andValuationofBonds(投資分析與投資組合管理)課件

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FrankK.Reilly&KeithC.BrownChapter19LecturePresentationSoftware1Chapter19-TheAnalysisandValuationofBondsQuestionstobeanswered:Howdoyoudeterminethevalueofabondbasedonthepresentvalueformula?Whatarethealternativebondyieldsthatareimportanttoinvestors?Chapter19-TheAnalysisand2Chapter19-TheAnalysisandValuationofBondsHowdoyoucomputethefollowingmajoryieldsonbonds:currentyield,yieldtomaturity,yieldtocall,andcompoundrealized(horizon)yield?Whatarespotratesandforwardratesandhowdoyoucalculatetheseratesfromayieldtomaturitycurve?Whatisthespotrateyieldcurveandforwardratecurve?Chapter19-TheAnalysisand3Chapter19-TheAnalysisandValuationofBondsHowandwhydoyouusethespotratecurvetodeterminethevalueofabond?Whatarethealternativetheoriesthatattempttoexplaintheshapeofthetermstructureofinterestrates?Whatfactorsaffectthelevelofbondyieldsatapointintime?Whateconomicforcescausechangesinbondyieldsovertime?Chapter19-TheAnalysisand4Chapter19-TheAnalysisandValuationofBondsWhenyieldschange,whatcharacteristicsofabondcausedifferentialpricechangesforindividualbonds?Whatismeantbythedurationofabond,howdoyoucomputeit,andwhatfactorsaffectit?Whatismodifieddurationandwhatistherelationshipbetweenabond’smodifieddurationanditsvolatility?Chapter19-TheAnalysisand5Chapter19-TheAnalysisandValuationofBondsWhatiseffectivedurationandwhenisituseful?Whatistheconvexityforabond,howdoyoucomputeit,andwhatfactorsaffectit?Underwhatconditionsisitnecessarytoconsiderbothmodifieddurationandconvexitywhenestimatingabond’spricevolatility?Chapter19-TheAnalysisand6Chapter19-TheAnalysisandValuationofBondsWhathappenstothedurationandconvexityofbondsthathaveembeddedcalloptions?Chapter19-TheAnalysisand7Chapter19-TheAnalysisandValuationofBondsWhatareeffectivedurationandeffectiveconvexityandwhenaretheyuseful?Whatisempiricaldurationandhowisitusedwithcommonstocksandotherassets?Whatarethestaticyieldspreadandtheoption-adjustedspread?Chapter19-TheAnalysisand8TheFundamentalsofBondValuationThepresent-valuemodelWhere:Pm=thecurrentmarketpriceofthebondn=thenumberofyearstomaturityCi

=theannualcouponpaymentforbondii=theprevailingyieldtomaturityforthisbondissuePp=theparvalueofthebondTheFundamentalsofBondValua9TheFundamentalsofBondValuationIfyield<couponrate,bondwillbepricedatapremiumtoitsparvalueIfyield>couponrate,bondwillbepricedatadiscounttoitsparvaluePrice-yieldrelationshipisconvex(notastraightline)TheFundamentalsofBondValua10TheYieldModelTheexpectedyieldonthebondmaybecomputedfromthemarketpriceWhere:i=thediscountratethatwilldiscountthecashflowstoequalthecurrentmarketpriceofthebondTheYieldModelTheexpectedyi11ComputingBondYieldsYieldMeasurePurposeNominalYieldMeasuresthecouponrateCurrentyieldMeasurescurrentincomeratePromisedyieldtomaturityMeasuresexpectedrateofreturnforbondheldtomaturityPromisedyieldtocallMeasuresexpectedrateofreturnforbondheldtofirstcalldateRealized(horizon)yieldMeasuresexpectedrateofreturnforabondlikelytobesoldpriortomaturity.Itconsidersspecifiedreinvestmentassumptionsandanestimatedsalesprice.Itcanalsomeasuretheactualrateofreturnonabondduringsomepastperiodoftime.ComputingBondYieldsYieldMea12NominalYield Measuresthecouponratethatabondinvestorreceivesasapercentofthebond’sparvalueNominalYield Measuresthecou13CurrentYieldSimilartodividendyieldforstocksImportanttoincomeorientedinvestorsCY=Ci/Pm

where:CY=thecurrentyieldonabondCi=theannualcouponpaymentofbond

iPm=thecurrentmarketpriceofthebondCurrentYieldSimilartodivide14PromisedYieldtoMaturityWidelyusedbondyieldfigureAssumesInvestorholdsbondtomaturityAllthebond’scashflowisreinvestedatthecomputedyieldtomaturitySolveforithatwillequatethecurrentpricetoallcashflowsfromthebondtomaturity,similartoIRRPromisedYieldtoMaturityWide15Computingthe

PromisedYieldtoMaturityTwomethodsApproximatepromisedyieldEasy,lessaccuratePresent-valuemodelMoreinvolved,moreaccurateComputingthe

PromisedYield16ApproximatePromisedYieldCoupon+AnnualStraight-LineAmortizationofCapitalGainorLossAverageInvestment=ApproximatePromisedYieldCoup17Present-ValueModelPresent-ValueModel18PromisedYieldtoCall

ApproximationMaybelessthanyieldtomaturityReflectsreturntoinvestorifbondiscalledandcannotbeheldtomaturityWhere:AYC=approximateyieldtocall(YTC)Pc

=callpriceofthebondPm=marketpriceofthebondCt

=annualcouponpaymentnc=thenumberofyearstofirstcalldatePromisedYieldtoCall

Approxi19PromisedYieldtoCall

Present-ValueMethodWhere:Pm

=marketpriceofthebondCi=annualcouponpaymentnc=numberofyearstofirstcallPc=callpriceofthebondPromisedYieldtoCall

Present20RealizedYieldApproximationWhere:ARY=approximaterealizedyieldtocall(YTC)Pf

=estimatedfuturesellingpriceofthebondCi

=annualcouponpaymenthp=thenumberofyearsinholdingperiodofthebondRealizedYieldApproximationWh21RealizedYield

Present-ValueMethodRealizedYield

Present-ValueM22CalculatingFutureBondPricesWhere:Pf

=estimatedfuturepriceofthebondCi=annualcouponpaymentn=numberofyearstomaturityhp=holdingperiodofthebondinyearsi=expectedsemiannualrateattheendoftheholdingperiodCalculatingFutureBondPrices23YieldAdjustments

forTax-ExemptBondsWhere:T=amountandtypeoftaxexemptionYieldAdjustments

forTax-Exe24WhatDeterminesInterestRatesInverserelationshipwithbondpricesForecastinginterestratesFundamentaldeterminantsofinterestratesi=RFR+I+RP where:RFR=realrisk-freerateofinterestI=expectedrateofinflationRP=riskpremiumWhatDeterminesInterestRates25WhatDeterminesInterestRatesEffectofeconomicfactorsrealgrowthratetightnessoreaseofcapitalmarketexpectedinflationorsupplyanddemandofloanablefundsImpactofbondcharacteristicscreditqualitytermtomaturityindentureprovisionsforeignbondriskincludingexchangerateriskandcountryriskWhatDeterminesInterestRates26WhatDeterminesInterestRatesTermstructureofinterestratesExpectationshypothesisLiquiditypreferencehypothesisSegmentedmarkethypothesisTradingimplicationsofthetermstructureWhatDeterminesInterestRates27ExpectationsHypothesisAnylong-terminterestratesimplyrepresentsthegeometricmeanofcurrentandfutureone-yearinterestratesexpectedtoprevailoverthematurityoftheissueExpectationsHypothesisAnylon28LiquidityPreferenceTheoryLong-termsecuritiesshouldprovidehigherreturnsthanshort-termobligationsbecauseinvestorsarewillingtosacrificesomeyieldstoinvestinshort-maturityobligationstoavoidthehigherpricevolatilityoflong-maturitybonds

LiquidityPreferenceTheoryLon29Segmented-MarketHypothesisDifferentinstitutionalinvestorshavedifferentmaturityneedsthatleadthemtoconfinetheirsecurityselectionstospecificmaturitysegments

Segmented-MarketHypothesisDif30TradingImplicationsoftheTermStructureInformationonmaturitiescanhelpyouformulateyieldexpectationsbysimplyobservingtheshapeoftheyieldcurve

TradingImplicationsoftheTe31YieldSpreadsSegments:governmentbonds,agencybonds,andcorporatebondsSectors:prime-grademunicipalbondsversusgood-grademunicipalbonds,AAutilitiesversusBBButilitiesCouponsorseasoningwithinasegmentorsectorMaturitieswithinagivenmarketsegmentorsectorYieldSpreadsSegments:governm32YieldSpreads MagnitudesanddirectionofyieldspreadscanchangeovertimeYieldSpreads Magnitudesandd33WhatDeterminesthe

PriceVolatilityforBondsBondpricechangeismeasuredasthepercentagechangeinthepriceofthebondWhere:EPB=theendingpriceofthebondBPB=thebeginningpriceofthebondWhatDeterminesthe

PriceVol34WhatDeterminesthe

PriceVolatilityforBondsFourFactors1.Parvalue2.Coupon3.Yearstomaturity4.PrevailingmarketinterestrateWhatDeterminesthe

PriceVol35WhatDeterminesthe

PriceVolatilityforBondsFiveobservedbehaviors1.Bondpricesmoveinverselytobondyields(interestrates)2.Foragivenchangeinyields,longermaturitybondspostlargerpricechanges,thusbondpricevolatilityisdirectlyrelatedtomaturity3.Pricevolatilityincreasesatadiminishingrateastermtomaturityincreases4.Pricemovementsresultingfromequalabsoluteincreasesordecreasesinyieldarenotsymmetrical5.Highercouponissuesshowsmallerpercentagepricefluctuationforagivenchangeinyield,thusbondpricevolatilityisinverselyrelatedtocouponWhatDeterminesthe

PriceVol36WhatDeterminesthe

PriceVolatilityforBondsThematurityeffectThecouponeffectTheyieldleveleffectSometradingstrategiesWhatDeterminesthe

PriceVol37TheDurationMeasureSincepricevolatilityofabondvariesinverselywithitscouponanddirectlywithitstermtomaturity,itisnecessarytodeterminethebestcombinationofthesetwovariablestoachieveyourobjectiveAcompositemeasureconsideringbothcouponandmaturitywouldbebeneficialTheDurationMeasureSincepric38TheDurationMeasureDevelopedbyFrederickR.Macaulay,1938Where:

t=timeperiodinwhichthecouponorprincipalpaymentoccursCt

=interestorprincipalpaymentthatoccursinperiodt

i=yieldtomaturityonthebondTheDurationMeasureDeveloped39CharacteristicsofDurationDurationofabondwithcouponsisalwayslessthanitstermtomaturitybecausedurationgivesweighttotheseinterimpaymentsAzero-couponbond’sdurationequalsitsmaturityThereisaninverserelationbetweendurationandcouponThereisapositiverelationbetweentermtomaturityandduration,butdurationincreasesatadecreasingratewithmaturityThereisaninverserelationbetweenYTManddurationSinkingfundsandcallprovisionscanhaveadramaticeffectonabond’sdurationCharacteristicsofDurationDur40ModifiedDurationandBondPriceVolatilityAnadjustedmeasureofdurationcanbeusedtoapproximatethepricevolatilityofabondWhere:m=numberofpaymentsayearYTM=nominalYTMModifiedDurationandBondPri41DurationandBondPriceVolatilityBondpricemovementswillvaryproportionallywithmodifieddurationforsmallchangesinyieldsAnestimateofthepercentagechangeinbondpricesequalsthechangeinyieldtimemodifieddurationWhere:P=changeinpriceforthebondP=beginningpriceforthebondDmod=themodifieddurationofthebondi=yieldchangeinbasispointsdividedby100DurationandBondPriceVolati42TradingStrategiesUsingDurationLongest-durationsecurityprovidesthemaximumpricevariationIfyouexpectadeclineininterestrates,increasetheaveragedurationofyourbondportfoliotoexperiencemaximumpricevolatilityIfyouexpectanincreaseininterestrates,reducetheaveragedurationtominimizeyourpricedeclineNotethatthedurationofyourportfolioisthemarket-value-weightedaverageofthedurationoftheindividualbondsintheportfolioTradingStrategiesUsingDurat43BondDurationinYearsforBondsYielding6PercentUnderDifferentTermsBondDurationinYearsforBon44BondConvexityEquation19.6isalinearapproximationofbondpricechangeforsmallchangesinmarketyieldsBondConvexityEquation19.6is45BondConvexityModifieddurationisalinearapproximationofbondpricechangeforsmallchangesinmarketyieldsPricechangesarenotlinear,butacurvilinear(convex)functionBondConvexityModifiedduratio46Price-YieldRelationshipforBondsThegraphofpricesrelativetoyieldsisnotastraightline,butacurvilinearrelationshipThiscanbeappliedtoasinglebond,aportfolioofbonds,oranystreamoffuturecashflowsTheconvexprice-yieldrelationshipwilldifferamongbondsorothercashflowstreamsdependingonthecouponandmaturityTheconvexityoftheprice-yieldrelationshipdeclinesslowerastheyieldincreasesModifieddurationisthepercentagechangeinpriceforanominalchangeinyieldPrice-YieldRelationshipforB47ModifiedDurationForsmallchangesthiswillgiveagoodestimate,butthisisalinearestimateonthetangentlineModifiedDurationForsmallcha48DeterminantsofConvexityTheconvexityisthemeasureofthecurvatureandisthesecondderivativeofpricewithresecttoyield(d2P/di2)dividedbypriceConvexityisthepercentagechangeindP/diforagivenchangeinyieldDeterminantsofConvexityThec49DeterminantsofConvexityInverserelationshipbetweencouponandconvexityDirectrelationshipbetweenmaturityandconvexityInverserelationshipbetweenyieldandconvexityDeterminantsofConvexityInver50ModifiedDuration-ConvexityEffectsChangesinabond’spriceresultingfromachangeinyieldaredueto:Bond’smodifieddurationBond’sconvexityRelativeeffectofthesetwofactorsdependsonthecharacteristicsofthebond(itsconvexity)andthesizeoftheyieldchangeConvexityisdesirableModifiedDuration-ConvexityEf51DurationandConvexity

forCallableBondsIssuerhasoptiontocallbondandpayoffwithproceedsfromanewissuesoldataloweryieldEmbeddedoptionDifferenceindurationtomaturityanddurationtofirstcallCombinationofanoncallablebondplusacalloptionthatwassoldtotheissuerAnyincreaseinvalueofthecalloptionreducesthevalueofthecallablebondDurationandConvexity

forCa52OptionAdjustedDurationBasedontheprobabilitythattheissuingfirmwillexerciseitscalloptionDurationofthenon-callablebondDurationofthecalloptionOptionAdjustedDurationBased53ConvexityofCallableBondsNoncallablebondhaspositiveconvexityCallablebondhasnegativeconvexityConvexityofCallableBondsNon54LimitationsofMacaulayandModifiedDurationPercentagechangeestimatesusingmodifieddurationonlyaregoodforsmall-yieldchangesDifficulttodeterminetheinterest-ratesensitivityofaportfolioofbondswhenthereisachangeininterestratesandtheyieldcurveexperiencesanonparallelshiftInitialassumptionthatcashflowsfromthebondarenotaffectedbyyieldchanges

LimitationsofMacaulayandMo55EffectiveDurationMeasureoftheinterestratesensitivityofanassetUseapricingmodeltoestimatethemarketpricessurroundingachangeininterestratesEffectiveDuration EffectiveConvexityP-=theestimatedpriceafteradownwardshiftininterestratesP+=theestimatedpriceafteraupwardshiftininterestratesP=thecurrentpriceS=theassumedshiftinthetermstructureEffectiveDurationMeasureoft56EffectiveDurationEffectivedurationgreaterthanmaturityNegativeeffectivedurationEmpiricaldurationEffectiveDurationEffectivedu57EmpiricalDurationActualpercentchangeforanassetinresponsetoachangeinyieldduringaspecifiedtimeperiodEmpiricalDurationActualperce58YieldSpreadsWithEmbeddedOptionsStaticYieldSpreadsConsiderthetotaltermstructureOption-AdjustedSpreadsConsiderchangesinthetermstructureandalternativeestimatesofthevolatilityofinterestratesYieldSpreadsWithEmbeddedOp59TheInternet

InvestmentsOnlineTheInternet

InvestmentsOnlin60EndofChapter19TheAnalysisandValuationofBondsEndofChapter1961Futuretopics

Chapter20BondPortfolioManagementStrategiesFuturetopics

Chapter20BondP62LecturePresentationSoftware

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InvestmentAnalysisand

PortfolioManagement

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FrankK.Reilly&KeithC.BrownChapter19LecturePresentationSoftware63Chapter19-TheAnalysisandValuationofBondsQuestionstobeanswered:Howdoyoudeterminethevalueofabondbasedonthepresentvalueformula?Whatarethealternativebondyieldsthatareimportanttoinvestors?Chapter19-TheAnalysisand64Chapter19-TheAnalysisandValuationofBondsHowdoyoucomputethefollowingmajoryieldsonbonds:currentyield,yieldtomaturity,yieldtocall,andcompoundrealized(horizon)yield?Whatarespotratesandforwardratesandhowdoyoucalculatetheseratesfromayieldtomaturitycurve?Whatisthespotrateyieldcurveandforwardratecurve?Chapter19-TheAnalysisand65Chapter19-TheAnalysisandValuationofBondsHowandwhydoyouusethespotratecurvetodeterminethevalueofabond?Whatarethealternativetheoriesthatattempttoexplaintheshapeofthetermstructureofinterestrates?Whatfactorsaffectthelevelofbondyieldsatapointintime?Whateconomicforcescausechangesinbondyieldsovertime?Chapter19-TheAnalysisand66Chapter19-TheAnalysisandValuationofBondsWhenyieldschange,whatcharacteristicsofabondcausedifferentialpricechangesforindividualbonds?Whatismeantbythedurationofabond,howdoyoucomputeit,andwhatfactorsaffectit?Whatismodifieddurationandwhatistherelationshipbetweenabond’smodifieddurationanditsvolatility?Chapter19-TheAnalysisand67Chapter19-TheAnalysisandValuationofBondsWhatiseffectivedurationandwhenisituseful?Whatistheconvexityforabond,howdoyoucomputeit,andwhatfactorsaffectit?Underwhatconditionsisitnecessarytoconsiderbothmodifieddurationandconvexitywhenestimatingabond’spricevolatility?Chapter19-TheAnalysisand68Chapter19-TheAnalysisandValuationofBondsWhathappenstothedurationandconvexityofbondsthathaveembeddedcalloptions?Chapter19-TheAnalysisand69Chapter19-TheAnalysisandValuationofBondsWhatareeffectivedurationandeffectiveconvexityandwhenaretheyuseful?Whatisempiricaldurationandhowisitusedwithcommonstocksandotherassets?Whatarethestaticyieldspreadandtheoption-adjustedspread?Chapter19-TheAnalysisand70TheFundamentalsofBondValuationThepresent-valuemodelWhere:Pm=thecurrentmarketpriceofthebondn=thenumberofyearstomaturityCi

=theannualcouponpaymentforbondii=theprevailingyieldtomaturityforthisbondissuePp=theparvalueofthebondTheFundamentalsofBondValua71TheFundamentalsofBondValuationIfyield<couponrate,bondwillbepricedatapremiumtoitsparvalueIfyield>couponrate,bondwillbepricedatadiscounttoitsparvaluePrice-yieldrelationshipisconvex(notastraightline)TheFundamentalsofBondValua72TheYieldModelTheexpectedyieldonthebondmaybecomputedfromthemarketpriceWhere:i=thediscountratethatwilldiscountthecashflowstoequalthecurrentmarketpriceofthebondTheYieldModelTheexpectedyi73ComputingBondYieldsYieldMeasurePurposeNominalYieldMeasuresthecouponrateCurrentyieldMeasurescurrentincomeratePromisedyieldtomaturityMeasuresexpectedrateofreturnforbondheldtomaturityPromisedyieldtocallMeasuresexpectedrateofreturnforbondheldtofirstcalldateRealized(horizon)yieldMeasuresexpectedrateofreturnforabondlikelytobesoldpriortomaturity.Itconsidersspecifiedreinvestmentassumptionsandanestimatedsalesprice.Itcanalsomeasuretheactualrateofreturnonabondduringsomepastperiodoftime.ComputingBondYieldsYieldMea74NominalYield Measuresthecouponratethatabondinvestorreceivesasapercentofthebond’sparvalueNominalYield Measuresthecou75CurrentYieldSimilartodividendyieldforstocksImportanttoincomeorientedinvestorsCY=Ci/Pm

where:CY=thecurrentyieldonabondCi=theannualcouponpaymentofbond

iPm=thecurrentmarketpriceofthebondCurrentYieldSimilartodivide76PromisedYieldtoMaturityWidelyusedbondyieldfigureAssumesInvestorholdsbondtomaturityAllthebond’scashflowisreinvestedatthecomputedyieldtomaturitySolveforithatwillequatethecurrentpricetoallcashflowsfromthebondtomaturity,similartoIRRPromisedYieldtoMaturityWide77Computingthe

PromisedYieldtoMaturityTwomethodsApproximatepromisedyieldEasy,lessaccuratePresent-valuemodelMoreinvolved,moreaccurateComputingthe

PromisedYield78ApproximatePromisedYieldCoupon+AnnualStraight-LineAmortizationofCapitalGainorLossAverageInvestment=ApproximatePromisedYieldCoup79Present-ValueModelPresent-ValueModel80PromisedYieldtoCall

ApproximationMaybelessthanyieldtomaturityReflectsreturntoinvestorifbondiscalledandcannotbeheldtomaturityWhere:AYC=approximateyieldtocall(YTC)Pc

=callpriceofthebondPm=marketpriceofthebondCt

=annualcouponpaymentnc=thenumberofyearstofirstcalldatePromisedYieldtoCall

Approxi81PromisedYieldtoCall

Present-ValueMethodWhere:Pm

=marketpriceofthebondCi=annualcouponpaymentnc=numberofyearstofirstcallPc=callpriceofthebondPromisedYieldtoCall

Present82RealizedYieldApproximationWhere:ARY=approximaterealizedyieldtocall(YTC)Pf

=estimatedfuturesellingpriceofthebondCi

=annualcouponpaymenthp=thenumberofyearsinholdingperiodofthebondRealizedYieldApproximationWh83RealizedYield

Present-ValueMethodRealizedYield

Present-ValueM84CalculatingFutureBondPricesWhere:Pf

=estimatedfuturepriceofthebondCi=annualcouponpaymentn=numberofyearstomaturityhp=holdingperiodofthebondinyearsi=expectedsemiannualrateattheendoftheholdingperiodCalculatingFutureBondPrices85YieldAdjustments

forTax-ExemptBondsWhere:T=amountandtypeoftaxexemptionYieldAdjustments

forTax-Exe86WhatDeterminesInterestRatesInverserelationshipwithbondpricesForecastinginterestratesFundamentaldeterminantsofinterestratesi=RFR+I+RP where:RFR=realrisk-freerateofinterestI=expectedrateofinflationRP=riskpremiumWhatDeterminesInterestRates87WhatDeterminesInterestRatesEffectofeconomicfactorsrealgrowthratetightnessoreaseofcapitalmarketexpectedinflationorsupplyanddemandofloanablefundsImpactofbondcharacteristicscreditqualitytermtomaturityindentureprovisionsforeignbondriskincludingexchangerateriskandcountryriskWhatDeterminesInterestRates88WhatDeterminesInterestRatesTermstructureofinterestratesExpectationshypothesisLiquiditypreferencehypothesisSegmentedmarkethypothesisTradingimplicationsofthetermstructureWhatDeterminesInterestRates89ExpectationsHypothesisAnylong-terminterestratesimplyrepresentsthegeometricmeanofcurrentandfutureone-yearinterestratesexpectedtoprevailoverthematurityoftheissueExpectationsHypothesisAnylon90LiquidityPreferenceTheoryLong-termsecuritiesshouldprovidehigherreturnsthanshort-termobligationsbecauseinvestorsarewillingtosacrificesomeyieldstoinvestinshort-maturityobligationstoavoidthehigherpricevolatilityoflong-maturitybonds

LiquidityPreferenceTheoryLon91Segmented-MarketHypothesisDifferentinstitutionalinvestorshavedifferentmaturityneedsthatleadthemtoconfinetheirsecurityselectionstospecificmaturitysegments

Segmented-MarketHypothesisDif92TradingImplicationsoftheTermStructureInformationonmaturitiescanhelpyouformulateyieldexpectationsbysimplyobservingtheshapeoftheyieldcurve

TradingImplicationsoftheTe93YieldSpreadsSegments:governmentbonds,agencybonds,andcorporatebondsSectors:prime-grademunicipalbondsversusgood-grademunicipalbonds,AAutilitiesversusBBButilitiesCouponsorseasoningwithinasegmentorsectorMaturitieswithinagivenmarketsegmentorsectorYieldSpreadsSegments:governm94YieldSpreads MagnitudesanddirectionofyieldspreadscanchangeovertimeYieldSpreads Magnitudesandd95WhatDeterminesthe

PriceVolatilityforBondsBondpricechangeismeasuredasthepercentagechangeinthepriceofthebondWhere:EPB=theendingpriceofthebondBPB=thebeginningpriceofthebondWhatDeterminesthe

PriceVol96WhatDeterminesthe

PriceVolatilityforBondsFourFactors1.Parvalue2.Coupon3.Yearstomaturity4.PrevailingmarketinterestrateWhatDeterminesthe

PriceVol97WhatDeterminesthe

PriceVolatilityforBondsFiveobservedbehaviors1.Bondpricesmoveinverselytobondyields(interestrates)2.Foragivenchangeinyields,longermaturitybondspostlargerpricechanges,thusbondpricevolatilityisdirectlyrelatedtomaturity3.Pricevolatilityincreasesatadiminishingrateastermtomaturityincreases4.Pricemovementsresultingfromequalabsoluteincreasesordecreasesinyieldarenotsymmetrical5.Highercouponissuesshowsmallerpercentagepricefluctuationforagivenchangeinyield,thusbondpricevolatilityisinverselyrelatedtocouponWhatDeterminesthe

PriceVol98WhatDeterminesthe

PriceVolatilityforBondsThematurityeffectThecouponeffectTheyieldleveleffectSometradingstrategiesWhatDeterminesthe

PriceVol99TheDurationMeasureSincepricevolatilityofabondvariesinverselywithitscouponanddirectlywithitstermtomaturity,itisnecessarytodeterminethebestcombinationofthesetwovariablestoachieveyourobjectiveAcompositemeasureconsideringbothcouponandmaturitywouldbebeneficialTheDurationMeasureSincepric100TheDurationMeasureDevelopedbyFrederickR.Macaulay,1938Where:

t=timeperiodinwhichthecouponorprincipalpaymentoccursCt

=interestorprincipalpaymentthatoccursinperiodt

i=yieldtomaturityonthebondTheDurationMeasureDeveloped101CharacteristicsofDurationDurationofabondwithcouponsisalwayslessthani