understanding mul/-asset factor models: factor exposure ... · bloomberg’s factor model mojvajon...
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UnderstandingMul/-AssetFactorModels:FactorExposureInterpreta/on
AcademicAdvisor:Mar$jnBoonsBPIGAAdvisors:CarlaMiranda,JoãoAbrantes
RitaSousaCosta|1018MiguelMarquesMendes|947
MasterinFinance–January2016
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AGENDA
Mo:va:onandObjec:ves
Bloomberg’sFactorModel
Interpre:ngExposures
Replica:onProcess
Results
Conclusion
Appendix
1
2
3
4
5
6
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MOTIVATIONANDOBJECTIVESMoJvaJon
andObjecJves
Bloomberg’sFactorModel
InterpreJngExposures
ReplicaJonProcess
Results
Conclusion
Appendix
Inlightoftheweaknessesexposedduringthefinancialcrisisof2008,thebankingindustryhasbeenincreasingfocusonRiskManagementissues.
CurrentSituaJon
RiskManagementDivisionatBPIGestãodeAc:vos(GA)
Strivestopromoteriskculturewithinthe
organiza:on
InanefforttoincreaseawarenessofporZoliomanagerstotherisks
beingincurred
Withthepurposeofincreasingcoopera:onbetweenporZolio
managersandtheriskmanagementteam
Introduc:onofBloomberg’sAIMso\ware,throughthePorZolioandRiskAnaly:cs
(PORT<GO>)tool
EstablishmentofinternallimitstoconstrainporZolioex-ante
vola:lity/trackingerror
Developmentofariskmonitoringsystemwhich
accountsforthesourcesofrisk
• PROBLEM:limitsimposedfailtoacknowledgewheretheriskiscomingfrom(i.e.whichfactorscontributethemosttoporZoliorisk)
• Thisso\wareallowsthedecomposiJonofporWolioriskandreturnusingfactormodels
• Thesemodelsprovideex-antevola:lity/TEandsourcesofrisk(i.e.factors) 3
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MOTIVATIONANDOBJECTIVESMoJvaJon
andObjecJves
Bloomberg’sFactorModel
InterpreJngExposures
ReplicaJonProcess
Results
Conclusion
Appendix
4
PreviousworkbyNOVAstudentsfocusedonthedevelopmentofthisriskmonitoringsystemwiththepurposeofcapturingthesourcesofBPIGA’sporZolios’risk.
RiskMonitoringSystem
Thesystemwassetuproughlyinthefollowingmanner:
“Types”offactorscontribu:ngthemostto
porZolioriskweredetermined
SeveralporZolioswereanalyzed
Typeofrisktobemonitored–absoluteorrela:ve–wasdefined
HistoricalanalysisoftopcontributorstoporZolio
riskwasperformed
Limitsweredefinedforeachtypeoffactorbasedroughlyonthe95%and99%percen:leofthesta:s:caldistribu:onoffactorcontribu:ons
Foreachoftheselimits,warningswereestablished:• Warning1(95%percen:le)–wheneverafactoroftheconsideredtypesreachesthislimit,ananalysisofthecausesthatledtosuchcontribu:onlevelismadeandreportedtotheporZoliomanager
• Warning2(99%percen:le)–inthiscase,thesitua:onisreportedtotheAdministra:on
RiskManagementteamchecksonamonthlybasiswhetheranylimitshavebeenreached
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MOTIVATIONANDOBJECTIVESMo:va:on
andObjec:ves
Bloomberg’sFactorModel
Interpre:ngExposures
Replica:onProcess
Results
Conclusion
Appendix
TheriskmonitoringsystemcurrentlyinplaceaccountsforthesourcesofporZoliorisk,but there is a lack of understanding by porZolio and risk managers regarding themeaningofeachfactorexposureandcontribu:ontorisk.Without understanding its output, managers lose confidence in the model (i.e. inBloomberg’sPORTtooloutputregardingporZoliorisk).
PROBLEM
5
ReplicaJngBloomberg’sprocedureThe lack of understanding across the porZoliomanagement division of Bloomberg’sprocedureincalcula:ngfactorreturnsandexposuresisthemainfocusofourwork,aswefindthatitisthemainissueholdingbackthisriskmonitoringsystem.In an effort to beYer understand the process through which Bloomberg calculatesfactorreturns,wesetouttoreplicatewhatisdoneinthemodel.Successfully replica:ngall theprocedurewill increase theconfidenceofmanagers inBloomberg’soutput.
SOLUTION
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BLOOMBERG’SFACTORMODELMoJvaJon
andObjecJves
Bloomberg’sFactorModel
InterpreJngExposures
ReplicaJonProcess
Results
Conclusion
Appendix
6
FactorModels
Layonthefundamentalthatassetswithiden:calcharacteris:cs(industry,country,style,etc.)shouldhaveasimilarperformance.
Arebasedontheneedofinvestorstounderstandthetruesourcesoftheirrisk.
Provideadetaileddecomposi:onofporZolioriskandreturnintofactors.
Factorsareasetofcommonvariablesthatdriveandexplainriskandreturnofasecurity.
Riskfactorsdis:nguisheachsecurityintheporZolioandhelpcrea:ngaspecificriskprofileforthem,givenbyexposurestothesefactors.
!!,! = !!,!,!!!,! + !!,! !
!!!
!!,! isthelocalexcessreturnofassetninperiodt!!,!,!istheexposureofassetntofactork!!,!isthereturnoffactorkinperiodt!!,!istheresidualofassetn’sreturn
FactorReturns Non-FactorReturns
Afactormodeldiscriminatesreturnsandriskintwocomponents,theasset-specificcomponent–solelyrelatedtotheassetitself–andthesystema:ccomponent–determinedbytheriskfactors.
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BLOOMBERG’SFACTORMODELMoJvaJon
andObjecJves
Bloomberg’sFactorModel
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ReplicaJonProcess
Results
Conclusion
Appendix
Therearethreecommontypesoffactormodels.Thesethreedifferintheirapproachtoconstruc:ngexposurestoriskfactorsandfactorreturns.Theyallhavesomespecificadvantagesanddisadvantages,relatedtothedataintensityandinterpretability.
7
FactorApproachType Advantages Disadvantages
StaJsJcal
Similartowhatprincipalcomponentanalysisdoes1.Determinesbothfactorreturnsandfactorexposuresfromassetreturns.
• Easytobuild• Requirearela:velylow
amountofdata
• Interpretability–thereisnocleareconomicmeaningassociatedtoeachprincipalcomponent
Explicit
Specifyfactorreturnsinordertocalculateexposurestofactors.AlsoknownasexogenousorJme-seriesmodels(becausefactorreturnsarespecifiedoutsideofthemodeland:me-seriesregressionsareruntogetfactorexposures).
• Thesemodelsallowforanarbitrarynumberoffactors,aslongaswehavesufficientfactordataforthe:me-seriesintervalusedfores:ma:on
• Rela:velydataintensive–securityreturnsandfactorreturnsarerequiredtoperformaregressionanalysistodeterminefactorexposures
• Exposurestofactorscanbenon-intui:ve
• Poorpredic:vepower
Implicit
Definesecurityexposurestofactorsandusethesetocalculatefactorreturnsthrougharegressionofsecurityreturnsonfactorexposures.Alsoknownasendogenousmodelsorcross-secJonalmodels(asfactorreturnsaredeterminedfromthemodelbycross-sec:onalregressions)
• Exposuresaremoreintui:ve
• Performwellout-of-sample(astheyimposerela:velymorestructurethanothermodels)
• Themostdataintensivemodel–bothsecurityreturnsandsecurityexposuresarenecessary
FactorModelsTypes
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BLOOMBERG’SFACTORMODELMoJvaJon
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8
Market
Dummyvariables:unitexposureto
security’smarketandzerotoeveryother
market.Thisfactoristhemainriskcontributorfordiversifiedlong-only
porZolios.
Country
Dummyvariables:unitexposureto
security’scountryofissue.
Currency
Dummyvariables:unitexposuretotradingcurrency.
Industry
Dummyvariables:unitexposureto
industryinwhichitoperates.
IndustryfactorsarebasedontheGICSIndustryGroupmembership(seeAppendix1foralistofIndustryfactors).
Style
Thesefactorscharacterize
securi:esusingvariablessuchassize,momentum,tradingac:vity,leverage,etc.
Eachexposureisdefinedasthe
“amount”ofeachofthesevariablesasecurityhas.
EquityModelFactors
BloombergFactorModelsareconstructedwithanimplicitfactorapproach.Thismeansthatfactorreturnsarecalculatedminimizingthesumofsquarederrors–εi2–intheregressionofsecuri:es’returnsontheirexposurestothefactors.Theerrorcomponentinthisregressionisthenon-factorreturnofeachsecurity.Itisimportanttostressthatsecuri:es’returnsand,mostimportantly,exposuresareinputsofthisprocess,whichmeansthatBloombergspecifiesthemapriori.Wewillfocuslateronexposures:howtheyarecalculatedandhowtheyshouldbeinterpreted.
Intheequitymodels,therearefivetypesofequityfactors:Market,Country,Industry,CurrencyandStyle.
Bloomberg’sModelsEquityandFixedIncomeFactors
Equity
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BLOOMBERG’SFACTORMODELMoJvaJon
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9
Curve
These factors are taken directly from themarket, by looking at the changes along theyield curvenine tenorpoints - 6M,1Y,2Y,3Y,5Y, 7Y, 10Y, 20Y and 30Y – and the squaredaverage curve change along those points. Theexposures to these factors are the key ratedura:onandop:on-adjustedconvexity
Vola:lity
The exposure of each security to thevola:lity factor is measured by itsvola:litydura:on,which iscomputedbythebond’svegadividedbyitsprice.
Spread
The level of the spread in eachbond reflects the addi:onalamount of return investorsrequire for takingaddi:onal risk.Changes in the spread reflectchanges in the perceived risk ofthe security. These might comefromforcescommontoallbondswithclosecharacteris:cs,orfromspecific shocks to one issuer.Common forces are captured bythese systema:c spread factors,including sovereign, agency,corporate (Investment GradedandHighYield)anddistressed.
FixedIncomeModelFactors
Forthefixedincomemodels,therearetwotypesoffactors:thosewhosereturnsareobservableinthemarket,inwhichcasetheobservedchangeissimplyuseddirectly(explicitfactors),andthoseobtainedbyacross-sec:onalregression(implicitfactors).Theexplicitfactorsarecurrency,yieldcurveandvolaJlityfactors.Theimplicitfactorsarethespreadfactors.
!!" = − !"#! ∙ ∆!! + !!!"# ∙ (∆!)!
!
!!!
!!"isthereturnduetochangesinyields!"#!istheKeyRateDurationatpoint!∆!!istheyieldchangeatpoint!OACistheoption-adjustedconvexity∆!istheaveragechangeintheyield
!!"# = !"#$!+ !" ∙ ∆!
!!"#isthereturnduetochangesinvolatility!isthebond’scleanprice!"isthebond’saccruedinterest∆!istheaveragechangeinvolatility
FixedIncome
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BLOOMBERG’SFACTORMODELMoJvaJon
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Forthemul:-assetmodel,Bloombergusesadifferentapproachintheconstruc:onofthefactorcovariancematrix.Thedifferenceliesinthewaywelookatthefactors.Themaingoalistoobtainacovariancematrixthatisdynamic,detailedandrobust.Toreachthatgoal,Bloombergdividesfactorsintothreetypestobuildafactormodelof“successivelycoarserfactors”.
• factorsthataremorespecifictoeachmodel
DetailedFactors
• unitemodelswithineachasset-class
CoreFactors
• unitemodelsacrossasset-classes
Core-of-coreFactors
Aswegodownintheselayers,welookatamoreparsimonioussegmentofthemodel.Thisprocedurefollowssomesteps:
Thisisthe“threelayerapproach”thatisusedtodis:llthecorerela:onshipsinthemodel.
1. Obtainreturnsforeachgroupoffactors.Detailedfactorreturnsareobtainedfromindividualmodels;coreandcore-of-corefactorreturnsareobtainedbydis:llingthedetailedfactors.
2. Buildacovariancematrixforthecore-of-corefactorsonly–matrixΩ
3. Determinesensi:vi:esofcorefactorstocore-of-corefactors–θ–andresidualrisk–J–fromthisrela:onship.
4. Buildcovariancematrixforthecorefactors–matrixΛ=θΩθ'+J.5. Determinesensi:vi:esofdetailedfactorstocorefactors–γ–
andresidualrisk–H–fromthisrela:onship.6. Usethesevaluestoconstructfactor-of-factor(F/F)covariance
matrixofdetailedfactors–ΣF/F=γΛγ'+H.7. Converttocorrela:onmatrixW,andtwistthismatrixinorder
toconstructfinalcorrela:onC,withthecorrela:onoftheindividualmodelsinthediagonalblocks.
8. Finally,convertcorrela:onmatrixCtoacovariancematrix–matrixΣfactors–bymul:plyingitbyadiagonalmatrixV,containingfactorvola:li:es Σfactors=VCV
FactorCovarianceMatrix(I)
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BLOOMBERG’SFACTORMODELMoJvaJon
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Individualfactorvola:li:esarees:matedwiththeGARCHmodel,followinganEWMAprocess:
!!!!! = !− ! !!! + !!!!!!
! = !− !!!
!"#$ !"#$ isthedecayfactor
!!isthefactorreturninperiodt-1,t
Oncewehavethefactorcovariancematrix,wecancalculateallmeasuresofriskrelatedtothesecuri:esintheporZolio,factorsandtheporZolioitself.Thevola:lityoftheporZoliocanthusbedeterminedtogetherwiththeexposuresoftheporZoliotothefactors.
! = !!×!!×!!! !istheportfoliovolatility!!istheexposuresmatrixoftheportfoliotothefactors
!!isthevariancecovariancematrixofthefactors
Bloo
mbe
rg’s Fa
ctor
Mod
els
Equity
Region/countrymodels
Globalmodel
FixedIncome
Mul:-Asset
Regional
Global
Eachmodelcoversadifferentuniverseofsecuri:es,withtheexcep:onoftheMul:-Assetmodel,whichusesexposuresfrombothEquityandFixedIncomemodels.
UsesexposuresfromEquityRegionmodels
UsesexposuresfromEquityGlobalmodel
FactorCovarianceMatrix(II)
Bloomberg’sModels:CoverageUniverse
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BLOOMBERG’SFACTORMODELMoJvaJon
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12
ForastocktobecoveredbyanyofBloomberg’sEquityModels,i.e.forastocktohaveanexposuretothefactorsofonemodel,thereareafewdatarequirements:• Stockpricemustbegreaterthan5%ofoneunitofthelocalcurrency;• PriceandmarketcapdataonBloomberg• Industryandcountrymembershipinforma:onareavailableDespitethesegeneralguidelines,commontoalloftheequitymodels,eachmodelcoversonlysecuri:eslistedonrelevantexchanges(seeAppendix2forfurtherdetailsonCoverageUniverse).Thetenequitymodelsavailablearethefollowing:TheGlobalmodeltakesabroaderlookintotheriskofagivensecurity,puxngitintoperspec:veinaglobalsetofstocks.
Asia Australia CanadaChina
A-Shares
EmergingEurope,Middle-East&Africa
(EMEA)
European Japan La:nAmerica US Global
IBM ListedontheNYSE
NYSEisamajorworldexchange
IBMiscoveredbytheUSandGlobalModel
Hasexposureto:USMomentum;GLMomentum
factor
USMomentum≠GLMomentum
USMomentumcomparesIBM’sexposuretoMomentumonalocallevelagainstAmericanstocks,whereastheGLMomentumisa{ributedonaGlobalenvironment.Moreover,whenconsideringtheMul:-AssetModel,choosingbetweentheRegionandGlobalmodelwillbeinfactchoosingbetweenwhichfactorstouse–thelocalortheglobalones.
Equity
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BLOOMBERG’SFACTORMODELMoJvaJon
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Whenitcomestobonds,coveragebytheFixedIncomeModelisdefinedindifferentterms.Themodelcovers:Ratherthansplixngintoseveralmodelscoveringsecuri:esfromcertainregionsoftheworld,themodelseparatestheworldintotwo–thedevelopedmarkets1andtheemergingmarkets–andconsidersbondsbasedonthecurrencytheyaredenominatedin(developedoremergingcurrencies).Therearefourcombina:onsconsideredinthemodel:Thelasttwocasesaregroupedtogethersincethereisveryfewdataforbondsdenominatedinemergingcurrenciesissuedbyemergingcountries.Hence,theFixedIncomemodelisseparatedintothreemodels,oneforeachcombina:on:Forabondtobecoveredinanyofthesemodels,thefollowingdataneedstobeavailable:singlesecurityprices,riskexposuresandinforma:ononcountry,sector,industry,etc.sothateachbondcanbemappedtothecorrectmodelfactors.
SovereignBonds AgencyBonds CorporateBonds HighYieldGraded
InvestmentGraded
Bondsdenominatedin38currencies
1.Bondsdenominatedinhardcurrencies(i.e.developedcurrencies)issuedbydevelopedcountries
2.Bondsdenominatedinhardcurrencies,issuedbyemergingcountries
3.Bondsdenominatedinemergingcurrencies,issuedbydevelopedcountries
4.Bondsdenominatedinemergingcurrencies,issuedbyemergingcountries.
1ForthepurposeoftheFixedIncomeriskmodel,thefollowingcountriesareconsideredtobedevelopedmarkets:Australia,Canada,US,Japan,Eurozone17na:ons,Denmark,NewZealand,Norway,SwedenandSwitzerland
G6Model EMHardCurrencyModel
EMLocalCurrencyModel
IncludesbondsdenominatedinUSD,EUR,JPY,GBP,CADandAUD(CHF,NOKandDKKwillalsobeaddedtothismarket)
FixedIncome
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BLOOMBERG’SFACTORMODELMoJvaJon
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14
Aspreviouslymen:oned,Bloomberg’sfactormodelsarebuiltusinganimplicitfactorapproach.Hence,itisnecessarytodeterminefactorexposuresinordertocalculatefactorreturnsthrougharegressionagainstsecuri:esreturns.Eachmodelhasanes:ma:onuniverse,whichistypicallyasubsetofthecoverageuniverse.Everysecurityinthees:ma:onuniversehasexposuretothemodelfactorsandisinturnusedasanobserva:onintheregressionthatwillul:matelyallowcalcula:ngfactorreturns.
Ingeneral,whenconsideringequitymodels,togettotheEs:ma:onUniverse,onetakestheCoverageUniverse,sortseverystockbymarketcapandfocusesonthecompaniesthatmakeupcumula:vely98%ofthemarketcapwithineachcountryrelevantforthemodels(seeAppendix2forthelistofcountriescoveredineachmodel).Somemodels,however,havefurtherrestric:onswhenitcomestoincludingastockinitses:ma:onuniverse,eventhoughsomeofthoserestric:onsarenotverydetailedinBloomberg’spapers(seeAppendix3formoreondetailsonthesespecialsitua:ons).Theglobalmodel’sEs:ma:onUniversefocusesoncompaniesthatcumula:velymakeup98%ofthemarketcapwithinseveraldifferentcountriesandcountrygroups,whicharedetailedinAppendix4.
EquityModels
EsJmaJonUniverse
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RebalancingtheEsJmaJonUniverse
Before Now
Universewasupdatedonlyonceayear,basedonthemarketshareofeachstock.
Itisrebalanceddynamicallyandweeklyinordertokeepthemodelsup-to-datewithmarketchanges
Imposed to keep the es:ma:on universe smooth and to minimize itsturnover: it isrequiredthatacertainstockmeetstheeligibilitycriteriaforseveralconsecu:veweeksbefore it is included inthees:ma:onuniverse,asitisrequiredthatastockviolatessuchcriteriaconsecu:velyforacertainnumberofweeksinordertobeexcludedfromit
GatekeepingSystem
Disclosedinforma:onaboutBloomberg’smodelsismuchlessspecificregardingfixedincomethanitisforequity.Itisknownthatthees:ma:onuniverseforthesemodelsisconstructedfromafewdifferentsources,suchas:• BankofAmericaMerrillLynchindices• Bloombergsecuritytermsandcondi:ons• Bvalpricing• BloombergAnaly:cs.Itisalsoknownthat,ingeneral,bondsclassifyforinclusioninthees:ma:onuniverseiftheyhaveatleastoneyeartomaturityremainingandalsoiftheysa:sfycertainrequirementsforminimumamountoutstanding,dependinguponcountryoforigina:onandtypeofbond.TheexampleprovidedspecifiesthatU.S.corporatebondsmustmeeta$250millionminimumamountoutstandingrequirementtobeincluded.Further,theserequirementsareconstantlybeingrevised.
FixedIncomeModels
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RiskFactorOrigins(I)
Beforegoingthroughthereasoningbehindtheinterpreta:onofeachstylefactorexposure,weneedfirsttoanalyzehowthesefactorswerechosenandwhytheywereintegratedintheBloomberg’sFactorModelinsteadofothers.TherootsoftheBloomberg’sFactormodellieontheMSCIBARRAfactormodels,andforthatreason,bothmodelsaresimilarinthewaytheyareconstructed.However,themostimportantfeaturetoaddresshereisrelatedtothestylefactors.Letusfocusanddescribetheprinciplesofthismodel,inordertounderstandthefounda:onsofBloomberg’sstylefactors.BARRAriskfactorsaremainlymicroeconomicandfundamentalcharacteris:csthatmostfirmsshareincommon.Intheenvironmentofawell-diversifiedporZolio,company-specificevents(idiosyncra:c)won’thavemuchimpactinporZolio’srisk.Thesystema:cpor:onbecomesincreasinglylargerastheporZoliogetslarger.
BloombergEuropeanEquityModel BARRAEuropeanEquityModel
• MarketFactor• 17countryfactors• 24industryfactors• 10stylefactors
• MarketFactor• 29countryfactors• 29industryfactors• 9stylefactors
• Theanalysisittakesisbasedonafundamentalreviewofanasset.• Itsanalysisconsistsconceptuallyindeterminingasecurity’sfuturevaluethroughmacroandmicroeconomiceventsandtheimpactonthesecurity.
• Differsfrompurefundamentalanalysisinitsfocus(factormodelsforecastriskandfundamentalanalysisaimatforecas:ngreturns)
MSCIBARRAModel
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RiskFactorOrigins(II)Thefundamentalandmicroeconomicvariablesformthestylefactorsinthismodel.ThenexttableshowsanexampleofasamplefundamentaldatausedinBarramodels:5variablesandthedescriptorsusedintheirconstruc:on.Onceiden:fiedthefactors,themodellinkseachstocktoeachfactors.Forthis,asetofmicroeconomiccharacteris:cs–descriptors–thatrelatetoeachfactorareusedareiden:fied.Havingiden:fiedthem,descriptorsarestandardizedacrossauniverseofstocks.Thisisdonebysubtrac:ngthees:ma:onuniverseaverageanddividingbythestandarddevia:onofthecoverageuniverseofstocks.Finally,thismodelperformsaweigh:ngschemeofthedescriptors,accordingtotheirimportanceinexplainingthefactor.Besidesthesestylefactors,security’sriskandreturnarealsofunc:onofitsindustry,currencyandcountry.Theseexposuresarecalculatedinasimplerway:acertainstockhasunitexposuretoitsindustry,currencyandcountryandnoexposuretoalltheothers.Interpreta:onisthesameasintheCAPM,despitethedifferencesinbothmodels.Exposuresmeasuresensi:vi:estopercentagevaria:onsinthefactors.Forinstance,ifastockhasanexposureof0.5tothesizefactor,andthesizefactorincreasesby20%,thestock’sreturnisexpectedtobe10%,allelseequal.
Value Growth EarningsVariaJon Leverage ForeignSensiJviy
-BookValue -Analystpredictedearnings -Trailingearnings -Forecastopera:ngincome -Sales -Forecastsales
-Five-yearpayout -Variabilityincapitalstructure -Growthinassets -Growthinsales
-Variabilityinearnings -Standarddevia:onofanalystpredictedearnings -Variabilityincashflows -Extraordinaryitemsinearnings
-Marketleverage -Bookleverage -Debttoassets -Seniordebtra:o
-Exchangeratesensi:vity -Oilpricesensi:vity -Sensi:vitytoothermarketindices -Exportrevenuesaspercentageoftotal
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ImplicitFactorApproachModel
SpecifiesfactorexposuresCalculatesfactorreturns
Exposures
Country,industry,currencyfactors–dummyvariablesStylefactors–hardertocalculateandinterpret
StyleFactorExposures
Reflectstockcharacteris:csthroughcon:nuousvariablese.g.stylefactorexposuresspecifyhowbigthestockis,howliquid,oronhowmuchleverageitoperates
Descriptors
Indicatorsusedtocalculatestylefactorexposures
Weigh:ng
Eachexposureisaweightedaverageofitsdescriptors
Wewillbrieflyexplainhowtheseexposuresareexactlycalculatedandwhicheffectstheyaresupposedtocaptureinthebehaviorofastock,aswellashowthedescriptorshelpdoingthatforeachcharacteris:c.
Thewaystylefactorsarecalculatedwillbefurtheraddressedlateron,alongwiththedescrip:onofthereplica:onprocess.Inthissec:on,thefocuswillbeonunderstandingstylefactorexposures.
UnderstandingStyleFactorExposures
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Thisfactorrepresentsanotherfeatureofthevaluefactor,beingsufficientlyrelevanttobeastandalonefactor.Theexposuretothisfactorisjustthemostrecentlyannouncedannualnetdividendsdividedbythemarketprice.Thereasoningisiden:caltothepreviousfactor.Stockswithhighdividendyieldshavehighexposurestothisfactor.
DividendYield
Thevaluefactordifferen:atesvaluestocksfromgrowthstocks.ThisfactorisalsoincludedintheFama-Frenchthree-factormodel–astheHML(high-minus-low)–andisbasedinthefindingthatvaluestocks(highbook-to-market,orlowmarket-to-bookra:os)havehigherreturnsthangrowthstocks.Thedescriptorsforthisfactorarera:os,whichintendedtoclassifystocksaccordingtothisperspec:ve.ThesearetheB/P,CF/P,E/P,EBITDA/EV,ForecastedE/PandSales/EV.Allofthesedescriptorsshowinthenumeratorabookmeasureandinthedenominatoramarketmeasure.Thismeansthatavaluestock,withhighvaluesforthesera:os,willhaveahighexposuretothisfactor.
Value
Webeginbylookingatthemomentumfactor.Thisissupposedtocapturetheeffectofmomentuminthereturnofastock,dis:nguishingbetweenstocksthathaverisenoverthepastyearfromstocksthathavefallen.Stocksthatraisedthemostoverthepastyeararesaidtohavehighexposuretothisfactor.Toavoidthepricereversaleffectinthisexposure,thetwomostrecentweeklyreturnsareexcludedofthecalcula:on.
Momentum
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Thisfactortriestocapturethedifferenceinreturnsbetweenstocksthathavehaddifferentlevelsofgrowthinthelastyears–dis:nguishingbetweenhighandlowgrowersintermsofreturns.ThehistoricindicatorsBloomberglooksattocalculatetheexposuretothegrowthfactorarethegrowthinTotalAssets(TAG),Sales(SG)andEarnings(EG).Bloomberglooksalsotonear-termforecastsofearnings(EFG)andsales(SFG)fromtheanalystes:matesdatabase.Thecomposi:onoftheformulausedtocalculateexposuretogrowthshouldbeinterpretedasthewayBloombergusestodefineit.Inthiscase,itweighsbetweenhistoricalandforwardlookingfundamentaldatafromanalysts.
Growth
Thetradingac:vityfactortriestouncovertheeffectthatliquidityandtradingfrequencyhaveinthestocksreturns.Inordertocapturethisfeatureinstocks’behavior,Bloombergusesaformulaonturnoverratherthantradingvolume,inordertoavoidcorrela:onwiththesizefactor.Thiswouldbedamaging,aswewouldbehidingarela:onbetweentwovariablesinthecross-sec:onalregression,whichcouldpoten:allyleadtowrongresults.
TradingAc:vity
ThisisanotherfactorthatispresentintheFFthree-factormodel,astheSMB(small-minus-big)factor,basedinthepercep:onthatsmallcapshavehadconsistentlyhigherreturnsthanbigcaps.Thecomposi:onforthisfactoristheMarketCapitaliza:onofthestock,SalesandTotalAssets.Thesewerethestockvariableschosentorepresentthesizeofastock:howmuchdoesthestockcost,howmuchdoesitsell,andonhowmuchcapitaldoesitoperate.Astockissaidtohaveahighexposuretothisfactorwhenithasabigmarketcap,salesand/ortotalassets.
Size
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Thisfactorrepresentsanotherfeatureofvola:lityofacompany,includingothermeasuresrelatedtotheopera:ngac:vi:esofthecompany.Thesearethevola:lityofearnings,cashflowsandsales,forthepast5years.
EarningsVariability
Bloombergincludesthisfactorinordertoaccountfortheeffectofvola:lityinthereturnofeachsecurity.Thisisn’tjusttoaccountforthevola:lityofthestocks’returns,buttoreachavaluethatcapturesabroaderconceptofvola:lity.Thisfactorisconstructedtodifferen:atemoreandlessvola:lestocksthroughameasurementofvola:litythatcomesfromseveraldis:nctperspec:ves.Theseare:returnvola:lityoverthelastyear,CAPMbeta,vola:lityoftheCAPMresidualsandacumula:verangegivenbythera:obetweenthemaximumandminimumpriceoverthelast5years.
Vola:lity
Thisfactorusesprofitmarginstomeasuretheperformanceofeachcompanyanddifferen:atebetweenmoneymakersandmoneylosers.Themeasuresofprofitabilityusedare:returnonequity(bookmeasure),returnoncapitalemployed,returnonassetsandEBITDAmargin.
Profitability
Thisvariablerepresentsthelevelofleverageofacompanygivenbyanaveragebetweenthreeindicators.Thisshoulddifferen:atestockswithdifferentlevelsofindebtednessintermsofreturns.Themeasuresofleverageusedtocalculatethelevelofdebtofeachstockarethebookleverage(DebtoverBookValueofthecompany),marketleverage(DebtoverMarketValueofthecompany)anddebttototalassets,whichareapproximatelyequalweighted.
Leverage
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Bloomberg’sFactorModelsBasics
Replica:onofBloomberg’sProcedure Be{erunderstandingof:
• Howthemodelswork• Howexposuresarecalculated
Issuebecomesevenmoreevidentwhenitcomestofixedincomefactors,ofwhichnoinforma:onisdisplayedonPORT
Bloomberg’sPORTtoolomitsagreatamountofinforma:onwhenitcomestodetailsonexposurescalcula:ons,i.e.:• whichdatafieldsareused• whatisthe:mespanofthedataused• howcertaindescriptorsarecalculated• howexactlyarethees:ma:onuniversescomposed
ReplicaJngprocessbecomeshighlyrestrainedwithoutsuchdetailedinforma:onregardingexposurescalcula:ons.Thedecisiontoreplicateanequitymodelimposeditselfduetothemen:onedrestric:ons.
A\ercarefullyanalyzingalloftheavailablemodels,itwasdecidedthatitwouldbebesttoreplicatetheEuropeanEquityFundamentalFactorModel.Pickingthismodelwasbasedonthefollowingcriteria:• Firstly,itwouldbebesttopickamodelwhosees:ma:onuniverseismadeupofsecuri:esthatwouldlikelyhave
alotofdataavailableonBloomberg(necessarytocalculateexposures);• Secondly,choosingamodelthataggregatesmorethanonecountrywouldallowustoreplicatethemodelmore
completely,aswewouldbeabletoincludeseveralcountryfactors.
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Below,alistofalltherestric:onsandfiltersimposedtoreachthesamplees:ma:onuniverseispresented:1. Tradingstatusofsecurity–Ac:ve2. Exchangeswherethesecurityistraded–WesternEurope3. Pricegreaterthan0.05(localcurrency)4. Securityhasmarketcapdata5. SecurityhasGICSindustrygroupdata6. Securityhascountrydata7. Securityhaspricedatasince01/01/2007(thisfilterallowedtheexclusionofsecuri:esthatwerenotquotedthroughthe
en:re:mespannecessarytocalculatesomefactorexposures)8. SecurityhasTotalAssets,Revenue,NetIncomeandCashdataavailablesincethefirstquarterof2007
Criteriarestrictedtheuniverseofsecuri:estoasampleofaround1000equiJes,aswastheobjec:ve.Eventhoughseveralfilterswereapplied,itwass:llnecessarytodealwithsomemissingdata,inwhichcaseswesimplyfilledtheinexistentdatapointsforeachsecuritywiththeaveragevalueacrossthesampleforacertaindate.
EsJmaJonUniverseDefiniJon
Defini:onofanes:ma:onuniversetocalculatefactorreturns,usingBloomberg’sEquityScreeningtool
FirstfiltersappliedtotheequityuniversewereinaccordancewiththeCoverageUniverserestric:ons
Then,morefilterswereappliedaccordingtoEs:ma:onUniverserestric:ons
Finally,filtersofthetype“HASDATA”wereusedtoreducethesamplesizetoaround1000securi:es
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CountryThematrixofcountryfactorexposuresisasetofbinaryvalues.Eachsecurityinthisuniversewillhaveaunitexposuretoitsowncountry,and0exposuretoallothercountriesintheEuropeanModel.
CountriespresentintheEuropeanModelare:Austria,Belgium,Denmark,Finland,France,Germany,Greece,Ireland,Italy,Luxembourg,Netherlands,Norway,Portugal,Spain,Sweden,Switzerland,UnitedKingdomandEmergingEurope.
Rela:velytotheremainingcountries,weaggregatedtheminthreegeographicalgroups:NorthernEurope(NE),CentralEurope(CE)andSouthernEurope(SE).Informa:ononhowweaggregatedcountriesinthesethreegroupscanbefoundinAppendix5.Sinceoures:ma:onuniverseisconsiderablysmallerthantheonewe’retryingtoreplicate,weshortenedalsothenumberoffactors,sothatthefactorreturnswehavetoes:materemainequallyrobustandsignificant.
Currency Thecurrencyexposuresofeachsecurityarealsobinaryvariables,whichequaltooneiftheshareisdenominatedinthatcurrencyandzeroifit’snot.
Wealsodecreasedthenumberofcurrencyexposuresrela:vetoBloomberg,assecuri:esfromsomeEasternEuropecountrieswerenotincluded.Seeannexxxx
Industry Ifasecuritybelongstoacertainindustry–oranindustrygroup,orsector,dependingonhowindustryfactorsareconstructed–thenitisassignedanexposurevalueof1tothisindustry,and0toallotherindustries.
IndustryfactorsareconstructedbasedontheGICSmembership.Itdividesindustriesin24industrygroupsand10sectors.WhentheGICSdataisn’tavailable,BloomberginferstheindustrygroupofasecurityonthebasisoftheBICS.
Duetothesamereasonwepointedinthecaseofthecountryfactors,wereducedthenumberofindustryfactorsfrom24to10.
Wefirstfocusonthebinaryfactors:country,currencyandindustryfactors.
BinaryFactorExposures
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StyleFactorExposuresInordertopromoteabe{ercomprehensionofthemodelanditsoutputbytheporZoliomanagersatBPIGA,weaimtodiscriminatetheprocedurebystepsandthoroughlyexplaineachoneofthem.Wenowsettoexplainthemosttechnicalpartofthereplica:on,thestylefactorexposures:• HowBloombergconstructseachoneofthem• Howwereplicatedit• ItwillnotalwaysbefeasibletocompletelymimicthewayBloombergconstructstheexposuresStylefactorsdifferfromthesebinaryfactorsastheycharacterizestocksinamoreelaboratewaythanjustzerosandones.Besidesrepor:ngthecountryofthestock,thecurrencyandtheindustryinwhichitoperates,inordertodecomposethewholeprofileofthatstock,wehavetolooktomorestylizedanddescrip:veinforma:onofacompanywhichmightbesignificantininfluenceitsperformanceintermsofriskandreturn.Ofcourse,thisrequiresmorethanjustbinaryvariables:ittakescon:nuousvariables.Morecomplexdatawillrequiremorecareindealingwiththesefactors.Wehavetomakeitrobustandhomogeneous.Todoso,weapplythesamereasoningandthesameproceduretotheconstruc:onofallstyleexposures.AswehaveexplainedwhendescribingmorebroadlytheBloomberg’sFactorModel,eachstylefactorconsistsofseveral“atomic”descriptors,whichreferstoapar:cularsecurityfeaturethatispartof.
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Totheoriginalvalueofdescriptor,subtractcountryrela:vemean(i.e.averageacrosssame-countrysecuri:es)
Dividebytheglobalstandarddevia:on(i.e.acrossallsecuri:esintheEs:ma:onUniverse)
Iteratethisprocessun:lthemeanisequalto0andstandarddevia:onisequalto1
Setextremevaluesbelow-3andabove3to-3and3,respec:vely
Forinstance,whenstandardizinganexposureofEDP,aPortuguesestock,onesubtractsthatexposurebytheaverageexposureonthatsamedayacrossallthePortuguesestocksintheuniverse,anddividebythestandarddevia:onoftheexposuresacrossallthestocks(andnotonlythePortuguese).
Thestandardiza:onprocessappliesbothtothedescriptorsandtothefinalvalueoftheexposure.A\erweigh:ngallthedescriptorstoformtheexposurestoeachstylefactors,thosevalueswillalsobestandardizedthesamewaythedescriptorswere.TheEuropeanmodelcoversaround45000securi:es.Itses:ma:onuniversecontainsanequally(butlower)greatnumberofsecuri:es.Ourstandardiza:onprocessisbasedonamuchloweruniverse.Hence,theaverageandthestandarddevia:onarecomputedrela:velytothestocksandcountriespresentinthises:ma:onuniverse.
Inordertocombinethefeaturesintostylefactors,wefirststandardizethedescriptors.Thisstandardiza:onhasitsownpar:culari:es.
StandardizaJonProcess
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Wehaveseenthatstylefactorexposuresareconstructedbasedon:1. Choosingdescriptors2. Standardizingdescriptors3. Weigh:ngdescriptorsinordertoreachtheexposuretoafactor4. StandardizingthedescriptorsweightedaveragetogettothefinalexposurevalueHavingexplainedthestandardiza:onprocessandthera:onalebehindthechosendescriptorsforeachfactor,wenowfocusontheweigh:ngofthedescriptors.
Tomergethedescriptorsintostylefactors,Bloomberghascomeupwithanalgorithmtodeterminetheweightofeachoneofthem.Thelogicbehindthisalgorithmistofindacommondimensionamongdescriptorswithinagivenstylefactor.Equalweigh:ngwouldbethesimplestwaytocombinethedescriptors,butBloombergdevelopedanotherwaythatisrobust,intui:veanddescribesmoreaccuratelythestylecharacteris:c,bycapturingthemostcommoninforma:oncontainedinthedescriptors.Themethodconsistsincalcula:ngacross-sec:onalSpearmanrankcorrela:onmatrixofdescriptors.Then,Bloombergextractsthefirstprincipalcomponentfromtheprincipalcomponentanalysis,whichexplainsdescriptorvariability.Theloadingsofthefirstprincipalcomponentarenormalizedtosumupto100%andthesearethepercentagevalueschosentoweightthedescriptors.Thelogicisthat,ifadescriptorhasthehighestcorrela:onwiththerestofthedescriptorsthatcomposethatstylefactor,thenthatdescriptorshouldbea{ributedthehighestweight,sinceitpointsmorecloselythanotherdescriptorstothecombinedstylecharacteris:c.
ExposuresCalibraJonInBloomberg’sequitymodels,exposuresofeachstocktoanyofthestylefactorsareupdatedeachweek,alongwiththees:ma:onuniverse.EveryWednesdaythemodelsarecalibratedandexposuresarerecalculatedusingthelatestdataavailable.
FactorWeighJng
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Wherern,tisthereturnofassetnat:met
Theexposurestothisfactorareconstructeddifferentlyfromtheotherfactors,astheyarenotcalculatedwiththeweigh:ngofsomeindicators.Theformulaincludeslastyearweeklyreturnsforthestocks,butskipsthetwomostrecentweekswiththepurposeofavoidingthepricereversaleffect
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Havingcoveredthecharacteris:csthatarecommonamongallofthestylefactors–atomicdescriptors,standardiza:onprocessandfactorweigh:ng–wenowgointogreaterdetailoneachofthestylefactors.Whenreplica:ngtheprocess,exposureswerecalculatedforeachweeksincethebeginningofSeptember2012un:lSeptember2015.
!"#$%&'# = !"# (1+ !!,!)!!!! !""#$
!!!!" !""#$
Momentum
Itisimportanttono:cethatanon-dividendpayingstockalsohasexposuretothisfactor:itisconsideredthatthedividendyieldissimplyzeroandthroughthestandardiza:onprocesstheexposureeventuallydeviatesfromzero.
DividendYield
!"#!"#$% = !"#$ !"#"$%&$ !"#$!"#$%
CalculaJngFactorExposures(I)
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WhereCF/PistheCashFlowtoPricera:o,E/PistheEarningstoPricera:o,EBITDA/EVistheEBITDAtoEnterpriseValuera:o,For.E/PistheForecastedEarningstoPricera:oandSales/EVistheSalestoEnterpriseValuera:oandEnterpriseValuewascalculatedas:
TheForecastedEarningstoPricera:otakesintoaccountboththe1-yearand2-yearforwardBloombergearningses:mates.OnPORT,itcanbeseenthataweightisa{ributedtoeachofthees:mates,butitisnotclearhowsuchweightisdetermined.Weverify,however,thatthisweightisthesameacrossallthesecuri:escoveredbythemodel.Over:me,Bloombergquantshavebeendecreasingtheweightappliedtothe1-yearforward-lookinges:mates,shi\ingittowardsthe2-yearforward-lookingearningses:mates.Forthesakeofsimplicitywehaveequallyweightedthetwoes:mates,thususingthefollowingformula:
MostofthedataextractedfromBloombergtogettothisexposureisreportedonaquarterlybasis,butnotnecessarilyontheexactsamedates.Tosimplifytheprocess,weconsideredthatquarterlydatawasalwaysreportedonthelastFridayofMarch,June,SeptemberandDecembereachyear.Thus,theonlyvariablecausingvalueexposurestochangeonaweeklybasisismarketcap.
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!"#$% = 0,13×!! + 0,18×!"! + 0,18×!! + 0,21×
!"#$%&!" + 0,16×!"#.!! + 0,13×!"#$%/!"
!" = !"#$%& !"# + !" !"#$ +max (!" !"#$ − !"#ℎ, 0)
Value
!"#.!! =! ∗ !"1+ 1− ! ∗ !"2
!
CalculaJngFactorExposures(II)
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Thesizeformula,justlikewiththevaluefactor,israthersimpletoapply:takingtheweightsgiventoeachdescriptorasseenonBloombergandmul:plyingthembythelogofMarketCap,SalesandTotalAssets.Again,sincebothSalesandTotalAssetsareonlyupdatedonaquarterlybasis,exposureschangeweeklyduetothevariabilityofMarketCap
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!"#$ = 0,28× log !"#$%& !"# + 0,36× log !"#$% + 0,36×log (!"#$% !""#$")
Size
Thisisthera:oofsharestradedoversharesoutstandingdaily,usingexponen:alweigh:ngofeachobserva:oninthepast2years(500tradingdays),withahalf-lifeof180days.Althoughthisexposurewouldchangeeveryday,forthepurposeofthemodelitisonlyupdatedonaweeklybasis
!"#$%&' !"#$%$#& = !"# !× !"# 2180 × !"#$%&
!ℎ!"#$ !"#$#%&'(&)
!!!!!"#
!!!!"" !"#$
TradingAc:vity
CalculaJngFactorExposures(III)
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WhereTAGistheTotalAssetgrowthoverthelast5years,SGistheSalesgrowthoverthelast5years,EGistheEarningsgrowthoverthelastfiveyears,EFGisthenear-termforecastedearningsandSFGisthenear-termforecastedSalesaccordingtoBloomberg’ses:mates.EFGiscalculatedasEFG=EF2/EF1andSFGiscalculatedasSFG=SFG2/SFG1
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!"#$%ℎ = 0,23×!"# + 0,26×!" + 0,15×!" + 0,16×!"# + 0,20×!"#
Thegrowthfactorwasoneofthemostcomplextoreplicate.ThisissoduetounclearnessbyBloombergonhowthegrowthrateofeachdescriptorisachieved.Whenreplica:ngthisfactorexposure,wecalculatedeachgrowthratebasedonquarterlyobserva:ons,astheaveragegrowthratebetweensamequartersover5years(i.e.averagebetweengrowthrates,forinstance,ofTotalAssetsfrom1Q2007to1Q2008,from1Q2008to1Q2009,etc.).
Growth
CalculaJngFactorExposures(IV)
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REPLICATIONPROCESSMoJvaJon
andObjecJves
Bloomberg’sFactorModel
InterpreJngExposures
Replica:onProcess
Results
Conclusion
Appendix
WhereBLevistheBookValueofLeverage,MLevistheMarketValueofLeverageandD2TAistheDebttoTotalAssetsra:o.BLeviscalculatedas:MLeviscalculatedas:D2TAiscalculatedas:
32
SimilarlytotheValueandSizefactors,theLeveragefactoronlychangesonaweeklybasisduetotheMLevdescriptor,sinceitincludesmarketcapdatainitscalcula:on.Inthesecases,thereplica:onnaturallydeviatesfromBloomberg’sprocedure,poten:allyleadingtodifferentresults
Leverage
!"#"$%&" = 0,34×!"#$ + 0,33×!"#$ + 0,33×!2!"
CalculaJngFactorExposures(V)
!"#$%& +max (!"#$%& − !"#ℎ, 0)!""# !"#$% + !"#$%& +max (!"#$%& − !"#ℎ, 0)
!"#$%& +max (!"#$%& − !"#ℎ, 0)!"#$%& !"# + !"#$%& +max (!"#$%& − !"#ℎ, 0)
!"#$%& +max (!"#$%& − !"#ℎ, 0)!"#$% !""#$"
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REPLICATIONPROCESSMoJvaJon
andObjecJves
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33
Thedescriptorsthatmakeuptheprofitabilityfactoruseexclusivelydataonlyreportedquarterly.Itisthusoneofthecasesinwhichthereplicatedexposuresonlychangefromquartertoquarterandwehavesimplyextendedsuchcalcula:onstoaweeklybasis.This,again,deviatesfromBloombergprocedure,itissobecausenoteverycompanyreportstheirfinancialsatthesame:me(whichwehaveconsideredso),thuscausingtheprofitabilityfactorexposuretochangeatdifferent:mes.Companiesexposuresareoverallaffectedbythisfacteveryweek,notbecausetheirindividualexposurechangesthisregularly,butduetothefactthatthemeanexposureacrossthees:ma:onuniversechangesandaffectseverysecuritythroughthestandardiza:onprocess.
!"#$%&'(%)%&* = 0,26×!"# + 0,28×!"#$ + 0,28×!"# + 0,18×!"#$%& !"#$%&
Profitability
Where:EarnVolreferstoEarningsvola:lityoverthelast5yearsdividedbythemedianofTotalAssetsoverthesameperiod;CFVolreferstoCashFlowsvola:lityoverthelast5yearsdividedbythemedianofTotalAssetsoverthesameperiod;andSalesVolreferstoSalesvola:lityoverthelast5yearsdividedbythemedianofTotalAssetsoverthesameperiod.SimilarlytotheProfitabilityfactor,thisexposureonlychangesonaquarterlybasis.Hence,thesameissuesandcharacteris:csapply
!"#$%"#&"'&(&)* = 0,34×!"#$!"# + 0,35×!"#$% + 0,31×!"#$%&'#
EarningsVariability
CalculaJngFactorExposures(VI)
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REPLICATIONPROCESSMoJvaJon
andObjecJves
Bloomberg’sFactorModel
InterpreJngExposures
Replica:onProcess
Results
Conclusion
Appendix
Vola:lity
Where:VLRTisthereturnvola:lityoverthelastyearβistheCAPMbeta1
σisthevola:lityoftheCAPMresidualsCRNGisacumula:verangecalculatedasthera:onbetweenmaxandminpriceofsecurityoverthelastyear
A\ercalcula:ngtheexposures,amodifica:onismadeintheexposurestothevola:lityfactor.Thischangeismadetoensurethattheexplanatoryvariablesofthecross-sec:onalregressionarenotcorrelatedtoeachother.Themodifica:onconsistsinregressingthevola:lityexposurestotheexposuresoftheotherfactors.Theresidualofthisregressionistheexposuretothefactorusedinthecross-sec:onalregressiontocalculatefactorreturns,a\erapplyingthestandardiza:onprocess,likeitisdoneforalltheotherexposures.
34
!"#$%&#&%' = 0,30×!"#$ + 0,14×! + 0,29×! + 0,26×!"#$
CalculaJngFactorExposures(VII)
1Calculatedthrougha:me-seriesregressionofsecurityreturnsonexcess-marketreturns.AGerman10YGovtBondwasusedasproxyfortheriskfreerateandtheS&P500asmarket,eventhoughtheEuropeanmodelwasbeingreplicated(sinceitisBloomberg’smarketproxyaswell).
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REPLICATIONPROCESSMoJvaJon
andObjecJves
Bloomberg’sFactorModel
InterpreJngExposures
Replica:onProcess
Results
Conclusion
Appendix
• 1.A{ribu:onofbinaryexposures:country,currency,industryandmarketfactors• 2.Calcula:onofstylefactors• 3.Modifica:ontothevola:lityfactor• 4.CalculaJonoffactorreturns
Replica:onProcessSteps
• Togettofactorreturns• Ofsecurityreturnsonsecurityexposurestofactors• Oneforeachperiodt• Foreveryweekfrom09/2012to09/2015
CrossSec:onalRegressions1
35
!!,! = !!,!,!!!,! + !!,! !
!!!
!!,! isthelocalexcessreturnofassetninperiodt!!,!,!istheexposureofassetntofactork!!,!isthereturnoffactorkinperiodt!!,!istheresidualofassetn’sreturn
CalculaJngFactorReturns
1E
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REPLICATIONPROCESSMoJvaJon
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Bloomberg’sFactorModel
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36
!"#$%& ! % !"#$%&'($&"# !" !"#$ = !! × !! × !!,!
!!
NextStep:PorWolioAnalysis
!! isvolatilityoftheportfolio!!istheportfolioexposuretofactork!!isthevolatilityoffactork!!,!istheportfoliocorrelationwithfactork
A\ergenera:ngandconstruc:ngamodel,thenextstepwillalwaysbeabouthowitcanbeapplied.HowcanthismodelhelpmanagingtheriskofaporIolio?Inthiscase,wehavereplicatedthemodelbygenera:nganoutputofweeklyfactorreturnsforthepast3years.Thereasonwechosetocalculatethesereturnsforthis:meperiodwastoenableustocomputethecorrela:onwhichwouldhelpusevalua:ngthequalityofourmodel,butmostimportantly,tocalculatefactorvola:li:es.Thisinvolvesa:me-seriesofobserva:onssincethefactorvola:li:esarecalculatedwitharolling-windowofoneyear.Hence,withthreeyearsofweeklyfactorreturns,wewillbeabletocalculateweeklyfactorvola:li:esforaperiodoftwoyears.ThenextthingPORTdoesistocomputethesefactorvola:li:es,andtheriskanalysismetricsthatmightbecalculatedwithinthecontextofaporZolio.Themostimportantisthefactors’contribu:onstorisk.CurrentlyatBPIGA,asetoflimitsisdefinedbasedonthehistoricaldistribu:onoffactorscontribu:onstorisk.Thoselimits,aswehavedescribedearlier,aresetclosetothe95%and99%percen:lesofhistoricalvalues,butmightbeadjustedwiththehelpofporZoliomanagers.Factorcontribu:ontoriskiscalculatedaccordingtotheformula:
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RESULTSMoJvaJon
andObjecJves
Bloomberg’sFactorModel
InterpreJngExposures
ReplicaJonProcess
Results
Conclusion
Appendix
37
Ourprimaryobjec:veforthisprojectwastohelppromo:ngabe{erriskcultureinBPIGAthroughabe{erunderstandingofBloomberg’sFactorModel.Hence,thegoalofthereplica:onthemodelistodiscriminatetheprocessbystepsandexploringeachstepinsteadofcontes:ngBloomberg’svalues.Thismeansthatourmostimportantresultwillalwaysbethewaywewereabletodothis,insteadofthevalueswecomputed,i.e.,theresultsarelessimportantthantheprocess.However,inordertocontrolfortheprocess,wehavetoanalyzetheresul:ngoutputandcompareitsomehowtoBloomberg’s,sothatweareabletovalidatewhatwedidwithsignificantconfidence.Themostefficientwaytodothisistocomputethecorrela:onsbetweenourstyleexposuresandtheonesfromBloomberg,foreachday.Comparingtheexposuresforthewholees:ma:onuniverse,however,bylookingatthecross-sec:onalcorrela:onswithBloombergwillunderratethequalityofthemodel,sincethees:ma:onuniverseisdifferentinsomewaysfromBloomberg’suniverse.Morespecifically,thepropor:onofeachcountry’sequi:esinthees:ma:onuniversewecreateddoesnotcorrespondtotheonefromBloomberg.Twomainissues:-Replica:ngthemodelwithamuchsmallersampleofstocks- Replica:ngeachcountry’spropor:onofstocksinthesample.Thisisnotpossibletoexecutebecause:
1. thereisnoclearinforma:ononthesepropor:on;2. itisdynamic,changingthrough:me.
Hence,wechosetocomparetheexposureswecalculatedforthePortuguesestocksonoursamplees:ma:onuniverseandverifythecorrela:onswithBloomberg’sexposures.
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RESULTSMoJvaJon
andObjecJves
Bloomberg’sFactorModel
InterpreJngExposures
ReplicaJonProcess
Results
Conclusion
Appendix
38
Wecalculatedthesecross-sec:onalcorrela:onsbetweenbothexposuresforeverymonthfromSeptemberof2012toSeptemberof2015–37observa:ons.Then,wecomputedtheaveragecorrela:onthroughthe37monthsforeachstyleexposureandsomeaddi:onalsta:s:cs,asshownlater.
0
0.2
0.4
0.6
0.8
1
Sep/12
Dec/12
Mar-13
Jun-13
Sep/13
Dec/13
Mar-14
Jun-14
Sep/14
Dec/14
Mar-15
Jun-15
Sep/15
CorrelaJonsBetweenReplicatedandBloombergExposures
EUDivYld
EUEarnVariab
EULeverage
EUMomentum
EUSize
EUTradeAct
Ourresultsshow:• 4factorswhoseexposuresaveragecorrela:onisverystrong(DividendYield,Leverage,SizeandTradeAc:vity)• 3whosecorrela:onisacceptable(Vola:lity,MomentumandEarningsVariability).Theexplana:onforthesemedium
correla:onsisrelatedwiththenaturaldifferencebetweentheoriginalandthereplica:onmodel,suchasdifferencesintheavailabledataandinthestandardiza:onprocess,whichwilloriginatedifferentvalueswiththeuseofdifferentes:ma:onuniverses.
• 3factorswhoseresultsarenotsostrong(Growth,ValueandProfit).
Wehavestrongconfidence,fromthisinforma:on,thattheexposurecalibra:onprocesswasdonecorrectly.Mostexposureshaveconsistentresults,andfortheoneswithworseresults,therearesomefeaturesthatcanexplaintheweakcorrela:onsandthesta:s:callynon-significantaverages.
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RESULTSMoJvaJon
andObjecJves
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ReplicaJonProcess
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Appendix
39
!"#! =!"! − !"!!!
!"!!!
!
!!!!
IssuesReplicaJngGrowthExposuresItisunclearhowBloombergcalculatesannualgrowthratesofeachdescriptorfromquartertoquarter.Fromtheavailableinforma:onthroughPORT,onBloomberg,onecanassumethefollowingformula:However,differentwaysofcalcula:nggrowthrateswereexperimentedinanefforttogetabe{ercorrela:onbetweenthemodel’sexposuresandthereplicatedones,butnosuccesswasachievedforthisfactorinpar:cularfactor.
IssuesReplicaJngProfitExposures- Descriptorsusedinthecalcula:onofthisexposureareonlyreportedquarterly.- FortheProfitfactor,aswellastotheGrowthfactor,thisproblemisevenmoreevident,sincenoneofthedescriptorscontainsaninputthatchangesmorefrequently.
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RESULTSMoJvaJon
andObjecJves
Bloomberg’sFactorModel
InterpreJngExposures
ReplicaJonProcess
Results
Conclusion
Appendix
40
CorrelaJon average min max stdev lower upper EUDivYld 0,86 0,45 0,99 0,16 0,54 1,17 EUEarnVariab 0,38 0,25 0,54 0,10 0,19 0,57 EUGrowth -0,05 -0,26 0,23 0,15 -0,33 0,24 EULeverage 0,92 0,76 0,98 0,06 0,80 1,03 EUMomentum 0,66 0,43 0,89 0,13 0,40 0,92 EUProfit 0,19 -0,26 0,68 0,31 -0,42 0,80 EUSize 0,99 0,98 1,00 0,01 0,98 1,00 EUTradeAct 0,99 0,97 0,99 0,00 0,98 0,99 EUValue 0,17 -0,49 0,68 0,28 -0,39 0,73 EUVola:lity 0,65 0,51 0,76 0,08 0,49 0,80
IssuesReplicaJngValueExposures- Oneofitsdescriptors(forecastedearnings-to-pricera:o)includesinitscalcula:onaweightappliedtotheoneandthetwo-yearforward-lookingearningses:mates-forsimplicity,itwasassumedequal-weighttobothbutthisnaturallydiffersfromwhatisdoneinthemodel.
- Withtheexcep:onofmarketcap,allotherinputsareonlyupdatedquarterly.Thisposesanissuebecausewehaveassumedthateverycompanyreportsthisinforma:onatthesame:mebutthisdoesnotnecessarilyverify.thusdifferen:a:ngthereplicatedexposurestotheonesprovidedonPORT,inpar:cularthroughthestandardiza:onprocess
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CONCLUSIONMoJvaJon
andObjecJves
Bloomberg’sFactorModel
InterpreJngExposures
ReplicaJonProcess
Results
Conclusion
Appendix
41
HavingsetouttoreplicateBloomberg’sprocedureincalcula:ngfactorreturns,themainobjec:veofourworkwastopromoteabe{erunderstandingofBloomberg’sFactorModelanditsporZolioanalysistool,PORT,toul:matelyaidtheRiskManagementteamintheirefforttopromoteariskcultureatBPIGestãodeAcJvos.Thedecisiontofocusourworkonthereplica:onprocessofBloomberg’sfactorexposurescalcula:onsthroughtheinves:ga:onofPORThelpedusgetamuchdeeperpercep:onofthefunc:onali:esofthistoolbutalsoofsomeissuesintermsofdatatransparencyonPORTaswell.Nevertheless,itisclearnowthathavinggonethroughthereplica:ngprocess,wehavebeenabletodocumentourfindingsindetailtopassontobothporZolioandriskmanagementteams.Withaclearerunderstandingofhowexposuresandfactorreturnsarecalculated,weexpecttoincreasetheimpactofPORTasarisktooltobeusedbyassetmanagersatBPIGA.
Bloomberg’sFactorModelsBasics
Replica:onofBloomberg’sProcedure Be{erunderstandingof:
• Howthemodelswork• Howexposuresarecalculated
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APPENDIX1MoJvaJon
andObjecJves
Bloomberg’sFactorModel
InterpreJngExposures
ReplicaJonProcess
Results
Conclusion
Appendix
42
GICSIndustryGroupsEnergy Materials CapitalGoods Commercial&ProfessionalServices Transporta:on Automobiles&Components ConsumerDurables&Apparel ConsumerServices Media Retailing Food&StaplesRetailing Food,Beverage&Tobacco Household&PersonalProducts HealthCareEquipment&Services Pharmaceu:cals,Biotechnology&LifeSciences Banks DiversifiedFinancials Insurance RealEstate So\ware&Services TechnologyHardware&Equipment Semiconductors&SemiconductorEquipment Telecommunica:onServices U:li:es
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APPENDIX2MoJvaJon
andObjecJves
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InterpreJngExposures
ReplicaJonProcess
Results
Conclusion
Appendix
43
CoverageUniverseforEquityFundamentalFactorModels
FundamentalFactorEquity
Model
Coverage Universe
Asia All equi:es listed on major exchanges in the following countries: China (B and offshoreshares),HongKong(andChinaH-shares),Indonesia,India,Pakistan,SriLanka,Bangladesh,Mauri:us,Korea,Malaysia,Philippines,Singapore,Thailand,TaiwanandVietnam.
Australia Allequi:eswithcountryof riskdefinedasAustraliaorNewZealandonBloomberg (field:COUNTRY_RISK_ISO_CODE). Note:itisnotrequiredthatastockispricedover5localcentstobecoveredbythismodel.
Canada All equi:es listed in Canada or which have Canada defined as the country of risk onBloomberg(field:COUNTRY_RISK_ISO_CODE).
ChinaA-Shares AllequityChina-Ashares. EmergingEurope,Middle-East&Africa(EMEA)
All equi:es listed on major exchanges in the following countries: United Arab Emirates,Botswana, Ghana, Kenya, Nigeria, Senegal, Bahrain, Cyprus, Bulgaria, Croa:a, CzechRepublic, Estonia, Hungary, Latvia, Lithuania, Poland, Romania, Serbia, Slovakia, Slovenia,Egypt, Israel, Jordan, Kuwait, Morocco, Oman, Qatar, Russia, Ukraine, Kazakhstan, SaudiArabia,Tunisia,TurkeyandSouthAfrica.
European Allequi:eslistedonEuropeanexchanges,includingGDRs.
Japan Allequi:eslistedonJapaneseexchanges. La:nAmerica All equi:es listed onmajor exchanges in the following countries: Argen:na, Brazil, Chile,
Mexico,Colombia,Jamaica,Panama,Peru,Trinidad&TobagoandVenezuela. US Allequi:eslistedontheUnitedStatesexchanges,includingADRs.
Global Allequi:eslistedonmajorexchanges.
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APPENDIX3AMoJvaJon
andObjecJves
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InterpreJngExposures
ReplicaJonProcess
Results
Conclusion
Appendix
44
EmergingMarketsFactorCountryGroupings
UnitedArabEmirates[AE]
Botswana,Ghana,Kenya,Nigeria,Senegal[AFG]
Bahrain[BH]
Cyprus[CY]Bulgaria,Croa:a,CzechRepublic,Estonia,Hungary,Latvia,Lithuania,Poland,Romania,Serbia,Slovakia,Slovenia[EEG]Egypt[EG]
Israel[IL]
Jordan[JO]
Kuwait[KW]
Morocco[MA]
Oman[OM]
Qatar[QA]
Russia,Ukraine,Kazakhstan[RUG]
SaudiArabia[SA]
Tunisia[TN]
Turkey[TR]
SouthAfrica[ZA]
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APPENDIX3BMoJvaJon
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Results
Conclusion
Appendix
45
LaJnAmericaFactorCountryGroupingsArgen:na[AR] Brazil[BR] Chile[CL] Mexico[MX] La:nAmericaGroup[LAG]:Colombia,Jamaica,Panama,Peru,Trinidad&Tobago,Venezuela
AsiaFactorCountryGroupingsChina(B-sharesandoffshoreshares)[CN]
HongKong(andChinaH-shares)[HKG]
Indonesia[ID]
India,Pakistan,SriLanka,Bangladesh,Mauri:us[ING]
Korea[KR]
Malaysia[MY]
Philippines[PH]
Singapore[SG]
Thailand[TH]
Taiwan[TW]
Vietnam[VN]
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APPENDIX4MoJvaJon
andObjecJves
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ReplicaJonProcess
Results
Conclusion
Appendix
46
GlobalModelFactorCountryGroupingsArgen:na(AR)Australia(AU)Austria(AT)Brazil(BR)Belgium(BE)Canada(CA)Chile(CL)China(CN)EasternEuropeDeveloped:Hungary(HU)Poland(PL)CzechRepublic(CZ)EasternEuropeFron:er:Albania(AL)Belarus(BY)BosniaHerzegovina(BA)Bulgaria(BG)Croa:a(HR)Cyprus(CY)Estonia(EE)
Latvia(LV)Lithuania(LT)Macedonia(MK)Romania(RO)Serbia(RS)Slovakia(SK)Slovenia(SI)Ukraine(UA)EmergingLa:nAmerica:Bolivia(BO)Colombia(CO)Ecuador(EC)Jamaica(JM)Peru(PE)TrinidadandTobago(TT)EmergingMiddleEast:Egypt[EG]Jordan(JO)Morocco(MA)Tunisia(TN)Bahrain(BA)Kuwait(KW)
Lebanon(LB)Oman(OM)Qatar(QA)SaudiArabia(SA)Fron:er:Bangladesh(BD)Kazakhstan(KZ)Pakistan(PK)SriLanka(SK)Vietnam(VN)Finland(FI)France(FR)+Luxembourg,MonacoGermany(DE)GreatBritain(GB)+Gibraltar,Guernsey,IsleofMan,Jersey,Bri:shVirginIslandsGreece[GR]HongKong(HK)India(IN)Indonesia(ID)Ireland(IE)Israel(IL)Italy(IT)
Japan(JP)Korea(KR)Malaysia(MY)Mexico(MX)Netherlands(NL)NewZealand(NZ)Norway(NO)Philippines(PH)Portugal(PT)Russia(RU)Singapore(SG)Spain(ES)SouthAfrica(SA)Sweden(SW)Switzerland(CH)+LiechtensteinTurkey(TR)Taiwan(TW)Thailand(TH)USA(US)+Bermuda,Bahamas,CaymanIslands
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APPENDIX5MoJvaJon
andObjecJves
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ReplicaJonProcess
Results
Conclusion
Appendix
47
EsJmaJonUniverseSpecialSituaJons
Model EsJmaJonUniverseAustralia Star:ngfromtheCoverageUniverse,whichincludesallequi:eswithcountryofriskdefined
as Australia or New Zealand (field: COUNTRY_RISK_ISO_CODE), Bloomberg considers onlythose stocks with country of risk Australia and further imposes requirements on liquidity,priceandminimumsize.
European TheCoverageUniverseincludesallequi:estradedonEuropeanexchanges,however,whenitcomestotheEs:ma:onUniverse,BloombergexcludesallcompaniesincorporatedoutsideofEuropeandfocusesoncompaniesthataccountfor98%ofthemarketcapinthesecountries:Austria, Belgium, Denmark, Finland, France, Germany, Greece, Ireland, Italy, Netherlands,Norway,Portugal,Spain,Sweden,SwitzerlandandUK.Also,acompanyisalsoincludedifitismemberofamajorEuropeanequityindex.
Japan Thismodel coversallequi:es listedon Japaneseexchanges,butexcludeson itsEs:ma:onUniverse companies incorporatedoutsideof Japan.Also, if a company is amemberof theTOPIXindex,itisautoma:callyincludedintheuniverse.
US CompaniesincorporatedoutsideoftheUSareexcludedfromtheEs:ma:onUniverseofthismodel,butifacompanyisamemberoftheS&P500,itisincludedintheuniverseregardless.
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APPENDIX6AMoJvaJon
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Conclusion
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48
NorthernEurope CentralEurope SouthernEurope Denmark Finland Iceland Norway Sweden
Austria Belgium France Germany Luxembourg Netherlands Switzerland UnitedKingdom
Greece Ireland Italy Portugal Spain
CountryFactorAggregaJoninReplicaJonModel
Thereasoningbehindtheaggrega:oninthesethreegroupsismainlygeographic,butitalsorelatestotheeconomiccharacteris:csofeachcountryandthecountryriskstheyface(that’swhyweincludedIrelandintheSEfactor).
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APPENDIX6BMoJvaJon
andObjecJves
Bloomberg’sFactorModel
InterpreJngExposures
ReplicaJonProcess
Results
Conclusion
Appendix
49
CurrencyFactorsinReplicaJonModel IndustryFactorsinReplicaJonModelEuro BasicMaterialsGreatBri:shPound Communica:ons
NorwegianKrone Consumer(Cyclical)
SwissFranc Consumer(Non-cyclical)
IcelandicKrone Diversified
SwedishKrone Energy
DanishKrone Financials
Industrial
Technology
U:li:es
Insteadofusingthe24sectorsasindustryfactors,weusedthe10industrygroupsinthereplica:onmodel
Rela:velytoBloomberg’smodel,somecurrencies(EasternEurope)werenotincluded.
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BIBLIOGRAPHYMoJvaJon
andObjecJves
Bloomberg’sFactorModel
InterpreJngExposures
ReplicaJonProcess
Results
Conclusion
Appendix
50
• Baturin,N.,Cahan,E.(2015).GlobalEquityFundamentalFactorModel
• Baturin,N.,Cahan,E.(2015).EuropeanEquityFundamentalFactorModel
• Gan,Y.,Miranyan,L.(2015).FixedIncomeFundamentalFactorModel
• Bloomberg,BloombergPorZolio&RiskAnaly:csResearch.(2012).BloombergMul$-Asset
RiskModel
• Baturin,N.,Cahan,E.(2015).AsiaEquityFundamentalFactorModel
• Baturin,N.,Cahan,E.(2015).EmergingEMEAEquityFundamentalFactorModel
• Baturin,N.,Cahan,E.(2015).La$nAmericaEquityFundamentalFactorModel
• Bender,J.,Nielsen,F.(2010).TheFundamentalsofFundamentalFactorModels
• Menchero,J.(2010).Characteris$csofFactorPorWolios
• Parish,S.,Ballantyne,P.(2010).UnderstandingFactorRisk