Chapter6TheRiskandTermStructureofInterestRates©2005PearsonEducationCanadaInc.©2005PearsonEducationCanadaInc.6-2RiskStructureofLong-TermBondsinCanada©2005PearsonEducationCanadaInc.6-3IncreaseinDefaultRiskonCorporateBonds©2005PearsonEducationCanadaInc.6-4AnalysisofFigure6-2:IncreaseinDefaultRiskonCorporateBondsCorporateBondMarket1.Reoncorporatebonds,Dc,Dcshiftsleft2.Riskofcorporatebonds,Dc,Dcshiftsleft3.Pc,icCanadaBondMarket4.RelativeReonCanadabonds,DT,DTshiftsright5.RelativeriskofCanadabonds,DT,DTshiftsright6.PT,iTOutcome:Riskpremium,ic–iT,rises©2005PearsonEducationCanadaInc.6-5BondRatings©2005PearsonEducationCanadaInc.6-6CorporateBondsBecomeLessLiquidCorporateBondMarket1.LessliquidcorporatebondsDc,Dcshiftsleft2.Pc,icCanadaBondMarket1.RelativelymoreliquidCanadabonds,DT,DTshiftsright2.PT,iTOutcome:Riskpremium,ic–iT,risesRiskpremiumreflectsnotonlycorporatebonds’defaultrisk,butalsolowerliquidity©2005PearsonEducationCanadaInc.6-7TaxAdvantagesofMunicipalBondsintheUnitedStates©2005PearsonEducationCanadaInc.6-8AnalysisofPreviousFigure:TaxAdvantagesofMunicipalBondsMunicipalBondMarketintheUnitedStates1.TaxexemptionraisesrelativeRETeonU.S.municipalbonds,Dm,Dmshiftsright2.Pm,imU.S.TreasuryBondMarket1.RelativeRETeonTreasurybonds,DT,DTshiftsleft2.PT,iTOutcome:imiT6-9TermStructureFactstobeExplained1.Interestratesfordifferentmaturitiesmovetogetherovertime2.Yieldcurvestendtohavesteepupwardslopewhenshortratesarelowanddownwardslopewhenratesarehigh3.YieldcurveistypicallyupwardslopingThreeTheoriesofTermStructure1.ExpectationsTheory2.SegmentedMarketsTheory3.LiquidityPremium(PreferredHabitat)TheoryA.ExpectationsTheoryexplains1and2,butnot3B.SegmentedMarketsexplains3,butnot1and2C.Solution:CombinefeaturesofbothExpectationsTheoryandSegmentedMarketsTheorytogetLiquidityPremium(PreferredHabitat)Theoryandexplainallfacts©2005PearsonEducationCanadaInc.©2005PearsonEducationCanadaInc.6-10InterestRatesonDifferentMaturityBondsMoveTogether©2005PearsonEducationCanadaInc.6-11YieldCurves©2005PearsonEducationCanadaInc.6-12ExpectationsHypothesisKeyAssumption:BondsofdifferentmaturitiesareperfectsubstitutesImplication:RETeonbondsofdifferentmaturitiesareequalInvestmentstrategiesfortwo-periodhorizon1.Buy$1ofone-yearbondandwhenitmaturesbuyanotherone-yearbond2.Buy$1oftwo-yearbondandholditExpectedreturnfromstrategy2(1+i2t)(1+i2t)–11+2(i2t)+(i2t)2–1=11Since(i2t)2isextremelysmall,expectedreturnisapproximately2(i2t)©2005PearsonEducationCanadaInc.6-13ExpectedReturnfromStrategy1(1+it)(1+iet+1)–11+it+iet+1+it(iet+1)–1=11Sinceit(iet+1)isalsoextremelysmall,expectedreturnisapproximatelyit+iet+1Fromimplicationaboveexpectedreturnsoftwostrategiesareequal:Therefore2(i2t)=it+iet+1Solvingfori2tit+iet+1i2t=26-14ExpectedReturnfromStrategy1Moregenerallyforn-periodbond:it+iet+1+iet+2+...+iet+(n–1)int=nInwords:Interestrateonlongbond=averageshortratesexpectedtooccuroverlifeoflongbondNumericalexample:One-yearinterestrateoverthenextfiveyears5%,6%,7%,8%and9%:Interestrateontwo-yearbond:(5%+6%)/2=5.5%Interestrateforfive-yearbond:(5%+6%+7%+8%+9%)/5=7%Interestrateforonetofiveyearbonds:5%,5.5%,6%,6.5%and7%.©2005PearsonEducationCanadaInc.©2005PearsonEducationCanadaInc.6-15ExpectationsHypothesisandTermStructureFactsExplainswhyyieldcurvehasdifferentslopes:1.Whenshortratesexpectedtoriseinfuture,averageoffutureshortrates=intisabovetoday’sshortrate:thereforeyieldcurveisupwardsloping2.Whenshortratesexpectedtostaysameinfuture,averageoffutureshortratesaresameastoday’s,andyieldcurveisflat3.OnlywhenshortratesexpectedtofallwillyieldcurvebedownwardslopingExpectationsHypothesisexplainsFact1thatshortandlongratesmovetogether1.Shortraterisesarepersistent2.Ifittoday,iet+1,iet+2etc.averageoffutureratesint3.Therefore:itint,i.e.,shortandlongratesmovetogether©2005PearsonEducationCanadaInc.6-161.Whenshortratesarelow,theyareexpectedtorisetonormallevel,andlongrate=averageoffutureshortrateswillbewellabovetoday’sshortrate:yieldcurvewillhavesteepupwardslope2.Whenshortratesarehigh,theywillbeexpectedtofallinfuture,andlongratewillbebelowcurrentshortrate:yieldcurvewillhavedownwardslopeDoesn’texplainFact3thatyieldcurveusuallyhasupwardslopeShortratesaslikelytofallinfutureasrise,soaverageoffutureshortrateswillnotusuallybehigherthancurrentshortrate:therefore,yieldcurvewillnotusuallyslopeupwardExplainsFact2thatyieldcurvestendtohavesteepslopewhenshortratesarelowanddownwardslopewhenshortratesarehigh©2005PearsonEducationCanadaInc.6-17SegmentedMarketsTheoryKeyAssumption:BondsofdifferentmaturitiesarenotsubstitutesatallImplication:Marketsarecompletelysegmented:interestrateateachmaturitydeterminedseparatelyExplainsFact3thatyieldcurveisusuallyupwardslopingPeopletypicallyprefershortholdingperiodsandthushavehigherdemandforshort-termbonds,whichhavehigherpriceandlowerinterestratesthanlongbondsDoesnotexplainFact1orFact2becauseassumeslongandshortratesdeterminedindependently©2005PearsonEducationCanadaInc.6-18LiquidityPremium(PreferredHabitat)TheoriesKeyAssumption:Bondsofdifferentmaturitiesaresubstitut