Cndin Journl of Aiiminisrlive Sciences Revue cndienne des sciences de T dminisrion 24: 135-145(2007) Published online 13 June 2007 in Wiley Inerscience (www.inerscience.wiley.com). DOI: 10.1002/CJAS.n Refining i\/lomenum Sregies by Condiioning on Prior Long-erm Reurns: Cndin Evidence Ewiu;! imerscie>ce* Richrd Deves Peer Miu* McMser Universiy Absrc Cross-secionl reurns in Cnd re predicble using boh momenum nd reversl sregies. Synergies relized by focusing on he enire erm srucure of prior reurns led o beer predicbiliy. An enhnced index sregy hsed on hese synergies is profible mos of he ime fier conrolling for rnscion coss, lhough he degree of profibiliy chnges over ime. Simulion shows h recen profibiliy is minly ribuble o he shor-side of he momenum sregy. Copyrigh 2007 ASAC. Published by John Wiley & Sons, Ld. JEL Clssificions: G12, G14 Keywords: momenum, reversl Resume Au Cnd, les rendemens "cross-secionl".wn visibles grce ux sregies du momenum de l conversion inverse. Les synergies que Von relise en se concenrn sur oue l.srucure erme des rendemens nerieurs debouchen sur une meilleure previsibilie, Une sregie d'index melioree b.s^e sur ces synergies es g^n^rlemen renble pres le recouvremen des fris de rnscion. Mis son degre de renbilie chnge vec le emps. L simulion monre que l renbilie recene es principlemen due u crcere incomple de l sregie du momenum. Copyrigh 2007 ASAC. Published by John Wiley & Sons, Ud. Mos-clfe : noneium, coiversion iiverse There is bundi evideice h risk-djused reums re predicble by condiioiing merely oi heir lgged counerprs. Impornly, he sign o" he correlion is horizon-dependen. Jegdeesh (1990) finds h for shoreri (one-monh) inervls here is relible reversl. A similr reversl effec holds for long-erm (3-5 yer) inervls (De Bond & Thler, 1985). Sill, he firs is likely lrgely explicble by microsrucure effecs (Boudoukh. Richrdson. & Whielw. 1994) nd he second les in pr by x effecs (Klein, 2001). The inermedie-erm (3-12 monh) momenum firs documened by Jegdeesh nd Timn (1993) is he mos roubling finding, given h i cnno be explined by he hree-fcor model of Fm nd French (1993) (e.g.. *Plese ddress correspondence o: Peer Miu. DeGrooe School of Business. McMser Universiy. 1280 Min Sree Wes. Hmilon. Onrio, Cnd. L8S 4M4. Emil: mi upee@ me mser, c see Fm & French, 1996). Jegdeesh nd Timn show, for exmple, h long-shor zero-cos porfolio formed on he bsis of reums over he previous six monhs erns n verge excess reurn of 0.95%/monb over he nex six monhs. Much reserch hs been conduced o invesige boh robusness of he momenum phenomenon nd poenil refinemens. I exiss, no jus he level of he firm, bu lso he level of he indusry (Moskowiz & Grinbl. 1999) nd syle (Brberis & Shleifer, 2003). Moskowiz nd Grinbl find h indusry momenum, hough subsnil, does no subsume firm-specific momenun. While rnscion coss led o some erosion of monenum profibiliy, hey remin relible for insiuionl invesors (Korjczyk & Sdk, 2004). For prciioners seeking o genere lph here is no reson o employ univrie filers. Along hese lines. Lee nd Swminhn (2000) show h rding volume Copyrigh 2007 ASAC. Published by John Wiley & Sons. Ld. 135 24(21. 135-145
REFINING MOMENTUM STRATEGIES BY CONDITIONING ON PRIOR LONG-TERM RETURNS cn be used o enhice moneiun sregy. Griibl nd Moskowiz (2004) condiion on he erm srucure of prior reurns, finding h shor- nd long-erm prior reums re negively correled wih fuure reurns, while inermedie-erm reums re posiively correled. Moreover, hey find h profis emed re incresed by condiioning on he full erm smcure versus n pproch h jus condiions on he "momenun" segmen. Oher broder mulivrie pproches incorporing vlue id ddiionl fcors hve been successfully invesiged (e.g., Hugen & Bker, 1996; Hnn & Redy, 2005). Severl inernionl sudies of momenum hve been conduced. Rouwenhors (1998) exmined 12 Europen counries nd found momenum profis of 1 % per monh from long-shor sregy. Griffin, Ji, nd Mrin (2003), who deeced momenum in mos counries excep Jpn, documened (mrginlly significn) Cndin momenun profi of 0.52%/monh. In previous work concenring on Cndin mrkes, Clery nd Inglis (1998) found excess monenum reurns of 4.10% per qurer.' The purpose of his ricle is o revisi momenum predicbiliy nd profibiliy in he environmen of Cndin finncil mrkes. Oher hn using he les d nd including firms of boh smll nd lrge mrke cpilizion, we re he firs o risk-djus reums using he Fm-French hree-fcor model in his conex, rher hn relying exclusively on rw reums or CAPMlphs.- In ddiion, his sudy ess wheher momenum profi in Cnd cn be improved on by condiioning on he erm srucure of prior reums (s in Grinbl & Moskowiz, 2004). In oher words, is i pproprie o employ sregies cpilizing on boh he momenum nd reversl phenomen? This join effec hs no been sudied by previous sudies on Cndin mrkes. To preview, we find h, despie some evidence of recen dissipion, he momenum phenomenon is sill presen in Cnd, nd is enhnced by condiioning on prior long-erm reums. In he following secion we invesige reum predicbiliy using prior reums. Nex we consider wo-wy sor on bob inermedie-erm nd long-erm ps reums. We hen exnine sregy relibiliy by incorporing rnscion coss nd esing for cyclicliy in profibiliy. We find h mos of he recen vlue dded is for shor-enbled momenum rders. Finlly, we offer our conclusions. Evidence on Reum Predicbiliy Using Prior Reums We firs invesige wheher Cndin sock reums re predicble from prior inermedie-erm (3-12 monh) reurns. The reurn d h we use re monhly reums on he common equiy of ol of 3,780 firms obined from he Torono Sock Exchnge - Cndin Finncil Mrkes Reserch Cener (TSX-CFMRC) Dbse covering he period from June 1982 o My 2004 nd fully djused for dividends nd sock splis. Book vlues nd mrke vlues re obined from COM- PUSTAT over he period June 1985- My 2004. Merging he wo dbses, we come up wih ol of 974 firms wih mching nmes nd ickers.-^ Securiies re rnked by prior reums nd hen formed ino five quiniles. The op 20% of socks by ps reum re pu ino quinile 5 (P5), he nex highes group re pu ino quinile 4 (P4). nd so on down o he lowesreuming quinile 1 (PI). Prior reums re clculed from ime Jl o 0 nd fuure perfonnnce, which is bsed on ime 0 o K inervls, is mesured using boh rw reurns nd Fm-French hree-fcor lphs. The procedure employed o clcule he ler is described in he ppendix. Tble 1 presens resuls for J] = -3, -6, -9, -12, -18. -24, -30, -36, nd K = 3, 6, 9, 24. Oher hn he fc h hey use deciles, his ble follows closely he procedure of Jegdeesh nd Timn (1993)/ For now we resric our discussion o cses of porfolio formion bsed on prior inermedie-erm reums where Jl = -12 or less (in bsolue erms). For breviy purposes, he ble only provides resuls for exreme quiniles (P5 nd PI) nd heir differences (P5-P1). More precisely, he ler re long-shor zero-cos porfolios bsed on buying he high-momenum socks nd shor-selling he lowmomenum socks. Beginning wih rw reums nd referring o he Jl = -6, K = 6 ble box, he verge rw reum for P5 ws 2.157%/monh nd for PI 0.820%/monh. This resuled in differenil long-shor zero-cos reurn of 1.337%/ monh (which compounds o 17.28%/yer): vlue which is sisiclly significn ( = 2.831). Noe h o he exen h he risk ssocied wih he exreme porfolios is idenicl, his nd oher rw reum differences re risk-free. A glnce hrough oher boxes in he ble indices h he momenum phenomenon relibly exiss in Cnd, wih sisicl significnce he 10% or beer level, for ll Jl = -3. -6, -9,-12 nd K = 3, 6, 9 combinions wih he excepion of P5-P1 (-12, 9). In his cse, he P5-P1 vlue is smll nd sisiclly insignificn. For K = 3 nd 6, reum differences rnge from 1.011% o 1.734%/monh, compounding o 12.8% o 22.9%/yer. These numbers re much lrger hn he 0.52%/monh cied in Griffin, Ji nd Mrin (2003) for 1975-2000 smple period. They re, however, of he sme order of mgniude s he 4.10%/qurer demonsred by Clery nd Inglis (1998) for 1979-1990 smple period using only he lrges 238 firms in he Copyrigh 2007 ASAC. Published by John Wiley & Sons, Ld. 136 24(21. 135-145
REFINING MOMENTUM STRATEGIES BY CONDITIONING ON PRIOR LONG-TERM RETURNS Torono Sock Exchnge by mrke cpilizion.' Noe h only (roughly) he firs 25% of our smple period inersecs h of he ler pper, suggesing h momenum is robus Cndin phenomenon. I is lso ineresing o noe h he momenum reums shown in Tble I re lso of he sme order of mgniude s hose ppering in Jegdeesh nd Timn (1993) using U.S. d. For he P5-Pl(-6,6) cse, he rw reurn difference is 0.95%/ monh vs, our 1.337%/monh. Turning o Fm-French risk-djusmen, we nurlly observe h lphs so genered re much lower hn corresponding rw reums. For P5(-6,6) nd PI (-6. 6) he lphs re -0.387% nd 1.077%, respecively. Of course i is differences h mer, nd on his bsis we see h risk-djusmen mkes lile difference: high-momenum porfolios sill ouperfomi (nd lowmomenum porfolios sill underperform). Differencing hese wo lphs yields 1.464%/monh (which compounds o 19.05%/yeir). Noice h evidence in fvour of momenum is even sronger under Fm-French riskdjusmen. The reson is he differen lodings of he PI nd P5 porfolios. High-momenum porfolios on verge hve lower mrke, size, nd vlue bes hn lowmomenum porfolios. Since high-momenum firms end Tble 1 Rw Reurns nd Alphs Associed wih (J1, K) Combinions Associed wih Momenum/Reversl Sregies K 3 6 9 24 Jl PI P5 P5-P1 PI P5 P5-P1 PI P5 P5-PI PI P5 P5-P1-3 -6 -y -12-18 -24-30 -36 Rw Rw Rw Rw Rw Rw Rw Rw 0.953 1.710-0.202-0.570 0.758 1.207-0.454 -L027 0.575 0.907-0.625-1.361 0.669 1.028-0.579-1.231 1.026 1.566-0.324-0.680 1.327 1.912-0.090-0.176 1.667 2.294 0.199 0.370 1.752 2.251 0.232 0.386 2.239 4.634 1.170 4.270 2.298 4.820 1.218 5.212 2.309 4.953 1.166 4.853 2.253 5.020 1.195 5.544 1.527 3.449 0.503 2.588 1.154 2.685 0.134 0.695 1.042 2.566 0.073 0.393 1.154 2.974 0.219 1.089 1.286 2.959 1371 3.095 1.541 2.995 1.672 3.191 1.734 3.361 1.790 3.409 1.584 2.840 1.773 3.755 0.501 0.895 0.828 1.489-0.173-0.296 0.224 0.393-0.625-1.005-0.126-0.215-0.598-0.866-0.013 --0.020 1.062 1.856-0.153-0.423 0.820 1.335-0.387-0.924 0.685 1.103-0.564-1.305 0.849 L3i8-0.463-1.017 1.269 I.8H6-0.125-0.255 1.601 2.293 0.156 0.306 1.775 2.407 0.288 0.528 1.813 2.344 0.289 0.487 2.072 4.635 1.023 4.680 2.157 4.826 1.077 5.248 2.118 4.814 1.045 4.955 1.885 4.302 0.865 4.312 1.262 2.933 0.255 1.361 0.956 2.312-0.026-0.140 0.963 2.442 0.008 0.046 1.090 2.875 0.168 0.842 1.011 2.574 1.176 2.970 1.337 2.831 1.464 3.076 1.433 2.925 1.609 3.273 1.035 1.935 1.329 2.504-0.006-0.011 0.380 0.689-0.645 -I.IOI -0.182-0.325-0.812-1.285-0.279-0.476-0.723 '1.054-0.121-0.189 1.084 1.983-0.102-0.311 0.903 1.535-0.323-0.840 0.879 1.443 -O.400-0.969 1.077 1.681-0.259-0.579 1.410 2.190 0.026 0.059 1.748 2.490 0.288 0.566 1.906 2.575 0.408 0.747 1.851 2.407 0.325 0.555 2.043 4.722 0.969 4.896 2.055 4.692 0.989 5.750 1.828 4.232 0.788 3.954 1.547 3.594 0.539 2.847 1.055 2.499 0.055 0.302 0.844 2.068-0.131-0.691 0.905 2.331-0.044-0.237 1.060 2.829 0.137 0.684 0.959 2.867 1.071 3.180 1.152 2.747 1.312 3.118 0.949 2.033 1.187 2.555 0.470 0.908 0.797 1.565-0.355-0.692 0.029 0.058-0.904-1.541-0.419-0.754-1.000-1.573-0.452-0.767-0.791-1.160-0.189-0.298 1.685 3.207 0.489 1.615 1.667 3.013 0.422 L261 1.767 3.089 0.493 1.383 1.899 3.272 0.619 1.689 2.128 3.456 0.790 1.956 2.272 3.418 0.865 1.889 2.479 3.461 1.019 1.970 2.391 3.376 0.930 1.825 1.599 3.892 0.564 3.31} 1.346 3.311 0.326 1.980 1.105 2.772 0.111 0.679 0.946 2..^78 -(K046-0.285 0.820 2.073-0.164-0.934 0.877 2.271 -O.iO5-0.569 0.932 2-511 -0.026-0.142 0.914 2.533-0.031-0.166-0.087-0.350 0.075 0.311-0.321-1.031-0.096-0.319-0.662-1.795-0.382-1.082-0.953-2.459-0.664-1.808-1.308-2.938-0.954-2.301-1.396-2.673-0.969-2.0(H -1.547-2.595-1.045-1.905-1.476-2.466-0.961-1.754 Copyrigh 2007 ASAC. PubUshed by John Wiley & Sons, Ld. 137 24(21. 135-145
REFINING MOMENTUM STRATEGIES BY CONDITIONING ON PRIOR LONG-TERM RETURNS o hve higher mrke cpilizion levels nd lower book-o-mrke rios, i is no surprising o see lower risk-djused reums on he low-momenum porfolios relive o he high-momenum porfolios, which leds o differenil lphs h exceed rw reum differences. Resuls for K = 24 re of ineres. As K moves ino his erriory, he sign of P5-PI is for he mos pr negive, suggesing h momenum evenully dissipes. The Cndin d re hus consisen wih slow overrecion rher hn slow recion. I is ineresing o compre hese resuls o hose using U.S. d. Only in Lee nd Swminhn (2000) do we see hin of such evenul momenum dissipion nd in h pper i kes full five yers for he complee dissipion of profi.* Coninuing o refer o Thle 1, s Ji increses, we re effecively moving ino he erriory where reversl hs been shown o be he norm since lenghy period of success ofen predes wek performnce. To invesige wh holds in Cndin d, we now refer o cses of porfolio formion bsed on prior long-erm reums where Jl = -18 or more (in bsolue erms). The firs hing o noice is h, when formion periods re 18 monhs or longer, here is no evidence of posiive reum seril correlion. Only for he J] =-18. K = 3 comhinion re boh he rw reurn nd lph differences (P5-P1) posiive, bu hey re sisiclly insignificn. In ll oher cses, he sign of P5-P1 is negive, suggesing reversl. When K = 18 or 24. one cn lwys conclude reversl he 5% confidence level or beer using rw reum differences. If we use differenil lphs, we cn drw he sme conclusion 10% or beer hree qurers of he ime. The highes (negive) vlue for P5-P1 is -1.547%/monh for Jl = -30, K = 24, which compounds o -18.7%/yer. Using lphs, he vlue drops o --1.045%/monh, which compounds o -13.29%/yer. Two-wy Sor Using Boh Prior Inermedie-erm nd Long-erm Reums In his secion we consider long-shor zero-cos porfolios hsed on wo-wy prior inermedie-erm nd long-erm reurn sor. Following Grinbl nd Moskowiz (2004), he prior reum inervls re nonoverlpping so s no o confound he momenum nd reversl segmens. Le J2 equl he beginning of he prior long-erm reum relive o he porfolio formion de, nd Jl coninue o equl he beginning of he prior inermedie-erm reurn relive o he porfolio fomiion de. For exmple, for J2 = -18 nd Jl = -6, he prior longerm reum would be mesured from 18 o 6 monhs prior o porfolio formion nd he prior inermedie-erm reum would be mesured over he six monhs prior o porfolio formion. While we only show resuls using holding period of 6 monhs (K = 6), robusness ess esblished h resuls were similr for K = 3 nd K = 9. Insed of using quiniles, we now use single-vrible erciles, since, in wo-wy symmeric sor, he number of porfolios is he squre of he number of single-vrible erciles (nine). For breviy, from his poin on we only repor resuls for lphs, bu hose for rw reums re lwys brodly similr. Refer o Tble 2. The 'P' porfolios priion securiies ino erciles in erms of inermedie-erm reums, forming porfolios PI, P2, nd P3 (excly s ws done before o form quiniles). Then, wihin ech 'P' porfolio, we rnk securiies ino highes hird, middle hird, nd lowes hird wih respec o nonoverlpping long-erm reurns, forming porfolios PlQl, P1Q2, P1Q3. P2Q1, P2Q2, P2Q3, P3Q1, P3Q2. nd P3Q3. As n exmple, refer o he Jl = -9, J2 ^ -30 cse. For given Q group, reums rise s we move from PI o P3. Addiionlly, for given P group, reums fll s we move from Ql o Q3. This implies h he P3-PI porfolios lwys hve posiive lph differences (wih one of hem being sisiclly significn). Furher, we see h he Q3-QI porfolios lwys hve negive lph differences (wih 2 of he 3 being sisiclly significn). Condiioning on boh prior inermedie-erm nd long-erm reurns leds o even greer profibiliy. Tbe long-shor zero-cos porfolio h ccomplishes his is P3Q1-P1Q3. Noe h i is long high inermedie-erm reums nd low long-erm reums, nd shor low inermedie-erm reums nd high long-erm reums. This porfolio generes n lph difference of 2.48%/monh. implying hefy 34.2%/yer, resul h hs -sisic of 5.72.' Wh is mos noble here re he synergies h exis when one condiions on he erm srucure of prior reums. To see his, using he sme box, suppose one follows momenum sregy lone. Tbe verge profi is 1.14% (which is he verge of 0.80%. 0.78% nd 1.83%). On he oher hnd, if one follows reversl sregy lone, he verge profi is 0.86% (which is he verge of 1.68%, 0.26% nd 0.64%). So on verge one-segmen sregy generes 1% excess reum, versus 2.48% excess reum for wo-segmen sregy.^ Relibiliy of Term Srucure Sregy When considering employing n invesmen sregy, i is imporn for mrke prciioners o hve comfor level h is use is likely o genere lph. In Copyrigh 2007 ASAC. Published by John Wiley & Sons. Ld. 138 Cn J Adm Se 242J. 135-145
REHNING MOMENTUM STRATEGIES BY CONDITIONING ON PRIOR LONG-TERM RETURNS 7^^ 1^ rj r^ 77? =p M -e fs IN <N -; O o OOO-- OOO--fN'*i OQ O - o^o '^ o ^ I 7 7 7=^7 '*K CS <N I T I S 777 I/1 «N p r^ ; p ^ ood^ 7?^ qp < p d f-icj-^ f T I»; I C.o I-S E 5 p p 777 777 ~ d "i (^ 777 r^rrioo '^ ^P od d ddd--''*i d Oj - dddd-:-- d dddd-~;fs dddd-^ri <5 5 s i 777 777 777 oop dd o C d " d NcyO r-;pu^ d d d CM CO C: i dddocj-j d ddo ;-- dddo ^M ddd ci»n SS f^ fl f^ o-!!!?5 ^s" E L e Q s e Copyrigh 2007 ASAC. Published by John Wiley & Sons, Ld. 139 2401. 135-145
REFINING MOMENTUM STRATEGIES BY CONDITIONING ON PRIOR LONG TERM RETURNS Ihis secion, we presen simulion which explores dynmic profibiliy - h is, does he sregy hold up well over ime, or is is success resriced o only cerin subperiods? If profibiliy is someimes high nd oher imes low nd undependbie, mngers re more likely o look fvourbly on sregies h hve performed well in he recen ps compred o hose which hve mosly conribued lph in he more disn ps. In ddiion o exploring cyclicliy. we lso ccoun for rnscion coss. To do so, we resric ourselves o subsmple of he mos liquid Cndin firms. This is pproprie, s Clery, Kerr nd Schmiz (2002). in sudying rnscion coss on he Torono Sock Exchnge, documen wide vriion depending on liquidiy. They noe h for he mos liquid socks be verge hlfspred ws bou 45 bsis poins (during 1989-98), while for less liquid socks spreds re much higher. If we resric ourselves o be lrges 25% (by mrke cpilizion) of firms in our smple, his cu kes us o n verge of 115 firms. The ler loosely corresponds o ody's S&P/TSX 60 Index commingled wih he S&P/ TSX Mid-cp Index. Furher, o provide comfor o prciioners h sregy hs been efficcious recenly, i is useful o work wih moving performnce windows. Specificlly, we simule he ime series of compounded porfolio reums over five-yer (moving) invesmen horizons. We consider momenum nd reversl sregies where K = 6, J1 = -6 nd J2 = -30.'' We herefore form porfolios bsed on simulneously observing he prior long-erm reurn from monh -30 o monb -7 nd be prior inermedieerm reum from monb -6 o monb -1, wih porfolios being held for six monhs. Enhnced indexion is employed for bis simulion: n index porfolio is overlid wih long-shor sregy emping o cpilize on momenum nd reversl endencies. A be beginning of ech five-yer invesmen horizon under con.siderion, we inves $1 million in porfolio which is mde up of bree componens: (1) Index: $(1/9) million long posiion in ech of he nine porfolios using he wo-wy sor pproch described in he previous secion (i.e., PlQI, P1Q2, P1Q3, P2QI, P2Q2, P2Q3, P3Q!, P3Q2. nd P3Q3); Figure 1. Cumulive lph for erm srucure sregy over five-yer invesmen windows (op 25% of firms by mrke cpilizion) 500% 400% i Cumulive lph (Pre-Trnsclion Cos) 97.5 percenile (Pre-Trnscion Cos) 2.5percenile (Pre-Trnscion Cos) Cumulive lph (Pos-Trnscion Cos) 300% 200% 100% 0% -100% Jun-90 My-92 My 94 My-96 My-98 My-00 My-02 My 04 ending monh Copyrigh 2007 ASAC. Published by John Wiley & Sons. Ld. 140 24(21. 135-145
RERNING MOMENTUM STRATEGIES BY CONDmONlNG ON PRIOR LONG-TERM RETURNS Figure 2. Alph for momenum nd reversl sregies over five-yer invesmen windows (op 25% of firms by mrke cpilizion) 4.00% 3.00% mornenum reversl 2.00% 1.00% 0.00% r"'\ '' v.., ^ K'V"" / -1.00% Jun-90 My^92 My-94 My^96 My-98 My-00 My-02 My-04 ending monh (2) Long: $1 million long posiion in P3QI, from which we expec o genere he lrges posiive reurn; nd (3) Shor:%\ million shor posiion in PI Q3. which we predic o perfonn he wors mong he nine. Consisen wih Jegdeesh nd Timn (1993). ech monh end, we replce 1/6"' of our porfolio, holding ech miniporfolio for six monhs. Addiionl reblncing is required o ensure we minin he iniil relive composiion of posiions. In order o hve sufficien prior long-erm reums o devise our sregies, we consider he irs ive-yer invesmen horizon o spn from June 1985 lo June 1990. The second invesmen horizon is herefore from July 1985 o July 1990, nd he res re consruced in he sme one-monh rolling fshion. We rck ol of 168 of such ive-yer invesmen horizons, wih he ls one covering he period from My 1999 o My 2004. In Figure 1. we plo he ccumuled reurn, boh pre- nd pos-rnscion coss, bsed on Fm- French lphs, gins he ending monh of he invesmen horizon. Elkins/McSherry, rnscion cos nlysis irni which rcks ol execuion coss for insiuionl invesors in mos developed mrkes, esimes ol coss (commissions, fees nd mrke impc) for insiuionl invesors in Cnd rnging from 62.47 bsis poins in 1996 o 35.93 bsis poins by 2005. In our simulion, we use hisoricl Elkins/ McSherry d."* While i is ppren h he momenum-reversl wo-wy sor sregy (virully) lwys generes posiive lph, cyclicliy in profibiliy is ppren: he bes performnce occurs boh erly in he smple nd firly le in he smple (excep for he ls couple of yers). In erms of sisicl significnce, only erly in he smple is i possible o feel comforble h he sregy will py of wih high degree of confidence, hough ler here is period of relive comfor. Lo (2004) hs recenly suggesed h his cyclicliy is o be expeced in world where mrkes re subjec o evoluionry forces. Opporuniies h exis becuse of fuly heurisics nd limis o rbirge my evpore since given enough ime nd compeiive forces, ny counerproducive heurisic will be reshped o fi he curren environmen. On he oher hnd, if some of hose exploiing priculr opporuniies leve he mrke, profibiliy Copyrigh 2007 ASAC. Published by John Wiley & Sons. Ld. 141 240), 135-145
REFINING MOMENTUM STRATEGIES BY CONDITIONING ON PRIOR LONG-TERM RETURNS Figure 3. Cumulive lph for jus long nd jus shor erm srucure sregy over five-yer invesmen windows (op 25% of firms by mrke cpilizion) 300% 250% long shor 200% 9-150% 100% v, 50% 0% -50% Jun-90 My-92 My-94 My-96 My-98 My-00 My-02 My-04 ending monh my be rekindled. No surprisingly, rnscion coss erode lph somewh. In fc, erosion is signiicn enough o mke he sregy unproible for bou four yers worh of inervls in he erly o mid-90s. While die resuls of he simulion provide some comfor, wo oher issues re germne. Firs, is momenum merely he resul of d mining nd hus unlikely o be successful going forwrd? Second, wh re he sources of lph? As for he firs, he rgumen h behviourl fcors ply role, long wih he limis o rbirge rgumen of Shleifer (2000), sugges h d mining is no behind momenum, nd h he phenomenon is no necessrily esily rbirged wy. Dniel, Hirshleifer, nd Subrhmnym (1998) formule model where invesors suffer overconfidence (in he sen.se h hey overesime he precision of heir own prive signls) nd self-ribuion bis (in ribuing success o heir own biliies). In such world, here cn be inermedie-lg posiive seril correlion nd longlg negive seril correlion. More recenly, Grinbl nd Hn (2005) offer n explnion for momenum consisen wih prospec heory, menl ccouning nd he disposiion effec of Shefrin nd Smn (1985). In effec, he endency for winners/losers o be sold oo quickly/slowly suggess delyed recion o good/bd news becuse reference-poin-influenced invesors hve demnd curves h reflec recen performnce. Cooper, Guierrez nd Hmeed (2004) show h momenum profis exis exclusively fer up-mrke ses, nd rgue h his finding is perfecly consisen wih he model of Dniel, Hirshleifer nd Subrhmnym becuse overconidence is posiively correled wih mrke performnce (see Smn. Thorley. & Vorkink; 2006; Deves, Luders, & Schroder; 2006)." As for sources of lph, wo poins re considered. To wh exen does profibiliy rise from plying momenum nd o wh exen does i rise from plying reversl? Furher, is lph vilble from going long, going shor, or boh? Figures 2 nd 3 provide relevn clues. Firs, in Figure 2, we plo momenum lphs nd reversl lphs in isolion. In he firs cse, we condiion only on momenum (using prior inermedie-erm reums), nd in he second cse we condiion only on reversl (using prior long-erm reums). Here, we simule he reurns from long-shor zero cos porfolios rher hn from he ne long porfolios shown in Figure 1. In Copyrigh 2007 ASAC. Published by John Wiley & Sons. Ld. 142 24(2 ) 135-145
REHNING MOMENTUM STRATEGIES BY CONDITIONING ON PRIOR LONG-TERM RETURNS he former cse, he porfolios re P3-P1 (for momenum), nd, in he ler cse, he porfohos re Q1-Q3 (for reversl). We see h for mos of he smple, momenum hs been more relible profi driver hn reversl. The one excepion ws in he mid-90s when here ws lile o choose beween hem. Nex, in Figure 3. we look long versus shor profibiliy. Here., we plo he ccumuled ne reums bsed on Fm-French lphs over 5-yer invesmen horizons for he long posiion in P3Q1 long wih he negive of hose for P1Q3 (i.e., he ccumuled ne reurns of shor posiion in P1Q3). One reson his disincion mers is h erlier, when rnscion coss were ccouned for, coss specific o shor selling were no considered. These include he inbiliy o fully uilize shor sle proceeds coupled wih poenil nonvilbiliy ny cos. Lmen nd Thler (2(X)3) illusre h someimes, becuse of he ler, ppren profibiliy is illusory. Clerly he disincion is imporn here. On one hnd, in he erly pr of he smple, boh long nd shor rnscions conribued o lph. On he oher hnd, for lmos he ls 10 yers of inervls, he sregy becme n enirely shor-side one.'" I could well be h he incresing presence of long erm srucure-oriened rders led o n rbirging wy of he opporuniy on he long side. Wh cn we conclude? Bsed on recen hisory, he erm srucure of prior reums sregy seems o hve converged o shor momenum sregy. So he quesion becomes: Could shor-enbled insiuionl rders sill profi from momenum during his period? Though one cnno be cegoricl wihou n in-deph sudy of he mrke for borrowing equiies in he Cndin environmen long he lines of he Geczy, Muso, nd Reed's (2002) U.S. sudy, given he brod similriy beween Cndin nd U.S. equiy mrkes nd he evidence of he ler pper, he nswer is probbly yes. Nonvilbiliy ws very unlikely o be n issue since we re concenring on he mos liquid Cndin socks, nd he loss of shor-sle proceeds is rrely significn unless securiy is "specil," nd, gin, highly liquid socks re very unlikely o be in his cegory.'^ More specificlly, Geczy. Muso. nd Reed, using unique dbse of cul shor-selling coss nd consrins, documen h he profibiliy of long-shor momenum sregy is lile ffeced by heir considerion. Conclusion Trding bsed on he erm smcure of prior reums hs over ime offered scope for profi-king in Cnd. While momenum is he mjor pr of i, porfolio mngers hve lso been ble o cpilize on long-erm prior reversls. Bes of ll, synergies hve been relized by focusing on he enire erm srucure of prior reums. Condiioning on boh inermedie-emi nd long-erm prior reurns, profis o zero-cos long-shor sregy were ofen vilble in our d. Recenly, hough, sregy condiioning on prior reums seems o hve become only momenum sregy execuble on he shor side. This my well be becuse long erm smcure-oriened rders hve sough o rbirge i wy. If one kes he view h mrkes re forever moving owrds n efficien-mrkes idel, hen one migh expec shor rbirge o evenully elimine ll erm smcure-bsed opporuniies. Conversely, if one believes h mrkes re subjec o evoluionry forces nd heir dynmics re such h equilibrium is n ever-moving rge, hen i would be jus s likely h full reurn o profibiliy migh occur in he fuure. \ Noes 1 Erlier work on Cndin momenum ws underken by Foerser, Prihr, nd Schmiz (1994), Foerser (1996) nd Kn nd Kirikos (1996). Addiionlly. Co nd Wei (2002) looked Cndin indusry-level momenum. Rher hn using individul socks, hey form porfolios using he 14 indusry subgroups of TSE300 Composie Index over he period of 1961-1999. They documen boh momenum nd reversl phenomenon he indusrylevel, which re similr o hose he firm-level. Sregies coningen on boh prior inermedie-erm nd long-erm reums re however no invesiged. Assoe nd Sy (2003) find evidence of shor-erm (one-monh) reversl for Cnd consisen wih Jegdeesh (1990). The effec urns ou o be oo smll o be exploied hough. 2 Becuse of d limiions (s will be described), our smple runs from June 1985 o My 2004. 3 Noe h boh cive nd incive firms re included in he wo dbses, nd we exclude russ nd unis nd only consider publicly rded ordinry shres. Book vlue is clculed following Fm nd French (1993), defining book common equiy s he COMPUSTAT book vlue of sockholders' equiy, plus blnce-shee deferred xes nd invesmen x credi (if vilble), minus he hook vlue of preferred sock for he ls fiscl yer end. Depending on vilbiliy, we use he redempion, liquidion, or pr vlue (in h order) o esime he vlue of preferred sock. 4 Similr o Jegdeesh nd Timn (1993), in order o increse he power of he ess, porfolios wih overlpping holding periods re formed. In priculr monh, he overll porfolio conins 1/N miniporfolios, one being seleced in he curren monh bsed on he les sor, nd he oher N-1 miniporblios hving lredy been seleced (nd coninuing o be held) from previous sors. In ll Copyrighl 2007 ASAC. Published by John Wiley & Sons, Ud. 143 24(21. 135-145
REHNrNG MOMENTUM STRATEGIES BY CONDITIONING ON PRIOR LONG-TERM RETURNS miniporfolios, he procedure is o buy equl dollr mouns of every sock in given quinile. Missing reurns of ny sock during he holding period re replced by he conemporneous equl-weighed reurns of ll he socks in he CFMRC dbse. Besides hving coninuously vlid reurn infonnion over he full formion period, firm needs o hve vlid book nd mrke vlues he beginning of he holding period in order o be eligible for considerion. Firms wih negive book common equiy re lso excluded. Noe h using vlueweighed porfolios does no ler he significnce of our resuls. 5 Clery nd Inglis (1998) form equl-weighed porfolios bsed on prior inermedie-erm {12-monh} reurns. Noe h one deprure from he presen sudy is h hey form zero-cos porfolios using op nd boom deciles rher hn quiniles. In unrepored work using deciles, profis re significnly lrger hn for he quinile sregies presened here. 6 They conjecure h his regulriy is consisen wih "momenum life cycle." where down-nd-ou socks rde lile bu evenully um up. nd winners rding high volume evenully pek nd urn down, 7 We lso exmine he end-of-yer effec by mesuring he verge performnce of our sregies seprely for he monhs of Jnury nd for he res of he yer. The much sronger reversl effec in Jnury cn more hn offse he slighly weker momenum effec resuling in higher lph for he long-shor zero-cos porfolio of P3QI -P1Q3 during Jnury hn he res of he yer. Neverheless, we cn sill genere n lph difference of 2.40%/monh { = 5.26) even if we exclude Jnury for he cse of Jl = -9 nd J2 = -30. 8 Admiedly, his chrcerizion underses wh cn he genered by pure momenum or pure reversl sregy, since i would of course be possible o do beer if we move o quiniles (or even deciles). Sill, one will recll h even doing so will no genere profis h re comprble o hose coming from he wo-segmen pproch. 9 The reder will noe h we hve no chosen he combinion h performs bes ex pos. 10 Elkins/McSherry esimes mrke impc by compring he cul verge price for block rde wih he volumeweighed verge price - he men of he dy's high, low, opening nd closing price - of he sock in quesion. We hnk Henry MrigUno of he compny for providing us wih ol rding cos d for 1996-2004. We hen rn simple ime rend (coss hve been declining) nd used fied vlues for 1985-2004. This ws necessry o bck-exrpole, nd i lso seemed judicious becuse ech yer's esime ws subjec o smpling error. 11 Rionl explnions of momenum hve lso been proposed. See. for exmple. Chordi nd Shjvkumr (2002) nd Wng (2005). 12 One cn inui from Tble 2 h long profibiliy exised from 1985 o 1994. For exmple, he (long) P3QUJ2. JI. K) - P3Q1 (-30, -9.6) porfolio hd excess reurn predicbiliy (before rnscion coss) of 102 bsis poins/monh which is well wihin rnscion coss. 13 A "specil" securiy hs when len, becuse of scrciy, lower hn verge ineres rebe going o he borrower. References Assoe. K., & Sy, O. (2003). Profibiliy of he shor-run conrrin sregy in Cndin sock mrkes, Cndin Journl of Adminisrive Sciences. 20, 311-319. Brberis, N., & Shleifer. A. (2003). Syle invesing. Journl of Finncil Economics, 68, 161-199. Berkowiz, M.. & Qiu. J. (2003). Ownership, risk nd performnce of muul fund mngemen compnies. Journl of Economics nd Business, 55, 109-132. Boudoukh, J.. Richrdson, M,P.. & Whielw, R.F. (1994). A le of hree schools: Insighs on uocorrelions of shorhorizon sock reums. Review of Finncil Sudies. 7. 539-573. Co, M., & Wei, J. (2002). Uncovering secor momenums. Cndin Invesmen Review (Winer). 14-22. Chordi, T, & Shivkumr, L. (2002). Momenum, business cycle, nd lime-vrying expeced reurns. Journl of Finnce, 57, 9S5-\i)20. Clery. S., & Inglis, M. (1998). Momenum in Cndin sock reums. Cndin Journl of Adminisrive Sciences, /5. 279-291. Clery, S.. Kerr, K.. & Schmiz, J. (2002). Trnscion coss for TSE-lised socks. Cndin Invesmen Review (Spring), p. 20 ff. (5 pges). Cooper. M.. Guierrez Jr., R.C, & Hmeed, A. (2004). Mrke ses nd momenum. Journl of Finnce, 59, 1345-1365. Dniel, K.. Hirshleifer, D.. & Subrhmnym, A. (1998), Invesor psychology nd securiy mrke under- nd overrecions. Journl of Finnce, 53, 1839-1885. Deves, R.. Luders, E., & Schroder, M. (2006). The dynmics of overconfidence: Evidence from sock nrke forecsers. Mnuscrip in preprion. De Bond, W. F. M.. & Thler. R. (1985). Does he sock mrke overrec? Journl of Finnce. 40, 793-807. Fm, E.F., & French, K.R. (1993). Common risk fcors in he reums on socks nd bonds. Journl of Finncil Economics, 33, 3-56. Fm. E.F.. & French. K.R. (1996), Mulifcor explnions of sse pricing nomlies. Journl of Finnce, 51, 55-84. Foerser, S. (1996). Bck o he fuure, gin: In defence of momenum-bsed rding sregies nd now you see hem, hen you don'. Cndin Invesmen Review, 9 (Summer), p. 13 ff. Foerser, S., Prihr, A., & Schmiz, J. (1994). Bck o he fuure: Price momenum models. Cndin Invesmen Review, 7(4). 9ff. Geczy, C.C.. Muso, D.K., & Reed, A.V. (2002). Socks re specil oo: An nlysis of he equiy lending mrke. Journl of Finncil Economics, 66, 241-269. Griffin. J.M., Ji. X., &. Mrin, S. (2003). Momenum invesing nd business cycle risk: Evidence from pole o pole. Journl of Finnce, 63, 2515-2547. Grinbl, M.. & Hn. B. (2005). Prospec heory, menl ccouning nd momenum. Journl of Finncil Economics, 78, 311-339. Copyrigh 2007 ASAC. Published by John Wiley & Sons. Ld. 144 24(2). 135-145
RKFINING MOMENTUM STRATEGIES BY CONDITIONING ON PRIOR LONG-TERM RETURNS Grinbl. M.. & Moskowiz, T.J. (2(X)4). Predicing sock price movemens from ps reums: The role of consisency nd x-loss selling. Journl of Finncil Economics, 71, 541-579. Hnn. J.D., & Redy, M.J. (2005). Profible predicbiliy in he cross secion of sock reurns. Journl of Finncil Economics, 78, 463-505. Hugen, R.A.. & Bker. N.L. (1996). Commonliy in he deerminns of expeced sock reums. Journl of Finncil Economics, 41, 401-439. Jegdeesh. N. (1990). Evidence of predicble behvior of securiy reums. Journl of Finnce, 45, 881-898. Jegdeesh. N., & Timn, S. (1993). Reums o buying winners nd selling losers: Implicions for sock mrke efficiency. Journl of Finnce, 48, 65-91. Kn. R.. & Kirikos, G. (1996). Now you see hem, hen you don': The phenomenl reums rding sregy cn produce when esed using hisoricl d ofen vnish once heory is pu ino prcice. Cndin Invesmen Review, 9 (Summer), p. 9 f\ Klein, P. (2(K)1). The cpil gin lock-in effec nd longhorizon reum reversl. Journl of Finncil Economics, 59, 33-62. Korjczyk, R., & Sdk. R. (2004). Are momenum profls robus o rding coss? Journl of Finnce. 59, 1039-1082. Lmon, O.A.. & Thler. RH. (2003). Cn he mrke dd nd subrc? Mispricing in ech sock crve-ous. Journl of Poliicl Economy. III. 227-268. Lee, C.M.C., & Swminhn, B. (2(M)0). Price momenum nd rding volume. Journl of Finnce, 55, 2017-2069. Lo. A.W. (2004). The dpive mrkes hypohesis. Journl of Porfolio Mngemen. (30"' Anniversry Issue), 15-29. Moskowiz, T. J., & Grinbl. M. (1999). Do indusries explin momenum? Journl of Finnce, 54, 1249-1290. Rouwenhors, K.G. (1998). Inemionl momenum sregies. Journl of Finnce, 53, 267-284. Shefrin, H.. & Slmn. M. (1985). The disposiion o sell winners oo erly nd ride losers oo long: Theory nd evidence. Journl of Finnce, 40, 777-790. Shleifer, A. (2000). Inefficien Mrkes: An Inroducion o Behviorl Finnce. Clrendon Lecures in Economics, Oxford. UK: Oxford Universiy Press. Smn, M.. Thorley, S., & Vorkink. K. (2006). Invesor overconfidence nd rding volume. Review of Finncil Sudies, 19, 1465-1498. Wng. K.Q. (2005). Why does he CAPM fil o explin momenum? Mnuscrip in preprion. Appendix Risk-Adjusing Using he Fm-French Three- Fcor Model This ppendix describes our (convenionl) procedure for risk-djusing using he Fm-French hreefcor model (1993). Firs we noe h Berkowiz nd Qiu (2003) hve shown h his model is pproprie lor Cndin equiies. We consruc he hree Fm-French fcors for Cnd over he period July 1985-My 2004 following Fm nd French (1993). Our proxy for he mrke fcor is he reum on he CFMRC monhly vlueweighed index in excess of he 30-dy reum on Cndin T-bills (boh obined from he CFMRC dbse). To proxy for he size nd book-o-mrke fcors, we consruc porfolios ccording o he mrke vlues nd he book-o-mrke rios of he firms in our dse. In he consrucion of he book-o-mrke fcor, he booko-mrke rio of ech firm is he book common equiy (defined in noe no. 3) for he ls H.scl yer end. divided by mrke equiy he end of ls December. A he end of ech June, ll he firms wih vlid reurn informion over he nex welve monhs, s well s vlid book vlue nd mrke vlue informion, re sored nd pu ino wo group.s: smll nd big (S nd B), ccording o heir curren mrke cpilizions. A he sme ime, firms re sored ccording o heir book-o-mrke equiy nd grouped ino he boom 30% (), middle 40% (M). nd op 30% {H) in ccordnce wih heir rnked vlues. We hen consruc six porfolios (S/L, S/M, S/H, B/L, B/M, B/H) from he inersecion of hese wo groupings. Monhly vlue-weighed reums on he six porfolios re clculed from July of one yer o June of he nex yer. The six porfolios re reformed he end of June of he nex yer. To proxy for he size fcor, he monhly reurn on he SMB (smll minus big) porfolio mesures he difference beween he simple verge of he reurns on he hree smll-sock porfolios {S/L, S/M, S/H) nd he simple verge of he reums on he hree big-sock porfolios [B/U B/M, B/H). To proxy for he book-o-mrke fcor, he monhly reum on he HML (high minus low) porfolio mesures he difference beween he simple verge of he reums on he wo high book-o-mrke porfolios {S/H nd B/H) nd he simple verge of he reums on he wo low book-o-mrke porfolios {S/L nd B/L). Monhly ime-series of he hree fcors re hus obined for he period of July 1985 o My 2004. The FAMA-FRENCH lphs (") re esimed by regressing he ime-series monhly reums of ech porfolio/sregy (r'j) in excess of he 30-dy reurn on Cndin T-bills {rfj) on mrke (r.,), size (SMB,) nd book-o-mrke {HML,) fcors (s described bove) over he relevn ime periods, s follows: (1) Copyrigh <D 2007 ASAC. Published by John Wiley & Sons. Lid. 145 2412i. 135-145