ONE SECURITY, FOUR MARKETS: CANADA-US CROSS-LISTED OPTIONS AND UNDERLYING EQUITIES

Transcription

1 ONE SECURITY, FOUR MARKETS: CANADA-US CROSS-LISTED OPTIONS AND UNDERLYING EQUITIES Michal Czerwonko **** Nabil Khoury* Sylianos Perrakis** Marko Savor*** This version May 2010 JEL CODE: G14, G15 KEYWORDS: coningen claims, marke microsrucure, inerlising, price discovery *Professor of Finance and Desjardins Chair in he Managemen of Derivaive Producs, Universiy of Quebec in Monreal, ** Professor of Finance Concordia Universiy, ***assisan professor, Universiy of Quebec in Monreal and **** posdocoral fellow, McGill Universiy & Desjardins Chair in he Managemen of Derivaive Producs respecively. The auhors are paricularly graeful o C. Fisee and O. Touzani for heir able assisance. Financial suppor from he Auorié des marches financiers and from he Desjardins Chair in he Managemen of Derivaive Producs is graefully acknowledged. Corresponding auhor: N. Khoury, [email protected], phone (514) #6717 fax (514)

2 ONE SECURITY, FOUR MARKETS: CANADA-US CROSS-LISTED OPTIONS AND UNDERLYING EQUITIES Absrac In his paper we examine he relaive conribuions of US and Canadian markes o price discovery for Canadian cross-lised opions and heir cross-lised underlying socks. We use wo differen economeric approaches in assessing he conribuions of each marke o price discovery, he informaion shares approach and he common facor approach. Our empirical resuls are consisen in boh approaches. We show ha on average price discovery for crosslised Canadian socks and opions akes place overwhelmingly in he underlying asse markes, where Canadian equiy markes dominae he discovery process. The resuls show ha opion markes informaion shares remain comparable, alhough slighly higher in he US, which conrass wih he fac ha is relaive volume is almos en imes greaer han ha of Canadian opions markes. The resuls also indicae a high degree of inegraion beween Canadian and US markes for he underlying socks of cross-lised opions and show ha he foreign exchange marke does no conribue o he co inegraion beween hese markes o any significan exen. An analysis of he deerminans of he relaive informaion shares beween firms wih all markes analyzed simulaneously shows ha he mos imporan facor explaining he informaion shares is he volailiy of underlying reurns.

3 ONE SECURITY, FOUR MARKETS: CANADA-US CROSS-LISTED OPTIONS AND UNDERLYING EQUITIES I. Inroducion I is well known ha price discovery for opioned socks, he process by which new informaion is embodied in rading aciviy, can ake place eiher in he opion marke or in he marke for he underlying asse. 1 Similarly, when a securiy is cross-lised in wo differen inernaional markes he discovery process can ake place in eiher marke. The increased rend in inernaional crosslising of securiies, paricularly in US venues, has simulaed a growing body of research on his issue. 2 There are several argumens on wheher he home venue or he US venue is he mos appropriae for he discovery process, he former because of he obvious informaion advanages and he laer because of he higher liquidiy. Likewise, here are advanages and disadvanages in using he opion raher han he underlying asse for price discovery. In his paper we use an inegraed sample of Canadian opioned socks, and heir opions all of which are cross-lised in he US, in order o assess he imporance of each one of he four markes for he price discovery process. We hen examine he facors ha deermine he relaive weigh of each marke in ha process. We use wo complemenary economeric approaches in our empirical work: he informaion shares approach as in Hasbrouck (1995), and he common facor approach as in Gonzalo and Granger (1995). 3 We find consisen resuls in boh cases. Specifically, we find ha Canadian and US markes are highly inegraed for opions and heir underlying socks. We also find ha conrary o he resuls of Chakravary e al (2004) almos all discovery akes place in he underlying sock markes in boh Canada and he US. These wo markes, hough, are major conribuors o he discovery process, and none of he wo is dominan in ha process, alhough Canada has a significanly larger informaion share on average. As for he foreign exchange 1 For empirical evidence on his issue see Sephan and Whaley (1990), Chan, Chung and Johnson (1993), and Chakravary, Gulen and Mayhew (2004). 2 See, for insance, Eun and Sabherwal (2003), and Grammig, Melvin and Schlag (2005). 3 We also used he lead-lag analysis, as in Sephan and Whaley (1990); he resuls are available from he auhors on reques. Alhough his analysis has several biases as discussed in Hasbrouk (1995), is resuls poin o a large and consisen degree of inegraion beween all four markes. 3

4 marke, i does no seem o conribue o he price discovery process o any significan exen. Finally, hese average resuls do in fac correspond o significan differences in he discovery process paern beween he firms in our sample. Thus, alhough he insignificance of he opions marke is presen in mos cases, here are a small number of firms in boh Canada and he US for which an imporan amoun of price discovery akes place in he opion markes. An analysis of he deerminans of he discovery process shows ha he mos imporan facor explaining he differences in informaion shares of he wo underlying naional sock markes is he volailiy of underlying reurns. The key issue in he lieraure on inernaional cross-lising is he informaional advanage of he home venue as compared o he superior liquidiy of he foreign venue. I could be argued ha he home marke where informaion presumably originaes, should dominae price discovery, as in Solnik (1996), and Bacidore and Sofianos (2002). On he oher hand, he sheer breadh and deph of he foreign venue, paricularly if i is he U.S. marke, suggess ha i may assume a leading role in his regard. Several sudies ha have examined his issue from he perspecive of he inernaional cross-lising of socks have repored mixed resuls. Mehodologically he earlier sudies rely mosly on he lead-lag analysis, while he pos-1995 sudies adop primarily he informaion shares approach of Hasbrouck (1995). Lieberman e al. (1999) find ha he price discovery of five ou of six Israeli socks cross-lised on NYSE occurs in he home marke and Kao e al. (1990) reach he same conclusion for seven UK, eigh Japanese and eigh Ausralian socks, also cross-lised on NYSE. Similarly, Grammig e al. (2005) repor ha price discovery of he hree German socks inerlised on NYSE and Frankfur mainly akes place in he home venue. On he oher hand Law and Dilz (1994) and Wang e al. (2002) repor ha causaliy is bidirecional, bu wih a sronger impac of he foreign venue in he firs sudy and he opposie in he second sudy. In Canada-US cross-lising Eun and Sabherwal (2003) have analysed he exen of U.S. exchanges conribuion o he price discovery of 62 Canadian socks lised on he Torono Sock Exchange (TSE) and cross-lised in he US by examining midpoin bid-ask quoes a 10 minue inervals for a six monh period. They repor, on he basis of he magniude of he coefficiens of adjusmen of TSE prices o price deviaions on U.S. markes, ha prices on he TSE and U.S. sock markes are coinegraed and muually adjusing bu ha he TSE dominaes 4

5 price discovery for a majoriy of socks. These coinegraion resuls are no surprising, given ha mos sudies have found ha Canadian and US financial markes are highly inegraed. 4 When here are also raded opions on a given sock, price discovery can ake place eiher in he underlying or in he opion marke. Wih heir greaer poenial for leverage and heir bounded downside risk, opion markes may presumably arac informed rading, resuling in urn in opion prices leading sock prices whenever new informaion arrives. On he oher hand hese advanages are severely curailed by he fac ha financial markes are boh dynamically incomplee and are subjec o fricions such as ransacion coss. In paricular, opion markes are less liquid and have much wider quoed spreads han sock markes. So, i is perhaps no surprising ha empirical evidence on he lead-lag relaionship beween observed sock prices and sock prices implied by observed opion values has yielded mixed resuls. Manaser and Rendleman (1982) find, on he basis of daily daa on call opion implied prices compared o hose of heir underlying socks ha price changes in opion markes lead price changes in sock markes. Anhony (1988) also concludes from causaliy ess ha rading in call opions leads rading in heir socks. Kumar, Sarin and Shasri (1992) repor abnormal opion reurns 30 minues before he execuion of block rades in heir underlying socks and Cao, Chen and Griffin (2000) find abnormal rading volume in opions prior o akeover announcemen. Under a differen approach, Gendron, Khoury and Yourougou (1994) esimae he probabiliy of price reversals in Canadian opions and in heir underling socks and conclude ha new informaion arrives firs in opion markes. On he oher hand, Sephan and Whaley (1990) by analysing daa on CBOE call opions for he firs quarer of 1986 find ha price changes in he sock marke lead price changes in he opion marke by abou 15 o 20 minues on average. Chan, Chung and Jonhson (1993) also find no evidence ha opions lead heir underlying socks. More recenly Chakravary, Gulen and Mayhew (2004) find evidence ha abou 18% of price discovery occurs in he opion marke and ha i increases when he volume of ransacions in opions is higher han ha of heir underlying socks and when he opion effecive bid ask spread is narrower. 4 See, for insance, Bracker, Docking and Koch (1999), Carmichael and Samson (1996), Normandin (2004), and Kryzanowski and Zhang (2002). 5

6 In his paper we ake advanage of he unique srucure of he Canadian financial markes and heir close inegraion wih he US wih respec o he rading of securiies of he major Canadian firms. These firms are all opioned, and boh heir common shares and he opions wrien on hem are cross-lised in he US. We may hus use a sample of hese firms o analyse he conribuion of he foreign and home venue opion and equiy markes o he price discovery process using an inegraed approach where all opion and underlying equiy markes are considered simulaneously, ogeher wih he foreign exchange marke. We use wo differen ses of saisical hypoheses, one based on a modified version of Hasbrouk s (1995) mehodology adaped o he issue under sudy and a second model based on he Gonzalo and Granger (1995) common facor approach. The price discovery performance of each marke is hen analyzed using a saisical procedure adaped o panel daa in order o idenify is mos imporan deerminans. The paper hus conribues o he price discovery lieraure by providing, o he bes of our knowledge, he firs evidence on he relaive shares of U.S. and Canadian markes in he discovery process of cross-lised Canadian opions and heir underlying socks, and on he deerminans of hose shares wih all markes analyzed simulaneously. In he nex secion we describe he economeric mehodologies embodied in he wo differen approaches ha we adop in he empirical work. Secion III conains he resuls of hese approaches and secion IV analyzes he differences in he deerminans of informaion shares beween he firms in our sample. Secion V concludes. II. The empirical models II.1 Economic & Economeric Theory The empirical work of his paper is based on wo differen marke microsrucure models developed simulaneously by Hasbrouck (1995) and by Gonzalo and Granger (1995), wih an imporan earlier conribuion by Sephan and Whaley (1990). There is an unobservable efficien price for a Canadian firm s sock expressed in Canadian currency ha follows a logarihmic random walk, which is equivalen o he sandard seing in he asse pricing heory ha he asse prices ne of dividends are maringales. This price is embodied in he observable prices of four 6

7 disinc insrumens rading in four markes, wo of which are in Canadian and wo in US currency. 5 k Le S, k = C, U, denoe he sock prices in $Can and $US respecively, k and I, k = C, U, similarly denoe he sock prices implied from he opion markes. The logarihmic exchange rae Ein $Can/$US also follows a random walk. E = E + v. (1) 1 Wihou loss of generaliy we assume ha S C is he efficien price following he random walk and inroducing he innovaion componen γ S = S + γ. (2) C C 1 All error erms have zero mean and are serially and conemporaneously uncorrelaed. For insance, E ( γ ) = 0, E ( v γ ) = 0, E( γ γ ) = 0, i j, ec. A similar random walk characerizes he i j US share price, which adjuss o he las observed exchange rae and Canadian price and includes is own random errorδ S = S + E + δ (3) U C 1 1 The implied sock prices from he opion markes are obained by invering he corresponding observed opion prices in he Canadian and US markes. We use he Black-Scholes-Meron (BSM) expression as a simple ranslaion formula wihou necessarily assuming ha his expression is a valid represenaion of he opion value. A key issue is he volailiy o be used in he BSM expression, which may iself be following is own random process. We use a lag of one minue 6 k in esimaing he implied volailiy (IV) σ, k = C, U from he corresponding opion marke, which is hen used as an inpu a ime for he inversion of he BSM expression k k k F ( I, σ ), se equal o he corresponding observed opion price O a ime. Thus, we have 5 In wha follows all symbols in our expressions denoe he naural logarihms of he corresponding dollar prices and exchange raes. 6 We also ried various lags beween 3 and 60 minues wihou any appreciable difference in he resuls. 7

8 1 I = F ( O, σ ) = S + ς, U I = F ( O U, σ U ) = S C + E + ξ. (4) C 1 C C Neglecing for he momen he exchange rae and focusing on he wo pairs of naional markes, we noe ha one approach o he analysis of he price discovery process is he lead-lag model, which considers he srucure of he error erms in he acual and he implied sock prices. For insance, in he case of he Canadian marke his lead-lag model would consis of he relaionship beween he error erms γ and ς. In a perfec marke wihou any fricions and any observaional delays hese wo erms should be equal. Since his is no he case, price discovery can be sudied by a pair of models of he following form 7 k = K ς = a + b γ + ε k k k = K k = K δ = c + d γ + η, (5) k k k = K where K is he arbirarily chosen number of leading and lagging regressors. Price discovery is represened by he nonzero and non-conemporaneous coefficiens. Apar from he fac ha his model canno accoun for he analysis of price discovery in more han wo markes, especially in he presence of exchange rae effecs, he lead-lag model may be misleading when he variables are coinegraed. For his reason, we shall focus our coinegraion analysis on a number of differen combinaions of he random walks given by expressions (1)-(4). In general erms, le P denoe a vecor of prices ha in he empirical applicaions will conain a number n of elemens ranging from 2 o 5, as well as one or wo common rends, associaed wih he sock price and he exchange rae. Since he prices observed in differen markes are kep from drifing apar by inermarke arbirage boh inernaionally and beween he opions and he underlying rading venues, he prices are coinegraed of order one (I(1)). In oher words, he price vecor P may be represened by a nonsaionary vecor auoregression wih q lags. Then i can be shown by he Granger Represenaion Theorem 8 ha here exiss a vecor error correcion represenaion (VECM) 7 See Sephan and Whaley (1990). 8 See Engle and Granger (1987). 8

9 q ' αβ 1 i q i= 1 P = P + A P + e, (6) where α and β are [nxr] marices conaining respecively adjusmen parameers and coinegraing vecors, r is he coinegraion rank, [nxn] marices A i describe he shor-erm dynamics of he process and Ω is he covariance of he serially-uncorrelaed error erms e. The ' erm αβ P 1 represens he equilibrium dynamics beween he prices. The coinegraion rank r is deermined by he number of common sochasic rends in he daa. 9 In paricular, we expec o have he coinegraion rank r equal o n 1 when here is no exchange rae in model (6), since in his case here is a single common rend, he efficien price. The inclusion of he exchange rae in model (6) will add an addiional common rend, hus seing he coinegraion rank r equal o n 2. In all empirical applicaions we use he Johansen (1990) es o deermine his coinegraion rank. Even hough he common efficien price is no observable, is random-walk variance may be esimaed in model (6) as 10 σ = ψω ψ, (7) 2 ' RW where ψ are rows of an [nxn] marix Ψ given by 11 Ψ = 1 q ' ' β α I Ai β α i= 1, (8) where [nx(n r)] marices α and β are non-rivial orhogonal complemens o α and β in (6), he A i marices are as in (6) and I is an ideniy marix. 12,13 Noe ha if here is no exchange rae 9 See Sock and Wason (1988). 10 See Hasbrouck (1995). 11 See Johansen (1990). 12 See Johansen (1995) for esimaion mehods of hese orhogonal complemens. 9

10 in he model (6), all rows of Ψare idenical, oherwise we have a row corresponding o he exchange rae random walk variance ha is clearly differen from he ohers. This case is ouside he scope of his paper, and in wha follows we define ψ as corresponding o he common efficien price. Then he informaion share (IS) of a given marke is defined 14 as he proporion of he random walk variance ha is aribuable o he innovaions in ha marke. If he covariance marix Ω is diagonal hen we have a clean decomposiion ino conribuions of each marke o he oal variance of he permanen componen, wih he conribuion for he j-h marke equal o ψ Ω 2 j jj 2 RW σ. This diagonal propery will hold if he underlying random walk hypohesis is well saisfied by he daa, i.e. if here is lile conemporaneous correlaion beween he residuals in (6). If he off-diagonal elemens are non-zero hen we apply he Cholesky decomposiion o he covariance marix Ω. In his case, which is he one ha prevails in our daa, he conribuion of each marke o he price discovery is no unique, varying wih he ordering of variables in he Cholesky decomposiion. Accordingly, we search over all possible roaions for he minimal and maximal IS for each marke, which consiue he bounds on his quaniy. 15 The Gonzalo and Granger (1995) decomposiion ino he permanen and ransiory componens sars wih he same VECM model (6). Then we have he following decomposiion of he price vecor: P = C f + C Z, (9) 1 2 where f and Z respecively represen he permanen and ransiory componens, C1 and C2 are loading marices, and f ' α = P and Z ' = β P wih α and β as before. Noe ha he I(1) permanen componen f need no be a random walk. Of ineres o us is he [nx(n r)] 13 In mos of he marke microsrucure applicaions of his model he marices Ψwere esimaed as cumulaive impulse-response funcions whose convergence properies are no well known. Baillie a al. (2002) poined ou ha (8) is a superior esimaion approach. 14 See Hasbrouck (1995). 15 See Hasbrouck (1995). 10

11 marix α, specifically is column corresponding o he price vecor. 16 Under he addiional assumpion hazdoes no Granger-cause 17 f his marix may be idenified up o a non-singular muliplicaion marix. The inerpreaion of he permanen componen f is ha i is a weighed average (linear combinaion) of he observed prices wih he componen weighs in α. Booh e al. (1999), Chu e al. (1999), and Harris e al. (1995) sugges measuring price discovery by using componen weighs normalized o 1 or shares (CS). The inerpreaion of CS is ha he marke which reacs he leas o he innovaions in oher markes will display he highes relaive weigh in he permanen componen. As shown in Baillie a al. (2002) and De Jong (2002), CS may be esimaed also by normalizing o 1 he row vecor ψ in (8). 18 This approach sipulaes ha IS and CS are clearly relaed. As demonsraed in he former sudy, IS is a second-degree raional funcion of CS and of Cholesky decomposiion erms for a non-diagonal VECM error covariance marix. Baillie a al. (2002) also showed ha for symmerical sysems, i.e. wih he number of markes n even and wih he coinegraing vecors coefficiens in β in (6) close in magniude bu of reciprocal signs in differen markes, as we may expec in our seup for he models wihou he exchange rae, he midpoin values of IS are close o CS. In our daa we observe subsanive correlaions beween he residuals in he VECM model (6) even a he highes admissible sampling frequency. Hence, he Gonzalo and Granger (1995) approach offers an a foriori imporan cross-validaion for he resuls of he Hasbrouck (1995) model In case here is exchange rae in model (6) one of he wo columns in α will correspond o he exchange rae permanen componen. 17 See Granger (1980). 18 See Gonzalo and Granger (1995) for an alernaive esimaion mehod. 19 There is an ongoing debae in he marke microsrucure and he relaed economeric lieraure abou he relaive meris of he Hasbrouck (1995) and Gonzalo and Granger (1995) approaches. As De Jong (2002) poins ou, CS for a given marke ignores he variance of an innovaion in his marke while i measures he weigh of his innovaion in he incremen of he efficien price. On he oher hand, IS measures he share in he oal variance of he efficien price conribued by a given marke. In a recen work, Yan and Zivo (2007) analyze he performance of IS and CS in he srucural VAR framework and poin ou ha IS a high sampling frequencies may be adversely affeced by noise. In conclusion, he auhors recommend using hese wo measures in conjuncion. 11

12 II.2 Applicaions of he Economeric Model We apply he above VECM model (6) o he following price vecor cases. Firs here are he prices in he wo purely naional markes, in which he exchange rae E does no ener, n=2 and k k P = [ S, I ], k = C, U. Here we have a single common rend. Nex we inroduce he exchange k l rae and we consider n=3 and P [ E, S, S ], = k, l = C, U, k l or k l P = [ E, I, I ], k, l = C, U, k l. Las, we examine he mos general case n=5 and C U C U P = [ E, S, S, I, I ]. In all hese cases here are wo common rends and he rows of he marix Ψare no idenical. The number of coinegraing relaions is equal o n-1 when he exchange rae does no ener and o n-2 when here are wo common rends. This ranslaes o single hypohesized coinegraing vecor ' k k β = [1, 1] in equaion (6) for he case where [, ],, P = S I k = C U, bu also o he single coinegraing vecor hypohesized ' k l β = [1, 1, 1] for he cases [,, ],,,, P = E S S k l = C U k l k l and P = [ E, I, I ], k, l = C, U, k l. In his las case he elemens ψof he [3x3] marix ij ψ 11 ψ12 ψ13 Ψ = ψ 21 ψ 22 ψ 23 denoe he cumulaive effecs on price i of a uni shock in price j. If we ψ 31 ψ 32 ψ 33 denoe he op row of he marix as corresponding o he exchange rae and he wo boom rows as corresponding o, say, he US- and Canadian-raded sock prices respecively, hen we anicipae cerain paricular properies of he marix Ψ. Specifically, we expecψ12 = ψ 21 = 0, ψ = ψ and ψ 23 = ψ 33. The cumulaive effecs of he exchange rae on he respecive sock prices ψ 21 and ψ 31 remain ambiguous since he prices of paricular equiies may differ wih respec o heir sensiiviy o he exchange rae. Since we are no ineresed in his sudy in he exchange rae per se, we do no repor any resuls relaed o he informaion shares in he marke for he exchange rae. In addiion, as our resuls in a laer secion will demonsrae, he exchange rae has a small effec on he informaion shares of he considered securiies. Therefore, in he majoriy of applicaions we drop his variable from he esimaion of he sysem (6). Las, he 12

13 vecor P = [ E, S C, S U, I C, I U ] has n-2=3 coinegraing relaions. The corresponding hypohesized coinegraing marix is ' β = We esimae sysem (6) and derive he error correcion form and he covariance marix Ω for each day for each one of he inerlised underlying securiies in our sample in he various seings described above. In preliminary seps, we derive he opimal number of lags esimaed by minimizing he Akaike 20 informaion crierion for an unresriced vecor auo regression (VAR) and apply he Johansen (1990) es o VECM model (6) o deermine he number of coinegraing relaions. As suggesed in he previous secion, we adop Johansen (1990) maximum likelihood esimaion for VECM as an economeric approach o derive he esimaes for our wo main models based on Hasbrouck (1995) and Gonzalo and Granger (1995). 21 II.3 Daa and empirical mehodology Our sudy uses daa on quoes in equiy and opion markes boh in Canada and in he US. More specifically, he iniial sample consiss of inraday quoes on opions raded boh in Canadian and US markes during he 6 monhs from Sepember 2007 o February 2008 inclusively. 22 As noed in Hasbrouck (1995), he use of quoes raher han rade prices is suppored by he fac ha opion quoes change more frequenly han rade execuions, which makes i more likely o observe he required lack of correlaion in cross marke innovaions. The daa 23 include all available ime samped price quoes on he seleced opion series. In oal 62 differen opion series were included in he analysis, which number was reduced o 50 by our filers as explained below. Each opion quoe was firs mached o he corresponding ime samped quoes on he underlying securiy ha was obained from he Torono Sock Exchange daa apes. The daa was hen 20 The use of his crierion resuled in beer residuals auocorrelaion properies compared o he use of he Schwarz informaion crierion, which sysemaically resuled in a lower number of included lags. 21 Gonzalo (1994) presens he evidence in favor of he use of maximum likelihood VECM compared o oher esimaion mehods. This approach performs well even if he sysem is overparamerized by including a large number of lags. 22 Quoes ha were no updaed in he 15 minues prior o each observaion were eliminaed from he analysis. 23 The daa was made available o he auhors by he Monreal Exchange (ME). 13

14 mached o US marke informaion, which is comprised of naional bes bid and offer (NBBO) quoes obained from an independen source 24 ha compiles daa from all US opion markes and heir corresponding underlying securiy s quoe informaion. Each observaion was also mached o he conemporaneous quoe on he exchange rae. Table I presens he descripive saisics for all markes in his analysis and For he period under sudy, we have 122 days for which here was rading in boh he US and Canada, which resuls in poenially 6050 company-days. By accouning for he availabiliy of daa, 25 we noe he following numbers of company-days simulaneously available for all he specified variables: S C, I C ; S U, I U ; S C, S U ; I C, I U ; S C, I C, S U, I U Table I approximaely here C U For he implied prices ( I, I ) derived from he opion quoes we firs obain he implied k volailiies σ, k = C, U by invering he BSM expression a ime by using he conemporaneously observed opion and underlying securiy prices, and hen we use his C U volailiy o compue ( I, I ) as in (4). In all cases we use he bid-ask midpoin as a measure of he sock and opion prices. In he resuls ha we presen we used a one-minue ime lag beween he implied price esimaes a and he corresponding implied volailiy esimaes a. We also verified ha varying his lag beween one and sixy minues did no significanly affec our resuls. Since he daa includes quoes for several conracs on each underlying securiy a each insan, our final esimaes of he implied sock prices are averages across all observed quoes for each series a any given insan. These averages were sraified wih respec o he opion conracs moneyness and ime o mauriy. As menioned earlier, his esimaion of implied underlying securiy prices is hen mached wih he corresponding price quoes in he observed equiy markes and included in he esimaion of each marke s informaion share using equaion (8). A key empirical issue is he chosen lengh of he sampling inerval. I is imporan o noe ha in order for he IS esimaes o be informaive 24 See markedaaexpress.com 25 The mos imporan facor in limiing he use of daa is he availabiliy of opions quoes. 14

15 he correlaions of he price innovaions across he markes under sudy should be minimized by selecing as shor a sampling inerval as he daa may afford. 26 A suggesed, one second sampling inerval may minimize poenial correlaions even if hey are no eliminaed compleely. 27 Grammig e al. (2005) use a 10 second and a 1 minue sampling inervals and also find ha he ime aggregaion is likely o influence he degree of correlaion across markes, bu ha he wo inervals yield similar resuls. 28 A problem ha arises in Canadian opion markes in his conex is ha hey have been shown 29 o be ofen exremely hin for many opion series, where price quoes are no updaed as frequenly as in more liquid markes. The Canadian informaion share resuling from informaion flows may hus be dilued by he greaer liquidiy levels in he US o he exen ha he frequency of price quoe updaes is posiively relaed o marke aciviy. A en second sampling is hus used in his sudy as a compromise beween he issue of marke hinness in Canadian opion markes and he need o minimize he correlaion in cross marke innovaion. We furher deal wih he problem of opion marke hinness by resricing our empirical resuls o a subsample of he observaions ha saisfies he following frequency of quoing crieria. We eliminae from our sample all firms ha did no show a leas 80 days of daa ou of a possible 122 days. Of he remaining firms we eliminae all hose ha did no show a leas 100 observaions for a given opion conrac. These filers eliminaed 12 of he 62 firms. To verify he uniformiy of he remaining sample, we spli i ino a frequenly updaed quoes subsample of 28 firms wih a leas 500 observaions for a given opion conrac, and an infrequenly updaed quoes subsample of 22 firms wih less han 500 bu above 100 such observaions. We repor separaely he resuls for hese wo subsamples, as well as for he aggregae sample and as he resuls show, in almos all cases he differences beween he wo subsamples are well wihin he limis of saisical error. 26 In our daa for a one-minue sampling inerval he correlaion of he Canadian and US underlying sock price incremens was of he order of 0.9, resuling in bounds on IS of app. 0 and See Hasbrouck (1995). Yan and Zhivo (2009), however, argue ha very shor sampling inervals lead o incorporaing he microsrucure noise in he esimaes. 28 See Grammig, Melvin and Schlag (2005). 29 See Khoury, Perrakis and Savor (2010). 15

16 As noed earlier, he exisence of conemporaneous correlaions of residuals in he VECM model (6) yields lower and upper bounds on IS. We esablish hese bounds by searching over all possible Cholesky facorizaions of he covariance marix Ω. Then we compare he midpoins of hese bounds o he Gonzalo and Granger componen shares (CS), whose esimaion doesn depend on he random walk hypohesis and hus admis conemporaneous correlaion of residuals wihou resuling in a bounded quaniy. III. Empirical Resuls III.1 The Hasbrouck (1995) informaion shares resuls for marke pairs Nex we esimae he Hasbrouck (1995) informaion shares model, by applying he vecor auoregressions error correcion form (VEC) (6) and hen esimaing he informaion shares bounds for each marke as analyzed in he previous secion. In order for he informaion bounds o be informaive he sampling inerval mus be such as o minimize he effecs of poenial conemporaneous correlaions. Our analysis shows ha he sampling inerval ha bes suis our sudy in erms of conrolling poenial conemporaneous correlaions and providing reliable informaion bounds is a 10 seconds inerval. We will herefore use his ime frame in he remaining analysis. We sar from pairwise comparisons of he informaion shares of relevan markes and hen proceed o an examinaion of all four markes pu ogeher. Tables II and III approximaely here Tables II and III presens he resuls of each marke compared separaely o each one of he oher relevan markes. In he equiy markes pair Table III shows ha he Canadian equiy markes have a significanly higher informaion share han heir US counerpars. For he aggregae sample he average informaion share for Canadian as shown in Table III equiies is bounded beween 40.2% and 81.0%, while he US equiies average bounds are 19.0% and 59.8% for he lower and upper bounds respecively. When he foreign exchange marke is included in he 16

17 analysis, is average informaion share appears negligible. These resuls can be conrased wih hose peraining o he pair of opion markes, for which Table III shows ha Canadian opions conain on average beween 40.7% and 44.8% of he informaion share while US opions conain a slighly higher informaion share of beween 55.2% and 59.3%. Again, when he foreign exchange marke is considered separaely, unrepored resuls show ha is average informaion share is negligible. 30 On he oher hand, he resuls for he wo pairs of opion and equiy markes wihin each counry show ha mos of he average informaion share is associaed wih equiy markes for boh US and Canada. Indeed, Table II shows ha he Canadian equiy markes average informaion share lies beween 93.5% and 96.4% compared o 89.8% and 95.0% for US equiies. The same pairwise comparison shows ha he wo opion markes average informaion shares are bounded beween only 3.6% and 6.5% and beween 5.0% and 10.2% in Canada and in he US respecively. These resuls conras wih hose of Chakravary e al (2004), where opion markes have significanly higher average informaion shares compared o heir corresponding equiies, ranging from 17.5% o 18.3%. Noe also ha our resuls exhibi considerably igher bounds when analyzing equiy versus opion markes wihin each counry compared o iner-counry comparisons. As noed in Hasbrouck (1995) he widh of he informaion share bounds increases wih he correlaion of he residuals. Table IV shows ha his correlaion remains very srong beween Canadian and US equiy markes (ρ = 63.2% on average) and much weaker for oher marke pairs (2.8% ρ 16.5%) This resul is indicaive of he srong co-movemen beween Canadian and US equiy markes. 31 III.2 The Hasbrouck (1995) informaion shares resuls for all markes considered simulaneously Tables V and VI show he resuls for he Hasbrouck (1995) informaion marke shares model wih all markes considered simulaneously. More specifically, he informaion shares are 30 For conciseness purposes all resuls for he analysis where he foreign exchange markes are considered separaely are no repored bu remain available from he auhors upon reques. 31 These resuls conras wih hose of Grammig e al (2005) using German inernaionally cross-lised socks. 17

18 esimaed for opions and heir underlying equiy markes boh in Canada and in he US, wih all markes being inegraed in he model on a common currency basis. The resuls show a wide range of equiy average informaion share bounds beween firms. For he aggregae sample in he Canadian marke for he underlying securiies he range exends from a low of 35.9% o a high of 76.4% while he bounds for US equiy markes range from 16.4% o 57.0%. The corresponding resuls for he informaion shares of opion implied prices also provide consisen resuls wih igher share bounds. The informaion share of Canadian opions exhibis an average lower bound of 2.4% and an average upper bound of 4.9%. The informaion share of he Canadian opion marke is slighly lower han ha of he US opion marke, where average informaion shares range from 3.2% o 7.7%. The inclusion of he foreign exchange rae in he simulaneous analysis does no however affec he informaion shares resuls of he four oher markes o any significan exen. Table IV approximaely here The resuls of Tables V and VI, where all four markes are examined simulaneously, are fully consisen wih hose of he pair-wise comparisons of Tables II and III. The relaive imporance of each marke s informaion share reveals ha Canadian equiy markes have a greaer informaion share han US equiies, while he Canadian opion markes informaion share is less imporan han is US counerpars. These resuls are all he more relevan when relaive ransacions volumes of hese markes are aken ino consideraion. Indeed he Canadian equiy marke informaion share is higher han ha of is US counerpar even hough is proporional share in oal volume of ransacions in boh markes is 38.7% compared o 47.8% for he US equiy marke. The conras is even more sriking in he opion markes, where he US marke exhibis only slighly higher informaion han is Canadian counerpar while is proporional share in oal volume of ransacions average 12.3% compared o 1.3% for he Canadian opion marke. These resuls are also consisen wih hose repored by Solnik (1996), Bacidore and Sofianos (2002), Lieberman e al. (1999), Kao e al. (1990) and Grammig e al. (2005) lending suppor o he higher informaiveness of he home marke in spie of he superior liquidiy of he foreign venue where he securiies are cross lised and conras he findings of Law and Dilz (1994), and Wang e al. (2002) in his regard. 18

19 III.3 The Gonzalo-Granger (1995) resuls for all markes considered simulaneously Table VI displays he resuls of he Gonzalo-Granger (1995) componen shares model (CS) and compares hem o he corresponding midpoins of he Hasbrouck (1995) informaion share model (IS). As his able shows, he resuls for he Gonzalo-Granger (1995) model coincide, on average, almos exacly wih he Hasbrouck (1995) model average mid-poins when we consider a symmerical sysem in VECM model (6), i.e. when here is no exchange rae in he model. This is an expeced resul since, as indicaed in Baillie a al. (2002), IS midpoins for symmerical sysems coincide wih CS. The inclusion of he exchange rae in model (6) on average raises he exchange rae CS relaive o he midpoin IS for his variable. One of he advanages of CS is ha a 2 χ-disribued likelihood raio es is available. 32 Table VI also displays aggregaed resuls for his es, i.e. i indicaes he oal proporion of days ha CS for a given variable was saisically differen from zero a he 10% significance level for he Gonzalo and Granger (1995) Q-es, which in his case is χ 2 -disribued wih one degree of freedom. The coincidence of he midpoin IS and CS shown in Table VI validaes he use of he former quaniy as he dependen variable for he explanaory models presened in he nex secion. Tables V and VI also confirm he uniformiy of he sample ha we used in our empirical work, since he resuls for he frequenly quoed and infrequenly quoed subsamples are virually idenical in mos cases o hose of he aggregae sample. The able also shows he midpoin IS and he CS measures for all pairs of markes. The coincidence of he IS and CS resuls is also preserved in he pairwise comparisons beween markes, wih boh measures showing he dominan role played by he underlying sock in he discovery process in boh Canada and he US. Tables V and VI approximaely here 32 See Gonzalo and Granger (1995) for deails. 19

20 III.5 Facors driving he informaion shares beween firms As noed earlier, he informaion shares differ subsanially among firms in all four markes. In he equiy markes he average informaion shares bounds midpoin varies from a low of 37.1% o a high of 60.7% for Canada, and from 20.1% o 45.7% for he US. Similarly, for he wo naional opion markes he average informaion shares are almos always low, bu a small number of firms, 6 in Canada and 7 in he US ou of he 62 firms of he oal sample, have average informaion shares bounds midpoins ha exceed 10%, while 1 firm in Canada and 3 firms in he US have average informaion above 20%, of a magniude comparable o he resuls of Chakravary e al (2004) for he major US firms opions. Panels A o D in Figure 1 show he informaion shares midpoins disribuions for he Canadian and US equiy and opion markes respecively. Similar variabiliy also exiss for he ineremporal evoluion of average informaion shares in he four markes, aggregaed for all 50 firms in our sample and shown in Panels A and B of Figure 2; his ineremporal variaion will no be examined in his version of he paper. In his subsecion we seek o idenify observable marke or firm characerisics ha drive he differences in informaion shares beween firms and deermine he marke where mos price discovery akes place. (Figure 1 abou here) (Figure 2 abou here) There is relaively lile heoreical research on he locaion of price discovery when a securiy rades in muliple markes. I is clear ha such discovery will be driven by he choices of informed raders. Chowdhry and Nanda (1991) show ha under cerain condiions one of he markes emerges as he dominan locaion for rading in he mulimarke securiy. Noneheless, he facors ha deermine his dominan locaion are no easy o idenify empirically. Easley, O Hara and Srinivas (1998) idenify condiions ha induce informed rading in he opion, raher han in he underlying sock marke; hese, however, have lile relevance o mos of he socks in our case, since he opion markes have small informaion shares. 20

21 We invesigae he deerminans of he informaion shares by panel leas squares regressions wih a oal of 50 cross secions (one for each firm), resuling in 6050 poenial observaions. Table VII presens he resuls of he regressions for he four separae pairs of markes, he wo naional sock and opion markes and he underlying and implied US and Canadian markes respecively. We choose one of he shares as he dependen variable. For he independen variables we use firs of all wo variables ha reflec he relaive liquidiy of he wo markes, namely he relaive volume and he relaive effecive spread of he wo markes. Second, we use where appropriae an indicaor of marke uncerainy, he inraday variance in he underlying sock marke. As noed in Chakravary e al. (2004) and Capelle-Blancard (2003), in he pairs of naional sock and opion markes his variable will have a negaive effec on he price discovery in he opion marke. Las, we include in he pairwise regressions where he wo markes are in differen counries an indicaor of he exchange rae uncerainy, he inraday variance of he exchange rae, as well as a firs-order auoregressive erm. The model is as follows: SHARE = α + β VEX + β VS_ CA + β VS_ US + β RSPR + β RVOL + AR(1) + ε i i 1 i 2 i 3 i 4 i 5 i i (10) Where SHARE is he midpoin of he upper and lower bound of he firs marke s informaion share, VEX is he inradaily variance of he exchange rae, VS_CA and VS_US are he inegraed inraday variances for he Canadian-raded and US-raded underlying securiies respecively, RSPR is he raio of he firs marke s effecive spread o he second marke s, RVOL is he raio of he firs marke s volume o he second marke s, and AR(1) is he auoregressive erm. Table VII exhibis he resuls of he marke pairs analysis. In he firs wo panels represening he naional markes he dependen variables are he opion informaion shares in he US and Canada respecively. The relaive volume and spread variables coefficiens have he expeced signs everywhere bu only one of hem is significan. In he oher wo panels i is he US opion and underlying sock informaion shares ha are he dependen variables. Here he marke liquidiy variables coefficiens, he relaive spreads and volumes of he Canadian o he US marke have he expeced signs whenever hey are significan, in he case of he spreads for he opion markes 21

22 pair and in he case of volume for he underlying sock pair; he remaining coefficiens have he wrong sign bu are no significan. 33 More ineresing are he esimaes of he coefficiens of he uncerainy variables, he inraday variances of he underlying socks and he exchange rae. For he laer, we noe ha alhough i is no significan (and very small) in he purely naional markes, i is a srongly negaive and highly significan deerminan of he US opion marke and sock marke informaion shares. Since he firms are Canadian, hese resuls conform o our inuiion ha he informed raders are also Canadian, who would rade a home when subjeced o exchange rae risk. On he oher hand, he effecs of he volailiy of he underlying socks in Canada and he US are less easy o inerpre. The Canadian volailiy shifs informed rading away from Canadian and owards US socks and opions, as expeced. I also, however, shifs such rading owards opions from underlying in boh Canada and he US, wih all effecs being highly significan. Alhough his las shif conradics he resuls of Chakravary e al (2004) and he heoreical conjecures of Capelle- Blancard (2003) abou uncerainy shifing informed rade away from he opion marke, i is consisen wih raders using he opion marke o speculae on volailiy changes. As for he US volailiy, i shifs informed rading from US owards Canadian socks and opions, bu i also shifs such rading away from he opions and owards he underlying in boh Canada and he US as prediced by he earlier sudies, wih all effecs being again significan. Table VI approximaely here We now analyse he facors affecing each marke share wih all marke considered simulaneously as in he analysis underlying Table V and VI and wihin he framework of equaion (10), as follows: SHARE = α + βvex + β VS_ CA + β VS_ US + β RSPR_ S + β RSPR_ O + i i 1 i 2 i 3 i 4 i 5 i β RVOL_ S + β RVOL_ O + AR(1) + ε 6 i 7 i i (11) 33 Noe he exreme volailiy for he CA o US opion volume raio repored in Table I on a firm-day basis, which indicaes a need for a normalizaion of his variable for he regression analysis. 22

23 Where SHARE is he midpoin of he upper and lower bound of each marke s informaion share, VEX is he inradaily variance of he exchange rae, VS_CA and VS_US are he inegraed inraday variances for he Canadian-raded and US-raded underlying securiies respecively, RVOL_S (RVOL_O) is he raio of Canadian share volume (opion conrac volume) o he similar quaniy in he US, RSPR_S (RSPR_O) is he raio of he underlying securiy (opion) average effecive spread in Canada o he similar quaniy in he US, and AR(1) is he firs-order auoregressive erm. The resuls, shown in Table VIII, confirm he conclusions of he pairwise informaion share analysis. The marke liquidiy variables, he relaive spreads and relaive volumes, have weak and mosly non-significan effecs on informaion shares. 34 Mos of he relaive spread coefficiens have he righ sign bu none of hem is significan. Of he relaive volume variables coefficiens only one is significan and has he wrong sign; mos of he coefficiens are very small. As for he volailiy variables coefficiens, hey confirm srongly he pairwise resuls. The US inraday variance has srong and significan impacs in shifing informed rading away from boh USraded socks and opions and owards he Canadian marke for he underlying securiy. The Canadian inraday variance has similarly srong and significan posiive effecs on boh US underlying and opion informaion shares, a corresponding negaive effec on he Canadian underlying informaion share, bu a posiive and significan effec on he Canadian opion marke s informaion share, which can again be inerpreed as evidence of rading on volailiy. Las, he exchange rae uncerainy has srongly posiive effecs on boh Canadian markes informaion shares and a similarly srong negaive effec on he US opion marke s informaion share. As already noed, his is evidence ha price discovery, presumably by informed raders, akes place in he home marke when rading in he US is subjeced o exchange rae uncerainy. 34 This is perhaps no surprising, since he marke srucure of he Canadian opion marke has been shown o be compeiive even wihou any consideraion of he cross-lising of opions in he US, implying ha he marke makers spread is close o he perfecly compeiive level. See Khoury, Perrakis and Savor (2010). 23

24 IV. Conclusion This paper examines he issue of price discovery for opioned Canadian securiies cross lised in US markes. More specifically, he sudy provides an analysis of he relaionship beween Canadian and US opion and equiy markes for cross lised securiies in an inegraed model ha also accouns for he foreign exchange dynamics beween he wo counries. We find ha he foreign exchange marke s conribuion o he price discovery process is insignifican and we drop i from our empirical work. We hen use wo differen economeric approaches o he coinegraion analysis of he four markes and find essenially he same resuls wih all approaches, which adds o he robusness of our findings. In unrepored resuls we also sudy he pair-wise lead-lag relaionships ha exis among he various pairs of Canadian and US sock and opion markes, and we find a high level of inegraion beween all four markes.. The informaion share analysis was conduced using he Hasbrouck (1995) mehodology for marke pair seings and was modified o accoun for he aggregae dynamics of all markes simulaneously. In addiion, he proposed approach was validaed using an alernaive mehodology, which is an adapaion of Gonzalo & Granger (1995). The findings conras wih previous resuls by Chakravary e al (2004) and show ha equiy markes exhibi on average a much higher informaion share han opion markes boh in local pair-wise comparisons and in he inegraed model ha accouns for all markes simulaneously. The analysis also concludes ha Canadian equiy markes informaion shares dominae heir US counerpars while he opposie resul can be observed for opion markes. These resuls are all he more relevan when relaive ransacions volumes of hese markes are aken ino consideraion. Our daa shows ha US markes exhibi greaer relaive volumes han in Canada. This difference is almos enfold for opions, even hough he Canadian opions informaion share is only slighly lower han is US counerpar, while he informaion share is greaer in Canada for equiy markes. The analysis also shows ha he esimaes derived from he proposed adapaion of Gonzalo & Granger (1995) coincide, on average, almos exacly wih our proposed Hasbrouck (1995) adapaion, which furher validaes he conclusions presened in his paper. 24

25 In boh he pair-wise and inegraed models, he foreign exchange dynamics exhibi lile or almos no informaion share in he price discovery process. The analysis also shows ha he inegraed model informaion shares differ from hose of he pair-wise analysis. The inegraed model resuls exhibi lower informaion shares for each individual marke alhough he overall relaive imporance of each marke in he price discovery process is mainained. This observaion poins o he imporance of analysing he Canadian and US muli-marke seing using an inegraed approach where all markes are considered simulaneously. The resuls also validae he imporance of he home marke in he price discovery process for he securiies of ineres in his sudy. Since here are wide variaions in informaion shares in he cross secion of he firms in he sample, bu also in he ineremporal variaion of he shares across he 122 days of our sample, we also examine he deerminans of he informaion shares of each marke in panel regressions. We find ha marke liquidiy variables such as relaive spread and relaive volume have very lile impac on he informaion shares, hus conradicing srongly he resuls of Chakravary e al (2004). On he oher hand, uncerainy in he wo naional sock markes and in he foreign exchange marke urns ou o be a srong deerminan of he informaion shares in each marke. We find srong evidence ha foreign exchange uncerainy shifs price discovery owards he home marke. As for uncerainy in he underlying equiy markes, i also shifs discovery owards he compeing equiy and opion markes in he oher counry; we also find some evidence of volailiy rading in he form of increased informaion share in he Canadian marke in response o an increase in uncerainy in he Canadian equiy marke. 25

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29 Table I Descripive saisics This able provides he descripive saisics for variables used in esimaing equaions (10) and (11) as well as oher relevan descripors of he daa. The variables include inegraed variances calculaed on an inraday basis for C$/C$, he Canada-US foreign exchange rae reurn, CA Underlying, he Canadianraded equiy reurn, US Underlying, he US-raded equiy reurn (if no saed oherwise, all quaniies were derived per firm-day; all variance saisics are annualized). Correlaions [4]-[6] were derived firs for each firm and hen summarized in he presened saisics. Effecive spreads are compued as double he absolue value of he difference beween ransacion price and he average beween quoed bid and ask prices. The effecive spread raios are calculaed on a common currency basis. All volume figures are calculaed on a daily basis per firm for he underlying markes and per conrac for opions. # Variable N Mean Median 5 h Perc. 95 h Perc. S. Dev 1 Inegraed Variance of C$/U$ Inegraed Variance of CA Underlying Inegraed Daily Variance of US Underlying Correlaion beween [2] and [3] Correlaion beween [1] and [2] Correlaion beween [1] and [3] Raio of CA o US Sock Effecive Spreads Raio of CA o US Opions Effecive Spreads Raio CA o US Sock Share Volume Raio CA o US Sock Share Volume (per firm) Raio CA o US Opion Conrac Volume Raio CA o US Opion Conrac Volume (per firm) Raio of CA Opions o Sock Effecive Spreads Raio of US Opions o Sock Effecive Spreads Raio of CA Opions Conrac o Sock Share Volume Raio of US Opions Conrac o Sock Share Volume

30 Table II Pair-wise minimal and maximal informaion share aggregae resuls esimaed separaely for naional equiy-opions markes This able provides minimal and maximal informaion share bounds calculaed based on he Hasbrouck (1995) model where each naional marke pair is considered separaely. Opions Socks Opions Socks min max min max min max min max Canadian markes pair-wise comparison (3369 firm days) A: Frequenly updaed quoes sub-sample US markes pair-wise comparison (3412 firm-days) Canadian markes pair-wise comparison (2561 firm-days) B: Infrequenly updaed quoes sub-sample US markes pair-wise comparison (2479 firm-days) Canadian markes pair-wise comparison (5930 firm-days) C: Aggregae sample US markes pair-wise comparison (5891 firm-days)

31 Table III Pair-wise minimal and maximal informaion share aggregae resuls esimaed separaely for Canada-US sock and opions markes This able provides minimal and maximal informaion share bounds calculaed based on he Hasbrouck (1995) model where each marke pair is considered separaely according o he ype of securiy. Min max min max A: Frequenly updaed quoes sub-sample (3413 firm-days for socks, 3368 firm-days for opions) Canadian socks US socks Canadian opions US opions B: Infrequenly updaed quoes sub-sample (2628 firm-days for socks, 2423 firm-days for opions) Canadian socks US socks Canadian opions US opions C: Aggregae sample (6041 firm-days for socks, 5791 firm-days for opions) Canadian socks US socks Canadian opions US opions Table IV Average residual correlaions from VEC model esimaed for inegraed Canadian and US sock and opions markes This able provides he average residual correlaion marix from VEC model esimaed on a four marke common currency basis. CA underlying CA implied US underlying US implied CA underlying CA implied US underlying US implied

32 Table V Minimal and maximal informaion share aggregae resuls esimaed for inegraed Canadian and US sock and opions markes This able provides minimal and maximal informaion share bounds calculaed based on he Hasbrouck (1995) model where all markes are considered simulaneously on a common currency basis. Canadian markes inegraed comparison US markes inegraed comparison Opions Socks Opions Socks min max min max min max min max A: Frequenly updaed quoes sub-sample (3365 firm-days) B: Infrequenly updaed quoes sub-sample (2387 firm-days) C: Aggregae sample (5752 firm-days) Table VI Informaion shares (midpoins) and componen shares aggregae resuls esimaed for inegraed Canadian and US sock and opions markes This able provides midpoin informaion shares calculaed based on he Hasbrouck (1995) model and Gonzalo and Granger (1995) componen shares where, for boh models, all markes are considered simulaneously on a common currency basis. Type of esimae Canadian markes US markes Opions Socks Opions Socks A: Frequenly updaed quoes sub-sample (3365 firm-days) Informaion shares Componen Shares Saisically significan days (%) B: Infrequenly updaed quoes sub-sample (2387 firm-days) Informaion shares Componen Shares Saisically significan days (%) C: Aggregae sample (5752 firm-days) Informaion shares Componen Shares Saisically significan days (%)

33 Table VII Pair-wise model informaion share drivers This able provides he resuls for model (10) ha esimaes he impac on Hasbrouck (1995) informaion shares where each marke pair is considered separaely. The variables include inegraed variances calculaed on an inraday basis for VEX, he Canada-US foreign exchange rae reurn, VS_CA, he Canadian-raded equiy reurn, VS_US, he US-raded equiy reurn (all variance saisics are annualized), RSPR_CA (RSPR_US), he raio of he opion average effecive spread o he average underlying effecive spread for Canada (US) where effecive spreads are compued as double he absolue value of he difference beween ransacion price and he average beween quoed bid and ask prices, RSPR_S (RSPR_O), he raio of he underlying securiy (opion) average effecive spread in Canada o similar quaniy for US where effecive spread raios are calculaed on a common currency basis, and RVOL_S (RVOL_O), he raio of he share volume (opion conrac volume) in Canada o similar quaniy for US where volume figures are calculaed on a daily common-currency basis per firm for he underlying markes and per conrac for opions. AR(1) is a firs-order auoregressive erm. Dependen Variable OPTIONS vs. STOCKS CANADA vs. US US markes Canadian markes Opion markes Sock markes Implied Price Informaion Share Implied Price Informaion Share Implied Price Informaion Share (US) Underlying Price Informaion Share (US) Explanaory Variables esimae p-value esimae p-value esimae p-value esimae p-value Consan VEX VS_CA VS_US RSPR_CA E RSPR_US -2.79E RVOL_CA RVOL_US RSPR_S RSPR_O RVOL_S RVOL_O AR(1) Adjused R squared F-Saisic p-value N cross-secions N obs

34 Table VIII Inegraed model informaion share drivers This able provides he resuls for model (11) ha esimaes he impac on Hasbrouck (1995) informaion shares where all markes are considered simulaneously. The variables include inegraed variances calculaed on an inraday basis for VEX, he Canada-US foreign exchange rae reurn, VS_CA, he Canadian-raded equiy reurn, VS_US, he US-raded equiy reurn (all variance saisics are annualized), RSPR_S (RSPR_O), he raio of he underlying securiy (opion) average effecive spread in Canada o similar quaniy for US where effecive spread raios are calculaed on a common currency basis and where effecive spreads are compued as double he absolue value of he difference beween ransacion price and he average beween quoed bid and ask prices, and RVOL_S (RVOL_O), he raio of he share volume (opion conrac volume) in Canada o similar quaniy for US where volume figures are calculaed on a daily common-currency basis per firm for he underlying markes and per conrac for opions. AR(1) is a firs-order auoregressive erm. Dependen Variable Implied Price Informaion Share Canadian Markes Underlying Price Informaion Share Implied Price Informaion Share US Markes Underlying Price Informaion Share Explanaory Variables esimae p-value esimae p-value esimae p-value esimae p-value Consan VEX VS_CA VS_US RSPR_S RSPR_O RVOL_S E RVOL_O -1.07E E AR(1) Adjused R squared F-Saisic p-value N cross-secions N obs

35 Figure 1 Disribuion of ime-average informaion shares for 50 firms in our sample from four-marke model This figure provides an illusraion of he disribuion of ime-average informaion shares calculaed based on he Hasbrouck (1995) model where all markes are considered simulaneously on a common currency basis. 50 A: Canadian Opions 30 B: Canadian-raded Underlying Proporion of Observaions (%) Proporion of Observaions (%) Informaion Share Informaion Share 50 C: US Opions 30 D: US-raded Underlying Proporion of Observaions (%) Proporion of Observaions (%) Informaion Share Informaion Share 35

36 Figure 2 Ineremporal variaion for firm-average informaion shares from four-marke model This figure provides an illusraion of he disribuion of he cross-secional average informaion shares calculaed on a daily basis using he Hasbrouck (1995) model where all markes are considered simulaneously on a common currency basis A: Opions 0.8 B: Underlying Equiies Informaion Share Informaion Share Trading Day Trading Day CA US CA US 36