投资学第章利率期限结构

CHAPTER15TheTermStructureofInterestRatesInformationonexpectedfutureshorttermratescanbeimpliedfromtheyieldcurveTheyieldcurveisagraphthatdisplaystherelationshipbetweenyieldandmaturityThreemajortheoriesareproposedtoexplaintheobservedyieldcurveOverviewofTermStructureFigure15.1TreasuryYieldCurvesBondPricingYieldsondifferentmaturitybondsarenotallequalNeedtoconsidereachbondcashflowasastand-alonezero-couponbondwhenvaluingcouponbondsTable15.1YieldsandPricestoMaturitiesonZero-CouponBonds($1,000FaceValue)YieldCurveUnderCertaintyAnupwardslopingyieldcurveisevidencethatshort-termratesaregoingtobehighernextyearWhennextyear’sshortrateisgreaterthanthisyear’sshortrate,theaverageofthetworatesishigherthantoday’srateFigure15.2Two2-YearInvestmentProgramsFigure15.3ShortRatesversusSpotRatesfn=one-yearforwardrateforperiodnyn=yieldforasecuritywithamaturityofnForwardRatesfromObservedRatesExample15.4ForwardRates4yr=8.00% 3yr=7.00% fn=?(1.08)4=(1.07)3(1+fn)(1.3605)/(1.2250)=(1+fn)fn=.1106or11.06%DownwardSlopingSpotYieldCurve

Example

Zero-CouponRates

BondMaturity 12% 1 11.75% 2 11.25% 3 10.00% 4 9.25% 5ForwardRatesforDownwardSloping

YCExample1yrForwardRates

1yr [(1.1175)2/1.12]-1= 0.1150062yrs [(1.1125)3/(1.1175)2]-1= 0.1025673yrs [(1.1)4/(1.1125)3]-1 = 0.0633364yrs [(1.0925)5/(1.1)4]-1 = 0.063008 InterestRateUncertaintyWhatcanwesaywhenfutureinterestratesarenotknowntodaySupposethattoday’srateis5%andtheexpectedshortrateforthefollowingyearisE(r2)=6%then:Therateofreturnonthe2-yearbondisriskyforifnextyear’sinterestrateturnsouttobeaboveexpectations,thepricewilllowerandviceversaInterestRateUncertaintyContinuedInvestorsrequireariskpremiumtoholdalonger-termbondThisliquiditypremiumcompensatesshort-terminvestorsfortheuncertaintyaboutfuturepricesExpectationsLiquidityPreferenceUpwardbiasoverexpectationsTheoriesofTermStructureExpectationsTheoryObservedlong-termrateisafunctionoftoday’sshort-termrateandexpectedfutureshort-termratesLong-termandshort-termsecuritiesareperfectsubstitutesForwardratesthatarecalculatedfromtheyieldonlong-termsecuritiesaremarketconsensusexpectedfutureshort-termratesLong-termbondsaremoreriskyInvestorswilldemandapremiumfortheriskassociatedwithlong-termbondsTheyieldcurvehasanupwardbiasbuiltintothelong-termratesbecauseoftheriskpremiumForwardratescontainaliquiditypremiumandarenotequaltoexpectedfutureshort-termratesLiquidityPremiumTheoryFigure15.4YieldCurvesFigure15.4YieldCurves(Concluded)InterpretingtheTermStructureIftheyieldcurveistoriseasonemovestolongermaturitiesAlongermaturityresultsintheinclusionofanewforwardratethatishigherthantheaverageofthepreviouslyobservedratesReason:HigherexpectationsforforwardratesorLiquiditypremiumFigure15.5PriceVolatilityofLong-TermTreasuryBondsFigure15.6TermSpread:Yieldson10-YearVersus90-DayTreasurySecuritiesForwardRatesasForwardContractsIngeneral,forwardrateswilln