金融学（第四版）课件：Interest Rates and Bond Prices

InterestRatesandBondPrices

2TheTimeValueofMoneyTheinterestrateisthecosttoborrowersofobtainingmoneyTheinterestrateisthereturn(oryield)onmoneytolendersTherefore,theinterestrateistherewardforpostponingpurchasesintothefuturethehighertheinterestrate,themorewillinganindividualwillbetopostponepurchasesintothefutureandlendinthepresent3TheTimeValueofMoneyTheinterestratelinksthepresenttothefutureplaysapivotalroleinspending,saving,lending,andborrowingdecisionsTheinterestraterepresentsthetimevalueofmoneyspecifiesthetermsuponwhichanindividualcantradeoffpresentpurchasingpowerforfuturepurchasingpower4Compounding:FutureValuesCompoundinganswersthefollowingwhatisthefuturevalueofmoneylent(orborrowed)today?Theamountthatisoriginallylentistheprincipal5Compounding:FutureValuesThegeneralrelationshipisAmountrepaid=principal+interestTheamountofinterestisInterest=principalinterestrateInterest=principaliSubstituting,wegetAmountrepaid=principal(1+i)V1=V0(1+i)6ExampleJosephagreestolendafriend$1,000foroneyearataninterestrateof6%V1=V0(1+i)V1=$1,000(1+0.06)V1=$1,000(1.06)V1=$1,0607Compounding:TheFutureValueofMoneyLentTodayPaymentToday$1,000FutureValue$1,0608CompoundingWhatifJoseph’sfriendwantstoborrowthemoneyfortwoyears?assumethathemakesnopaymentsuntiltheendoftheloanThisiswherecompoundingcomesintoplaycompounding

meanstocombine,addto,orincrease9CompoundingInthefinancialworld,compoundingreferstotheincreaseinthevalueoffundsfromearninginterestoninterestV2=V0+iV0+i(V0+iV0)thelasttermistheinterestthatisearnedoninterestWecanreducethisequationtoV2=V0(1+i)210CompoundingInfact,thisequationcanbegeneralizedforanymaturityofnyearsVn=V0(1+i)nInourexample,V0=$1,000,i=0.06,andn=2V2=$1,000(1+0.06)2V2=$1,000(1.1236)V2=$1,123.6011Discounting:PresentValuesDiscountinganswersthefollowingwhatisthepresentvalueofmoneythatistobereceived(orpaid)inthefuture?Tocalculatepresentvalue,wecansimplyrearrangetheformulaforfuturevaluethistime,wesolveforV012Discounting:ThePresentValueofMoneytoBeReceivedintheFutureFuturePayment$1,060ValueToday$1,00013ExampleSupposeamoviestarhasbeenofferedthefollowingdealeither$6,000,000todayof$7,500,000infiveyearstheinterestrateis6%14ExampleThismeansthatyouwouldonlyhavetoinvest$5,604,436.30todayataninterestrateof6%tohave$7,500,000infiveyearsThus,the$6,000,000todayisthebetterdeal15InterestRates&BondPricesBondsgenerallysharethefollowingcharacteristicshaveamaturity>10yearshaveafaceorparvalue(F)of$1,000perbondtheissueragreestomakeperiodicinterestpaymentsoverthetermtomaturityandtorepaythefacevalueatmaturitytheperiodicpaymentsarecalledcouponpayments16InterestRates&BondPricesAbondrepresentsastreamoffuturepaymentsTofinditspresentvalue(thepriceitwilltradeatinfinancialmarkets)weneedtocomputethepresentvalueofeachfuturecouponpaymentcomputethepresentvalueofthefinalrepaymentofthefacevalueonthematuritydate17InterestRates&BondPricesTheappropriateformulais18ExampleSupposethatJaneisabouttobuyabondthatwillmatureinoneyearthefacevalueis$1,000thecouponpaymentis$60theprevailingmarketinterestrateis6%Janewillbewillingtopay19ExampleSupposethatthemarketinterestraterisesto8%ThepriceofthebondnowbecomesJanewouldbebuyingthebondforapricebelowitsparvaluethisiscalledadiscountfromparraisestheyieldtomaturityonthebond20InterestRates&BondPricesAsthemarketinterestraterises,thepriceofexistingbondsfallspotentialpurchaserscanpurchasenewlyissuedbondswithhigheryieldstomaturitytheyieldtomaturityonexistingbondsmustrisetoremaincompetitivethisoccurswhenthepriceonexistingbondsfallsthepricewillfalluntiltheyieldtomaturityofthebondisequaltothecurrentinterestrate21ExampleSupposethatthemarketinterestratefallsto4%ThepriceofthebondnowbecomesJanewouldbebuyingthebondforapriceaboveitsparvaluethisiscalledapremiumaboveparlowerstheyieldtomaturityonthebond22InterestRates&BondPricesAsthemarketinterestratefalls,thepriceofexistingbondsrisesthehigheryieldstomaturityofexistingbondsareattractivetopotentialinvestorsthisraisesthepriceofthesebondstheprocesscontinuesuntiltheyieldtomaturityonexistingbondsisequaltothecurrentinterestrate23TheDeterminantsofthe

InterestRateChangesintheinterestrateinfluencethebehaviorofnetborrowersandnetlendersTheborrowingandlendingbehaviorofnetborrowersandnetlendersinfluencestheinterestrateInthemarketforloanablefunds,supplyanddemandarethekeytodetermininginterestrates24TheDeterminantsofthe

InterestRateThedemandforloanablefundsoriginatesfromhousehold,business,government,andforeignnetborrowerstheyarespendingmorethantheircurrentincomeNetborrowersarewillingtoborrowmoreatlowerinterestrates,ceterisparibusthedemandforloanablefundswillbedownwardsloping25TheDeterminantsofthe

InterestRateThetotalsupplyofloanablefundsoriginatesfromtwosourceshousehold,business,government,andforignnetlenderstheyspendlessthantheircurrentincometheFedsuppliesreservestothefinancialsystemthatleadtoincreasesinthegrowthrateofmoneyandloansassumethatthisisfixed(fornow)26TheDeterminantsofthe

InterestRateNetlendersarewillingtosupplymorefundsathigherinterestratesthesupplyofloanablefundswillbeupwardslopingTheequilibriuminterestrateoccurswherethequantityoffundssuppliedisequaltothequantityoffundsdemanded27TheSupplyofandDemandforFundsInterestRate(Percent)LoanableFunds(inBillions)DemandSupply$500E1628ChangesintheDemandforLoanableFundsMovementsinGDPareamajordeterminantofshiftsinthedemandforfundswhenGDPrises,firmsandhouseholdsaremorewillingandabletoborrowAnotherfactorthataffectsthedemandforloanablefundsisanincreaseintheexpectedproductivityofcapitalinvestments29AShiftintheDemandforFundsInterestRate(Percent)LoanableFunds(inBillions)DD$500E1Supply6$6008E2D’D’30ChangesintheSupplyofLoanableFundsOneofthefactorsaffectingthesupplyoffundsismonetarypolicytheFed’sabilitytoalterthegrowthrateofmoneyintheeconomymeansthatitcanhaveadirecteffectonthecostandavailabilityoffunds31AShiftintheSupplyofFundsInterestRate(Percent)LoanableFunds(inBillions)Demand$500E1SS6$5504E2S’S’32TheDeterminantsofthe

InterestRateThedeterminantsofinterestratescanbesummarizedasfollowsi=f

(Y+,M-)theinterestrateisapositivefunctionofincomeorGDP(Y)andanegativefunctionofthemoneysupply(M)anincreaseinYincreasesthedemandforfundsanincreaseinMincreasesthesupplyoffunds33InflationandInterestRatesLendersareconcernedwithtwothingsnominalinteresthowmanydollarswillbereceivedinthefutureinreturnforlendingnowinflationtherealpurchasingpowerthefundswillbeworthuponrepayment34InflationandInterestRatesThemarketinterestrate(thenominalinterestrate)isnotanadequatemeasureoftherealreturnonaninterest-bearingassetTheappropriatemeasureistherealinterestratethereturnontheassetcorrectedforchangesinthepurchasingpowerofmoneythenominalinterestrateminustheexpectedrateofinflation35InflationandInterestRatesi=r+peTheinflationpremiumistheamountofnominalinterestthatwillcompensatealenderfortheexpectedlossofpurchasingpoweraccompanyinganyinflationequaltotheexpectedinflationrate(pe)Nominalinterestratesriseandfallasexpectedinflationrisesandfalls36ExampleSupposethatthecommercialpaperrateis5%andthecurrentexpectedrateofinflationis3%theexpectedrealinterestrateis2%Ifborrowersandlendersexpecttheinflationratetobe6%,theexpectedrealinterestratebecomes-1%thisdropintherealcostofborrowingandrealreturnonlendingwillincreasethedemandforfundsandlowerthesupplyoffunds37TheSupplyofandDemandforFundsInterestRate(Percent)LoanableFunds(inBillions)DDE1SS5$500E28D’D’S’S’38TheDeterminantsofthe

InterestRateWecannowsummarizethedeterminantsofinterestratesasfollowsi=f

(Y+,M-,pe+)thenominalinterestrateispositivelyrelatedtotheexpectedinflationrate39TheCyclicalMovementofInterestRatesDuringarecession,incomeandGDPfallandtheFedmayattempttostabilizetheeconomybyincreasingthemoneysupplyreducesthedemandforfundsincreasesthesupplyoffundsTheresultisadeclineintheinterestrate40TheCyclicalMovementofInterestRatesDuringanexpansion,incomeandGDPriseandtheFedmayattempttoslowthegrowthrateofthemoneysupplyincreasesthedemandforfundsdecreasesthesupplyoffundsTheresultisariseintheinterestrate41SummaryofMajorPointsTheinterestrateisthereturnonlendingtoday(spendinginthefuture)andthecostofborrowingtoday(repayinginthefuture)theinterestraterepresentsthetimevalueofmoneyandspecifiesthetermsunderwhichonecantradepresentpurchasingpowerforfuturepurchasingpower42SummaryofMajorPointsCompoundinganswersthequestion:whatisthefuturevalueofmoneylenttoday?itistheincreaseinthefuturevalueoffundsfromearninginterestoninterestDiscountinganswersthequestion:whatisthepresentvalueofmoneytobereceivedinthefuture?hereagaintheinterestratelinksthepresentwiththefuture43SummaryofMajorPointsAbondisastreamoffuturepaymentsthepriceofabondwillbeequaltothepresentvalueofthediscountedfuturestreamofincomewhentheinterestratechanges,thispresentvaluewillchangealsowhentheinterestraterises,thepriceofoutstandingbondswillfallwhentheinterestratefall,thepriceofoutstandingbondswillrise44SummaryofMajorPointsCeterisparibus,thequantitydemandedofloanablefundsisinverselyrelatedtotheinterestrateCeterisparibus,thequantitysuppliedofloanablefundsispositivelyrelatedtotheinterestrate45SummaryofMajorPointsChangesininterest