Understanding Mul/-Asset Factor Models: Factor Exposure ... · BLOOMBERG’S FACTOR MODEL MoJvaJon and Objecves Bloomberg’s Factor Model InterpreJng Exposures ReplicaJon Process

UnderstandingMul/-AssetFactorModels:FactorExposureInterpreta/on

AcademicAdvisor:Mar$jnBoonsBPIGAAdvisors:CarlaMiranda,JoãoAbrantes

RitaSousaCosta|1018MiguelMarquesMendes|947

MasterinFinance–January2016

AGENDA

Mo:va:onandObjec:ves

Bloomberg’sFactorModel

Interpre:ngExposures

Replica:onProcess

Results

Conclusion

Appendix

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2

3

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5

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MOTIVATIONANDOBJECTIVESMoJvaJon

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InterpreJngExposures

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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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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

MOTIVATIONANDOBJECTIVESMo:va:on

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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

BLOOMBERG’SFACTORMODELMoJvaJon

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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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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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Market

Dummyvariables:unitexposureto

security’smarketandzerotoeveryother

market.Thisfactoristhemainriskcontributorfordiversifiedlong-only

porZolios.

Country


security’scountryofissue.

Currency

Dummyvariables:unitexposuretotradingcurrency.

Industry


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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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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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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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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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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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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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

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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.

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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)

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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.

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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.

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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.

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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.

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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.

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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.

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Wherern,tisthereturnofassetnat:met

Theexposurestothisfactorareconstructeddifferentlyfromtheotherfactors,astheyarenotcalculatedwiththeweigh:ngofsomeindicators.Theformulaincludeslastyearweeklyreturnsforthestocks,butskipsthetwomostrecentweekswiththepurposeofavoidingthepricereversaleffect

28

Havingcoveredthecharacteris:csthatarecommonamongallofthestylefactors–atomicdescriptors,standardiza:onprocessandfactorweigh:ng–wenowgointogreaterdetailoneachofthestylefactors.Whenreplica:ngtheprocess,exposureswerecalculatedforeachweeksincethebeginningofSeptember2012un:lSeptember2015.

!"#$%&'# = !"# (1+ !!,!)!!!! !""#$

!!!!" !""#$

Momentum

Itisimportanttono:cethatanon-dividendpayingstockalsohasexposuretothisfactor:itisconsideredthatthedividendyieldissimplyzeroandthroughthestandardiza:onprocesstheexposureeventuallydeviatesfromzero.

DividendYield

!"#!"#$% = !"#$ !"#"$%&$ !"#$!"#$%

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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

!

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Thesizeformula,justlikewiththevaluefactor,israthersimpletoapply:takingtheweightsgiventoeachdescriptorasseenonBloombergandmul:plyingthembythelogofMarketCap,SalesandTotalAssets.Again,sincebothSalesandTotalAssetsareonlyupdatedonaquarterlybasis,exposureschangeweeklyduetothevariabilityofMarketCap

30

!"#$ = 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

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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

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WhereBLevistheBookValueofLeverage,MLevistheMarketValueofLeverageandD2TAistheDebttoTotalAssetsra:o.BLeviscalculatedas:MLeviscalculatedas:D2TAiscalculatedas:

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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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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

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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.

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!"#$%&#&%' = 0,30×!"#$ + 0,14×! + 0,29×! + 0,26×!"#$

CalculaJngFactorExposures(VII)

1Calculatedthrougha:me-seriesregressionofsecurityreturnsonexcess-marketreturns.AGerman10YGovtBondwasusedasproxyfortheriskfreerateandtheS&P500asmarket,eventhoughtheEuropeanmodelwasbeingreplicated(sinceitisBloomberg’smarketproxyaswell).


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• 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

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!!,! = !!,!,!!!,! + !!,! !

!!!

!!,! isthelocalexcessreturnofassetninperiodt!!,!,!istheexposureofassetntofactork!!,!isthereturnoffactorkinperiodt!!,!istheresidualofassetn’sreturn

CalculaJngFactorReturns

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!"#$%& ! % !"#$%&'($&"# !" !"#$ = !! × !! × !!,!

!!

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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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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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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!"#! =!"! − !"!!!

!"!!!

!

!!!!

IssuesReplicaJngGrowthExposuresItisunclearhowBloombergcalculatesannualgrowthratesofeachdescriptorfromquartertoquarter.Fromtheavailableinforma:onthroughPORT,onBloomberg,onecanassumethefollowingformula:However,differentwaysofcalcula:nggrowthrateswereexperimentedinanefforttogetabe{ercorrela:onbetweenthemodel’sexposuresandthereplicatedones,butnosuccesswasachievedforthisfactorinpar:cularfactor.

IssuesReplicaJngProfitExposures-  Descriptorsusedinthecalcula:onofthisexposureareonlyreportedquarterly.-  FortheProfitfactor,aswellastotheGrowthfactor,thisproblemisevenmoreevident,sincenoneofthedescriptorscontainsaninputthatchangesmorefrequently.

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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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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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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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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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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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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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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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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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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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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.

BIBLIOGRAPHYMoJvaJon

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•  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

Understanding Mul/-Asset Factor Models: Factor Exposure ... · BLOOMBERG’S FACTOR MODEL MoJvaJon and Objecves Bloomberg’s Factor Model InterpreJng Exposures ReplicaJon Process

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