ChapterFifteenTheTermStructureofInterestRatesExplorepatternofinterestratesfordifferent-termassetsIdentifyfactorsthataccountforpatternanddeterminewhatinformationmaybegleanedfromananalysisofthetermstructureofinterestratesDemonstratehowpricesofTreasurybondsmaybederivedfrompricesandyieldsofstrippedzero-couponTreasurysecuritiesExamineextenttowhichtermstructurerevealsmarket-consensusforecastsoffutureinterestratesChapterOverview?2021McGraw-HillEducation15-2RelationshipbetweenyieldandmaturitymaybeshowngraphicallyinayieldcurveYieldcurveisaplotofyieldtomaturityasafunctionoftimetomaturityKeyconcernoffixed-incomeinvestorsCentraltobondvaluationAllowsinvestorstogaugetheirexpectationsforfutureinterestratesagainstthoseofthemarketTheYieldCurve?2021McGraw-HillEducation15-3TreasuryYieldCurves?2021McGraw-HillEducation15-4YieldsondifferentmaturitybondsarenotequalConsidercashflowofeachbondasastand-alonezero-couponbondBondstrippingandbondreconstitutionofferopportunitiesforarbitrageThevalueofthebondshouldbethesumofthevaluesofitspartsYieldCurve:BondPricing?2021McGraw-HillEducation15-5PricesandYieldstoMaturitieson

Zero-CouponBonds($1,000FaceValue)?2021McGraw-HillEducation15-6Valuea3-year,10%couponbondusingdiscountratesfromTable15.1:Price=$1,082.17andYTM=6.88%6.88%islessthanthe3-yearrateof7%ValuingCouponBonds?2021McGraw-HillEducation15-7PureYieldCurveReferstothecurveforstripped,orzero-coupon,TreasuriesMaydiffersignificantlyfromtheon-the-runyieldcurveOn-the-RunYieldCurveReferstotheplotofyieldasafunctionofmaturityforrecentlyissuedcouponbondssellingatornearparvalueTypicallypublishedbythefinancialpressBondPricing:

TwoTypesofYieldCurves?2021McGraw-HillEducation15-8Considertwo2-yearbondstrategies:Buythe2-yearzeroofferinga2-yearYTMof6%andholdituntilmaturityFacevalueis$1,000,soitispurchasedtodayfor$1,000/(1.06)2=$890andmaturesintwoyearsto$1,000Total2-yeargrowthfactoris$1,000/$890=1.1236Investthesame$890ina1-yearzero-couponbondwithaYTMof5%anduponmaturityreinvesttheproceedsinanother1-yearbondTheYieldCurveunderCertainty?2021McGraw-HillEducation15-9Two2-YearInvestmentPrograms?2021McGraw-HillEducation15-10SpotrateTheratethatprevailstodayforatimeperiodcorrespondingtothezero’smaturityShortrateAppliesforagiventimeinterval(e.g.,oneyear)ReferstotheinterestrateforthatintervalavailableatdifferentpointsintimeSpotRatesandShortRates?2021McGraw-HillEducation15-11MultiyearcumulativereturnsonallcompetingbondsshouldbeequalWhataboutHPRsovershorterperiods,suchasoneyear?Inaworldofcertainty,allbondsmustofferidenticalreturns,orinvestorswillflocktothehigher-returnsecurities,biddinguptheirprices,andreducingtheirreturnsHolding-PeriodReturns?2021McGraw-HillEducation15-12ShortRatesversusSpotRates?2021McGraw-HillEducation15-13rn=shortrateinyearnyn=YTMofazero-couponbondwithann-period maturityForwardRates?2021McGraw-HillEducation15-14

TheforwardinterestrateisaforecastofafutureshortrateRatefor4-yearmaturity=8%Ratefor3-yearmaturity=7%ForwardRatesContinued?2021McGraw-HillEducation15-15Theinvestorwantstoinvestfor1yearBuythe2-yearbondtodayandplantosellitattheendofthefirstyearfor$1000/1.06=$943.40orBuythe1-yearbondtodayandholdtomaturityWhatifnextyear’sinterestratediffersfrom6%?Theactualreturnonthe2-yearbondisuncertain!InterestRateUncertaintyand

ForwardRates?2021McGraw-HillEducation15-16Investorsrequireariskpremiumtoholdalonger-termbondThisliquiditypremiumcompensatesshort-terminvestorsfortheuncertaintyaboutfuturepricesInterestRateUncertaintyand

ForwardRatesContinued?2021McGraw-HillEducation15-17ExpectationsHypothesisTheorySimplesttheoryofthetermstructureStatesforwardrateequalsmarketconsensusexpectationoffutureshortinterestratef2=E(r2)

andliquiditypremiumsarezeroLiquidityPreferenceTheoryLong-termbondsaremoreriskyf2>E(r2)Theexcessoff2overE(r2)

istheliquiditypremiumPredictedtobepositiveYieldcurvehasanupwardbiasbuiltintothelong-termratesbecauseoftheliquiditypremiumTheoriesofTermStructure?2021McGraw-HillEducation15-18YieldCurveExamples

(1of2)?2021McGraw-HillEducation15-19PanelA:ConstantExpectedShortRate.LiquidityPremiumof1%.PanelB:DecliningExpectedShortRates.IncreasingLiquidityPremiums.YieldCurveExamples

(2of2)?2021McGraw-HillEducation15-20PanelD:IncreasingExpectedShortRates.IncreasingLiquidityPremiums.PanelC:DecliningExpectedShortRates.ConstantLiquidityPremiums.Yieldcurvereflectsexpectationsoffutureshortrates,butalsoreflectsotherfactorssuchasliquiditypremiumsAnupwardslopingcurvecouldindicate:Ratesareexpectedtoriseand/orInvestorsrequirelargeliquiditypremiumstoholdlongtermbondsInterpretingtheTermStructure

(1of2)?2021McGraw-HillEducation15-21TheyieldcurveisagoodpredictorofthebusinesscycleLong-termratestendtoriseinanticipationofeconomicexpansionInvertedyieldcurvemayindicatethatinterestratesareexpectedtofalla