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1、InterestRates1.Definition2.FluctuationofinterestratesShiftsonDemandShiftsonSupply3.Typesofinterestrates4.AnalysisofBondValuation5.RiskandTermStructureofInterestRates(TSIR)1.5.1DeterminantsofRiskStructure(RSIR)2.5.2TSIR(YieldCurve).Theories:3.A)PureExpectationsTheory4.B)MarketSegmentationTheory5.C)Li
2、quidityTheory6.PredictivePoweroftheYieldCurve1.6.1Futureinterestrates2.6.2Economicgrowth7.Conclusions11.InterestRate(i)i=CostofborrowingorlendingmoneyItplaysapivotalrolein:theInvestmentandFinancingofassets(real,financial)byindividuals,companies,governmentsandFItheperformanceoftheeconomyDeterminedint
3、heDebtMarkets(supplyanddemand)andbygovernmentintervention.lCentralBankMonetarypolicy(i,M)Isthereanappropriatelevelofi?2InterestRatelHowtheinterestratesaredetermined?lWhatexplainsthefluctuationofinterestrates?lMostaccuratemeasureofinterestrate:YieldtomaturityExampleappliedtobondvaluation3Determinatio
4、nofInterestRate(i)Approaches1)AnalysisofDemandofloanablefundsandSupplyofloanablefunds2)AnalysisofDemandforandsupplyofbondsSupplyofloanablefundsbyhouseholdsandfirms.Thehigherthei thehigherthequantityofloanablefundsofferedDemandofloanablefundsbyhouseholdsandfirmsReasonsforConsumer?ForFirms?TotalDemand
5、=DemandbyhouseholdsandfirmsDeterminantsoftheDemandandSupply4SupplyandDemandforLoanableFundsInterestRate(i)SupplyQuantity of loanable funds DemandQ*i*5 Whatdeterminesthesupplyofloanablefunds?Thesupplyofloanablefundsisdeterminedbytheinterestrateofferedtosavers.Ahigherinterestrateinduceshouseholdstocon
6、sumelesstoday(save)infavorofgreaterconsumptioninthefuture.Firmalsomayhaveexcessofcashthatmaybeloaned(e.g.,purchaseofotherfirmsbondissue)insteadofinvested(realassets)becauseofthenonavailabilityofprojectswith+NPV. Whatdeterminesthedemandforloanablefunds?Itcomesfrom:consumerswhowishtoconsumemoretodayth
7、antomorrow,individuals,financialandnon-financialfirmstoinvestinfinancialassetsfinancialandnon-financialfirmstoinvestinrealassetsDemanddependsontheinterestrateatwhichthesethreegroupscanborrow.Thelowertheinterestratethehigherthedemandandvice-versa.62.Fluctuationofinterestrates Whatmightcausethesupplyo
8、rdemandforloanablefundstoshift,andhowwouldthataffectinterestrates?Factorsthatshiftthedemandcurve.a)Recession:Itdecreasesdemandatallinterestrates,shiftingthedemandcurveinwardsandcausingtheequilibriuminterestratetofall.Quantity ($)AB Interest Rate SDDiiQQ7b)Anincreaseofthegovernmentdeficit.C)Riseinexp
9、ectedinflationshiftsthedemandcurvetotheright.Sameas(b)NominalInterestrate=realinterestrate+rateofexpectedinflationD)increaseonthegrowthrateofpopulation.Sameas(b)e)Businesscycleexpansion.ExpectedincreaseineconomicgrowthSameas(b)iQ ($)DD SAB8ExamplesthatshifttheSupplycurvetotheright a)Increasesinthemo
10、neysupplybytheCentralBank,causingtheinterestratetofall.b)b)Increasesinrealpersonalincomemakepeoplemorewillingtomakeloans(e.g.depositsinbanksaccounts)c)Increaseintaxexemptfinancialinstruments.Note:ifweassumethatthecentralbankcontrolstheamountofmoneysupplyatfixedquantitytheSupplyCurveformoneySwouldbea
11、verticalline.iQ ($)SSAB93.VarietyofInterestRatesT-billrate(1year)Discountrate:CentralBankchargestobanksInCanadaiscalledtheOvernightBankRateCommercialpaperrate:ShorttermdiscountbondsPrimerate:ShorttermRatechargedtolargestfirms(creditworthy)Corporatebondrate:LongtermratefordebtissuedbyfirmsLIBOR:Ratet
12、hatlargestcreditworthyinternationalbanksdealinginEurodollarschargeeachotherforlargeloans.Fixedrates,floatingrates,etc.Theydifferbecauseofthedifferencesinmaturity,riskoflenders104. AnalysisofBondValuationItshedslightontheconceptofinterestrate.Bond.Contractinwhichaborroweragreestopayabondholder(thelen
13、der)aspecificamountofmoneyinaperiodoftime.Example:Howmuchwouldyoupayforabondthatpromisesacouponrateof$100eachyearforaperiodof10yearsandtheprincipalamountof$1,000(parvalue=nominalvalue=facevalue)attheendofthe10thyear?Assumei=5%,i=10%,i=15%11FormulaP=Coupon/(1+i)+Coupon/(1+i)2+Coupon/(1+i)10+FaceValue
14、/(1+i)10C=$100C=$100C=$100P=?123 9 10C=$100$100 + $1,000Ifi=5%P=$100/(1+0.05)+$100/(1+0.05)2+$100/(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 r
15、ateoryieldtomaturity)fromabovemakesthepresentvalueofabondspaymentsequaltoitscurrentpriceP?A:?i = 5%12YTM=InterestratethatequatesthePresentValueofpaymentsreceivedfromadebtinstrument(e.g.,bond)withitsvaluetodayP.Alternatively,istherateofinterestearnedonabondifitisheldtomaturity.TheYTMisthemostimportan
16、tandaccuratewayofcalculatinginterestrates.IfP=$1,386WhatistheYTM=i?$1,386=$100/(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=effectiveyi
17、eldonabond=i$1,00010%Interest Rate = i = YTM5% $1,386$74915%Scenarios:1.Assume 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 t
18、he interest rate (YTM)?13PerpetuityBondpayingoutafixedamountofmoneyeachyearforever.ExampleTheCanadiangovernmentissuesabondthatwillpaytoperpetuity$50ayear.Iftheinterestrateis3%annual,a)whatisthebondworthtoday?b)Wouldyoubuythebondfor$1,500?ThepresentvalueofaperpetuityiseasilyobtainedasPDV=perpetuity/R
19、A:EffectiveYield(YTM)onaBond(perpetuity)PercentagereturnthatonereceivesbyinvestinginabondAssumepriceoftheperpetuityaboveis$1,666.67andyoureceiveaperpetualcouponrateof$50peryear.Whatistheeffectiveyieldrateorrateorreturn?A:Now,supposethecurrentinterestrateis4%.Wouldyoupay$1,666.67forthebond?145.Riskan
20、dTermStructureofInterestRatesVarietyofdifferentinterestrate=f(maturity,risk,liquidity,taxes).I I)Assumingvariousdebtinstruments(bonds)havesame maturity,theiriswilldifferbecauseofdifferences in risk.RiskStructureofInterestRates(RSIR).RSIRexpressestherelationsofinterestratesforvariousbondinstrumentswh
21、osedeterminantsare(1)defaultrisk,(2)liquidity,and(3)taxes (SeeFig.1,p.110,Miskhinetal.-LongTermBonds)II II)Assumingvariousbondshavesame risktheirismaydifferbecauseofthedifferencesinmaturities.TermStructureofInterestRates(TSIR).TSIRexpressesthetherelationshipamongis(YTMs)onzerocoupondiscountbondswith
22、differentmaturities.155.15.1DeterminantsofRISKSTRUCTUREOFINTERESTRATES(RSIR)InterestratesoncorporatebondsarehigherthanthoseonCanadabonds(SeeFigure1)Reasons1.HigherDefaultRisk2.LowerLiquidity3.Taxconsiderationsonispayments.Canadian(Cdn)bondsaredefault-freebondsDifferenceinis=RiskPremium1.EffectofDefa
23、ultriskoninterestratesAssumeinitiallyacorporatebondswithnodefaultrisk,likeCanadabonds(withsamematurity).Possibilityofastrongrecessionincreasesthepossibilityofdefaultofcorporatebonds.WhatwilltheeffectbeoninterestratesofcorporatebondsandCanadabonds?Whatwillhappentotheriskpremiumofcorporatebonds?ii Pri
24、ce of bonds, PPQuantity of Corporate Bonds Quantity of Canada Bonds(a) Corporate bond market (b) Default-free Cdn bond marketic1Pc1Pc2ic2PT2PT1iT2iT1iT2 ic2RiskPremium= ic2 - iT2Dc2Dc1ScDT1DT2STDecrease inInterest rate16Investmentadvisoryfirmsprovidersofdefaultriskinformationonbonds:StandardsandPoor
25、sCanada,DominionBondRatingService.Investmentgrade-bonds(AAA)vs.Junkbonds(D)(SeeFig.3,p.113,Mishkinetal.)RiskpremiumonBBBcorporatebondrates(Corporates-CanadaSpread,1980-2019)172.EffectofLiquidityoninterestratesLiquidity.Abilitytobuyorsellanassetquicklyandinlargevolumewithoutsubstantiallyaffectingthea
26、ssetsprice.Corporatebondsvs.CanadabondsWhichonesaremoreliquid?Spread?AssumeinitiallycorporatebondsandCanadabondsareequallyliquid,ceteris paribus.a)Whichevent(s)woulddecreasetheliquidityofcorporatebonds?Why?b)WhatwilltheeffectbeoninterestratesofcorporatebondsandCanadabonds?c)Whatwillhappentotherisk(l
27、iquidity)premiumofcorporatebonds?Drawtheirrespectivegraphs(demandandsupplycurvesofCorporatesandCanadabonds).183.TaxConsiderationsHowdoestaxationaffecttheinterestrate(YTM)onbonds?Governmentbondsthatpaynotaxesyieldlowerinterestrates(e.g.,U.S.municipalbondsormunis).Munisareadvantageousforhightax-bracke
28、tinvestors.Example:SupposeCharlieWhite(aUSinvestor)has2alternativestoinvesthissavings(say$1,000)1)investa$1,000facevaluemunithatsellsfor$,1000,withcouponpaymentsof$80.2)2)investa$1,000facevaluetaxablebondthatsellsfor$1,000andhasacouponpaymentof$120.Thetax-bracketis35%.3)4)a)Whichoptionshouldhechoose
29、?Why?5)b)SupposeJaneRedisfacedwithsimilaroptionsbuthertax-bracketis30%.Whatoptionwouldbebestforher?6)c)DoesitmattertoknowthematurityofthebondstoobtaintheirYTM?195.25.2TermStructureofInterestRates(TSIR)TheTSIRreferstotherelationshipbetweenYTMandtermtomaturityforbondsofsame riskclass.TheYieldCurveisth
30、egraphicalrepresentationoftheTSIR.TheYieldCurveshapecanbea)Upward-slopingLongTermisShortTermisb)FlatLongtermis=ShortTermisc)Downward-sloping(invertedyieldcurve)LTisShortTermisaverageoffutureSTratesisexpectedcurrentshorttermratesDownward-slopingLongTermisShortTermisaverageoffutureSTratesisexpectedcur
31、rentshorttermratesFlatLongTermis=ShortTermisaverageoffutureSTratesisexpected=currentshorttermrates24Expectedholding-periodyields(HPY)onbondsofallmaturities(withsamerisk)oughttobeaboutequal,thatis:1.HPY(1-yearbond)=HPY(2-yearbond)=HPY(n-yearbond)2.Ifweknowtheone-yearHPY(commonlycalledyield)ontwobonds
32、ofn-1,andnmaturities,wecanobtainthemarketexpectationofthefutureshort-terminterestrateonyearn(alsocalledforwardrate).ImplicationsofExpectationsTheory25Example-Ifone-yearbondsofferan8%annualyield(return)andtheprincipalandinterestarereinvestedat10%attheendoffirstyearwhile-two-yearbondshaveanYTM(i,orann
33、ualyield,orcommonlycalledyield*)of8.995%,bothbondsmusthavesameholdingperiodyield(HPY),thatis:*Inpracticeyieldreferstoone-yearinterestrate.1.Two-yearHPYforbothtypesofbondsTwo-yearHPYof1-yearbonds=(1+0.08)(1+0.1)-1=0.188or18.8%Two-yearHPYof2-yearbonds=(1.08995)(1.08995)-1=0.188or18.8% 2.One-yearHPY(co
34、mmonlycalledyield)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-yearbonds)1/2-1=(1.188)1/21=0.08995or8.995%.3.Theexpectedyeartwointerestrate,i2,(orforward
35、rate)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%26GeneralizingGeneralizing1.One-yearHPY(oryield)for1-yearbondsreinvestedTperiods(att+1rate)Yieldof1-yearbonds=(1+i1)(1+i2)+(1+
36、iT)1/T-1BasedonpreviousexampleT=2HPY(1-yearbonds)=(1+0.08)(1.1)1/21=0.08995or8.9952.One-yearHPYforn-yearbonds(usuallygiven)Ifitisnotgiven,itcanbeobtainedfromthen-yearHPYfor1-yearbondsreinvestedeachyear,asfollowsYieldofn-yearbonds=(1+n-yearHPYofone-yearbonds)1/n1BasedontheexampleofpreviousslideYieldo
37、f2-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-yearbonds)n(1+in)=(1+yieldofn-yearbonds)n/(1+yieldofn-1yearbonds)n-1in=(1+yieldofn-yearbonds)n/(1+yieldofn-1yearb
38、onds)n-11Basedonpreviousexampletheexpectedyear2interestrate(orforwardrate)is(1+i2)=(1+yieldoftwoyearsbonds)2/(1+yieldofoneyearbonds)1=i2=(1.08995)2/1.08-1=1.0999-1=9.99910%27SolvethefollowingproblemsAssumetheExpectationsTheoryholds1.a)DeterminetheOne-yearHPY(oryield,assumedannual)for1-yearbondsreinv
39、ested3periodssuchastheexpectedinterestratesare5,6and7percent,foryears1,2and3,respectively.b)Determinetheyieldfor3-yearbonds.2.Determinethethree-yearHPYfor3-yearbondsthathaveyieldstomaturity(oryields,assumedannual) of5.9968%3.Assumethattwo-yearmaturitybondsofferyields(assumed annual)of5.4988%,andthre
40、e-yearbondshaveyieldsof5.9968%.Determinetheexpectedone-yearinterestrate(forward rate)forthethirdyear.4.WhatdoesthistellyouaboutthemonetarypolicytopursebytheBankofCanada?28B)MarketSegmentationTheoryThistheoryholdsthatlong-andshort-termmaturitybondsaretradedinessentiallydistinctorsegmentmarkets(bondsa
41、renotperfectsubstitutes)Thetradingoflong-termborrowersandlendersdetermineratesonlong-termbonds.Similarly,thetradingofshort-termborrowersandlendersdetermineratesonshort-termbonds.Variousequilibriumrates(accordingtomaturityofbonds)Theirexplanationofupwardslopingyieldcurve?A:?Thisviewofthemarketisnotsu
42、pportedbyempiricalfacts.Itdoesnotexplaintheshapeoftheyieldcurve(forlowandhighshortterminterestrates)andwhyyieldsonbondsofdifferentmaturitiestendtomovetogether(SeeFigure5,p.117,Mishkinetal.)2930C)LiquidityPremiumTheoryThetheorythatinvestorsdemandariskpremiumonlongtermbonds.Theriskpremiumrequiredtohol
43、dlongertermbondsiscalledliquiditypremiumInvestorsandfirmsarewillingtoholdthesebonds.Why?A:Yieldcurvewillbeupwardslopingevenintheabsenceofanyexpectationsoffutureincreasesinrates.Iftheliquiditypreferencetheoryisvalid,theforwardrateofinterestisnotagoodestimateofmarketexpectationsoffutureinterestrates.W
44、hy?A:31Pure Expectations Theory Yield CurveLiquidity Premium TheoryYield CurveInterest RateYears to MaturityRelationship between the Expectations Theory and the Liquidity Premium TheoryLiquidity Premium5101520 25 30032WhattheoryexplainsbettertheTSIR?TheLiquiditypremiumtheoryexplainsbettertheempirica
45、lfactssuchas1.Thatinterestratesondifferentmaturitybondsmovetogetherovertime.2.Thatyieldcurvestendtobeupwardslopingwhenshort-terminterestratesarelowandtobeinvertedwhenshort-terminterestratesarehigh.3.Itexplainsthatyieldcurvestypicallyslopeupwardbyrecognizingthattheliquiditypremiumriseswithabondsmatur
46、ity(becauseofinvestorspreferencesforshort-termbonds).33InsummaryTheliquiditypremiumtheorypredictsthebehaviouroffutureshortterminterestratesbylookingattheslopeoftheyieldcurve:1.AsteeplyrisingyieldcurveindicatesthatSTisSTisareexpectedtoriseinthefuture2.AmoderatelyrisingyieldcurveindicatesthatSTisareno
47、t expected to riseorfallmuchinthefuture.3.Aflatyieldcurve,indicatesthatSTisareexpectedtofall moderatelyinthefuture.4.Aninvertedyieldcurve,indicatesthatSTisareexpectedtofallsharplyinthefuture.34YieldcurvesandthemarketsexpectationsofFutureShort-TermInterestRatesYTM Term to Maturitya) Short term intere
48、st rates expected to riseYTM Term to 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
49、term interest rates expected to fall sharply356.PredictivePoweroftheyieldcurve6.1FutureinterestratesDoestheslopeoftheyieldcurveprovidesareliableforecastoffutureis?A:RecentresearchshowsthattheTSIRprovidesinformationfortheveryshortrun,overthenextseveralmonths,andthelongrun,overseveralyears.Itprovidesu
50、nreliableforecastininterestratesovertheintermediateterm,thetimeinbetween366.2Recessions,economyrecoveries(andinflation)(basedonastudybyA.EstrellaandF.Mishkin(2019),FRBY)If10-yearGovernmentbondrateis1.21%above3-monthT-billrateProbabilityofrecessiononeyearaheadis5%.(Upward-slopingorDownward-slopingyie
51、ldcurve?)-Betterinvestmentstrategy:stocks,shorttermT-bills,orLTbonds?-Assumethedifferenceinyieldsis4%(whichisveryhighforhistoricalstandards).*Whatwouldyouexpecttohappentotheyieldcurve?*Whattypeofsecuritywouldyouinvest(disinvest)?If10-yearGovernmentbondrateis2.40%belowthe3-monthT-billrateProbabilityo
52、frecessiononeyearaheadisabout90%.(Upward-slopingorDownward-slopingyieldcurve?377.ConclusionsTheInterestrate(i)isusuallydeterminedbytheinteractionofthedemandandsupplyofloanableloans.VariousfactorsaffectthedirectionofiCentralbanksinterveneregularlyonthedirectionofinterestratestoachieveitsgoals.Changesinihaveimpactonthevalueoffinancialclaimsthatmayresultinlargelosses(forinvestorsand/orfirms)lInterest Rates arecarefullymonitoredonadailyandintra-daybasisTSIRisanimportantforecastingtoolofthedirectionofinterestratesalongwithscheduledpressannouncementsbyCentralBanks38
