Fixed_Income_Attribution_Model(债券投资组合归因分析方法和模型)

Fixed_Income_Attribution_Model(债券投资组合归因分析方法和模型)

FixedIncomeAttributionModel

Thispaperproposesaflexiblefixedincomeattributionmodelthatcanbeadaptedtoalargerangeofinvestmentprocesses.TheStatProreturnbreakdownmodelcanfitaverylargerangeoffixedincomeinvestmentprocesses.Pricingtechniquesareusedtounderstandtheimpactbond-specificfactorshaveonsecurityreturns.Thisallowsustogiveanaccurateanddetailedsecurityperformancedecomposition.Bondspecificsnaturallyleadtopartic-ularmanagementmethodsandthereforerequireadaptedex-postperformanceattributionanalysis.

MathieuCubilié

isaperformancemeasurementconsultantatStatProPlc,whereheisproductmanagerforStatProFixedIncome,thecompanybondperformancemeasurementandattributionsystem.MathieuholdsapostgraduatedegreeinMarketFinanceandEconomicsfromToulouseUniversityandbeganhiscareeratSinopia-Asset-Management,HSBC-groupquantitativemanagementsubsidiary,inParis,whereheexperiencedbondportfoliomanagement.lendsitselftotheuseofderivativeproducts.Unfortunately,futurescontractsarereplicatingbond

Oncethevariousperformancecontributionsarecom-maturitybehaviorsratherthanbondindexreturns.Asaputed,theycanbeconsideredaselementarybuildingresult,bondmanagerspracticebenchmarksampling.blocksthatcanberearrangedaccordingtotheportfolioThistechniqueconsistsoftryingtotracklargeindices

withalimitednumberofassets.managementdecisionprocess.INTRODUCTION

Thesinglecurrencyreturnattributionmodelisflexible

enoughtopermitconcurrentelementaryreturndecom-positions.Itisalsoabletoattributeatdifferentlevelsofdetailcorrespondingtoseveralavailableattributioneffectaggregationcapacities.Tofinish,wewillseehowthissinglecurrencymodelcaneasilybeusedinamulti-currencyenvironment.FIXEDINCOMEMARKETS

Bondandequitymarketsareclearlydifferent;equityindicesareintra-dayquoting,whileveryfewbondindicesare.Asaconsequence,bondmanagersrequiremarketindicatorsduringthedaytoruntheirinvest-ments.Actually,they’reusingasampleofliquidbondsrepresentingthevariousmarketliquidmaturities.ThissetofbondsisknownastheYieldCurve.TheYieldCurvesarecontinuouslyquotedandthereinformationisaccessable.Theyrepresentdifferentmarkets:mainly

localcurrencyTreasurymarketsandalsocreditmar-THEPRICEEFFECTkets.

Amajordifferencewithequitymarketsisthatbond

Indexreplicationmanagementisadifficultexercise;marketsaretraded“over-the-counter”whileequitybondindicescontainseveralthousandsofsecurities,marketsareorganizedmarkets.Pricesareproprietytomanywithverylargeminimaltradesize.Thismeansbrokersandindexproviders.Thisleadstoasituationmanagerswouldrequirehugeamountsofinvestmentswherepricedifferencebetweenasecurityheldinatocloselyreplicateanindex.Thissituationdefinitelyportfolioandintheindexcanbeverysignificant.ThisWinter2005/2006

-49-TheJournalofPerformanceMeasurement

Inamulti-currencyuniverse,aftermakingyieldmarketandcurrencyallocationdecisions,managershavetodefinewhichbondinparticulartheywanttoinvestin.Theyusuallyhavedurationobjectivesagainstthebenchmarkreflectingtheirmarketexpectation.Marketanticipationsaremainlyyieldcurvemovementsandcreditspreadvariation.Bondswillthereforebeselect-edfortheircharacteristics:theirduration,thespreadtheyoffer,andallotherspecificities.

Toachievethisgoal,bondmanagementisruledmorebyriskcontrolthantheequitymarket.Inthebondarea,riskisfirstreflectedbytheDuration.MANGEMENTPROCESSES

Despitethefactthattherearemanyinvestmentprocess-es,bondmanagersgenerallyfacethesameconsiderations.

Fixed_Income_Attribution_Model(债券投资组合归因分析方法和模型)

phenomenon,knownas“pricedifferenceeffect,”canrepresentalargepartoftheexcessreturn.Thisphe-nomenoncanexistinanorganizedmarketwherebackofficesystemsarenotfedbyindexdata.Thisismuchlessimportanceinequitymarkets,asvolatilityremainshighcomparedtothepricedifferenceeffect.Forbonds,thepricedifferenceeffectcanbeevenmoreimportantthantheexcessreturn.Insuchcase,aperformanceattributionexercisemaybemisleading.

Thereturnformedbytwoconsecutiveintermediarypricesisconsideredasecurityreturncontribution.Withthisapproach,itispossibletogoasfarasrequiredinthereturnbreakdownandtoadheretotherealmanage-mentprocess.

Itisnotsufficienttoworkatthesecuritylevelonly,asmostofthemanagementdecisionsarenotmadeinde-pendentlyfromoneanother,whichmakestheirimpactdifficulttomeasure.Forinstance,selectingalong-termmaturitybondontheyieldcurvealsomeans,inthegeneralcaseselectingahighdurationbond.Ifthisbondisacorporateone,thisalsomeansitissupposedtodeliverahigheryieldthanthereferencemarket.Ofcourse,thisalsoexposestheinvestmenttospreadvari-ationsthatwillimpactthesecurityreturn.

Whateverthereferenceaccountreturnsource(backorfrontoffice),afirstrequirementistocleantheinitialportfolioreturnfromthepriceeffect.Thismeansthatthefirststepistorepriceportfoliosandbenchmarks,usingthesamepricebase.Forsimplicityreasons,itiscommonlyacceptedthattheportfolioisrepricedusingthebenchmarkpricesforcommonsecurities.

Noncommonsecuritieswillkeepthebackofficeprices.Whatabouttransactions?PricingtechniquescanonlyThisisextendedtocommonexchangeratesforsecuri-explainpricereturnsandthereforeignorestheimpacttiesinmulti-currencyportfoliosusingbenchmarksrates.oftransactionsmadebythemanager.Forthisreason,

wealsothinkanaccurateattributionmodelmustbetransactionbasedandmustclearlyidentifytheir

impact.

RETURNCONTRIBUTIONS

Forsimplicityreasonswewillconsiderplainvanillabondsinthischapter.

Let’sfocusontheportfolioreturn,andlet’srunafirst

Inthefollowing,wewillconcentrateonunderstandingdecompositionofeachinstrumentpricereturn.Inaddi-theportfoliorecomputedreturn.tion,wewillmeasurethetradeimpactbycomputing

thereturnusingtheModifiedDietzandtheall-inprice

rManagement=rreference+rPricereturnandconsidertheirdifference.SECURITYPRICINGTECHNIQUES

InordertounderstandtheportfolioorbenchmarkrModified

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