金融學（第四版）課件：The Structure of Interest Rates

TheStructureofInterestRates

2FromOneInterestRatetoManyNumeroustypesoffinancialclaimsaretradedinfinancialmarketsInterestratesgenerallymoveupanddowntogether3FromOneInterestRatetoManyTherearefourprimarydeterminantsoftherelationshipsamonginterestratestermtomaturitycreditriskliquiditytaxtreatment4TermtoMaturityThemajorcharacteristicdistinguishingonetypeofTreasurysecurityfromanotheristhetermtomaturityTreasurybillshaveshorttermstomaturityofoneyearorlessTreasurynotesandbondshavelongmaturitiesofoneyearormore5TermtoMaturityThepatternofrelationshipsamonginterestratesandthetimetomaturityarereferredtoinfinancialmarketsasthetermstructureofinterestrates6TheYieldCurveAyieldcurvevisuallyrepresentsthetermstructureofinterestratesshowstherelationshipbetweeninterestrates(yields)onparticularfinancialinstruments(securities)andtheirtermstomaturityEachtypeofassetisrepresentedonasingleyieldcurvecontrolsforfactorsotherthantermtomaturity7InterestRatesonTreasurySecurities8YieldCurves9TheExpectationsTheoryTheexpectationstheorypostulatesthattheyieldcurveisdeterminedbyborrowers’andlenders’expectationsoffutureinterestrateschangesintheslope(shape)ofthecurveresultfromchangesintheseexpectations10ExampleSupposeyouhavefundstolendforatwo-yearperiodandthecurrentyieldoneaone-yearbill(i1)is5%andthecurrentyieldonatwo-yearnote(i2)is5.99%Supposeyouexpectthattheyieldonone-yearsecurities(ie1)willbe7%oneyearfromnow11ExampleYouhavetwooptionsbuyaone-yearsecuritytodayandanotheroneyearfromnowbuyatwo-yearsecuritytodayWhichoptionwillgiveyouahigherexpectedrateofreturn?12ExampleTocalculatetheexpectedreturnofthefirstoption,wefindthegeometricaverageofthetworatesweassumethattheinterestearnedduringthefirstyearwillearninterestduringthesecondyear13ExampleThelongrate(i2)canbecalculatedas(1+i2)=[(1+i2)(1+ie1)]1/2i2=[(1+i1)(1+ie1)]1/2–1i2=[(1.05)(1.07)]1/2–1=5.99%Thisistherateofthetwo-yearsecurityYouwillbeindifferentbetweenthetwooptions14HypotheticalYieldCurveTermtoMaturityYieldtoMaturity(percent)1525.99yieldcurve15TheExpectationsTheorySupposethatexpectationsaboutfuturerateschangesothatie1

risesfrom7to9percent(1+i2)=[(1+i2)(1+ie1)]1/2i2=[(1+i1)(1+ie1)]1/2–1i2=[(1.05)(1.09)]1/2–1=6.98%16TheExpectationsTheoryYouwillnolongerbeindifferentbetweenthetwooptionsyouandotherswillwantshort-termsecuritiesthosewhoownlong-termsecuritieswillwanttosellthemandbuyshort-termsecuritiesthepriceoflong-termsecuritieswillfallandtheiryieldswillrisethiswillcontinueuntilthelongraterisesto6.98%17TheExpectationsTheoryTheinterestratechangedasaresultofachangeintheinterestrateexpectationsofthelenderaffectedthedemandforsecuritiesTheexpectationsoftheborrowerarealsoimportant18TheExpectationsTheoryWhenborrowersbelievethattheaverageofcurrentandexpectedfutureshort-termsecuritiesisgreaterthantherateonlong-termsecurities,theywillincreasetheirsupplyoflong-termsecuritiesthiswilllowerthepriceofexistinglong-termsecuritiesthiswillraisethelong-terminterestrate19TheExpectationsTheoryIfexpectationsaboutfuturerateschangesuchthatfutureratesareexpectedtobehigher,theyieldcurvewillshiftthelongratewillriserelativetotheshortrateandtheyieldcurvewillgetsteeper20NewHypotheticalYieldCurveTermtoMaturityYieldtoMaturity(percent)155.99originalyieldcurve2newyieldcurve6.9821TheExpectationsTheoryWecansolvefortheinterestrateexpectedtoprevailinthefuturebylookingatthecurrentstructureofinterestrates(1+i2)=[(1+i1)(1+ie1)]1/2(1+i2)2={[(1+i1)(1+ie1)]1/2}2(1+i2)2=(1+i1)(1+ie1)(1+i2)2/(1+i1)=(1+ie1)ie1=[(1+i2)2/(1+i1)]–122AlternativeYieldCurveShapesWhenarisingyieldcurveisobservedinthemarket,theexpectedshort-terminterestrate(ies)isexpectedtoriseabovecurrentshortrates(is)Aflatyieldcurveimpliesthatinterestratesareexpectedtoremainconstant(ies=is)Anegativelyslopedyieldcurveimpliesthatinterestratesareexpectedtodecline(ies<is)23AlternativeYieldCurveShapesYieldtoMaturityTermtoMaturityYieldtoMaturityTermtoMaturityARiseExpectedinInterestRates(ies>is)YieldtoMaturityTermtoMaturityNoChangeExpectedinInterestRates(ies=is)ADeclineExpectedinInterestRates(ies<is)24DeterminingInterestRateExpectationsRememberthattheinterestrateisdeterminedbyseveralsupplyanddemandfactorsThismustmeanthattheexpectedshort-terminterestratemustbedeterminedbyexpectationsofY,M,andpe25DeterminingInterestRateExpectationsApositively-slopedyieldcurvereflectsexpectationsofrisinginterestratesfutureincreasesinincomerisinginflationexpectationsareductioninthefuturegrowthrateofthemoneysupplyThus,apositively-slopedyieldcurveshouldoccuratabusinesscycletroughandduringthefirsthalfoftherecovery26DeterminingInterestRateExpectationsAnegatively-slopedyieldcurvereflectsexpectationsoffallinginterestratesfuturedeclinesinincomefallinginflationexpectationsanincreaseinthefuturegrowthrateofthemoneysupplyThus,anegatively-slopedyieldcurveshouldoccuratabusinesscyclepeakandduringtheearlypartofarecession27NecessaryModificationstotheExpectationsTheoryOverthelast50years,yieldcurveshavealmostalwaysbeenpositivelyslopeddofinancialmarketparticipantsalwaysexpectshort-terminterestratestorise?Borrowersandlendersmaynotbeindifferentbetweenshort-andlong-termsecuritiesmanyborrowersandlendershavepreferredhabitats28NecessaryModificationstotheExpectationsTheoryResearchsuggeststhatinvestorsmaybewillingtoswitchpreferredhabitatsfromshort-termtolonger-termfinancialclaimsiftheyareprovidedaliquiditypremiumanextrareturnrequiredtoinducelenderstolendlongtermratherthanshorttermthesizeofthepremiumispresumedtorisewiththetermtomaturity29NecessaryModificationstotheExpectationsTheorySupposethatthecurrentshortrateandtheexpectedshortrateareboth5%accordingtotheexpectationstheory,theyieldcurvewouldbeflatIftheissueroflong-termbondsmustofferaninterestpremiumtogetinvestorstobuythem,theyieldcurveisactuallyupward-sloping30TheRoleofLiquidityPremiumsTermtoMaturityYieldtoMaturity(percent)YieldCurveBasedonExpectations(ies=is)LiquidityPremiumObservedYieldCurve=Expectations(ies=is)+LiquidityPremium31NecessaryModificationstotheExpectationsTheoryWecansummarizetherelationshipbetweenlong-terminterestrates(il),short-terminterestrates(is),andtheliquiditypremium(l)32CreditRiskCreditriskreferstotheprobabilityofadebtornotpayingtheprincipalorinterestdueonanoutstandingdebtThreemajorcredit-ratingagenciesevaluateaborrower’screditriskandassigntheborrowertoaparticularriskclassStandard&Poor’sMoody’sFitchInvestorsService33CreditRiskInthecaseofbusinessfirms,thecredit-ratingagenciesexamineseveralthingsthepatternofrevenuesandcoststhedegreeofleverage(dependenceonborrowedfunds)thepasthistoryofdebtredemptionthevolatilityoftheindustry34CreditRiskInthecaseofstateandlocalgovernments,thecredit-ratingagenciesexamineseveralthingsthetaxbasethelevelofoutstandingdebtthecurrentandexpectedbudgetconditiongrowthinspending35CreditRatings36CreditRiskInvestorsaregenerallyriskaversetheymustberewardedorcompensatedwithextrainterestforacceptingmoreriskthisextrareturniscalledariskpremiumthesizeincreaseswiththeriskinessoftheborrower37TaxabilityInterestincomeearnedfromsecuritiesissuedbystateandlocalgovernmentsisexemptfromfederalincometaxafter-taxyield=i–it=i(1–t)wheretisthemarginaltaxrate

theratepaidonthelastdollarofincomethetaxpayerearns38TaxabilityIngeneral,wewouldexpectthesubstitutionofsecuritiestoresultintheyieldonmunicipalsbeingapproximatelyequaltotheyieldonasimilarlyratedtaxablecorporatebondminustheportionthatistaxedaway39TaxabilityThemarketwillgravitatetotheratethatmakesthe“average”taxpayerindifferentbetweenmunicipalsandsimilarlyratedcorporatebondsindividualsinhightaxbracketswillbeespeciallyattractedtomunicipalsbecausetheyaresubjecttoataxrateabovetheaveragemarginalrate40SummaryofMajorPointsTheyieldcurveisagraphicalrepresentationoftherelationshipbetweeninterestrates(yields)onaparticularsecurityanditstermtomaturityavisualdepictionofthetermstructureofinterestratesAuniquecurveexistsforeachtypeoffinancialasset41SummaryofMajorPointsThemostwidelyacceptedexplanationfortheshape(slope)andposition(level)oftheyieldcurveistheexpectationstheorypostulatesthatthelong-termrateisthegeometricaverageofthecurrentshort-termrateandtheshort-termratesexpectedtoprevailoverthetermtomaturityofthesecuritytakescompoundingintoeffect42SummaryofMajorPointsTheslopeoftheyieldcurvedependsontheinterestratesexpectedtoprevailonshort-termsecuritiesinthefutureapositivelyslopedcurvereflectsexpectationsofariseinfutureshort-termratesanegativelyslopedcurvereflectsexpectationsofafallinfutureshort-termrates43SummaryofMajorPointsExpectationsaboutfutureshort-termratesdependonexpectationsaboutfu