Diversified or Concentrated Factor Tilts?

Transcription

1 VOLUME 42 NUMBER 2 WINTER 2016 Dversfed or Concentrated Factor Tlts? NOËL AMENC, FRÉDÉRIC DUCOULOMBIER, FELIX GOLTZ, ASHISH LODH, AND SIVAGAMINATHAN SIVASUBRAMANIAN The Voces of Influence journals.com

2 Dversfed or Concentrated Factor Tlts? NOËL AMENC, FRÉDÉRIC DUCOULOMBIER, FELIX GOLTZ, ASHISH LODH, AND SIVAGAMINATHAN SIVASUBRAMANIAN NOËL AMENC s a professor of fnance at EDHEC-Rsk Insttute and the CEO of ERI Scentfc Beta n Sngapore. noel.amenc@edhec-rsk.com FRÉDÉRIC DUCOULOMBIER s an assocate professor of fnance at EDHEC-Rsk Insttute and a busness development drector for Asa ex Japan and the Mddle East at ERI Scentfc Beta n Sngapore. frederc.ducoulomber@edhecrsk.com FELIX GOLTZ s the head of appled research at EDHEC-Rsk Insttute and a research drector at ERI Scentfc Beta n Nce, France. felx.goltz@scentfcbeta.com ASHISH LODH s a deputy research drector at ERI Scentfc Beta n Nce, France. ashsh.lodh@scentfcbeta.com SIVAGAMINATHAN SIVASUBRAMANIAN s a quanttatve research analyst at ERI Scentfc Beta n Nce, France. svagamnathan.svasubramanan@ scentfcbeta.com At the outset, smart beta was conceved as a response to two drawbacks of broad-market, captalzaton-weghted (hereafter, market-cap) ndces. The frst drawback s that such portfolos typcally provde lmted access to long-term rewarded rsk factors, such as sze or value, among others. The second problem s that these portfolos do not effcently dversfy unrewarded rsks due to excessve concentraton n the stocks wth the largest market caps. Several studes have proposed methods to desgn ndces wth mproved dversfcaton as an answer to ths problem. 1 However, n recent years, the queston of dversfcaton has taken a back seat to the queston of approprate factor tlts, whch has become smart-beta provders prme concern. Dealng wth the queston of obtanng the rght factor exposures gves rse to a consensus, because t provdes space for actve managers who had lttle lattude n a framework of smart-beta offerngs purely focused on mprovng dversfcaton. Factor nvestng has become an opportunty to sell stock-pckng approaches as systematc strateges. Factor nvestng assumes that the lnk between stock returns and stock characterstcs drves strategy performance. A factor model postulates that expected stock returns are related to factor exposures, and factor nvestng essentally ams at capturng exposures that wll lead to hgher longterm returns. Factor nvestng thus poses the problem of estmatng expected returns through factor exposures. Ultmately, return estmaton wll be senstve to both the tme perod and the selecton of crtera used for factor dentfcaton. In ths artcle, we conduct a detaled comparson of the performance and rsks of concentrated and dversfed factor-tlted ndces for sx factor tlts n both the long and short terms. We dscuss the conceptual ssues wth lnkng factor exposures to expected returns and argue n favor of dversfyng factor-tlted portfolos. Then, usng long-term U.S. stock data, we emprcally compare the performance of concentrated and dversfed factor-tlted portfolos on broad and narrow factor-fltered stock unverses. RELATED LITERATURE AND CONCEPTUAL CONSIDERATIONS Factor Investng and Expected Return Estmaton In ths subsecton, we revew the lterature on the lnk between factor exposures and returns. We emphasze that ths lnk s 1) based on very long-term perods and not lkely to hold consstently for any short horzon and 2) subject to consderable estmaton rsk, especally at the stock level. DIVERSIFIED OR CONCENTRATED FACTOR TILTS? WINTER 2016

3 An mportant dea behnd factor nvestng s that portfolos that tlt toward a range of well-documented factors have been rewarded wth hgher returns. However, t s well known that expected returns are notorously hard to estmate (see Merton [1980]). We should also note wth Black [1993] that we need decades of data for accurate estmates of average expected return. We need such a long perod to estmate the average that we have lttle hope of seeng changes n expected returns. Thus, ntroducng propretary factor defntons or concentratng on stock wth the strongest exposure to factors that delver the hghest expected return s a rsky busness, as far as out-of-sample data relablty s concerned. Moreover, estmatng returns at the ndvdual stock level s lkely to lead to a large amount of nose. Black [1993] emphaszed that expected returns cannot be relably estmated for ndvdual stocks. For ths reason, studes that document factor prema (such as Fama and French [1993], among many others too numerous to cte) rely on portfolo-sortng approaches. Rather than tryng to determne dfferences n returns between ndvdual stocks, researchers have created groups of stocks and tested broad dfferences n returns across these. Therefore, when consderng whether to create a concentrated portfolo or a dversfed one for a gven factor tlt, we should keep n mnd that the more concentrated the portfolo becomes, the more t reles on the exstence of a detaled and strct relatonshp between stock returns and factor exposure. If we recognze that there s a lot of nose n estmatng the lnk between returns and stock-level characterstcs, the standard way to address ths ssue s to make broad dstnctons between groups of stocks. The assumpton that a broadly dversfed portfolo of many dfferent, low-valuaton stocks has a hgher long-term expected return than a broadly dversfed portfolo of hgh-valuaton stocks s qute dfferent from the assumpton that the return of any ndvdual stock wth a gven valuaton rato wll strctly be hgher than the return of any stock wth a hgher valuaton rato. If we beleve that valuaton characterstcs provde an exact and determnstc lnk for stock returns, we would strve to buld the most concentrated portfolos, usng the rght stocks. If we beleve that valuaton characterstcs let us dstngush between dfferences n returns that hold (on average) across many stocks, we would strve to buld well-dversfed portfolos wth the desred valuaton tlt. Moreover, f we beleve that we can estmate the lnk between factor exposure and expected returns wth a hgh degree of accuracy, we would tend to use the varable that appears to be assocated wth the hghest returns. However, f we are agnostc about our capacty to precsely lnk returns to stock characterstcs, we would tend to favor parsmonous and well- documented varables that have stood the test of tme. OVERVIEW OF EMPIRICAL TESTS OF FACTOR PREMIA Ratonal factor nvestng does not rely on fndng underprced stocks but rather seeks to dentfy factors that lead to systematc rsks that nvestors are unwllng to bear wthout a commensurate reward. It does not requre an ablty to pck stocks by beng better than the market at processng nformaton. Rather, t tres to dentfy rsk factors wth strong emprcal evdence n favor of a postve rsk premum, relatve to the broad market. Exhbt 1 summarzes the semnal lterature on emprcal tests of the sx factors we consder n our study: sze, value, momentum, low rsk, proftablty, and nvestment. We report the man fndngs from the followng seven papers: Fama and French [1992], Jegadeesh and Ttman [1993], Ang et al. [2006], Frazzn and Pedersen [2014], Fama and French [2015], Hou, Xue, and Zhang [2015a], and Novy-Marx [2013]. Panel A dscusses ther methodology and underlyng data. Panel B provdes the man results and ther relevance. The lterature on factor prema hghlghts the exstence of statstcally and economcally sgnfcant prema over the long term, but t s partcularly nterested n nether the varablty n premum sgnfcance over tme nor how rsk-adjusted performance vares n the short term, despte beng based on factor portfolos that are reconsttuted at least annually. However, the short- and medum-term dynamcs of these prema are an mportant practcal ssue for nvestors, even when the nvestment horzon s long term, as they reman subject to short- and medum-term reportng oblgatons. Managng the rsks of factor nvestng presupposes recognzng them, and t s clear that the reference lterature has not really addressed the ssue. The lterature s focus has been on explanng long-term dfferences n stocks expected returns. The recognton of these rsks justfes evaluatng varous methods of mple- WINTER 2016 THE JOURNAL OF PORTFOLIO MANAGEMENT

4 E XHIBIT 1 Summary of Emprcal Tests on Rsk Factor Prema DIVERSIFIED OR CONCENTRATED FACTOR TILTS? WINTER 2016

5 E XHIBIT 1 (Contnued) mentng the factor nvestment paradgm and provdes an angle to better apprecate the relevance of opposng approaches to factor nvestng: concentrated versus dversfed approaches. Smart-beta provders often refer to the evdence of long-term rsk prema n the academc lterature to justfy ther approaches to factor nvestng but neglect the medum- and short-term rsks. THE NEED FOR DIVERSIFICATION WITHIN FACTOR-TILTED PORTFOLIOS We revew the phlosophy behnd dversfed factor tlts. Postve exposure to rewarded factors s obvously a strong and useful contrbutor to expected returns. However, we must be careful to avod the ptfalls descrbed prevously: short-term varatons n long-term rewarded factors, fraglty of the lnk to expected returns, and possble data-mnng rsks. A way to lmt rsks wth factor-based strateges s to draw on a portfolo property that s a more robust source of mproved rsk-adjusted returns: dversfcaton. Dversfcaton approaches rely on estmates of rsk parameters more than on estmates of expected return parameters. In fact, most dversfcaton approaches used n practce are purely rsk-based portfolo constructons that do not requre any drect nputs of expected returns. Products that am to capture explct rsk-factor tlts through concentrated portfolos effectvely neglect adequate dversfcaton. Ths s a serous ssue because dversfcaton has been descrbed as the only free lunch n fnance. Dversfcaton lets nvestors capture a gven exposure wth the lowest level of total rsk, as t elmnates non-systematc rsk. In contrast, takng on factor exposures exposes nvestors to systematc rsk factors. Rewards for dong so do not consttute a free lunch. They are compensaton for rsk n the form of systematc factor exposures. Capturng rsk prema assocated wth systematc factors may be attractve for nvestors who can accept the systematc rsk exposure n return for commensurate compensaton. WINTER 2016 THE JOURNAL OF PORTFOLIO MANAGEMENT

6 However, very concentrated factor-tlted strateges may also take on other, unrewarded rsks. Unrewarded rsks come n the form of dosyncratc (.e., frm-level) rsk, as well as other unrewarded rsks (e.g., currency rsk, sector rsks, and other unrewarded mcro or macroeconomc factors). Fnancal theory does not provde any reason that such rsk should be rewarded. Therefore, a sensble approach to factor nvestng should not only look to obtanng a factor tlt but also to achevng proper dversfcaton wthn that factor tlt. To llustrate ths pont, we focus on the value factor, but the dscusson carres over to other factors. In fact, f the objectve were to obtan the most pronounced value tlt, for example, the only unleveraged long-only strategy that would acheve ths goal would be holdng 100% n the sngle stock wth the largest value tlt, as measured (for example) by ts book-to-market rato or estmated senstvty to the value factor. Ths thought experment clearly shows that the objectve of maxmzng factor tlt strength s not reasonable. Moreover, ths extreme case of a strong factor tlt ndcates the potental ssues wth hghly concentrated factor ndces. Even f the approprateness of such an extreme approach had been establshed, any value premum so captured would necessarly come wth a large amount of dosyncratc rsk. Ths rsk s not rewarded, and therefore, we should not expect the strategy to lead to an attractve rsk-adjusted return. Addtonally, t s unlkely that the same stock wll persstently have the hghest value exposure wthn a gven nvestment unverse. Therefore, a perodcally rebalanced factor ndex wth such an extreme concentraton level wll lkely generate 100% one-way turnover at each rebalancng date, as the stock that the strategy held prevously s replaced wth a new stock that dsplays the hghest value exposure at the rebalancng date. Although the practcal mplementatons of concentrated factor-tlted ndces wll be less extreme than ths example, we can expect problems wth hgh levels of both dosyncratc rsk and turnover whenever ndex constructon focuses too much on concentraton and pays too lttle attenton to dversfcaton. Interestngly, Benjamn Graham hmself outlned the mportance of dversfcaton for a gven factor tlt many decades ago. As noted by Asness et al. [2015], the 1973 edton of Graham s famous book on value nvestng reads: In the nvestor s lst of common stocks there are bound to be some that prove dsappontng But the dversfed lst tself, based on the above prncples of selecton should perform well enough across the years. At least, long experence tells us so. Amng at a hghly concentrated value portfolo would be completely nconsstent not only wth fnancal theory but also wth the prncples put forth by the early advocates of value nvestng. Cap-weghted portfolos of value stock selectons may at frst seem to be a more neutral mplementaton than equally weghted portfolos. However, t s well known that cap-weghtng has a tendency to lead to very hgh concentraton, gven the heavy-taled nature of market-cap dstrbuton across stocks. It s well documented n the academc lterature that smple cap-weghted, value-tlted portfolos have not led to attractve performance. In fact, across dfferent studes on equty rsk factors, Fama and French emphaszed the need for a well-dversfed portfolo as a proxy for a factor tlt. For example, Fama and French [2012] sad that they ensure that [they] have lots of stocks n each [factor-tlted] portfolo and argue that factor-tlted portfolos should be well dversfed n order to obtan factor tlts that are relable, n the sense that factor exposures can be estmated wth precson. 2 Hou, Xue, and Zhang [2015b] explctly recognzed the need for dversfcaton, recallng that valueweghted portfolo returns can be domnated by a few bg stocks. (See also Fama and French [2015].) Factor constructon reflects ths need for dversfcaton. Fama and French [2012] defned the sze factor as the dfference between the returns on dversfed portfolos of small stocks and bg stocks and the value factor as the dfference between the returns on dversfed portfolos of hgh book-to-market (value) stocks and low bookto-market (growth) stocks. Thus, the value and sze factors are not based on concentrated portfolos wth the maxmum factor-related characterstc. To acheve dversfcaton, the standard Fama and French value factor ncludes a broad selecton of stocks and uses a two-tered weghtng approach. In partcular, the value factor s an equally weghted combnaton of sub-portfolos for dfferent market-cap ranges, effectvely overweghtng smaller stocks and ncreasng the effectve number of stocks. The fact that the most wdely cted research documentng the value factor s relevance does not use smple cap-weghted factors, but rather constructs more balanced portfolos, shows the lack of academc support for ndustry practces usng smple cap-weghted factor ndces. DIVERSIFIED OR CONCENTRATED FACTOR TILTS? WINTER 2016

7 Moreover, several authors adopt equally weghted (EW) approaches to factor portfolos. Asparouhova, Bessembnder, and Kalcheva [2013] revewed the lterature and summarze that examnng papers publshed n only two premer outlets, The Journal of Fnance and The Journal of Fnancal Economcs, over a recent fve-year (2005 to 2009) nterval, we are able to dentfy 24 papers that report EW mean returns and compare them across portfolos. (Also see Plyakha, Uppal, and Vlkov [2014].) As a recent example, Hou, Xue, and Zhang [2015b] addressed the dversfcaton ssue by formng factor portfolos that equally weght ther component stocks, whle excludng the smallest stocks due to mplementaton concerns. Overall, t appears that the approach that proposes to construct concentrated factor ndces s supported nether by the academc lterature nor by common sense. On the contrary, there s a strong theoretcal motvaton for constructng well-dversfed factor-tlted portfolos. Cochrane [1999] emphaszed that any portfolo should be constructed so as to provde the effcent rsk-return trade-off, n a mean varance sense, at a gven level of factor exposure. Fama [1996] showed that rewarded factors can be understood as multfactor mean varanceeffcent portfolos themselves. Thus no form of factor nvestng can neglect dversfcaton as a method to construct portfolos that are not merely exposed to a gven factor but also are effcent. PERFORMANCE OF CONCENTRATED VERSUS DIVERSIFIED TILTED PORTFOLIOS Data and Methodology In ths secton, we compare portfolos for sx factor tlts, each wth dfferent stock selecton flters that are constructed usng two dfferent weghtng schemes: cap weghtng (CW) and equal weghtng (EW). We use two grades of flters: the broad flterng selects the top 50% of stocks, n terms of factor scores, from the stock unverse at each rebalancng, and the narrow flterng selects the top 20% of stocks. We assgn all stocks factor scores that are determned by ther fundamental stock characterstcs or past returns. We thus assgn each stock sx factor scores. 3 To construct factor-tlted portfolos, we select the top 50% or top 20% stocks by ther factor scores at each annual rebalancng. Ths means that we choose approxmately 250 and 100 stocks from the broad unverse of 500 U.S. large-cap stocks. The factor-tlted cap-weghted portfolo weghts the selected stocks n the proporton of ther total market captalzaton. The equally weghted portfolo weghts the selected stocks n equal dollar proportons. We rebalance all factor-tlted portfolos annually on the thrd Frday n June. The analytcs on U.S. portfolos n subsequent sectons use 40 years of weekly total returns, that s, returns wth dvdends renvested. Stocklevel data for portfolo constructon and portfolo valuaton come from CRSP and WRDS. The long/short factor returns used for regresson come from Kenneth French s data lbrary. 4 Exhbt 2 shows detaled performance comparsons between heavly concentrated (CW) portfolos and dversfed (EW) portfolos. In the long run, on average across the sx factor tlts, 5 the 50% CW portfolo s rsk-adjusted performance s nferor to that of the 50% EW portfolo. The average Sharpe rato goes up from 0.55 to 0.66 when we move from CW to EW portfolos. Smlarly wth the narrow stock selecton, we see an mprovement n Sharpe rato from 0.58 to 0.67 by usng EW over CW. Movng from CW to EW ndubtably ncreases the trackng error wth respect to the broad cap-weghted benchmark. But the rsk-adjusted outperformance, or nformaton rato, remans hgher for EW factor-tlted portfolos. For the 50% selecton case, on average, the nformaton rato of EW factor-tlted portfolos s 0.66, compared wth a mere 0.33 for CW factor-tlted portfolos. We also report the hstorcal probablty of outperformance over a three-year nvestment horzon, 6 defnng ths as the emprcal frequency of outperformng the cap-weghted reference ndex over a gven nvestment horzon. It s an ntutve and relevant measure for nvestment practtoners and shows how often and consstently the strategy has outperformed the cap-weghted reference ndex n the past for all possble entry ponts. The probablty of outperformance over ths medum nvestment horzon provdes an apprecaton of the stablty across tme of a strategy s outperformance. The outperformance probablty of EW factor-tlted portfolos s hgher than that of ther CW counterparts. For example, for the 50% stock selecton, the outperformance probablty of the EW factor-tlted portfolos s 76% on average, compared wth 68% for the CW factor-tlted portfolos. Increasng factor concentraton by selectng the top 20% stocks n terms of factor scores, nstead of the top 50% stocks, does not have a meanngful effect on rsk- adjusted returns. For a gven weghtng scheme, WINTER 2016 THE JOURNAL OF PORTFOLIO MANAGEMENT

8 E XHIBIT 2 Performance of Cap-Weghted and Equal-Weghted Factor Indces Notes: The analyzed tme perod s 40 years: December 31, 1974, to December 31, All fgures reported are average fgures across sx factors: sze, momentum, low volatlty, value, low nvestment, and hgh proftablty. All factor-tlted portfolos are rebalanced annually on the thrd Frday n June. The analyss s done usng weekly total returns (dvdends renvested) n U.S. dollars. The portfolos are constructed usng a U.S. stock unverse that contans the 500 largest stocks by total market cap. The market-cap-weghted ndex of these 500 stocks s the benchmark. The yeld on secondary market, three-month U.S. Treasury blls s the rsk-free rate. All rsk and return statstcs are annualzed and the Sharpe rato and nformaton rato are computed usng annualzed fgures. Outperformance probablty (three years) s the probablty of obtanng postve relatve returns f one nvests n the strategy for a perod of three years at any pont durng the strategy s hstory. We compute t usng a rollng wndow of three years (the length) and a step sze of one week. Average relatve returns n postve (negatve) perods s the mean of only postve (negatve) rollng three-year annualzed relatve returns. Extreme relatve returns n postve (negatve) perods are the 95th (5th) percentle of only postve (negatve) rollng three-year annualzed relatve returns. Sources: CRSP and WRDS. ncreasng concentraton through more strngent stock selecton (.e., gong from 50% to 20%) leaves the average Sharpe ratos and nformaton ratos at relatvely smlar levels overall. There s no added value, from a rsk-adjusted performance perspectve, n havng moreconcentrated factor-tlted portfolos. Note that factortlted portfolos average performance and Sharpe rato, rrespectve of weghtng scheme (CW or EW), reman hgher than those of the broad CW ndex, showng that the sx chosen rsk factors do earn (on average) a postve rsk premum n the long run. To have a deeper understandng of performance, we study the tme-varyng average relatve performance, volatlty, and trackng error, shown n Exhbt 3. The graphs are plotted usng a rollng tme wndow of three years length and a step sze of one month. By defnton, rskfactor exposure means experencng losses or drawdowns n bad tmes n exchange for better-than-average market performance n the long term. The relatve performance of EW and CW-tlted portfolos clearly represent the perods n whch factor rsk s rewarded and factor exposure leads to losses. However, the CW factor-tlted ndces to some extent mss out on the opportunty to beneft from factor prema, as evdenced by much lower levels of outperformance over most perods. A vsual nspecton of the graphs also shows that CW and EW portfolos volatlty and trackng error are almost the same, but ther respectve relatve returns dffer by a wde margn. In comparng the left and rght sdes of the Exhbt 3 graph of trackng error, we can drectly compare the 50% and 20% selecton-based portfolos and see that ncreasng stock selecton severty also ncreases trackng error. Concentratng n fewer stocks ncreases the trackng error by a large amount. The rollng three-year trackng error for 20% stock selecton portfolos can reach (on average) 13% to 14%. Therefore, holdng a factor-tlted portfolo that contans very few stocks may also present a dsadvantage for nvestors who face trackng-error constrants. Exhbt 3 showed that for the same level of total rsk, measured by portfolo volatlty, the CW factortlted portfolos posted lower returns than dd the EW factor-tlted portfolos, so much of the rsk CW portfolos take must be unrewarded or dosyncratc n nature. Addtonal analyss of performance statstcs over shorter tme perods suggests that dversfed approaches to factor ndces consstently provde stronger performance than DIVERSIFIED OR CONCENTRATED FACTOR TILTS? WINTER 2016

9 E XHIBIT 3 Rollng Wndow Excess Returns, Volatlty, and Trackng Error of Cap-Weghted and Equal-Weghted Factor Indces Notes: The analyzed tme perod s 40 years: December 31, 1974, to December 31, All fgures reported are average fgures across sx factors: sze, momentum, low volatlty, value, low nvestment, and hgh proftablty. All factor-tlted portfolos are rebalanced annually on the thrd Frday n June. The analyss s done usng weekly total returns (dvdends renvested) n U.S. dollars. The portfolos are constructed usng a U.S. stock unverse that contans the 500 largest stocks by total market cap. The market-cap-weghted ndex of these 500 stocks s the benchmark. All rsk and return statstcs are annualzed and computed usng a rollng wndow of three years (the length) and a step sze of one month. Sources: CRSP and WRDS. WINTER 2016 THE JOURNAL OF PORTFOLIO MANAGEMENT

10 do concentrated approaches, n partcular by avodng short-term rsk durng market downturns. 7 We analyze the dosyncratc rsk of concentrated and dversfed factor portfolos to show that the results n Exhbt 3 are consstent wth portfolo theory (.e., more concentraton leads to more dosyncratc rsk, whch s unrewarded). In order to strp out the systematc component of portfolo rsk, we use a Carhart four-factor regresson model (Carhart [1997]): MKT R () RF () β [ ( t) ( t)] SMB HML UMD +β SMB( () +β HML( () +β UMD () +ε() R (t) s the returns of portfolo, RF(t) s the rsk free rate, RM(t) s market returns, and SMB(t), HML(t), UMD(t) are long/short factor returns. 8 We then report the standard devaton of the resdual returns (ε (t)), whch s the resdual rsk, ts nterquartle range, regresson alpha, and the annualzed alpha per unt of resdual standard devaton. The use of such a mult-factor model captures any addtonal factor exposures ntroduced by equally weghtng stocks, compared wth cap-weghtng them. Indeed, the model captures mplct tlts of equally weghted portfolos to factors such as sze, and we then compare resdual performance and rsk statstcs across equally weghted and cap-weghted portfolos. Another way to quantfy the rsk reducton acheved by dversfcaton s to compare the portfolo s volatlty (1) wth the volatlty of ts factor benchmark that has been leveraged to match ts returns. The factor benchmark s a synthetc portfolo wth Carhart betas that are the same as those of the factor-tlted portfolo. Mathematcally, t can be constructed as follows: MKT SMB RB () R F( () = β [ ( ) ( t)] +β SMB( () HML UMD +β HML( () +β UMD() (2) The betas on the rght-hand sde of Equaton (2) are obtaned from the regresson of portfolo n Equaton (1), and therefore RB (t) s the returns of the factor benchmark of portfolo. Because the magntude of systematc rsk s dentcal across the portfolo and ts factor benchmark, the dfference n volatlty for the same return level can only be explaned by dversfcaton, or n other words, the reducton of dosyncratc rsk. Ths excess volatlty can be expressed as follows (Ret operator gves the annualzed returns and Vol operator gves the annualzed volatlty of the tme seres of returns): Δ Vol = [ R ( R ()) ( RFt ( ))] Vol ( R ( t)) Vol ( R( t)) Ret( ( ( t)) Ret( ( ( t)) (3) Exhbt 4 shows that, rrespectve of the weghtng scheme chosen, the resdual rsk s larger n the case of E XHIBIT 4 Dversfcaton Effects n Cap-Weghted and Equal-Weghted Factor Indces Notes: The tme perod of analyss s 40 years: December 31, 1974, to December 31, All fgures reported are average fgures across sx factors: sze, momentum, low volatlty, value, low nvestment, and hgh proftablty. All factor-tlted portfolos are rebalanced annually on the thrd Frday n June. The analyss s done usng weekly total returns (dvdends renvested) n U.S. dollars. The portfolos are constructed usng a U.S. stock unverse that contans the 500 largest stocks by total market cap. The market-cap-weghted ndex of these 500 stocks s the benchmark. The yeld on secondary market, three-month U.S. Treasury blls s the rsk-free rate. We use a Carhart four-factor model for regresson and annualze the reported alpha. Volatlty reducton s the dfference between volatlty of the leveraged factor benchmark and ts respectve portfolo (as descrbed n Equaton (3)). The market factor s the excess returns of the cap-weghted benchmark over the rsk-free rate. The sze, value, and momentum factors come from Kenneth French s data lbrary. Sources: CRSP and WRDS. DIVERSIFIED OR CONCENTRATED FACTOR TILTS? WINTER 2016

11 narrow stock selecton. The average standard devaton of regresson resduals ncreases when we move from broad to narrow stock selecton, from 0.51% to 0.82% for CW, and from 0.61% to 0.79% for EW. The nterquartle range of the resduals s also hgher n the case of narrow stock selecton portfolos, whch shows that the portfolo s dosyncratc rsk ncreases as the number of stocks falls. Annualzed alpha per unt of resdual standard devaton, whch s a measure of unexplaned dosyncratc rsk-adjusted performance, ncreases on average from 1.24 n the case of 50% CW factor-tlted portfolos to 2.34 n the case of 50% EW factor-tlted portfolos. Smlarly, reducton n volatlty wth respect to the respectve factor benchmark s hgher for EW factortlted portfolos than for CW factor-tlted portfolos. A frequent crtcsm of EW as a weghtng scheme s that EW portfolos overweght small-cap stocks, thus posng mplementaton challenges because small-cap stocks are relatvely less lqud. Exhbt 5 shows that swtchng from a 50% CW factor-tlted portfolo to EW brngs fewer mplementaton challenges than swtchng to a narrower 20% stock selecton whle remanng cap-weghted. On average, turnover does not show any consderable ncrease when movng from a 50% CW factor-tlted portfolo to a 50% EW factor-tlted portfolo. The average turnover of 50% CW factor-tlted portfolos s 29.25%, whle that of 50% EW portfolos s 32.58%. On the other hand, swtchng to 20% CW factor-tlted ncreases the average turnover by a hgh margn: from 29.25% to 48.15%. Ths s an nterestng fndng because when appled to a full unverse wthout a factor tlt, EW s known to ncrease turnover. In the case of factor-tlted ndces, the turnover s manly generated by varatons n stocks characterstcs and, thus, by changes n whch stocks are selected. Therefore, the weghtng scheme does not contrbute much addtonal turnover. Because they strongly underweght smaller stocks, cap-weghted portfolos exhbt low days-to-trade (DTT) numbers. 9 DTT s an ndcator of the tme requred to trade the least-lqud postons n the portfolo. DTT ncreases when movng from CW to EW, but t remans well behaved. The ncrease n DTT when movng from a 50% CW portfolo to a 50% EW portfolo s smlar to that of movng from a 50% CW portfolo to a 20% CW portfolo. We can use addtonal lqudty management rules to mprove the turnover and DTT of an equally weghted strategy or that of other alternatve weghtng schemes. It has been shown that such mplementaton hurdles can be easly managed by usng smple tradng rules wthout adversely affectng portfolo performance (Amenc, Goltz, and Gonzalez [2014] and Gonzalez, Svasubramanan, and Ye [2015]). Overall, our results provde a strong dstncton concernng the potental added value of usng an mproved weghtng scheme for a factor-tlted portfolo versus usng a more concentrated stock selecton. In fact, narrowng stock selectons for strong factor tlts does not add value. For a gven weghtng scheme, narrowng factor-based stock selecton does not lead to a meanngful mprovement n rsk-adjusted return. As portfolos E XHIBIT 5 Implementaton of Cap-Weghted and Equal-Weghted Factor Indces Notes: The tme perod of analyss s 40 years: December 31, 1974, to December 31, All fgures reported are average fgures across sx factors: sze, momentum, low volatlty, value, low nvestment, and hgh proftablty. All factor-tlted portfolos are rebalanced annually on the thrd Frday n June. The analyss s done usng weekly total returns (dvdends renvested) n U.S. dollars. The portfolos are constructed usng a U.S. stock unverse that contans the 500 largest stocks by total market cap. The market-cap-weghted ndex of these 500 stocks s the benchmark. The reported turnover s annual one-way turnover and s averaged over 40 annual rebalancngs from December 31, 1974, to December 31, A stock s days to trade, or DTT, s the number of days requred to trade the total stock poston n a portfolo of $1 bllon, assumng that 10% of average daly traded volume (ADTV) can be traded every day. For each portfolo, the reported DTT value s the 95th percentle of DTT values across all 10 annual rebalancngs from December 31, 2004, to December 31, 2014 and across all stocks. Sources: CRSP and WRDS. WINTER 2016 THE JOURNAL OF PORTFOLIO MANAGEMENT

12 concentrate n fewer stocks wth stronger factor characterstcs, average return ncreases, but so do volatlty and trackng error. Importantly, narrower selectons lead to pronounced ncreases n turnover and other mplementaton challenges. Strong factor tlts thus brng mplementaton challenges wthout provdng better rsk-adjusted performance. Moreover, narrower stock selectons lead to ncreases n dosyncratc and thus unrewarded rsk. Usng a better-dversfed weghtng scheme such as EW mproves rsk-adjusted performance consderably, compared wth captalzaton weghtng the same stock selecton. Ths dversfcaton creates more outperformance than concentraton, as the EW portfolo bult on a selecton of 50% of stocks consderably outperforms the CW portfolo bult on a selecton of 20% of stocks. In terms of mplementaton, swtchng from cap weghtng a broad (50%) stock selecton to equally weghtng brngs fewer mplementaton challenges than does swtchng to a narrower (20%) stock selecton whle remanng cap weghted. In partcular, turnover does not show any consderable ncrease when movng from CW to EW. Ths s an nterestng fndng because, when appled to a full unverse wthout a factor tlt, EW s known to ncrease turnover. In the case of factor-tlted ndces, the turnover s manly generated by varatons n stocks characterstcs and thus changes to whch stocks are selected. Therefore, the weghtng scheme does not contrbute much addtonal turnover. In terms of days-to-trade, EW factor-tlted ndces have more challenges than do CW factor-tlted ndces, but ncreases n days-to-trade reman well behaved. Overall, usng an mproved weghtng scheme such as EW on a factor-tlted stock selecton adds value, because rsk-adjusted performance mproves relatve to CW whle mplementaton challenges reman lmted. CONCLUSION In ths artcle, we compare dfferent approaches factor ndex desgn. We analyze broad and narrow stock selectons and two dfferent weghtng schemes, equal weghtng and cap-weghtng. From a conceptual perspectve, several ssues arse wth hghly concentrated portfolos, such as cap-weghted portfolos of narrow stock selectons. Frst, concentraton n a few stocks reflects hgh confdence n the precson of the lnk between expected returns and factor exposure. We know that expected returns are notorously dffcult to estmate wth precson, however, even when dong ths through factor exposures. Broadly dversfed factortlted portfolos reflect the vew that we are only able to dentfy broad dfferences n expected returns across groups of stocks. Moreover, t s well known that factor prema can be dentfed relably only for broadly dversfed tlted portfolos. Emprcal studes of factor prema nsst on the necessty of constructng broad portfolos that are not unduly nfluenced by a small number of stocks, whch has led the major studes n ths area to adopt approaches that lead to dversfed portfolos, notably by selectng large numbers of stocks and by usng more balanced weghtng approaches than smple cap weghtng for the selected stocks. Our emprcal analyss confrms that concentrated factor-tlted portfolos come wth problems. In fact, tryng to mprove the performance of cap-weghted factor-tlted portfolos by selectng fewer stocks that are most strongly tlted to the factor does not have any effect on the rsk-adjusted performance. Narrow stock selectons may mprove returns compared wth broad selectons, but these ncreases are accompaned by hgher volatlty and hgher trackng error, whch keeps performance ratos the Sharpe and nformaton ratos vrtually unchanged. In addton, factor-tlted portfolos on narrow stock selectons present real drawbacks, such as hgh dosyncratc rsk, hgher turnover, and longer tmes to trade portfolos. Conversely, f we focus on deconcentraton by usng a smple equal-weghtng approach to weght stocks, we can acheve better Sharpe ratos and nformaton ratos over both long and short nvestment horzons. The equally weghted portfolos ncur margnally hgher but manageable levels of turnover and n total do not pose mplementaton problems. These observatons stand true across the sx rsk factors tested. Equally weghtng stocks n a factor-tlted portfolo of course consttutes a startng pont for more sophstcated dversfcaton strateges that may help nvestors obtan addtonal dversfcaton benefts (see Amenc et al. [2014]). ENDNOTES 1 See, for example, Chouefaty and Cognard [2008], DeMguel et al. [2009], Mallard, Roncall, and Teletche [2010], and Amenc et al. [2011], among others, 2 Fama and French [2012] stated: Dversfcaton enhances regresson fts, whch ncreases the precson of the ntercepts that are the focus of the tests of competng asset prcng models. DIVERSIFIED OR CONCENTRATED FACTOR TILTS? WINTER 2016

13 3 We use the followng factor scores for each of these sx factor tlts: Md Cap, total market captalzaton; Value, bookto-market (B/M) rato (wth B/M defned as the rato of the avalable book value of shareholders equty to company market cap); Momentum, total returns over past 52 weeks, mnus the last 4 weeks; Low Volatlty, standard devaton of weekly stock returns over the past 104 weeks; Low Investment, past twoyear total asset growth rate; Hgh Proftablty: gross proft-tototal asset rato. The factor scores for Md Cap, Low Volatlty, and Low Investment factors are nverted. Ths s because, by defnton, they measure ther degree of beng large-cap, hgh-volatlty, and hgh-nvestment stocks respectvely, and we are nterested n stocks wth opposte characterstcs. 4 Weekly returns on SMB, HML, and UMD long/short factors n the U.S. can be obtaned from the followng web lnk: french/data_lbrary.html. 5 The fndngs hold wth a great degree of consstency across the sx factors. Space restrctons prevent us from lstng results for each factor tlt n the man text, but these are ncluded n the Onlne Appendx 1. 6 We compute the frequency of obtanng postve excess returns f one nvests n the strategy for three years, usng a rollng-wndow analyss wth one-week step sze. 7 We have calculated returns durng the worst calendar years n terms of returns to the cap-weghted market ndex (see onlne Appendx 3). Overall, the return mprovement of dversfed over concentrated factor ndces s partcularly strong durng these down markets. Moreover, we have analyzed performance and rsk durng non-overlappng perods of three calendar years (see Onlne Appendx 2). Results suggest that equally weghtng leads to hgher returns n 9 out of 13 sub-perods. 8 The regresson s performed usng weekly total returns. The yeld on secondary market, three-month U.S. Treasury blls s the rsk-free rate. The market factor s the excess return of the cap-weghted benchmark over the rsk-free rate. The sze (SMB), value (HML), and momentum (UMD) factors come from Kenneth French s data lbrary. 9 A stock s days-to-trade, or DTT, s the number of days requred to trade the total stock poston n a portfolo of $1 bllon, assumng that 10% of average daly traded volume (ADTV) can be traded every day. For each portfolo, the reported DTT value s the 95th percentle of DTT values across all 10 annual rebalancngs from December 31, 2004, to December 31, 2014, and across all stocks. REFERENCES Amenc, N., F. Goltz, A. Lodh, and L. Martelln. Towards Smart Equty Factor Indces: Harvestng Rsk Prema wthout Takng Unrewarded Rsks. The Journal of Portfolo Management, Vol. 40, No. 4 (2014), pp Amenc, N., F. Goltz, and N. Gonzalez. Investablty of Scentfc Beta Indces. ERI Scentfc Beta Whte Paper Seres, Amenc, N., F. Goltz, L. Martelln, and P. Retkowsky. Effcent Indexaton: An Alternatve to Cap-Weghted Indces. Journal of Investment Management, Vol. 9, No. 4 (2011), pp Ang, A., R. Hodrck, Y. Xng, and X. Zhang. The Cross- Secton of Volatlty and Expected Returns. Journal of Fnance, Vol. 61, No. 1 (2006), pp Asness, C., A. Frazzn, R. Israel, and T. Moskowtz, Fact, Fcton, and Value Investng. The Journal of Portfolo Management, Vol. 42, No. 1 (2015), pp Asparouhova, E., H. Bessembnder, and I. Kalcheva. Nosy Prces and Inference Regardng Returns. Journal of Fnance, Vol. 68, No. 2 (2013), pp Black, F. Estmatng Expected Return. Fnancal Analysts Journal, Vol. 49, No. 5 (1993), pp Carhart, M. On Persstence n Mutual Fund Performance. Journal of Fnance, Vol. 52, No. 1 (1997), pp Chouefaty, Y., and Y. Cognard, Towards Maxumum Dversfcaton. The Journal of Portfolo Management, Vol. 35, No. 1 (2008), pp Cochrane, J. Portfolo Advce for a Multfactor World. Workng Paper No. 7170, NBER, DeMguel, V., L. Garlapp, F. Nogales, and R. Uppal. A Generalzed Approach to Portfolo Optmzaton: Improvng Performance by Constranng Portfolo Norms. Management Scence, Vol. 55, No. 5 (2009), pp Fama, E. Multfactor Portfolo Effcency and Multfactor Asset Prcng. Journal of Fnancal and Quanttatve Analyss, Vol. 31, No. 4 (1996), pp Fama, E., and K. French. The Cross-Secton of Expected Stock Returns. Journal of Fnance, Vol. 47, No. 2 (1992), pp Common Rsk Factors n the Returns on Stocks and Bonds. Journal of Fnancal Economcs, Vol. 33, No. 1 (1993), pp Sze, Value, and Momentum n Internatonal Stock Returns. Journal of Fnancal Economcs, Vol. 105, No. 3 (2012), pp WINTER 2016 THE JOURNAL OF PORTFOLIO MANAGEMENT

14 . A Fve-Factor Asset Prcng Model. Journal of Fnancal Economcs, Vol. 116, No. 1 (2015), pp Frazzn, A. and L. Pedersen. Bettng aganst Beta. Journal of Fnancal Economcs, Vol. 111, No. 1 (2014), pp Gonzalez, N., S. Svasubramanan, and S. Ye. Scentfc Beta Maxmum Deconcentraton Indces. ERI Scentfc Beta Whte Paper Seres, Hou, K., C. Xue, and L. Zhang. A Comparson of New Factor Models. Workng paper, Oho State Unversty, 2015a.. Dgestng Anomales: An Investment Approach. Revew of Fnancal Studes, Vol. 28, No. 3 (2015b), pp Jegadeesh, N., and S. Ttman. Returns to Buyng Wnners and Sellng Losers: Implcatons for Stock Market Effcency. Journal of Fnance, 48 (1993), pp Mallard, S., T. Roncall, and J. Teletche. The Propertes of Equally Weghted Rsk Contrbuton Portfolos. The Journal of Portfolo Management, Vol. 36, No. 4 (2010), pp Merton, R. On Estmatng the Expected Return on the Market: An Exploratory Investgaton. Journal of Fnancal Economcs, Vol. 8, No. 4 (1980), pp Novy-Marx, R. The Other Sde of Value: The Gross Proftablty Premum. Journal of Fnancal Economcs, Vol. 108, No. 1 (2013), pp Plyakha, Y., R. Uppal, and G. Vlkov, Equal or Value Weghtng? Implcatons for Asset-Prcng Tests. Workng paper, SSRN, To order reprnts of ths artcle, please contact Dewey Palmer at dpalmer@journals.com or DIVERSIFIED OR CONCENTRATED FACTOR TILTS? WINTER 2016