(26)-CFA固定收益证券

CFA固定收益证券Chapter3.9SpotRatesandBondPricingI:DefinitionofSpotRatesandLinearInterpolationMethod第三章第九节：即期利率与债券定价I:即期利率的定义与线性插值法PricingABondusingaSingleDiscountRate-LimitationConsidera5-year$10,000parvalue,10%annualcouponbond,itscashflowisshownbelow:

9/13/2023Page110001000110001000012534100001100010000121000012301234100011000012534PV1PV2PV3PV4PV5PV++++=iiiiiTheoreticalTreasurySpotRateCurveTheyieldsofzero-couponbondsarecalledspotrates.Cashflowswithdifferentmaturitieshavedifferentspotrates.Wecanusespotratestodiscounteachcashflowofacouponbondtogetthebondprice.Theyieldsofzero-couponTreasurysecuritiesarecalledTreasuryspotrates.ThegraphicaldepictionoftherelationshipbetweentheTreasuryspotratesandmaturityiscalledtheTreasury

SpotRateCurve.Thecurveisusedasabenchmarktoconstructspotratesforothersecurities.Thereisfewzero-couponTreasurysecuritieswithamaturitygreaterthanoneyear,itisnotpossibletoconstructsuchacurvesolelyfromobservationsofTreasurysecurities.Rather,wecanderivethiscurvefromtheTreasuryyieldcurve.SuchacurveiscalledaTheoreticalTreasurySpotRateCurve.9/13/2023Page2On-the-RunIssuesofTreasurySecuritiesAtheoreticalspotratecurvecanbeconstructedfromtheYTMsofon-the-runTreasurysecurities.Theon-the-runissuesarethemostrecentlyauctionedissueofagivenmaturity.WearegoingtouseU.S.TreasurysecuritiestoillustratehowtoconstructtheoreticalspotratecurveusingTreasuryyieldcurve.Theon-the-runTreasuryissuesinU.S.includes:9/13/2023Page3T-Bills3-month6-month1-yearT-Notes2-year3-year5-year7-year10-yearT-Bond30-yearOn-the-RunIssuesofTreasurySecuritiesThereisanobservedyieldforeachoftheon-the-runissues.Forthecouponissues(T-notesandT-bond),theymaynotbeactuallytradingatpar.Toderivespotrates,weneedtoassumeallon-the-runcouponissuesaretradingatpar,whichrequirestosettheircouponratesequaltotheiryieldtomaturity.9/13/2023Page4LinearInterpolationThegoalistoconstructatheoreticalspotratecurvewith60spotrates,rangingfromthe6-monthrateto30-yearrate.Excludingthe3-monthbill,thereareonly8maturitypointsavailablewhenonlyon-the-runissueareused.The52missingmaturitypointsareinterpolatedfromthesurroundingmaturitypointsontheparyieldcurve.Thesimplestinterpolationmethod,andtheonemostcommonlyused,isLinearExtrapolation.Specifically,giventheyieldontheparyieldcurveattwomaturitypoints,thefollowingiscalculated:9/13/2023Page5LinearInterpolationExample1:Supposethattheyieldsforthe2-yearand5-yearon-the-runissuesare6%and6.6%,respectively.Calculatetheyieldsformissingmaturitiesbetweenthesetwomaturitypoints.Solution:Thereare5semiannualperi