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CHAPTER10TheTermStructureofInterestRates
15-2Theyieldcurveisagraphthatdisplaystherelationshipbetweenyieldandmaturity.Informationonexpectedfutureshorttermratescanbeimpliedfromtheyieldcurve.OverviewofTermStructure
15-3Figure10.1TreasuryYieldCurves
15-4BondPricingYieldsondifferentmaturitybondsarenotallequal.Weneedtoconsidereachbondcashflowasastand-alonezero-couponbond.Bondstrippingandbondreconstitutionofferopportunitiesforarbitrage.Thevalueofthebondshouldbethesumofthevaluesofitsparts.
15-5Table10.1PricesandYieldstoMaturitiesonZero-CouponBonds($1,000FaceValue)
15-6Example10.1ValuingCouponBondsValuea3year,10%couponbondusingdiscountratesfromTable15.1:Price=$1082.17andYTM=6.88%6.88%islessthanthe3-yearrateof7%.
15-7TwoTypesofYieldCurvesPureYieldCurveThepureyieldcurveusesstrippedorzerocouponTreasuries.Thepureyieldcurvemaydiffersignificantlyfromtheon-the-runyieldcurve.On-the-runYieldCurveTheon-the-runyieldcurveusesrecentlyissuedcouponbondssellingatornearpar.Thefinancialpresstypicallypublisheson-the-runyieldcurves.
15-8YieldCurveUnderCertaintySupposeyouwanttoinvestfor2years.Buyandholda2-yearzero-or-Rolloveraseriesof1-yearbondsEquilibriumrequiresthatbothstrategiesprovidethesamereturn.
15-9Figure10.2Two2-YearInvestmentPrograms
15-10YieldCurveUnderCertaintyBuyandholdvs.rollover:Nextyear’s1-yearrate(r2)isjustenoughtomakerollingoveraseriesof1-yearbondsequaltoinvestinginthe2-yearbond.
15-11SpotRatesvs.ShortRatesSpotrate–theratethatprevailstodayforagivenmaturityShortrate–therateforagivenmaturity(e.g.oneyear)atdifferentpointsintime.Aspotrateisthegeometricaverageofitscomponentshortrates.
15-12ShortRatesandYieldCurveSlopeWhennextyear’sshortrate,r2,isgreaterthanthisyear’sshortrate,r1,theyieldcurveslopesup.Mayindicateratesareexpectedtorise.Whennextyear’sshortrate,r2,islessthanthisyear’sshortrate,r1,theyieldcurveslopesdown.Mayindicateratesareexpectedtofall.
15-13Figure10.3ShortRatesversusSpotRates
15-14fn=one-yearforwardrateforperiodnyn=yieldforasecuritywithamaturityofnForwardRatesfromObservedRates
15-15Example10.4ForwardRatesTheforwardinterestrateisaforecastofafutureshortrate.Ratefor4-yearmaturity=8%,ratefor3-yearmaturity=7%.
15-16InterestRateUncertaintySupposethattoday’srateis5%andtheexpectedshortrateforthefollowingyearisE(r2)=6%.Thevalueofa2-yearzerois:Thevalueofa1-yearzerois:
15-17InterestRateUncertaintyTheinvestorwantstoinvestfor1year.Buythe2-yearbondtodayandplantosellitattheendofthefirstyearfor$1000/1.06=$943.40.0r-Buythe1-yearbondtodayandholdtomaturity.
15-18InterestRateUncertaintyWhatifnextyear’sinterestrateismore(orless)than6%?Theactualreturnonthe2-yearbondisuncertain!
15-19InterestRateUncertaintyInvestorsrequireariskpremiumtoholdalonger-termbond.Thisliquiditypremiumcompensatesshort-terminvestorsfortheuncertaintyaboutfutureprices.
15-20ExpectationsLiquidityPreferenceUpwardbiasoverexpectationsTheoriesofTermStructure
15-21ExpectationsTheoryObservedlong-termrateisafunctionoftoday’sshort-termrateandexpectedfutureshort-termrates.fn=E(rn)andliquiditypremiumsarezero.
15-22Long-termbondsaremorerisky;therefore,fngenerallyexceedsE(rn)TheexcessoffnoverE(rn)istheliquiditypremium.Theyieldcurvehasanupwardbiasbuiltintothelong-termratesbecauseoftheliquiditypremium.LiquidityPremiumTheory
15-23Figure10.4YieldCurves
15-24Figure10.4YieldCurves
15-25InterpretingtheTermStructureTheyieldcurvereflectsexpectationsoffutureinterestrates.Theforecastsoffutureratesarecloudedbyotherfactors,suchasliquiditypremiums.Anupwardslopingcurvecouldindicate:RatesareexpectedtoriseAnd/orInvestorsrequirelargeliquiditypremiumstoholdlongtermbonds.
15-26InterpretingtheTermStructureTheyieldcurveisagoodpredictorofthebusinesscycle.Longtermratestendtoriseinanticipationofeconomicexpansion.Invertedyieldcurvemayindicatethatinterestratesareexpectedtofallandsignalarecession.
15-27Figure10.6TermSpread:Yieldson10-yearvs.90-dayTreasurySecurities
15-28ForwardRatesasForwardContractsIngeneral,forwardrateswillnotequaltheeventuallyrealizedshortrateStillanimportantconsiderationwhentryingtomakedecisions:Lockinginloanrates
15-29Figure10.7EngineeringaSyntheticForwardLoan
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