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LecturePresentationSoftware
toaccompany
InvestmentAnalysisand
PortfolioManagement
SeventhEdition
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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
toaccompany
InvestmentAnalysisand
PortfolioManagement
SeventhEdition
by
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
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