Size Matters, if You Control Your Junk

Transcription

1 Size Maers, if You Conrol Your Junk CLIFF ASNESS, ANDREA FRAZZINI, RONEN ISRAEL, TOBIAS MOSKOWITZ, AND LASSE H. PEDERSEN Preliminary and incomplee version Firs draf: January 2015 *No for quoaion wihou permission Absrac The size premium has been challenged along many frons: i has a weak hisorical record, varies significanly over ime, in paricular weakening afer is discovery in he early 1980s, is concenraed among microcap socks, predominanly resides in January, is no presen for measures of size ha do no rely on marke prices, is weak inernaionally, and is subsumed by proxies for illiquidiy. We find, however, ha hese challenges are dismanled when conrolling for he qualiy, or he inverse junk, of a firm. A significan size premium emerges, which is sable hrough ime, robus o he specificaion, more consisen across seasons and markes, no concenraed in microcaps, robus o non-price based measures of size, and no capured by an illiquidiy premium. Conrolling for qualiy/junk also explains ineracions beween size and oher reurn characerisics such as value and momenum. Asness is Managing Principal a AQR Capial Managemen, Two Greenwich Plaza, Greenwich, CT 06830, cliff.asness@aqr.com. Frazzini is a AQR Capial Managemen, Two Greenwich Plaza, Greenwich, CT 06830, e- mail: andrea.frazzini@aqr.com. Israel is a AQR Capial Managemen, Two Greenwich Plaza, Greenwich, CT 06830, ronen.israel@aqr.com. Moskowiz is a he Booh School of Business, Universiy of Chicago, NBER, and AQR Capial, obias.moskowiz@chicagobooh.edu. Pedersen is a he Copenhagen School of Business, NYU, CEPR, NBER, and AQR Capial, lhp001@gmail.com. We hank Jacques Friedman, Ani Ilmanen, Bryan Kelly, John Liew, Sco Richardson, Laura Serban, and Eric Wu for helpful commens. We also hank Xiao Qiao, Kaushik Vasuvedan, and Alex Benne for ousanding research assisance. Moskowiz hanks he Cener for Research in Securiy Prices for financial suppor. The views expressed here are hose of he auhors and no necessarily hose of AQR Capial or is employees.

2 The finding ha size is relaed o expeced reurns daes back a leas o Banz (1981), who found ha small socks in he U.S. (hose wih lower marke capializaions) have higher average reurns han large socks, a relaion which is no accouned for by marke bea. The relaion beween size and reurns is imporan for several reasons. Firs, he size anomaly has become one of he focal poins for discussions of marke efficiency. Second, he size facor has become one of he saples of curren asse pricing models used in he lieraure (e.g., Fama and French (1993, 2014)). Third, he size premium implies ha small firms face larger coss of capial han large firms, wih imporan implicaions for corporae finance, incenives o merge and form conglomeraes, and broader indusry dynamics. Fourh, he size effec has had a large impac on invesmen pracice, including spawning an enire caegory of invesmen funds, giving rise o indices, and serving as a cornersone for muual fund classificaion. Given he imporance of he size effec, i has naurally come under heavy scruiny. Considering a long sample of U.S. socks and a broad sample of global socks, we confirm he common criicisms of he sandard size facor: a weak hisorical record in he U.S. and even weaker record inernaionally makes he size effec marginally significan a bes, long periods of poor performance, concenraion in exreme, difficul o inves in microcap socks, concenraion of reurns in January, absen for measures of size ha do no rely on marke prices, and subsumed by proxies for illiquidiy. 1 However, we find ha measures of size sudied by he lieraure load srongly and consisenly negaively on a large variey of qualiy facors. A a broad level, qualiy is a characerisic or se of characerisics of a securiy ha invesors are willing o pay a high price for, all else equal. Asness, Frazzini, and Pedersen (2014), using he Gordon growh model, illusrae various dimensions of qualiy ha can be measured in a number of ways profiabiliy, profi growh, low risk in erms of reurn-based measures and sabiliy of earnings, and high payou and/or conservaive invesmen policy. We find a srong and robus size effec when conrolling for a firm s qualiy or is inverse junk and we find ha he resuls are very consisen across a variey of measures. Conrolling for qualiy/junk reconciles many of he empirical irregulariies associaed wih he size premium ha have been documened in he lieraure and resurrecs a larger and more robus size effec in he daa. To undersand his, noe ha large firms end o be high qualiy firms on each of he above dimensions, while small firms end o be junky (i.e., have he opposie characerisics). Given ha high qualiy socks end o ouperform junk socks in general, including when comparing 1 Similar criicisms are leveled by he praciioner communiy, for example in Hsu and Kalesnik (2014) and Kalesnik and Beck (2014). 1

3 socks of similar size (Asness, Frazzini, and Pedersen (2014), Fama and French (2014)), his means ha he size effec is fighing a headwind due o he low qualiy of small socks. Said differenly, small qualiy socks ouperform large qualiy socks and small junk socks ouperform large junk socks, bu he sandard size effec suffers from a size-qualiy composiion effec. We begin by oulining he challenges o he size effec in more deail. Firs, many papers find ha he size effec is simply no very significan, producing only a small abnormal reurn and Sharpe raio, wih marginal saisical significance. Second, ohers have argued ha he size effec has disappeared since he early 1980s when i was originally discovered and published (parly conribuing o is overall weak effec). Dichev (1998), Chan, Karceski, and Lakonishok (2000), Horowiz, Loughran, and Savin (2000), Amihud (2002), and Van Dijk (2011) find ha small firms do no ouperform big firms during he 1980s and 1990s, rendering he small firm premium obsolee. Schwer (2003) suggess ha he small-firm anomaly disappeared shorly afer he iniial publicaion of he papers ha discovered i and coinciding wih an explosion of small cap-based funds and indices. Gompers and Merick (2001) argue ha insiuional invesors demand for large socks in he 1980s and 1990s increased he prices of large companies relaive o small companies ha accouns for a large par of he size premium s disappearance over his period. More recenly, Israel and Moskowiz (2013), McLean and Poniff (2013), and Chordia, Subrahmanyam, and Tong (2014) examine he aenuaion of a hos of anomalies, including size, following original publicaion, declines in rading coss, and increases in acive money managemen. Collecively, he resuls indicae a decrease in he reurns o size, hough he evidence of reducion is saisically weak. Third, he size effec appears o be concenraed among only he smalles, microcap socks. Horowiz, Loughran, and Savin (2000) find ha removing socks wih less han $5 million in marke cap causes he small firm effec o vanish. Crain (2011) and Bryan (2014) find ha he small sock effec is concenraed among he smalles 5% of firms. Since microcap socks of his size are ypically highly illiquid, researchers have quesioned he efficacy of size-based sraegies ne of rading coss. Fourh, mos of he reurns relaed o size seem o occur in January, paricularly he firs few rading days of he year, and are largely absen he res of he year (Reinganum (1981), Roll (1981), and Keim (1983)). Gu (2003) and Easerday, Sen, and Sephan (2009) also find ha he January effec has declined over ime, coinciding wih he decline in he small firm premium, as does Van Dijk (2011) in a review of he size lieraure. Reurns coming mosly from January are no damning, bu are puzzling, as mos of our asse pricing heory would imply a more even monhly disribuion 2

4 of average reurns. Hence, i raises he quesion of wha drives he size effec and wheher i is simply a manifesaion of insiuional and liquidiy fricions heighened a year-end. Fifh, following he original argumen of Ball (1978), Berk (1995a) argues ha because size is ypically measured by marke capializaion (price imes shares ousanding), which conains marke prices, any misspecificaion in he asse pricing model is likely o show up in a cross-secional relaion beween size and reurns. Consisen wih his argumen, Berk (1995b, 1997) shows ha using non-price based measures of size does no yield a relaion beween size and average reurns. Sixh, a hos of papers argue and show ha size may jus be a proxy for a liquidiy effec. Measures of liquidiy suggesed by Brennan and Subrahmanyam (1996), Amihud (2002), Hou and Moskowiz (2005), Sadka (2006), and Ibboson, Chen, Kim, and Hu (2013) and measures of liquidiy risk (he covariance wih changes in liquidiy), such as hose of Pasor and Sambaugh (2003) and Acharya and Pedersen (2005), seem o capure he reurns o size. Crain (2011) summarizes he evidence on size and liquidiy. Sevenh, ohers (e.g., Crain (2011) and Bryan (2014)) sugges ha he size anomaly is weak and no very robus in inernaional equiy markes, and hence he size effec may possibly be he resul of daa mining. These seven dauning challenges o he size effec, however, can be largely, if no fully, explained by conrolling for qualiy. In paricular, he performance of he lowes qualiy small socks explains why he size effec appears weak, is inconsisency over ime, is concenraion among he mos exreme small socks, he poor performance of non-price based measures of size, is seasonal variaion, in paricular January, and is variaion across indusries and oher inernaional markes. Junky small socks also conribue significanly o size s relaion o illiquidiy, parly explaining why illiquidiy seems o explain size s reurns. Conrolling for qualiy/junk, he size premium emerges as a much larger, more sable and more robus reurn premium. A simple way o conrol for qualiy is o accoun for he co-variaion of a sock s reurns wih he Qualiy-Minus-Junk (QMJ) facor proposed by Asness, Frazzini, and Pedersen (2014), or any of is sub-componens based on profiabiliy, profi growh, safey, and payou. Conrolling for qualiy (QMJ), we find a large and significan size premium, which is sable across ime, measures of size, seasons, indusries, and inernaional markes. Conrolling for QMJ and various versions of qualiy/junk no only resusciaes he overall size effec, i more han doubles he average performance of he size facor and is significance, resurrecs he size effec in he 1980s and 1990s where i was oherwise conspicuously absen, resores a monoonic relaion beween he size of a firm and is average reurns (so he size effec is no longer concenraed among he inies firms), 3

5 discovers ha non-price-based size measures perform jus as well as marke-capializaion-based porfolios conrary o Berk s (1995b) finding, revives he reurns o size ouside of January while simulaneously diminishes he reurns o size in January, recovers a more robus size effec in almos wo dozen oher inernaional equiy markes, and reduces size s exposure o boh liquidiy levels and liquidiy risk across several measures. 2 Socks wih very poor qualiy (i.e., junk ) are ypically very small, have low average reurns, and are ypically disressed and illiquid securiies. These characerisics drive he srong negaive relaion beween size and qualiy and he reurns of hese junk socks chiefly explain he sporadic performance of he size premium and he challenges ha have been hurled a i. In summary, conrolling for junk produces a robus size premium ha is presen in all ime periods, wih no reliably deecable differences across ime from July 1957 o December 2012, in all monhs of he year, across all indusries, across nearly wo dozen inernaional equiy markes, and across five differen measures of size no based on marke prices. Afer reviving he size premium, we urn our aenion o he ineracions beween size and oher anomalies found in he lieraure, shedding new ligh on he relaion beween size and oher crosssecional predicors of reurns such as value and momenum. We find ha accouning for junk explains why small growh socks underperform and small value socks ouperform he Fama and French (1993, 2014) models. The relaion beween size and qualiy/junk also has impor for heory, presening anoher challenge for asse pricing models. For example, he reurns o size are much sronger and more sable afer conrolling for junk. This makes risk-based explanaions for he size effec more challenging no only because of is very high Sharpe raio (e.g., Hansen and Jagannahan (1997)), bu also because he riskies small socks he small junk socks are no he securiies ha drive a significan posiive size premium, as a risk sory implies. Raher, i is he low-volailiy, high-qualiy socks ha seem o drive he high expeced reurns. These resuls are difficul o reconcile in a riskbased framework and sugges ha high qualiy small socks may be underpriced, hough, as always, here remains he possibiliy of new risk-based explanaions we have no ye considered. In addiion, 2 Our resuls may be relaed o Hou and Van Dijk (2013), who examine wha hey call profiabiliy shocks o firms and find ha in he 1980s and 1990s small firms experience negaive profiabiliy shocks ha help explain ex pos heir dismal performance during his period. However, while Hou and Van Dijk (2013) seek o explain he ex pos performance of size during his ime period, our sudy seeks o find ex ane measures of qualiy, across muliple measures of qualiy in addiion o profiabiliy, ha have power o explain expeced reurns. We find ha ex ane measures of a variey of qualiy merics can explain variaion in he expeced reurns o size reurns across ime, seasons, and markes. 4

6 he fac ha non-price based measures of size work a leas as well as marke-based measures, suggess ha size is no picking up an omied risk facor as suggesed by Berk (1995a). Finally, while small firms are cerainly less liquid on average, we find ha various liquidiy proxies offered in he lieraure do no fully explain he size effecs we find when conrolling for qualiy/junk. Conrolling for junk, which seems o be relaed o illiquidiy, we find ha he subsanial remaining size premium is less sensiive o liquidiy or liquidiy risk and ye delivers an even bigger reurn premium no explained by oher facors. This implies eiher ha he size premium conrolling for junk is no as sensiive o liquidiy premia, or ha beer and differen liquidiy proxies are needed o capure he added reurns we find for size once conrolling for junk. I also implies ha a small-qualiy porfolio is likely lower cos and higher capaciy o implemen han a small porfolio ha ignores qualiy and herefore loads on illiquid junk, reducing any micro-srucure and pracical objecions o he size resuls. Again he ask of heory is made more difficul in his regard. These resuls renew he size anomaly, puing i on more equal fooing wih oher anomalies such as value and momenum in erms of is efficacy and robusness. Moreover, he ineracion beween size, qualiy/junk, and oher cross-secional predicors of reurns may shed ligh on oher anomalies. Asse pricing heory and subsequen empirical work may consider why size and junk are relaed and, in paricular, why hey co-vary so srongly wih each oher. The paper proceeds as follows. Secion I briefly describes he daa and reviews he evidence on he size effec, highlighing he seven challenges o he size premium idenified in he lieraure. Secion II shows ha nearly all of hese challenges are resolved afer conrolling for a firm s qualiy/junk. Secion III analyzes ineracions beween size and growh and value and momenum afer conrolling for qualiy/junk. Secion IV concludes. I. Daa and Preliminary Analysis: Reexamining he Size Anomaly We deail he daa used in his sudy and reexamine he evidence of he size effec by replicaing some of he challenges idenified in he lieraure using an updaed sample. A. Daa We examine long-shor equiy syle porfolios commonly used in he lieraure peraining o size. For U.S. equiies, we obain sock reurns and accouning daa from he union of he CRSP apes and he XpressFeed Global daabase. Our U.S. equiy daa include all available common socks on he merged CRSP/Compusa daa beween July 1926 and December We include delising reurns when available in CRSP. 5

7 Size. For size porfolios, we primarily use Fama and French s SMB, (Small minus Big), facor and a se of value-weighed decile porfolios based on marke capializaion sors, obained from Ken French s webpage. The decile porfolios are formed by ranking socks every June by heir marke capializaion (price imes shares ousanding) and forming deciles based on NYSE breakpoins, where he value-weighed average reurn of each decile is compued monhly from July o June of he following year. The size facor, SMB, is he average reurn on hree small porfolios minus he average reurn on hree big porfolios formed by ranking socks independenly by heir marke cap and heir book-o-marke equiy raio (BE/ME) every June and forming wo size porfolios using he NYSE median size and hree book-o-marke porfolios using 30, 40, and 30 percen breakpoins, respecively. The inersecion of hese groups forms six size and BE/ME porfolios spli by small and large (e.g., Small value, small middle, small growh and large value, large middle, and large growh) whose value-weighed monhly reurns are compued from July o June of he following year. The SMB facor is hen simply he equal-weighed average of he hree small porfolios minus he equalweighed average of he hree large porfolios. Fama and French facors. In addiion o SMB, he value facor, HML or High minus Low, is formed from he equal-weighed average reurn of he wo value porfolios minus he wo growh porfolios, HML = ½ (Small Value + Big Value) - ½ (Small Growh + Big Growh). Fama and French (1993) also add he marke facor, RMRF, which is he value-weighed index of all CRSPlised securiies minus he one-monh Treasury bill rae. Momenum facor. Ken French s websie also provides a momenum facor, which is a longshor porfolio consruced in a similar manner, where six value-weighed porfolios formed on size and prior reurns (he cumulaive reurn in local currency from monhs -12 o -2) are used. The porfolios are he inersecions of wo porfolios formed on size and hree porfolios formed on prior reurns. The momenum facor, UMD or Up minus Down, is consruced as UMD = ½ (Small Up + Big Up) - ½ (Small Down + Big Down). Shor-erm reversal facor. Ken French s websie also provides a shor-erm reversal facor, STREV, which is formed similar o he momenum facor excep using pas reurns from jus he mos recen monh -1 insead of -12 o -2. Non-price based size porfolios. We also form SMB and value-weighed size decile porfolios using non-price based measures of size, as suggesed by Berk (1995b, 1997), in lieu of a firm s marke capializaion o rank socks. Specifically, using he same mehodology as for SMB above, we form five ses of non-price size porfolios based on book value of asses, book value of equiy, sales, propery, plan, and equipmen (PP&E), and number of employees. 6

8 Qualiy minus junk. We form a qualiy minus junk facor, QMJ, following Asness, Frazzini, and Pedersen (2014), which is formed by ranking socks on measures of qualiy/junk based on heir profiabiliy, growh, safey, and payou. The moivaion for heir measures comes from he Gordon growh model, where dividing boh sides of P = D/(r-g) wih he book value and rearranging erms, yields profiabiliy and payou in he numeraor and required reurn and growh in he denominaor. Hence, he componens profiabiliy and payou menioned above approximae he numeraor, while safey (measured by reurn-based measures) proxies for he required reurn, r, and growh is designed o capure, g. The deails of each of hese measures are provided in Asness, Frazzini, and Pedersen (2014), and we use several variaions of heir qualiy and junk measures, as well as relaed measures of invesmen and profiabiliy from Fama and French (2014), and some measures no used by eiher Asness, Frazzini, and Pedersen (2014) or Fama and French (2014), for robusness. Qualiy or junk is measured from a combinaion of hese measures and QMJ is formed in a manner similar o he mehodology used by Fama and French (1993) where socks are ranked by size and qualiy/junk measures independenly ino wo size and hree qualiy/junk groups and he inersecion of he groups forms six porfolios where QMJ is equally long he wo qualiy porfolios and shor he wo junk porfolios. 3 Inra-indusry porfolios. We also form SMB porfolios wihin each of 30 indusries used by Fama and French (1997) and available on Ken French s websie, where we consruc SMB in a similar fashion wihin each indusry so ha we obain 30 SMB indusry-neural porfolios. Liquidiy. We form decile porfolios based on liquidiy levels using monhly urnover (number of shares raded divided by shares ousanding) following Ibboson, Chen, Kim, and Hu (2013) and bid-ask spread as a percenage of share price following Amihud and Mendelson (1986) and use Pasor and Sambaugh (2003) s liquidiy risk facor-mimicking porfolio, available from Rober Sambaugh s webpage. Inernaional daa. We form many of he above porfolios and facors in each of 23 oher developed equiy markes following he same mehodology. Our inernaional equiy daa include all available common socks on he XpressFeed Global daabase for 23 developed markes from January 1983 o December We assign individual socks o he corresponding marke based on he locaion of he primary exchange. For inernaional companies wih securiies raded in muliple markes, we use he primary rading vehicle idenified by XpressFeed. 3 The deails on he individual variables used o measure each componen of qualiy and heir consrucion are provided in Asness, Frazzini, and Pedersen (2014). This daa is available a hps:// 7

9 Our global porfolio consrucion closely follows Fama and French (1996 and 2012) and Asness and Frazzini (2012). The porfolios are counry neural in he sense ha we form long-shor porfolios wihin each counry and hen compue a global facor by weighing each counry s long-shor porfolio by he counry s oal (lagged) marke capializaion. The marke facor, RMRF, is he value-weighed reurn on all available socks across all markes minus he one-monh U.S. Treasury bill rae. The size and value facors are consruced using six value-weighed porfolios formed on size and book-o-marke. A he end of June of year, socks are assigned o wo size-sored porfolios based on heir marke capializaion. While for he U.S., he size breakpoin is he median NYSE marke equiy, for he inernaional sample he size breakpoin is he 80h percenile by counry in order o roughly mach he U.S. size porfolios. Since some counries have a small cross secion of socks in he early years of our sample, we also use condiional sors ha firs sor on size, hen on book-o-price, in order o ensure we have enough securiies in each porfolio (whereas he U.S. sors are independen). Porfolios are value-weighed and reconsruced every monh and rebalanced every calendar monh o mainain value weighs. 4 In order o be included in any of our ess we require a firm o have a non-negaive book value and non-missing price a fiscal yearend as well as in June of calendar year. All porfolio reurns are in $US and excess reurns are relaive o he one-monh U.S. Treasury bill rae. B. Reexamining he evidence on size alone Table 1 replicaes he evidence on he size effec from he lieraure using he full sample including recen daa. The firs hree columns repor resuls for SMB and he second hree columns for he difference in reurns beween deciles 1 and 10 (a more exreme difference in size han SMB and also unadjused hrough bivariae sors for book-o-price like SMB).The firs row repors he mean, sandard deviaion, and -saisic of he size premium over he full sample period from July 1926 o December SMB yields a 23 basis poin premium per monh ha is saisically significan a he 5% level (-saisic = 2.27). The decile spread reurns also yield a posiive reurn of 55 basis poins per monh, which is also significan. This firs resul highlighs ha he size effec is 4 To obain shareholders equiy we use Sockholders Equiy (SEQ), bu if no available, we use he sum of Common Equiy (CEQ) and Preferred Sock (PSTK). If boh SEQ and CEQ are unavailable, we will proxy shareholders equiy by Toal Asses (TA) minus he sum of Toal Liabiliies (LT) and Minoriy Ineres (MIB). To obain book equiy, we subrac from shareholders equiy he preferred sock value (PSTKRV, PSTKL, or PSTK depending on availabiliy). Finally, o compue book value per share (B) we divide by common shares ousanding (CSHPRI). If CSHPRI is missing, we compue company-level oal shares ousanding by summing issue-level shares (CSHOI) a fiscal yearend for securiies wih an earnings paricipaion flag in he securiy pricing file. 8

10 relaively weak compared o oher anomalies such as value and momenum ha each exhibi much sronger and more reliable reurn premia. 5 The nex wo rows repor he reurns o size in he monhs of January and February hrough December, separaely. The reurns o SMB are enormous in January a 2.3% per monh and he 1-10 spread in size decile reurns is even larger a 6.8% in January. However, February hrough December SMB delivers only 4 basis poins and he 1-10 porfolio spread -1 basis poin, boh of which are saisically and economically no differen from zero. Hence, wha reliable posiive premium exiss for size appears o solely reside in January and is absen he res of he year. The nex wo rows repor resuls over he original sample period sudied by Banz (1981) from 1936 o 1975 and he ou-of-sample period from Banz (1981), peraining o 1926 o 1935 and 1976 o As Table 1 indicaes, SMB is insignifican over Banz s original sample period and he 1-10 decile spread is marginally significan (-saisic of 1.82), hough he mean reurns are similar o he full period resuls. The resuls from Banz (1981) over he same ime period for similar decile porfolios are sronger han wha we find here, which is likely due o daa errors being fixed by CRSP afer his paper was published. 6 The ou-of-sample evidence from Banz (1981) is acually a bi sronger for SMB, bu weaker for he decile spread reurns. Overall, he original size effec sudied by Banz (1981) is weaker han originally found, consisen wih he findings of Israel and Moskowiz (2013). However, he size effec has experienced significan variaion over ime, including over relaively long-erm periods. The nex four rows of Table 1 repor resuls over four sample periods: 1) he full period over which qualiy/junk measures are available, he QMJ period from July 1957 o December 2012; 2) he period from July 1957 o December 1979 shorly before he discovery and publicaion of he size effec, which we erm he Golden age because he lae 1970s was when mos researchers were looking a he size effec, when is performance was highes; 3) he period from January 1980 o December 1999, which we call he Embarrassmen period because his is when he size effec appears o have vanished promply afer being discovered and published; and 4) he period from January 2000 o December 2012, which we erm he Resurrecion period as he size effec appears o be revialized during his period. The summary saisics in Table 1 highligh hese resuls. 5 For example, Harvey, Liu, and Zhu (2014) noe ha -saisics greaer han 3.0 are likely required o pass he 5% significance es in he presence of he daa mining ha has aken place by researchers pouring over he same reurn series. 6 Over ime CRSP has fixed many daa errors, which are more common among he smalles firms, and hese may have conribued posiively o he reurns of size. One such error was a delising bias as noed by Shumway (1997), who showed ha many sudies focusing on small socks had inflaed reurns due o misreamen of he delising reurns o hese socks. 9

11 Indeed, consisen wih he lieraure, he size effec seems o have disappeared in he 1980s and 1990s following is discovery, bu also appears o have made a comeback in he las hireen years. Since our primary sample, which conains qualiy measures, is from July 1957 o December 2012, we also repor he reurns in January only and in he monhs February o December over his period. Consisen wih he longer sample resuls, he enire size premium seems o be born in he monh of January only and is conspicuously absen he res of he year, and like before, he more exreme size be from he 1-10 porfolio spreads exaggeraes he January size effec. These las resuls illusrae perhaps he wo bigges challenges o he robusness and inerpreaion of he size effec, where all of he reurns o size seem o be coming from he mos exreme small socks in January. Excluding he very smalles socks in January, here is lile evidence of a size premium. The las hree rows of Table 1 repor summary saisics for hree oher sample periods we will examine ha perain o daa availabiliy on oher facors. The resuls over hese subsample periods, which are parially covered by he oher sample periods above, are consisen wih our previous findings and no unusual over any of hese subsamples. Overall, here is a weak size effec, whose variaion over ime and across seasons is subsanial, as documened in he lieraure. We urn our aenion o hese empirical challenges, as well as four ohers, hrough he lens of qualiy/junk in he nex secion. II. The Size Effec, Conrolling for Junk: Addressing Seven Challenges In his secion we analyze he seven challenges ha have been propelled a he size premium, afer accouning for he qualiy/junk of he sock. 1. The Size effec is no very significan Table 2 repors ime series regression resuls of SMB on a variey of facors. The firs row of he firs four row sanza of Panel A of Table 2 repors resuls of SMB regressed on he marke porfolio, RMRF, over he July 1957 o December 2012 ime period, which is he full sample period over which qualiy/junk measures are available. The inercep or alpha from he regression is 12 basis poins (bps) per monh wih a -saisic of 1.12, which is insignificanly differen from zero, suggesing ha he CAPM explains he reurns o SMB prey well. The nex row adds he lagged reurn on he marke from he previous monh in order o capure delayed price responses of socks, paricularly small socks, o marke-wide news (following he resuls and implicaions of Lo and MacKinlay (1988), Hou and Moskowiz (2005), and in he spiri of Asness, Krail, and Liew (2001) o accoun for non-synchronous price responses due o liquidiy differences and lead-lag effecs among 10

12 socks). SMB has a significanly posiive coefficien on he lagged marke reurn, which furher pushes down he alpha o 7 bps. The hird row repors resuls ha add HML and UMD o capure value and momenum exposure. The alpha now is 14 bps wih a -saisic of In he presence of he marke and he oher Fama and French facors (excluding SMB of course), here appears o be no reliable size premium. Finally, he fourh row adds he QMJ facor o he regression. Recall, QMJ is a composie longshor porfolio giving equal weigh o long profiable, growing, safe, and high payou companies and shor unprofiable, sagnan, risky, and low payou firms. SMB loads very significanly and negaively on QMJ, driving SMB s alpha from 14 o 49 bps per monh ha is almos five sandard errors from zero (-sa = 4.89). The addiion of QMJ no only raises significanly he average reurn o size, bu also increases he precision of he SMB premium as well since QMJ explains a subsanial fracion of he variaion in SMB s reurns. The R-square rises from 15 o 37 percen wih he inclusion of his one addiional facor. Figure 1 shows he impac of conrolling for qualiy/junk on he size effec by examining SMB hedged wih respec o he marke, is lagged value, HML and UMD facors and QMJ. Figure 1 plos he cumulaive sum of reurns over ime of SMB hedged wih he marke, is lagged value, HML, UMD, and QMJ, and SMB unhedged. The plo uses he full sample esimaes of he beas from July 1957 o December 2012 o esimae he hedged reurns o SMB. 7 As Figure 1 shows, hedging SMB for exposure o junk significanly improves reurns. 8 For robusness, Figure 2 repors resuls across 30 differen indusries. We form SMB porfolios (long he smalles half of firms and shor he larges half of firms) wihin each of 30 indusries available from Ken French s daa library. We hen examine wheher he improvemen in SMB afer conrolling for qualiy/junk is similar wihin each indusry. Though no 30 compleely independen ess, his provides 30 differen samples of firms from which we can es he robusness of he resuls. Specifically, we compue he alpha of SMB wihin each indusry relaive o he marke, is lagged value, HML and UMD. We hen repea his compuaion using he same facors plus QMJ and compare he difference wihin each indusry. The firs plo in Figure 2 shows he improvemen in SMB alpha afer conrolling for QMJ for each of he 30 indusries. The resuls are remarkably consisen. For every single indusry, here is posiive improvemen in SMB s reurns afer 7 We have also used he pas rolling 120-monhs of reurns o esimae he regression models and beas in order o calculae he hedged reurn, represening an implemenable ou-of-sample hedge porfolio, and found similar hough slighly weaker resuls (presumably due o he noise in esimaing he hedge). 8 Comparing he hedged reurns o SMB using QMJ versus hose jus using he marke, is lagged value, HML and UMD facors yields very similar resuls, oo, in ha he key hedge variable is QMJ ha resurrecs size. 11

13 conrolling for qualiy/junk, and for mos indusries he improvemen is significan (wih significance, of course, harder o achieve in a much smaller sample of firms wihin a single indusry). The second figure plos he beas of each SMB porfolio on QMJ, which are all negaive and are he mirror image of he improvemen in alphas in he plo above i. These resuls indicae ha he relaion beween size and qualiy/junk is very robus. No a single indusry fails o find a srong negaive relaion beween size and qualiy, and as a resul, he size premium is consisenly alive and well wihin every single indusry. QMJ makes shor work of his firs, and perhaps mos imporan, challenge o he size effec, as i simulaneously resurrecs he reurn premium o size as well as explains much of is variaion, ransforming i from a small and insignifican effec o a large and saisically srong one, doing so consisenly across every indusry. 2. Variaion in he size premium over ime Figure 1 anicipaes he resuls in his secion as casual perusal shows a far more consisen size premium when hedged for QMJ exposure. More formally, he remaining sanzas of rows of Panel A of Table 2 repea he regressions above over he hree subsample periods we defined earlier golden age, embarrassmen, and resurrecion corresponding o he periods over which he size premium varies subsanially. During he golden age from July 1957 o December 1979 here is a more posiive size premium of abou 25 bps when adjusing for he marke, is lagged value, HML and UMD (hough he -saisic is only 1.52). This is no surprising since we defined he golden age based on SMB s higher posiive reurns ex pos. Adding QMJ, however, makes he age more golden as i more han doubles he alpha o 57 bps wih a -sa of Looking a he embarrassmen period, from 1980 o 1999, where we know SMB did no do well, we see consisenly negaive alphas, unil we add QMJ. Adding QMJ resores SMB s posiive alpha over his period o a robus and sizeable 50 bps (-sa of 3.06), which is he same magniude as SMB s alpha over he golden age period. Hence, conrolling for qualiy/junk fully explains he very differen performance of he size premium over hese wo seemingly very differen periods. Despie SMB performing reasonably well over he golden age and performing very poorly over he embarrassmen period, once we conrol for QMJ, he performance of SMB over boh periods is exacly he same. In oher words, i s he performance of QMJ (and, as we will see shorly, he performance of junk in paricular) ha drives he apparen variaion over ime in SMB s performance. 12

14 Finally, looking a he resurrecion period, we see again posiive SMB alphas wih respec o he marke, is lagged value, HML and UMD facors, bu even larger alphas once we conrol for QMJ. Like he oher wo sub periods, he alpha of SMB in he presence of QMJ is of similar magniude and highly significan. Hence, accouning for junk, he premium for size is robus, posiive, and sable, exhibiing far less variaion hrough ime. 9 The QMJ facor consruced by Asness, Frazzini, and Pedersen (2014) is a composie of many facors and measures designed o capure qualiy/junk by looking a variables ha proxy for a variey of aribues, including profiabiliy, safey, payou, and growh. In heir paper, Asness, Frazzini, and Pedersen (2014) show ha various combinaions of heir measures as well as individual measures yield very similar resuls. We, oo, show ha various measures of qualiy/junk give similar resuls on he efficacy of he size effec. Panel B of Table 2 repeas he full period regressions for SMB using each of he various four subcomponens of QMJ in place of he full QMJ facor. Despie he vasly differen measures, in each case he loading on qualiy is significanly negaive and SMB s alpha is significanly posiive and more sable. For example, conrolling for profiabiliy insead of QMJ, SMB s alpha is 42 bps, a 30 bps improvemen from he base case of conrolling for he marke, is lagged value, HML and UMD and almos four sandard errors from zero. Conrolling for safey or payou as measures of qualiy yields very similar numbers. The weakes qualiy measure is growh (consisen wih Asness, Frazzini, and Pedersen s (2014) findings as well), ye even here here is a marginally significan 20 bps size premium when conrolling for his relaively weak measure of qualiy, and again SMB loads significanly negaively on he growh componen. 10 These resuls are very consisen and indicae he relaion beween size and qualiy/junk is quie robus across differen measures. One concern wih QMJ is ha i is consruced using a variey of measures, some of which individually have been shown o predic reurns, and hence may overfi he hisorical reurn daa (a form of collecive daa mining from he lieraure). Using he QMJ subcomponens separaely parly addresses his concern, bu as a furher robusness es, we also employ some relaed facors from oher work and by oher auhors. We sar by looking a a single measure of safey from Frazzini and 9 Oher facors do exhibi variaion over ime in heir relaion o SMB. One noable example is he lagged reurn on he marke, which is significan in he firs wo sub periods bu insignifican in he mos recen sub period. This is consisen wih markes becoming much more liquid over ime, resuling in less of a lead-lag effec for small socks and hence less of a delayed reacion o he marke for small firms. 10 Growh provides he weakes resuls, where he SMB alpha is no saisically significan. However, growh is he poores measure of qualiy/junk according o Asness, Frazzini, and Pedersen (2014), and ye i sill increases SMB s alpha relaive o omiing i as a facor and he coefficien on qualiy as measured by growh is sill significanly negaive. Given ha hree ou of four subcomponens deliver significanly posiive alphas and growh produces alpha improvemen wih he same sign and direcion, he overall resuls across differen measures are quie robus. 13

15 Pedersen (2013) sudy of being agains bea (BAB). A version of BAB is one par of he safey composie employed in consrucing QMJ, bu here we break i ou separaely because unlike he oher measures in QMJ, BAB is available going back much furher o January 1931, providing an ou of sample es. The firs row of Panel C of Table 2 employs he being agains bea or BAB zero-cos facor, which is a dollar-neural sraegy of going long low bea and shor high bea socks from Frazzini and Pedersen (2013), in place of QMJ over he same sample period as QMJ from July 1957 o December As he able indicaes, his measure of safey is also able o capure some of he qualiy/junk specrum as he alpha of SMB is pushed upward o 25 basis poins (-saisic of 2.42), and here is a srong negaive loading on BAB of wih a -saisic of Comparing hese resuls o only adjusing for he Fama-French facors (row 3 a he op of Table 2 Panel A, where he alpha is only 14 bps wih a -sa of 1.23) he SMB alpha nearly doubles and is now reliably differen from zero. The nex wo rows of Panel C of Table 2 repor he same regression resuls over he ou-of-sample period from January 1931 o June The SMB alpha on jus he marke, is lagged value, HML and UMD facors is only 6 bps over his period, bu increases o 16 bps wih he inclusion of BAB as a qualiy meric in he regression. Alhough he -sa on he alpha is only 0.90 over his shorer sample period, here is sill an improvemen from adding a measure of qualiy o he model, even a simple one such as BAB. The negaive loading of SMB on BAB is wih a -sa of -4.99, indicaing ha even his very simple measure of qualiy is srongly and reliably negaively relaed o size. The nex wo rows of Panel C repor he regression resuls over he full period for which BAB is available January 1931 o December 2012, where SMB s alpha is an insignifican 7 bps relaive o he marke, is lagged value, HML and UMD facors, bu rises o a significan 23 bps per monh (sa of 2.50) wih he inclusion of BAB as a measure of qualiy. The las wo rows of Table 2 Panel C use a measure of qualiy or junk ha is no used among any of he subcomponens of QMJ, due o limied daa availabiliy. We use deb raings on firms o creae a credi spread ha should be relaed o oher measures of qualiy, bu credi raings are only available for enough firms beginning in July Specifically, we use he equiy reurn difference beween firms wih A-raed or higher deb minus he equiy reurns of firms wih C-raed or below deb, where he marke capializaion-weighed average of reurns is compued for each group. We call his facor Cred, which capures he equiy reurn difference beween firms wih high crediworhy deb minus low raed deb. As he las wo rows of Panel C of Table 2 show, even over his very shor ime period, here is a robus negaive loading of SMB on his credi spread facor (-0.08 coefficien wih a -saisic of -5.73), bu he SMB alpha is only pushed up o 35 bps per monh (- 14

16 saisic of 2.12) given he small average reurns o he credi facor. Neverheless, he consisen negaive relaionship beween size and anoher, oally differen measure of qualiy, provides a nice robusness es. Finally, Panel D of Table 2 examines he Fama and French (2014) five-facor model, which conains he RMW ( robus minus weak ) profiabiliy facor and CMA ( conservaive minus aggressive ) invesmen facor which may pick up elemens of qualiy/junk as well. Indeed, profiabiliy is one measure used in QMJ s consrucion hough in a differen form, so his can be hough of as a robusness check by specificaion of he profi facor. Fama and French (2014) offer hree separae versions of heir new profiabiliy and invesmen facors from soring on combinaions of size and profiabiliy and invesmen. We show he resuls for he 2x3 versions of heir facors from Kenneh French s websie in Panel D of Table 2, bu noe ha he resuls are nearly idenical for heir 2x2 and 2x2x2x2 facor specificaions. As he firs row of Panel D of Table 2 repors, SMB has an insignifican 16 bps alpha relaive o he marke, is lagged value, and HML and UMD. As he second row indicaes, adding he wo new Fama and French (2014) profiabiliy and invesmen facors, RMW and CMA, respecively, SMB loads significanly negaively on RMW (he profiabiliy facor) and marginally negaively on CMA (he invesmen facor), which doubles is alpha o 33 bps per monh (-saisic of 2.81). These resuls are consisen wih boh of he new Fama and French (2014) facors being relaed o qualiy/junk, hough here is a much sronger relaionship for profiabiliy han invesmen. Inuiively, boh profiabiliy and invesmen are characerisics ha should differ widely among high versus low qualiy firms. In essence, he new Fama and French (2014) facors pick some of his up. The hird row of Panel D hen adds QMJ o he regression. Two ineresing hings happen: 1) he negaive coefficiens on RMW and CMA disappear, being soaked up by he very srong negaive loading on QMJ and 2) SMB s alpha rises even higher o 54 bps per monh. Hence, QMJ seems o capure he explanaory power of Fama and French s (2014) profiabiliy and invesmen facors on he size effec. The fourh row of Panel D repeas his las regression using simple BAB in place of QMJ as a qualiy measure. In his case, BAB, which SMB loads significanly negaively on, only parially capures he negaive exposure o Fama and French s (2014) profiabiliy facor RMW, consisen wih BAB being a relaed, bu noisy measure of qualiy. The nex wo rows of Panel D of Table 2 repea he regressions adding he credi facor, Cred, o he regression over he shorer sample period July 1987 o December 2012 when he credi daa is available, as anoher robusness es. Over his shorer sample period, he Fama and French (2014) profiabiliy and invesmen facors sill exhibi a negaive relaion wih SMB, hough he loading on 15

17 invesmen is no reliably differen from zero. Adding QMJ, BAB, and Cred o he regression eliminaes he negaive exposure o RMW, where each of QMJ, BAB, and Cred all have reliably negaive loadings wih respec o SMB. Overall, he resuls indicae ha oher forms of capuring he qualiy of firms, including Fama and French s (2014) profiabiliy and invesmen facors, BAB, and credi, are all negaively relaed o size and are helpful in resurrecing he size premium, where he resuls are no paricularly sensiive o any paricular measure of qualiy or junk. Finally, aking a simple equal-weighed average of hese oher four simple (no composies like from QMJ) facors RMW, CMA, BAB, and Cred, where we ake he average of whaever measures have available daa a he ime, meaning Cred is excluded prior o July 1987 in wha we call a qualiy index (QIndex), produces now very familiar resuls. SMB has a srong negaive loading on qualiy and he alpha of SMB remains large and significan a abou 39 bps per monh wih a -saisic of Adding QMJ o his regression, which conains he qualiy measures no used in he QIndex we jus consruced, adds addiional explanaory power, where boh qualiy measures (QIndex and QMJ) exhibi significan negaive loadings, he R-square increases from 0.30 o 0.40 and SMB s alpha rises from 39 o 54 bps per monh. These resuls show ha wo differen composies of qualiy ha each use separae and independen measures, deliver similar resuls and when used simulaneously, each provide addiional explanaory power in capuring he reurns o size and resoring is posiive reurn premium. The robusness of our resuls on he size effec o differen measures of qualiy should furher alleviae any daa mining concerns. Hence, he second challenge o he size effec ha i varies significanly hrough ime has been me. The variaion in he size premium over long sreches of ime is almos compleely explained by he performance of qualiy and junk. Thus, i is he reurns o qualiy and junk, and no size, ha have confounded previous resuls. 3. Is he size premium concenraed in exreme socks? Figure 3 examines he reurns o size more finely by looking across size-sored decile porfolios. From his analysis we can address anoher criicism of he size facor: wheher he size premium is concenraed in he exremes or wheher here is monooniciy in he relaionship beween size and average reurns. The op graph of Figure 3 plos he alphas of each size decile wih respec o hree facor models: 1) he marke model (RMRF), 2) he Fama and French facors RMRF, RMRF lagged a monh, HML, and UMD and 3) hese same facors augmened wih he QMJ facor, all regressions are run over he 16

18 full sample period from July 1957 o December As he figure shows, he marke-adjused alphas and alphas adjused for Fama and French facors are higher for he smalles decile of socks (decile 1) compared o he larges (decile 10), bu are oherwise prey fla across deciles 2 hrough 9 and exhibi no reliable paern (e.g., decile 3 appears o be highes, and decile 1 is lower han deciles 4 hrough 9 when adjusing for he Fama and French facors). In shor, here is no consisen relaion beween size and average reurns across he deciles in erms of marke or Fama and French-adjused alphas. This is consisen wih claims in he lieraure ha he size effec is concenraed in he exremely small, microcap socks and no nearly monoonic. However, when adding QMJ as a facor, no only is a very large difference in average reurns beween he smalles and larges size deciles observed, bu, perhaps more ineresingly, here is an almos perfec monoonic relaionship beween he size deciles and he alphas. As we move from small o big socks, he alphas seadily decline and evenually become negaive for he larges socks. Hence, conrolling for qualiy/junk resores a monoonic relaion beween size and average reurns ha is absen oherwise. The second graph in Figure 3 repeas he plo over he golden age period for size from July 1957 o December Over his sub period we know here is a significan size premium, even in he presence of he marke and he Fama and French facors. However, while a significan difference in alphas does indeed exis beween deciles 1 and 10 over his period, he relaion beween size and average reurns is closer o bu sill no nearly monoonic, even over he golden age period. The marke-adjused and Fama and French alphas are larger for smaller socks, bu are essenially he same across he firs five size deciles wih no reliable decline in alpha as size ges bigger. Likewise, larger socks exhibi lower alphas on average, bu here is also no reliable paern from deciles 6 hrough 9. Conrolling for QMJ, however, we see a srong monoonic relaionship beween size and alpha. Hence, even over he period where size worked, here is lile evidence of a igh monoonic relaion beween size and average reurns, unless we conrol for qualiy/junk. The fac ha, as we have already shown, QMJ resurrecs he size premium may in par be relaed o resoring monooniciy as well, since a larger absolue premium may reduce he influence of noise on each porfolio. Bu, i does no have o work ou his way. QMJ could have jus as easily raised he reurns on all size deciles equally and no improved monooniciy, or i could have added more o he larger deciles or o random deciles and acually reduced monooniciy. The fac ha as size increases we see proporionaely more alpha when including QMJ, suggess ha qualiy/junk exposure is indeed relaed o size in a monoonic way and conrolling for qualiy/junk resores a igh linear relaion beween size and average reurns. 17