金融市场与机构 Jeff Madura 03

3StructureofInterestRates©2003South-Western/ThomsonLearningChapterObjectivesLearnwhyindividualinterestratesdifferorwhysecuritypricesvaryorchangeAnalyzetheoriesexplainingwhyratesvarybytermormaturity,calledthetermstructureofinterestratesFactorsAffectingSecurityYieldsRisk-averseinvestorsdemandhigheryieldsForaddedriskinessRiskisassociatedwithvariabilityOfreturnsIncreasedriskinessgenerateslowersecuritypricesorhigherinvestorrequiredratesofreturnFactorsAffectingSecurityYieldsSecurityyieldsandpricesareaffectedbylevelsandchangesin:Defaultrisk(alsocalledCreditRisk)LiquidityTaxstatusTermtomaturitySpecialcontractprovisionssuchasembeddedoptionsFactorsAffectingSecurityYieldsBenchmark—risk-freetreasurysecuritiesforgivenmaturityDefaultriskpremium=riskysecurityyield–treasurysecurityyieldofsamematurityDefaultriskpremium=marketexpecteddefaultlossrateRatingagenciessetdefaultriskratingsAnticipatedoractualratingschangesimpactsecuritypricesandyieldsFactorsAffectingSecurityYieldsTheLiquidityofasecurityaffectstheyield/priceofthesecurityAliquidinvestmentiseasilyconvertedtocashAtminimumtransactionscostInvestorspaymore(loweryield)forliquidinvestmentLiquidityisassociatedwithshort-term,lowdefaultrisk,marketablesecuritiesFactorsAffectingSecurityYieldsTaxstatusofincomeorgainonsecurityimpactsthesecurityyieldInvestorconcernedwithafter-taxreturnoryieldInvestorsrequirehigheryieldsForhighertaxedsecuritiesFactorsAffectingSecurityYieldsYat=Ybt(1–

T)Where:Yat

=after-taxyieldYbt

=before-taxyieldT=investor’smarginaltaxrateFactorsAffectingSecurityYieldsExample:ataxablesecuritythatoffersabefore-taxyieldof14percent.Theinvestor’staxrateis20percent.Calculatetheafter-taxyield.

Yat

=14%(1–0.2) =11.2%Thefullytaxablepre-taxequivalentcorporatebondfora11.2%municipalbondis:

Ybt

=11.2%/(1–.2)=14%FactorsAffectingSecurityYieldsTermtomaturityInterestratestypicallyvarybymaturity.Thetermstructureofinterestratesdefinestherelationshipbetweenmaturityandyield.TheYieldCurveistheplotofcurrentinterestyieldsversustimetomaturity.YieldCurveAnupward-slopingyieldcurveindicatesthatTreasurySecuritieswithlongermaturitiesofferhigherannualyieldsYield%TimetoMaturityYieldCurveShapesNormalLevelorFlatInvertedFactorsAffectingSecurityYieldsSpecialProvisionsCallFeature:enablesborrowertobuybackthebondsbeforematurityataspecifiedpriceCallfeaturesareexercisedwheninterestrateshavedeclinedInvestorsdemandhigheryieldoncallablebonds,especiallywhenratesareexpectedtofallinthefutureFactorsAffectingSecurityYieldsSpecialprovisionsConvertiblebondsConvertibilityfeatureallowsinvestorstoconvertthebondintoaspecifiednumberofcommonstocksharesInvestorswillacceptaloweryieldforconvertiblebondsbecauseinvestorreturnsincludeexpectedreturnonequityparticipationEstimatingtheAppropriateYieldTheappropriateyieldtobeofferedonadebtsecurityisbasedontherisk-freerateforthecorrespondingmaturityplusadjustmentstocapturevarioussecuritycharacteristicsYn=

Rf,n+DP+LP+TA+CALLP+CONDEstimatingtheAppropriateYieldYn

=Rf,n+DP+LP+TA+CALLP+CONDWhere:Yn

=yieldofann-daysecurityRf,n =yieldonann-dayTreasury (risk-free)securityDP =defaultpremium(creditrisk)LP =liquiditypremiumTA =adjustmentfortaxstatusCALLP =callfeaturepremiumCOND =convertibilitydiscountTheTermStructureofInterestRatesPureExpectationsTheoryLiquidityPremiumTheorySegmentedMarketsTheoryTheoriesExplainingShapeofYieldCurveTheTermStructureofInterestRatesPureExpectationsTheoryLong-termratesareaverageofcurrentshort-termandexpectedfutureshort-termratesYieldcurveslopereflectsmarketexpectationsoffutureinterestratesInvestorsselectmaturitybasedonexpectationsTheTermStructureofInterestRatesPureExpectationsTheoryAssumesinvestorhasnomaturitypreferencesandtransactioncostsarelowLong-termratesareaveragesofcurrentshortratesandexpectedshortratesForwardrate:market’sforecastofthefutureinterestrateTheTermStructureofInterestRatesExpectedhigherinterestratelevelsExpansivemonetarypolicyExpandingeconomyExpectedlowerinterestratelevelsTightmonetarypolicyRecessionsoon?Upward-SlopingYieldCurveDownward-SlopingYieldCurveTheTermStructureofInterestRatesLiquidityPremiumTheoryInvestorsprefershort-term,moreliquid,securitiesLong-termsecuritiesandassociatedrisksaredesirableonlywithincreasedyieldsExplainsupward-slopingyieldcurveWhencombinedwiththeexpectationstheory,yieldcurvescouldstillbeusedtointerpretinterestrateexpectationsTheTermStructureofInterestRatesSegmentedMarketsTheoryTheoryexplainingsegmented,brokenyieldcurvesAssumesinvestorshavematuritypreferenceboundaries,e.g.,short-termvs.long-termmaturitiesExplainswhyratesandpricesvarysignificantlybetweencertainmaturitiesTheTermStructureofInterestRatesUsesofthetermstructureForecastinterestratesThemarketprovidesaconsensusforecastofexpectedfutureinterestratesExpectationstheorydominatestheshapeoftheyieldcurveForecastrecessionsFlatorinvertedyieldcurveshavebeenagoodpredictorofrecessions.SeeExhibit3.14.InvestmentandfinancingdecisionsLenders/borrowersattempttotimeinvestment/financingbasedonexpectationsshownbytheyieldcurveRidingtheyieldcurveTimingofbondissuanceExhibit3.14YieldCurveasaSignalforRecessions76543210–1–2–3–41955196019651970197519801985199019952000*Thegeneralshapeoftheyieldcurveismeasuredasthedifferentialbetweenannualized10-yearandthree-monthinterestrates.Recessionaryperiodsareshaded.Year2001InterestRateDifferential(10-YearRateMinusThree-MonthRate)TreasuryDebtManagementandtheYieldCurveU.S.TreasuryattemptstofinancefederaldebtatthelowestoverallcostTreasuryusesamixtureofBills,Notes,andBondstofinanceperiodicdeficitsandrefinanceoutstandingsecuritiesTreasuryfocusesonshort-termissuance,phasingout30-yearbondsTreasury10-yearbondnowthestandardissueLeavethelong-termissuancetoprivateissuersHistoricReviewoftheTermStructureYieldcurveslevelsandshapesatvarioustimesindicate:InflationexpectationsLevelofeconomicactivityorphaseofbusinesscycleMonetarypolicyatthetimeUsuallyhighpositiveslopeinshort-termRepresentsdemandforliquidityShort-termsecuritiesdesired;higherprices;lowerratesShort-termsecuritiesprovideliquiditywithmaturityExhibit3.17YieldCurvesatVariousPointsinTime051015202530171615141312111098765234February17,1982January2,1985Oct