《債券市場(chǎng)：分析與策略（第七版）》Ch05

Chapter5

FactorsAffectingBondYieldsandtheTermStructureofInterestRates

5-1Copyright?2010PearsonEducation,Inc.PublishingasPrenticeHallLearningObjectivesAfterreadingthischapter,youwillunderstandwhytheyieldonaTreasurysecurityisthebaseinterestratethefactorsthataffecttheyieldspreadbetweentwobondswhatayieldcurveisaspotrateandaspotratecurvehowtheoreticalspotratesarederivedusingarbitrageargumentsfromtheTreasuryyieldcurvewhatthetermstructureofinterestratesiswhythepriceofaTreasurybondshouldbebasedontheoreticalspotratesaforwardrateandhowaforwardrateisderived5-2Copyright?2010PearsonEducation,Inc.PublishingasPrenticeHallLearningObjectives

(continued)Afterreadingthischapter,youwillunderstandhowlong-termratesarerelatedtothecurrentshort-termrateandshort-termforwardrateswhyforwardratesshouldbeviewedashedgeableratesthevarioustheoriesaboutthedeterminantsoftheshapeofthetermstructure:pureexpectationstheory,theliquiditytheory,thepreferredhabitattheory,andthemarketsegmentationtheorythemaineconomicinfluencesontheshapeoftheTreasuryyieldcurvewhattheswapcurve/LIBORcurveisandwhyitisusedasaninterestratebenchmark5-3Copyright?2010PearsonEducation,Inc.PublishingasPrenticeHallBaseInterestRatesThesecuritiesissuedbytheU.S.DepartmentoftheTreasuryarebackedbythefullfaithandcreditoftheU.S.government.InterestratesonTreasurysecuritiesarethekeyinterestratesintheU.S.economyaswellasininternationalcapital.Theminimuminterestratethatinvestorswantisreferredtoasthebaseinterestrateorbenchmarkinterestratethatinvestorswilldemandforinvestinginanon-Treasurysecurity.Thisrateistheyieldtomaturity(hereafterreferredtoassimplyyield)offeredonacomparablematurityTreasurysecuritythatwasmostrecentlyissued(“ontherun”).Exhibit5-1(seeOverhead5-5)showstheyield.Theseyieldsrepresentthebenchmarkinterestrate.5-4Copyright?2010PearsonEducation,Inc.PublishingasPrenticeHallExhibit5-1

U.S.TreasurySecurityYieldsonDecember28,2007MaturityYield3-month3.016-month3.292-year3.093-year3.045-year3.4910-year4.0730-year4.495-5Copyright?2010PearsonEducation,Inc.PublishingasPrenticeHallBenchmarkSpreadsThedifferencebetweentheyieldsofanytwobondsiscalledayieldspreadasgivenbelowforbondsAandB:yieldspread=yieldonbondA–yieldonbondBThenormalwaythatyieldspreadsarequotedisintermsofbasispoints.Theyieldspreadreflectsthedifferenceintherisksassociatedwiththetwobonds.WhenbondBisabenchmarkbondandbondAisanon-benchmarkbond,theyieldspreadisreferredtoasabenchmarkspread;thatis,benchmarkspread=yieldonnon-benchmarkbond–yieldonbenchmarkbondThebenchmarkspreadreflectsthecompensationthatthemarketisofferingforbearingtherisksassociatedwiththenon-benchmarkbondthatdonotexistforthebenchmarkbond.Thus,thebenchmarkspreadcanbethoughtofasariskpremium.5-6Copyright?2010PearsonEducation,Inc.PublishingasPrenticeHallBenchmarkSpreads

(continued)Exhibit5-2(seeOverhead5-8)providesinformationonbenchmarkspreadsforactualtradesforfourissues.Thefourissuestradedareshowninthesecondcolumnoftheexhibit.Thetradepriceandtheresultingyieldforeachissueareshowninthefourthandfifthcolumns.TheappropriateTreasurybenchmarkforeachtradedbondisshowninthesixthcolumn.TheyieldfortheTreasurybenchmarkissueonthetradedateisshownintheseventhcolumn.ThebenchmarkspreadisthenthedifferencebetweentheyieldonthetradedissueandtheyieldontheTreasurybenchmarkissueandisshowninthelastcolumn.5-7Copyright?2010PearsonEducation,Inc.PublishingasPrenticeHallExhibit5-2

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/T4.7502/15/20374.619123.65-8Copyright?2010PearsonEducation,Inc.PublishingasPrenticeHallBenchmarkSpreads

(continued)Somemarketparticipantsmeasuretheriskpremiumonarelativebasisbytakingtheratiooftheyieldspreadtotheyieldlevel.Thismeasure,calledarelativeyieldspread,isasfollows:relativeyieldspread=(yieldonbondA–yieldonbondB)/yieldonbondBTheyieldratioisthequotientoftwobondyields:yieldratio=yieldonbondA/yieldonbondBThefactorsthataffecttheyieldspreadinclude:thetypeofissuer,theissuer’sperceivedcreditworthinessthetermormaturityoftheinstrumentprovisionsthatgranteithertheissuerortheinvestortheoptiontodosomethingthetaxabilityoftheinterestreceivedbyinvestorstheexpectedliquidityofthesecurity5-9Copyright?2010PearsonEducation,Inc.PublishingasPrenticeHallBenchmarkSpreads

(continued)TypesofIssuersThebondmarketisclassifiedbythetypeofissuer,includingtheU.S.government,U.Sgovernmentagencies,municipalgovernments,credit(domesticandforeigncorporations),andforeigngovernments.Theseclassificationsarereferredtoasmarketsectors.Differentsectorscanbeperceivedtosignifydifferentrisksandrewards.Somemarketsectorsarefurthersubdividedintocategoriesintendedtoreflectcommoneconomiccharacteristics.Forexample,withinthecreditmarketsector,issuersareclassifiedasfollows:industrial,utility,finance,andnon-corporate.Thespreadbetweentheinterestrateofferedintwosectorsofthebondmarketwiththesamematurityiscalledanintermarketsectorspread.Thespreadbetweentwoissueswithinamarketsectoriscalledanintramarketsectorspread.5-10Copyright?2010PearsonEducation,Inc.PublishingasPrenticeHallBenchmarkSpreads

(continued)PerceivedCreditWorthinessofIssuerDefaultriskorcreditriskreferstotheriskthattheissuerofabondmaybeunabletomaketimelyprincipaland/orinterestpayments.Mostmarketparticipantsrelyprimarilyoncommercialratingcompaniestoassessthedefaultriskofanissuer.ThespreadbetweenTreasurysecuritiesandnon-Treasurysecuritiesthatareidenticalinallrespectsexceptforqualityisreferredtoasacreditspread.ExamplesofcreditspreadsonDecember28,2007,areprovidedinExhibit5-3(seeOverhead5-12).TheTreasuryyieldsforcomputingthecreditspreadswerethoseshowninExhibit5-2(aswasseeninOverhead5-8).Ascanbeseen,foragivenmaturity,thehigherthecreditratingis,thesmallerthecreditspread.5-11Copyright?2010PearsonEducation,Inc.PublishingasPrenticeHallExhibit5-3

CorporateBondYieldsandRiskPremiumMeasuresRelativetoTreasuryYieldsonDecember28,2007MaturityRatingCorporateYield(%)TreasuryYield(%)YieldSpread(bps)5-yearAAA4.603.491115-yearAA4.913.4914210-yearAAA5.034.079610-yearAA5.324.07125Note:Y.TheoriginalsourceisValuBond.5-12Copyright?2010PearsonEducation,Inc.PublishingasPrenticeHallBenchmarkSpreads

(continued)InclusionofOptionsItisnotuncommonforabondissuetoincludeaprovisionthatgiveseitherthebondholderand/ortheissueranoptiontotakesomeactionagainsttheotherparty.ThepresenceofanembeddedoptionhasaneffectonthespreadofanissuerelativetoaTreasurysecurityandthespreadrelativetootherwisecomparableissuesthatdonothaveanembeddedoption.Ananalyticalmeasurecalledtheoption-adjustedspread(OAS)istheyieldspreadafteradjustingforthevalueoftheembeddedoptions.Absentanyembeddedoptions,thelowerratedbondwouldhaveahigherbenchmarkspread.5-13Copyright?2010PearsonEducation,Inc.PublishingasPrenticeHallBenchmarkSpreads

(continued)TaxabilityofInterestBecauseofthetax-exemptfeatureofmunicipalbonds,theyieldonmunicipalbondsislessthanTreasurieswiththesamematurity.ThisisseeninExhibit5-4(seeOverhead5-15)Theyieldonataxablebondissueafterfederalincometaxesarepaidiscalledtheafter-taxyield:after-taxyield=pretaxyield×(1–marginaltaxrate)Alternatively,wecandeterminetheyieldthatmustbeofferedonataxablebondissuetogivethesameafter-taxyieldasatax-exemptissue.Thisyieldiscalledtheequivalenttaxableyieldandis:equivalenttaxableyield=tax-exemptyield/(1–marginaltaxrate)5-14Copyright?2010PearsonEducation,Inc.PublishingasPrenticeHallExhibit5-4

AAAMunicipalYieldsversusAAACorporateYields

MaturityMunicipalYield(%)CorporateYield(%)YieldRatio5-year3.354.910.6810-year3.875.030.7720-year4.595.320.86Note:Y.TheoriginalsourceisValuBond.5-15Copyright?2010PearsonEducation,Inc.PublishingasPrenticeHallBenchmarkSpreads

(continued)Themunicipalbondmarketisdividedintotwomajorsectors:generalobligationsandrevenuebonds.Stateandlocalgovernmentsmaytaxinterestincomeonbondissuesthatareexemptfromfederalincometaxes.Somemunicipalities’exemptinterestincomefromallmunicipalissuesfromtaxation;othersdonot.Somestatesexemptinterestincomefrombondsissuedbymunicipalitieswithinthestatebuttaxtheinterestincomefrombondsissuedbymunicipalitiesoutsidethestate.MunicipalitiesarenotpermittedtotaxtheinterestincomefromsecuritiesissuedbytheU.S.Treasury.ThuspartofthespreadbetweenTreasurysecuritiesandtaxablenon-Treasurysecuritiesofthesamematurityreflectsthevalueoftheexemptionfromstateandlocaltaxes.5-16Copyright?2010PearsonEducation,Inc.PublishingasPrenticeHallBenchmarkSpreads

(continued)ExpectedLiquidityofanIssueBondstradewithdifferentdegreesofliquidity.Bondswithgreaterexpectedliquiditywillhaveloweryieldsthatinvestorswouldrequire.Treasurysecuritiesarethemostliquidsecuritiesintheworld.TheloweryieldofferedonTreasurysecuritiesrelativetonon-Treasurysecuritiesreflectsthedifferenceinliquidity.EvenwithintheTreasurymarket,on-the-runissueshavegreaterliquiditythanoff-the-runissues.5-17Copyright?2010PearsonEducation,Inc.PublishingasPrenticeHallBenchmarkSpreads

(continued)FinanceabilityofanIssueAportfoliomanagercanuseanissueascollateralforborrowingfundssoastocreateleverage.Thetypicalmarketusedbyportfoliomanagerstoborrowfundsusingasecurityascollateralforaloanistherepurchaseagreement(repo)market.Whenaportfoliomanagerwantstoborrowfundsviaarepoagreement,adealerprovidesthefunds.Theinterestratechargedbythedealeriscalledthereporate.Thereisnotonereporatebutastructureofratesdependingonthematurityoftheloanandthespecificissuebeingfinanced.Withrespecttothelatter,therearetimeswhendealersareinneedofparticularissuestocoverashortposition.Whenadealerneedsaparticularissue,thatdealerwillbewillingtooffertolendfundsatalowerreporatethanthegeneralreporateinthemarket.5-18Copyright?2010PearsonEducation,Inc.PublishingasPrenticeHallBenchmarkSpreads

(continued)TermToMaturityThetermtomaturityisthetimeremainingonabond’slife.Thevolatilityofabond’spriceisdependentonitstermtomaturity.Allotherfactorsconstant,thelongerthetermtomaturityofabond,thegreaterthepricevolatilityresultingfromachangeinmarketyields.Bondsareclassifiedintothreematuritysectors:Short-termbondshaveatermtomaturityofbetween1to5yearsIntermediatebondshaveatermtomaturityofbetween5and12yearsLong-term

bondshaveatermtomaturitygreaterthan12yearsThespreadbetweenanytwomaturitysectorsofthemarketiscalledamaturityspread.Therelationshipbetweentheyieldsonotherwisecomparablesecuritieswithdifferentmaturitiesiscalledthetermstructureofinterestrates.5-19Copyright?2010PearsonEducation,Inc.PublishingasPrenticeHallTermStructureofInterestRates(continued)YieldCurveTheyieldcurveisthegraphicaldepictionoftherelationbetweentheyieldonbondsofthesamecreditqualitybutdifferentmaturities.InvestorshavetypicallyconstructedyieldcurvesfromobservationsofpricesandyieldsintheTreasurymarketfortworeasons:First,Treasurysecuritiesarefreeofdefaultrisk,anddifferencesincreditworthinessdonotaffectyields.Therefore,theseinstrumentsaredirectlycomparable.Second,asthelargestandmostactivebondmarket,theTreasurymarketoffersthefewestproblemsofilliquidityorinfrequenttrading.Thedisadvantageisthattheyieldsmaybebiaseddownwardbecausetheyreflectfavorablefinancingopportunities.Exhibit5-5(seeOverhead5-21)showsthreetypicalshapesfortheyieldcurve.5-20Copyright?2010PearsonEducation,Inc.PublishingasPrenticeHallExhibit5-5

ShapeofPrice-YieldRelationshipforanOption-FreeBondYieldMaturity(a)PositiveInvertedFlatMaturityMaturityYieldYield(b)(c)5-21Copyright?2010PearsonEducation,Inc.PublishingasPrenticeHallTermStructureofInterestRates(continued)WhytheYieldCurveShouldNotBeUsedToPriceaBondThebondpricingformulaassumesthatoneinterestrateshouldbeusedtodiscountallthebond’scashflows.Becauseofthedifferentcashflowpatterns,itisnotappropriatetousethesameinterestratetodiscountallcashflows.Eachcashflowshouldbediscountedatauniquerateappropriateforthetimeperiodinwhichthecashflowwillbereceived.Thecorrectwaytothinkaboutbondsisthattheyarepackagesofzero-couponinstruments.Eachzero-couponinstrumentinthepackagehasamaturityequaltoitscouponpaymentdateor,inthecaseoftheprincipal,thematuritydate.Thevalueofthebondshouldequalthevalueofallthecomponentzero-couponinstruments.5-22Copyright?2010PearsonEducation,Inc.PublishingasPrenticeHallTermStructureofInterestRates(continued)WhytheYieldCurveShouldNotBeUsedToPriceaBondTodeterminethevalueofeachzero-couponinstrument,itisnecessarytoknowtheyieldonazero-couponTreasurywiththatsamematurity.Thisyieldiscalledthespotrate,andthegraphicaldepictionoftherelationshipbetweenthespotrateandmaturityiscalledthespotratecurve.Becausetherearenozero-couponTreasurydebtissueswithamaturitygreaterthanoneyear,itisnotpossibletoconstructsuchacurvesolelyfromobservationsofmarketactivityonTreasurysecurities.Rather,itisnecessarytoderivethiscurvefromtheoreticalconsiderationsasappliedtotheyieldsoftheactuallytradedTreasurydebtsecurities.Suchacurveiscalledatheoreticalspotratecurveandisthegraphicaldepictionofthetermstructureofinterestrate.5-23Copyright?2010PearsonEducation,Inc.PublishingasPrenticeHallTermStructureofInterestRates(continued)ConstructingtheTheoreticalSpotRateCurveforTreasuriesBondAdefault-freetheoreticalspotratecurvecanbeconstructedfromtheyieldonTreasurysecurities.TheTreasuryissuesthatarecandidatesforinclusionareon-the-runTreasuryissueson-the-runTreasuryissuesandselectedoff-the-runTreasuryissuesallTreasurycouponsecurities,andbillsTreasurycouponstrips

Afterthesecuritiesthataretobeincludedintheconstructionofthetheoreticalspotratecurveareselected,themethodologyforconstructingthecurvemustbedetermined.Iftheon-the-runTreasuryissueswithorwithoutselectedoff-the-runTreasuryissuesareused,amethodologycalledbootstrapping

isused.5-24Copyright?2010PearsonEducation,Inc.PublishingasPrenticeHallTermStructureofInterestRates(continued)On-the-RunTreasuryIssuesTheon-the-runTreasuryissuesarethemostrecentlyauctionedissueofagivenmaturity.Theseissuesinclude3-month,6-month,and1-yearTreasurybills;2-year,5-year,and10-yearTreasurynotes;and30-yearTreasurybond.Treasurybillsarezero-couponinstruments;thenotesandthebondarecouponsecurities.Thereisanobservedyieldforeachoftheon-the-runissues.Forthecouponissues,theseyieldsarenottheyieldsusedintheanalysiswhentheissueisnottradingatpar.Instead,foreachon-the-runcouponissue,theestimatedyieldnecessarytomaketheissuetradeatparisused.Theresultingon-the-runyieldcurveiscalledtheparcouponcurve.5-25Copyright?2010PearsonEducation,Inc.PublishingasPrenticeHallTermStructureofInterestRates(continued)On-the-RunTreasuryIssuesThegoalistoconstructatheoreticalspotratecurvewith60semiannualspotrates:6monthrateto30-yearrate.Excludingthethree-monthbill,thereareonlysixmaturitypointsavailablewhenonlyon-the-runissuesareused.The54missingmaturitypointsareextrapolatedfromthesurroundingmaturitypointsontheparyieldcurve.Thesimplestinterpolationmethod,andtheonemostcommonlyused,islinearextrapolation.Specifically,giventheyieldontheparcouponcurveattwomaturitypoints,thefollowingiscalculated:Theyieldforallintermediatesemiannualmaturitypointsisfoundbyaddingtotheyieldatthelowermaturitytheamountcomputedhere.5-26Copyright?2010PearsonEducation,Inc.PublishingasPrenticeHallTermStructureofInterestRates(continued)On-the-RunTreasuryIssuesTherearetwoproblemswithusingjusttheon-the-runissues.First,thereisalargegapbetweensomeofthematuritiespoints,whichmayresultinmisleadingyieldsforthosematuritypointswhenestimatedusingthelinearinterpolationmethod.Specifically,theconcerniswiththelargegapbetweenthefive-yearand10-yearmaturitypointsandthe10-yearand30-yearmaturitypoints.Thesecondproblemisthattheyieldsfortheon-the-runissuesthemselvesmaybemisleadingbecausemostofferthefavorablefinancingopportunityintherepomarketmentionedearlier.Thismeansthatthetrueyieldisgreaterthanthequoted(observed)yield.5-27Copyright?2010PearsonEducation,Inc.PublishingasPrenticeHallTermStructureofInterestRates(continued)On-the-RunTreasuryIssuesAsshowninExhibit5-6(seeOverhead5-29),wecanconverttheparyieldcurveintothetheoreticalspotratecurveusingbootstrapping.ToexplaintheprocessofestimatingthetheoreticalspotratecurvefromobservedyieldsonTreasurysecurities,weconsiderasix-monthTreasurybillwhereitsannualizedyieldisthesix-monthspotrateandaone-yearTreasurywhereitsannualizedyieldistheoneyearspotrate.Giventhesetwospotrates,wecancomputethespotrateforatheoretical1.5-yearzero-couponTreasury.Giventhetheoretical1.5-yearspotrate,wecanobtainthetheoretical2-yearspotrateandsoforthuntilwederivetheoreticalspotratesfortheremaining15half-yearlyrates.ThespotratesusingthisprocessrepresentthetermstructureofinterestratesandcanbeviewedinExhibit5-7(seeOverhead5-30).5-28Copyright?2010PearsonEducation,Inc.PublishingasPrenticeHallExhibit5-6MaturityandYieldtoMaturityfor20HypotheticalTreasurySecuritiesPeriodYearsYieldtoMaturity/CouponRate(%)10.55.2521.05.5031.55.7542.06.0052.56.2563.06.5073.56.7584.06.8094.57.00105.07.10115.57.15126.07.20136.57.30147.07.35157.57.40168.07.50178.57.60189.07.60199.57.702010.07.805-29Copyright?2010PearsonEducation,Inc.PublishingasPrenticeHallExhibit5-7TheoreticalSpotRatesPeriodYearsYieldtoMaturity/CouponRate(%)10.55.2521.05.5031.55.7642.06.0252.56.2863.06.5573.56.8284.06.8794.57.09105.07.20115.57.26126.07.31136.57.43147.07.48157.57.54168.07.67178.57.80189.07.79199.57.932010.08.075-30Copyright?2010PearsonEducation,Inc.PublishingasPrenticeHallTermStructureofInterestRates(continued)On-the-RunTreasuryIssueandSelectedOff-the-RunTreasuryIssuesOneoftheproblemswithusingjusttheon-the-runissuesisthelargegapsbetweenmaturities,particularlyafterfiveyears.Tomitigatethisproblem,somedealersandvendorsuseselectedoff-the-runTreasuryissues.

AllTreasuryCouponSecuritiesandBillsUsingonlyon-the-runissues,evenwhenextendedtoincludeafewoff-the-runissues,failstorecognizetheinformationembodiedinTreasurypricesthatarenotincludedintheanalysis.Thus,itisarguedthatitismoreappropriatetouseallTreasurycouponsecuritiesandbillstoconstructthetheoreticalspotratecurve.5-31Copyright?2010PearsonEducation,Inc.PublishingasPrenticeHallTermStructureofInterestRates(continued)TreasuryCouponStripsTreasurycouponstripsarezero-couponTreasurysecurities.Itwouldseemlogicalthattheobservedyieldonstripscouldbeusedtoconstructanactualspotratecurve.Therearethreeproblemswithusingtheobservedratesonstrips.First,theliquidityofthestripsmarketisnotasgreatasthatoftheTreasurycouponmarket.Second,thetaxtreatmentofstripsisdifferentfromthatofTreasurycouponsecurities.Finally,therearematuritysectorsinwhichnon–U.S.investorsfinditadvantageoustotradeoffyieldfortaxadvantagesassociatedwithastrip.5-32Copyright?2010PearsonEducation,Inc.PublishingasPrenticeHallTermStructureofInterestRates(continued)UsingtheTheoreticalSpotRateCurveExhibit5-8(seeOverhead5-34)showshowtovalueaTreasurybondproperlyusingthetheoreticalspotrates.Thebondintheillustrationisahypothetical10-yearTreasurysecuritywithacouponrateof10%.ArbitrageforcesaTreasurytobepricedbasedonspotratesandnottheyieldcurve.TheabilityofdealerstopurchasesecuritiesandcreatevaluebystrippingforcesTreasurysecuritiestobepricedbasedonthetheoreticalspotrates.5-33Copyright?2010PearsonEducation,Inc.PublishingasPrenticeHallExhibit5-8TheoreticalSpotRatesPeriodYearCashFlowSpotRate(%)PVof$1atSpotRatePVofCashFlow10.555.250.9744214.87210721.055.500.9471884.73594231.555.760.9183514.59175642.056.020.8881564.44078252.556.280.8567244.28361963.056.550.8242064.12103073.556.820.7907573.95378384.056.870.7632563.81628094.557.090.7307183.653589105.057.200.7019523.509758115.557.260.6756973.378483126.057.310.6500283.250138136.557.430.6224483.112238147.057.480.5978892.989446157.557.540.5739192.869594168.057.670.5476252.738125178.557.800.5217662.608831189.057.790.5026652.513325199.557.930.4777292.3886432010.01058.070.45326847.593170TheoreticalValue=115.42065-34Copyright?2010PearsonEducation,Inc.PublishingasPrenticeHallTermStructureofInterestRates(continued)ForwardRatesFromtheyieldcurvewecanextrapolatethetheoreticalspotrates.Inaddition,wecanextrapolatethemarket’sconsensusoffutureinterestrates.Toseetheimportanceofknowingthemarket’sconsensusforfutureinterestrates,considerthefollowingtwoinvestmentalternativesforaninvestorwhohasaone-yearinvestmenthorizon.Alternative1:Buyaone-yearinstrument.Alternative2:Buyasix-monthinstrumentandwhenitmaturesinsixmonths,buyanothersix-monthinstrument.Withalternative1,theinvestorwillrealizetheone-yearspotrateandthatrateisknownwithcertaintybutwithalternative2,theinvestorwillrealizethe6-monthspotrate,butthe6-monthrate6monthsfromnowisunknown.Therefore,foralternative2,theratethatwillbeearnedoveroneyearisnotknownwithcertainty.ThisisillustratedinExhibit5-9(seeOverhead5-36)5-35Copyright?2010PearsonEducation,Inc.PublishingasPrenticeHallEXHIBIT5-9

TwoAlternativeOne-YearInvestmentsTotalDollarsatEndofOneYearper$100Investment6months1yearToday5-36Copyright?2010PearsonEducation,Inc.PublishingasPrenticeHallTermStructureofInterestRates(continued)RelationshipBetweenSix-MonthForwardRatesandSpotRatesIngeneral,therelationshipbetweenat-periodspotrate(zt),thecurrentsix-monthspotrate(z1),andthesixmonthforwardratesiszt

=[(1+z1)(1+f1)(1+f2)···(1+ft–1)]1/t

–1whereft

isthesix-monthforwardratebeginningtsix-monthperiodsfromnow.OtherForwardRatesItisnotnecessarytolimitourselvestosix-monthforwardrates.Thespotratescanbeusedtocalculatetheforwardrateforanytimeinthefutureforanyinvestmenthorizon.5-37Copyright?2010PearsonEducation,Inc.PublishingasPrenticeHall5-38TermStructureofInterestRates(continued)ForwardRateasaHedgeableRateAnaturalquestionaboutforwardratesishowwelltheydoatpredictingfutureinterestrates.Theforwardratemayneverberealizedbutisimportantinwhatittellsinvestorsabouthisexpectationrelativetowhatthemarketconsensusexpects.Somemarketparticipantsprefernottotalkaboutforwardratesasbeingmarketconsensusratesbutrefertoforwardratesasbeinghedgeablerates.Forexample,bybuyingtheone-yearsecurity,theinvestorcanhedgethesix-monthratesixmonthsfromnow.Copyright?2010PearsonEducation,Inc.PublishingasPrenticeHallTermStructureofInterestRates(continued)DeterminantsoftheShapeoftheTermStructureIfweplotthetermstructure–theyieldtomaturity,orthespotrate,atsuccessivematuritiesagainstmaturity–whatisitlikelytolooklike?Exhibit5-5(aswasseeninOverhead5-21)

showedthreegenericshapesthathaveappearedfortheU.S.Treasuryyieldcurvewithsomefrequencyovertime.Exhibit5-10(seeOverhead5-40)showsfiveselectivedailyTreasuryyieldcurvesintabularform.Twomajortheoriesh