固定收益證-券Bond-Price-Volati課件

Copyright?2010PearsonEducation,Inc.PublishingasPrenticeHall4-1

Chapter4

BondPriceVolatility

Copyright?2010PearsonEducation,Inc.PublishingasPrenticeHall4-2LearningObjectivesAfterreadingthischapter,youwillunderstandtheprice-yieldrelationshipofanoption-freebondthefactorsthataffectthepricevolatilityofabondwhenyieldschangetheprice-volatilitypropertiesofanoption-freebondhowtocalculatethepricevalueofabasispointhowtocalculateandinterprettheMacaulayduration,modifiedduration,anddollardurationofabondwhydurationisameasureofabond’spricesensitivitytoyieldchangesCopyright?2010PearsonEducation,Inc.PublishingasPrenticeHall4-3LearningObjectives(continued)Afterreadingthischapter,youwillunderstandthespreaddurationmeasureforfixed-rateandfloating-ratebondshowtocomputethedurationofaportfolioandcontributiontoportfoliodurationlimitationsofusingdurationasameasureofpricevolatilityhowpricechangeestimatedbydurationcanbeadjustedforabond’sconvexityhowtoapproximatethedurationandconvexityofabondthedurationofaninversefloaterhowtomeasureaportfolio’ssensitivitytoanonparallelshiftininterestrates(keyratedurationandyieldcurvereshapingduration)Copyright?2010PearsonEducation,Inc.PublishingasPrenticeHall4-4Exhibit4-2

ShapeofPrice-YieldRelationshipforan

Option-FreeBondPriceMaximumPriceYieldCopyright?2010PearsonEducation,Inc.PublishingasPrenticeHall4-5PriceVolatilityCharacteristics

ofOption-FreeBondsTherearefourpropertiesconcerningthepricevolatilityofanoption-freebond:Althoughthepricesofalloption-freebondsmoveintheoppositedirectionfromthechangeinyieldrequired,thepercentagepricechangeisnotthesameforallbonds.Forverysmallchangesintheyieldrequired,thepercentagepricechangeforagivenbondisroughlythesame,whethertheyieldrequiredincreasesordecreases.Forlargechangesintherequiredyield,thepercentagepricechangeisnotthesameforanincreaseintherequiredyieldasitisforadecreaseintherequiredyield.Foragivenlargechangeinbasispoints,thepercentagepriceincreaseisgreaterthanthepercentagepricedecrease.

Anexplanationforthesefourpropertiesofbondpricevolatilityliesintheconvexshapeoftheprice-yieldrelationship.Copyright?2010PearsonEducation,Inc.PublishingasPrenticeHall4-6PriceVolatilityCharacteristics

ofOption-FreeBonds(continued)CharacteristicsofaBondthatAffectitsPriceVolatilityTherearetwocharacteristicsofanoption-freebondthatdetermineitspricevolatility:couponandtermtomaturity.First,foragiventermtomaturityandinitialyield,thepricevolatilityofabondisgreater,thelowerthecouponrate.Thischaracteristiccanbeseenbycomparingthe9%,6%,andzero-couponbondswiththesamematurity.Second,foragivencouponrateandinitialyield,thelongerthetermtomaturity,thegreaterthepricevolatility.ThiscanbeseeninExhibit4-3(SeeOverhead4-9)bycomparingthefive-yearbondswiththe25-yearbondswiththesamecoupon.Copyright?2010PearsonEducation,Inc.PublishingasPrenticeHall4-7EXHIBIT4-3InstantaneousPercentagePriceChangeforSixHypotheticalBondsSixhypotheticalbonds,pricedinitiallytoyield9%:9%coupon,5yearstomaturity,price=100.00009%coupon,25yearstomaturity,price=100.0006%coupon,5yearstomaturity,price=88.13096%coupon,25yearstomaturity,price=70.35700%coupon,5yearstomaturity,price=64.39280%coupon,25yearstomaturity,price=11.0710Yield(%)Changeto:ChangeinBasisPointsPercentagePriceChange(coupon/maturityinyears)9%/59%/256%/56%/250%/50%/256.00-30012.8038.5913.4742.1315.56106.047.00-2008.3223.468.7525.4610.0961.738.00-1004.0610.744.2611.604.9127.108.50-502.005.152.115.552.4212.728.90-100.401.000.421.070.482.428.99-10.040.100.040.110.050.249.011-0.04-0.10-0.04-0.11-0.05-0.249.1010-0.39-0.98-0.41-1.05-0.48-2.369.5050-1.95-4.75-2.05-5.09-2.36-11.2610.00100-3.86-9.13-4.06-9.76-4.66-21.2311.00200-7.54-16.93-7.91-18.03-9.08-37.8912.00300-11.04-23.64-11.59-25.08-13.28-50.96Copyright?2010PearsonEducation,Inc.PublishingasPrenticeHall4-8EXHIBIT4-4PriceChangefora100-Basis-PointChangeinYieldfora9%25-YearBondTradingatDifferentYieldLevelsYieldLevel(%)InitialPriceNewPriceaPriceDeclinePercentDecline7$123.46$110.74$12.7210.308110.74100.0010.749.709100.0090.879.139.131090.8783.077.808.581183.0776.366.718.081276.3670.555.817.611370.5565.505.057.161465.5061.084.426.75

a

Asaresultofa100-basis-pointincreaseinyield.Copyright?2010PearsonEducation,Inc.PublishingasPrenticeHall4-9MeasuresofBondPriceVolatilityMoneymanagers,arbitrageurs,andtradersneedtohaveawaytomeasureabond’spricevolatilitytoimplementhedgingandtradingstrategies.Threemeasuresthatarecommonlyemployed:pricevalueofabasispointyieldvalueofapricechangedurationCopyright?2010PearsonEducation,Inc.PublishingasPrenticeHall4-10Copyright?2010PearsonEducation,Inc.PublishingasPrenticeHall4-10MeasuresofBondPriceVolatility(continued)PriceValueofaBasisPointThepricevalueofabasispoint,alsoreferredtoasthedollarvalueofan01,isthechangeinthepriceofthebondiftherequiredyieldchangesby1basispoint.Copyright?2010PearsonEducation,Inc.PublishingasPrenticeHall4-11Copyright?2010PearsonEducation,Inc.PublishingasPrenticeHall4-11MeasuresofBondPriceVolatility(continued)YieldValueofaPriceChangeAnothermeasureofthepricevolatilityofabondusedbyinvestorsisthechangeintheyieldforaspecifiedpricechange.Copyright?2010PearsonEducation,Inc.PublishingasPrenticeHall4-12Copyright?2010PearsonEducation,Inc.PublishingasPrenticeHall4-12MeasuresofBondPriceVolatility(continued)DurationTheMacaulaydurationisonemeasureoftheapproximatechangeinpriceforasmallchangeinyield:whereP

=priceofthebondC

=semiannualcouponinterest(indollars)y

=one-halftheyieldtomaturityorrequiredyieldn

=numberofsemiannualperiods(numberofyearstimes2)M

=maturityvalue(indollars)Copyright?2010PearsonEducation,Inc.PublishingasPrenticeHall4-13Copyright?2010PearsonEducation,Inc.PublishingasPrenticeHall4-13MeasuresofBondPriceVolatility(continued)DurationInvestorsrefertotheratioofMacaulaydurationto1+yasthemodifiedduration.Theequationis:wherey

=one-halftheyieldtomaturityorrequiredyield.Themodifieddurationisrelatedtotheapproximatepercentagechangeinpriceforagivenchangeinyieldasgivenby:wheredP=changeinprice,dy=changeinyield,P

=priceofthebond.Copyright?2010PearsonEducation,Inc.PublishingasPrenticeHall4-14EXHIBIT4-5CalculationofMacaulayDurationandModifiedDurationfor5-Year9%BondSellingtoYield9%Couponrate:9.00%Term(years):5Initialyield:9.00%Period,tCashFlowPVof$1at4.5%PVofCFt×PVCF1$4.500.9569374.3062204.3062224.500.9157294.1207858.2415634.500.8762963.94333511.8300044.500.8385613.77352615.0941054.500.8024513.61103018.0551464.500.7678953.45553120.7331874.500.7348283.30672823.1470984.500.7031853.16433325.3146694.500.6729043.02807027.2526210$104.500.64392767.290443672.90442100.00000826.87899Copyright?2010PearsonEducation,Inc.PublishingasPrenticeHall4-15EXHIBIT4-6CalculationofMacaulayDurationandModifiedDurationfor5-Year6%BondSellingtoYield9%Couponrate:6.00%Term(years):5Initialyield:9.00%Period,tCashFlowPVof$1at4.5%PVofCFt×PVCF1$3.000.9569372.8708132.8708123.000.9157292.7471905.4943733.000.8762962.6288907.8866643.000.8385612.51568410.0627353.000.8024512.40735312.0367663.000.7678952.30368713.8221273.000.7348282.20448515.4313983.000.7031852.10955516.8764493.000.6729042.01871318.1684110103.000.64392766.324551663.24551Total88.130923765.89520Copyright?2010PearsonEducation,Inc.PublishingasPrenticeHall4-16Copyright?2010PearsonEducation,Inc.PublishingasPrenticeHall4-16MeasuresofBondPriceVolatility(continued)PropertiesofDurationThemodifieddurationandMacaulaydurationofacouponbondarelessthanthematurity.TheMacaulaydurationofazero-couponbondequalsitsmaturity;butazero-couponbond’smodifieddurationislessthanitsmaturity.LowercouponratesgenerallyhavegreaterMacaulayandmodifiedbonddurations.Copyright?2010PearsonEducation,Inc.PublishingasPrenticeHall4-17Copyright?2010PearsonEducation,Inc.PublishingasPrenticeHall4-17MeasuresofBondPriceVolatility(continued)ApproximatingthePercentagePriceChangeThebelowequationcanbeusedtoapproximatethepercentagepricechangeforagivenchangeinrequiredyield:wheredP=changeinprice,P

=priceofthebondanddy=changeinyield.Supposethattheyieldonanybondchangesby100basispoints.Then,substituting100basispoints(0.01)fordyintotheaboveequation,weget:Thus,modifieddurationcanbeinterpretedastheapproximatepercentagechangeinpricefora100-basis-pointchangeinyield.Copyright?2010PearsonEducation,Inc.PublishingasPrenticeHall4-18Copyright?2010PearsonEducation,Inc.PublishingasPrenticeHall4-18MeasuresofBondPriceVolatility(continued)PortfolioDurationThedurationofaportfolioissimplytheweightedaveragedurationofthebondsintheportfolios.Portfoliomanagerslookattheirinterestrateexposuretoaparticularissueintermsofitscontributiontoportfolioduration.Thismeasureisfoundbymultiplyingtheweightoftheissueintheportfoliobythedurationoftheindividualissuegivenas:contributiontoportfolioduration=weightofissueinportfolio×

durationofissue.Copyright?2010PearsonEducation,Inc.PublishingasPrenticeHall4-19Copyright?2010PearsonEducation,Inc.PublishingasPrenticeHall4-19MeasuresofBondPriceVolatility(continued)PortfolioDurationPortfoliomanagerslookatportfoliodurationforsectorsofthebondmarket.Copyright?2010PearsonEducation,Inc.PublishingasPrenticeHall4-20EXHIBIT4-7CalculationofDurationandContributiontoPortfolioDurationforaAssetAllocationtoSectorsoftheLehmanBrothersU.S.AggregateIndex:October26,2007SectorPortfolioWeightSectorDurationContributiontoPortfolioDurationTreasury0.0004.950.00Agency0.1213.440.42Mortgages0.4493.581.61CommercialMortgage-BackedSecurities0.1395.040.70Asset-BackedSecurities0.0173.160.05Credit0.2746.351.741.0004.52Copyright?2010PearsonEducation,Inc.PublishingasPrenticeHall4-21EXHIBIT4-8CalculationofDurationandContributiontotheLehmanBrothersAggregateIndexDuration:October26,2007SectorWeightinIndexSectorDurationContributiontoIndexDurationTreasury0.2304.951.14Agency0.1053.440.36Mortgages0.3813.581.36CommercialMortgage-BackedSecurities0.0565.040.28Asset-BackedSecurities0.0103.160.03Credit0.2196.351.39Total1.0004.56Copyright?2010PearsonEducation,Inc.PublishingasPrenticeHall4-22Copyright?2010PearsonEducation,Inc.PublishingasPrenticeHall4-22MeasuresofBondPriceVolatility(continued)PortfolioDurationWhiletheportfolioandtheindexhavethesameduration,thespreaddurationfortherecommendedportfoliois4.60vs.3.49fortheindex.Thelargerspreaddurationfortherecommendedportfolioisexpectedgiventhegreaterallocationtonon-Treasurysectors.Copyright?2010PearsonEducation,Inc.PublishingasPrenticeHall4-23EXHIBIT4-9CalculationofSpreadDurationandContributiontoPortfolioSpreadDurationforanAssetAllocationtoSectorsoftheLehmanBrothersU.S.AggregateIndex:October26,2007SectorPortfolioWeightSectorSpreadDurationContributiontoPortfolioSpreadDurationTreasury0.0000.000.00Agency0.1213.530.43Mortgages0.4493.621.63CommercialMortgage-BackedSecurities0.1395.040.70Asset-BackedSecurities0.0173.160.05Credit0.2746.351.79Total1.0004.60Copyright?2010PearsonEducation,Inc.PublishingasPrenticeHall4-24EXHIBIT4-10CalculationofSpreadDurationandContributiontotheLehmanBrothersAggregateIndexSpreadDuration:October26,2007SectorWeightinIndexSectorSpreadDurationContributiontoIndexSpreadDurationTreasury0.2300.000.00Agency0.1053.530.37Mortgages0.3813.621.38CommercialMortgage-BackedSecurities0.0565.040.28Asset-BackedSecurities0.0103.160.03Credit0.2196.531.43Total1.0003.49Copyright?2010PearsonEducation,Inc.PublishingasPrenticeHall4-25ConvexityBecauseallthedurationmeasuresareonlyapproximationsforsmallchangesinyield,theydonotcapturetheeffectoftheconvexityofabondonitspriceperformancewhenyieldschangebymorethanasmallamount.Copyright?2010PearsonEducation,Inc.PublishingasPrenticeHall4-26Exhibit4-12

LineTangenttothePrice-YieldRelationshipPriceYieldy*p*ActualPriceTangentLineaty*(estimatedprice)Copyright?2010PearsonEducation,Inc.PublishingasPrenticeHall4-27Convexity(continued)Theapproximationwillalwaysunderstatetheactualprice.Copyright?2010PearsonEducation,Inc.PublishingasPrenticeHall4-28Exhibit4-13.PriceApproximationUsingDurationPriceYieldy3p*ActualPriceTangentLineaty*(estimatedprice)y*y1y2y4ErrorinEstimatingPriceBasedonlyonDurationErrorinEstimatingPriceBasedonlyonDurationCopyright?2010PearsonEducation,Inc.PublishingasPrenticeHall4-29Copyright?2010PearsonEducation,Inc.PublishingasPrenticeHall4-29Convexity

(continued)MeasuringConvexityThepercentagechangeinthepriceofthebondduetoconvexityortheconvexitymeasureis:Where

Thepercentagepricechangeduetoconvexityis:Copyright?2010PearsonEducation,Inc.PublishingasPrenticeHall4-30Copyright?2010PearsonEducation,Inc.PublishingasPrenticeHallConvexity

(continued)MeasuringConvexityIngeneral,ifthecashflowsoccurmtimesperyear,convexityisadjustedtoanannualfigureasfollows:Copyright?2010PearsonEducation,Inc.PublishingasPrenticeHall4-31EXHIBIT4-14CalculationofConvexityMeasureandDollarConvexityMeasureforFive-Year9%BondSellingtoYield9%Couponrate:9.00%Term(years):5Initialyield:9.00%Price:100Period,tCashFlow1/(1.045)t+2t(t+1)CFt(t+1)CF(1.045)t+214.500.87629697.88624.500.8385612722.64134.500.8024515443.33244.500.7678959069.11054.500.73482813599.20164.500.703185189132.90174.500.672904252169.57184.500.643927324208.63294.500.616198405249.56010104.500.58966311,4956,778.18612,9807,781.020Copyright?2010PearsonEducation,Inc.PublishingasPrenticeHall4-32EXHIBIT4-15CalculationofConvexityMeasureandDollarConvexityMeasureforFive-Year6%BondSellingtoYield9%Couponrate:6.00%Term(years):5Initialyield:9.00%Price:88.1309Period,tCashFlow1/(1.045)t+2t(t+1)CFt(t+1)CF(1.045)t+213.000.87629665.25723.000.8385611815.09433.000.8024513628.88843.000.7678956046.07353.000.7348289066.13463.000.70318512688.60173.000.672904168113.04783.000.643927216139.08893.000.616198270166.37310103.000.58966311,3306,680.89112,3207,349.446Copyright?2010PearsonEducation,Inc.PublishingasPrenticeHall4-33Convexity

(continued)Usingdurationandconvexitymeasurestogethergivesabetterapproximationoftheactualpricechangeforalargemovementintherequiredyield.SomeNotesonConvexity

Threepointstoknowforabond’sconvexityandconvexitymeasure.Convexityreferstothegeneralshapeoftheprice-yieldrelationship,whiletheconvexitymeasurerelatestothequantificationofhowthepriceofthebondwillchangewheninterestrateschange.Theapproximationpercentagechangeinpriceduetoconvexityistheproductofthreenumbers:?,convexitymeasure,andsquareofthechangeinyield.Inpracticedifferentvendorscomputetheconvexitymeasuredifferentlybyscalingthemeasureindissimilarways.Copyright?2010PearsonEducation,Inc.PublishingasPrenticeHall4-34Convexity

(continued)ValueofConvexity

Uptothispoint,wehavefocusedonhowtakingconvexityintoaccountcanimprovetheapproximationofabond’spricechangeforagivenyieldchange.Theconvexityofabond,however,hasanotherimportantinvestmentimplication,whichisillustratedinExhibit4-16(seeOverhead4-43).Copyright?2010PearsonEducation,Inc.PublishingasPrenticeHall4-35Exhibit4-16

ComparisonofConvexityofTwoBondsPriceYieldBondABondBBondABondBBondBHasGreaterConvexityThanBondACopyright?2010PearsonEducation,Inc.PublishingasPrenticeHall4-36Convexity

(continued)ValueofConvexity

Themarketconsidersabond’sconvexitywhenpricingit.Ifinvestorsexpectthatmarketyieldswillchangebyverylittle,investorsshouldnotbewillingtopaymuchforconvexity.Ifthemarketpricesconvexityhigh,investorswithexpectationsoflowinterestratevolatilitywillprobablywantto“sellconvexity.”

PropertiesofConvexity

Alloption-freebondshavethefollowingconvexityproperties.AsportrayedinExhibit4-17(seeOverhead4-45),therequiredyieldincreases(decreases),theconvexityofabonddecreases(increases).Thispropertyisreferredtoaspositiveconvexity.Foragivenyieldandmaturity,lowercouponrateswillhavegreaterconvexity.Foragivenyieldandmodifiedduration,lowercouponrateswillhavesmallerconvexity.Copyright?2010PearsonEducation,Inc.PublishingasPrenticeHall4-37Exhibit4-17

ChangeinDurationasthe

RequiredYieldChangesPriceYieldAsyield↓Slope(duration)↑Asyield↑Slope(duration)↓123Copyright?2010PearsonEducation,Inc.PublishingasPrenticeHall4-38AdditionalConcernswhen

UsingDurationTherearetwootherconcernsaboutusingdurationthatweshouldpointout.First,inthederivationoftherelationshipbetweenmodifieddurationandbondpricevolatility,weassumethatallcashflowsforthebondarediscountedatthesamediscountrate.Second,thereismisapplicationofdurationtobondswithembeddedoptions.Copyright?2010PearsonEducation,Inc.PublishingasPrenticeHall4-39Don’tThinkofDurationasaMeasureofTimeMarketparticipantsoftenconfusethemainpurposeofdurationbyconstantlyreferringtoitassomemeasureoftheweightedaveragelifeofabond.CertainCMObondclassesareleveragedinstrumentswhosepricesensitivityorduration,asaresult,areamultipleoftheunderlyingmortgageloansfromwhichtheywerecreated.Thus,aCMObondclasswithadurationof40doesnotmeanthatithassometypeofweightedaveragelifeof40years.Instead,itmeansthatfora100-basis-pointchangeinyield,thatbond’spricewillchangebyroughly40%.LikeaCMObondclass,weinterpretthedurationofanoptioninthesameway.Copyright?2010PearsonEducation,Inc.PublishingasPrenticeHall4-40ApproximatingaBond’sDurationandConvexityMeasureCopyright?2010PearsonEducation,Inc.PublishingasPrenticeHall4-41ApproximatingaBond’sDurationandConvexityMeasureDurationofanInverseFloaterThedurationofaninversefloaterisamultipleofthedurationofthecollateralfromwhichitiscreated.Assumingthatthedurationofthefloaterisclosetozero,itcanbeshownthatthedurationofaninversefloaterisasfollows:whereL

istheratiooftheparvalueofthefloatertotheparvalueoftheinversefloater.Copyright?2010PearsonEducation,Inc.PublishingasPrenticeHall4-42MeasuringaBondPortfolio’sResponsivenesstoNonparallelChangesinInterestRatesYieldCurveReshapingDuration

Theyieldcurvereshapingdurationapproachfocusesonthesensitivityofaportfoliotoachangeintheslopeoftheyieldcurve.

KeyRateDuration

Themostpopularmeasureforestimatingthesensitivityofasecurityoraportfoliotochangesintheyieldcurveiskeyrateduration.Thebasicprincipleofkeyratedurationistochangetheyieldforaparticularmaturityoftheyieldcurveanddeterminethesensitivityofasecurityorportfoliotothatchangeholdingallotheryieldsconstant.Copyright?2010PearsonEducation,Inc.PublishingasPrenticeHall4-43Allrightsreserved.Nopartofthispublicationmaybereproduced,storedinaretrievalsystem,ortransmitted,inanyformorbyanymeans,electronic,mechanical,photocopying,recording,orotherwise,withoutthepriorwrittenpermissionofthepublisher.PrintedintheUnitedStatesofAmerica.Copyright?2010PearsonEducation,Inc.PublishingasPrenticeHall5-44Chapter5

FactorsAffectingBondYieldsandtheTermStructureofInterestRatesCopyright?2010PearsonEducation,Inc.PublishingasPrenticeHall5-45LearningObjectivesAfterreadingthischapter,youwillunderstandwhytheyieldonaTreasurysecurityisthebaseinterestratethefactorsthataffecttheyieldspreadbetweentwobondswhatayieldcurveisaspotrateandaspotratecurvehowtheoreticalspotratesarederivedusingarbitrageargumentsfromtheTreasuryyieldcurvewhatthetermstructureofinterestratesiswhythepriceofaTreasurybondshouldbebasedontheoreticalspotratesaforwardrateandhowaforwardrateisderivedCopyright?2010PearsonEducation,Inc.PublishingasPrenticeHall5-46LearningObjectives

(continued)Afterreadingthischapter,youwillunderstandhowlong-termratesarerelatedtothecurrentshort-termrateandshort-termforwardrateswhyforwardratesshouldbeviewedashedgeableratesthevarioustheoriesaboutthedeterminantsoftheshapeofthetermstructure:pureexpectationstheory,theliquiditytheory,thepreferredhabitattheory,andthemarketsegmentationtheorythemaineconomicinfluencesontheshapeoftheTreasuryyieldcurvewhattheswapcurve/LIBORcurveisandwhyitisusedasaninterestratebenchmarkCopyright?2010PearsonEducation,Inc.PublishingasPrenticeHall5-47BaseInterestRatesThesecuritiesissuedbytheU.S.DepartmentoftheTreasuryarebackedbythefullfaithandcreditoftheU.S.government.InterestratesonTreasurysecuritiesarethekeyinterestratesintheU.S.economyaswellasininternationalcapital.Theminimuminterestratethatinvestorswantisreferredtoasthebaseinterestrateorbenchmarkinterestratethatinvestorswilldemandforinvestinginanon-Treasurysecurity.Thisrateistheyieldtomaturity(hereafterreferredtoassimplyyield)offeredonacomparablematurityTreasurysecuritythatwasmostrecentlyissued(“ontherun”).Exhibit5-1(seeOverhead5-5)showstheyield.Theseyieldsrepresentthebenchmarkinterestrate.Copyright?2010PearsonEducation,Inc.PublishingasPrenticeHall5-48Exhibit5-1

U.S.TreasurySecurityYieldsonDecember28,2007MaturityYield3-month3.016-month3.292-year3.093-year3.045-year3.4910-year4.0730-year4.49Copyright?2010PearsonEducation,Inc.PublishingasPrenticeHall5-49BenchmarkSpreadsThedifferencebetweentheyieldsofanytwobondsiscalledayieldspreadasgivenbelowforbondsAandB:yieldspread=yieldonbondA–yieldonbondBThenormalwaythatyieldspreadsarequotedisintermsofbasispoints.Theyieldspreadreflectsthedifferenceintherisksassociatedwiththetwobonds.WhenbondBisabenchmarkbondandbondAisanon-benchmarkbond,theyieldspreadisreferredtoasabenchmarkspread;thatis,benchmarkspread=yieldonnon-benchmarkbond–yieldonbenchmarkbondThebenchmarkspreadreflectsthecompensationthatthemarketisofferingforbearingtherisksassociatedwiththenon-benchmarkbondthatdonotexistforthebenchmarkbond.Thus,thebenchmarkspreadcanbethoughtofasariskpremium.Copyright?2010PearsonEducation,Inc.PublishingasPrenticeHall5-50BenchmarkSpreads

(continued)Exhibit5-2(seeOverhead5-8)providesinformationonbenchmarkspreadsforactualtradesforfourissues.Thefourissuestradedareshowninthesecondcolumnoftheexhibit.Thetradepriceandtheresultingyieldforeachissueareshowninthefourthandfifthcolumns.TheappropriateTreasurybenchmarkforeachtradedbondisshowninthesixthcolumn.TheyieldfortheTreasurybenchmarkissueonthetradedateisshownintheseventhcolumn.ThebenchmarkspreadisthenthedifferencebetweentheyieldonthetradedissueandtheyieldontheTreasurybenchmarkissueandisshowninthelastcolumn.Copyright?2010PearsonEducation,Inc.PublishingasPrenticeHall5-51Exhibit5-2

U.S.TreasurySecurityYieldsonDecember28,2007IssuerIssueRatingTradePriceYield(%)TreasuryBench-markBench-markYield(%)Bench-markSpread(bps)GeneralElect.CapitalCorp.GE4.12509/01/2009Aaa/AAA100.1824.008US/T3.12511/30/20093.218

79.0

EIDuPontDeNemours&Co.DD501/15/2013A2/A100.6814.843US/T3.37511/30/20123.616122.7TheCoca-ColaCompanyKO5.3511/15/2017Aa3/A102.5335.020US/T4.2511/15/20174.20181.9Wal-MartStoresInc.WMT6.508/15/2037Aa2/AA109.0105.855US/T4.7502/15/20374.619123.6Copyright?2010PearsonEducation,Inc.PublishingasPrenticeHall5-52BenchmarkSpreads

(continued)Somemarketparticipantsmeasuretheriskpremiumonarelativebasisbytakingtheratiooftheyieldspreadtotheyieldlevel.Thismeasure,calledarelativeyieldspread,isasfollows:relativeyieldspread=(yieldonbondA–yieldonbondB)/yieldonbondBTheyieldratioisthequotientoftwobondyields:yieldratio=yieldonbondA/yieldonbondBThefactorsthataffecttheyieldspreadinclude:thetypeofissuer,theissuer’sperceivedcreditworthine