Smart Beta Multifactor Construction Methodology: Mixing versus Integrating

THE JOURNAL OF SPRING 2018 VOLUME 8 NUMBER 4 JII.IIJOURNALS.com ETFs, ETPs & Indexing Smar Bea Mulifacor Consrucion Mehodology: Mixing versus Inegraing TZEE-MAN CHOW, FEIFEI LI, AND YOSEOP SHIM

Smar Bea Mulifacor Consrucion Mehodology: Mixing versus Inegraing TZEE-MAN CHOW, FEIFEI LI, AND YOSEOP SHIM TZEE-MAN CHOW is senior vice presiden of produc research a Research Affiliaes, LLC, in Newpor Beach, CA. chow@rallc.com FEIFEI LI is direcor and head of invesmen managemen a Research Affiliaes, LLC, in Newpor Beach, CA. li@rallc.com YOSEOP SHIM is vice presiden of produc research a Research Affiliaes, LLC, in Newpor Beach, CA. shim@rallc.com Equiy facor premiums have been exensively researched and documened. Due o rapid advancemens in smar bea produc offerings in recen years, exposure o premiums beyond he radiional marke bea is now widely available a very low cos hrough ransparen rule-based indexing sraegies. Since he early 2000s, smar bea producs ha focus on a single facor, such as value, low volailiy, or qualiy, have emerged as viable and aracive invesmen opions. Each facor is expeced o deliver a premium over he long run, bu none is guaraneed o perform well a all imes. During and afer he global financial crisis, for insance, he U.S. value facor regisered a cumulaive 12.0% loss in 2007 and 2008, and he U.S. momenum facor recorded a loss of 52.6% in 2009. 1 Seeking o diversify heir acive risk exposures, many invesors have accordingly urned o sraegies ha exploi muliple facors. The rising populariy of mulifacor smar bea sraegies raises pracical quesions. As Harvey, Liu, and Zhu [2015] poined ou, academics have idenified hundreds of facors. How can invesors choose he robus and implemenable ones (see Beck e al. [2016])? Once hey have seled on a promising se of facors, wha is he opimal allocaion (see Alighanbari and Chia [2016])? Should hey mainain a saic exposure o he seleced facors, or can hey furher improve reurns by means of dynamic reallocaions (see Arno, Beck, and Kalesnik [2016])? The quesions surrounding facor selecion and allocaion have been widely debaed. Our research focuses on a pracical issue ha has received less aenion: he rade-offs marke paricipans should consider when choosing beween invesmen vehicles wih differen approaches o building mulifacor porfolios. Specifically, we sudy and compare wo disinc mehodologies. The firs one, henceforh called he inegraing approach, is a process ha searches he universe of eligible securiies for hose ha have desirable exposures o all arge facors. The second, hereafer he mixing approach, is a wo-sep process of idenifying sand-alone singlefacor porfolios and allocaing asses across hem o achieve he desired exposure o muliple facors. Inuiively, he inegraing approach has he advanage of selecing securiies from he enire opporuniy se, whereas he mixing approach has he obvious benefis of flexibiliy in facor allocaion and simpliciy in performance aribuion. The few researchers who have compared he wo mehodologies generally suppor he inegraing approach. (We discuss heir sudies in he lieraure review.) Ye we observe ha smar bea invesors increasingly favor he mixing approach. As an indicaion of adopion raes, Exhibi 1 shows he oal amoun of exchange-raded fund (ETF) SPRING 2018 THE JOURNAL OF INDEX INVESTING

E XHIBIT 1 Toal Asses in Mulifacor Smar Bea ETFs and Muual Funds (Sepember 2011 December 2016) Source: Research Affiliaes, LLC, using daa from Morningsar Direc. and muual fund asses under managemen (AUM) in mulifacor smar bea sraegies and he breakdown by porfolio consrucion process over ime. Toal asses have grown from near zero in lae 2011 o jus below $8 billion a he end of 2016. Iniially, all of he asses were invesed in inegraing sraegies. In he pas hree years, however, invesmens overwhelmingly flowed ino he mixing sraegies. 2 By he end of he period, he raio of asses in mixing sraegies o asses in inegraing sraegies was 5:3. Wha is causing he discrepancy beween heoreical resuls and acual adopions? We believe i is driven by preferences ha go beyond risk and reurn. Our research in he Unied Saes and developed markes confirms ha inegraing efficienly creaes a mulifacor porfolio ha delivers excepional backesed performance. Noneheless, his mehod generaes porfolio characerisics ha smar bea invesors who value ransparency and low implemenaion coss do no welcome. Firs, he inegraing approach ypically resuls in a concenraed porfolio wih a high urnover rae resuling from rebalancing. These aribues lead o greaer acive risk, much of which is idiosyncraic, and higher implemenaion coss. Second, should he invesor desire o change he allocaion across facors, he inegraing mehodology would necessiae rebuilding he porfolio from he boom up. Finally, he inegraing approach requires regression analysis o quanify he sources of reurn. In conras, he mixing approach faciliaes reallocaing across facors and is ailor-made for he familiar Brinson model of performance aribuion analysis. Thus, invesors may favor he mixing approach despie lower expeced reurns because is simpler mehodology and beer diversificaion make for lower rading coss, less unexplained risk, convenien adjusmens o facor weighs, and easier idenificaion of he conribuors o resuls. We surmise ha he wo porfolio consrucion mehods are aracive o differen clieneles. Acive invesors can poenially achieve higher reurns wih an inegraing approach o mulifacor invesing as par of a sophisicaed invesmen process ha includes companyspecific risk analysis and skillful rading o minimize implemenaion coss. Smar bea invesors who value inuiive, ransparen, low-cos sraegies and face sricer inernal scruiny may well prefer he mixing approach. LITERATURE REVIEW AND OUR CONTRIBUTION Coinciden wih he surging populariy of smar bea funds, which Andrew Ang has described as he vehicle o deliver facor invesing (BlackRock [2018]), a few very recen aricles specifically compare mixing SMART BETA MULTIFACTOR CONSTRUCTION METHODOLOGY: MIXING VERSUS INTEGRATING SPRING 2018

facor porfolios o consrucing long-only mulifacor sraegies by inegraing securiies ha collecively yield he desired exposures. The auhors of hese papers variously describe he wo approaches as op-down versus boom-up porfolio consrucion or combining subporfolios versus building a porfolio of securiies. Whaever erminology hey adop, however, hey suppor wha we call inegraing as he more efficien approach o achieving superior risk-adjused reurns. Clarke, de Silva, and Thorley [2016] used mean variance efficiency in assessing porfolio consrucion mehods. As a reference poin, hey calculaed he poenial improvemen in risk-adjused reurn as he difference beween he Sharpe raio of a cap-weighed benchmark and ha of a porfolio consruced wih unconsrained opimizaion. Tesing four commonly cied facors (low bea, small size, value, and momenum) in he U.S. marke, hey compared forming long-only mulifacor porfolios by inegraing securiies hrough opimizaion agains mixing four long-only facor porfolios. Clarke, de Silva, and Thorley found he former capures 90% of poenial Sharpe raio improvemen, whereas he laer capures only 40%. Fizgibbons e al. [2016] repored ha inegraing is preferable because i favors securiies wih balanced, posiive exposures o muliple facor characerisics and avoids hose ha have offseing exposures. On he basis of hypoheical simulaions, Fizgibbons e al. idenified hree scenarios in which inegraing is more effecive han mixing: when facors are negaively correlaed, when invesors have a higher risk olerance, and when he sraegy is open o many facors. Bender and Wang [2016] similarly argued ha inegraing is superior because of he cross-secional ineracion of facors. They demonsraed hrough back esing ha global porfolios inegraing value, low-volailiy, qualiy, and momenum facors ouperform heir mixing counerpars, especially when pairing uncorrelaed facors, such as value and qualiy or value and momenum. Basing heir argumens on eiher simulaions or backess, he researchers cied generally overlooked porfolio characerisics ha make implemenaion challenging. 3 Using opimizaion o consruc inegraed porfolios ends o cause a high urnover rae: Selecing securiies ha rank high on muliple uncorrelaed facors ends o yield a concenraed porfolio. Concenraion and urnover are characerisics associaed wih high implemenaion coss (see Chow e al. [2017]). Our principal conribuion o he lieraure is o se forh he pracical challenges of he inegraing approach. These echnical issues have invesmen consequences: Taking expeced implemenaion coss ino accoun reduces or eliminaes he performance advanage of inegraing. Given is oher benefis (ransparency, flexibiliy in allocaion across facors, and ease of performance aribuion), mixing may be he more raional approach o mulifacor invesing. SUPERIOR HISTORICAL PERFORMANCE OF AN INTEGRATED MULTIFACTOR STRATEGY We conduced exensive comparisons of inegraing versus mixing, wih facors consruced in he Unied Saes and developed markes using he mos widely acceped sock characerisics. Namely, our ess included value, momenum, profiabiliy, invesmen, and low-bea facors, represened by socks wih he highes book-o-marke raio, he highes railing one-year reurn skipping he mos recen monh, he highes operaing profiabiliy, he lowes asse growh, and he lowes marke bea, respecively. (see Carhar [1997]; Frazzini and Pedersen [2014]; and Fama and French [2015] for deailed explanaions for he facor characerisics.) To keep our es seup simple, we consruc our facors as long-only invesable porfolios based on hose desirable characerisics. We selec he op 20% of he large-cap equiy universe by each of he facor characerisics. 4 We hen capializaion weigh he seleced socks. (We include he resuls based on an equal-weigh scheme in he robusness secion.) The value, profiabiliy, and invesmen facor porfolios are rebalanced annually following Fama and French [2015], whereas he momenum and low-bea facor porfolios are rebalanced quarerly in accordance wih widely adoped invesmen pracice. 5 Our mixing mulifacor sraegy is an equalweigh combinaion of hose five-facor porfolios. We rebalance he facor allocaions o equal weighs every quarer. On he oher hand, our inegraing mulifacor sraegy is consruced in a way similar o ha for individual facor porfolios. We selec he op 20% of he large-cap universe by he average facor score. 6 Again, he seleced socks are weighed by marke capializaion. The inegraing mulifacor sraegy is also rebalanced quarerly. SPRING 2018 THE JOURNAL OF INDEX INVESTING

E XHIBIT 2 Simulaion of U.S. Single- and Mulifacor Sraegies (June 1968 December 2016) Alhough we conduced he ess in boh he U.S. and developed markes, we will focus on he U.S. resuls for he flow of his aricle. The conclusion highlighed in he following secions equally applies o developed markes. The resuls for developed markes, based on he comprehensive es in he final secion, are presened in he Appendix as a robusness check. Exhibi 2 shows he long-erm reurn and risk of simulaed single- and mulifacor sraegies. All of he facor sraegies ouperformed he cap-weighed benchmark, wih excess reurns ranging from 0.57% o 3.51% per year. As expeced, he inegraing approach performed excepionally well: I achieved boh he highes absolue reurn (13.59%) and he highes Sharpe raio (0.65). PRACTICAL CHALLENGES IN REALIZING PERFORMANCE On closer inspecion, i appears ha he superior performance of he inegraing mulifacor sraegy comes wih several characerisics noably, high concenraion and urnover ha compromise is invesabiliy. Exhibi 3 compares he diversificaion, measured as he number of holdings, 7 of he wo mulifacor simulaions. Over he enire sample period, he inegraing sraegy is generally less han one-hird as diversified as he mixing sraegy. The reason for his difference is inuiive. For example, if a securiy has relaively high reurn momenum bu medium o low exposure o oher facors, i belongs o he momenum facor porfolio and herefore eners he mixing sraegy a approximaely one-fifh of is heoreical maximum weigh (he weigh i would have if i were held by all facor porfolios). 8 This securiy hus diversifies he holdings of he mixing sraegy, bu i is likely excluded from he inegraing sraegy because of is mediocre average of characerisics. Exhibi 4 shows ha he inegraing approach resuls in consisenly higher urnover han he mixing approach. The long-erm average urnover rae of he inegraing sraegy (135.4%) is more han wice ha of he mixing sraegy (68.0%). 9 Alhough he concenraion of he inegraing sraegy undoubedly conribues o he high urnover rae, is porfolio consrucion process also conribues o his difference. All of he socks facor characerisics are reassessed every ime he inegraing sraegy is rebalanced. One of hem, he railing one-year reurn for momenum, is highly volaile. To mainain meaningful exposure o he momenum facor, he enire inegraing sraegy is rebalanced quarerly. By conras, a large proporion of he mixing sraegy (relaed o he value, profiabiliy, and invesmen facors) can be reconsiued annually. Thus, he mixing sraegy affords he praciioner more flexibiliy o deal wih signals ha decay wih differen speeds, whereas a naively consruced inegraing sraegy mus compor wih he fasesdecaying signal. Concenraion and urnover are direcly relaed o he cos of implemenaion. A sraegy ha holds fewer names and frequenly makes concenraed rades incurs higher rading coss. We use he linear framework presened by Aked and Moroz [2015] o quanify SMART BETA MULTIFACTOR CONSTRUCTION METHODOLOGY: MIXING VERSUS INTEGRATING SPRING 2018

E XHIBIT 3 Concenraion of U.S. Mulifacor Sraegies (June 1968 December 2016) E XHIBIT 4 Annual Turnover Raes of U.S. Mulifacor Sraegies (June 1968 December 2016) he difference in he expeced cos of rading: The asse value los hrough marke impac increases proporionally wih he size of he rade. Specifically, he marke price of he raded securiy moves agains he rade by 30 bps, on average, for every 10% of he securiy s daily volume ha he rade consumes. Exhibi 5 repors he expeced marke impac coss of he facor sraegies a an assumed AUM of $1 billion or $5 billion. (This AUM is he aggregae of all asses adoping he sraegy.) Because of he high urnover rae and concenraion, he momenum facor is he mos cosly o implemen. The inegraing mulifacor sraegy ranks second; a $5 billion AUM, i incurs SPRING 2018 THE JOURNAL OF INDEX INVESTING

E XHIBIT 5 Expeced Coss and Ne-of-Cos Performance of Facor Sraegies (June 1968 December 2016) esimaed rading coss of 149.6 bps per year, more han eigh imes as expensive as he mixing sraegy. Exhibi 5 also shows he performance of he facor sraegies ne of expeced coss. A $5 billion AUM, he difference in raes of reurn beween he inegraing and mixing sraegies shrinks from 176 bps (3.71% versus 1.75%) o 44 bps (2.01% versus 1.57%), and he difference in Sharpe raios falls from 0.17 o 0.07. This cos esimaion model assumes all managers racking he index rade in unison near he end of he rebalance dae o minimize racking error agains an index. Acive managers who are allowed more laiude can sraegically spread ou rades o avoid amassing marke impac coss. Viewed as a smar-bea indexing sraegy, however, much of he reurn advanage of inegraing appears o be washed ou a a modes level of adopion. In addiion o he implemenaion challenges, he high concenraion of he inegraing sraegy resuls in anoher unwelcome oucome. As Exhibis 2 and 5 show, he inegraing approach, wih he highes Sharpe raio, is more mean variance efficien han oher sraegies due in par o is below-marke-average reurn volailiy. When evaluaing he sources of excess reurn and acive risk, however, i becomes uncerain ha inegraing is efficien in facor invesing. Invesors expec consisen excess reurns from exposure o robus facors, bu we have found evidence ha he concenraed inegraing approach displays high idiosyncraic risk, casing doub on is fuure performance. We define he percenage of acive risk explained by facors as he R 2 from an excess reurn risk aribuion regression: ~ s R R benchmark α M + β ( Mk RF) +β SMB H R C + β HML β RMW + β CMA W B + β WML β BAB +ε The dependen variable is he reurn of he sraegy in excess of he reurn of a cap-weighed benchmark; he explanaory variables represen an augmened facor model, he Fama French five-facor model plus he momenum and low-bea facors. 10 Wih he excepion of SMB, our sraegies explicily arge hese facors, and in consrucing hem, we use he same ranking variables employed in he creaion of he facor model. Therefore, lile or no model misclassificaion should be presen in our risk aribuions. Exhibi 6 shows he percenage of acive risk explained by facors of mulifacor sraegies a various levels of concenraion. They range from very diversified (selec he op 75% of socks) o very concenraed (selec only he op 10%). The proporion of acive risk explained decreases seadily as he seleciveness of he consrucion process increases. When he sraegy is very concenraed, he percenage of acive risk explained drops o 50%; a his poin, he uninended idiosyncraic risk is jus as prevalen as he sysemaic facor risk. Exhibi 6 also shows ha he arge facors consisenly explain a lower proporion of he acive risk of he inegraing sraegy han of he mixing sraegy. SMART BETA MULTIFACTOR CONSTRUCTION METHODOLOGY: MIXING VERSUS INTEGRATING SPRING 2018

E XHIBIT 6 Percenage of Acive Risk Explained by Facors a Various Levels of Concenraion (U.S. mulifacor sraegies, June 1968 December 2016) From his perspecive, he inegraing approach is less efficien han is Sharpe raio migh indicae because is higher reurn comes wih greaer idiosyncraic volailiy. Exhibi 7 shows he decomposiion of acive risk ino facor risk and idiosyncraic risk for he sraegies we have examined. In his exhibi, he percenage of risk explained by argeed facors is, as before, he R 2 of he regression based on relevan facors specified in Equaion (1). Acive risk by argeed facor is he square roo of he produc of racking error squared and R 2, and idiosyncraic acive risk is he square roo of he produc of racking error squared and (1 R 2 ). Given ha combining individual facors expands he coverage of he mixing porfolio, i is no surprising ha he inegraing porfolio has a subsanially greaer racking error. Wha sands ou is he fac ha he inegraing sraegy s idiosyncraic risk (4.81%) is more han 2.5 imes ha of he mixing sraegy (1.91%). This ells us ha a large porion of he 3.51% excess reurn earned by he inegraing sraegy comes from sources unrelaed o he arge facors. We are confiden ha he premium aribuable o robus facors is more likely o persis han he exra performance associaed wih idiosyncraic risk. If a sraegy is necessarily concenraed, perhaps because i aims for a high expeced reurn, hen is company-specific risk should be acively managed wih he help of analyss who have experise and insigh a he individual securiy level and/or a quaniaive model ha is more sophisicaed han a simple facor model. I is less effecive o implemen such a sraegy as a smar bea index. Alhough our analysis capures he superior performance of he inegraing mulifacor sraegy in backesed paper porfolios, i also shows he downside of he sraegy s higher level of concenraion compared o he mixing sraegy. Smar bea sraegies should be well diversified. They are inended o efficienly provide facor exposures by applying a simple, ransparen mehodology wih low ransacion coss o broad cross secions of securiies. To assess he suiabiliy of mulifacor sraegies in a passive and sysemaic smar bea chassis, we reevaluaed heir risk and reurn a higher levels of diversificaion. INTEGRATING VERSUS MIXING AT DIFFERENT DIVERSIFICATION LEVELS Acknowledging ha highly concenraed porfolios are expensive o rade and inefficien in providing sysemaic facor exposures, we relaxed he SPRING 2018 THE JOURNAL OF INDEX INVESTING

E XHIBIT 7 Decomposiion of Acive Risk (U.S. sraegies, June 1968 December 2016) selecion consrain. For horough esing, we varied he seleciviy in consrucing boh he single-facor porfolios and he inegraing mulifacor porfolio from 5% o 95% wih incremens of 5% in he oal number of socks. As noed earlier, when he underlying facor porfolios are combined, he mixing mulifacor sraegy produces a much broader porfolio han he inegraing sraegy. To ensure comparabiliy, we use he number of holdings in he laes inegraing and mixing porfolios as a measure of concenraion. Exhibi 8 compares he reurn, volailiy, Sharpe raio, value-added, racking error, and informaion raio of he U.S. inegraing and mixing mulifacor sraegies wih equivalen numbers of end-of-period holdings. 11 Consisen wih our earlier findings, a high levels of concenraion, he inegraing approach produces higher Sharpe raios because i has higher reurn and lower volailiy han he mixing approach. For example, wih approximaely 200 names, he inegraing sraegy yields a reurn of 13.58%, volailiy of 13.30%, and a Sharpe raio of 0.65, whereas he mixing sraegy has a reurn of 12.83%, volailiy of 15.90%, and a Sharpe raio of 0.50. In conras, he considerably higher racking error of he inegraed porfolio (7.20% versus 4.87%) resuls in a lower informaion raio (0.49) han he mixed porfolio (0.57). Wih larger numbers of holdings, however, we observe ha boh paper porfolio reurns and ransacion coss decrease. We also observe ha he empirical advanage of inegraing over mixing diminishes. A approximaely 600 names, he Sharpe raio of he mixing and inegraing sraegies are pracically he same (0.49 versus 0.48), whereas he mixing approach regisers a higher informaion raio (0.50 versus 0.37). Wih even more holdings, he mixing sraegy has beer risk-adjused performance characerisics han he inegraing sraegy. For insance, a he level of 800 names, he mixing sraegy has a reurn of 11.78%, volailiy of 14.20%, and a Sharpe raio of 0.49, compared o he inegraing sraegy s reurn of 10.80%, volailiy of 14.70%, and Sharpe raio of 0.40. We repor he same comparison based on he effecive number of holdings in he Appendix, where we observe very similar paerns in performance characerisics. Pursuing his comparison, we ook marke impac coss ino accoun o reflec real-world implemenaions. The implemenaion cos is esimaed wih he assumpion of $5 billion in AUM. Exhibi 9 repors he neof-cos performance characerisics of he inegraing and mixing sraegies a similar levels of concenraion. As expeced, he marke impac cos is appreciably greaer on less-diversified porfolios. For example, for porfolios wih 200 names, he reducion in reurn due o marke impac is abou 90 bps for boh approaches, whereas i is less han 10 bps for porfolios wih 800 names. The crossing poin of Sharpe raios beween he inegraing and mixing approaches remains more or less unchanged afer considering marke impac coss. The inegraing mulifacor sraegy produces a higher neof-cos Sharpe raio when he porfolio has fewer han 600 holdings. For insance, a he level of 200 names, on a ne-of-cos basis, he inegraing sraegy yields a reurn of 12.68% and a Sharpe raio of 0.59, whereas he mixing sraegy has a reurn of 11.88% and a Sharpe SMART BETA MULTIFACTOR CONSTRUCTION METHODOLOGY: MIXING VERSUS INTEGRATING SPRING 2018

E XHIBIT 8 Comparisons Based on Number of End-of-Period Holdings (U.S. mulifacor sraegies, June 1968 December 2016) raio of 0.44. Wih more holdings, however, he mixing sraegy again has boh a higher Sharpe raio and a higher informaion raio han he inegraing sraegy. For example, a he level of 800 names, when ne of ransacion coss, he mixing sraegy has a higher reurn (11.67% versus 10.77%), higher Sharpe raio (0.48 versus 0.40), and higher informaion raio (0.50 versus 0.41) han he inegraing sraegy. As a robusness check, we repor, in he Appendix, he resuls of he same ess using equal-weighed facor porfolios. We generally observe paerns similar o he es resuls based on capializaion weighing. The crossing poin beween he Sharpe raios of he inegraing and mixing sraegies is around 700 names. For concenraed porfolios, he inegraing approach yields beer performance characerisics before implemenaion coss. Because of higher urnover, however, he marke impac is much larger han ha of capializaion-weighed porfolios. This eliminaes he advanage of inegraing over mixing. For diversified porfolios, he mixing approach leads o beer performance boh before and afer rading coss. This evidence confirms ha our findings are no driven by he choice of a paricular weighing scheme. In he Appendix, we also repor ou-of-sample robusness ess, which replicae he same mulifacor porfolios in developed markes over he period of July 1990 o December 2016. The resuls are consisen wih our findings in he U.S. marke. For a highly concenraed porfolio, he inegraing sraegy has a higher Sharpe raio han he mixing sraegy. For a porfolio conaining more han approximaely 1,000 names, however, he mixing approach produces boh a higher Sharpe raio and a higher informaion raio han he inegraing approach. QUALITATIVE CONSIDERATIONS The foregoing quaniaive analysis of he wo approaches o mulifacor smar bea invesing is informaive, bu many pracical consideraions are hard o measure. For example, he governance srucure in which praciioners operae may influence invesmen decisions. Many invesmen professionals serve as agens for he end invesors (principals). I is no enough for an agen and a principal o agree abou he facor allocaion on he basis of expeced reurns and risks; he agen mus also be equipped o ariculae he sources of performance SPRING 2018 THE JOURNAL OF INDEX INVESTING

E XHIBIT 9 Ne-of-Cos Comparison Based on End-of-Period Number of Holdings (U.S. mulifacor sraegies, June 1968 December 2016) Noe: Coss are esimaed assuming $5 billion in AUM. in erms ha make sense o he principal, especially when he porfolio is no doing well. The mixing approach faciliaes aribuion analysis using a familiar and ransparen model. Given is more opaque consrucion mehodology, he relaive performance of an inegraing porfolio can be more challenging o explain. A relaed consideraion is he end invesor s level of financial and quaniaive sophisicaion. The inegraing approach can work well wih an invesor who clearly recognizes he risks of daa snooping and overfiing in backesed resuls. In addiion, as we have already remarked, he inegraing approach works beer when an invesor holds only a subse of he universe, bu he resuling concenraion leads o higher urnover and, consequenly, o higher rading coss, which may wipe ou a subsanial porion of he performance advanage. Passive execuion ha focuses on minimizing racking error agains he benchmark ends o bunch rades around he marke close on rebalance daes. In he ineres of reducing implemenaion coss, sophisicaed principals are more likely o olerae racking error ha arises from proacive rade managemen. CONCLUSION Inegraing and mixing are he wo mos popular porfolio consrucion approaches used in mulifacor smar bea sraegies. The inegraing approach (which ranks and selecs securiies on he basis of a composie score) ends o demonsrae a srong in-sample performance advanage, especially when he seleced subse is small and rading coss are disregarded. However, he SMART BETA MULTIFACTOR CONSTRUCTION METHODOLOGY: MIXING VERSUS INTEGRATING SPRING 2018

high degree of freedom in compuing composie scores makes his mehodology vulnerable o overfiing. To help invesors form realisic expecaions, providers mus ake conscienious seps o avoid daa-snooping bias in heir produc developmen pracices. In addiion, given he relaively higher implemenaion coss associaed wih concenraed porfolio holdings, i is imporan o have sophisicaed end invesors who can olerae racking error and praciioners who can ake acical advanage of he available liquidiy in he marke o lower he rading coss. The performance advanage associaed wih he inegraing approach hen can be preserved. The mixing approach (in which he ranking and sock selecion are done wih individual facor-specific signals o form sand-alone subporfolios o which a weighing scheme is hen applied) exhibis sronger performance when he porfolio is more broadly diversified. Because he rades parially cancel one anoher ou across facor sleeves, he mulifacor sraegy creaed his way does no experience as much inefficien rading, and he broad coverage of he porfolio holdings end o reduce marke impac coss furher. This more flexible approach offers a greaer degree of ransparency, and i is easier for invesors o undersand he performance drivers when differen facors deliver differen reurns. We recommend he mixing approach for mulifacor smar bea index consrucion because of is broadly diversified holdings and easier implemenaion as well as is ransparency and simpliciy from a governance perspecive. The inegraing approach, on he oher hand, is more suiable for sysemaic acive sraegies. A PPENDIX ROBUSTNESS TESTS E XHIBIT A1 Ne-of-Cos Comparisons Based on Effecive Number of Holdings (U.S. mulifacor sraegies, June 1968 December 2016) Noe: Coss are esimaed assuming $5 billion in AUM. SPRING 2018 THE JOURNAL OF INDEX INVESTING

E XHIBIT A2 Ne-of-Cos Comparison Based on Number of Holdings wih Equal Weighing (U.S. mulifacor sraegies, June 1968 December 2016) Noe: Coss are esimaed assuming $5 billion in AUM. E XHIBIT A3 Ne-of-Cos Comparison Based on Number of Holdings (developed markes, July 1990 December 2016) (coninued) SMART BETA MULTIFACTOR CONSTRUCTION METHODOLOGY: MIXING VERSUS INTEGRATING SPRING 2018

E XHIBIT A3(coninued) Ne-of-Cos Comparison Based on Number of Holdings (developed markes, July 1990 December 2016) Noe: Coss are esimaed assuming $5 billion in AUM. Source: Research Affiliaes, LLC, using daa from Worldscope/Daasream. ENDNOTES 1 We used high minus low (HML) and winners minus losers (WML) in he U.S. marke from Dr. Kenneh French s Daa Library as proxies for he value and momenum facors. 2 In Exhibi 1, he inegraing sraegies primarily include he Morningsar Facor Til, MSCI Diversified Muliple Facor, and Harford Mulifacor sraegies; he principal mixing sraegies are he Goldman Sachs AciveBea, EDHEC Scienific Bea, MSCI Facor Mix A-Series, John Hancock Mulifacor, and J.P. Morgan Equiy Risk Premium Muli-Facor sraegies. 3 Fizgibbons e al. [2016] poined ou ha inegraing facors improves rading efficiency and reduces urnover by neing ou offseing rades iniiaed by uncorrelaed facors. This is a legiimae implemenaion-relaed argumen, no for comparing he inegraing and mixing approaches bu for invesing wih a single or muliple sraegy provider. I is common o have a provider offer mixures of is own singlefacor sraegies. 4 For he U.S. markes, we use he universe of he U.S. socks from he CRSP/Compusa daabase o consruc our porfolios. Following Fama and French [2015], we define he U.S. large-cap equiy universe as socks whose marke capializaions are greaer han he median marke capializaion on he NYSE. We hen selec he op 20% of he large-cap socks by desired characerisics. For example, o simulae he value facor, we consruc he porfolio from he large-cap socks above he 80h percenile by book-o-marke raio. For inernaional markes, we use he universe of 23 developed counries from he Worldscope/Daasream daabase o consruc our porfolios. The developed large-cap universe is defined as socks ha represen he op 86% of he enire universe by marke capializaion. Facor porfolios are hen consruced using he same mehodology as for he U.S. facors. 5 In academic papers, including hose by Fama and French [2015] and Frazzini and Pedersen [2014], momenum and low-bea facors are rebalanced monhly. However, because of heir high urnover and implemenaion cos, monhly rebalancing is rarely adoped, and quarerly or even semiannual rebalancing is preferred among invesmen praciioners. For example, he AQR Momenum Index and S&P 500 Low Volailiy Index are rebalanced quarerly, and he MSCI Momenum Index and S&P 500 Minimum Volailiy Index are rebalanced on a semiannual basis. 6 We sandardize facor characerisics by calculaing cross-secional Z-scores for each measure. Sandardized scores of ouliers are capped a ±3. We hen ake he average of hose five-facor scores for each sock. 7 If diversificaion is measured by he effecive number of holdings, hen he inegraing sraegy is generally less han half as diversified as he mixing sraegy. The effecive number of holdings is he inverse of he Herfindahl index, which is a measure of concenraion compued as he sum of he squared weighs of porfolio consiuens. 8 Hisorically, we find very few socks ha rank well in all merics. 9 Our esing did no apply urnover limiing echniques, such as banding, o eiher sraegy. 10 We obain he ime series of reurns for he Fama French five-facor model (Mk-RF, small minus big [SMB], HML, robus minus weak [RMW], and conservaive minus aggressive [CMA]) and WML from Dr. Kenneh French s Daa Library, and he reurns of he low-bea facor (BAB) from AQR Capial Managemen, LLC. SPRING 2018 THE JOURNAL OF INDEX INVESTING

11 We repor only hose sraegies ha are comparable under boh consrucion mehodologies. For insance, he inegraing sraegy a a 5% selecion level is oo concenraed, whereas he mixing sraegy a a 95% selecion level is oo diversified. Thus, such exreme sraegies are excluded from he figures because hey are no appropriae for comparison purposes. REFERENCES Aked, M., and M. Moroz. The Marke Impac of Passive Trading. The Journal of Trading, Vol. 10, No. 3 (2015), pp. 1-8. Alighanbari, M., and C.P. Chia. Mulifacor Indexes Made Simple: A Review of Saic and Dynamic Approaches. The Journal of Index Invesing, Vol. 7, No. 2 (2016), pp. 87-99. Arno, R.D., N. Beck, and V. Kalesnik. Timing Smar Bea Sraegies? Of Course! Buy Low, Sell High! Research Affiliaes, Sepember 2016. hps://www.researchaffiliaes.com/en_us/publicaions/aricles/541_iming_smar_bea_ sraegies_of_course_buy_low_sell_high.hml. Beck, N., J. Hsu, V. Kalesnik, and H. Koska. Will Your Facor Deliver? Examinaion of Facor Robusness and Implemenaion Coss. Financial Analyss Journal, Vol. 72, No. 5 (2016), pp. 58-82. Bender, J., and T. Wang. Can he Whole Be More han he Sum of he Pars? Boom-Up versus Top-Down Mulifacor Porfolio Consrucion. The Journal of Porfolio Managemen, Vol. 42, No. 5 (2016), pp. 39-50. Carhar, M.M. On Persisence in Muual Fund Performance. The Journal of Finance, Vol. 52, No. 1 (1997), pp. 57-82. Chow, T., F. Li, Y. Garg, and A. Pickard. Cos and Capaciy: Comparing Smar Bea Sraegies. Research Affiliaes, July 2017. hps://www.researchaffiliaes.com/en_us/ publicaions/aricles/625-cos-and-capaciy-comparingsmar-bea-sraegies.hml. Clarke, R., H. de Silva, and S. Thorley. Fundamenals of Efficien Facor Invesing. Financial Analyss Journal, Vol. 72, No. 6 (2016), pp. 9-26. Fama, E.F., and K.R. French. A Five-Facor Asse Pricing Model. Journal of Financial Economics, Vol. 116, No. 1 (2015), pp. 1-22. Fizgibbons, S., J. Friedman, L. Pomorski, and L. Serban. Long-Only Syle Invesing: Don Jus Mix, Inegrae. Whie paper, AQR Capial Managemen, LLC, 2016. Frazzini, A., and L.H. Pedersen. Being agains Bea. Journal of Financial Economics, Vol. 111, No. 1 (2014), pp. 1-25. Harvey, C., Y. Liu, and H. Zhu. and he Cross-Secion of Expeced Reurns. Review of Financial Sudies, Vol. 29, No. 1 (2015), pp. 5-68. To order reprins of his aricle, please conac David Rowe a drowe@iijournals.com or 212-224-3045. BlackRock. Smar Bea: Facor-Based Invesing wih ETFs. 2018. hps://www.blackrock.com/insiuions/ en-au/invesmen-capabiliies-and-soluions/ishares-efs/ smar-bea. SMART BETA MULTIFACTOR CONSTRUCTION METHODOLOGY: MIXING VERSUS INTEGRATING SPRING 2018