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1、InterestRates1.Definition2.FluctuationofinterestratesShiftsonDemandShiftsonSupply3.Typesofinterestrates4.AnalysisofBondValuation5.RiskandTermStructureofInterestRates(TSIR)5.1DeterminantsofRiskStructure(RSIR)5.2TSIR(YieldCurve).Theories:A)PureExpectationsTheoryB)MarketSegmentationTheoryC)LiquidityThe
2、ory6.PredictivePoweroftheYieldCurve6.1Futureinterestrates6.2Economicgrowth7.Conclusions1资本市场和金融机构2InterestRa1.InterestRate(i)i=CostofborrowingorlendingmoneyItplaysapivotalrolein:theInvestmentandFinancingofassets(real,financial)byindividuals,companies,governmentsandFItheperformanceoftheeconomyDetermi
3、nedintheDebtMarkets(supplyanddemand)andbygovernmentintervention.lCentralBankMonetarypolicy(i,M)Isthereanappropriatelevelofi?2资本市场和金融机构2InterestRaInterestRatelHowtheinterestratesaredetermined?lWhatexplainsthefluctuationofinterestrates?lMostaccuratemeasureofinterestrate:YieldtomaturityExampleappliedto
4、bondvaluation3资本市场和金融机构2InterestRaDeterminationofInterestRate(i)Approaches1)AnalysisofDemandofloanablefundsandSupplyofloanablefunds2)AnalysisofDemandforandsupplyofbondsSupplyofloanablefundsbyhouseholdsandfirms.Thehigherthei thehigherthequantityofloanablefundsofferedDemandofloanablefundsbyhouseholdsa
5、ndfirmsReasonsforConsumer?ForFirms?TotalDemand=DemandbyhouseholdsandfirmsDeterminantsoftheDemandandSupply4资本市场和金融机构2InterestRaSupplyandDemandforLoanableFundsInterestRate(i)SupplyQuantity of loanable funds DemandQ*i*5资本市场和金融机构2InterestRa Whatdeterminesthesupplyofloanablefunds?Thesupplyofloanablefunds
6、isdeterminedbytheinterestrateofferedtosavers.Ahigherinterestrateinduceshouseholdstoconsumelesstoday(save)infavorofgreaterconsumptioninthefuture.Firmalsomayhaveexcessofcashthatmaybeloaned(e.g.,purchaseofotherfirmsbondissue)insteadofinvested(realassets)becauseofthenonavailabilityofprojectswith+NPV. Wh
7、atdeterminesthedemandforloanablefunds?Itcomesfrom:consumerswhowishtoconsumemoretodaythantomorrow,individuals,financialandnon-financialfirmstoinvestinfinancialassetsfinancialandnon-financialfirmstoinvestinrealassetsDemanddependsontheinterestrateatwhichthesethreegroupscanborrow.Thelowertheinterestrate
8、thehigherthedemandandvice-versa.6资本市场和金融机构2InterestRa2.Fluctuationofinterestrates Whatmightcausethesupplyordemandforloanablefundstoshift,andhowwouldthataffectinterestrates?Factorsthatshiftthedemandcurve.a)Recession:Itdecreasesdemandatallinterestrates,shiftingthedemandcurveinwardsandcausingtheequilib
9、riuminterestratetofall.Quantity ($)AB Interest Rate SDDiiQQ7资本市场和金融机构2InterestRab)Anincreaseofthegovernmentdeficit.C)Riseinexpectedinflationshiftsthedemandcurvetotheright.Sameas(b)NominalInterestrate=realinterestrate+rateofexpectedinflationD)increaseonthegrowthrateofpopulation.Sameas(b)e)Businesscyc
10、leexpansion.ExpectedincreaseineconomicgrowthSameas(b)iQ ($)DD SAB8资本市场和金融机构2InterestRaExamplesthatshifttheSupplycurvetotheright a)IncreasesinthemoneysupplybytheCentralBank,causingtheinterestratetofall.b)Increasesinrealpersonalincomemakepeoplemorewillingtomakeloans(e.g.depositsinbanksaccounts)c)Incre
11、aseintaxexemptfinancialinstruments.Note:ifweassumethatthecentralbankcontrolstheamountofmoneysupplyatfixedquantitytheSupplyCurveformoneySwouldbeaverticalline.iQ ($)SSAB9资本市场和金融机构2InterestRa3.VarietyofInterestRatesT-billrate(1year)Discountrate:CentralBankchargestobanksInCanadaiscalledtheOvernightBankR
12、ateCommercialpaperrate:ShorttermdiscountbondsPrimerate:ShorttermRatechargedtolargestfirms(creditworthy)Corporatebondrate:LongtermratefordebtissuedbyfirmsLIBOR:RatethatlargestcreditworthyinternationalbanksdealinginEurodollarschargeeachotherforlargeloans.Fixedrates,floatingrates,etc.Theydifferbecauseo
13、fthedifferencesinmaturity,riskoflenders10资本市场和金融机构2InterestRa4. AnalysisofBondValuationItshedslightontheconceptofinterestrate.Bond.Contractinwhichaborroweragreestopayabondholder(thelender)aspecificamountofmoneyinaperiodoftime.Example:Howmuchwouldyoupayforabondthatpromisesacouponrateof$100eachyearfor
14、aperiodof10yearsandtheprincipalamountof$1,000(parvalue=nominalvalue=facevalue)attheendofthe10thyear?Assumei=5%,i=10%,i=15%11资本市场和金融机构2InterestRaFormulaP=Coupon/(1+i)+Coupon/(1+i)2+Coupon/(1+i)10+FaceValue/(1+i)10C=$100C=$100C=$100P=?123 9 10C=$100$100 + $1,000Ifi=5%P=$100/(1+0.05)+$100/(1+0.05)2+$10
15、0/(1+0.05)10+$1,000/(1+0.05)10=$1,386i=10%P=$100/(1+0.10)+$100/(1+0.10)2+$100/(1+010)10+$1,000/(1+0.010)10=$1,000i=15%P=$100/(1+0.15)+$100/(1+0.15)2+$100/(1+015)10+$1,000/(1+0.015)10=$749Whichi(discount rateoryieldtomaturity)fromabovemakesthepresentvalueofabondspaymentsequaltoitscurrentpriceP?A:?i =
16、 5%12资本市场和金融机构2InterestRaYTM=InterestratethatequatesthePresentValueofpaymentsreceivedfromadebtinstrument(e.g.,bond)withitsvaluetodayP.Alternatively,istherateofinterestearnedonabondifitisheldtomaturity.TheYTMisthemostimportantandaccuratewayofcalculatinginterestrates.IfP=$1,386WhatistheYTM=i?$1,386=$1
17、00/(1+i)+$100/(1+i)2+$100/(1+i)10+$1,000/(1+i)10=$1,000A:YTM=i=5%IfP=$1,000WhatistheYTM?YTM=10%IfP=$749WhatistheYTM?YTM=15%WhatistherelationshipbetweentheBondpriceandthei?Why?PriceofbondFig.Yieldtomaturityofabond=effectiveyieldonabond=i$1,00010%Interest Rate = i = YTM5% $1,386$74915%Scenarios:1.Assu
18、me you bought the bond in $1,000 and interest rates increased to 15%. Did you benefit? 2.Assume you bought a corporate bond and the credit rating of the firm is downgraded to junk (default)3. What is the expected effect in the interest rate (YTM)?13资本市场和金融机构2InterestRaPerpetuityBondpayingoutafixedam
19、ountofmoneyeachyearforever.ExampleTheCanadiangovernmentissuesabondthatwillpaytoperpetuity$50ayear.Iftheinterestrateis3%annual,a)whatisthebondworthtoday?b)Wouldyoubuythebondfor$1,500?ThepresentvalueofaperpetuityiseasilyobtainedasPDV=perpetuity/RA:EffectiveYield(YTM)onaBond(perpetuity)Percentagereturn
20、thatonereceivesbyinvestinginabondAssumepriceoftheperpetuityaboveis$1,666.67andyoureceiveaperpetualcouponrateof$50peryear.Whatistheeffectiveyieldrateorrateorreturn?A:Now,supposethecurrentinterestrateis4%.Wouldyoupay$1,666.67forthebond?14资本市场和金融机构2InterestRa5.RiskandTermStructureofInterestRatesVariety
21、ofdifferentinterestrate=f(maturity,risk,liquidity,taxes).I)Assumingvariousdebtinstruments(bonds)havesame maturity,theiriswilldifferbecauseofdifferences in risk.RiskStructureofInterestRates(RSIR).RSIRexpressestherelationsofinterestratesforvariousbondinstrumentswhosedeterminantsare(1)defaultrisk,(2)li
22、quidity,and(3)taxes (SeeFig.1,p.110,Miskhinetal.-LongTermBonds)II)Assumingvariousbondshavesame risktheirismaydifferbecauseofthedifferencesinmaturities.TermStructureofInterestRates(TSIR).TSIRexpressesthetherelationshipamongis(YTMs)onzerocoupondiscountbondswithdifferentmaturities.15资本市场和金融机构2InterestR
23、a5.1DeterminantsofRISKSTRUCTUREOFINTERESTRATES(RSIR)InterestratesoncorporatebondsarehigherthanthoseonCanadabonds(SeeFigure1)Reasons1.HigherDefaultRisk2.LowerLiquidity3.Taxconsiderationsonispayments.Canadian(Cdn)bondsaredefault-freebondsDifferenceinis=RiskPremium1.EffectofDefaultriskoninterestratesAs
24、sumeinitiallyacorporatebondswithnodefaultrisk,likeCanadabonds(withsamematurity).Possibilityofastrongrecessionincreasesthepossibilityofdefaultofcorporatebonds.WhatwilltheeffectbeoninterestratesofcorporatebondsandCanadabonds?Whatwillhappentotheriskpremiumofcorporatebonds?ii Price of bonds, PPQuantity
25、of Corporate Bonds Quantity of Canada Bonds(a) Corporate bond market (b) Default-free Cdn bond marketic1Pc1Pc2ic2PT2PT1iT2iT1iT2 ic2RiskPremium= ic2 - iT2Dc2Dc1ScDT1DT2STDecrease inInterest rate16资本市场和金融机构2InterestRaInvestmentadvisoryfirmsprovidersofdefaultriskinformationonbonds:StandardsandPoorsCan
26、ada,DominionBondRatingService.Investmentgrade-bonds(AAA)vs.Junkbonds(D)(SeeFig.3,p.113,Mishkinetal.)RiskpremiumonBBBcorporatebondrates(Corporates-CanadaSpread,1980-2001)17资本市场和金融机构2InterestRa2.EffectofLiquidityoninterestratesLiquidity.Abilitytobuyorsellanassetquicklyandinlargevolumewithoutsubstantia
27、llyaffectingtheassetsprice.Corporatebondsvs.CanadabondsWhichonesaremoreliquid?Spread?AssumeinitiallycorporatebondsandCanadabondsareequallyliquid,ceteris paribus.a)Whichevent(s)woulddecreasetheliquidityofcorporatebonds?Why?b)WhatwilltheeffectbeoninterestratesofcorporatebondsandCanadabonds?c)Whatwillh
28、appentotherisk(liquidity)premiumofcorporatebonds?Drawtheirrespectivegraphs(demandandsupplycurvesofCorporatesandCanadabonds).18资本市场和金融机构2InterestRa3.TaxConsiderationsHowdoestaxationaffecttheinterestrate(YTM)onbonds?Governmentbondsthatpaynotaxesyieldlowerinterestrates(e.g.,U.S.municipalbondsormunis).M
29、unisareadvantageousforhightax-bracketinvestors.Example:SupposeCharlieWhite(aUSinvestor)has2alternativestoinvesthissavings(say$1,000)1)investa$1,000facevaluemunithatsellsfor$,1000,withcouponpaymentsof$80.2)2)investa$1,000facevaluetaxablebondthatsellsfor$1,000andhasacouponpaymentof$120.Thetax-bracketi
30、s35%.a)Whichoptionshouldhechoose?Why?b)SupposeJaneRedisfacedwithsimilaroptionsbuthertax-bracketis30%.Whatoptionwouldbebestforher?c)DoesitmattertoknowthematurityofthebondstoobtaintheirYTM?19资本市场和金融机构2InterestRa5.2TermStructureofInterestRates(TSIR)TheTSIRreferstotherelationshipbetweenYTMandtermtomatur
31、ityforbondsofsame riskclass.TheYieldCurveisthegraphicalrepresentationoftheTSIR.TheYieldCurveshapecanbea)Upward-slopingLongTermisShortTermisb)FlatLongtermis=ShortTermisc)Downward-sloping(invertedyieldcurve)LTisShortTermisaverageoffutureSTratesisexpectedcurrentshorttermratesDownward-slopingLongTermisS
32、hortTermisaverageoffutureSTratesisexpectedcurrentshorttermratesFlatLongTermis=ShortTermisaverageoffutureSTratesisexpected=currentshorttermrates24资本市场和金融机构2InterestRaExpectedholding-periodyields(HPY)onbondsofallmaturities(withsamerisk)oughttobeaboutequal,thatis:1.HPY(1-yearbond)=HPY(2-yearbond)=HPY(n
33、-yearbond)2.Ifweknowtheone-yearHPY(commonlycalledyield)ontwobondsofn-1,andnmaturities,wecanobtainthemarketexpectationofthefutureshort-terminterestrateonyearn(alsocalledforwardrate).ImplicationsofExpectationsTheory25资本市场和金融机构2InterestRaExample-Ifone-yearbondsofferan8%annualyield(return)andtheprincipa
34、landinterestarereinvestedat10%attheendoffirstyearwhile-two-yearbondshaveanYTM(i,orannualyield,orcommonlycalledyield*)of8.995%,bothbondsmusthavesameholdingperiodyield(HPY),thatis:*Inpracticeyieldreferstoone-yearinterestrate.1.Two-yearHPYforbothtypesofbondsTwo-yearHPYof1-yearbonds=(1+0.08)(1+0.1)-1=0.
35、188or18.8%Two-yearHPYof2-yearbonds=(1.08995)(1.08995)-1=0.188or18.8% 2.One-yearHPY(commonlycalledyield)yieldof1-yearbonds=(1+0.08)(1+0.1)1/2-1=(1.188)0.51=0.08995or8.995%yieldof2-yearbonds=8.995%(given)IfitisnotgivenyoucanobtainitfromTwo-yearHPYof1-yearbondsYieldof2-yearbonds=(1+two-yearHPYof1-yearb
36、onds)1/2-1=(1.188)1/21=0.08995or8.995%.3.Theexpectedyeartwointerestrate,i2,(orforwardrate)isobtainedasfollows(1+yieldofoneyearbonds)1(1+i2)=(1+yieldoftwoyearsbonds)2(1+i2)=(1+yieldoftwoyearsbonds)2/(1+yieldofoneyearbonds)1=(1.08995)2/1.08-1=1.0999-1=9.999 10%26资本市场和金融机构2InterestRaGeneralizingGeneral
37、izing1.One-yearHPY(oryield)for1-yearbondsreinvestedTperiods(att+1rate)Yieldof1-yearbonds=(1+i1)(1+i2)+(1+iT)1/T-1BasedonpreviousexampleT=2HPY(1-yearbonds)=(1+0.08)(1.1)1/21=0.08995or8.9952.One-yearHPYforn-yearbonds(usuallygiven)Ifitisnotgiven,itcanbeobtainedfromthen-yearHPYfor1-yearbondsreinvestedea
38、chyear,asfollowsYieldofn-yearbonds=(1+n-yearHPYofone-yearbonds)1/n1BasedontheexampleofpreviousslideYieldof2-yearbonds=(1+two-yearHPYof1-yearbonds)1/21=(1.188)1/21=0.08995or8.995%.3.Expectedyearninterestrate,in,(orforwardrate)Itisobtainedasfollows:(1+yieldofn-1yearbonds)n-1(1+in)=(1+yieldofn-yearbond
39、s)n(1+in)=(1+yieldofn-yearbonds)n/(1+yieldofn-1yearbonds)n-1in=(1+yieldofn-yearbonds)n/(1+yieldofn-1yearbonds)n-11Basedonpreviousexampletheexpectedyear2interestrate(orforwardrate)is(1+i2)=(1+yieldoftwoyearsbonds)2/(1+yieldofoneyearbonds)1=i2=(1.08995)2/1.08-1=1.0999-1=9.99910%27资本市场和金融机构2InterestRaS
40、olvethefollowingproblemsAssumetheExpectationsTheoryholds1.a)DeterminetheOne-yearHPY(oryield,assumedannual)for1-yearbondsreinvested3periodssuchastheexpectedinterestratesare5,6and7percent,foryears1,2and3,respectively.b)Determinetheyieldfor3-yearbonds.2.Determinethethree-yearHPYfor3-yearbondsthathaveyi
41、eldstomaturity(oryields,assumedannual) of5.9968%3.Assumethattwo-yearmaturitybondsofferyields(assumed annual)of5.4988%,andthree-yearbondshaveyieldsof5.9968%.Determinetheexpectedone-yearinterestrate(forward rate)forthethirdyear.4.WhatdoesthistellyouaboutthemonetarypolicytopursebytheBankofCanada?28资本市场
42、和金融机构2InterestRaB)MarketSegmentationTheoryThistheoryholdsthatlong-andshort-termmaturitybondsaretradedinessentiallydistinctorsegmentmarkets(bondsarenotperfectsubstitutes)Thetradingoflong-termborrowersandlendersdetermineratesonlong-termbonds.Similarly,thetradingofshort-termborrowersandlendersdetermine
43、ratesonshort-termbonds.Variousequilibriumrates(accordingtomaturityofbonds)Theirexplanationofupwardslopingyieldcurve?A:?Thisviewofthemarketisnotsupportedbyempiricalfacts.Itdoesnotexplaintheshapeoftheyieldcurve(forlowandhighshortterminterestrates)andwhyyieldsonbondsofdifferentmaturitiestendtomovetoget
44、her(SeeFigure5,p.117,Mishkinetal.)29资本市场和金融机构2InterestRa30资本市场和金融机构2InterestRaC)LiquidityPremiumTheoryThetheorythatinvestorsdemandariskpremiumonlongtermbonds.TheriskpremiumrequiredtoholdlongertermbondsiscalledliquiditypremiumInvestorsandfirmsarewillingtoholdthesebonds.Why?A:Yieldcurvewillbeupwardslo
45、pingevenintheabsenceofanyexpectationsoffutureincreasesinrates.Iftheliquiditypreferencetheoryisvalid,theforwardrateofinterestisnotagoodestimateofmarketexpectationsoffutureinterestrates.Why?A:31资本市场和金融机构2InterestRaPure Expectations Theory Yield CurveLiquidity Premium TheoryYield CurveInterest RateYear
46、s to MaturityRelationship between the Expectations Theory and the Liquidity Premium TheoryLiquidity Premium5101520 25 30032资本市场和金融机构2InterestRaWhattheoryexplainsbettertheTSIR?TheLiquiditypremiumtheoryexplainsbettertheempiricalfactssuchas1.Thatinterestratesondifferentmaturitybondsmovetogetherovertime
47、.2.Thatyieldcurvestendtobeupwardslopingwhenshort-terminterestratesarelowandtobeinvertedwhenshort-terminterestratesarehigh.3.Itexplainsthatyieldcurvestypicallyslopeupwardbyrecognizingthattheliquiditypremiumriseswithabondsmaturity(becauseofinvestorspreferencesforshort-termbonds).33资本市场和金融机构2InterestRa
48、InsummaryTheliquiditypremiumtheorypredictsthebehaviouroffutureshortterminterestratesbylookingattheslopeoftheyieldcurve:1.AsteeplyrisingyieldcurveindicatesthatSTisSTisareexpectedtoriseinthefuture2.AmoderatelyrisingyieldcurveindicatesthatSTisarenot expected to riseorfallmuchinthefuture.3.Aflatyieldcur
49、ve,indicatesthatSTisareexpectedtofall moderatelyinthefuture.4.Aninvertedyieldcurve,indicatesthatSTisareexpectedtofallsharplyinthefuture.34资本市场和金融机构2InterestRaYieldcurvesandthemarketsexpectationsofFutureShort-TermInterestRatesYTM Term to Maturitya) Short term interest rates expected to riseYTM Term t
50、o Maturity b) Short term interest rates expected to stay the same (E.g. the YTM used is considered constant for each period in the computation of NPV projects) YTM Term to Maturityc) Short term interest rates expected to fall moderatelyYTM Term to Maturityd) Short term interest rates expected to fal
51、l sharply35资本市场和金融机构2InterestRa6.PredictivePoweroftheyieldcurve6.1FutureinterestratesDoestheslopeoftheyieldcurveprovidesareliableforecastoffutureis?A:RecentresearchshowsthattheTSIRprovidesinformationfortheveryshortrun,overthenextseveralmonths,andthelongrun,overseveralyears.Itprovidesunreliableforeca
52、stininterestratesovertheintermediateterm,thetimeinbetween36资本市场和金融机构2InterestRa6.2Recessions,economyrecoveries(andinflation)(basedonastudybyA.EstrellaandF.Mishkin(1996),FRBY)If10-yearGovernmentbondrateis1.21%above3-monthT-billrateProbabilityofrecessiononeyearaheadis5%.(Upward-slopingorDownward-slopi
53、ngyieldcurve?)-Betterinvestmentstrategy:stocks,shorttermT-bills,orLTbonds?-Assumethedifferenceinyieldsis4%(whichisveryhighforhistoricalstandards).*Whatwouldyouexpecttohappentotheyieldcurve?*Whattypeofsecuritywouldyouinvest(disinvest)?If10-yearGovernmentbondrateis2.40%belowthe3-monthT-billrateProbabi
54、lityofrecessiononeyearaheadisabout90%.(Upward-slopingorDownward-slopingyieldcurve?37资本市场和金融机构2InterestRa7.ConclusionsTheInterestrate(i)isusuallydeterminedbytheinteractionofthedemandandsupplyofloanableloans.VariousfactorsaffectthedirectionofiCentralbanksinterveneregularlyonthedirectionofinterestrates
55、toachieveitsgoals.Changesinihaveimpactonthevalueoffinancialclaimsthatmayresultinlargelosses(forinvestorsand/orfirms)lInterest Rates arecarefullymonitoredonadailyandintra-daybasisTSIRisanimportantforecastingtoolofthedirectionofinterestratesalongwithscheduledpressannouncementsbyCentralBanks38资本市场和金融机构2InterestRa
