiblebondis20-46LearningObjectives(continued)Afterreadingthischapter,youwillunderstandthepremiumpaybackperiodthedownsideriskassociatedwithaconvertiblebondmeasuresfromoptionstheorythatareusedforconvertiblebonds:delta,gamma,andvegatheprosandconsofinvestinginaconvertiblebond