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Chapter4 UnderstandingInterestRates PresentValue AdollarpaidtoyouoneyearfromnowislessvaluablethanadollarpaidtoyoutodayWhy Adollardepositedtodaycanearninterestandbecome 1x 1 i oneyearfromtoday DiscountingtheFuture TimeLine 100 100 Year 0 1 PV 100 2 100 100 n 100 1 i 100 1 i 2 100 1 i n Cannotdirectlycomparepaymentsscheduledindifferentpointsinthetimeline SimplePresentValue FourTypesofCreditMarketInstruments 1 SimpleloanLenderprovidestheborrowerwithanamountoffunds whichmustberepaidtothelenderatthematuritydatealongwithanadditionalpaymentfortheinterest Ex commercialloans2 Fixed paymentloanLenderprovidestheborrowerwithanamountoffunds whichmustberepaidbymakingthesamepaymenteveryperiod Ex Mortgages 3 CouponbondPaystheownerofthebondafixedinterestpaymenteveryyearuntilthematuritydate whenaspecifiedfinalamountisrepaid Ex Treasurybonds notesandcorporatebonds Threepiecesofinformation 1 Issuer 2 Maturitydate 3 Couponrate4 Discount zerocoupon bondIsboughtatapricebelowitsfacevalueandthefacevalueisrepaidatthematuritydate Ex treasurybills YieldtoMaturity Theinterestratethatequatesthepresentvalueofcashflowpaymentsreceivedfromadebtinstrumentwithitsvaluetoday Alsocalledinternalrateofreturn Mostaccuratemeasureofi SimpleLoan FixedPaymentLoan CouponBond Whenthecouponbondispricedatitsfacevalue theyieldtomaturityequalsthecouponrateThepriceofacouponbondandtheyieldtomaturityarenegativelyrelatedTheyieldtomaturityisgreaterthanthecouponratewhenthebondpriceisbelowitsfacevalue Table1YieldstoMaturityona10 Coupon RateBondMaturinginTenYears FaceValue 1 000 ConsolorPerpetuity Abondwithnomaturitydatethatdoesnotrepayprincipalbutpaysfixedcouponpaymentsforever Forcouponbonds thisequationgivesthecurrentyield aneasytocalculateapproximationtotheyieldtomaturity DiscountBond RateofReturn Table2One YearReturnsonDifferent Maturity10 Coupon RateBondsWhenInterestRatesRisefrom10 to20 RateofReturnandInterestRates 1 Thereturnequalstheyieldtomaturityonlyiftheholdingperiodequalsthetimetomaturity2 Ariseininterestratesisassociatedwithafallinbondprices resultinginacapitallossiftimetomaturityislongerthantheholdingperiod3 Themoredistantabond smaturity thegreaterthesizeofthepercentagepricechangeassociatedwithaninterest ratechange RateofReturnandInterestRates cont d 4 Themoredistantabond smaturity thelowertherateofreturnthatoccursasaresultofanincreaseintheinterestrate5 Evenifabondhasasubstantialinitialinterestrate itsreturncanbenegativeifinterestratesrise Interest RateRisk Interest raterisk theriskinessofanasset sreturnthatresultsfrominterest ratechanges Pricesandreturnsforlong termbondsaremorevolatilethanthoseforshorter termbondsThereisnointerest rateriskforanybondwhosetimetomaturitymatchestheholdingperiod RealandNominalInterestRates NominalinterestratemakesnoallowanceforinflationRealinterestrateisadjustedforchangesinpricelevelsoitmoreaccuratelyreflectsthecostofborrowingExanterealinterestrateisadjustedforexpectedchangesinthepricelevelExpostrealinterestrateisadjustedforactualchangesinthepricelevel FisherEquation FIGURE1RealandNominalInterestRates Three MonthTreasuryBill 1953 2008 Sources Nominalratesfromwww federalreserve gov releases H15 TherealrateisconstructedusingtheprocedureoutlinedinFredericS Mishkin TheRealInterestRate AnEmpiricalInvestigation Carnegie RochesterConferenceSeriesonPublicPolicy15 1981 151 200
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