Post on 31-May-2020
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
1
2
3
4
5
6
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MOTIVATIONANDOBJECTIVESMoJvaJon
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Bloomberg’sFactorModel
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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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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
andObjec:ves
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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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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
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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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
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.
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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
!
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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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!"#$%ℎ = 0,23×!"# + 0,26×!" + 0,15×!" + 0,16×!"# + 0,20×!"#
Thegrowthfactorwasoneofthemostcomplextoreplicate.ThisissoduetounclearnessbyBloombergonhowthegrowthrateofeachdescriptorisachieved.Whenreplica:ngthisfactorexposure,wecalculatedeachgrowthratebasedonquarterlyobserva:ons,astheaveragegrowthratebetweensamequartersover5years(i.e.averagebetweengrowthrates,forinstance,ofTotalAssetsfrom1Q2007to1Q2008,from1Q2008to1Q2009,etc.).
Growth
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WhereBLevistheBookValueofLeverage,MLevistheMarketValueofLeverageandD2TAistheDebttoTotalAssetsra:o.BLeviscalculatedas:MLeviscalculatedas:D2TAiscalculatedas:
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SimilarlytotheValueandSizefactors,theLeveragefactoronlychangesonaweeklybasisduetotheMLevdescriptor,sinceitincludesmarketcapdatainitscalcula:on.Inthesecases,thereplica:onnaturallydeviatesfromBloomberg’sprocedure,poten:allyleadingtodifferentresults
Leverage
!"#"$%&" = 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
CalculaJngFactorExposures(VI)
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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
1E
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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
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1
Sep/12
Dec/12
Mar-13
Jun-13
Sep/13
Dec/13
Mar-14
Jun-14
Sep/14
Dec/14
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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
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• 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