Multi-Market Trading and Liquidity: Theory and Evidence

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1 Mult-Mrket Trdng nd Lqudty: Theory nd Evdence Shmuel Bruch, G. Andrew Kroly, b* Mchel L. Lemmon Eccles School of Busness, Unversty of Uth, Slt Lke Cty, UT 84, USA b Fsher College of Busness, Oho Stte Unversty, Columbus, OH 430, USA Abstrct We develop nd test new model of mult-mrket trdng to expln the dfferences n the foregn shre of trdng volume of nterntonlly cross-lsted stocks. The model derves n equlbrum whch predcts tht, under frly generl condtons, the dstrbuton of trdng volume cross exchnges competng for order flow s relted to the correlton of the cross-lsted sset returns tht rse n the respectve mrkets. Tht s, volume s proportonlly hgher on the exchnge n whch the cross-lsted sset returns hve greter correlton wth returns of other ssets trded on tht mrket. We test ths predcton wth weekly stock returns nd volume dt on 5 non-u.s. stocks cross-lsted on mjor U.S. exchnges. We fnd strong emprcl support for the predcton, even fter controllng for potentl endogenety effects s well s host of other frm-specfc, ssuespecfc nd country-level fctors. JEL clssfcton: F30, G4, G5. Keywords: Interntonl fnnce; cross-lstngs; trdng; lqudty Current Verson: Februry, 006 We thnk n nonymous referee nd the edtor s well s semnr prtcpnts t the Unverstà d Bologn, Unversty of Uth, Georg Stte Unversty, Lousn Stte Unversty, New York Stock Exchnge, Unversty of North Croln t Chpel Hll, Texs A&M Unversty nd t the NYSE Conference on the Future of Globl Equty Trdng for helpful comments. We re especlly grteful to comments nd dscussons wth Pul Bennett, Hnk Bessembnder, Ekkehrt Boehmer, Robert Hrdy (Fleet Speclsts, Chrstn Leuz, Als Roell, Gdeon Sr, René Stulz, Glenn Surnmer (VDM Speclsts, nd Ingrd Werner Roger Loh provded exceptonl reserch ssstnce for whch we re lso grteful. * Correspondng uthor contct nformton: Tel.: ; fx: Eml ddress: (G. A. Kroly

2 I. Introducton Wth the enhnced globlzton of fnncl mrkets, the number of non-u.s. frms choosng to cross-lst shres on U.S. exchnge hs ncresed substntlly. In 990, there were only 35 non-u.s. stocks lsted on the New York Stock Exchnge (NYSE nd Nsdq, but, by the end of 00, the number hs more thn doubled to over 850. If one ncludes stocks trdng over the counter (OTC nd s prvte plcement ssues, the number of non-u.s. compnes wth shres trdng n the U.S. now exceeds,300. Ths drmtc ncrese reflects not only U.S. nvestors' need for nterntonl dversfcton, but lso the desre of foregn compnes to ccess globl cptl, broden ther shreholder bse, nd enhnce compny vsblty. Corportons generlly vew U.S. cross-lstngs s vlue-enhncng decsons, but there s dsgreement bout the sources of the beneft. One of the benefts most-frequently cted n surveys of compny mngers nd nvestors lke s the ncresed lqudty n shre trdng ssocted wth the U.S. lstng (Mttoo, 99; Fnto nd Krmel, 997. Indeed, emprcl evdence ndctes tht U.S. lstng s ccompned by lrge 40 to 50 percent ncrese n the number nd vlue of shres trded n the combned U.S. nd home mrket compred to tht n the home-mrket before the lstng (Smth nd Sofnos, 997; Foerster nd Kroly, 998. However, not ll compnes experence the benefts of ncresed lqudty. In fct, remrkble feture of trdng ctvty n cross-lsted stocks on U.S. exchnges s the gret vrblty n the U.S. frcton of globl trdng. For some stocks, U.S. trdng typclly represents less thn 5 percent of globl trdng n ny gven month, whle, n other stocks, U.S. trdng comprses well over 90 percent of globl trdng. Moreover, t s not smply country-level fctors, lke regultory restrctons or the extent of overlppng trdng hours, tht dctte these outcomes, s there s sgnfcnt cross-sectonl dversty n the U.S. frcton of trdng even mong stocks from the sme country. Consder, s n exmple, the dfferent experences for two frms from the sme home mrket over the sme perod (Fgure. Monthly trdng volume (n number of shres trded on the NYSE for Tomkns, U.K. engneerng compny, hs rrely rsen over percent of ts combned globl volume (NYSE nd the London Stock Exchnge snce t lsted on the NYSE n 988, whle GlxoSmthKlne, U.K. phrmceutcl compny, hs mntned U.S. frcton of trdng over 30 percent, t lest for ll but the lst yers of the decde. Understndng why such dfferent mult-mrket trdng envronments rse s of prmount mportnce for mngers of ll cross-lsted compnes, but especlly those wth lttle U.S.-bsed trdng ctvty, s t potentlly reflects on the long-term vblty of the lstng nd ts potentl s vehcle for rsng cptl, for brodenng the shreholder bse nd for enhncng the compny s vsblty nd profle. Globl nvestors, prtculrly rbtrgeurs tht ctvely trde n both overses ordnres nd ther equvlent cross-lsted shres n the U.S., lso cre bout how the trdng ctvty s pportoned cross the two mrkets s t ffects the fesblty of ther strteges. Moreover, understndng the fctors tht ffect the dstrbuton of globl trdng volume s lso mportnt to stock exchnges, whch compete wth ech other for new lstngs nd for order flow mong exstng lstngs. In ths pper, we develop new model of mult-mrket trdng to expln the vrton n the U.S. shre of globl trdng volume cross the smple of non-u.s. stocks cross-lsted on U.S. exchnges. The model derves n equlbrum whch predcts tht, under frly generl condtons,

3 the dstrbuton of trdng volume cross exchnges competng for order flow s relted to the correlton of the cross-lsted sset returns wth the returns of other ssets trded n the respectve mrkets. The model s bsed on stndrd Kyle (985 frmework wth two stock exchnges nd three ssets: one sset trded exclusvely n the frst mrket, second sset trded exclusvely n the second mrket nd the cross-lsted sset, whch s trded on both exchnges. The two exchnges re segmented n tht the rsk-neutrl mrket mkers observe the order flow of ssets only on ther own exchnge. The nformed trders, who observe prvte nformton bout the dfferent ssets, nd dscretonry lqudty trders re ble to trde on ether mrket nd even cross mrkets. Becuse the sset returns on ech exchnge re correlted, compettve mrket mkers, when prcng n sset, cn nfer nformton not only from the sset's own order flow, but lso from the order flow of other ssets trded on the exchnge. Indeed, n equlbrum, the more correlted the returns of the two ssets, the more relevnt the order flows to one sset re for the prcng of the other sset, nd the less senstve the prce of ny one sset to ts own order flow. Ths outcome gudes the lqudty trders n choosng where to trde the cross-lsted sset: the hgher the correlton n returns of the cross-lsted sset wth the domestc sset, the more nformtve the domestc sset's order flow, whch leds both lqudty nd nformed trders to submt lrger proporton of ther orders n the cross-lsted sset to tht exchnge. Tht s, proportonlly more volume tkes plce on the mrket n whch the cross-lsted sset hs greter correlton wth the other ssets trded on tht mrket. Our new model of mult-mrket trdng represents n mportnt deprture from the bestknown models to dte, ncludng Pgno (989, Chowdhry nd Nnd (CN, 99 nd Domowtz, Glen nd Mdhvn (DGM, 998 n tht nether exchnge desgn nor ssumptons of dfferentl trdng costs ply centrl role n determnng the dstrbuton of trdng volume cross exchnges. 3 For exmple, Pgno s two-perod model wth rsk-verse nvestors bstrcts from symmetrc nformton consdertons nd focuses on the role of trders' expecttons of other trders' ctons. Hs key result s knfe-edge Nsh-type of equlbrum n whch both mrkets cn survve, but only f number of specl ssumptons bout exchnge desgn, such s equl trnsctons costs nd equl numbers of trders n ech mrket, hold. CN does llow for symmetrc nformton, lke we do, by extendng the frmework of Kyle (985 nd Admt nd Pflederer (988 to llow smultneous trdng n multple mrkets. Ther nformed nvestors trde strtegclly to mxmze profts from ther prvte nformton by loctng trdes cross mrkets ccordng to whch mrkets re thck wth lqudty trders. Lqudty nturlly clusters n prtculr mrket, whch CN defne s ther wnner tkes most equlbrum. We dffer from CN becuse we model the trdng decsons of both nformed nd dscretonry lqudty trders nd becuse the exchnges n our model provde dfferent lqudty n the cross-lsted sset by mens of the jont dstrbuton of the sset returns trded on ech exchnge nd not by wy of ssumptons bout the number of smll lqudty trders tht re confned to ech mrket. Our model s lso dfferent from tht of DGM who extend the model of Glosten nd Mlgrom (985 to llow nvestors to trde n the home-mrket or the new cross-lsted mrket t dfferentl costs of executon due to the bd-sk spred nd the dfferent costs of nformton cquston n the two mrkets. Ther model reles on ncrementl nformton cquston costs to ensure tht locl nvestors wll fnd t cheper to trde loclly, unless there s perfect trnsprency n quotes between the two mrkets, n whch cse cross-lstng wll lower voltlty due to lower spreds from greter volume overll nd more ntense competton for order flow from both exchnges cn rse. They conclude tht CN's wnner tkes most equlbrum s complcted by

4 the degree of trnsprency between the two mrkets. Our model does not rely on ssumptons bout nformton cquston costs to yeld the mportnt dfferences n trdng costs. Rther, the choce of where to trde stems from the lqudty tht rses endogenously from the extent of the correlton of the cross-lsted sset's returns wth the returns of other ssets trded on prtculr exchnge. We proceed to test the key predcton of our model nd fnd strong emprcl support. We exmne weekly trdng stock prce nd volume dt from the home mrket nd the NYSE/Nsdq for 5 compnes from 4 emergng nd developed countres round the world. We compute the verge U.S. frcton of globl trdng for ech stock bsed on vlble dt from Jnury 995 to December 004. Usng U.S. dollr-denomnted home-mrket returns on the stock, we construct U.S. nformton fctor, whch s our proxy of the correlton of the cross-lsted stock s returns wth nformton sgnls bout the vlues of other ssets trded n the home nd U.S. mrket. The rto s computed from mult-ndex mrket model regressons of the ndvdul stock's returns on U.S.-dollr-denomnted returns of the home mrket ndex nd U.S. mrket ndex (S&P 500. Specfclly, we mesure the fctor s the ncrementl explntory power of the U.S. mrket n terms of the dfference n R-Squred of two-ndex model ncludng the U.S. ndex reltve to the R-Squred of sngle-ndex model wth just the home mrket ndex, djusted for degrees of freedom. Even fter controllng for potentl endogenety effects s well s host of other frmspecfc (e.g. mrket cptlzton, U.S nsttutonl ownershp, foregn ownershp restrctons, nd home mrket nlyst coverge, ssue-specfc (e.g. NYSE versus Nsdq s well s regonl nd country fctors (e.g. tme-zone effects, we fnd tht the U.S. frcton of globl trdng s strongly, postvely relted to the U.S. nformton fctor, whch s consstent wth our theory. Our pper mkes n mportnt contrbuton to the exstng emprcl work on mult-mrket trdng. To dte, the most comprehensve emprcl study of the dstrbuton of globl trdng n nterntonlly cross-lsted stocks s Pultkonk nd Sofnos ( Ther study exmnes 996 trdng volume dt for 54 NYSE-lsted non-u.s. stocks. They estmte n econometrc model explnng the vrton n the U.S. shre of globl trdng volume drwng from country-specfc, compny-specfc nd ssue-specfc fctors. The most mportnt vrble n ther model s the tmezone fctor; 40 percent of the vrton of the U.S. mrket shre cn be explned by the hours of overlp n trdng between the NYSE nd the home mrket for the stock. Surprsngly, other vrbles, lke dfferentl trdng costs, n ndustry dummy, mrket cptlzton, whether or not the ssue ws ssocted wth cptl rsng nd wht knd of cross-lstng s employed (drect ordnry lstng, New York Regstered Shre, Amercn Depostry Recept (ADR, Globl Regstered Shre, expln reltvely lttle of the cross-sectonl vrton. Our theoretcl model predcts new nformton fctor vrble for consderton n the model nd we fnd strong emprcl support for ths vrble, even fter controllng for tme-zone effects nd other vrbles. 5 The remnder of ths pper s orgnzed s follows. Secton develops our mult-mrket model of trdng. We outlne the predctons of the model, s well s seres of testble lterntve hypotheses, for our emprcl nlyss whch follows n Secton 3. We descrbe the smple of frms, dt sources, vrble constructon, econometrc model nd mn results. Secton 4 concludes the pper. 3

5 II. Anlytcl Frmework nd Testble Hypotheses A. The Model We consder world wth two stock exchnges (denoted by subscrpts nd. Two ssets re lsted on ech exchnge. Exchnges re orgnzed s stndrd Kyle (985 mrket, where compettve rsk-neutrl mrket mkers mke the mrket for the ssets lsted on ther exchnge. To hve menngful seprton between exchnges, we ntroduce the followng segmentton. We ssume tht before settng the prces, mrket mkers observe the net order flow of ll the ssets trded on ther exchnge. They do not, however, observe the orders submtted to the other exchnge. After ech round of trdng, publc nnouncement s mde fter whch the rsk-neutrl mrket mkers gree tht the prces of the ssets trded on the frst nd second exchnges hve chnged by the nnovtons, υ, υ R, respectvely. Specfclly, where, υ υ = F s ε = F s ε 0 0 F = nd F =. ( b b s, ε nd ε re zero men normlly dstrbuted rndom vrbles tht tke vlues n R. Furthermore, s s ndependent from ε nd ε, nd the covrnce mtrx of s, denoted by P, s dgonl, 0 P =. ( 0 We do not mpose restrcton on the covrnce mtrx of the εs, nor ny on the correlton between ε nd ε. In prtculr, we cn ssume the second element of ε nd ε re dentcl, so the nnovtons n the second sset trded on ech exchnge re dentcl. We herefter refer to the second sset on ech exchnge s the cross-lsted sset. Smlrly, we refer to the frst sset on ech exchnge s the locl sset. The nnovton n the prce of the locl sset trded on the frst exchnge depends on s, but not on s ; whle the nnovton n the prce of the locl sset trded on the second exchnge depends on s but not s. The prmeters,, b, mesure the exposure of the cross-lsted sset to s nd s, respectvely. Wthout loss of generlty, we ssume the vlue of the ssets pror to the nnovton s zero nd tht nterest rtes re zero. There re two strtegc rsk-neutrl nformed trders. One of them observes s, whle the other observes s. The nformed trders my submt orders to both exchnges nd for ll ssets. Let x, x R ( =, be the mrket order the -th nformed trder submts to the frst nd second exchnge, respectvely. Let x = x x nd x = x x be the ggregte nformed orders submtted to the frst nd second exchnge, respectvely. 4

6 Next, we consder the unnformed lqudty trders. We tke the lqudty demnd for ech sset s gven, nd ssume the lqudty demnd for both the locl sset nd the cross-lsted sset re uncorrelted stndrd norml vrbles. However, to dscuss volume ptterns of the cross-lsted sset, we hve to llow the lqudty trders who trde the cross-lsted sset to choose to whch exchnge they prefer to submt ther order, or even to llow them to splt ther order between both exchnges. As n Admt nd Pflederer (988, we ssume tht there re n rsk-neutrl dscretonry lqudty trders, ech of whom hs to trde certn mount of the cross-lsted stock. Let w be the mount the -th dscretonry trder hs to trde. The mrket vews w s zero men norml rndom vrble. Furthermore, cov(w, w j equls zero for j. Thus, n n = vr w = vr( w (3 = = We let α(w be the frcton of the demnd the -th dscretonry trder submts to the frst exchnge. When α = (0, then the -th trder submts hs entre order to the frst (second exchnge. Let R nd R be the covrnce mtrx of lqudty demnd on the frst nd second exchnge, respectvely. We hve, R = 0 n = 0 vr( α ( w w nd R = 0 n = 0. vr(( α ( w w We denote by y R nd y R, the ggregte order flow (.e. the totl orders submtted by both nformed trders nd lqudty trders submtted to the frst nd second exchnge, respectvely. Anonymty of trde nd segmentton of mrkets mply tht mrket mkers n the frst exchnge cn only observe y whle mrket mkers n the second exchnge cn only observe y. Mrket mkers n ech exchnge set prces p R nd p R to cler the mrkets. The expected proft of the frst nd second nformed trders, condtonl on ther nformton, re (superscrpt t denotes the trnspose operton E E t t [( p x s ] ( υ p x s ] t t [( p x s ] E[ ( υ p x s ] υ (4 υ, (5 respectvely. The only nformton dscretonry lqudty trder possesses s the knowledge of hs own lqudty shock. The expected proft of the -th dscretonry trder who trdes the cross-lsted sset s, E ( υ p w E ( υ p w. (6 α w ( α w An equlbrum s defned s prce rules p, p : R R, strteges for the nformed trders x, x R, =,, nd n order splttng decson for the dscretonry lqudty trders { α w } n such = tht, 5

7 The prce rules stsfy the condton p ( y y = E[ υ ] nd p y = E[ υ ]. (7 ( y x nd x mxmze (4 nd (5, respectvely, for ech relzton of s. α (w mxmzes (6 for ech relzton of w. A lner equlbrum s n equlbrum n whch ( there exst two mtrces, Λ nd Λ, such tht, p ( y = Λ y nd p ( y Λ y =, ( the nformed trders' strteges re lner n the sgnls;.e. there exst two mtrces, β nd β, such tht, x β x = s nd x = s x β, nd ( the order splttng decsons of ll dscretonry lqudty trders re dentcl. In prtculr, they re ndependent of ther lqudty shocks;.e. α = α for some constnt α. In the followng, we focus on the propertes of lner equlbrum. Let the sclr λ be the second row, second column entry of the mtrx Λ. Then, λ s the prce mpct of mrket order for the cross-lsted sset on the frst exchnge. Indeed, chnge n the demnd for the cross-lsted sset on the frst exchnge by the mount results n prce chnge of the cross-lsted sset on the frst exchnge by λ. Smlrly, λ, the second row second column entry of the mtrx Λ, s the prce mpct of mrket order for the cross-lsted sset on the second exchnge. Theorem. A lner equlbrum exsts. Let the mtrces F, F nd P be gven by ( nd (. Let the mtrces R, R, Λ, Λ, β, β, nd the sclr, α, be soluton to the system of equtons, 0 R = 0 α ( t β = Λ Λ F t t = F Pβ ( R βpβ Λ = 0 R (8 0 ( α ( t β = Λ Λ F Λ α t t = F Pβ ( R β Pβ λ λ λ =, 6

8 7 subject to the second order condtons tht -(Λ t Λ nd -(Λ t Λ re negtve semdefnte mtrces. Then, the mtrces R, R, Λ, Λ, β, β, nd the constnt, α, form lner equlbrum. The proof of Theorem s gven n the Appendx. Notce tht the second order condtons mply tht α [0, ]. To solve the system, we use the elmnton method. For n rbtrry postve α, we solve the frst three mtrx equtons n (8 subject to the second order condton. To emphsze tht the soluton we get depends on the rbtrry choce of α, we wrte the soluton s functon of α. In prtculr, we get ( ( ( α α α α α λ b b b = (9 nd, ( ( ( ( ( ( ( α α α α α λ b =. (0 To fnd the equlbrum α, we solve the lst equton n (8 for α usng (9 nd (0. We get four possble solutons for α: (, 0,, ( b b b b b b. ( The frst soluton does not stsfy the condton α [0, ]. 7 The solutons α = 0 nd α = re the trvl equlbr. If dscretonry lqudty trder conjectures ll other lqudty trders trde t the frst (second exchnge, he too, regrdless of wht the vlues of nd b re, submts hs orders to the frst (second exchnge. The fourth possble soluton n ( s the nterestng one, becuse ths soluton depends on the vlues of nd b. The fourth soluton, however, s vld n certn regon. Tht sd, there s fmly of equlbr wth propertes tht chnge contnuously wth the prmeters nd b. We use tht fmly of equlbr to present our comprtve sttcs relted to trdng volume on the two exchnges. We fnd t smpler to fx b nd let vry. Becuse of the symmetry of the model, nlogous results hold when we fx nd let b vry. The followng corollry formlzes ths result. Corollry. Let b, nd be gven. Then, for ech, there s lner equlbrum, Λ (, Λ (, β (, β (, α(, such tht the element of the mtrxes, Λ (, Λ (, β (, β (, nd α(, re contnuous n. Moreover, α(, the porton of trde submtted to the frst exchnge, ncreses wth. Furthermore, f b < ( < nd f, b b b b, (

9 then ll trde of the cross-lsted sset tkes plce on the frst (second exchnge. The proof of the corollry s strghtforwrd. If b < nd <, then there s lner equlbrum wth, 3 3 ( b b α =. (3 3 3 b b b Dfferentton wth respect to shows α s ncresng n. However, f b nd, then (3 my be smller thn zero or greter thn one. In the former cse, we use the trvl equlbr n whch α = 0 nd, n the ltter, we use the trvl equlbr n whch α =, so tht the fmly of equlbr hs propertes tht vry contnuously n. It s worth contrstng the equlbrum soluton from our model wth two other well known models of mult-mrket trdng: Pgno (989 nd Chowdry nd Nnd (99. Pgno shows tht n equlbrum exsts n hs model n whch both mrkets cn survve, but only f number of restrctve ssumptons re stsfed, such s equl trnsctons costs nd n equl number of trders n ech mrket. If these restrctons re not stsfed then only sngle mrket remns open n equlbrum. In Chowdhry nd Nnd s equlbrum, nformed trders wll llocte more of ther trdes to the mrket tht s thck wth lqudty trders. However, the extent to whch lqudty trde clusters n gven mrket s drven by exogenous ssumptons bout the number of smll lqudty trders n ech mrket. In contrst, we mke no ssumpton regrdng the dstrbuton of smll lqudty trders nd endogenze the choce of where to trde for both the nformed nd the dscretonry lqudty trders. Two of the possble equlbr n our model hve only sngle mrket survve. However, n contrst to Pgno, these sngle mrket equlbr re not stble n the followng sense: f we were to ntroduce n our model trders who re confned to trde n one mrket (smll lqudty trders, then ths mrket would ttrct lso nformed nd dscretonry trdng;.e., the trvl equlbr wth concentrton would dspper. Thus, the nturl equlbrum outcome n our model s to hve trde occurrng n both mrkets. Moreover, the fct tht the propertes of the fmly of equlbr tht we derve chnge contnuously s functon of the prmeters nd b llow us to derve cross-sectonl predctons bout dfferences n trdng volume cross stocks whle holdng other prmeters constnt. Fgure llustrtes the results presented n the corollry. The fgure shows how the equlbrum porton of trdng volume n the frst exchnge vres wth the senstvty,, of the cross-lsted sset's vlue to s. The grph dsplys three representtve fmles of equlbr for three dfferent rtos of the vrnce of s reltve to the vrnce of s, whch s normlzed to one. The fgure demonstrtes tht for smll enough, ll trde tkes plce on the second exchnge (.e. α = 0 whle for lrge enough ll trde occurs on the frst exchnge. The ntuton for ths result, whch forms the bss for our emprcl nlyss, s s follows. When prcng n sset, mrket mkers cn nfer nformton not only from the sset's own order flow, but lso from the order flow of other ssets trded on the sme exchnge. In equlbrum, the more correlted the returns of the two ssets, the more relevnt the order flows to one sset re for the prcng of the other sset, nd the less senstve the prce of ny one sset to ts own order flow. Ths outcome ncreses the lqudty of the cross-lsted sset, whch gudes the lqudty trders n choosng where to trde. Tht s, proportonlly more volume tkes plce on the mrket n whch the cross-lsted sset hs greter 8

10 correlton wth the other ssets trded on tht mrket. In ll but extreme cses both mrkets remn open, however, becuse the dscretonry lqudty trders splt ther orders cross the two exchnges n order to mnmze ther verge trdng costs. 8 B. Model Extenson One mportnt ssumpton n our model s tht the compettve rsk-neutrl mrket-mkers, before settng prces, observe the net order flow of the ssets trded on ther own exchnge, but do not observe the order flow n the other exchnge. Ths mtters becuse locl mrket mkers re thus conferred comprtve dvntge n understndng locl nnovtons by vrtue of ther exclusve vew of the locl sset s order flow. How resonble ths ssumpton bout unobservblty of order flow cross mrkets s n relty, however, s uncler. 9 There my, fter ll, be compettve multmrket-trdng scenros n whch the mrkets re so close (sy, geogrphclly or n the sme tme zone tht ths complete unobservblty restrcton s flse. In order to nvestgte the robustness of our model s predctons, we developed n extenson to the model tht llows for complete observblty of the order flow n the other mrket for the mrket mkers whle mntnng some nformton symmetry between the two groups of mrket mkers. To keep the model trctble, we mke two smplfyng ssumptons: ( there exsts only the cross-lsted sset, nd ( lqudty trders cn choose how much to trde, but re confned to do so only n ther own mrket (e.g., no order-splttng. Now, mrket mkers n the two competng exchnges cn observe demnd for the cross-lsted sset n both exchnges, but the specl role prevously plyed by the purely-domestc ssets n understndng the locl nnovton s replced wth n exogenous sgnl. The resultng equlbrum defnes prce rules tht re lner n the exogenous sgnl tht the mrket mkers observe nd n the order flows to both exchnges. More mportntly, so long s the exogenous sgnls observed by the mrket mkers re not dentcl, the key comprtve sttcs obtn. Tht s, the dfferentl prce mpct of mrket orders for the crosslsted sset on the two exchnges s drectly relted to the reltve mgntude of the exposures of the sset s prce nnovtons to the sgnls n the two mrkets. The hgher s the exposure to the sgnl on gven exchnge, the greter the lqudty tht exchnge provdes nd the more ggressvely dscretonry lqudty trders trde n tht exchnge. The model extenson mkes cler tht t s not the unobservblty of order flow per se tht drves our predctons bout volume. Rther, the necessry condton for our result s tht the locl mrket mker n ech mrket hs some comprtve dvntge reltve to hs counterprt n the other mrket n understndng the locl nnovton to whch the cross-lsted stock s prtlly exposed. Of course, there my be more complex generlztons whch we hve not consdered for whch these nferences my be less cler. The detls of the extended model re furnshed n n ppendx (whch s vlble from the uthors upon request. C. Testble Alterntve Hypotheses There my be severl possble resons why overses nvestors my wsh to trde shres of cross-lsted stocks n prtculr mrket tht re not relted to nformtonl motves t ll. Addtonlly, there my be nformtonl motves for trdng tht stem from nformtonl dvntges fvorng one nvestor over nother tht re unrelted to our centrl hypothess bout 9

11 mrket-mkers nferrng news from the order flows of other stocks trdng on gven mrket. Wthn the frmework of our model, these ddtonl fctors cn be thought of s mrket frctons tht keep trders cptve n specfc trdng venue. In ths subsecton, we propose number of lterntve testble hypotheses whch we explot n the emprcl nlyss to render ddtonl power to the tests. Among non-nformton-relted fctors tht mght nfluence the extent of U.S. shre of trdng volume of cross-lsted stocks, dfferences n trdng costs (commssons, trnsctons txes or regultory restrctons (foregn ownershp lmts, currency convertblty constrnts re mong the most mportnt. Emprcl evdence ndctes tht U.S. mrkets hold n bsolute dvntge over most other mrkets n terms of trnsctons costs, 0 nd emergng mrkets clerly re subject to much hgher trnsctons costs nd regultory brrers thn developed mrkets, so t s mportnt to control for these country-level dfferences n our emprcl nlyss. Becuse most of these fctors mnfest themselves t the country level, they cnnot expln cross-sectonl dfferences n the proporton of U.S. trdng mong stocks from the sme country, whch s our focus. However, there re lso frm-specfc brrers n some emergng mrkets tht relte to the mxmum number of home-mrket shres tht re llowed to become elgble to trde overses n cross-lsted form. Ths s the cse, for exmple, n severl Koren, Twnese nd Indn compnes trdng on mjor US exchnges wth explct celngs on the number of shres tht cn become ADRs. Cost consdertons ssocted wth the bredth nd composton of the ownershp bse of the frm mght lso nfluence the extent of trdng n dfferent mrkets. It mght be, for exmple, tht dfferences n trnsctons costs mtter less for retl thn nsttutonl nvestors, who re more strtegc n ther trde-executon decsons. Insttutonl trders re more lkely to splt ther orders cross mrkets to mnmze the net prce mpct of ther trdes, even f there s perceved bsolute dvntge n terms of lower overll trnsctons costs n the U.S. If ths s true, lrger U.S. ownershp bse wll be ssocted wth hgher frcton of overll trdng n the U.S., but ths effect wll be even greter f the U.S. ownershp bse s domnted by retl nvestors thn more strtegclly-motvted nsttutons tht ctvely seek to mnmze ther overll trdng costs. These nferences wll reverse, however, f nsttutons re n fct more lkely to be constrned by prudentl polces by ther pln sponsors or oversght bords tht lmt them from drectly holdng stock brod nd tht requre them to hold only ADRs or other forms of cross-lsted shres nsted. Another non-nformtonl fctor s relted to the dversfcton opportuntes tht crosslsted stocks present for overses nvestors. Cross-lsted stocks wth low return correltons wth the U.S. mrket should be good cnddtes for dversfcton purposes. Ths predcton s prtculrly useful to us s t represents specfc testble lterntve to the centrl hypothess of our model; tht s, cross-lsted stocks whose returns re wekly correlted wth other U.S. stocks furnsh mrket mkers lower qulty nformton bout order flow dynmcs nd re less lkely to ttrct U.S. trdng volume. Informtonl motves tht re not necessrly relted to the correlton structure of returns re lso lkely n mportnt fctor n determnng the globl dstrbuton of trdng volume for crosslsted stocks. For exmple, t hs been rgued tht locl nvestors hve n nformtonl dvntge reltve to foregn nvestors. 3 The nformton herrchy tht fvors locl nvestors my rse from geogrphc proxmty to the compny s mn busness opertons (Covl nd Moskowtz, 999, 0

12 lnguge brrers for foregn nvestors (Grnbltt nd Kelohrju, 999; Hu, 00 or greter fmlrty wth frm s opertons, ccountng prctces or ts cptl mrket envronment. Whle such dvntges need not ffect the locton of trdng volume, n mny cses t wll be cheper nd qucker to trde n the home mrket, especlly f the nformton s short-lved nd speed of executon s crtcl. Bsed on ths rgument, we predct tht frms wth certn ttrbutes wll mtgte ths nformtonl dsdvntge for foregners. For exmple, the fct tht lrger compnes re more vsble thn smller frms should led to postve correlton between mrket cptlzton nd foregn trdng volume (Merton, 987; Kng nd Stulz, 997. If fmlrty bs exsts mong nvestors (Grnbltt nd Kelohrju, 999; Hu, 00, then cross-lsted compnes wth lrger frcton of foregn sles should be more lkely to develop n ctve foregn mrket for the trdng of ther shres. Smlrly, greter fmlrty my rse from lrger contngent of ndustry peers trdng n one venue reltve to nother, fctor tht some hve suggested s rtonle for cross-lstngs n the frst plce (Pgno, Roell nd Zechner, 003; Srkssn nd Schll, 004. If the totl mrket cptlzton of peer frms from the sme globl ndustry sector s the cross-lsted frm s hgher n the foregn mrket thn n the frm s home mrket, we would predct hgher foregn trdng volume would rse. 4 Fnlly, more reserch publshed by nlysts cn ncrese the publc nformton vlble to ll nvestors (Lng, Lns nd Mller, 003; Bley, Kroly nd Slv, 005, so we predct tht the number of nlysts followng the cross-lsted stocks s postvely relted to foregn trdng volume. In the next secton, we descrbe the emprcl tests of our theory. The smple of U.S. crosslsted stocks s frst dentfed; we then outlne how our nformton fctor vrble s constructed. In ddton, we dscuss vrous proxy vrbles we propose to evlute the testble lterntve hypotheses defned bove. A. Dt nd Smple III. Emprcl Anlyss In ths secton we provde some emprcl evdence regrdng the relevnce of the model developed n the erler prt of the pper. The prmry predcton of the model, s expressed n Corollry, s tht when the vlue of the cross-lsted stock s more senstve to nformton n the U.S. mrket reltve to nformton n the home mrket then the U.S. wll hve hgher shre of the overll trdng volume n the stock. To exmne ths predcton we collect n ntl smple of ll stocks cross-lsted on U.S. exchnges wth lstng dtes pror to Jnury, 999 tht lso hve stock prce dt vlble for both the U.S. nd the home mrket from Dtstrem Interntonl. Ths ntl smple conssts of 384 cross-lsted stocks wth dly dt on stock prce, trdng volume, nd the mrket vlue of equty over the perod begnnng n Jnury 99 nd endng n December 004. Cross-lsted securtes, whch trde n the U.S. n the form of ADRs, re often bundled n rto dfferent from one-to-one. For exmple, the ADR for Telefonos de Mexco, Mexcn compny, represents 0 underlyng Mexcn shres, whle the ADR for Norsk Hydro, Norwegn compny, represents sngle underlyng Norwegn shre. To compute the U.S. shre of trdng volume n ech stock we requre n ccurte mesure of the bundlng rto between the home mrket nd cross-lsted securtes. We obtn the most recent bundlng rto for ech stock from Ctbnk's Unversl Issunce Gude. Unfortuntely, mny cross-lsted securtes lter there bundlng rtos over tme. To ensure tht we obtn n ccurte representton of the bundlng rtos for the stocks

13 n the smple we compre the bundlng rtos from the Ctbnk Unversl Issunce Gude to the yerly verge of the rto the month end prce n the U.S. mrket to the month end prce n the home mrket (converted to U.S. Dollrs. If the prce rto dffers from the reported bundlng rto by more thn 0% we ttempt to reconcle the dscrepncy by exmnng other sources (such s the rtos reported long wth the frm nmes n Dtstrem. After elmntng stocks for whch we re unble to obtn n ccurte bundlng rto we re left wth fnl smple of 5 cross-lsted securtes representng 4 dfferent countres. By wy of comprson, Pultkonk nd Sofnos (999 employ smple of 54 stocks cross-lsted on the NYSE. Pultkonk nd Sofnos lso provde detled descrpton of the dfferent types of cross-lsted securtes. B. Vrble Constructon nd Econometrc Model To test the predcton of the model we requre mesure of the senstvty of the stock's vlue to nformton n the U.S. reltve to nformton n the home mrket. Eun nd Sberwhl (003 compute mesure of the U.S. nformton shre usng n error correcton model nd ntrdly dt for smple of 5 Cndn stocks. Whle ther mesure s ntutvely ppelng t cnnot be employed n our settng both becuse we lck ntrdly dt nd becuse mny of the stocks n our smple re not trded durng the sme hours n both the U.S. nd home mrkets due to dfferences n tme zones cross countres. Insted we tke more mcro vew of mesurng the senstvty of the stock's vlue to nformton n the U.S. mrket. Our underlyng sserton s tht stock prces respond prmrly to new nformton, nd we focus on the reltve nformtveness of mrket movements n the U.S. nd the home country. Specfclly, for ech stock, we perform vrnce decomposton of returns converted to U.S. dollrs to estmte the contrbuton of nformton contned n U.S. mrket ndex returns reltve to the nformton content of ndex returns n the home mrket. To perform the vrnce decomposton we frst estmte the followng two tme-seres regressons for ech stock: R R t t = α = α k = k = β β, H, t k, H, t k R R Home, t k Home, t k ε t k = β, US, t k R US, t k ε t, (4 where R t s the return (mesured n U.S. dollrs for stock n perod t, R Home,tk s the return denomnted n U.S. dollrs on the mrket ndex n the stock's home country n perod tk, nd R US,tk s the dollr denomnted return on the U.S. mrket ndex n perod tk. The led nd lg terms n the regressons re used to ccount for non-synchronous trdng cross mrkets n dfferent tme zones. In ddton, to del wth the possblty of nfrequent trdng t the stock level we bse our nlyss on weekly returns. The frst regresson n equton (4 s consdered the restrcted regresson nd the second regresson n equton (4 s consdered the unrestrcted regresson. Assumng n observtons for the stock, sx regressors n the unrestrcted model, nd three restrctons, we compute n F-sttstc for ech stock tht mesures the explntory power of the unrestrcted model reltve to the explntory power of the restrcted model s follows: ( RUR ( R RR / 3, (5 /( n 6 UR

14 By constructon, ths mesure cptures the ncrementl contrbuton of U.S. mrket movements n explnng vrton n the frm's stock prce over nd bove the nformton bout the frm's stock prce contned n movements n the frm's home mrket ndex. Our theory, therefore, predcts tht hgher vlues of ths U.S. nformton fctor wll correspond to hgher U.S. shres of overll trdng volume. The U.S. nformton fctor s computed for ech stock nd ech smple yer usng mnmum of 36 months nd mxmum of 48 months of pst dt. Ths estmton perod ensures tht we obtn resonbly precse estmtes of the U.S. nformton senstvty of the stocks. 5 To the extent tht the nformton fctor contns mesurement error, we expect n ttenuton bs towrd zero for the coeffcent estmte on ths vrble n our crosssectonl regresson nlyss, whch bses gnst fndng support for our hypothess. For ech yer n the smple, the U.S. shre of overll trdng volume for ech stock s computed s the weekly verge cross the yer of the rto of the number of shres trded n the U.S. mrket, djusted usng the bundlng rto of U.S. shres to home mrket shres, dvded by the totl trdng volume n both the U.S. nd the home mrket. In computng the U.S. shre of trdng volume, we nclude only trdng volume n the U.S. nd the home mrket. Some of the securtes re lso cross-lsted n London or on other globl exchnges, such s Frnkfurt. We do not nclude the trdng volume from the other exchnges n our mesure of the U.S. shre of trdng volume. Our nformton fctor s computed usng returns nd t s lkely tht returns nd volume re contemporneously correlted for resons outsde of those predcted by our model. Becuse of ths t s mportnt tht our nformton fctor s computed usng dt from dfferent perod from the perod n whch we mesure trdng volume. To ccomplsh ths, we employ pnel pproch nd lg the U.S. nformton senstvty mesure one yer. Specfclly, the mesure of the stock's U.S. nformton senstvty computed usng returns from yers s used to predct the stock's U.S. volume shre n 995 nd so on through the end of the smple perod. Ths expermentl desgn nsures tht the nformton fctor s predetermned t the tme tht t s ncluded s n ndependent vrble n the regresson. Stocks re llowed to enter nd ext the pnel over tme. Our pnel contns,46 observtons for 5 cross-lsted stocks coverng the yers 995 through 004. In ddton to the U.S. nformton fctor we lso control for severl other fctors tht could ffect the U.S. shre of overll trdng volume. These other fctors re relted to the testble lterntve hypotheses dscussed n the prevous secton. Frst, there re number of country level fctors tht mght ffect the U.S. shre of trdng volume t the country level. For exmple, there re systemtc dfferences n mrket sze nd development, trdng commssons, nd the legl envronment cross countres. In ddton, Pultkonk nd Sofnos (999 fnd tht prmry fctor ffectng dfferences n the U.S. shre of trdng volume cross stocks re tme zone effects: stocks from countres wth tme zone closer to tht n the U.S. exhbt hgher shre of U.S. trdng volume. In some of our specfctons, we control for tme zone effects usng set of ndctor vrbles for dfferent tme zones clssfed n three-hour ncrements reltve to New York. For exmple, Jpn nd Kore (whch re 0 hours behnd New York nd Austrl (whch s 9 hours behnd New York re clssfed n tme zone -3, whle Hong Kong nd the Phlppnes, whch re both 3 hours hed of New York re clssfed n tme zone 4. In the specfctons usng tme zone ndctors we lso nclude n ndctor for emergng mrkets versus developed mrkets where we use the emergng mrket defnton suppled by the Interntonl Fnnce Corporton (IFC. We 3

15 predct tht emergng mrkets re more lkely to hve bndng regultory constrnts nd hgher overll trdng costs compred to developed mrkets, thus ledng to proportonlly more U.S. trdng volume for these stocks. In other specfctons, we control drectly for country level dfferences usng country level fxed effects. The ll-encompssng use of country fxed effects llows us to focus on dfferences cross stocks wthn countres whle removng the effect of ll fctors tht re common to ll frms wthn country. Our regresson specfctons lso nclude vrety of frm specfc mesures tht could potentlly ffect the stock's U.S. shre of trdng volume. All of the stocks n our smple re lsted on the NYSE or Nsdq/Amex, nd we nclude n ndctor equl to one for frms lsted on Nsdq/Amex n order to ccount for systemtc dfferences n ether ctul or reported trdng volume cross lstng exchnges. We lso control for frm sze usng the nturl logrthm of the stock's verge mrket vlue of equty converted to U.S. dollrs. Frm sze mght proxy for the fmlrty of the frm to U.S. nvestors. If ths s the cse, then we expect frm sze to be postvely relted to the U.S. shre of trdng volume. Another reson to control for frm sze s tht lrge frms re lkely to mke up substntl proporton of the mrket cptlzton of the mrket ndex n the home country. Ths could nduce spurous postve correlton between the frm's return nd the return on the home mrket ndex nd bs downwrd the U.S. nformton fctor for the stock. As ddtonl proxes for the vsblty of the frm to U.S. nvestors, we use the percentge of foregn sles reported by the frm, nd the dfference n the percentge of the globl mrket cptlzton of the frm s ndustry locted n the U.S. nd the percentge of globl ndustry mrket cptlzton for the frm s ndustry n the home country. The foregn sles dt s drwn nnully from the Worldscope dtbse (Item WC0873 bsed on fscl-yer-end of December 3. The reltve ndustry cptlzton vrble s from Dtstrem Interntonl nd s bsed on Level 3 ndustry groupng codes for the home mrkets (whch nclude ten globl sectors. We expect both foregn sles nd the U.S. shre of the frm s ndustry to be postvely ssocted wth the U.S. shre of trdng volume. To cpture frm-specfc constrnts on the U.S. shre of trdng volume due to regultory restrctons on foregn ownershp, we collect the nnul nvestble weghts from Stndrd nd Poor s Emergng Mrket Dtbse whch mesure, s frcton of the mrket cptlzton of the frm, tht whch s free from explct foregn nvestment restrctons. Hgher nlyst coverge n the home mrket potentlly reduces the costs of nformton cquston for foregn nvestors trdng n the locl mrket. We mesure nlyst coverge usng the nturl logrthm of one plus the number of nlysts tht report ernngs estmtes for the stock n the home country. These dt re from the Interntonl Summry dtbse from Thomson Fnncl s Insttutonl Brokers Estmte System (I/B/E/S. We follow Lng, Lns nd Mller (003 n defnng nlyst coverge for cross-lsted shre s the number of estmtes tht comprse the consensus one-yer-hed ernngs estmte for tht fscl yer. The dt re obtned monthly s of the thrd Thursdy of ech month, nd we use the December vlues to mesure nlyst coverge for the followng yer. We expect hgher nlyst coverge n the home mrket to be negtvely relted to the U.S. shre of trdng volume; however, ths reltonshp could be complcted f the nformton generted by the home-mrket nlysts works to overcome, rther thn excerbte, the nformtonl dvntge of locls over foregners. Fnlly, we control for the frcton of the frm's shres owned by U.S. nsttutons. We would delly lke brekdown of the full ownershp bse of these cross-lsted frms, but the detled dt 4

16 re not redly vlble. Thomson Fnncl s 3F dtbse provdes qurterly dt on the percentge of shres held by U.S. nsttutons bsed on flngs to the Securtes nd Exchnge Commsson. We collpse the qurterly dt nto nnul horzons to lgn wth our pnel regresson nlyss. To the extent tht nsttutonl ownershp s correlted wth the overll sze of the U.S. nvestor bse nd, f the U.S. mrket offers bsolute dvntges n trdng costs reltve to the home mrket, we expect tht the shre of U.S. trdng volume wll be postvely correlted wth U.S. nsttutonl ownershp. Ths predcton s less cler, however, f the U.S. nsttutonl ownershp bse domntes the U.S. retl bse. If the more strtegclly-motvted nsttutons would be more nclned to splt ther orders cross mrkets to mnmze the overll net prce mpct of ther trdes, the U.S. shre of trdng volume wll be less postvely correlted wth U.S. nsttutonl ownershp. If these U.S. nsttutons, however, re bound by prudentl polces tht preclude them from drectly holdng stock brod nd tht requre them to hold the cross-lsted shres nsted, then the U.S. shre of trdng volume wll be more postvely correlted wth U.S. nsttutonl ownershp. C. Summry sttstcs Tble I reports summry sttstcs for the stocks n our smple for ech country wthn subsmples of developed nd emergng mrkets. There re 0 stocks from the 4 countres n the smple clssfed s developed mrkets nd 50 stocks from the 0 countres n the smple clssfed s emergng mrkets. Cross lsted stocks from Cnd (78 nd the Unted Kngdom (40 mke up substntl porton of the smple, however, severl other countres, ncludng Austrl (3, Frnce (4, Jpn (9, the Netherlnds (4, Chle ( nd Mexco (4 re lso well represented. The U.S. shre of trdng volume for cross-lsted frms from emergng mrkets verges 33%, whch s nerly twce the verge U.S. shre of trdng volume of 7% for cross-lsted frms from developed mrkets. There s lso substntl vrton n the verge U.S. shre of trdng volume cross countres, vryng from low of bout % for Itly nd Swtzerlnd to hgh of round 60% for Chle nd Mexco. The verge vlue of the U.S. nformton fctor n emergng mrkets s.0, slghtly hgher thn the verge of.83 for cross-lsted frms n developed mrkets. Ths suggests tht, on verge, movements n the U.S. mrket provde more ncrementl prce-relevnt nformton for cross-lsted stocks from emergng mrkets reltve to those from developed mrkets. The verge mrket vlue of equty for stocks from developed mrkets s $8.43 bllon compred to $7.79 bllon for the verge emergng mrket stock, lthough these vlues re hghly skewed nd vry wdely cross countres. In terms of the U.S. venue of lstng, 33% of cross lsted frms n developed mrkets re lsted on Nsdq compred to only % of cross-lsted frms n emergng mrkets. On verge, pproxmtely 0 nlysts follow frms n the home country n developed mrkets compred to n verge of bout 4 nlysts n emergng mrkets. The number of home country nlysts vres gretly cross countres, however. The percentge of shres held by U.S. nsttutons verges 8.88% n developed mrkets nd 6.74% n emergng mrkets. Chn, Hong Kong, Twn nd Itly exhbt the lowest levels of U.S. nsttutonl ownershp, whle Cnd, Fnlnd, nd Isrel exhbt hgh levels of ownershp by U.S. nsttutons. The nvestble weght s 00 percent for ll developed mrket frms, but verges only 79 percent for emergng mrket frms (nterestngly, Kore s the country wth the lowest frcton of ccessblty t 33 percent over ths perod. The dfference n the percentge of the globl mrket cptlzton of the frm s ndustry locted n the U.S. nd tht n the home mrket (U.S. Industry Reltve s bout 40% on verge cross both developed nd emergng mrkets. The verge percentge of foregn sles reported by frms s nerly 59% n developed mrkets compred to only % for frms n 5

17 emergng mrkets. Fnlly, we lso note tht severl of our vrbles re not unformly vlble for ll of the observtons n our pnel. Investble weghts (,3 observtons nd U.S. nsttutonl ownershp (,8 observtons hve the brodest coverge, nd the percentge of foregn sles the lest (8 observtons. We report ll of our subsequent results usng the lrgest number of observtons possble. Tble II reports the correlton mtrx for the vrbles. Becuse our nterest s prmrly on whether the model cn expln dfferences n the shre of U.S. trdng volume cross frms wthn countres the correltons re reported fter subtrctng the country men from ech vrble. Consstent wth the predcton of our model, the U.S. nformton fctor nd the U.S shre of trdng volume re postvely correlted. The sgns of the correltons on the other vrbles re lso generlly consstent wth ntuton. Lrger frms hve lower shre of U.S. trdng volume. The U.S. shre of trdng volume s lower when more nlysts follow the frm n the home country nd s hgher when U.S. nsttutons hold lrger frcton of the frms shres nd when the frms hve hgher nvestble weghts (fewer frm-level foregn ownershp constrnts. The U.S. shre of trdng volume s lso hgher for frms wth more foregn sles, when the frm's ndustry s more overrepresented (by mrket cptlzton n the U.S, nd when the nvestble weght s hgher. D. Multvrte Regresson Anlyss To further nvestgte the fctors tht ffect the U.S. shre of trdng volume, Tble III reports results of multvrte regresson nlyss. The dependent vrble n the regressons s the logstc trnsformton of the U.S. shre of trdng volume. We employ the logstc trnsformton to ccount for the fct tht the U.S. volume shre s bounded between zero nd one. All of the specfctons nclude the U.S. nformton fctor from equton (5, frm sze, nd the ndctor vrble for cross-lsted frms lsted on Nsdq/Amex. In some specfctons we lso nclude vrous combntons of the other control vrbles. To control for country level dfferences ll of the regressons nclude ether the ndctors for tme zone nd emergng mrkets or country fxed effects. The tble reports Whte (980 heteroscedstcty-consstent t-sttstcs djusted for clusterng t the frm level. All of the ndependent vrbles re lgged one yer. The results reported n Tble III provde strong support for the predcton of the model. In model (, whch employs the brodest possble smple nd controls for country effects usng the tme zone nd emergng mrket ndctors, the coeffcent on the U.S. nformton fctor s 0.44 (tsttstc = 4.5, ndctng tht frms wth hgher vlue of the U.S. nformton fctor hve hgher U.S. shres of trdng volume. The coeffcent estmtes on the control vrbles lso pper resonble. Lrger frms exhbt lower shre of trdng volume n the U.S., nd frms from emergng mrkets hve hgher U.S. shre of trdng volume, ll else equl. The Nsdq ndctor s not sttstclly dfferent from zero. Model ( dds ddtonl control vrbles for home nlyst coverge, U.S. nsttutonl ownershp nd the reltve shre of the frm's ndustry locted n the U.S. Model (3 dds the nvestble weght nd model (4 dds foregn sles to the specfcton s well. Becuse of mssng vlues, the number of observtons drops from,46 n model ( to 958 n model (, 888 n model (3 nd 70 n model (4. In ll four specfctons, the coeffcent on the U.S. nformton fctor remns postve nd sttstclly sgnfcnt t the 0 percent level or better. Models (5 through (8 repet the regressons n Models ( through (4 but drop the tme zone nd emergng mrket ndctors n fvor of country fxed effects. The results re very smlr. The coeffcent estmte on the U.S. nformton fctor n model (5 s 0. (t-sttstc =

18 ndctng slghtly smller effect of U.S. nformton on the U.S. shre of trdng volume compred to model ( fter controllng for country level dfferences. Compred to model ( the negtve effect of frm sze on the U.S. volume shre s slghtly smller. Models (6 to (8 yeld results smlr to those n models ( to (4, wth one notble excepton: the explntory power of the nvestble weght vrble s much lrger nd postve wth country dummes nd wthout the emergng mrkets ndctor. Ths result suggests tht there s strong clusterng n the nvestble weght vrble mong emergng mrkets. Overll, the multvrte nlyss reported n Tble III provdes support for the de presented n our model tht cross-lsted frms for whch prce relevnt nformton contned n U.S. mrket movements s lrger wll lso exhbt lrger shre of ther trdng volume n the U.S. mrket. In ddton, frms wth more U.S. nsttutonl ownershp re ssocted wth more U.S. trdng volume nd frms wth more home country nlyst followng exhbt less trdng volume n the U.S. Also, the hgher s the nvestble weght for cross-lsted frm, the hgher the U.S. shre of trdng volume. The estmtes on the U.S. shre of the frm's ndustry nd foregn sles re not sgnfcnt n ny of the specfctons. To ssess the mgntude of these effects we compute the percentge chnge n trdng volume mpled by movement from the 5th to the 75th percentle n ech of the vrbles of nterest bsed on the regresson coeffcents n Model (5. 6 The effect of the U.S. nformton fctor on the U.S. shre of trdng volume s economclly menngful, but s somewht smller n mgntude thn the effects of nlyst coverge nd nsttutonl ownershp. Movng from the 5th to the 75th percentle of the U.S. nformton fctor mples n ncrese n the U.S. shre of trdng volume of over 5%. Ths compres to 34% declne n the U.S. shre of trdng volume for chnge of smlr mgntude n home-mrket nlyst coverge nd 6% ncrese ssocted wth chnge of smlr mgntude n nsttutonl ownershp. One ddtonl robustness test we nvestgted reltes to the concern bout the restrctve ssumpton bout the unobservblty of order flow n the competng mrket for mrket mkers. We developed n extended model n Secton II.B whch demonstrtes tht the key predcton of our model holds when observblty n order flow cross mrkets s llowed so long s the locl mrket mker mntns some nformtonl dvntge reltve to the foregn mrket mker n understndng the locl porton of the nnovton n the vlue of the cross-lsted sset. Alterntvely, f the observblty of order flow elmntes the comprtve dvntge of the locl mrket mker, then the explntory power of our nformton fctor for the U.S. frcton of trdng volume should be gretly dmnshed. We performed supplementry regresson nlyss to test ths possblty. As proxy for the degree of observblty mong mrket mkers n competng exchnges we creted n ndctor vrble for countres tht hve substntl overlp n trdng hours wth the U.S. The overlp vrble s equl to one for cross-lsted stocks from Cnd, Mexco nd Ltn Amerc, nd s equl to zero for cross-lsted stocks from As nd Europe. Usng specfctons smlr to models ( nd (5 n Tble III, but ncludng the overlp vrble (n leu of tme zone ndctors nd when country ndctors re not ncluded nd n ntercton term between the overlp vrble nd the U.S. nformton fctor, we found tht the overlp vrble ws postvely nd sgnfcntly relted to the U.S. trdng volume, ndctng tht stocks from countres n smlr tme zone to the U.S. exhbt greter shre of U.S. trdng volume. Nevertheless, the nformton fctor remned sgnfcnt, postvely relted to the frcton of trdng volume. The ntercton vrble ws postve but not sgnfcnt, ndctng tht, f nythng, the effect of the nformton fctor on the shre of U.S. trdng volume s hgher n mrkets wth more overlp n trdng hours wth the U.S. 7

19 IV. Conclusons In consderng whether to cross-lst ther stock on foregn exchnge, such s the NYSE or Nsdq n the U.S., n ssue of concern for mngers s the trdng ctvty tht the cross-lstng wll ttrct. The dstrbuton of trdng volume potentlly reflects on the long-term vblty of the lstng nd ts potentl s vehcle for rsng cptl, for brodenng the shreholder bse nd for enhncng ts vsblty nd profle. In ddton, understndng the fctors tht ffect the dstrbuton of trdng volume n cross-lsted securtes re lso mportnt for stock exchnges s they ttempt to ttrct new lstngs nd compete wth one nother for order flow. The ssue s prtculrly relevnt tody s polcy debte s mny non-u.s. frms re thretenng to de-regster nd de-lst from U.S. mrkets followng the pssge of the Srbnes-Oxley Act of 00 nd ts ncresed costs of complnce, udtng ndependence nd penltes for flse reportng. 7 Indeed, n prt to llevte these concerns, the Securtes nd Exchnge Commsson proposed n December 005 new Rule h-6 tht would ese the burden on non-u.s. frms to rrnge termnton of regstrton n the U.S., one mportnt condton of whch s bsed on the frcton of ther overll trdng volume tht tkes plce n the U.S. 8 In ths pper, we develop nd test theoretcl model of mult-mrket trdng to expln the dfferences n the foregn shre of trdng volume of nterntonlly cross-lsted stocks. The model derves n equlbrum whch predcts tht, under frly generl condtons, the dstrbuton of trdng volume cross exchnges competng for order flow s relted to the correlton of the cross-lsted sset returns to returns of other stocks n the respectve mrkets. Tht s, volume s proportonlly hgher on the exchnge n whch the cross-lsted sset returns hve greter correlton wth returns of other ssets trded on tht mrket. We test ths predcton wth monthly stock returns nd volume dt on 5 non-u.s. stocks cross-lsted on mjor U.S. exchnges. We fnd strong emprcl support for the predcton, even fter controllng for possble endogenety effects nd for other frm-specfc, ssue-specfc nd country-level fctors. Our work contrbutes both to the theoretcl nd emprcl lterture on mult-mrket trdng nd provdes n explnton for the gret vrblty tht s observed n the dstrbuton of trdng ctvty cross exchnges n cross-lsted securtes. Nevertheless, there re mny questons tht we leve unnswered. An open queston remns bout the fundmentls forces underlyng the nformton fctor tht we ntroduce s n mportnt explntory vrble for the globl dstrbuton of trdng n cross-lsted securtes. One possblty s tht t rses from the nture of the busness ctvtes of the frm relted to geogrphy (mportnt U.S.-bsed opertons nd ssets or ndustrl membershp (globlly compettve ndustry tht we hve not cptured fully n our foregn sles nd ndustry-peer proxy vrbles. A more detled emprcl nlyss here would be worthwhle, especlly gven evdence n Pgno, Roell nd Zechner (00 nd Srkssn nd Schll (004 tht trde, colonl tes, common lnguge nd culture nd smlr ndustrl structure ply mportnt roles n the selecton of overses trdng venues for nterntonl frms. Indeed, there s sgnfcnt body of new reserch tht s re-exmnng the nterntonl cross-lstng decson of frms n the context of these nd other corporte governnce-relted explntons (Kroly, 006. It s stll uncler how ptterns n the dstrbuton of trdng ctvty cross globl exchnges my be lnked to these explntons. For exmple, s t possble for frm to rtonlze decson to crosslst on n overses exchnge n spte of low nformton fctor nd poor prospects for ny knd of U.S. mrket shre of trdng? 8

20 Another open queston s whether the delers nd speclsts tht mke mrkets n non-u.s. stocks on U.S. exchnges perform ther functon n wy tht s lkely to nfluence the proporton of trdng ctvty n the U.S. Indeed, Bcdore nd Sofnos (00 document wth propretry dt tht the nventory mngement behvor (postons closer to zero nd prtcpton nd stblzton rtes (hgher of NYSE speclsts n non-u.s. stocks re very dfferent thn for U.S. stocks. More recent ppers by Bcdore, Bttlo, Glpn nd Jennngs (005 nd Moulton nd We (005 show tht ther mrket-mkng ctvtes re sgnfcntly dfferent even wth gven trdng dy when the home-mrket for the cross-lsted shres re open nd when they re closed. Our effort to now hs lso mde only modest progress n understndng the jont dynmcs of nformton fctors nd the globl dstrbuton of trdng volume over tme, n generl, nd round mportnt events lke the cross-lstngs themselves. Indeed, Hllng, Pgno, Rndl nd Zechner (004 show tht the foregn volume shres declne sgnfcntly n the frst three yers followng lstng. Fnlly, the problem of explnng mrket shres of trdng volume exsts n domestc mrket settngs lso, nd t remns yet to be seen whether the ntuton underlyng our model hs pplcblty there. There re mny competng explntons for why exchnges do or do not compete successfully gnst thrd-mrket delers or electronc communctons networks (ECNs or why the lsted Chcgo Bord Optons Exchnge (CBOE s losng mrket shre to the newer electronclly-trded Interntonl Securtes Exchnge (ISE. To ths end, t s useful to recognze Bruch nd Sr (004 who hve extended trdng model smlr to ours to expln why some frms lst ther shres on one mrket over nother (Nsdq versus NYSE nd why some frms swtch lstngs. 9

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