1.05.第5章 風(fēng)險(xiǎn)和期限結(jié)構(gòu)如何影響利率

第五章風(fēng)險(xiǎn)和期限如何影響利率第一節(jié)利率的風(fēng)險(xiǎn)結(jié)構(gòu)

第二節(jié)利率的期限結(jié)構(gòu)1ChapterPreview本章主要研究風(fēng)險(xiǎn)對利率的影響和期限結(jié)構(gòu)對利率的影響。利率的風(fēng)險(xiǎn)結(jié)構(gòu)

RiskStructureofInterestRates利率的期限結(jié)構(gòu)

TermStructureofInterestRates2第一節(jié)利率的風(fēng)險(xiǎn)結(jié)構(gòu)Tostartthisdiscussion,wefirstexaminetheyieldsforseveralcategoriesoflong-termbondsoverthelast85years.Youshouldnoteseveralaspectsregardingtheserates,relatedtodifferentbondcategoriesandhowthishaschangedthroughtime.3RiskStructureofLongBondsintheU.S.Interestratesofbondswithdifferentrisks/release/h15/data.htm4Twoimportantfeaturesofinterest-ratebehaviorforbondsFigure1showsthefeaturesasfollowing:

在任何一年內(nèi)，不同種類的債券利率各不相同；利率之間的利差(spread)隨著時間的推移而變動。5FactorsAffectingRiskStructureofInterestRatesDefaultRisk(違約風(fēng)險(xiǎn))Liquidity(流動性)IncomeTaxesFactor(所得稅因素)6一、DefaultRisk(違約風(fēng)險(xiǎn))影響債券利率的一個特征是其違約風(fēng)險(xiǎn)(riskofdefault)。當(dāng)債券發(fā)行者不能或不愿按事先約定支付利息或面值時，就出現(xiàn)違約風(fēng)險(xiǎn)。美國聯(lián)邦政府的債券通常是沒有違約風(fēng)險(xiǎn)的(美國政府可以通過增加稅收來履行還款義務(wù))。這種債券被稱為無風(fēng)險(xiǎn)債券(default-freebonds).7RiskPremium(風(fēng)險(xiǎn)溢價)具有違約風(fēng)險(xiǎn)的債券和無違約風(fēng)險(xiǎn)的債券之間的利差稱為風(fēng)險(xiǎn)溢價(riskpremium)，它表明人們持有高風(fēng)險(xiǎn)債券所必須獲得的利息。具有違約風(fēng)險(xiǎn)的債券通常具有正的風(fēng)險(xiǎn)溢價，而且違約風(fēng)險(xiǎn)越大風(fēng)險(xiǎn)溢價越大。8IncreaseinDefaultRiskonCorporateBonds9公司債違約風(fēng)險(xiǎn)增長的分析CorporateBondMarketRiskofcorporatebonds

,Dc

,Dcshiftsleft

Pc

,ic

TreasuryBondMarketRelativeriskofTreasurybonds

,DT

,DTshiftsright

PT

,iT

OutcomeRiskpremium,ic-iT,rises10債券的評級BondRatingsBaa(Moody)orBBB(S&P)或以上級別的稱為投資級別證券；以下級別的稱為稱為垃圾債券Junkbonds。11二、Liquidity(流動性)影響債券利率的另一個因素是流動性liquidity;債券的流動性越強(qiáng)越受歡迎。在眾多長期債券中，美國的國債流動性最強(qiáng)。因?yàn)槠浣灰追秶鷱V泛，容易被出售，而且交易成本低。12LiquidityPremium(流動性溢價)公司債券的流動性比國債要差。Becausefewerbondsforanyonecorporationaretradedanditmaybehardtofindbuyersquickly.

公司債券與國債之間的利差(thatis,theriskpremiums)不僅反映了公司債券的違約風(fēng)險(xiǎn)，還反映了其流動性風(fēng)險(xiǎn)。所以風(fēng)險(xiǎn)溢價有時也被稱為流動性溢價。13DecreaseinLiquidityofCorporateBondsRiskpremiumreflectsnotonlycorporatebonds'defaultriskbutalsolowerliquidity14公司債流動性降低的反應(yīng)CorporateBondMarketLiquidityofcorporatebonds

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,Dcshiftsleft

Pc

,ic

TreasuryBondMarketRelativelymoreliquidTreasurybonds,DT

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OutcomeRiskpremium,ic-iT,rises15三、IncomeTaxesFactor(所得稅因素)美國的市政府債券(municipalbonds)的利息支付不用繳納聯(lián)邦所得稅(federalincometaxes)。這對于市政債券的需求來說，與提高預(yù)期收益具有相同的影響效果。16市政府債券的稅收優(yōu)勢17市政府債券的稅收優(yōu)勢分析MunicipalBondMarketTaxexemptionraisesrelativeReonmunicipalbonds,Dm

,Dmshiftsright

Pm

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TreasuryBondMarketRelativeReonTreasurybonds

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Outcome

im<iT18第二節(jié)利率的期限結(jié)構(gòu)具有相同風(fēng)險(xiǎn)、流動性和稅收因素的債券也可能因?yàn)榈狡谄谙薜牟町惗哂胁煌睦仕健?9不同到期期限的債券的利率變動20收益率曲線YieldCurvesDynamicyieldcurvethatcanshowthecurveatanytimeinhistory

http:///charts/YieldCurve.html21美國不同到期期限國債利率22第二節(jié)利率的期限結(jié)構(gòu)具有不同到期期限的債券的利率會同時變動。當(dāng)短期利率較低時，收益率曲線更有可能陡峭向上傾斜；當(dāng)短期利率較高時，收益率曲線更有可能向下傾斜。收益率曲線通常是向上傾斜。23期限結(jié)構(gòu)理論P(yáng)ureExpectationsTheory純預(yù)期理論P(yáng)ureExpectationsTheoryexplains1and2,butnot3MarketSegmentationTheory市場細(xì)分理論MarketSegmentationTheoryexplains3,butnot1and2LiquidityPremiumTheory流動性溢價理論Solution:CombinefeaturesofbothPureExpectationsTheoryandMarketSegmentationTheorytogetLiquidityPremiumTheoryandexplainallfacts24一、純預(yù)期理論KeyAssumption關(guān)鍵假設(shè): Bondsofdifferentmaturitiesareperfectsubstitutes(完全替代品)。Implication隱含假設(shè):

Reonbondsofdifferentmaturitiesareequal.25純預(yù)期理論——投資策略考慮兩種投資策略：Buy$1ofone-yearbondandwhenmaturesbuyanotherone-yearbondBuy$1oftwo-yearbondandholdit26Expectedreturnfromstrategy2Since(i2t)2isextremelysmall,expectedreturnisapproximately2(i2t).27Expectedreturnfromstrategy1Sinceit(iet+1)isalsoextremelysmall,expectedreturnisapproximatelyit+iet+1.28純預(yù)期理論——投資策略Fromimplicationaboveexpectedreturnsoftwostrategiesareequal;ThereforeSolvingfori2t(1)29n周期債券的利率Equation2states:n周期債券的利率等于在這個周期內(nèi)出現(xiàn)的短期債券利率的平均值(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純預(yù)期理論對期限結(jié)構(gòu)的解釋當(dāng)預(yù)計(jì)未來的短期利率上升時，未來短期利率的平均值比當(dāng)前的短期利率高，所以收益率曲線向上傾斜。當(dāng)預(yù)計(jì)未來的短期利率不變時，未來短期利率的平均值與當(dāng)前的短期利率相同，所以收益率曲線是平坦的。當(dāng)預(yù)計(jì)未來的短期利率下降時，收益率曲線向下傾斜。32純預(yù)期理論與第1個事實(shí)短期利率的提高將會提高人們對未來短期利率的預(yù)期。Ifit

today,iet+1,iet+2etc.

averageoffuturerates

int

Therefore:it

int

(i.e.,shortandlongratesmovetogether)33純預(yù)期理論與第2個事實(shí)短期利率較低，人們會認(rèn)為未來短期利率將會提高，所以長期利率會高于當(dāng)前的短期利率。yieldcurvewillhavesteepupwardslope.短期利率較高，人們會認(rèn)為未來短期利率將會降低，所以長期利率會低于當(dāng)前短期利率。yieldcurvewillhavedownwardslope.34純預(yù)期理論與第3個事實(shí)收益率曲線向上傾斜，意味著預(yù)期未來的短期利率會上升。而短期利率既有可能上升也有可能下降，按照純預(yù)期理論的解釋收益率曲線最常見的形式應(yīng)該是水平的。Doesn'texplainfact3—thatyieldcurveusuallyhasupwardslope.35二、市場分割理論KeyAssumption:Bondsofdifferentmaturitiesarenotsubstitutes(替代品)atallImplication:

市場是完全獨(dú)立的，不同到期期限的債券利率由該債券自身的供求狀況決定。36市場分割理論對期限結(jié)構(gòu)的解釋Explainsfact3—thatyieldcurveisusuallyupwardslopingPeopletypicallyprefershortholdingperiodsandthushavehigherdemandforshort-termbonds,whichhavehigherpricesandlowerinterestratesthanlongbonds37市場分割理論對期限結(jié)構(gòu)的解釋Doesnotexplainfact1orfact2becauseitsassumeslong-termandshort-termratesaredeterminedindependently38三、流動性溢價理論ThistheorymodifiesPureExpectationsanditalsohasfeaturesofMarketSegmentationTheory.39三、流動性溢價理論KeyAssumption: Bondsofdifferentmaturitiesaresubstitutes,butarenotperfectsubstitutesImplication:

一種債券的預(yù)期回報(bào)率影響不同期限的另一種債券的預(yù)期回報(bào)率，但是投資者對于不同到期期限的債券有所偏好。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流動性溢價理論對期限結(jié)構(gòu)的解釋Comparingwiththoseforthepureexpectationstheory,liquiditypremiumtheoryproducesyieldcurvesmoresteeplyupwardslopedExplainsfact3—thatusualupwardslopedyieldcurvebyliquiditypremiumforlong-termbonds46流動性溢價理論對期限結(jié)構(gòu)的解釋Explainsfact1andfact2usingsameexplanationsaspureexpectationstheorybecauseithasaverageoffutureshortratesasdeterminantoflongrate47YieldCurvesandtheMarket’sExpectationsofFutureShort-TermInterestRates48四、用期限結(jié)構(gòu)對利率進(jìn)行預(yù)測PureExpectationsTheory:Investin1-periodbondsorintwo-periodbond

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