1.05.第5章 风险和期限结构如何影响利率

第五章风险和期限如何影响利率第一节利率的风险结构

第二节利率的期限结构1ChapterPreview本章主要研究风险对利率的影响和期限结构对利率的影响。利率的风险结构

RiskStructureofInterestRates利率的期限结构

TermStructureofInterestRates2第一节利率的风险结构Tostartthisdiscussion,wefirstexaminetheyieldsforseveralcategoriesoflong-termbondsoverthelast85years.Youshouldnoteseveralaspectsregardingtheserates,relatedtodifferentbondcategoriesandhowthishaschangedthroughtime.3RiskStructureofLongBondsintheU.S.Interestratesofbondswithdifferentrisks/release/h15/data.htm4Twoimportantfeaturesofinterest-ratebehaviorforbondsFigure1showsthefeaturesasfollowing:

在任何一年内，不同种类的债券利率各不相同；利率之间的利差(spread)随着时间的推移而变动。5FactorsAffectingRiskStructureofInterestRatesDefaultRisk(违约风险)Liquidity(流动性)IncomeTaxesFactor(所得税因素)6一、DefaultRisk(违约风险)影响债券利率的一个特征是其违约风险(riskofdefault)。当债券发行者不能或不愿按事先约定支付利息或面值时，就出现违约风险。美国联邦政府的债券通常是没有违约风险的(美国政府可以通过增加税收来履行还款义务)。这种债券被称为无风险债券(default-freebonds).7RiskPremium(风险溢价)具有违约风险的债券和无违约风险的债券之间的利差称为风险溢价(riskpremium)，它表明人们持有高风险债券所必须获得的利息。具有违约风险的债券通常具有正的风险溢价，而且违约风险越大风险溢价越大。8IncreaseinDefaultRiskonCorporateBonds9公司债违约风险增长的分析CorporateBondMarketRiskofcorporatebonds

,Dc

,Dcshiftsleft

Pc

,ic

TreasuryBondMarketRelativeriskofTreasurybonds

,DT

,DTshiftsright

PT

,iT

OutcomeRiskpremium,ic-iT,rises10债券的评级BondRatingsBaa(Moody)orBBB(S&P)或以上级别的称为投资级别证券；以下级别的称为称为垃圾债券Junkbonds。11二、Liquidity(流动性)影响债券利率的另一个因素是流动性liquidity;债券的流动性越强越受欢迎。在众多长期债券中，美国的国债流动性最强。因为其交易范围广泛，容易被出售，而且交易成本低。12LiquidityPremium(流动性溢价)公司债券的流动性比国债要差。Becausefewerbondsforanyonecorporationaretradedanditmaybehardtofindbuyersquickly.

公司债券与国债之间的利差(thatis,theriskpremiums)不仅反映了公司债券的违约风险，还反映了其流动性风险。所以风险溢价有时也被称为流动性溢价。13DecreaseinLiquidityofCorporateBondsRiskpremiumreflectsnotonlycorporatebonds'defaultriskbutalsolowerliquidity14公司债流动性降低的反应CorporateBondMarketLiquidityofcorporatebonds

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Pc

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TreasuryBondMarketRelativelymoreliquidTreasurybonds,DT

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PT

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OutcomeRiskpremium,ic-iT,rises15三、IncomeTaxesFactor(所得税因素)美国的市政府债券(municipalbonds)的利息支付不用缴纳联邦所得税(federalincometaxes)。这对于市政债券的需求来说，与提高预期收益具有相同的影响效果。16市政府债券的税收优势17市政府债券的税收优势分析MunicipalBondMarketTaxexemptionraisesrelativeReonmunicipalbonds,Dm

,Dmshiftsright

Pm

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TreasuryBondMarketRelativeReonTreasurybonds

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Outcome

im<iT18第二节利率的期限结构具有相同风险、流动性和税收因素的债券也可能因为到期期限的差异而具有不同的利率水平。19不同到期期限的债券的利率变动20收益率曲线YieldCurvesDynamicyieldcurvethatcanshowthecurveatanytimeinhistory

http:///charts/YieldCurve.html21美国不同到期期限国债利率22第二节利率的期限结构具有不同到期期限的债券的利率会同时变动。当短期利率较低时，收益率曲线更有可能陡峭向上倾斜；当短期利率较高时，收益率曲线更有可能向下倾斜。收益率曲线通常是向上倾斜。23期限结构理论PureExpectationsTheory纯预期理论PureExpectationsTheoryexplains1and2,butnot3MarketSegmentationTheory市场细分理论MarketSegmentationTheoryexplains3,butnot1and2LiquidityPremiumTheory流动性溢价理论Solution:CombinefeaturesofbothPureExpectationsTheoryandMarketSegmentationTheorytogetLiquidityPremiumTheoryandexplainallfacts24一、纯预期理论KeyAssumption关键假设: Bondsofdifferentmaturitiesareperfectsubstitutes(完全替代品)。Implication隐含假设:

Reonbondsofdifferentmaturitiesareequal.25纯预期理论——投资策略考虑两种投资策略：Buy$1ofone-yearbondandwhenmaturesbuyanotherone-yearbondBuy$1oftwo-yearbondandholdit26Expectedreturnfromstrategy2Since(i2t)2isextremelysmall,expectedreturnisapproximately2(i2t).27Expectedreturnfromstrategy1Sinceit(iet+1)isalsoextremelysmall,expectedreturnisapproximatelyit+iet+1.28纯预期理论——投资策略Fromimplicationaboveexpectedreturnsoftwostrategiesareequal;ThereforeSolvingfori2t(1)29n周期债券的利率Equation2states:n周期债券的利率等于在这个周期内出现的短期债券利率的平均值(2)30NumericalexampleOne-yearinterestrateoverthenextfiveyears

isexpectedtobe5%,6%,7%,8%,and9%Interestrateontwo-yearbond:(5%+6%)/2=5.5%Interestrateforfive-yearbond:(5%+6%+7%+8%+9%)/5=7%Interestrateforone-tofive-yearbonds:5%,5.5%,6%,6.5%and7%31纯预期理论对期限结构的解释当预计未来的短期利率上升时，未来短期利率的平均值比当前的短期利率高，所以收益率曲线向上倾斜。当预计未来的短期利率不变时，未来短期利率的平均值与当前的短期利率相同，所以收益率曲线是平坦的。当预计未来的短期利率下降时，收益率曲线向下倾斜。32纯预期理论与第1个事实短期利率的提高将会提高人们对未来短期利率的预期。Ifit

today,iet+1,iet+2etc.

averageoffuturerates

int

Therefore:it

int

(i.e.,shortandlongratesmovetogether)33纯预期理论与第2个事实短期利率较低，人们会认为未来短期利率将会提高，所以长期利率会高于当前的短期利率。yieldcurvewillhavesteepupwardslope.短期利率较高，人们会认为未来短期利率将会降低，所以长期利率会低于当前短期利率。yieldcurvewillhavedownwardslope.34纯预期理论与第3个事实收益率曲线向上倾斜，意味着预期未来的短期利率会上升。而短期利率既有可能上升也有可能下降，按照纯预期理论的解释收益率曲线最常见的形式应该是水平的。Doesn'texplainfact3—thatyieldcurveusuallyhasupwardslope.35二、市场分割理论KeyAssumption:Bondsofdifferentmaturitiesarenotsubstitutes(替代品)atallImplication:

市场是完全独立的，不同到期期限的债券利率由该债券自身的供求状况决定。36市场分割理论对期限结构的解释Explainsfact3—thatyieldcurveisusuallyupwardslopingPeopletypicallyprefershortholdingperiodsandthushavehigherdemandforshort-termbonds,whichhavehigherpricesandlowerinterestratesthanlongbonds37市场分割理论对期限结构的解释Doesnotexplainfact1orfact2becauseitsassumeslong-termandshort-termratesaredeterminedindependently38三、流动性溢价理论ThistheorymodifiesPureExpectationsanditalsohasfeaturesofMarketSegmentationTheory.39三、流动性溢价理论KeyAssumption: Bondsofdifferentmaturitiesaresubstitutes,butarenotperfectsubstitutesImplication:

一种债券的预期回报率影响不同期限的另一种债券的预期回报率，但是投资者对于不同到期期限的债券有所偏好。40LiquidityPremiumTheory–MainPointInvestorsprefershortratherthanlongbonds

mustbepaidpositiveliquiditypremium,lnt,toholdlongtermbonds41LiquidityPremiumTheory–YieldCurve42LiquidityPremiumTheory-EquationResultsinfollowingmodificationofPureExpectationsTheory(3)43NumericalExample4（P77）One-yearinterestrateoverthenextfiveyears:5%,6%,7%,8%,and9%Investors'preferences(Psychological)forholdingshort-termbondsandliquiditypremiumforone-tofive-yearbonds:0%,0.25%,0.5%,0.75%,and1.0%44NumericalExampleInterestrateonthetwo-yearbond:0.25%+(5%+6%)/2=5.75%Interestrateonthefive-yearbond:1.0%+(5%+6%+7%+8%+9%)/5=8%Interestratesononetofive-yearbonds:5%,5.75%,6.5%,7.25%,and8%45流动性溢价理论对期限结构的解释Comparingwiththoseforthepureexpectationstheory,liquiditypremiumtheoryproducesyieldcurvesmoresteeplyupwardslopedExplainsfact3—thatusualupwardslopedyieldcurvebyliquiditypremiumforlong-termbonds46流动性溢价理论对期限结构的解释Explainsfact1andfact2usingsameexplanationsaspureexpectationstheorybecauseithasaverageoffutureshortratesasdeterminantoflongrate47YieldCurvesandtheMarket’sExpectationsofFutureShort-TermInterestRates48四、用期限结构对利率进行预测PureExpectationsTheory:Investin1-periodbondsorintwo-periodbond

Solveforforwardrate,(4)49Numericalexample(P80)i1t=5%,i