Stock Return Cross-Autocorrelations and Market Conditions in Japan *

Transcription

1 So eurn Cross-Auoorrelions n Mre Coniions in Jpn * Allueen Hmee Nionl Universiy of Singpore Yuno usni Hong ong Universiy of Siene n Tehnology Asr We show h hnges in mre oniions signifinly ffe ross-uoorrelions n spee of jusmen in weely so reurns. We fin signifin posiive ross-uoorrelions eween weely reurns on porfolio of smll firms n lgge lrge firm porfolio reurns only when he lgge ggrege mre hs experiene eline in vlue in he shor n long horizons. These posiive reurn ross-uoorrelions re lso ssoie wih lower norml porfolio ring volume n greer elys in he jusmen of iniviul so pries o (negive) mre-wie informion priulrly for smll firms. The effe of lgge mre ses nno e expline y mre mirosruure ises suh s non-synhronous ring or hin ring. * We hn Jennifer Conr JB Chy Trun Chori Hrol Zhng n nonymous referee n seminr priipns HUST 2002 APFA/PACAP/FMA Finne Conferene (Toyo) n FMA 2003 Conferene (Denver) for helpful ommens. Hmee nowleges he finnil suppor from he Nionl Universiy of Singpore Aemi eserh Grn. All remining errors re ours.

2 I. Inrouion There is eviene of susnil ross-uoorrelions in shor-horizon so reurns in he U.S. so mre. Lo n Minly (1990) show h weely reurns on porfolio of smll firms re more preile hn reurns on porfolio forme using lrge mre vlue firms. In priulr hey fin signifin ross-orrelion eween lgge reurns of lrge sos n urren reurns of smll sos u no vie vers. Muh reserh hs een evoe o ienifying he soures of he le-lg pern in reurns. 1 The symmery in reurn ross-uoorrelions hs een riue o sluggish jusmen of so pries o ommon informion (Lo n Minly (1990) Brennn Jegeesh n Swminhn (1993) Meh (1993) Brinh le n Noe (1995) MQueen Pinegr n Thorley (1996) n Chori n Swminhn (2000)). These ppers sugges h firm-speifi hrerisis suh s firm size nlys overge rnsion oss insiuionl ownership n ring volume help o explin he ross-seionl ifferenes in he jusmen of so pries o ommon informion. For exmple Brennn Jegeesh n Swminhn (1993) show h reurns on low nlys overge sos en o lg reurns on high-overge sos suggesing h less nlys overge slows he jusmen of sos o ommon informion. Chori n Swminhn (2000) fin h reurns on porfolio of sos wih high ring volume le reurns on porfolio of low ring volume sos whih hey inerpre s eviene h high volume helps in he spee of jusmen. 2 Meh (1990) presens rnsion os explnion: 1 Lehmnn (1990) Jegeesh (1990) n Conr Hmee n Nien (199) repor signifin negive uoorrelion in iniviul so reurns onsisen wih overreion in pries. 2 Differenil prie jusmens n rise from severl soures. For exmple in he inomplee informion moel in Meron (1987) invesors follow smll suse of sos euse of high se-up oss of informion proessing. Consequenly more informion is ghere for suse of seuriies (e.g. lrge firms) where he ville informion n he iliy o e signifin posiions re huge relive o he fixe informion quisiion oss. Invesors on ggrege re more (less) liely o losely follow lrge (smll) firms. Holen n Surhmnym (1992) show h he spee of jusmen o informion is more rpi when here re more informe invesors following he so. 2

3 pries jus slowly when hnges in vluion re smll relive o rnsion oss (suh s i-s spre). However Meh lso fins h he ime series hnges in he re of prie jusmen nno e expline y his rnsion os moel. In his pper we llow he ime-series vriions in prie jusmen elys o e epenen on wheher he mre-wie informion represens goo or news. Severl ppers inluing Miller (1977) n Jones n Lmon (2002) sugges h i es longer for negive informion o e fully inorpore ino so pries. 3 In hese moels rionl rirgeurs nno shor n overprie seuriy euse of shor-sle onsrins or prohiiive shoring oss. This slow jusmen o negive informion is suppore y invesor heerogeneiy in he form of uninforme or irrionl invesors or ifferenes of opinion mong invesors. For insne some invesors suh s muul funs n oher insiuionl invesors fe shor-sle resriions y heir hrer. Chen Hong n Sein (2002) show h reuion in he reh of ownership hs similr effe s shor-sle onsrin in h he pessimisi invesors si on he sielines n heir negive informion oes no ge impoune in he pries immeiely. The higher holing oss of shor posiions o exploi news (suh s hose ue o mrgin requiremens sos h go on speils riss of lener relling he sse n ohers) me news rvel slowly (see Gezy Muso n ee (2002) n Areu n Brunnermeier (2002)). This is onfirme y Hong Lim n Sein (2000) who show h sos wih low nlys following seem o re more sluggishly o news hn goo news. Togeher hese ppers n e exene o prei ifferenil elys (n ross-uoorrelions) epening on he se of he mre. If negive mre-wie news e longer o e impoune in pries ue o he ining 3 Dimon n Verehi (1987) show h so prie jusmen proess is impee y he shor-sle onsrin priulrly in he ssimilion of negive (prive) informion. 3

4 onsrins impose y ring resriions spee of jusmen shoul e slower fer ggrege mre elines. In his suy we invesige he role of mre s se on he spee of prie jusmen n is effe on ross-uoorrelions in reurns n prie jusmen elys mong sos re in Jpn. There re wo mjor enefis o using he lrge ross-seion of seuriies re in he Jpnese so mre o onu our experimen. Firs he Jpnese so mre unergoes mjor hnges in mre oniions over our smple perio inluing he ull mre run-up perio of he 1980s followe y he prolonge er mre of he 1990s. Seon lmos ll repore eviene on he soures of symmeri reurn ross-uoorrelions is onfine o he U.S. mre. A nole exepion is he Chng MQueen n Pinegr (1999) suy whih fins h ireionl symmery in porfolio reurn ross-uoorrelions in he U.S. oes no hol in severl Asin mres inluing Jpn. Hene Jpnese seuriies provie ifferen hisory of so reurns n provie nurl experimen o exmine he role of hnges in mre oniions on shor-erm prie perns. We efine he long horizon mre oniion s n UP se if he lgge vlue-weighe mre reurn over he long horizon (ps 12 or 26 wees) is posiive n s se if he lgge mre reurn is negive. We fin h signifin ross-uoorrelions in sizesore weely Jpnese seuriy reurns follow eline in ggrege mre vlue. For exmple fer onrolling for he effes of own lgge reurns negive 1% reurn on porfolio of lrge firms les o erese of 0.72% in he reurn on he smll firm porfolio following mre ses. On he oher hn similr reurn on he lrge firm porfolio generes n insignifin 0.13% erese in he reurn on he smll firm porfolio following UP ses.

5 Speifi onrols for mre-mirosruure effes suh s non-synhronous n hin ring o no ler our min finings. MQueen Pinegr n Thorley (1996) show h shor-horizon mre oniioning hs signifin effe on ross-uoorrelions in U.S. size-sore porfolios reurns: rossuoorrelions re higher in shor-horizon UP ses. To exmine he relive imporne of shor n long horizon mre ses we implemen wo-sge shor n long horizon mre oniioning proess. Our resuls sugges h he ross-uoorrelions in he Jpnese mre is signifin only when he mre is in oh he shor n long-horizons (- ses). We hen proee o ompue mesures of ely in iniviul seuriies n onfirm h so pries respon more slowly o negive mre-wie informion in he - ses. Similrly we fin h norml ring volume is lso signifinly lower following - ses priulrly for smll firms onsisen wih ining ring onsrins following news. Overll our resuls poin o elys in jusmen of smll firms o negive ggrege shos s n imporn soure of ross-uoorrelions in so reurns. The pper is orgnize s follows. Seion II isusses he n our min empiril resuls on he imp of mre ses. Seion III onsiers plusile explnions n provies some rousness hes for our resuls. Seion IV onlues he pper. A reen pper y Cooper Guierrez n Hmee (200) shows h he meium-erm momenum profis re lso epenen on he se of he mre. 5

6 II. Cross-Auoorrelions n Mre Ses A. D We oin our omes from he Pifi Bsin Cpil Mre eserh Cener (PACAP) se minine y he Universiy of hoe Isln. We olle ily mre reurns n iniviul so reurns monhly ring iviy n yerly mre pilizion from PACAP for ll Jpnese seuriies lise on he Toyo So Exhnge (TSE) over he smple perio from Jnury 1979 o Deemer We use mre pilizion he en of he previous yer s our proxy for size. We use wo mesures of ring iviy: ring volume whih we mesure s he yen vlue of shres re; n urnover whih we mesure s he numer of shres re uring he perio ivie y he numer of shres ousning he eginning of he perio. Mre reurn is he reurn on TOPIX vlue-weighe mre inex of ll shres lise on he Firs Seion of he TSE. Mos of he previous lierure on ross-uoorrelion perns in shor-horizon so reurns uses weely. Using weely reurns helps o miige mre mirosruure rele prolems suh s nonsynhronous ring. Therefore we fous our empiril ess on weely size-se porfolio reurns. We onsru he size porfolios s follows: in Deemer of eh yer we rn ll sos se on heir mre pilizion n ivie hem ino five (quinile) porfolios. In forming hese porfolios we exlue sos wih missing size he en of yer n sos wih less hn five monhly urnover poins in yer. Quinile 1 porfolios (S1) omprise smllsize n quinile 5 porfolios (S5) omprise lrge-size sos. We eep he omposiion of he porfolios over he nex yer (Jnury o Deemer of yer 1) n lule he equl-weighe weely porfolio reurns for eh size sore porfolio. We repe his proeure o genere 6

7 weely reurns from Jnury 1979 o Deemer We follow he snr onvenion of luling weely reurns from Wenesy lose o he following Wenesy lose. Sine we wn o exmine he orrelions oniionl on he mre se we lssify he se s UP or epening on wheher he lgge mre reurn over he previous L wees is posiive or negive. Longer horizons for L woul eer pure rmi shifs in he mre se u using longer horizons lso hs he offseing effe of inrese lusering of UP n ses. On he oher hn shor oniioning horizon my e unuly influene y weely fluuions in mre reurns. Sine here is no heoreil guie on L we use he reurn on he vlue-weighe mre inex TOPIX over he previous 12 n 26 wees o eermine he mre se. A he eginning of eh wee if he lgge 12-wee (or 26-wee) mre reurn is posiive (negive) we lssify he se s n UP () se. B. Desripive Sisis Our smple omprises more hn 1500 sos re on he Toyo So Exhnge. This lrge size provies us wih suffiien ross-seion o perform porfolio ess. Pnel A of Tle 1 presens he esripive sisis for he equl-weighe size quinile porfolios for he smple perio of Jnury 1979 o Deemer We ompue he summry sisis s verge vlues in he yer following he porfolio rning perio. As expee he reurns on he smlles firms is ssoie wih he highes men of 0.3% per wee n voliliy of 3.20% ompre o 0.13% n 2.32% respeively for he lrges firms. We lso oserve monooni eline in he firs-orer reurn uoorrelions (AC1) s we move from he smlles o he lrges size quinile. The uoorrelion funion elines rpily s we loo longer lgs of wo o four wees for ll porfolio quiniles. Beuse he uoorrelions lg n eyon re sisilly 7

8 insignifin we se ll our susequen nlysis of porfolio uoorrelions on uoorrelions of up o four lgs. On verge lrger firms hve higher yen volumes hn smller firms. The relion eween urnover n firm size is less ovious. The summry sisis lso inie here is siliy in he firm hrerisis eween he rning n es perios. Pnel B of Tle 1 presens he ross-uoorrelion mries for he size quinile porfolios. Alhough we repor he full ross-uoorrelion mries lg 1 (-1) o onserve spe we repor only he resuls for he exreme porfolios (S1 n S5) lg 2 (-2) o lg (-). Pnel B shows h here is eviene of symmery in he ross-uoorrelions in size-sore porfolio reurns. The orrelion eween he reurns on lgge lrge firms porfolio ( 5-1 ) n urren smll firms porfolio ( 1 ) of 0.2 is higher hn he orrelion eween reurns on lgge smll firms porfolio ( 1-1 ) n urren lrge firms porfolio ( 5 ) of Pnel B lso shows h he ross-uoorrelions ey rpily longer lgs of wo o four wees. We fin h he moun of reurn uoorrelions n he symmery in ross-uoorrelions in he size-sore porfolios in Tle 1 re omprle o hose repore for he U.S. (e.g. Lo n Minly (1990)). [Inser Tle 1 ou here] If he pries of smll firms jus o ommon informion slower re hn o he pries of lrge firms hen prie inreses in lrge firms in perio shoul e followe y prie inreses in smll firms in perio 1. Therefore posiive ross-uoorrelions re onsisen wih smller firms jusing slowly o ommon informion. However his simple nlysis oes no onrol for own-uoorrelion effes. In iion our primry hypohesis is h hese orrelions hnge over ime epening on mre oniions. Our nlysis in he nex seion 8

9 formlly onrols for own reurn uoorrelions effes s well s ess for he imp of mre se. C. Veor Auo-egressions To formlly es for eviene of signifin ross-uoorrelions in size porfolios we perform veor-uoregressive regression (VA) ess. We op he ivrie unoniionl VA proeure use in Brennn Jegeesh n Swminhn (1993). To es for le-lg relion eween reurns on he smlles n lrges size quinile porfolios S1 n S5 we esime he following equions: where 1 ( = 0 ε (1) = 0 γ (2) 1 ) is he urren reurn (reurn lg ) on he smll firm porfolio (S1) n 5 ( 5 ) is he urren reurn (reurn lg ) on he lrge firm porfolio (S5). In he VA seing mesures how well he lgge reurns on porfolio S5 n prei he reurns on porfolio S1 eyon he informion onine in S1. Uner he null hypohesis h here is no le-lg relion eween lrge n smll firms we expe he sum of oeffiiens = 0. This es orrespons o he snr Grnger usliy es for le-lg relion eween he porfolios. The sene of ny reverse le-lg relion eween he wo porfolios implies h = 0. Brennn Jegeesh n Swminhn (1993) show h he ie h he 9

10 lgge reurn on he rpily jusing porfolio preis he urren reurn on slowly jusing porfolio n e ese y he ross-equion hypohesis: =. Our primry hypohesis is h ross-uoorrelions epen on mre oniions. To es his preiion we wo ummy vriles o he VA moel D n D whih UP orrespon o he UP n mre ses in perio - respeively. We esime ivrie oniionl VA for he size porfolios using he following speifiion: 1 = 0 1 UP 1 UP UP 5 5 UP ε (3) 5 = 0 1 UP 1 UP UP 5 5 UP γ () We perform he VA ess seprely for he UP n ses. For insne we es wheher porfolio S5 respons fser hn S1 o ommon informion following he se in equions (3) n () y performing ross equion es =. Sine he porfolio uoorrelions ie ou eyon lg of four wees we esime he VA moels for he wo exreme size quiniles S1 n S5 wih four-wee lgs ( = ). The firs wo pnels in Tle 2 repor hree ses of esimes: unoniionl VA esimes using equions (1) n (2) (in Pnel A); he oniionl VA resuls where he UP n lgge mre 10

11 oniion is efine using lgge 12-wees mre reurn (Pnel B); n lgge 26-wees mre reurn (Pnel B). 5 Pnel A of Tle 2 shows h fer we onrol for he effes of is own lgge reurns lgge lrge firm reurns signifinly ffe he reurns on smll firms ( = 0.35). The lgge reurns on lrge n smll firm porfolios ogeher explin ou 9% of he vriion in he weely reurns of smll firm porfolio. As expee he lgge smll firm reurns o no prei lrge firm reurns ( = -0.05). 6 The unoniionl VA ess sugges le-lg pern in size-sore porfolio reurns h is similr o h of U.S. sos. Pnel B of Tle 2 presens he effe of mre se on size porfolios. We efine he mre se y using he reurn on TOPIX over he previous 12 n 26 wees. The rossuoorrelions eween lgge reurns on lrge firms n urren reurns on smll firms is signifin only in he mre se wih = 0.72 n is signifinly higher hn he oeffiiens in he UP se ( UP = 0.13). 7 In oher wors fer onrolling for he effes of own lgge reurns we fin h 1% erese in he reurn on he lrge firm porfolio les o 0.72% (0.13%) erese in he reurn on he smll firm porfolio following (UP) 5 We noe h sine we re using lgge weely porfolio reurns (up o four lgs) in he VA frmewor he mre se oul hnge uring he shor inervl (wee - o -1). We seprely exmine he se of mre in he shor horizon in Seion III.E. 6 We noe h he sum of oeffiiens n e negive sine we re mesuring he relive spee of jusmens. This resul n e riue o smll vrine of he resiul omponens of reurn in he VA equions. 7 We onfirm his fining y using Wl es whih rejes he null hypohesis h UP = onvenionl signifine levels. 11

12 se. Furhermore he preile smll firm reurn in he se is high relive o he unoniionl men weely reurn of 0.3. This fining emonsres h he mgniue of he le-lg effes is eonomilly imporn in he mre se. We fin h he rossequion Wl es of he le-lg relion is signifin only in he se. The VA esimes h use he lgge 26-wees mre reurn o efine he mre se proue ienil resuls. These resuls n ll susequen finings re rous o he lerne efiniions of mre ses. [Inser Tle 2 ou here] Overll he ifferene in he le-lg perns in he UP n mre ses is sriing. We fin h he le-lg relion eween lrge n smll firm porfolio reurns is exlusive o he se. To he exen h ross-uoorrelions refle slow iffusion of ommon informion our finings sugges h smll firms re slower o respon o mre-wie news. Conversely reen mre gin (UP mre se) inreses he relive spee of so prie jusmen for oh lrge n smll firms. III. Plusile Explnions n ousness Ches A. Do mre friions explin our resuls? Tehnilly mre mirosruure effes suh s he i-s oune non-synhronous ring n sle pries n genere he le-lg pern in reurns (Lo n Minly (1990) n Boouh ihrson n Whielw (199)). Using weely reurns in forming he porfolios reues he possiiliy h our finings re ue o non-synhronous ring. Furher onrols for non-synhronous ring effes o no ler our min finings. For exmple we oin similr resuls (no repore here) when we reform he weely reurns using Wenesy o Tuesy 12

13 pries sipping y eween wo onseuive wees. The sip-y weely reurns voi he prolems ssoie wih i-s errors. A he sme ime hese reurns provie srier filer for non-synhronous ring. Ahn Bououh ihrson n Whielw (2002) sugges h porfolio uoorrelions n ross-uoorrelions n e inue y sle pries ssoie wih hin ring n h ollr volume is eer proxy o pure he effe of sle pries. To ensure h he rossuoorrelions repore in his pper re no riven y sle pries we firs sor ll sos eh yer se on he yen volume of shres re. We hen elimine he oom 20% of sos h hve he lowes vlue of shres re eh yer. We use he remining 80% of sos o form five size-sore porfolio quiniles wih yerly relning. We repe our VA ess for he le-lg effes in UP n mre ses using hese more ively re seuriies. Pnel C of Tle 2 shows h our finings re rous o elimining he exremely low volume sos. We oninue o fin signifin (insignifin) ross-uoorrelions of 0.63% (0.06%) eween lgge reurns on lrge firms n urren reurns on smll firms following (UP) ses. We onlue h mre friions suh s non-synhronous ring i-s oune n hin ring effes nno explin he relion eween mre se n he lgge jusmen of pries o ommon informion. B. Effe of he mgniue of mre reurn We exmine he efiniion of mre se h inorpores he mgniue of lgge mre reurn. If he higher se ross-uoorrelions re ue o smller firms slower jusmen o negive informion he mgniue of he negive informion even shoul 13

14 mer in he eeion of elys in informion ssimilion. We pply hreshol rierion o he efiniion of mre vriles. We efine he mre se s (UP) se only if he umulive lgge mre reurns over he ps 12 wees is less (more) hn -3% (3%). If he mre reurn is eween -3% n 3% hen we efine he mre se s FLAT. If he mre reurn is eween zero n 3% n -3% n zero respeively hen we furher suivie he FLAT mre se ino low posiive n low negive reurn ses FLAT_POS n FLAT_NEG. 8 This formulion llows us o ssess if he slow inorporion of news persiss in exreme negive mre ses. To implemen he es we moify VA equions (3) n () o llow for four ses of he mre (UP FLAT_POS FLAT_NEG n ): where 1 5 = 0 FLAT _ POS FLAT _ NEG = 0 1 FLAT _ POS FLAT _ NEG 1 UP 1 1 UP FLAT _ POS FLAT _ NEG 1 UP UP FLAT _ POS FLAT _ NEG UP FLAT _ POS FLAT _ NEG 5 UP FLAT _ POS FLAT _ NEG UP UP FLAT _ POS ε FLAT _ NEG FLAT _ POS γ FLAT _ NEG (5) (6) D equls one if STATE is of ype UP FLAT_POS FLAT_NEG or n zero STATE oherwise. Pnel A Tle 3 presens our esime of he ove VA speifiion for our smple 8 We oin similr resuls when we se he hreshol 2%. 1

15 perio The ross-uoorrelion eween he urren reurn on smll firms n lgge reurns on lrge firms is signifin 0.8 in he se ompre o n insignifin 0.08 in he UP se. The ross-uoorrelions of 0.58 n 0.33 in he FLAT_NEG n FLAT_POS mre ses re insignifin. We oserve h he ross-uoorrelion oeffiiens eome monoonilly weer s we progress from he high negive mre se o high posiive mre se. Consisen wih our expeions he preiive iliy of lrge so reurns is sronges following n exreme mre se. [Inser Figure 1 ou here] Figure 1 shows h he Jpnese so mre inex TOPIX experiene run-up uring Jpn s so mre ule perio of 1980s. The ull mre oo he inex from 50 in Jnury 1979 o ove 2000 in This rise ws followe y he ule ursing in he 1990s wih he mre inex level ropping y lmos hlf o ou 1100 in Deemer We re inerese in fining ou if he effe of mre ses on reurn ross-uoorrelions in Jpn is ue o ifferenes in mre oniions uring he ule versus he rsh perios or if i refle he generl issue of reion o posiive versus negive ommon informion. To es his lerne hypohesis we spli he smple ino wo superios: n We perform he oniionl VA ess y using equions (5) n (6) for eh superio n he resuls re presene in pnels B n C of Tle 3. We oninue o fin h he rossuoorrelions eween lgge lrge so reurns n urren smll so reurns re signifin only in he se in eh su-perio. This eviene poins o he symmeri influene of mre ses in explining he ime series vriion in he prie jusmen proess. [Inser Tle 3 ou here] 15

16 C. Veor Auo-regressions using Volume Porfolios Chori n Swminhn (2000) sugges h volume plys signifin role in heir nlysis of ross-uoorrelions in so reurns. Aoring o Chori n Swminhn low ring volume elys he prie jusmen proess so h pries of low volume sos jus o ommon informion lg. We exmine if here is signifin ross-uoorrelions in volume sore quinile porfolios in UP n mre ses onrolling for firm size. To onsru he volume porfolios we firs follow he sme proeure s efore forming he size porfolios o oin five quinile porfolios (S1 o S5). Then we rn ll sos in eh of he quinile porfolios se on heir verge yen volume in yer n ivie hem ino five volume-se porfolios. In his wy we ree 25 size-volume porfolios. 9 We hen hoose he wo exreme volume quinile porfolios wihin eh size quinile for furher nlysis. Tle presens he VA ess for he volume sore porfolios wihin size quiniles 1 3 n 5 using he speifiion in equions (5) n (6). For he se of reviy we repor he oeffiiens orresponing o he UP n ses only. Consisen wih he finings in Chori n Swminhn (2000) we fin h high ring volume inreses he spee of ssimilion of ommon informion. More impornly he resuls show h he rossuoorrelions eween he lgge reurn on he high volume porfolio n he urren reurn on he low volume porfolio is signifin in ll size quiniles u only in ses. For exmple mong he lrges firms he reurn ross-orrelion eween lgge high volume porfolio n urren low volume porfolio is signifin (insignifin) 0.6 (0.03) in he (UP) mre se. Alhough ifferenes in ring volume onriue o he spee of jusmen of pries low volume sos experiene slower jusmen in he negive mre se. 16

17 [Inser Tle ou here] D. Cross-Auoorrelions n Mre Coniions in he U.S. Severl ppers repor signifin symmeri ross-uoorrelions in size-sore porfolio reurns in he U.S. mres (inluing Lo n Minly (1990) Meh (1993) MQueen Pinegr n Thorley (1996) Chori n Swminnhn (2000) n ohers). We verify if our finings exen eyon he Jpnese mre y repeing our nlysis using he se of ll orinry ommon sos re on he Amerin n New Yor So Exhnges over he perio 1979 o We form five size quiniles he eginning of eh yer y soring ll firms in he Cenre for eserh in Seuriy Pries (CSP) NYSE/AMEX so file y heir mre pilizion he en of Deemer of he previous yer. We follow he meho ouline in Seion II.B o ompue Wenesy-o-Wenesy weely reurns. As we i in our nlysis of he Jpnese we use he umulive reurn on he CSP vlue-weighe mre inex over he previous 12 wees (L = 12) o eermine if he mre se is UP (posiive) or (negive). 10 Pnel A of Tle 5 presens he esimes of VA equions (3) n () for he U.S. size quinile porfolio reurns. The esimes re similr o hose of he Jpnese sos: he rossuoorrelion eween urren reurns on smll sos n lgge reurns on lrge sos exlusively follows mre ses. Furhermore when we e ino oun he mgniue of he mre se our esimes oninue o yiel similr onlusions. Pnel B of Tle 5 shows he esimes of he VA speifiion in equions (5) n (6). The rossuoorrelion is low n insignifin 0.1 following exreme UP se u in onrs i is high n signifin 0.85 following exreme se. The ross-uoorrelions re 9 We oin quliively similr resuls when we use urnover s our soring vrile for volume. 17

18 insignifin following he mile wo FLAT mre ses. Overll hese finings no only reinfore our inerpreion h here is signifin ely in prie jusmen o negive ommon informion u lso onfirm h he resuls re rous ross oh he Jpnese n U.S. mres. [Inser Tle 5 ou here] E. Effe of he Lengh of he Coniioning Horizon in Jpnese n U.S. mres We use long-horizon reurns (12 wees or longer) o efine he mre se. However MQueen Pinegr n Thorley (1996) (MPT) exmine ross-uoorrelions in size-sore porfolio reurns in he U.S. mres when oniione on lrge so reurns over he shorhorizon. The shor-horizon oniioning inervl use in MPT hs he sme lengh s he horizon over whih reurns re preie. Unlie he imp of long-horizon mre oniions MPT fin h posiive lrge so reurns over he shor inervl inreses he ross-uoorrelions in reurns in he U.S. mre. They fin h when reurns on lrge sos re posiive (i.e. when he mre se is UP) smll so reurns hve lower onemporneous orrelion wih lrge so reurns u higher ross-uoorrelion wih lgge lrge so reurns. Conversely when reurns on lrge sos re negive hey fin h smll so reurns hve high onemporneous orrelion wih lrge sos u hve insignifin ross-uoorrelions wih lgge lrge so reurns. Chng MQueen n Pinegr (1999) exen he MPT nlysis y invesiging monhly reurns in severl Asin mres n repor h he ireionl symmery in MPT is no universl. When hey oniion on posiive n negive shor-horizon monhly reurns hese uhors o no fin eviene of symmery in he ross-uoorrelion pern in monhly 10 Consisen wih MQueen Pinegr n Thorley (1996) weely U.S. quinile porfolio reurns exhii 18

19 Jpnese so reurns. Apprenly he imp of mre oniion on ross-uoorrelions epens on he horizon over whih mre oniion is mesure. Here we invesige if he elye prie reion o negive mre-wie news persiss when we mesure i over he long oniioning horizon fer onrolling for he posiive effe of shor-horizon mre oniion repore in MPT for U.S. sos. To o his we inroue wosge long n shor-horizon mre oniioning where we mesure he shor horizon over he previous four wees n he long horizon over he prior 12 wees (s previously efine). Speifilly he wo-sge mre se is efine s UP-UP (-) only if he umulive mre reurns is posiive (negive) over he long-horizon from wee -16 o -5 n posiive (negive) over he shor-horizon from wee - o -1. Similrly he wo-sge mre se is efine s UP- (-UP) if he umulive mre reurn is posiive (negive) over he long-horizon u negive (posiive) over he shor-horizon. We moify he VA se-up in equions (3) n () o llow for vriion in oh shor n long horizon mre oniions: 1 = 0 UP UP _ UP _ UP UP UP UP _ UP _ UP UP UP _ UP _ UP UP 5 UP _ UP _ ε (7) signifin ross-uoorrelions up o 7 lgs. To e onservive we repor he resuls when =7. 19

20 5 = 0 UP UP _ UP _ UP UP UP UP _ UP _ UP UP UP _ UP _ UP UP 5 UP _ UP _ γ (8) where D STATE equls one if STATE is of ype UP-UP UP- -UP or - n zero oherwise. The empiril esimes of he VA equions (7) n (8) for he Jpnese n U.S. size-sore weely porfolio reurns re repore in Pnels A n B of Tle 6 respeively. In Tle 6 Pnel A shows h he weely ross-uoorrelions in Jpnese so reurns re signifinly posiive in he - mre ses u no in he -UP ses. In oher wors he mre ses in he shor s well s he long horizons onriue o ross-uoorrelions in weely reurns. The empiril VA esimes in Pnel B of Tle 6 h uses he U.S. weely size-se porfolio reurns re slighly ifferen. The ross-uoorrelions re signifin in oh he - n UP-UP mre ses. Consisen wih MPT he shor-horizon UP mre se s posiively o weely reurn ross-uoorrelions. 11 Neverheless fer jusing for he ireionl symmery ue o he shor-erm mre oniioning repore in MPT for U.S. sos we oninue o fin h weely ross-uoorrelions re signifin in he long-horizon mre se. A longer oniioning perio minimizes he effe of high frequeny 11 MPT sugges h he higher shor-horizon UP mre ross-uoorrelions in he U.S. re onsisen wih symmery in posiive (shor-erm) fee ring y insiuions. The eviene in our pper inies h he effe of long-horizon mre oniion is sepre from h repore in MPT. We lso nlyze he rossuoorrelion perns in monhly reurns in size-sore quinile porfolios in Jpn n U.S. (resuls no repore 20

21 fluuions in he mre n is more liely o pure elys in prie jusmens ue o ring resriions onsisen wih he finings of prie jusmen elys in Hong Lim n Sein (2000) n Chen Hong n Sein (2002). 12 An ineresing exension woul e o exmine he eonomi soures of he ifferenil effes of long n shor horizon mre ses whih we leve for fuure reserh. [Inser Tle 6 ou here] F. Anorml Tring Volume n Mre Coniions If ring resriions suh s shor-selling onsrins uses smll firms o re slowly o negive mre-wie news hen ring iviy woul e lower following se. 13 To exmine if here re signifin hnges in ring iviy in eh mre se we require some mesure of inrese or erese in volume he porfolio level. The following wo mesures of norml ring for porfolio s ime re hosen: 1 L = AVOL 1s VOLs VOLs j (9) L j= 1 L VOLs VOLs j L j= AVOL 2s = 1 L (10) VOL s j L j= here). Overll our eviene using monhly reurns oes no hnge our min onlusions lhough he rossuoorrelions re no signifin for Jpn s noe y Chng MQueen n Pinegr (1999). 12 Our finings on signifin weely ross-uoorrelions in he - mre ses re lso rous o onrolling for onemporneous orrelions eween reurns on lrge n smll firms using he liner regression frmewor in MPT. 13 These ring resriions re liely o e exere in he Jpnese mre euse of he imposiion of oher prie limis in iion o shor-sle onsrins. im n hee (1997) show h pries of sos re in Jpn exhii greer ily prie oninuions (elye prie isovery) when he sos hi he upper or lower ily prie limis. George n Hwng (1995) n Lehmnn n Moes (199) repor h he resriion on mximum prie vriion eween res on he Toyo So Exhnge slows he inry prie isovery proess n les o orer reups. Togeher hese prohiiions reue ring n mpen he jusmen of pries o informion priulrly for smll firms. 21

22 where VOL s is he ggrege weely yen volume for size quinile s for wee n he enhmr weely expee level of volume ( L = 1 L VOLs j j ) is ompue s he verge weely volume for porfolio s over he previous 12 (L=12) wees whih orrespons o he numer of wees we use o efine he long horizon mre se. AVOL1 mesures he hnge in volume relive o he expee level of volume n AVOL2 mesures he perenge hnge in volume. A posiive AVOL1 (or AVOL2) implies n inrese in ggrege ring volume relive o he porfolio s expee ring volume. In Tle 7 he verge norml yen ring volume mesures (AVOL1 n AVOL2) show erese (inrese) in volume in he (UP) se priulrly for he smller size quiniles. For exmple he verge volume for he smlles size quinile sos rops y 11 illion yen in se u inreses y 7 illion yen in he UP se. In erms of perenge hnges in volume (AVOL2) here is 19 peren inrese in volume for he smlles quinile in he UP ses. The norml ring volume is signifinly lower in he se hn in he UP se for he smller firms iniing h he mre se is ssoie wih rop in ring volume priulrly for he smller sos. Our erlier resuls inie h he ross-uoorrelions re influene y mre ses in he long s well s he shor horizons. We exmine if he norml ring volume is ifferen when we oniion on oh long n shor horizon mre ses. The verge norml ring volume (AVOL1) esimes using he wo-sge mre oniioning re presene in Pnel B of Tle 7. The pern in he verge norml volume esimes sugges h oh shor n long horizon ses onriue o rop in volume. However for he smlles quinile he rop in norml ring is signifin in he - se. Consisen wih our resuls for ross-uoorrelions in Tle 6 he norml ring volume for he smll firms in he 22

23 - se is signifinly lower hn in he -UP se. In unrepore resuls we fin h he esimes re similr when we use AVOL2 n when he long-horizon mre se is mesure over 26 wees. Overll our resuls suppor he hypohesis h so reurn ross-uoorrelions rele o onsrins in ring iviy h impee he ssimilion of news in smll firms. [Inser Tle 7 ou here] G. Spee of Ajusmen in Iniviul Sos n Mre Coniions So fr we hve se our eviene on ross-uoorrelions on mesures erive from porfolio reurns. Now we exmine mesures of ely in n iniviul seuriy s response o ommon news ing ino oun he se of he mre. We oin he ely mesure y regressing weely iniviul so reurns on oh urren mre reurns n ps n fuure mre reurns oniioning on UP n mre ses. Our ie is o eermine if he lgge response of iniviul so reurns o informion in mre reurns is slower in mre se. We run he following ime-series Dimson e regression for eh so i for he enire smple perio: 1 = i i i UP m DUP β i m = 0 = 0 = β * γ ε (11) i m i where i is he reurn on so i n m is he reurn on he vlue-weighe mre inex TOPIX ime. D STATE equls one if STATE is of ype UP or n zero oherwise. The mre se is efine s UP () if he umulive mre reurn over he previous 12 wees is posiive (negive). If so juss slowly o ommon news i will hve higher orrelion wih lgge mre reurns n lower orrelion wih onemporneous mre reurn. The ely mesure pilizes on his inuiion. For eh firm ely in he se is 23

24 se on he sum of lgge es in he se ivie y he onemporneous e. We efine DELAY_ s log rnsformion of he spee of jusmen rio: DELAY _ i = 1 X i 1 e (12) where X i = βi βi 0. We efine DELAY_UP in he sme wy. These mesures of ely re losely rele o he spee of jusmen use in Chori n Swminhn (2000). Dely mesures how fs so res o ommon informion epening on he se of he mre; he longer he ely he slower is he spee of jusmen. Coniionl on he se of he mre he vlue of ely epens on he exen o whih he so s reurns orrele wih he lgge mre reurn relive o is onemporneous orrelion wih he mre. The logi rnsformion of X UPi n X i mpens he effe of exreme vlues so h he vlues of DELAY_UP i n DELAY_ i re y onsruion oune eween zero n one. A so h juss slowly o informion onine in lgge mre reurns will regiser DELAY loser o one. If he mre se is ssoie wih slower prie jusmen o ommon news we expe ely o e higher in he se. To ensure h our resuls re rous o how we mesure mre ses we e ino onsierion he effe of mgniue of mre reurns n he wo-sge mre oniioning isusse in Seions III.B n III.E. Firs we ompue ely using he following moifie regression: i = 0 = β i i = 0 β i UP m m UP 1 γ = = 0 i β i FLAT m ε i m FLAT (13) 2

25 where D STATE equls one if STATE is of ype UP or FLAT n zero oherwise. The mre se is efine s UP () if he umulive mre reurn over he previous 12 wees is more (less) hn 3% (-3%). If he mre reurn is eween -3% n 3% hen he mre se is efine s FLAT. We ompue he verge ely for firm i in eh of he hree mre ses: DELAY_UP DELAY_FLAT n DELAY_. Similrly our regression speifiion o oin esimes of elys in prie jusmen in iniviul firms using he wosge mre oniioning pproh is hus: i = 0 1 = = β γ i _ UP i i = 0 m β i UP _ UP ε m i m _ UP UP _ UP = 0 β = 0 β i UP _ i _ m m UP (1) where D STATE equls one if STATE is of ype UP-UP UP- - or - n zero oherwise. The verge ely for firm i in eh of he four ifferen mre ses re enoe s DELAY_UP_UP DELAY_UP_ DELAY UP n DELAY. In Pnel A of Tle 8 he empiril esimes of he verge ely elines s we move from smll o lrge firms onsisen wih he view h smller firms e longer o jus o ommon informion. More ineresingly here is signifinly higher ely in prie jusmens in he se. For he smlles quinile he verge ely vlue is 0.79 in he se ompre o n verge of 0.65 in he UP se. For he overll smple ely is signifinly higher in he se 0.68 ompre o 0.59 in he UP se. Pnel B of Tle 8 repors similr resuls when we use equion 13 o eermine he verge spee of jusmen for he hree mre ses. The resuls suppor our hypohesis h he 25

26 verge spee of jusmen in seuriy pries is signifinly higher in he se priulrly mong he smlles firms. The verge spee of jusmen grully inreses s he mre se eomes more posiive. 1 Finlly our esimes using he wo-sge mre oniioning in Pnel C Tle 8 orroore wih he fining in Tle 6 h ross-uoorrelions n prie jusmen elys in smll Jpnese sos follow mre se in oh he shor n long horizons. For exmple he smlles size quinile firms isply he highes prie ely of 0.79 in he - mre ses whih is signifinly ifferen from ely in he -UP ses. Hene he spee of prie jusmens is ffee y shor n long horizon mre oniions. [Inser Tle 8 ou here] IV. Conlusion In his pper we use weely reurns on seuriies re on he Jpnese So Exhnge o exmine he ime-series vriions in reurn ross-uoorrelions n spee of jusmen of so pries o ommon informion. We show h he se of he mre plys riil role in explining he re of prie jusmen. The se of he mre is mesure over he shor (wee -1 o -) n long (wee -5 o -16) horizons. When he mre se is oniione on umulive lgge mre reurns over he long horizon we fin h ross-uoorrelions in urren reurns on smll firms n lgge lrge so reurns re onfine o negive () mre se. The ross-uoorrelion oeffiiens eome monoonilly sronger s we progress from high posiive (UP) mre se o high negive () mre se. We lso fin h he symmeri ross-uoorrelions in UP n ses hol for high n low volume porfolios reinforing he role of ring volume in ffeing he spee of prie 1 The fining h ll ely mesures re ove 0.5 suggess h on verge he sos in he smple hve slower spee of jusmen relive o he vlue-weighe mre inex TOPIX. 26

27 jusmen (Chori n Swminhn (2000)). Our finings re rous o mre mirosruure onerns suh s non-synhronous ring hin ring prolems n i-s effes. We lso exmine he relive imporne of he mre ses mesure over he shor n long horizons in explining he ineremporl vriion in he re of jusmen of smll so pries o mre-wie informion. Using wo-sge shor n long horizon mre oniioning we show h urren weely reurns on porfolio of smll sos re signifinly orrele wih lgge weely reurns on lrge so porfolio only when he mre is in oh horizons (- ses). We sugges h ring resriions (e.g. shor-sle onsrins) n rnsion oss (e.g. shoring oss) preven so pries from immeiely refleing negive informion. This is suppore y our finings of erese norml ring volume following perios of eline in ggrege mre vlue in oh he shor n long horizons priulrly for smll sos. We lso oserve higher ring iviy when he long n shor mre oniioning inie UP ses suggesing fser re of informion ssimilion in pries of lrge s well s smll firms. Our inferene on he ifferenil spee of jusmen re srenghene y he oservion of higher prie jusmen elys o ommon informion in iniviul sos priulrly for firms wih smll mre pilizion when mre hs eline in vlue in he shor n long horizons. We lso pply our ess o he sos re on U.S. so mres. Consisen wih he finings in MQueen Pinegr n Thorley (1996) shor-horizon UP ses onriue o inrese ross-uoorrelions in reurns. Afer inorporing his ireionl symmery using he wo-sge mre oniioning pproh we oninue o fin h weely reurns on smll U.S. firms exhii signifin ross-uoorrelions in - ses similr o our finings for Jpnese sos. 27

28 The umulive eviene presene in his pper suppors he hypohesis h rossuoorrelions in reurns re rele o uner-reion of so pries o negive mre-wie informion. Overll our finings sugges h explnions for ross-seionl ifferenes in preiiliy in reurns nee o e exene o llow for iner-emporl epenene of spee of jusmen on shor n long horizon mre oniions. 28

29 eferenes Areu D. n Brunnermeier M Synhronizion ris n elye rirge. Journl of Finnil Eonomis 66: Ahn D.H.; Bououh J.; ihrson M.; n Whielw.F Pril jusmens or sle pries? Impliions from so inex n fuures reurn uoorrelions. eview of Finnil Suies 15: Brinh S. G.; le J..; n Noe T.H Of shephers sheep n he rossuoorrelions in equiy reurns. eview of Finnil Suies 8: Bououh J.; ihrson M.; n Whielw.F A le of hree shools: Insighs on uoorrelions of shor-horizon so reurns. eview of Finnil Suies 6: Brennn M. J.; Jegeesh. N.; n Swminhn B Invesmen nlysis n he jusmen of so pries o ommon informion. eview of Finnil Suies 6: Chng E.; MQueen G.; n Pinegr P Cross-uoorrelion in Asin so mres. Pifi-Bsin Finne Journl 7: Chen J.; Hong H.; n Sein J.C Breh of ownership n so reurns. Journl of Finnil Eonomis 66: Chori T. Swminhn B Tring volume n ross-uoorrelions in so reurns. Journl of Finne 55: Conr J.; Hmee A.; n Nien C Volume n uoovrines in shor-horizon iniviul seuriy reurns. Journl of Finne 9: Cooper M.; Guierrez.; n Hmee A Mre ses n momenum. Journl of Finne 59: Dimon D. n Verehi Informion ggregion in noisy expeions 29

30 eonomy. Journl of Finne 9: Gezy C.; Muso D.; n ee A Sos re speil oo: n nlysis of he equiy lening mre. Journl of Finnil Eonomi 66: George T.G. n Hwng C.Y Trnsiory prie hnges n prie-limi rules: eviene from Toyo So Exhnge. Journl of Finnil n Quniive Anlysis 30: Holen C. W. n Surhmnym A Long-live prive informion n imperfe ompeiion. Journl of Finne 7: Hong H.; Lim T.; n Sein J.C B news rvels slowly: Size nlys overge n he profiiliy of momenum sregies. Journl of Finne 55: Jones C.M. n Lmon O.A Shor-sle onsrins n so reurns. Journl of Finnil Eonomis 66: im.l. n hee S.G Prie limi performne: Eviene from he Toyo So Exhnge. Journl of Finne 52: Lehmnn B Fs mringles n mre effiieny. Qurerly Journl of Eonomis 105: Lehmnn B. n Moes D Tring n liquiiy on he Toyo So Exhnge: A ir s eye view. Journl of Finne 9: Lo A. W. n Minly A.C When re onrrin profis ue o so mre overreion? eview of Finnil Suies 3: MQueen G.; Pinegr M.; n Thornley S Delye reion o goo news n he rossuoorrelion of porfolio reurns. Journl of Finne 51: Meh T. S Porfolio reurn uoorrelion. Journl of Finnil Eonomis 3:

31 Meron.C A simple moel of pil mre equilirium wih inomplee informion. Journl of Finne 2: Miller E.M is uneriny n ivergene of opinions. Journl of Finne 32:

32 Inex Vlue Jn-79 Mr-81 My-83 Jul-85 O-87 De-89 Fe-92 My-9 Jul-96 Sep-98 De FIG. 1. Jpnese Mre Inex (TOPIX). The smple perio is

33 TABLE 1 Desripive Sisis n Auoorrelion Mries for Size Porfolios Pnel A: Desripive Sisis Porfolio Men S Dev Yen AC1 AC2 AC3 AC Size (%) (%) Volume Turnover S S S S S Pnel B: Auoorrelion Mries NOTE. Pnel A repors he esripive sisis for he size porfolios. The sisis inlue weely verge porfolio reurn (Men) snr eviion (S Dev) firs-orer o fourh-orer uoorrelion (AC1-AC) size yen volume n urnover for eh porfolio. The sisis re ompue using weely equl-weighe porfolio reurn en-of-yer size verge yen volume n urnover in he yer. S1 refers o smlles size quinile porfolio; S5 refers o he lrges size quinile porfolio. The weely reurns for eh seuriy re lule from Wenesy lose o he following Wenesy lose. Size is he mre pilizion he en of yer (in illions of Yen). Yen Volume is he vlue of shres re (in illions of Yen). Turnover is he perenge of he numer of shres re ivie y he numer of shres ousning. Pnel B repors he uoorrelion mries for he size porfolios. i refers o he weely equl-weighe porfolio reurn orresponing o he i h quinile ime. 33

34 TABLE 2 Veor Auo-egressions for Size Porfolios Pnel A: Unoniionl VA LHS SMALL LAGE 2 Wl-es S1 0.20** 0.35*** *** (2.06) (2.73) S (-0.72) (1.37) Pnel B: Coniionl VA; L = 12 wees LHS SMALL_UP LAGE_UP SMALL_ LAGE_ 2 Wl-es S1 0.*** *** 0.11 UP: 1.7 (5.7) (1.0) (-0.55) (2.77) S * : 37.83*** (0.75) (1.89) (-0.96) (0.5) L = 26 wees S1 0.6*** *** 0.12 UP: 0.5 (5.05) (0.99) (-0.87) (3.08) S : 53.36*** (1.11) (0.72) (-1.6) (1.) Pnel C: Coniionl VA (exlues sos in he lowes volume quinile L=12 wees) LHS SMALL_UP LAGE_UP SMALL_ LAGE_ 2 Wl-es S1 0.*** ** 0.07 UP: 0.00 (.72) (0.51) (-0.) (1.95) S : 29.89*** (0.88) (1.57) (-0.88) (0.8) NOTE. Pnel A repors he oeffiiens for he ivrie unoniionl VA wih he following speifiion: 1 = ε n 5 = γ Pnels B n C repor he oeffiiens for he ivrie oniionl VA wih he following speifiion: 1 = 0 UP 1 UP UP 1 UP 1 1 ε 5 = 0 UP 1 UP UP 1 UP 1 1 γ 1 ( 5 ) is he reurn on he smlles (lrges) size quinile porfolio ime. SI refers o porfolio of size quinile I. The VA is esime =. SMALL refers o or n LAGE refers o or. SMALL_UP (LAGE_UP) enoes he sum of oeffiiens UP ( UP ) or UP ( UP ) n SMALL_ (LAGE_) enoes he sum of oeffiiens ( ) or ( ). For Pnels B n C he mre se ummy vrile DUP ( D ) equls one if he lgge umulive mre reurn 3

35 over he previous L wees is posiive (negive). Pnel C exlues sos whih re in he lowes volume quinile (oom 20%). For Pnel A Wl-es is he es-sisi for he ross-equion null-hypohesis: =. For Pnels B n C UP is he es-sisi for he null-hypohesis: UP = UP n is he es-sisi for he null-hypohesis: =. 2 is he juse oeffiien of vriion. The -sisis re repore in prenheses. *** ** n * represen signifine he 1% 5% n 10% levels respeively. 35

36 TABLE 3 Veor Auo-egressions: Mgniue of Lgge Mre eurns n Su-Perio Anlysis Pnel A: Whole Perio ( ) LHS SMALL_UP LAGE_UP SMALL_FLAT_POS LAGE_FLAT_POS SMALL_FLAT_NEG LAGE_FLAT_NEG SMALL_ LAGE_ 2 Wl-es S1 0.5*** *** *** 0.11 UP: 0.22 (.80) (0.50) (2.93) (1.37) (-0.5) (1.61) (-0.61) (2.71) S ** : 37.30*** (0.8) (1.21) (0.1) (2.19) (-0.56) (-0.58) (-0.89) (0.83) Pnel B: Su-Perio 1 ( ) S1 0.*** ** ** 0.10 UP: 0.23 (.17) (0.01) (2.38) (1.00) (-0.9) (1.08) (-0.60) (2.36) S * : 19.86*** (0.9) (0.96) (-0.3) (1.9) (-1.11) (-0.79) (-1.20) (1.08) Pnel C: Su-Perio 2 ( ) S1 0.** * 0.09 UP: 0.02 (2.26) (0.21) (0.9) (0.92) (-0.6) (1.21) (-0.32) (1.67) S : 17.66*** (0.53) (0.05) (0.69) (0.7) (0.18) (-0.17) (-0.32) (0.39) NOTE. The le repors he oeffiiens for he i-vrie oniionl VA using wih he following speifiion: 1 = 0 UP 1 UP UP 5 UP FLAT _ POS 1 FLAT _ POS FLAT _ POS 5 FLAT _ POS 5 FLAT _ NEG = 0 FLAT _ NEG 1 UP 1 1 FLAT _ NEG UP FLAT _ NEG UP FLAT _ NEG 5 FLAT _ NEG 5 UP 5 FLAT _ NEG FLAT _ POS FLAT _ NEG FLAT _ POS FLAT _ POS FLAT _ POS ε γ 1 1 ( 5 ) is he reurn on he smlles (lrges) size quinile porfolio. SI refers o porfolio of size quinile I. The VA is esime = wees. The mre se is efine 36

37 s UP FLAT_POS FLAT_NEG or se on wheher he lgge 12-wees mre reurn is ove 3% eween zero n 3% eween -3% n zero or elow -3%. UP ( D STATE equls one if STATE ype is of ype UP FLAT_POS FLAT_NEG or n zero oherwise. SMALL_UP (LAGE_UP) enoes he sum of oeffiiens UP ) or UP ( UP ). The oeffiiens for he oher hree ses re similrly efine. Pnel A repors he resuls for he whole perio: 1979 o Pnel B n C repor he resuls for wo su-perios: n UP is he es-sisi for he null-hypohesis: UP = UP n is he es- sisi for he null-hypohesis: =. The -sisis re repore in prenheses. *** ** n * represen signifine he 1% 5% n 10% levels respeively. 37

38 TABLE Veor Auo-egression for Size-Volume Porfolios LHS SMALL_UP LAGE_UP SMALL_ LAGE_ 2 Wl-es SV *** -0.* 0.69*** 0.16 UP: 8.29*** (0.16) (.33) (-1.91) (3.67) SV ** -0.53* 0.66** 0.06 : 15.16*** (0.37 (2.02) (-1.68) (2.5) SV ** ** 0.10 UP: 0.79 (2.39) (1.51) (-1.22) (2.56) SV :.8** (1.5) (0.8) (-1.27) (1.18) SV *** 0.0 UP: 0.79 (1.52) (0.21) (-1.56) (2.73) SV :.8** (1.08) (-0.06) (-0.85) (0.86) NOTE. The le repors he oeffiiens for he ivrie oniionl VA using size-volume porfolios: 1 = 0 UP 1 UP UP 5 UP FLAT _ POS 1 FLAT _ POS 5 FLAT _ POS = 0 1 FLAT _ POS 1 5 UP 5 FLAT _ POS 1 UP FLAT _ POS FLAT _ NEG UP FLAT _ NEG 1 UP 1 ε FLAT _ NEG γ FLAT _ NEG FLAT _ POS 1 FLAT _ NEG FLAT _ NEG 5 FLAT _ POS 5 FLAT _ NEG FLAT _ NEG 1 ( 5 ) is he reurn on he lowes (highes) volume quinile porfolio wihin eh size quinile. SVIJ refers o porfolio of size quinile I n volume quinile J. The VA is esime = wees. The mre se is efine s UP FLAT_POS FLAT_NEG or se on wheher he lgge 12-wees mre reurn is ove 3% eween zero n 3% eween -3% n zero or elow -3%. D STATE equls one if STATE ype is of ype UP FLAT_UP FLAT_ or n zero oherwise. SMALL_UP (LAGE_UP) enoes he sum of oeffiiens UP ( UP ) or UP ( UP ) n SMALL_ (LAGE_) enoes he sum of oeffiiens ( ) or ( ). UP is he es-sisi for he null-hypohesis: UP = UP n is he es-sisi for he null- hypohesis: =. The -sisis re repore in prenheses. *** ** n * represen signifine he 1% 5% n 10% levels respeively. 38

39 39 TABLE 5 Veor Auo-egressions: US Size Porfolios Pnel A LHS SMALL_UP LAGE_UP SMALL_ LAGE_ 2 Wl-es S1 0.0*** ** 0.1 UP: 0.37 (5.13) (1.16) (0.7) (2.06) S : 15.35*** (-0.39) (0.10) (-1.9) (1.26) Pnel B LHS SMALL_UP LAGE_UP SMALL_FLAT_POS LAGE_FLAT_POS SMALL_FLAT_NEG LAGE_FLAT_NEG SMALL_ LAGE_ 2 Wl-es S1 0.*** ** 0.16 UP: 1.61 (.6) (0.77) (1.58) (1.51) (1.35) (0.09) (-0.68) (2.5) S ** 0.03 : 15.65*** (0.12) (-0.8) (-1.57) (1.26) (-0.76) (-1.10) (-1.51) (2.01) NOTE. A ivrie oniionl VA is esime for he size-sore weely quinile porfolio reurns of NYSE/AMEX sos for he perio 1979 o Pnel A repors he oeffiiens for he following VA speifiion: UP UP UP UP D D D D ε = = = = = * * * * UP UP UP UP D D D D γ = = = = = * * * * Pnel B repors he oeffiiens for he following VA speifiion: NEG FLAT NEG FLAT NEG FLAT NEG FLAT POS FLAT POS FLAT POS FLAT POS FLAT UP UP UP UP D D D D D D D D ε = = = = = = = = = _ 5 _ 1 _ 1 _ 1 _ 5 _ 1 _ 1 _ * * * * * * * *

40 5 = 0 UP 1 UP UP 5 UP FLAT _ POS 1 FLAT _ POS FLAT _ POS 5 FLAT _ POS FLAT _ NEG 1 FLAT _ NEG FLAT _ NEG 5 FLAT _ NEG 1 5 γ 1 ( 5 ) is he reurn on he smlles (lrges) size quinile porfolio. SI refers o porfolio of size quinile I. The VA is esime = 7 wees. In Pnel A he mre se is efine s UP () se if he lgge 12-wees mre reurn is posiive (negive). D STATE equls one if STATE ype is of ype UP () n zero oherwise. In Pnel B he mre se is efine s UP FLAT_POS FLAT_NEG or se on wheher he lgge 12-wees mre reurn is ove 3% eween zero n 3% eween -3% n zero or elow -3%. SMALL_UP (LAGE_UP) enoes he sum of oeffiiens UP ( UP ) or UP ( UP ). The 7 7 oeffiiens for he oher hree ses re similrly efine. UP is he es-sisi for he null-hypohesis: UP = UP n is he es-sisi for he nullhypohesis: =. The -sisis re repore in prenheses. 7 7 *** ** n * represen signifine he 1% 5% n 10% levels respeively. 0

41 TABLE 6 Veor Auo-egressions: Two-Sge Long- n Shor-Horizon Coniioning Pnel A LHS SMALL_UP-UP SMALL_UP_ SMALL UP SMALL LAGE _UP_UP LAGE _UP_ LAGE UP LAGE 2 S1 0.7*** *** 0.12 (5.1) (0.90) (0.52) (-0.70) (1.3) (0.71) (1.53) (2.20) S (0.62) (0.50) (-0.19) (-0.93) (1.3) (0.26) (0.55) (0.57) Pnel B S1 0.*** 0.57*** ** * 0.17 (.96) (3.63) (0.91) (-1.29) (2.17) (-1.36) (1.22) (1.68) S * (0.20) (0.57) (-0.11) (-1.70) (-0.22) (-1.08) (-0.02) (1.27) NOTE. A ivrie oniionl VA is esime for size-sore weely quinile porfolio reurns of TOPIX n NYSE/AMEX sos wih he following VA speifiion: 1 5 = 0 _ UP _ = 0 _ UP UP _ UP _ UP _ UP 5 1 UP _ UP _ UP 1 _ UP _ UP _ UP UP ε UP _ UP _ UP γ UP _ UP UP _ UP _ UP UP _ UP _ UP UP _ 1 _ UP UP UP UP _ UP _ 5 5 UP _ UP _ 1

42 1 ( 5 ) is he reurn on he smlles (lrges) size quinile porfolio. SI refers o porfolio of size quinile I. The VA is esime = wees for TOPIX sos (Pnel A) n = 7 wees for NYSE/AMEX sos (Pnel B). D UP _ UP ( D _ equls one if oh he lgge long-horizon (from = -16 o = -5) mre reurn n he shor-horizon (from = - o = -1) mre reurn is posiive (negive) n zero oherwise. Similrly D UP _ ( D _ UP ) equls one if he lgge long-horizon mre reurn is posiive (negive) n shor-horizon mre reurn is negive (posiive) n zero oherwise. SMALL_UP_UP (LAGE_UP_UP) enoes he sum of oeffiiens UP _ UP ( UP _ UP ) or = 1 similrly efine. The -sisis re repore in prenheses. *** ** n * represen signifine he 1% 5% n 10% levels respeively. UP _ UP ( UP _ UP ). The oeffiiens for he oher mre ses re 2

43 TABLE 7 Anorml Tring Volume n Mre Coniions Pnel A: Averge Anorml Volume (Long-Horizon Mre Coniioning) AVOL1 AVOL2 Porfolio UP UP= UP UP = S (3.89) (.07) (2.22) (-3.23) (6.28) (0.01) S (.12) (3.39) (2.23) (-3.57) (5.30) (-0.16) S (3.13) (1.03) (1.57) (-2.90) (3.6) (1.03) S (2.86) (1.) (1.2) (-2.70) (3.12) (0.57) S (-0.02) (0.69) (0.06) (0.09) (3.26) (1.86) MT (2.30) (2.05) (1.18) (-2.0) (3.30) (1.01) Pnel B: Averge Anorml Volume (Two-Sge Mre Coniioning) AVOL1 Porfolio UP-UP UP- -UP - -UP = - S (.28) (3.96) (-1.9) (0.97) (-.70) S (5.05) (3.0) (-1.55) (1.65) (-5.10) S (5.19) (3.8) (-3.70) (2.77) (-.56) S (3.85) (.21) (-3.8) (1.30) (-.55) S (1.50) (3.12) (-5.85) (1.60) (-0.17) MT (1.51) (2.87) (-.50) (0.26) (-1.80) NOTE. The le repors he verge norml yen ring volume for he size quinile porfolios (S1 o S5) n he mre porfolio (MT). Anorml ring volume AVOL1 n AVOL2 re efine s follows: 1 L = VOL s VOL s. j 1 L L j= AVOL 1s VOLs VOLs. j n AVOL 2s = L j= 1 L VOLs. j L j= where VOL s is he ggrege weely volume (in illions of yen) for size quinile s for wee. Mre volume is repore in rillions of yen. In Pnel A he mre se is efine s UP () se if he lgge long horizon (from =-16 o =-5) mre reurn is posiive (negive). In Pnel B he mre se is efine s UP-UP (- ) if oh he lgge long-horizon n shor-horizon (from =- o =-1) mre reurns re posiive (negive). Similrly he mre se is efine s UP- (-UP) if he lgge long-horizon mre reurn is posiive (negive) n shor-horizon mre reurn is negive (posiive). In Pnel A he olumn UP = repors he -sisis for he equliy of norml volume ross UP n ses. In Pnel B he olumn

44 -UP = - repors he -sisis for he equliy of norml vlue ross -UP n - ses. The -sisis re repore in prenheses.

45 TABLE 8 Spee of Ajusmen in Iniviul Firms n Mre Coniions Pnel A Porfolio DELAY_UP DELAY_ DELAY_UP = DELAY_ (-ss) S (-1.68) S (-13.18) S (-12.91) S (-9.3) S (-.78) Overll (-2.55) Pnel B Porfolio DELAY_UP DELAY_FLAT DELAY_ DELAY_UP = DELAY_ (-ss) S (-15.50) S (-15.72) S (-1.) S (-10.65) S (-6.85) Overll (-27.87) Pnel C Porfolio DELAY_UP_UP DELAY_UP_ DELAY UP DELAY DELAY UP = DELAY (-ss) S (-5.08) S (-.8) S (-5.16) S (-7.62) S (-7.87) Overll (-13.8) NOTE. This le repors he verge spee of jusmen mesure (DELAY) for he size quinile porfolios (S1 o S5) in eh mre se. DELAY is mesure using Dimson e regressions using wees of le n lgge mre reurns (see equions 9 n 11 in ex). In Pnel A mre se is efine s UP () se if he lgge long horizon (from =-16 o =-5) mre reurn is posiive (negive). In Pnel B mre se is efine s UP FLAT or se on wheher he lgge long horizon mre reurn is ove 3% eween 3% n -3% or elow -3% respeively. In Pnel C mre se is efine s UP_UP (_) se if oh he lgge long-horizon n he shor-horizon (from =- o =-1) mre reurns re posiive (negive). Similrly he mre se is efine s UP- (-UP) if he lgge long-horizon mre reurn is posiive (negive) n shorhorizon mre reurn is negive (posiive). The repore figures re he verge mesure of ely ross ll sos in he quinile (overll) in he orresponing mre se. In Pnel A he olumn DELAY_UP = DELAY_ repors he -sisis for he equliy of DELAY_UP n DELAY_. The -sisis olumn in Pnels B n C re similrly efine. 5