《债券市场：分析与策略（第七版）》Ch26

Chapter26

BondPerformance:MeasurementandEvaluation

26-1Copyright©2010PearsonEducation,Inc.PublishingasPrenticeHallLearningObjectivesAfterreadingthischapter,youwillunderstandthedifferencebetweenperformancemeasurementandperformanceevaluationthevariousmethodsforcalculatingtherateofreturnoversomeevaluationperiod:thearithmeticaveragerateofreturn,thetime-weightedrateofreturn,andthedollar-weightedrateofreturntheimpactofclientcontributionsandwithdrawalsonthecalculatedreturn26-2Copyright©2010PearsonEducation,Inc.PublishingasPrenticeHallLearningObjectives(continued)Afterreadingthischapter,youwillunderstandthedifferencebetweenperformancemeasurementandperformancethemethodofcalculatingreturnthatminimizestheeffectofclientcontributionsandwithdrawalswhyitisnecessarytoestablishabenchmarkhownormalportfoliosarecreatedandthedifficultiesofcreatingthemwhatafixed-incomeperformanceattributionmodelisandwhyitisusefulinassessingtheperformanceofamoneymanager26-3Copyright©2010PearsonEducation,Inc.PublishingasPrenticeHallPerformanceMeasuresThestartingpointforevaluatingtheperformanceofamanagerismeasuringreturn.Becausedifferentmethodologiesareavailableandthesemethodologiescanleadtoquitedisparateresults,itisdifficulttocomparetheperformancesofmanagers.Consequently,thereisagreatdealofconfusionconcerningthemeaningofthedataprovidedbymanagerstotheirclientsandtheirprospectiveclients.Thishasledtoabusesbysomemanagersinreportingperformanceresultsthatarebetterthanactualperformance.TomitigatethisproblemtheCommitteeforPerformanceStandardsoftheAssociationforInvestmentManagementandResearch(nowtheCFAInstitute)hasestablishedstandardsforcalculatingperformanceresultsandhowtopresentthoseresults.26-4Copyright©2010PearsonEducation,Inc.PublishingasPrenticeHallPerformanceMeasures(continued)AlternativeReturnMeasuresThedollarreturnrealizedonaportfolioforanyevaluationperiod(i.e.,ayear,month,orweek)isequaltothesumofthedifferencebetweenthemarketvalueoftheportfolioattheendoftheevaluationperiodandthemarketvalueatthebeginningoftheevaluationperiodanydistributionsmadefromtheportfolioInequationform,theportfolio’sreturncanbeexpressedasfollows:

whereRp

=returnontheportfolio,MV1=portfoliomarketvalueattheendoftheevaluationperiod;MV0=portfoliomarketvalueatthebeginningoftheevaluationperiod;and,D

=cashdistributionsfromtheportfoliototheclientduringtheevaluationperiod.26-5Copyright©2010PearsonEducation,Inc.PublishingasPrenticeHallPerformanceMeasures(continued)AlternativeReturnMeasuresEXAMPLE.

Toillustratethecalculationofareturn,assumethefollowinginformationforanexternalmanagerforapensionplansponsor:Theportfolio’smarketvalueatthebeginningandendoftheevaluationperiodis$25million

and$28million,respectively,andduringtheevaluationperiod$1millionisdistributedtotheplansponsorfrominvestmentincome.Whatistheportfolioreturn?InsertingourvaluesofMV1=$28,000,000,MV0=$25,000,000,andD

=$1,000,000,wehave:26-6Copyright©2010PearsonEducation,Inc.PublishingasPrenticeHallPerformanceMeasures(continued)AlternativeReturnMeasuresTherearethreeassumptionsinmeasuringreturnasgivenbytheaboveequation.Itassumesthataperiod’scashinflowintotheportfoliofrominterestiseitherdistributedorreinvestedintheportfolio.Iftherearedistributionsfromtheportfolio,theyoccurattheendoftheevaluationperiodorareheldintheformofcashuntiltheendoftheevaluationperiod.Nocashispaidintotheportfoliobytheclient.26-7Copyright©2010PearsonEducation,Inc.PublishingasPrenticeHallPerformanceMeasures(continued)AlternativeReturnMeasuresFromapracticalpointofviewthethreeassumptionslimittheportfolioreturnapplication.Thelongertheevaluationperiod,themorelikelytheassumptionswillbeviolated.Thus,areturncalculationmadeoveralongperiodoftime,iflongerthanafewmonths,wouldnotbeveryreliablebecauseoftheassumptionunderlyingthecalculationsthatallcashpaymentsandinflowsaremadeandreceivedattheendoftheperiod.Notonlydoestheviolationoftheassumptionsmakeitdifficulttocomparethereturnsoftwomanagersoversomeevaluationperiod,butitisalsonotusefulforevaluatingperformanceoverdifferentperiods.26-8Copyright©2010PearsonEducation,Inc.PublishingasPrenticeHallPerformanceMeasures(continued)AlternativeReturnMeasuresThewaytohandlepracticalissueswhencomputingaportfolioreturnistocalculatethereturnforashortunitoftimesuchasamonthoraquarter.Wecallthereturnsocalculatedthesubperiodreturn.Togetthereturnfortheevaluationperiod,thesubperiodreturnsarethenaveraged.Therearethreemethodologiesthathavebeenusedinpracticetocalculatetheaverageofthesubperiodreturns:thearithmeticaveragerateofreturnthetime-weightedrateofreturn(alsocalledthegeometricrateofreturn)thedollar-weightedrateofreturn.26-9Copyright©2010PearsonEducation,Inc.PublishingasPrenticeHallPerformanceMeasures(continued)ArithmeticAverageRateofReturnThearithmeticaveragerateofreturnisanunweightedaverageofthesubperiodreturnswiththegeneralformulaas:

whereRA

=arithmeticaveragerateofreturn;Rpk

=portfolioreturnforsubperiod

kfork=1,…,N;and,N

=numberofsubperiodsintheevaluationperiod.Itisimpropertointerpretthearithmeticaveragerateofreturnasameasureoftheaveragereturnoveranevaluationperiod.Theproperinterpretationisthatitistheaveragevalueofthewithdrawals(expressedasafractionoftheinitialportfoliomarketvalue)thatcanbemadeattheendofeachsubperiodwhilekeepingtheinitialportfoliomarketvalueintact.26-10Copyright©2010PearsonEducation,Inc.PublishingasPrenticeHallPerformanceMeasures(continued)ArithmeticAverageRateofReturnEXAMPLE.

Wenowillustratethecalculationofthearithmeticaveragerateofreturnasanunweightedaverageofthesubperiodreturnsusingthegeneralformula.Assumetheportfolioreturnswere–10%,20%,and5%inJuly,August,andSeptember,respectively.Whatisthearithmeticaveragemonthlyreturn?InsertinginourgivenvaluesofRp1

=–10%,Rp2

=20%,andRp3

=5%forN

=3,wehave:26-11Copyright©2010PearsonEducation,Inc.PublishingasPrenticeHallPerformanceMeasures(continued)Time-WeightedRateofReturnThetime-weightedrateofreturnmeasuresthecompoundedrateofgrowthoftheinitialportfoliomarketvalueduringtheevaluationperiod,assumingthatallcashdistributionsarereinvestedintheportfolio.Itisalsocommonlyreferredtoasthegeometricrateofreturnbecauseitiscomputedbytakingthegeometricaverageoftheportfoliosubperiodreturnscomputedfromequation.ThegeneralformulaisRT

=[(1+RP1)(1+RP2)...(1+RPN)]1/N

–1whereRT

isthetime-weightedrateofreturn,RPk

isthereturnforsubperiod

k,

andNisthenumberofsubperiods.26-12Copyright©2010PearsonEducation,Inc.PublishingasPrenticeHallPerformanceMeasures(continued)Time-WeightedRateofReturnEXAMPLE.

Letusassumethattheportfolioreturnswere10%,20%,and5%inJuly,August,andSeptember,asinourpreviousexample.Whatisthetime-weightedrateofreturn?InsertinginourgivenvaluesofRp1

=–10%,Rp2

=20%,andRp3

=5%forN

=3,wehave:RT

=[(1+RP1)(1+RP2)...(1+RPN)]1/N

–1RT=[(1+–0.10)(1+0.20)(1+0.05)]1/3

–1RT=[(0.90)(1.20)(1.05)]1/3–1RT=0.042808orabout4.28%26-13Copyright©2010PearsonEducation,Inc.PublishingasPrenticeHallPerformanceMeasures(continued)Time-WeightedRateofReturnIngeneral,thearithmeticandtime-weightedaveragereturnswillgivedifferentvaluesfortheportfolioreturnoversomeevaluationperiod.Thisisbecauseincomputingthearithmeticaveragerateofreturn,theamountinvestedisassumedtobemaintained(throughadditionsorwithdrawals)atitsinitialportfoliomarketvalue.Thetime-weightedreturn,ontheotherhand,isthereturnonaportfoliothatvariesinsizebecauseoftheassumptionthatallproceedsarereinvested.26-14Copyright©2010PearsonEducation,Inc.PublishingasPrenticeHallPerformanceMeasures(continued)Time-WeightedRateofReturnIngeneral,thearithmeticaveragerateofreturnwillexceedthetime-weightedaveragerateofreturn.Theexceptionisinthespecialsituationwhereallthesubperiodreturnsarethesame,inwhichcasetheaveragesareidentical.Themagnitudeofthedifferencebetweenthetwoaveragesissmallerthelessthevariationinthesubperiodreturnsovertheevaluationperiod.Forexample,supposethattheevaluationperiodisfourmonthsandthatthefourmonthlyreturnsareasfollows:RP1=0.04;RP2

=0.06;

RP3=0.02;

RP4=─0.02.Theaveragearithmeticrateofreturnis2.5%andthetime-weightedaveragerateofreturnis2.46%,whichisasmalldifference.Inourearlierexampleinwhichwecalculatedanaveragerateofreturnof25%butatime-weightedaveragerateofreturnof0%,thelargediscrepancyisduetothesubstantialvariationinthetwomonthlyreturns.26-15Copyright©2010PearsonEducation,Inc.PublishingasPrenticeHallPerformanceMeasures(continued)Dollar-WeightedRateofReturnThedollar-weightedrateofreturniscomputedbyfindingtheinterestratethatwillmakethepresentvalueofthecashflowsfromallthesubperiodsintheevaluationperiodplustheterminalmarketvalueoftheportfolioequaltotheinitialmarketvalueoftheportfolio.Cashflowsaredefinedasfollows:Acashwithdrawalistreatedasacashinflow.So,intheabsenceofanycashcontributionmadebyaclientforagiventimeperiod,acashwithdrawalisapositivecashflowforthattimeperiod.Acashcontributionistreatedasacashoutflow.Consequently,intheabsenceofanycashwithdrawalforagiventimeperiod,acashcontributionistreatedasanegativecashflowforthatperiod.Iftherearebothcashcontributionsandcashwithdrawalsthenifcashwithdrawalsexceedcashcontributions,thenthereisapositivecashflowifcashwithdrawalsarelessthancashcontributions,thenthereisanegativecashflow.26-16Copyright©2010PearsonEducation,Inc.PublishingasPrenticeHallPerformanceMeasures(continued)Dollar-WeightedRateofReturnThedollar-weightedrateofreturnissimplyaninternalrate-of-returncalculationandhenceitisalsocalledtheinternalrateofreturn.Thegeneralformulaforthedollar-weightedreturniswhereRD

=dollar-weightedrateofreturn;V0=initialmarketvalueoftheportfolio;VN

=terminalmarketvalueoftheportfolio;and,Ck

=cashflowfortheportfolio(cashinflowsminuscashoutflows)forsubperiod

k

fork

=1,...,N.Noticethatitisnotnecessarytoknowthemarketvalueoftheportfolioforeachsubperiodtodeterminethedollar-weightedrateofreturn.26-17Copyright©2010PearsonEducation,Inc.PublishingasPrenticeHallPerformanceMeasures(continued)Dollar-WeightedRateofReturnThedollar-weightedrateofreturnandthetime-weightedrateofreturnwillproducethesameresultifnowithdrawalsorcontributionsoccurovertheevaluationperiodandallinvestmentincomeisreinvested.Theproblemwiththedollar-weightedrateofreturnisthatitisaffectedbyfactorsthatarebeyondthecontrolofthemanager.Specifically,anycontributionsmadebytheclientorwithdrawalsthattheclientrequireswillaffectthecalculatedreturn.Thismakesitdifficulttocomparetheperformanceoftwomanagers.26-18Copyright©2010PearsonEducation,Inc.PublishingasPrenticeHallPerformanceMeasures(continued)AnnualizingReturnTheevaluationperiodmaybelessthanorgreaterthanoneyear.Typically,returnmeasuresarereportedasanaverageannualreturn.Thisrequirestheannualizationofthesubperiodreturns.Thesubperiodreturnsaretypicallycalculatedforaperiodoflessthanoneyear.Thesubperiodreturnsarethenannualizedusingthefollowingformula:annualreturn=(1+averageperiodreturn)numberofperiodsinyear

–126-19Copyright©2010PearsonEducation,Inc.PublishingasPrenticeHallPerformanceAttributionAnalysisBondattributionmodels

seektoidentifytheactivemanagementdecisionsthatcontributedtotheperformanceofaportfoliogiveaquantitativeassessmentofthecontributionofthesedecisionsTheperformanceofaportfoliocanbedecomposedintermsoffouractivestrategiesinmanagingafixed-incomeportfolio:interest-rateexpectationstrategiesyieldcurveexpectationsstrategiesyieldspreadstrategiesindividualsecurityselectionstrategies26-20Copyright©2010PearsonEducation,Inc.PublishingasPrenticeHallPerformanceAttributionAnalysis

(continued)BenchmarkPortfoliosToevaluatetheperformanceofamanager,aclientmustspecifyabenchmarkagainstwhichthemanagerwillbemeasured.Therearetwotypesofbenchmarksthathavebeenusedinevaluatingfixed-incomeportfoliomanagers:marketindexespublishedbydealerfirmsandvendorsnormalportfolios26-21Copyright©2010PearsonEducation,Inc.PublishingasPrenticeHallPerformanceAttributionAnalysis(continued)BenchmarkPortfoliosAnormalportfolioisacustomizedbenchmarkthatincludes“asetofsecuritiesthatcontainsallofthesecuritiesfromwhichamanagernormallychooses,weightedasthemanagerwouldweighttheminaportfolio.”Thusanormalportfolioisaspecializedindex.Itisarguedthatnormalportfoliosaremoreappropriatebenchmarksthanmarketindexesbecausetheycontrolforinvestmentmanagementstyle,therebyrepresentingapassiveportfolioagainstwhichamanagercanbeevaluated.26-22Copyright©2010PearsonEducation,Inc.PublishingasPrenticeHallPerformanceAttributionAnalysis(continued)BenchmarkPortfoliosTheconstructionofanormalportfolioforamanagerrequiresdefiningtheuniverseoffixed-incomesecuritiestobeincludedinthenormalportfoliodetermininghowthesesecuritiesshouldbeweighted(i.e.,equallyweightedorcapitalizationweighted)Plansponsorsworkwithpensionconsultantstodevelopnormalportfoliosforamanager.Theconsultantsusevendorsystemsthathavebeendevelopedforperformingtheneededstatisticalanalysisandthenecessaryoptimizationprogramtocreateaportfoliodisplayingsimilarfactorpositionstoreplicatethe“normal”positionofamanager.Aplansponsormustrecognizethatthereisacosttodevelopingandupdatingthenormalportfolio.26-23Copyright©2010PearsonEducation,Inc.PublishingasPrenticeHallPerformanceAttributionAnalysis(continued)PerformanceAttributionAnalysisModelThereareseveralvendorsofperformanceattributionmodels.TheperformanceattributionmodeldescribedinthetextisthatofGiffordFongAssociatesofLafayette,California.Theparticularsystemthatmonitorsandevaluatestheperformanceofafixed-incomeportfolioaswellastheindividualsecuritiesheldintheportfolioiscalledBONDPAR.BONDPARdecomposesthereturnintothoseelementsbeyondthemanager’scontrol,suchastheinterest-rateenvironmentandclient-imposed-durationpolicyconstraints,andthosethatthemanagementprocesscontributesto,suchasinterest-ratemanagement,sector/qualityallocations,andindividualbondselection.26-24Copyright©2010PearsonEducation,Inc.PublishingasPrenticeHallPerformanceAttributionAnalysis(continued)PerformanceAttributionAnalysisModelBONDPARanswersthefollowingsixquestions:Howdoeseachelementofthemanager’sreturncomparewiththesameelementsofreturnofthebenchmark?Whatisthecostofbeinginthebondmarket?Whateffectdoclientpolicieshaveonportfolioreturns?Hasthemanagersuccessfullyanticipatedinterest-ratechanges?Hasthemanagerbeensuccessfulatselectingtheissuingsectorandqualitygroupsthatenhancetheportfolio’sperformance?Hasthemanagerimprovedreturnsbyselectingindividualbondsbecauseofcompanyfundamentals?26-25Copyright©2010PearsonEducation,Inc.PublishingasPrenticeHallPerformanceAttributionAnalysis(continued)PerformanceAttributionAnalysisModelExhibit26-1showstheholdingsofahypotheticalportfolioandthetransactions.Alsoshownforeachsecurityarethebeginningandendingparamount,proceeds,accruedvalue,interestpaidduringtheevaluationperiod,andcapitalgainorloss.Exhibit26-2(seeOverhead26-27and26-28)showstheresultsoftheperformanceattributionanalysisfortheportfolioinExhibit26-1.The“evaluationperiodreturn”columninExhibit26-2isthereturnandcomponentsofreturnfortheportfolioovertheevaluationperiod.The“bondequivalentannualizedreturn”columnistheannualizedreturnandcomponentsofreturnfortheportfolioovertheevaluationperiod.26-26Copyright©2010PearsonEducation,Inc.PublishingasPrenticeHallExhibit26-2PerformanceAttributionAnalysisforaPortfoliowithBONDPAREval.PeriodReturn(%)BondEquiv.AnnualizedReturn(%)SalomenB.I.G.IndexEval.PeriodReturn(%)I.Interest-rateeffect(SALTreasuryIndex)1.Expected0.667.930.662.Unexpected–0.57–6.87–0.57Subtotal0.091.060.09II.Policyeffect3.Portfoliodurat’n

reqt.(4.60yrs)0.010.070.01III.Interestratemanagementeffect4.Duration0.060.690.005.Convexity–0.07–0.84–0.106.Yieldcurveshapechange–0.15–1.780.10Subtotal(optionsadjusted)–0.16–1.930.0026-27Copyright©2010PearsonEducation,Inc.PublishingasPrenticeHallExhibit26-2PerformanceAttributionAnalysisforaPortfoliowithBONDPAREval.PeriodReturn(%)BondEquiv.AnnualizedReturn(%)SalomenB.I.G.IndexEval.PeriodReturn(%)IV.OtherManagementEffects7.Sector/Quality08.BondSelectivity0.323.790.009.TransactionCosts–0.03–0.38–0.00Subtotal0.475.560.10V.TotalReturn0.414.760.20VI.SourcesofReturn1.CapitalGains–0.44–1.522.InterestIncome0.859.96TotalReturn0.414.7626-28Copyright©2010PearsonEducation,Inc.PublishingasPrenticeHallPerformanceAttributionAnalysis(continued)PerformanceAttributionAnalysisModelThedecompositionoftheevaluationperiodreturnisshowninthesectionslabeledI,II,III,andIVinExhibit26-2(seeOverhead26-27and26-28).SectionI,interest-rateeffect,isthereturnovertheevaluationperiodofthefullTreasuryindex.Thevaluesinthissectionareinterpretedasfollows.Thesubtotal0.09meansthattheactualmonthlyreturnonTreasurieswasninebasispoints.Thevalueof0.66indicatesthattheexpectedmonthlyreturnfrominvestinginTreasurybondsoverthisperiodwas66basispoints.26-29Copyright©2010PearsonEducation,Inc.PublishingasPrenticeHallPerformanceAttributionAnalysis(continued)PerformanceAttributionAnalysisModelTheresultsreportedinthesection“interest-rateeffect”inExhibit26-2canbeinterpretedasthecostofbeinginthebondmarket.Thatis,ifanyinvestorwantedtoinvestindefault-freebonds(i.e.,Treasurysecurities)andsimplyboughtaportfolioofTreasurysecurities,thereturnwouldhavebeenninebasispoints.Therefore,thiscomponentofreturnisconsideredoutofthemanager’scontrolbecausesuchareturnwouldhavebeenrealizedbyanyonewhodecidedtocommitfundstothebondmarket.26-30Copyright©2010PearsonEducation,Inc.PublishingasPrenticeHallPerformanceAttributionAnalysis(continued)PerformanceAttributionAnalysisModelSectionIIofExhibit26-2showsthepolicyeffect.Thisinformationprovidesthenecessaryinformationtoanalyzethedurationpolicyconstraintspecifiedbythemanager’sclient.BONDPARcalculatestheportionofthetotalreturnduetothepolicyconstraintandseparatesitfromtheinterest-rat