Factor Investing in South Africa - Peresec...2 FACTOR INVESTING IN SOUTH AFRICA Factor Investing in...

DERIVATIVE AND QUANTITATIVE RESEARCH

Factor Investing in South Africa

Emlyn Flint, Anthony Seymour and Florence Chikurunhe

EXECUTIVE SUMMARYRisk factors and systematic factor strategies are fast becoming an integral part of the global asset management landscape. In this report, we provide an introduction to, and critique of, the factor investing paradigm in a South African setting. We initially discuss the general factor construction process at length and construct a comprehensive range of risk factors for the South African equity market according to international factor modelling standards.

In this report, we focus on the size, value, momentum, profitability, investment, low volatility and low beta risk factors respectively. We critically examine the historical behaviour and robustness of these factors, paying particular attention to the issues of long-only versus long/short factors, the impact of size, the effect of rebalancing frequency and data, and the robustness of performance to alternative factor definitions.

We also review how these factors can be used generally in risk management and portfolio management. In the risk management space, we firstly consider risk attribution to factors and introduce the Factor Efficiency Ratio as a means of quantifying a fund’s desired versus undesired factor exposure. Secondly, we consider returns-based style analysis as a means of identifying a fund’s factor style mix and also as a method for replicating existing indices with long-only risk factors.

In the portfolio management space, we discuss several approaches for creating multi-factor portfolios. We start by considering the simplest case of portfolio mixing, which allocates to a set of predefined factor building blocks. We then review the integrated scoring approach, which accounts for multiple factors within the scoring process directly. Finally, we consider the constrained optimisation approach, which allows an investor to construct an optimal multi-factor portfolio that is as consistent with their return objectives and risk preferences as their constraint set will permit.

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CONTENTS

1. Introduction 2

2. Linear Factor Models in Finance 3

2.1. CAPM & APT 3

2.2. The Fama-French Model and its Extensions 4

2.2.1. Fama-French Three-Factor Model 4

2.2.2. Carhart Four-Factor Model 4

2.2.3. Fama-French Five-Factor Model 5

2.2.4. Asness et al. Six-Factor Model 5

2.2.5. Other Risk Factors 5

3. South African Equity Risk Factors 6

3.1. Generalised Factor and Signal Processing 7

3.2. Constructing South African Risk Factors 7

3.3. Factor Analysis 9

3.4. Factor Robustness 12

3.4.1. Long-only versus Long/Short Factors 12

3.4.2. Factor Size Effects 14

3.4.3. Rebalancing Frequency & Date 14

3.4.4. Portfolio Extremity 15

3.4.5.AlternativeFactorDefinitions 15

4. Factor-Based Risk Management 16

4.1. FactorRiskAttributionandtheFactorEfficiencyRatio 16

4.2. Return-Based Style Analysis & Fund Replication 18

5. Factor-Based Portfolio Management 19

5.1. Factor Portfolio Mixing and Integrated Factor Scores 20

5.2. Constrained Risk Factor Optimisation 20

6. Conclusion 22

References 23

2 FACTOR INVESTING IN SOUTH AFRICA

Factor Investing in South Africa1. INTRODUCTIONRisk factors and the strategies based thereon are fast becoming an integral part of the global asset management landscape.1Thefinancialindustryhasadoptedthemonikersmart beta to describe such strategies as the term is both highlymarketableandsufficientlybroadtocoverawiderangeofinvestmentproducts.However,inthisreportwewillrather make use of the terms risk factors and/or risk premiawhenreferringtounderlyingmarketdrivers,andsystematic strategieswhenreferringtothedynamicinvestmentstrategiesfollowedinordertogainexposuretotheseunderlyingriskfactors.Wedothisnotonlytobemorerigorousbutalsotodrawattentiontothepracticalfactthatidentifyingariskfactorand subsequently harvesting returns from such a factor are essentially separate problems and need to be approached as such.

ThelatestannualsmartbetasurveysfromFTSERussell,EDHECandMSCIallshowvariationsofthesametwomajortrends:firstly,therearealreadyanumberof largeinternational institutional investorsthathavesizeablefactor-basedportfoliosandsecondly,thatmanymoreinvestorsareeitherintheprocessofreviewingsuchstrategiesorarelookingtodoso in thenear future. Inorder tounderstandwhyrisk factor investinghasshownsucharemarkablegrowth inpopularity,itisworthbrieflyconsideringthegreaterhistoryofportfoliomanagementandassetpricing.

Nearly70yearsago,Markowitz (1952) introduced theefficient frontierapproach toassetallocationwhich isstill themostpopularframeworkforconstructingportfoliosofassets.Underthisframework,anoptimalportfolioisdefinedasthecombinationofassetsthatmaximisestheexpectedreturnoftheportfolioatagiventimehorizonforaspecifiedlevelofportfoliorisk(Meucci,2001).Intheorythen,theportfolioconstructionproblemhadbeensolved.Onesimplyneededtoinputtheexpectedreturnsandcovariancesoftheassetsintotheframeworkandoutwouldpopanoptimalportfoliospecifictoone’sriskpreferences.Whenappliedinpracticethough,themodelwasfoundtobeincrediblysensitivetosmallchangesintheestimatedmeanreturnsandtheoptimisationprocedurewouldalmostcertainlyoutputunreasonableallocations.ThisbehaviourledtoMichaud(1989)coiningtheinfamousphrase“error maximiser”.

Asaresult,academicsandpractitionersalikehavesincefocussedtheireffortsintotwomainareasinordertoaddresstheframework’sweaknesses.Thefirstareaisbasedonallthingsrisk-related:risk-basedportfolioconstruction,moreefficientriskestimates,andnewriskanddiversificationmeasures.Theresultofthisworkhasculminatedinarichriskbudgetinganddiversificationapproach.Roncalli(2013)providesanexcellentreviewofgeneralisedriskbudgetingandFlintetal.(2015)providesacomprehensivestudyofdiversificationintheSouthAfricanmarket.

Thesecondarea isbasedonallaspectsofcreatingbetterexpected returnestimates. Inparticular,academicsandpractitionershavebeenonthehuntfortheunderlyingbuildingblocksofassetclassesinasimilarmannertothewaythatphysicistshavehuntedfortheincreasinglysmallandelementaryparticlesfromwhichallmatteriscomprised.Theresultofthissearchinthefinancialindustryhasgivenrisetothecurrentfactorinvestingparadigm.Podkaminer(2013)describes risk factorsas the“smallestsystematicunits that influence investmentreturnandriskcharacteristics”andCazalet andRoncalli (2014) describe risk factor investing simply as “an attempt to capture systematic risk premia”.Homescu(2015)furtheraddsthattheaimoffactorinvestingistoconstructportfoliosinasystematicmannerinordertogain exposure to a range of underlying risk factors.

TheobjectiveofthisreportistoconstructacomprehensiverangeofriskfactorsfortheSouthAfricanequitymarket,analyse the historical behaviour of these factors and provide an overview of how such factors can be used in riskmanagementandportfoliomanagement.Inordertoachievethisobjective,thisresearchdrawsheavilyontheexcellentreviewswrittenbyAng(2014),CazaletandRoncalli(2014),Amencetal.(2014),Homescu(2015)andMeucci(2016).WealsomakereferencetoMutswari’s(2016)recentworkontestingthevalidityofanumberofrecentfactormodelsforSouth African stock returns.

Theremainderofthisreportissetoutasfollows.Sectiontworeviewsthesetoflinearfactormodelsusedinfinanceanddiscusses the Fama-French factor models at length. Section 3 discusses the general factor construction process and

1 Thefactorsandstrategiesareknownbymanynames.Someoftheseinclude:riskfactors,riskpremia,smartbeta,alternativebeta,systematicstrategies,quantitativestrategiesandrule-basedstrategies.

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the Fama-French construction methodology in detail. South African risk factors are introduced and thoroughly analysed. Section4thenconsiderstheapplicationofthesefactorsinriskmanagement,focussingonriskattributionandreturns-basedstyleanalysis.Factor-basedportfoliomanagementisdiscussedinSection5,withemphasisoncreatingmulti-factorportfolios,andSection6concludes.

2. LINEAR FACTOR MODELS IN FINANCEAlmostallfinancestudiesthroughouthistoryhaveshownthat there isatrade-offbetween risk and return. A natural questionforinvestorstheniswhatlevelofreturncanoneexpecttoobtainforexposingoneselftoagivenlevelofrisk?Traditionally,questionsofthisnaturehavebeenansweredbyusingLinearFactorModels,orLFM’s,whichpositalinear relationshipbetweenanasset’sexpectedreturnanditscovariancewiththeriskfactorsincorporatedinthemodel.

Meucci(2016)statesthatLFM’sareusedinalmosteverystepoftheriskandportfoliomanagementprocess,includingassetpricing,riskattributionandmodelling,alphaprediction,portfoliooptimisationandassetallocation.LFM’sarealsothe cornerstone of factor investing as they are the main quantitative tool used to create systematic factor strategies. In thissection,webrieflyreviewthekeyLFM’susedintheassetpricingliteratureanddiscussatlengththecommonlyusedFama-French-type factor models.

2.1. CAPM & APTThecapitalassetpricingmodel(CAPM)wasintroducedbySharpe(1964)andservesasthebasisforallotherfactormodelsofassetreturns.BasedontheframeworkdefinedbyMarkowitz(1952),Sharpeshowedthattheriskpremiumonanasset(orportfolioofassets)wasalinearfunctionofasinglemarketriskpremium,representedbythemarket-capitalisationindex.Mathematically,theCAPMstatesthat

[Ri] – Rf = bi ([Rm] – Rf ), (1)

whereRi and Rm are the returns on the ithassetandmarketportfoliorespectively,Rf istherisk-freerate,[ • ] represents

the expectation and bi is the beta – or sensitivity – of the ithassettothemarketportfolio,calculatedastheratioofthe

covariance of the asset and the market portfolio to the variance of the market portfolio:

ov [Ri , Rm] bi = ––––––––––– . (2) Var [ Rm]

Betathusmeasuresthelevelofnon-diversifiable,systematicriskembeddedwithinanyasset.Giventhatthereisonlyasinglemarketriskfactor,theCAPMstatesthattherewardfortakingonadditionalriskisdirectlyproportionaltotheunderlyingmarketrisk.Therefore,everyoneshouldholdthemarketportfolioinequilibriumasitistheonlyriskthatistrulyrewarded.Whileextremelyelegant,therehavebeencountlessstudiessinceitsintroductionthathaveshownthatthe theoretical CAPM is not validated by empirical evidence.

Ross(1976)proposedanalternativemodel,knownasarbitragepricingtheory(APT)basedontheincreasingevidenceof multiple market risk premia. Ross posited that the return of an asset is driven by a combination of random market factorsandthatthiscanbemodelledwithanLFM:

Ri = ai + ∑bijƑj + ei , (3)whereaiisaconstant,bi

j is the sensitivity of asset i to factor j,Ƒj is the return on factor j,andei is the iid error – or stock-specificrisk–term,whichisalsoindependentfromanyoftheriskfactors.ItcanbeshownfromEquation3thatunderAPT,theriskpremiumonanassetisgivenby

m

j = 1


[Ri] – Rf = ∑bij ([Ƒj] – Rf ), (4)Equations 3 and 4 form the basis of nearly all risk attribution systems and systematic factor strategies. One of the challengesinusingtheAPTthoughisthatitislefttotheusertodefinewhattheunderlyingmarketriskfactorsreallyare. In this vein,Cazalet andRoncalli (2014) define threemain risk factor categories. The first category comprisesfactors based purely on statistical asset data – e.g. PCA risk factors. The second category comprises factors based on macroeconomicdata–e.g.inflationandGDPgrowth.Thefinalcategorycomprisesfactorsbasedonmarketdata.Thiscanbefurtherclassifiedintothosefactorsbasedonaccountingdata–e.g.sizeandvalue–andthosebasedonpricedata–e.g.momentumandlowvolatility.Inthiswork,wefocusmostlyonthethirdcategoryofriskfactors.

2.2. The Fama-French Model and its Extensions

2.2.1. Fama-French Three-Factor ModelBasedonthepriorempiricalstudiesthatanalysednumerouspotentialriskfactors,FamaandFrench(1993)proposedathree-factormodelforequitystockreturns,whichhassincebecometheindustrystandard.Thismodellinearlycombinesaccounting- and price-based factors in the form

Ri – Rf = ai + bim(Rm – Rf ) + bi

smbRsmb + bihmlRhml + ei . (5)

Rsmb is the return on a long/short portfolio of small/big market capitalisation stocks and Rhml is the return on a long/short portfolioofhigh/lowbook-to-marketstocks.2Theseareknownasthesizefactorandvaluefactorsrespectively.Becausemarketcapitalizationandvalueratioindicatorsarecorrelated,FamaandFrench(1993)useatwo-waysortingprocedureto strip out any confounding factor effects. The value factor thus captures the value premium that is independent of the effectofsizeandthesizefactorcapturesthesizepremiumthatisindependentoftheeffectofvalue.

There has been much literature aimed at assessing the appropriateness of the Fama-French three-factor model in equitymarketsworldwide.IntheSouthAfricancontext,vanRensburg(2001)andvanRensburgandRobertson(2003)provide some of the earliest comprehensive assessments of Fama-French-based APT models on the Johannesburg StockExchange(JSE).Althoughnot testing theexactFama-French three-factormodel, theyshowconvincingly thatone needs to incorporate several risk factors in order to accurately model the cross-section of equity returns on the JSE.MorerecentstudiesinthesameveinincludetheworksofMutooniandMuller(2007),BasiewiczandAuret(2009,2010),Strugnelletal.(2011)andMullerandWard(2013),amongothers.Althoughthesestudiesreportdifferencesinthemagnitudesandsignificancelevelsofcertainequityriskfactors,theyallconcludethatabroaderAPT-basedfactormodelisrequiredtomodelSouthAfricanequitymarketscorrectly.Thedifferenceinstudyresultsisalsotobeexpected,giventhevariationsindataperiodandmethodacrossthevariousstudies.AsbothAmencetal.(2014)andCazaletandRoncalli(2014)note,riskfactorscanbebothcyclicalandmarket-specific.

2.2.2. Carhart Four-Factor ModelMotivatedbytheevidenceprovidedbyJegadeeshandTitman(1993)ontheexistenceofsignificantmedium-termpricemomentumtrends,Carhart (1997) introduceda four-factormodelbasedonFamaandFrench’sworkbut includingamomentum factor. This has since become the standard model used in fund performance and persistence literature. Mathematically,theCarhartfour-factormodelisgivenas:


smbRsmb + bihmlRhml + bi

wmlRwml + ei, (6)

2 Factor construction is discussed at length in Section 3.

m

j = 1

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whereRwml represents thereturnona long/shortportfolioofwinner/loserstocks,basedontheprevious12-month’spriceperformance.Althoughinitiallymetwithseverescepticism,themomentumfactorisnowreferredtoasthe“premiermarketanomaly” (FamaandFrench,2008).Studieshaveconfirmed thepresenceof thisanomalyacrossnumerousgeographies and asset classes,making it themost prevalentmarket factor to date (Moskowitz,Ooi andPedersen(2012),Asnessetal.(2013)).Perhapsthereasonforthispervasivenessisbecausethemomentumfactorisinessenceabehaviouralartefact,drivenbycognitivebiaseswhichareunlikelytodisappearinthenearfuture(Antonacci,2013).Thesameisperhapsnottrueaboutthejustificationsofthesizeandvaluefactors.

2.2.3. Fama-French Five-Factor ModelInthetimesinceFamaandFrench’s(1993)initialwork,manyauthorshaveshownthatthethree-factormodelandeventhefour-factormodelmaywellnotbesufficienttoexplainthevariationinthecrosssectionofassetreturns.Tothiseffect,FamaandFrench (2014) introducedanovel five-factormodelwhich included factors relating to theprofitabilityandlevelofinvestmentmadebyacompany.Incontrasttotheiroriginalmodel,whichisbasedonAPTandempiricalmarketresearch,thejustificationforthefive-factormodelstemsfromthebottom-updividenddiscountmodel.Specifically,FamaandFrench(2014)suggestthatexpectedstockreturn,asmodelledbythedividenddiscountmodel,isbasedonthreevariables,namely thebook-to-market ratio,expectedearningsandexpectedgrowth inbookequity–what theydub‘investment’.Fromtheirinvestigations,theypositthefollowingfive-factor model:


smbRsmb + bihmlRhml + bi

cmaRcma + birmwRrmw + ei, (7)

whereRcma represents thereturnona long/shortportfolioofconservatively/aggressively investedstocks,andRrmw representsthereturnonalong/shortportfolioofrobust/weakprofitabilitystocks.Apartfromthedividenddiscountmodel,theinclusionofthesetwofactorswasalsoinfluencedbytheworkofNovy-Marx(2013)andothers,whoshowedthathighprofitability(orquality)stocksarerewardedwithasignificantandconsistentpremium,evenafteraccountingforthereturnstemmingfromtheoriginalriskfactors.Asnessetal.(2013b)havesincerefinedNovy-Marx’sproxyofprofitability/qualityandproposedanewlong/shortfactorofquality/junkstocks,wherequalityisdefinedasacompositescorebasedonthedividenddiscountmodelandcomprisingnumeroussingleaccountingvalues.Fortheremainderofthispaper,wewillfocusonlyonFamaandFrench’s(2014)versionoftheprofitability(i.e.quality)factor.

2.2.4. Asness et al. Six-Factor ModelGiventhattheFama-Frenchfive-factormodelismotivatedbythedividenddiscountmodel,whichdescribesthelong-termbehaviourofexpectedstockreturns,theabsenceoftheshorter-termmomentumfactorbecomessomewhatmoreunderstandable.However,itsexclusionisstillsurprisinggiventhattheseverysameauthorsnamedmomentumasthepremiermarketanomaly.Inadditiontothisobservation,Asnessetal.(2015)alsosuggestthatvalueandmomentumarecomplementaryriskfactorsandshouldbeplacedtogether.Asaresult,theyproposeasix-factormodelextensionwhichincludesthemomentumfactorandmakesuseofaslightlyadjustedvaluefactor:


smbRsmb + bihmlR*hml + bi

wmlRwml + bicmaRcma + bi

rmwRrmw + ei (8)

Accordingtotheirresults,thesix-factormodelprovidesamorecompleteexplanationofthevariationinhistoricalUSstockreturnsthanthefive-factormodelandtheadjustedvaluefactor,whichwasshowntobenearlyredundantbyFamaandFrench(2014)beforeadjustment,nowremainsasignificantriskfactor.

2.2.5. Other Risk FactorsInwhathasnowbecomeoneoftheclassicempiricalfinancepapers,Harveyetal.(2015)surveyedhundredsofassetpricingpaperspublishedover the lastfiftyyearsand talliedmore than300 factors thatarepurported toexplain thevariationinthecross-sectionofexpectedreturns.ThisconcertedexerciseindataminingledtoCochrane(2011)coiningthephrase“thefactorzoo”.


The proliferation of purported factors is also partly a consequence of the popularity of the factor investing paradigm: factors are now everywhere and everything has become a factor. Cazalet andRoncalli (2014) suggest that this isarguablythemostperniciousfantasyinthefactorinvestingliterature.Instead,theystatethatthereareonlyahandfulofriskfactorsthatrepresenttrueriskpremiaormarketanomalies.Ang(2014)suggestsfourmaincriteriafordeterminingwhetheranobservedmarketphenomenonisactuallyatrueriskfactor:

1. Itshouldhavestrongsupportinacademicandpractitionerresearchandstrongeconomicjustifications.

2. Itshouldhaveexhibitedsignificantpremiumstodatethatareexpectedtopersist.

3. It should have history available during both quiet and turbulent market regimes.

4. Itshouldbeimplementableinliquid,tradedinstruments.

Althoughthefinalcriterionisnotstrictlyrequiredifonlyusingthefactormodelinariskattributionsetting,itisstillvitallyimportant for creating tradable systematic factor strategies.

Thefactorswehavediscussedsofarareallconsideredtobetrueriskfactorsinthesensethattheyareprevalentacrossnearlyallmarketsstudiedtodate,havevalideconomicand/orbehaviouraljustificationsandhavehistoriesstretchingbackmorethanahundredyearsinsomecases.Inadditiontothesewell-establishedriskfactors,therearealsoahandfulof recently discovered factors that are fast becoming accepted as true risk factors.

Twosuchrecentfactorsattempttocapturetheobservedempiricalphenomenathatlowvolatilitystocksoutperformhighvolatilitystocksand,similarly, that lowbetastocksoutperformhighbetastocks.Angetal. (2006)andBlitzandvanVliet(2007)popularisedtheideaofthelowvolatilityfactorandshowedsignificantpremiumlevelsattachedtothisfactoracrossarangeofmarkets.Bakeretal.(2014)andFrazziniandPedersen(2014)amongothershavesinceconfirmedtheirresultsandrefinedtheeconomicrationale,furtherjustifyingtheobservedriskpremia.

ThelowbetafactorcanbetracedallthewaybacktoBlack(1972)andtheleverageeffect.Despitethislengthyhistory,thefactorhasonlycomebackintovogueinthelasttenyears.Interestingly,vanRensburgandRobertson(2003)showedearlyonthatthelowbetaanomalycommandedasignificantpremiumintheSouthAfricanequitymarketandcouldbeaccessed by sorting portfolios into quintiles based on their CAPM betas.

Othercommonfactorsnotconsideredinthisworkarethecarry(i.e.dividendyield),liquidityandqualityfactors.ThecarryriskfactorisperhapsthemosteasilyacceptedinSouthAfricanmarkets,whereboththeFTSE/JSEDividendPlusIndexand dividend-based unit trusts have existed for many years already. The liquidity factor is also easily appreciated in South African markets given its extremely high levels of concentration and the constant problem of capacity that many of the larger fundmanagersarefacedwith.Eventhoughthestrategyisaccessedbygoinglongilliquidstocksandshortingliquidstocks,itisunlikelythatonecouldevereasilytradeaSouthAfricanliquidityfactorinanydecentsize.Forthisreason,weleavethisfactorforfutureconsideration.Finally,wehavethequalityfactor.Asmentionedabove,theFamaandFrench(2014)profitabilityfactorisessentiallyequivalenttotheNovy-Marx(2012)versionofquality.AlthoughthemoreinvolveddefinitionbyAsnessetal.(2013b)isarguablyabetterproxyforthetruequalityfactor,itisalsoconsiderablymorecomplicatedtomanufacture.Forthesakeofsimplicitythen,weleavethismoreadvancedqualityfactorforfutureconsideration.

3. SOUTH AFRICAN EQUITY RISK FACTORSInSection2,weoutlinedseveralofthemostpopularAPT-basedfactormodelsusedinpracticewhichhavebecomeessentialriskandportfoliomanagementtools.Althoughtheselectionofanoptimalmodelspecificationremainsanopenquestion,itisclearthattheunderlyingriskfactorsusedinthesecompetingmodelswillcontinuetoremainrelevantfortheforeseeablefuture.Tothisend,thereareseveralonline,open-sourceriskfactordatabasesforlargeinternationalequitymarkets.3However,anddespitetheSouthAfrican-basedfactorstudiesmentionedearlier,asimilardatabasedoesnotexist – or at least is not publically available – for the South African equity market.

OneofthegoalsofthisresearchistocreateagrowingdatabaseofSouthAfricanequityriskfactors–andunderlyingstockvariables–constructedaspertheinternationalassetpricingliterature.Inparticular,weconstructsevenFama-Frenchstylefactors:size,value,momentum,profitability,investment,lowvolatilityandlowbeta.Ourhopeindoingsois

3 Forexample,seethecomprehensiveriskfactordatabasesmaintainedbyKennethFrench(http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data_library.html)andAndreaFrazzini(http://www.econ.yale.edu/~af227/data_library.htm).

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to make available to market participants an independent factor database that enables one to run a number of important riskandportfoliomanagementfactorapplicationsinlinewithinternationalbestpractice.

3.1. Generalised Factor and Signal ProcessingThefactorsdiscussedinthisworkarebasedontheFama-Frenchportfoliosortingmethodology,whichwewilloutlineshortly.However,itisimportanttorealisethisissimplyaspecialcaseofamoregeneralsignalprocessingframework.Meucci(2016)outlinesthreestepsinthegeneralallocationpolicyforsystematicstrategies.Firstly,processthesetofcurrent information intooneormore factorsignals.Secondly, transform thesesignals intoasinglesetofconsistentcharacteristics(i.e.expectedreturnestimates)ontheunderlyingstocks.Thirdly,constructoptimalportfolioweightsasafunction of the transformed signal characteristics.

Theinitialstepcanbebrokenfurtherintodatacollection,signalgenerationandsignalprocessing.Consideramomentumsignal for example. After collecting the requisite price data and correcting for any corporate actions and dividend payments,oneusesadefined function tocreate factorscores.Thiscouldbeassimpleasprior12-month returnorsomethingmorecomplicatedlikeaHullmovingaveragefilter.Finally,thesescoresarefilteredovertimeand/orcross-sectionallyinordertocreatefactorsignals.Commonfilteringtechniquesincludesmoothingovertime,scoringtoreducevolatility,rankingcross-sectionally,twistingranksnonlinearly,andtrimmingorWinsoringoutliers.

Thesecondstepisnotusuallycarriedoutwhenconstructingsinglefactorsbut isvitally importantwhenconsideringmultiplefactors.Forexample,considerauniverseofstocksthathavebothmomentumandvaluescores.Onethenneedstodefineamethodologyforcreatingasingleconsistentcharacteristicvalueforeachstockthatisconsistentwithbothsets of factor scores. Such methods can vary from basic portfolio sorts to complex nonlinear programming solutions. We revisit this point in Section 5.1.

Finally,createanoptimalportfoliobased theestimatedstockcharacteristics,agivensatisfaction indexandasetofconstraints. This implementation step is ultimatelywhat separates systematic factor strategies from underlying riskfactorportfolios.Inspecialcases,onecandirectlytradetheunderlyingriskfactorsbutusuallyinvestorsarefacedwithreal-worldconstraintsthatmakethisimpossible.Forexample,long-onlyinvestorswantingtogainexposuretothelong/shortFama-Frenchvaluefactorneedtouseoptimisationtechniquesinordertomaximisetargetedfactorexposurewhileminimisingunwantedfactorexposures.SeeSection4.1and5.2formoreonthis.

3.2. Constructing South African Risk FactorsWenowconsidertheFama-Frenchconstructionmethodologyinlightofthegeneralfactorframeworkoutlinedabove.Thedatasetconsistsofthe383constituentsoftheFTSE/JSEAllShareIndex(ALSI)overtheperiodJanuary1996toAugust2016.AllavailabletotalreturnandfundamentalstockdatawereobtainedfromBloombergandINetforthe20-yearperiod.Duetoseverelimitationsonavailablefundamentaldata,theinitialstartingdatehadtobemovedforwardtoDecember2002,thusyieldingafinalsampleperiodofjustlessthan14years.

ThemajorityofFama-Frenchriskfactorsarebasedonfundamentalstockvariables,withtheremainderbasedonpriceinformationvariables.Thedefinitionsofeachsuchvariablewerekeptconsistentwiththerelevantinternationalliterature.Atanyparticularmonthintheanalysiswindow,thefactorvariablesaredefinedasfollows:

• Sizeisdefinedasthemarketvalueofthestockasattheendofthepreviousmonth.Thesharesinissuearetakendirectly from the underlying FTSE/JSE index data and multiplied by the index-recorded share price to obtain the gross market capitalisation.

• Valueisdefinedastheratioofbookvaluetomarketvalue(BtM).Thisratioiscomputedbytakingthemostrecentbook value six months prior to the current month and dividing it by the market value as at the end of the previous month.ThisisslightlydifferenttotheoriginaldefinitionbutisinlinewiththealterationproposedbyAsnessandFrazzini(2013).

• Momentumisdefinedasthepriortwelvemonthtotalstockreturn,lessthepriormonth’sreturntoaccountforanyshort-term reversal effects.

• Profitabilityisdefinedastheratioofoperatingprofit(totalannualrevenue,netofsalesandotherexpenses)tothe most recent book value for the previous year.


• Investmentisdefinedastherelativegrowthintotalassetssixmonthspriortothecurrentmonth.• Low volatilityisdefinedasthestandarddeviationofweeklytotalstockreturnsmeasuredoverthethreeyears

priortothecurrentmonth.Ifthreeyearsofweeklyreturndataarenotavailable,asmallerhistoryisusedwiththeminimumperiodrequiredbeingoneyear.ThisisthefactordefinitionproposedbyBlitzandvanVliet(2007).

• Low betaisdefinedastheCAPMbetaestimatedfromweeklyexcesstotalstockreturnsandexcessALSIreturns,measuredoverthethreeyearspriortothecurrentmonth.Ifthreeyearsofweeklyreturndataarenotavailable,asmallersampleisusedwiththeminimumperiodrequiredbeingoneyear.ThisisthefactordefinitionproposedbyBlitzandvanVliet(2007).

The stock universe available for factor construction at any given month is taken as the historical ALSI constituent basket forthatmonth.Inordertoisolatethetruepremiaoftheunderlyingfactors,FamaandFrench(1993)employabasictwo-wayportfoliosortingmethodology.Wecreatelong/shortfactorreturnsinaconsistentmanner:

1. Firstrankallstocksaccordingtotheirsizescore.Usingthe50thpercentileasabreakpoint,createtwosubsetsofstocks,namelyBig(allthestocksabovethebreakpoint)andSmall(stocksbelowthebreakpoint).

2. Independently rank all the stocks according to their value score. Taking the 30th and 70th percentiles as break points,constructthreevaluesubsets;namely,High value above the 70thpercentile,Neutralvaluebetweenthe30th and 70th,andLowvalue(i.e.growth)stocksbelowthe30th percentile.

3. Repeat thepreviousstep toconstructstocksubsetson thebasisofmomentum,profitability, investment, lowvolatilityandlowbetascoresrespectively.Notethatinthecaseofinvestment,lowvolatilityandlowbeta,theportfoliobelowthe30thpercentileistheonewhichisexpectedtorenderthepositivereturn.

4. Usethetwo-waysize/factorsortinordertocreateequally-weightedfactorportfolios,asdepictedinTable1.Forexample,thesize/valuesortingproceduregivesonesixportfolios:namely,SmallValue,SmallNeutralandSmallGrowth,andBigValue,BigNeutralandBigGrowth.

5. Construct long/short factor returns by averaging the returns on the Small High and Big High factor portfolios and subtractingtheaverageofthereturnsontheSmallLowandBigLowfactorportfolios.Repeatthisforeachsetofsortingtablestocreatethesixsize-agnosticfactorportfolios.

6. Construct long/short size factor returns for eachof the independent two-waysorting tablesbyaveraging thereturnson theSmallHigh,SmallNeutral andSmall Low factor portfoliosand subtracting theaverageof thereturnsontheBigHigh,BigNeutralandBigLowfactorportfolios.Thefinallong/shortsizefactorreturnisthencalculatedastheaverageofthevarioussizefactorreturnsacrossallfactorsincludedinthemodel.

TABLE 1: DEPICTION OF THE TWO-WAY FACTOR PORTFOLIO SORTS FOR THE CARHART FOUR-FACTOR MODEL.

Book-to-Market Value Portfolios 12-1m Momentum Portfolios

Growth Neutral Value Losers Neutral Winners

Small SG SN SV Small SL SN SW

Big BG BN BV Big BL BN BW

FollowingStep5above,thelong/shortvaluefactorreturniscalculatedas

1 1 Rhml = –– (R(SV) + R(BV)) – –– (R(SG) + R(BG)) 2 2 = R+hml – R

–hml (9)

1 1 = –– (R(SV) + R(SG)) – –– (R(BV) + R(BG)) 2 2 1 = –– (Rshml – R

bhml). (10) 2

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Equations9and10showhowtodecomposethelong/shortfactorreturnintoseparatelongandshortcomponentsaswellasintoseparatesizecomponents.Thesedecompositionsalsorepresentperhapsthetwomostcommonconstraintsfacedbyinvestorsintheriskfactorspace:namely,long-onlyandcapacityconstraints.WewillrevisitthisinSection3.3.

FollowingStep6,thesizefactorreturnfromthesize/valueportfoliosiscalculatedas

1 1 Rval = –– (R(SV) + R(SN) + R(SG)) – –– (R(BV) + R(BN) + R(BG)). (11) 3 3

Asimilarcalculationisdoneforthesize/momentumportfoliosandthefinalsizefactorreturnisthusgivenas

1 Rsmb = –– (R

val + Rmom ). (12) 2

OnedeparturefromthemethodologyofFamaandFrenchisthecontinueduseoftwo-wayratherthanm-waysortsforthelargerfactormodels.WedothisbecauseofthediscrepancybetweenthesizeoftheSAstockuniverse,whichrangesfrom150–171stocksoverthe14yearperiod,andthesizeoftheUSstockuniverse,whichnumbersinthethousands.Evenifoneweretouseonlytwoportfoliosperfactor,afour-waysortwouldcausetheaverageportfoliosizetodroptoonlytenstocks.Thisisclearlynotlargeenoughtoensureawell-diversifiedportfoliofreefromstock-specificrisk.

Rebalancingofthevalue,profitabilityandinvestmentfactorsoccursannuallyateachDecember-end.Thelowvolatilityandlowbetafactorsarerebalancedquarterly,beginningfromDecember-end,andthemomentumfactorisrebalancedmonthly.AsnotedinStep4,thestandardmethodologyistocreateequally-weightedfactorportfolios,althoughonecanalsoconsidervalue-weightedportfolios.Ifanyconstituentsofthefactorportfoliosdelistduringtheholdingperiod,anappropriate portfolio rebalance is done as at the close on the day prior to delisting as per standard indexing rules.

Insummary,theprocessoutlinedaboveensuresthatwecreaterealisticandtradabledailyriskfactorreturnsoverthecompletesampleperiod.Finally,weusetheALSItotalreturnlessthethree-monthNCDrateasaproxyfortheexcessmarket factor.

3.3. Factor Analysis

Figure 1 displays the cumulative log-performance of the eight South African long/short risk factors over the full 14-yearsampleperiod.Equal-weightedfactorsarerepresentedbythesolidlinesandcap-weightedfactorsbythedashedlines.Themost strikingobservation is that the scale of themomentum factor is significantly larger thananyof theotherfactors,includingthe(excess)marketfactor.Apartfromtheinternationalevidencethatsuggeststhatmomentumgenerallydoescommandthelargestriskpremium(Antonacci,2013),thestrongperformanceislikelyalsoduetotheunderlyingequitymarket’sstrongperformanceoverthesampleperiod,coupledwiththeextremelevelofconcentration.Onaverage,thetenlargeststocksintheALSIhavehistoricallyaccountedfornearly60%ofthetotalindexvalue(Flintetal.,2013).Therefore,anystrongunderlyingequitymarkettrend–positiveornegative–isalmostcertainlydrivenbythishandfuloflargecounters.Suchafeatureisexactlywhatthemomentumfactorattemptstocaptureandfurthermore,theequal-weightingschemepotentiallyprovidesincreaseddiversificationtostock-specificreversals.Lastly,onemustalso remember that the momentum portfolio rebalances monthly and thus a large proportion of this return could be lost in practice due to high turnover costs.

smb

smb smb


FIGURE 1: CUMULATIVE LOG-PERFORMANCE OF EQUAL-WEIGHT (SOLID) AND CAP-WEIGHT (DASHED) SOUTH AFRICAN RISK FACTORS, DEC 2002 TO AUG 2016

Market

Dec-02 Dec-06 Dec-10 Dec-14

Size Value Profitability

Dec-02 Dec-06 Dec-10 Dec-14 Dec-02 Dec-06 Dec-10 Dec-14 Dec-02 Dec-06 Dec-10 Dec-14

Investment


Momentum Low Volatility Low beta


Figure1alsoshowsthattheweightingschemeusedintheFama-Frenchsortingprocedurecanimpacttheperformanceoftheriskfactor,althoughthemagnitudeoftheeffectisveryfactor-dependent.Thediscrepancyinequal-andcap-weightedfactorsismostobviousforthemomentumfactorbutalsoaffectsvalueandprofitabilityfactorstosomeextent.Interestingly,wenotealmostnodifferenceineitherthetrendorreturnmagnitudeforthelowvolatilityandlowbetafactors.

TABLE 2: EQUAL-WEIGHT LONG/SHORT FACTOR SUMMARY STATISTICS, DEC 2002 TO AUG 2016

Market Size Value Profitability Investment MomentumLow

VolatilityLow Beta

Exp. Return (CAGR) 8.66% 0.11% 1.98% 5.70% 2.68% 20.88% 4.25% 3.38%

Volatility 15.95% 7.21% 10.45% 9.21% 10.18% 15.18% 15.90% 18.04%

Kurtosis 0.55 0.36 1.66 3.14 5.66 3.75 1.67 0.22

Skewness -0.12 -0.14 0.23 -0.93 1.01 -1.03 -0.22 -0.13

Return Range 27.31% 12.24% 20.54% 19.43% 24.35% 30.44% 33.23% 30.65%

Min Return -14.25% -7.63% -11.08% -12.90% -7.68% -18.62% -17.11% -13.71%

Max Return 13.05% 4.61% 9.46% 6.53% 16.68% 11.82% 16.13% 16.94%

Sharpe Ratio 0.54 -1.01 -0.52 -0.18 -0.46 0.89 -0.20 -0.22

Max Drawdown -47.4% -32.8% -47.6% -26.6% -40.6% -34.2% -45.4% -56.2%

Overthecompleteperiod,thesizepremiumhasremainedconsistentlysmallandhasinfactbeenslightlynegativesincethe2008financialcrisis;inlinewiththefindingsofStrugnelletal.(2011).AsTable2shows,theexpectedreturnonthesizefactorisonly0.1%,astarkcontrasttothe20.9%returnonthemomentumfactor.Thevaluefactor,arguablythemostwell-knownandacceptedriskpremium,hasalsostruggledsincethefinancialcrisis,thusgivingonlya2%annualreturnover the full period. This perhaps explains the poor performance of many South African value funds over the last decade.

Wealsonotethattheinvestmentfactorhasnotbeenparticularlywellrewardedoverthelastfiveyears,showingasimilarcontractionasinthevaluepremium.Thisisperhapssomewhatunderstandableasthelevelofannualassetgrowthandthebookvalueofacompanyaresurelysomewhatconnectedonafundamentallevel.Thishypothesisisalsosupportedbythefactthatinvestmentistheonlyfactortoshowapositivecorrelation0.31tovalue,evenifsmallinabsoluteterms.

11

Incontrasttothesize,valueandinvestmentfactors,profitabilityhasshownstrongperformanceoverthelastdecade,particularlyover thefinancialcrisisandrecoveryperiod.Thismakes intuitivesensethoughas this factoressentiallyproxiesthequalityofacompany’searningstreamsandonewouldexpecthighqualityearningsstreamstohavebeenthe least affected by the crisis and also to have participated strongly in the subsequent recovery rally. It also supports therecentindustrytrendininternationalmarketsoffocussingonquality-sortedversionsoftheotherfactors(Gray(2014),VogelandGray(2015)).

Tables2and3alsohighlightsomeinterestingpointsaboutthelowvolatilityandlowbetafactors.Incontrasttowhatonemightexpect,Table2showsthatthesetwofactorshavethesecondhighestandhighestreturnvolatilityrespectively.However, thisphenomenonactually confirms the rationalemotivating these factors; namely that there isan inverserelationshipbetweenvolatilityorbetaandtheactualriskpremiumawardedtothestock.Whatevertheeconomicreasoningthough,wenotethatbothfactorshaveperformedstronglysincethefinancialcrisis.Thestrongpositivecorrelationof0.78betweenthereturnsofthesetwofactorssuggeststhattheyarecapturingoverlappingpartsofthesameunderlyingfactor,whichonewouldexpect.However,wedonoteahigherkurtosis,lowervolatilityandlowermaximumdrawdownattachedtothelowvolatilityfactor.Onefinalpointofinterestwiththesefactorsistheirstrongpositivecorrelationsof0.62and0.55respectivelytotheprofitabilityfactor.Weleavethisobservationforfutureresearch.

TABLE 3: EQUAL-WEIGHT FACTOR CORRELATION MATRIX AND CORRELATIONS BETWEEN EQUAL-WEIGHT AND CAP-WEIGHT FACTOR RETURNS, DEC 2002 TO AUG 2016

Equal-Weight Market Size Value Profitability Investment MomentumLow

Volatility Low Beta

Mkt 1.00

Size -0.37 1.00

Value -0.20 0.09 1.00

Profitability -0.14 0.08 -0.26 1.00

Investment 0.01 -0.04 0.31 -0.51 1.00

Momentum 0.06 0.01 -0.41 0.40 -0.35 1.00

Low Vol -0.49 0.20 -0.03 0.62 -0.46 0.30 1.00

Low Beta -0.48 0.20 0.02 0.55 -0.33 0.33 0.78 1.00

EW vs CW Market Size Value Profitability Investment MomentumLow

Volatility Low Beta

0.94 0.73 0.84 0.68 0.70 0.73 0.95 0.92

Aswithallassetclasses,riskfactorsalsodisplayvaryingdegreesofcyclicalbehaviour.AlthoughthisisgraphicallyevidentinFigure1,weprovidemoretangibleevidenceofthisfeatureinTable4,whichpresentsfactorstatisticsforthreecontiguoussub-periods of 4 years. In particular,we consider the bullmarket fromDecember 2002 to June2007, the crisis andrecoveryrallyfromJune2007toDecember2011,andthepositivebutslowingmarketfromDecember2011toAugust2016.

Thereareclearandmeaningfuldifferencesinnearlyallfactorsandstatisticsacrossthesub-periods.Inparticular,noticethatthelargestdrawdownformostofthefactorshasactuallyoccurredinthemostrecentsub-periodandspecificallyoverthelasttwoyears.Twoofthemainreasonsforthis–althoughcertainlynottheonlyones–arethattheproportionofSA-specificrisktoglobalriskinthelocalmarkethasbeenconsistentlyincreasinglysince2012(Flintetal.,2015),andthatsomeofthelargestALSIconstituentshaveexperiencesignificantcompany-specificeventsintherecentpast.Thisobservationhighlightsthegeneralneedtoensurethatoneiseffectivelydiversifiedagainstthoseriskswhichdonotcarryanydiscernibleriskpremiaaswellasbeingdiversifiedacrosstheriskfactorsthatdocarryapositivepremiumoverthelong-term.Itisthislastreasonthathasdriventheriseofmulti-factorportfolios,discussedfurtherinSection5.


TABLE 4: LONG/SHORT FACTOR PERFORMANCE ACROSS THREE SUB-PERIODS: DEC 2002 – JUN 2007, JUN 2007 – DEC 2011, DEC 2011 – AUG 2016.

Statistic Period Market Size Value Profitability Investment MomentumLow

VolatilityLow Beta

Exp. Return (CAGR)

1 21.64% 7.59% 11.40% 1.88% 6.86% 38.48% -3.50% -0.91%

2 -2.52% -4.47% 0.78% 11.57% 3.29% 7.61% 7.45% 2.27%

3 8.26% -2.29% -5.24% 3.93% -1.76% 18.64% 9.06% 8.81%

Volatility

1 16.13% 7.89% 9.50% 9.75% 7.70% 15.52% 13.49% 17.44%

2 19.61% 6.68% 8.98% 7.18% 8.56% 12.30% 15.69% 16.64%

3 10.67% 6.67% 12.16% 10.31% 13.29% 16.63% 18.13% 20.00%

Share Ratio

1 1.34 0.02 0.42 -0.57 -0.07 2.00 -0.81 -0.48

2 -0.13 -1.78 -0.74 0.58 -0.48 0.02 0.00 -0.31

3 0.77 -1.45 -1.04 -0.34 -0.69 0.68 0.09 0.07

Max. Drawdown

1 -21.3% -8.0% -8.0% -16.4% -9.8% -19.7% -26.8% -39.3%

2 -47.4% -15.2% -15.2% -15.5% -9.5% -30.8% -45.4% -56.2%

3 -15.4% -32.8% -47.6% -26.6% -40.6% -34.2% -35.5% -38.1%

3.4. Factor RobustnessAswithanyempiricalfinancialstudy,oneneedstoaddressthequestionofrobustness.Inparticular,oneshouldalwaysbecognisantofthefactthattheconstructedfactorportfolioswillalwaysonlybenoisyproxiesofthetrueunderlyingriskfactors.Tothisend,weconsidertherobustnessofsuchfactorstothechoicesmadeduringtheconstructionprocess.WehavealreadyhighlightedonesuchchoiceinFigure1byshowingtheeffectthatweightingschemecanhave.Inthissectionwescrutiniseanumberofotherimportantconstructionchoices.

3.4.1. Long-only versus Long/Short FactorsOne of the most pertinent constraints for many investors is the inability to short sell assets either at all or to the extent that theywouldwish.Thisraisestheissueofwhetherlong-onlyfactorproxiesareabletoprovidesimilarriskfactorexposureincomparison to their long/short counterparts. A fundamental challenge in factor investing is the investability of the underlying factorportfolios.Itisallwellandgoodtocreatetheoreticallyappealinglong/shortfactorportfoliosandusetheseforriskattribution – see Section 4.1 – but this may all for nought if one cannot effectively allocate capital to such portfolios. Hence theproposaloflong-onlyfactorportfolios.Althoughsuchportfolioswillcontainresidualmarketriskbyconstruction,webelievethattheirinterpretationasriskfactorsstillremainsvalid.Furthermore,giventhatallthefactorswillonaveragehavesimilarlevelsofmarketriskexposure,thisresidualriskshouldlargelycanceloutinanyriskattributionexercises.

13

FIGURE 2: CUMULATIVE LOG-PERFORMANCE OF LONG-ONLY (SOLID) AND LONG/SHORT (DASHED) SOUTH AFRICAN RISK FACTORS, DEC 2002 TO AUG 2016

Market


Size Value Profitability


Investment




Figure2comparestheperformanceofthelong-onlycomponentofeachfactor(solidlines)againstthecompletelong/shortportfolios(dashedlines)andTable5givesthecorrelationmatrixofthelong-onlyfactorsaswellasthecorrelationsbetweenthelong-onlyandlong/shortversionsofeachfactor.Inthecaseofthemarketfactor,wearecomparingtheabsolutemarket returnwith itsexcess-to-cashcounterpart.Thecontrast inperformancebetween the long-onlyandlong/shortportfoliosisstark,barringforthemomentumfactor.It isalsoclearthatthelong-onlyriskfactors–barringsize–comfortablyoutperformtheabsolutemarketreturn.Thesuppositionofcontaminatinglatentmarketexposureisprovenbythestrongpositivecorrelationswiththemarketfactor.Furthermore,thecorrelationsbetweeneachriskfactorarenowalsoveryhighasaresult.Consideringthecorrelationsbetweenlong-onlyandlong/shortfactorversions,itisinterestingtonotethatdespitethesimilarityintrendbetweenthetwomomentumfactors,thecorrelationbetweenthesetwofactorsisonlymildlypositiveat0.31.Thisservesasapoignantreminderaboutthepitfallsofconflatingpricetrendand correlations. What Figure 2 does suggest though is that the short component of the momentum factor provides only limitedbenefitacrosstheperiod.

TABLE 5: LONG-ONLY FACTOR CORRELATION MATRIX AND CORRELATIONS BETWEEN LONG-ONLY AND LONG/SHORT FACTOR RETURNS, DEC 2002 TO AUG 2016

Long-Only Market Size Value Profitability Investment MomentumLow

Volatility Low Beta

Market 1.00

Size 0.71 1.00

Value 0.66 0.90 1.00

Profitability 0.76 0.91 0.84 1.00

Investment 0.75 0.88 0.90 0.81 1.00

Momentum 0.80 0.87 0.76 0.91 0.80 1.00

Low Volatility 0.62 0.86 0.80 0.89 0.69 0.81 1.00

Low Beta 0.55 0.81 0.74 0.83 0.66 0.78 0.85 1.00

L-O vs L/S Market Size Value Profitability Investment MomentumLow

Volatility Low Beta

0.18 0.41 0.17 0.42 0.31 0.07 0.16


3.4.2.FactorSizeEffectsAnotherconstraintfacedbymanyinvestorsisthatofcapacity.Evenifonehastheabilitytoshort,itmaybethatthemajority of a factor’s return stems from theSmall sub-portfolios of the factor. Such a size biaswould imply limitedinvestmentcapacityowing to thesmallmarketcapitalisationof theunderlyingstocksandpotential illiquidity issues.Severalauthorshavesuggestedthatsuchfactorsizebiasesexistinmanymarkets(Homescu,2015).IfpresentinthehighlyconcentratedSAequitymarket,thisbiaswouldhaveseriousramificationsontheprospectoflarge-scaleSAfactorinvesting.Figure3breaksdowneachfactorreturnintoitsBig(solidline)andSmall(dashedline)sub-portfoliosasperEquation 10. Note that these sub-portfolios are still long/short combinations and hence are of similar magnitudes to the completefactorreturnsshowninFigure1.

FIGURE 3: CUMULATIVE LOG-PERFORMANCE OF BIG (SOLID) AND SMALL (DASHED) SOUTH AFRICAN RISK FACTORS, DEC 2002 TO AUG 2016

Value




Profitability


Investment


Four of the six factors given in Figure 3 don’t display any significant size bias. Of the remaining two, momentuminterestinglyshowsaconsiderablebiastowardslargestocks,whileinvestmentdisplaysabiastowardssmallstocks.The momentum large-cap bias can be understood by once more considering the concentration argument laid out in Section 3.3.

3.4.3. Rebalancing Frequency & DateValue,profitabilityandinvestmentportfoliosarerebalancedannuallyatthebeginningofeachyear.Lowvolatilityandlowbetaportfoliosarerebalancedquarterlywiththefirstrebalanceoccurringatthebeginningoftheyear,andmomentumportfolios are rebalanced at the end of each month. The choice of rebalance frequency for each factor is driven by the timeframeoverwhichthefactorsignaldecays.Thereisalsothemorepracticalissuethatanybenefitgainedfrommorefrequentrebalancingmaybeoffsetbytheadditionaltransactioncosts.Forthemajorityofourfactors,thetimeframeoftheriskpremiaiswellestablished.However,giventherelativelynew‘discovery’ofthelowvolatilityandlowbetafactors,theeffectofrebalancefrequencyislesswelldocumented.Tothisend,wecomparedthereturnsfromthelowvolatilityandlowbetafactorswhenrebalancingmonthly,quarterly,biannuallyandannuallyandfoundonlyminordifferences.

Anotherrebalancingissuetoconsiderforthosefactorswithlongerholdingperiodsisthechoiceofmonthinwhichtoenacttherebalance.Asabove,wetesthowmuchofanimpactmovingrebalancedateshasbyconsideringthereturnsfromtwelvevaluefactorseachrebalancedindifferentmonthsoftheyearandagainfindnosignificantreturndifferences.Althoughitmayseemoddtoincludesuchanon-resultinourresearch,itisanincrediblyimportantonefromapracticalimplementationperspective.Furthermore, itshowcases the fact that the factorconstructionmethodologyoutlined inSection 3.2 is generally robust to rebalancing choices.

15

3.4.4. Portfolio ExtremityThestandardFama-Frenchtwo-waysortingprocedureuses the 50thpercentileofthesizescoreandthe30th and 70th percentilesof the factor scoresas the relevantsortingbreakpoints.Anaturalquestion then iswhetherusingmoreextreme percentile break points results in larger factor risk premia. The trade-off here is that one essentially creates ‘purer’factorportfoliosbutatthecostofincreasingtheportfolio’sidiosyncraticrisk.ThisisparticularlypressingintheSouthAfricanequitymarket,whichonlycontainsaround160counters.

FIGURE 4: CUMULATIVE LOG-PERFORMANCE OF STANDARD (SOLID) AND EXTREME (DASHED) SOUTH AFRICAN RISK FACTORS, DEC 2002 TO AUG 2016

Value




Profitability


Investment


To test the robustnessof the factors to the sortingmethodology,we createextreme factor portfolios using the20th

and 80thpercentilesoftherelevantfactorscoresassortingbreakpoints.Figure4givesthecomparisonbetweenthestandard(solidline)andextreme(dashedline)factors.Somewhatsurprisingly,onlytheextremevalueandmomentumfactorsshowanysignificantdifferencetotheirstandardcounterparts.Inbothcases,thedivergenceoftheextremefactorperformanceismostevidentinthelasttenyears,withthestartingpointseemingtobelinkedtothefinancialcrisis.Weleave further investigation of this phenomenon for future research.

3.4.5.AlternativeFactorDefinitionsAlthough varying the choice of sorting percentile can in some respects be considered as using an alternative factor definition,themoreobviousalternativeistouseadifferentfundamentalstockcharacteristicasaproxyfortheunderlyingfactorscore.Asanexample,wehavealreadydiscussed themultipledefinitionsof thequality factor inSection2.2.Inasimilarvein,anumberofauthorshaveconsideredalternativemeasures forvalueand for lowvolatility.Popularalternativevaluescorecandidatesincludeearnings-to-price,cashflow-to-priceandacompositescoredbasedonthesetwometricsaswellastheoriginalbook-to-marketratio(Amencetal.,2014).Inthelowvolatilityliterature,thealternativesarenotdifferentriskmeasuresbutratherdifferentcalculationmethodsforvolatility;themainvariablesbeingthelengthofthehistoricalestimationwindowandthefrequencyofreturndata.4BlitzandvanVliet(2007)suggestusingthreeyearsofweeklydata,Bakeretal.(2014)suggestsusingeither60monthlyor60weeklyreturnobservations,localresearchconsidersthreeyearsofmonthlydata,whileFrazziniandPedersen(2014)suggestoneyearofdailyreturndata.

4 Similar calculation method alternatives apply to the beta factor score.


FIGURE 5: CUMULATIVE LOG-PERFORMANCE OF VALUE FACTOR VARIANTS (LEFT) AND LOW VOLATILITY FACTOR VARIANTS (RIGHT), DEC 2002 TO AUG 2016

Value Variants Low Volatility Variants

Dec

-02

Jun-

03D

ec-0

3Ju

n-04

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05D

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5Ju

n-06

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n-08

Dec

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n-10

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n-12

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ec-1

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n-14

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Earnings-to-PriceBook-to-Market Cash Flow-to-Price Composite

Dec

-02

Jun-

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n-04

Dec

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Jun-

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Blitz-van Vliet Baker 1Baker 2 LocalFrazzini-Pedersen

Figure5givesthecumulativelog-performanceoflong/shortfactorsbasedonthesealternativevalueandlowvolatilityscores.Thevariantreturnrangeforbothfactorsisfairlysubstantialandparticularlysoforthevaluefactor.Furthermore,thebehaviourofthevariantvaluefactorsdifferssignificantlythroughouttheperiod,whichsuggeststhattheselectedstock characteristics capture different aspects of the true value risk factor. The relative outperformance of the composite valuescoresupportsthissuggestionandalsohighlightstheimportanceofreducingsignalnoise;inthiscaseachievedbyaveragingoutthecharacteristic-specificnoise.

For the lowvolatility factor,performanceof the factorsallshowthesamepattern, indicativeof the fact thatonly thecalculationmethodischanging,ratherthanthemeasureitself.Interestingly,bothofthetopperformingvariantsarethosethatusethesmallestestimationwindow–1yearand60weeksrespectively–aswellashigherfrequencydata–dailyandweeklyrespectively.

4. FACTOR-BASED RISK MANAGEMENTAtitscore,portfoliomanagementisaboutmakingdecisions:whentobuyorsellanygivenassetandinwhatquantity.Thesedecisionsaremadeinordertoaddvaluetoapassivebenchmark,beitanominatedindexoracash-basedrate.5 Inthissetting,‘addingvalue’isusuallydefinedintwoways.Thefirstisbyachievingapositivereturn,oralpha,overandabovethenominatedbenchmarkatanacceptablelevelofrisk.Thesecondisbyachievingaspecifiedtargetreturnatalowerlevelofriskthanthatofcomparablepassivemarketproducts.

Inbothcases,thestrengthofanyportfoliodecisionshouldbemeasuredbyhowmuchvalueitgeneratesforthefund,conditionalonthemarketandfundconstraintsfacedbythemanagerovertheperformanceperiod.InpriorPeregrineSecuritiesresearch,weshowedhowonecouldusethefundamentallawofactivemanagement(FLOAM)frameworkofClarkeetal.(2002)inordertodecomposeafund’srelativereturnandriskintocontributionsfromeachoftheunderlyingfundconstituents(Flintetal.,2015).

Webuildonthisworkherebutconsiderinsteadtheideaofriskattribution rather than risk decomposition.Inparticular,weconsiderhowtoattributeafund’srisk–absoluteorrelative–toagivensetofexternalriskfactors.Suchanattributionletsoneidentifywhatkindsoffactorriskafundisexposedtoandfurthermorecalculatehowlargethesefactorbetsare.Knowingthisallowsonetomakeinformedandefficientinvestmentdecisions.

4.1. FactorRiskAttributionandtheFactorEfficiencyRatioGivenaseriesoffundreturns–absoluteorrelative–wecanuseoneoftheLFM’sinSection2.2toattributerisktotheunderlyingriskfactorsconstructedinSection3.2.Althoughmoredifficultthanattributingrisktothefund’sconstituents,Meucci(2007,2016)describeshowonecanstillattributefundrisktoasetofexternalriskfactorsinanadditivefashion.Furthermore,ifonedoeshavesightofthefund’sholdings,itispossibletoattributerisksimilarlyforeachoftheunderlyingconstituentssothatthefund’sfactorriskcontributionscanbewrittenasalinearcombinationoftheconstituents’factorriskcontributions(seealsoRoncalliandWeisang,2012).Thisisperhapsthemostimportantfactorapplicationintheriskmanagementspace.Considerthepedagogicalexamplebelow.

5 Allportfoliomanagementshouldbeconsideredbenchmark-relative,eveniftheselectedbenchmarkisaconstantvalueofzero.

17

TABLE 6: SIMULATED FUND RISK FACTOR EXPOSURES

Fund1 Fund2 Fund3 Fund4 Benchmark

Market 0.5 0.1 0.1 0.2 0.25

Size 0.2 0.5 0.1 0.2 0.25

Value 0.2 0.2 0.5 0.1 0.25

Momentum 0.1 0.2 0.2 0.5 0.25

We select the Carhart four-factor risk model and make use of long-only risk factors. Let us assume that there are four funds that are currently under investigation. We simulate monthly returns for these funds using the factor exposures giveninTable6.Asmallrandomalphaterm(centredat0.25%)andalargerrandomnoiseterm(centredatzero)areaddedtoeachfund’smonthlyreturn.

Table 7 gives a comprehensive factor risk attribution for both the absolute and relative risk of each fund based on the Carhartfour-factormodel.Byconstruction,theestimatedbetasareverysimilartotheinputfundexposuresandtheR2 of theriskmodelisveryhigh.Table7alsoshowstheriskcontributionsofeachfactoraswellasthecatch-allresidualterm.Thesevaluesarealsocloselyrelatedtotheestimatedbetalevelsowingtothehighcorrelationbetweentheriskfactorsaswellastheirsimilarvolatilitylevels.Finally,contributionstotrackingerrorarealsocalculatedacrossthefundsforeachriskfactor.Becauseofthegoodfitoftheriskmodel,mostofthetrackingerrorstemsfromthefund-specificnoiseterm.

TABLE 7: CARHART RISK FACTOR ATTRIBUTION

Betas Fund1 Fund2 Fund3 Fund4 Benchmark

Alpha 0.38% 0.10% 0.35% 0.18% 0.00%

Market 0.52 0.05 0.14 0.23 0.23

Size 0.29 0.48 0.11 0.24 0.26

Value 0.15 0.24 0.51 0.06 0.24

Momentum 0.05 0.22 0.15 0.49 0.25

R2 94.2% 95.5% 94.6% 95.4% 95.9%

Risk (Volatility) 14.27% 13.88% 13.01% 14.68% 13.86%

Tracking Error 5.37% 4.71% 4.89% 4.48% n.a.

Risk Contributions

Market 52.9% 4.0% 13.8% 21.3% 22.8%

Size 23.8% 44.9% 10.2% 20.2% 24.0%

Value 12.9% 24.3% 55.5% 5.4% 23.4%

Momentum 4.6% 22.3% 15.1% 48.4% 25.7%

Residual 5.8% 4.5% 5.4% 4.6% 4.1%

Tracking Error Contributions

Market 30.9% 26.9% 14.3% -0.4% n.a.

Size -0.8% 9.5% 12.7% -0.7% n.a.

Value 3.9% 0.1% -1.6% 4.7% n.a.

Momentum 4.6% 0.8% 15.8% 29.5% n.a.

Residual 61.3% 62.6% 58.8% 66.8% n.a.


Inthecontextoffactorinvesting,whereinvestorsareactivelyseekingexposuretotheunderlyingriskfactors,riskandtracking error contributions become incredibly important as they provide a means of quantifying and thus evaluating suchexposure.Tothisend,HunstadandDekhayser(2015)introducetheFactorEfficiencyRatio(FER)asameansofgaugingtheamountofintendedversusunintendedfactorriskexposureinagivenfund(orasset).LettingƑd represent the set of kdesiredfactors,wecanwrite

∑ki=1RCi FER ( Ƒd) = ––––––––– , (13) 1 – ∑ki=1RCi

whereRCi is the generic risk contribution stemming from the ith desired risk factor. Hunstad and Dekhayser originally

considerthecontributionstoactiverisk(i.e.trackingerror)butonecanjustaseasilyuseanyconvexriskmeasuretocalculate risk contributions.6ThisFERisinterpretedasfollows:foreveryX%ofriskstemmingfromthedesiredfactorset,thefundtakesonanadditional1%ofriskfromundesiredfactors.Therefore,thehighertheFER,themoreefficientthe fund is at gaining desired factor exposure.

Consider the four fund example and further assume that all of these funds are marketed as composite value/momentum indices.Using this asour desired factor set,we calculateFER’sof 0.21, 0.87, 2.40and1.17 for eachof the fundsrespectively.Basedonthesescores,itisclearthatFund3providesonewiththemostefficientexposuretothedesiredvalue and momentum factors.

4.2. Return-Based Style Analysis & Fund ReplicationSharpe(1992)introducedtheconceptofreturns-basedstyleanalysis(RBSA)usedextensivelyinthefundmanagementliterature.Inessence,RBSAisaformofconstrainedregressionthatallowsonetodrawinferenceonfundsforwhichonly historical return data is available. Sharpe suggested using factors based on asset classes and interpreted the model outputasbeingindicativeofamanager’sstylemix.Ultimately,givenasetofhistoricalfundreturns,RBSAestimatesthestaticmixoftradablemarketindicesorfactorsthatmostcloselyreplicatesthefund’sreturns,Rpt. Letting b represent thevectoroffactorexposures,wecanformulatetheRBSAestimationproblemasfollows:

argmin∑ Rpt – ∑m j=1bj Ƒjt2 (14)

s.t. bj ≥ 0

∑ bj = 1.Inasense,theRBSAbetasrepresentthelong-onlyweightsofthereplicatingstyleportfolio.However,thisisnotstrictlytruebecausethebetasremainfixedacrosstheestimationwindowwhereasportfolioweightswouldchangeinlinewiththe performance of the underlying factors. Several improvements to the initial RBSA methodology have been suggested toaddressthis(andother)issues.TheseincludetheuseoftheKalmanfilter,correctionsforheteroscedasticityandtheinclusionofstructuralbreakdetectionmechanisms.AnotherpointwhichiscommontoallregressionbutgenerallynotconsideredinRBSAisthatofconfidenceintervalsaroundtheestimatedbetas.7Forexample,astyleweightof30%withaconfidenceintervalof+/-2%shouldbeviewedverydifferentlytoaweightof30%withaconfidenceintervalof+/-20%.

AvariationofRBSAthatisparticularlyrelevantintheindextrackingspaceistosolvefortheinitialnumberof‘shares’(ratherthanbetas)ofeachfactorthatminimisesthetrackingerror(ratherthansumofsquarederrors)oftheestimatedstyle portfolio to thegiven fund returns.Therefore, one cannot only use theRBSA framework tomeasurea givenfundmanager’sstylemixbutalso–aftersomeadjustment–tocreatetradablereplicatingportfoliosforafund.Thisalternativeusagehasbeenexploredatlengthinconnectionwithhedgefundreplication.

6 NotethatonehastotreatnegativeriskcontributionswithcautionwhencalculatingtheFERastheycanmateriallychangeitsinterpretation.Thesimplestsolutionistotakeabsolutevaluesofallriskcontributionsandreplacethe‘1’inthedenominatorwiththesumoftheabsoluteriskcontributions.

7 SeeLoboscoanddiBartolomeo(1997)foranapproximationformulaforconstructingconfidenceintervalsaroundtheconstrainedbetas.

T

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FIGURE 6: RBSA BETAS (LEFT) AND END-OF-PERIOD WEIGHTS (RIGHT) FOR THE FTSE/JSE DIVIDEND PLUS INDEX AND THE LONG-ONLY FAMA-FRENCH FIVE-FACTOR MODEL, DEC 2005 TO AUG 2016

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AsinSection4.1,weillustrateRBSAwithanillustrativeexample.WeattempttouncoverthestylemixoftheFTSE/JSEDividendPlusIndexbymakinguseofthelong-onlyFama-Frenchfive-factormodel.Figure6displaystheRBSAfactorexposures(leftpanel)andtheadjusted-RBSAreplicatingweights(rightpanel)fromDecember2005onwards.Wefitbothmodelsusingrolling36-monthwindowsandrecordthestaticbetasandend-of-periodweightsrespectively.

Although theexposuresaresimilar to the replicatingweights,onecanstilleasilysee thediscrepancies inFigure6.The R2ofbothmodelsisconsistentlyhigh,meaningthatthemajorityofvariationintheindexiswell-capturedbythefive-factormodel.Thestylemixoftheindexvariesconsiderablyovertheperiod,whichsuggeststhatthedividendyieldmeasure is actually a composite signal for a number of underlying risk factors. The largest exposure over the period has beentotheprofitabilityfactor–inlinewiththeyield-drivennatureoftheindex–withtheremaindermostlysplitbetweenthevalueandmarketfactors.Investmentexposureissporadicandhasbeenabsentoverthelastthreeyears.SizeisirrelevantfortheDividendPlusindex,whichistobeexpectedgiventhattheindexislimitedtolarge-andmid-capstocks.

TABLE 8: RBSA BETAS AND REPLICATING WEIGHTS FOR THE DIVIDEND PLUS INDEX AS AT 31 AUG 2016


RBSA Betas 19.0% 0.0% 50.0% 31.0% 0.0%

95%Conf.Interval 7.8%–30.3% -11.9%–11.9% 40.3%–59.7% 21.5%–40.5% -10.7%–10.7%

RBSA Weights 12.2% 0.0% 52.6% 35.3% 0.0%

Weight-Beta Spread -6.9% 0.0% 2.6% 4.3% 0.0%

Table8givestheRBSAbetasandend-of-periodweightsforthe36-monthperiodendingat31August2016.Althoughsimilarinnature,thereisstillanabsolutedifferenceof13.7%acrossthefactors.Thisdifferenceisdrivenbythevaryingperformance of the underlying factors and is directly related the level of factor dispersion over the period.

5. FACTOR-BASED PORTFOLIO MANAGEMENTIn addition to the risk management applications given above, risk factors are also used extensively in portfoliomanagement.Andwhiletheconceptoffactorinvestingisdefinitelynotnew,theriseofthesmartbetaphenomenonhasattractedsignificantattentiontothisarea.

Inthelastseveralyears,thefocushasstartedtomoveawayfromidentifyingadditionalriskfactorsandtowardsconstructingoptimalmulti-factorportfolios.Whilesomeauthorshavesaid that there isno formal framework inplace forcombiningsystematicfactorstrategies(DeFrancoetal.,2016),thefactofthematteristhatthemajorityoftheexistingoptimisationframeworks–risk/returnorrisk-only–arefullycapableofincorporatingbothfactorportfoliosandfactor-basedrisk/returnviews.Furthermore, theallocationpolicy for systematic strategiesoutlinedbyMeucci (2016)providesonewitha fullygeneralframeworkforcreatingoptimalmulti-factorportfoliosinthepresenceoftransactioncostsandfundconstraints.


Inthissectionwediscussseveralideasonhowtocreatesuchmulti-factorportfolios,rangingfromtheverysimpletothefairlycomplex.Notethatmostofthesearebasedonconceptsthatwehavealreadyintroducedandanalysedinprecedingsections.

5.1. Factor Portfolio Mixing and Integrated Factor ScoresAccordingtoFitzgibbonetal.(2016),twoofthemostcommonapproachesforcreatingmulti-factorportfoliosarethe‘portfolio mix’ and ‘integrated score’ methods. Portfolio mixing is simply the linear combination of factor portfoliosconstructedfromsingle-variablesortingprocedures.Forexample,consideravalueportfoliobasedsolelyonthetopquintileofbook-to-market stocksandamomentumportfoliobasedsolelyon the topquintileof twelvemonth returnstocks.Theseportfolioswouldthenbetakenasexistingbuildingblocksandtheonlychallengefacingtheinvestorwouldbetosetanappropriateweightforeachportfolio.Viewedinthis light,portfoliomixingcanbethoughtof inasimilarmanner to the decisions made in strategic asset allocation.

FIGURE 7: INTEGRATED SCORING EXAMPLES FOR MOMENTUM AND LOW VOLATILITY

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The integrated score approach goes one step further by mixing the underlying factor scores ex ante rather than mixing givenfactorportfoliosexpost.TheFama-Frenchtwo-waysortingmethodology–wherebystocksareselectedbasedontheir respective factor score ranks relative to a set of constant percentile break points – is perhaps the simplest example oftheintegratedscoreapproach.Ingeneral,theintegratedscoreapproachcombinesindividualfactorscoresinsomemannertocreateasingle,unifiedscore.Figure7displaysthisconceptgraphicallyandconfirmsthatthefieldof(non)linearprogrammingprovidesinvestorswithanaturalsetoftoolsforcreatingoptimalintegratedmulti-factorscores,andthus optimal multi-factor portfolios.

Lastlyandvery importantly,Hoffstein (2016)pointsout thatoneneeds toconsider thespeedof factordecaywhencreatingtheseintegratedsignals.Thisisparticularlyrelevantwhencombiningthefast-decayingmomentumsignalwithslowersignalslikevalueorprofitability,forexample.

5.2. Constrained Risk Factor OptimisationAmore technically rigorousapproach than thosegivenabove is to view theconstructionof anefficientmulti-factorportfolioasaconstrainedoptimisationproblem.Althoughmorecomplex,thisapproachallowsaninvestortoconstructamulti-factorportfoliothatisasconsistentwiththeirreturnobjectivesandriskpreferencesastheirconstraintsetwillpermit.Thereareanumberofoptimisationframeworksavailabletoinvestors, includingclassicalmean-varianceandrisk-based investing (Richard andRoncalli, 2015), among others.8 Belowwe sketch out two candidate optimisationapproaches that could be used to create constrained optimal multi-factor portfolios.

ThefirstapproachmakesuseoftheriskattributionframeworkintroducedinSection4.1.Assumingthatoneisgivenariskfactormodel,theproblemthenbecomesfindingtheunderlyingstockweightsthatprovidetherequisiteexposuretothetargetedriskfactors,whilstminimisingundesiredfactorexposures.Ifexposureisdefinedintermsofbeta,thenoneneedstosolvefortheportfolioofassetsthatminimisesthetotaldistancebetweenestimatedandtargetedbetas,wherethetargetlevelsfortheundesiredfactorsaresettozero.Alternatively,ifexposureisdefinedintermsofriskcontributions,thentheretwooptionsavailable.Thefirstoptionissimilartothebetaoptimisationbutwhereoneinsteadspecifiestargetrisk contribution levels. The second option is to solve for the portfolio of assets that maximises the FER for the set of

8 PleaseseeHomescu(2014)foracomprehensivereviewoftheavailableportfolioconstructionframeworks.

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desiredfactors.FERoptimisationisarguablymoreintuitiveandwill likelyprovidemorerobustresultsduetothefactthatitsimultaneouslyaccountsforthedesiredandundesiredfactorexposuresinasingle,monotonicmetric.Ofthetwoapproaches,wethereforefavourFERmaximisation.

The second optimisation approach makes use of mixed integer programming (MIP). A mixed integer program is one in whichsomevariablesarecontinuousandsomeareintegers.Suchasettingisidealforproblemsinwhichonehastofirstselectasubsetofassetsfromtheavailableuniverse–theintegervariables–andsubsequentlysearchforthesetofweights–thecontinuousvariables–thatminimisesanobjectivefunctionunderasetofconstraints.Ingeneral,mixedintegerprogramscanbequitehardtosolveunlessonecanformulatetheprobleminaveryparticularway.Thankfully,weareabletosetupbothlinear(MILP)andquadratic(MIQP)mixedintegerprogramsformostportfolioconstructionproblemswhichcanbesolvedfairlyeasily–albeitslowly–withfreelyavailableoptimisationtoolboxesandheuristicsolvers.InpriorPeregrineSecuritiesresearch,wehavesuccessfullyusedtheMIQP approach to replicate the Top40 indexwithonlyasmallnumberofstocksandalsoconstructoptimalhedgingbasketsforactivefunds(Flintetal.,2015).

Oneofthemainissueswithmulti-factorinvestingissmoothlytransitioningbetweenriskandreturnpreferencesinthefactorspacetoriskandreturnpreferencesintheassetspace.Thisisnotatrivialexercise.OnewayoflinkingthefactorandassetspacesinamannerwhichdoesnotaddadditionalestimationerrorwouldbetocombinetheintegratedscoreapproachwiththeriskattributionoptimisationbymeansofanMILP.Figure8presentsanexampleof thiscombinedapproachforalowvolatilityandmomentummulti-factorportfoliousingscoringdataasatAugust2016.

FIGURE 8: CREATING A MULTI-FACTOR PORTFOLIO BY COMBINING AN INTEGRATED SCORING SCREEN WITH AN MILP OPTIMISATION OF THE PORTFOLIO’S FACTOR EFFICIENCY RATIO

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One uses the integrated score as a screening tool to find the subset of assets that display the fundamental factorcharacteristicsmost in linewith thedesiredfactorset.Takingthissubsetof factor-screenedassetsasan input,onethensolvestheMILPproblemforthemaximumFERportfoliounderthegivenconstraints,wherethechoiceofassetsincludedintheportfolioandthesubsequentweightsattachedtothechosenassetsarebothvariablesintheoptimisation.Introducingtheintegratedscorescreenandsubsequentlymaximisingtheportfolio’sFERobviatestheneedtoexplicitlyassignfactor-consistentexpectedreturnestimatestoeachasset–adifficulttask–andthusalsoreducesthepotentialfor estimation error in the optimisation.


6. CONCLUSIONRisk factors and systematic factor strategies are fast becoming an integral part of the global asset management landscape.Inthisreport,wehaveattemptedtoprovideanintroductionto,andcritiqueof,thefactorinvestingparadigmin a South African setting.

We created a range of long/short and long-only risk factors for the South African equity market according to the standard Fama-Frenchfactorconstructionmethodology:size,value,momentum,profitability,investment,lowvolatilityandlowbeta.Historicalriskandreturncharacteristicsvariedsignificantlyacrossthefactorsaswellasacrossmarketregimes.Momentumhasbeen themost rewarded factorhistorically.Lowvolatility,profitabilityand lowbetahavealsoshownpositiveriskpremia,whilethesizefactor seems to be non-existent in South Africa. We then tested factor robustness at lengthandshowedtheeffectthateachofthemajordecisionstakeninthefactorconstructionprocesscanhave.Thelargestsucheffectstemsnaturallyfromthechoiceoflong-onlyorlong/shortfactors.Interestingly,wefoundthat,barringsize,alllong-onlyfactorshandilyoutperformedthemarket.

Inadditiontoconstructingthisfactordatabase,wealsoshowcasedseveralriskfactorapplications.Intheriskmanagementspace,weconsideredriskattributiontofactorsandintroducedtheFactorEfficiencyRatioasameasureofhowefficientlya fund gainsexposuretoasetofdesiredriskfactors.Wealsoconsideredreturns-basedstyleanalysiswithlong-onlyriskfactorsandshowedhowthiscouldbeusedtoestimateamanager’sstylemixortocreateareplicatingfactorportfoliofor an index.

Intheportfoliomanagementspace,weconsideredthe issueofcreatingmulti-factorportfolios.Wediscussedsimpleapproachessuchasportfoliomixingandintegratedscoring,andmorecomplexapproachesbasedonsolvingfortargetriskcontributionsoroptimisingtheFactorEfficiencyRatioforthedesiredfactors.Finally,weintroducedthemixedintegerprogrammingframeworkasameansofcombiningtheintegratedscoringapproachwiththeriskattributionoptimisationapproachinarobustmanner,thusallowingonetosmoothlytransitionbetweenpreferencesandconstraintsinthenon-tradable factor space and the tradable asset space.

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DERIVATIVES DEALING Gavin Betty +27 11 722 7506

Roberto Pharo +27 11 722 7504

EQUITY DEALING Warren Chapman +27 11 722 7516

Paul Tighy +27 11 722 7521

RESEARCH Anthony Seymour +27 11 722 7549

Florence Chikurunhe +27 11 722 7551

Emlyn Flint +27 11 722 7556

DERIVATIVES STRUCTURING AND CONSULTING Kobus Esterhuysen +27 11 722 7572

Edru Ochse +27 11 722 7570

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