Internationally Cross-Listed Stock Prices During Overlapping Trading Hours: Price Discovery and Exchange Rate Effects

Transcription

1 Inernaionally Cross-Lised Sock Prices During Overlapping Trading Hours: Price Discovery and Exchange Rae Effecs Joachim Grammig a, Michael Melvin b*, and Chrisian Schlag c Absrac We analyze exchange raes along wih equiy quoes for 3 German firms from New York (NYSE) and Frankfur (XETRA) during overlapping rading hours o see where price discovery occurs and how sock prices adjus o an exchange rae shock. Findings include a) he exchange rae is exogenous wih respec o he sock prices; b) exchange rae innovaions are more imporan in undersanding he evoluion of NYSE prices han XETRA prices; and c) mos (bu no all) of he fundamenal or random walk componen of firm value is deermined in Frankfur JEL classificaion: F3; G15 Keywords: inernaional sock markes; cross-lising; price discovery a Deparmen of Economics, Universiy of Tübingen, Tübingen, Germany b* Corresponding auhor, Deparmen of Economics, Arizona Sae Universiy, Tempe, AZ, USA,, Tel.: ; fax: address: mmelvin@asu.edu. c Faculy of Economics and Business Adminisraion, Goehe-Universiy, Frankfur am Main, Germany Acknowledgemens For commens on an earlier draf, hanks are due o he edior, Franz Palm, an associae edior, hree anonymous referees, Marcelo Fernandes, Andrew Karolyi, Pierre Gio, Paolo Paruolo, paricipans a he American Finance Associaion, European meeing of he Economeric Sociey, European Economic Associaion, European Financial Managemen Associaion, Sonderborg Conference on Microsrucure and High Frequency Daa, he Georgia Tech Inernaional Finance Conference, and seminars a he Ciy Universiy of Hong Kong, Hong Kong Polyechnic Universiy, Nanyang Technological Universiy and he Universiies of Arizona, Frankfur, Goeingen, and S. Gallen. We reain responsibiliy for any remaining errors.. 1

2 1. INTRODUCTION Socks of many non-u.s. firms are raded in he Unied Saes. The issue of where price discovery occurs for such firms is surprisingly undersudied. For insance, we lack evidence ha yields a firm answer o he quesion of wheher U.S. rading follows he home marke or he home marke follows he U.S. Furhermore, how do he prices in boh markes adjus o an exchange rae shock? Does arbirage avoidance require boh markes o simulaneously adjus o a new exchange rae or does he adjusmen end o occur all in one marke? While here is no paper ha aemps o address boh of hese issues as will be done here, here is a lieraure ha addresses he relaionship beween prices of foreign equiies and heir U.S. lisings. This lieraure is overwhelmingly focused on lowfrequency daily reurns so ha issues of non-synchronous prices are poenially imporan. Excepions include Ding, Harris, Lau, and McInish (1999), who examine he links beween Singapore and Malaysia rading for one Malaysian firm and Eun and Sabherwal (2003) who examine he links beween U.S. and Canadian rading for a sample of Canadian firms. These sudies show significan price discovery in boh he home and foreign marke. While hese papers are innovaive and insrucive, hey differ from he analysis developed below in ha hey do no model he exchange rae process, bu use exchange raes o conver equiy prices ino common unis across counries. In addiion, heir samples have more ime-aggregaion beween observaions han he sample employed below. Harris, McInish, and Wood (2001) examine high-frequency spread and ransacion price dynamics for Daimler-Chrysler afer he creaion of he global ordinary DCX shares and show how U.S. ineres in DCX rading decreased in he firs six monhs following he merger of Daimler-Benz and Chrysler. 2

3 While analysis in an inra-day seing is required o provide hard evidence, lowerfrequency sudies have found an independen effec of he U.S. marke. For insance, Kim, Szakmary, and Mahur (2000) use daily daa on 21 Japanese, 21 Briish, 5 Duch, 5 Swedish, and 4 Ausralian firms o esimae VAR models of he impac of he underlying shares, he New York afernoon exchange rae, and he U.S. marke index on ADR prices. They find ha he underlying shares appear o be mos imporan, bu here is a significan independen role for he exchange rae and he U.S. marke index in pricing ADRs. While heir paper does no specifically address he issue of price discovery, heir findings of a role for he U.S. facor sugges ha he issue of price discovery requires a more deailed analysis. Oher sudies using daily daa on individual socks have focused on oher markes. Kao, Linn, and Schallheim (1990) examine 7 U.K., 8 Japanese, and 8 Ausralian socks also raded in New York and find evidence ha he price in he home counry leads he price in New York. They conver home counry prices ino dollars using a daily exchange rae aken from he Wall Sree Journal. Lau and Dilz (1994) sudy 7 Japanese socks also raded in New York and find bi-direcional causaliy bu a sronger impac of NYSE reurns on Tokyo reurns han he reverse. They conver he Tokyo prices ino dollars using daily exchange raes from he Chicago Mercanile Exchange. Lieberman, Ben-Zion, and Hauser (1999) examine 6 Israeli socks ha are lised in New York and find ha price discovery appears o occur in Israel for five of he firms wih Teva having a dominan role for he U.S. They sugges ha he resul for Teva is due o Teva being a mulinaional firm. Their sudy convers he Israeli prices ino dollars using a daily exchange rae from he Bank of Israel. Wang, Rui, and Firh (2002) examine a group of Hong Kong socks ha are also raded in London and find bidirecional causaliy for local marke reurns beween he wo markes bu wih Hong Kong being he dominan marke. The exchange rae is no incorporaed ino heir analysis. 3

4 The evidence from low-frequency daily daa indicaes ha he issue of price discovery for cross-lised shares is raher unseled. Generally, he papers are no acually conducing ess for price discovery in he recen sense of he word bu are examining pricing links across markes. One may draw inference, however, ha while he majoriy of low-frequency evidence poins oward he home marke as being he dominan source of pricing, resuls are mixed and some sudies find he U.S. prices o be dominan. Aside from Kim, Szakmary, and Mahur, he low-frequency sudies do no allow for an independen role of he exchange rae bu, insead, ranslae home marke prices ino dollars. One goal of his paper is o provide evidence on he informaion shares of U.S. and home marke rading using conemporaneously sampled, high-frequency daa. A second goal is o provide evidence on he equiy price response a home and in he U.S. o an exchange rae shock. There is a large lieraure on he effec of exchange rae changes on equiy prices, bu his lieraure has focused on he foreign exchange exposure effec of exchange rae changes for a single firm in is home counry. Such sudies have (quie properly) conduced analyses a a low ime series frequency as hey were concerned wih issues relaed o he managemen of foreign exchange risk exposure. There is a limied lieraure ha examines higher-frequency evidence of exchange rae changes and sock prices. Karolyi and Sulz (1996) examined he deerminans of correlaions beween open o close daily reurns on 8 Japanese socks raded in he Unied Saes wih a mached sample of U.S. socks. Their daa included daily reurns on yen/dollar fuures conracs. They found ha shocks o he currency fuures reurns had no measurable influence on he Japanese and U.S. sock price correlaions. Bailey, Chan, and Chung (2000) sudied he impac of he Mexican peso/u.s. dollar exchange rae on prices of Mexican firms raded on he NYSE. They sampled sock prices and exchange raes a 30-minue inervals and found ha peso depreciaion was associaed wih decreases in he sock 4

5 prices. Ours is he firs sudy o examine he high-frequency response of pairs of inernaionally cross-lised equiy prices o exchange raes a he ime resoluion relevan for arbirageurs. One migh hink of price discovery for a U.S.-lised European sock, e.g. he German Deusche Telekom o be deermined in he following way. News in Germany is mos imporan for his sock, so during home marke business hours, he price flucuaes wih public and privae informaion revelaion. Once U.S. rading begins in he ADR, 1 he price of he sock may include relevan informaion coming from he Norh American marke as invenory and informaion-based rading occurs during he overlap beween European and American rading hours. In addiion, dollar/euro exchange rae flucuaions will have implicaions for he sock prices in boh Europe and America. Afer an exchange rae shock, arbirage will resric he ADR price so ha i does no deviae oo far from he home marke price when boh are measured in a common currency. For insance, dollar depreciaion would end o increase he dollar price of he ADR and/or lower he euro price of he underlying home-marke shares. Since here has been no inra-daily analysis of how inernaional sock prices adjus o exchange rae shocks, we do no know if adjusmen is symmeric in boh he home counry and he U.S. markes or if mos or all of he adjusmen o an exchange rae shock occurs in one marke locaion. Our analysis will provide a firs look a his issue. The use of high-frequency, inra-day daa allows a view of he marke dynamics ha canno be achieved in daily daa or lower-frequency inra-day daa. Besides he issue of non-synchronous quoes ha arises in using closing prices from differen inernaional markes, one canno make meaningful inferences regarding price discovery excep a he high-frequency relevan for acual rading. Furhermore, he paern of adjusmen of sock prices o exchange rae shocks would be los due o ime aggregaion. Traders 1 Foreign firms ypically lis in he Unied Saes in he form of American Deposiary Receips (ADRs). 5

6 respond quickly o new informaion, so o infer he sock price response o an exchange rae shock one mus examine he daa immediaely afer he change in he exchange rae. A a low frequency, here will be many reasons why sock prices change so ha one canno clearly idenify he link beween a change in he exchange rae and a subsequen change in he price of a sock. The gain from using high-frequency daa is essenially ha here may be one-way causaliy exising among variables a a high sampling frequency ha dissolves ino conemporaneous correlaion a a lower sampling frequency. We invesigae he issue of price discovery for hree large German blue-chip firms ha are raded on he XETRA sysem in Germany and he New York Sock Exchange (NYSE) in he Unied Saes: Daimler-Chrysler, Deusche Telekom, and SAP. The paper is organized as follows: Secion 2I presens a brief overview of relevan insiuional deail regarding he rading venues, rading mechanisms, and firms sudied. Secion 3 inroduces he basic equilibrium relaionships in he conex of a simple microsrucure model of he marke. Secion 4 provides he framework for analysis and discusses issues of mehodology. Secion 5 presens and discusses he daa and esimaion resuls. Finally, a summary and conclusion is provided in Secion INSTITUTIONAL DETAILS Many European socks (like in our sample Deusche Telekom (DT) and SAP) are raded in he Unied Saes in he form of ADRs lised on he NYSE. This dollardenominaed U.S. rading is no an exchange of acual shares of he firms, bu raher rade in negoiable insrumens issued by a deposiary bank ha represen ownership of he underlying shares as issued in he home marke. For example, DT ADRs rade one-forone and SAP ADRs a a 12 o 1 raio agains he underlying shares. This means ha 12 6

7 SAP ADRs are issued for each share of he underlying sock held by he deposiary. 2 DaimlerChrysler (DCX) is raded in he Unied Saes as a global regisered share (GRS), someimes called a global ordinary. This is a single securiy ha is raded globally alhough i is quoed and seled in U.S. dollars in New York and euros in Frankfur. 3 DCX is raded on he NYSE in he Unied Saes. German rading in hese firms occurs via he elecronic rading nework known as XETRA. XETRA is he elecronic rading sysem of he Deusche Börse, he Frankfur Sock Exchange (FSE). Trading on he FSE occurs on he floor of he exchange as well as on XETRA. The FSE floor operaes in a similar manner o he NYSE floor. The equivalen of he NYSE specialis is he amlicher Kursmakler. The makler quoes bid and ask prices and conducs daily call aucions a he Frankfur opening (9:00), noon, and a he close of floor rading a 13:30. Since FSE floor rading ends before he NYSE opens, our daa will come from he XETRA sysem, which overlaps wih he NYSE morning. XETRA is an order-driven sysem wih no designaed marke makers. I is an anonymous, open limi order book. XETRA has no designaed marke makers, bu he FSE maklers are allowed o paricipae on XETRA and here is much volunary marke making. 4 Banks and insiuional invesors are main providers of liquidiy hrough he limi orders hey submi o he marke. ADRs are issued by a deposiary bank accumulaing shares of he underlying foreign sock. Since ADRs are issued a a fixed muliple relaive o he underlying shares, hey end o rade in a very limied range around he price of he underlying share, exchange-rae adjused. However, ADRs and underlying shares are close, bu no perfec, 2 Following a 3 o 1 sock spli on 1 May, 2000, SAP ADRs now rade a a 4 o 1 raio agains he German shares. 3 See Karolyi (2003) and Harris, McInish, and Wood (2001) for a deailed analysis and discussion of he DaimlerChrysler global ordinary sock. 4 Theissen (2002) provides a discussion of he FSE and XETRA. For small cap socks raded on XETRA, here exis designaed sponsors who ac as marke makers by submiing limi buy and sell orders simulaneously. 7

8 subsiues. Firs, hey are priced in U.S. dollars and rade and sele jus as any oher sock in he Unied Saes. The dollar price of he ADR will differ from he home marke price by a facor incorporaing he exchange rae. In addiion, foreign exchange risk migh influence he differenial beween he ADR and home marke share prices. One can, in principle, arbirage he price difference beween he ADR and underlying shares by new ADR issues or cancellaions. This is no a riskless arbirage due o he ime required o conver underlying shares ino ADRs or cancel ADRs and conver ino underlying shares. In addiion, here are conversion fees, he presence of he inermediary deposiary bank, and possible voing and oher corporae conrol righs ha may differ beween holders of he underlying shares and holders of he ADRs. For hese reasons, ADRs are no perfec subsiues for he underlying shares. Sill, we expec he prices of he wo asses o move closely ogeher over ime. GRSs differ from ADRs in ha hey do no involve a deposiary inermediary and have no issues of conversion beween differen forms since he same securiy is raded inernaionally. Since he GRS is quoed in local currency in each marke locaion, prices will differ across markes by an exchange rae facor. In general, global ordinary shares should be very close subsiues across inernaional markes as hey allow all sockholders o paricipae in corporae maers (dividends, disribuions, and conrol issues) regardless of heir locaion. They may no be perfec subsiues since here is local selemen and here may be less han perfec coordinaion across he mulinaional selemen insiuions involving ransfer and clearance issues. 5 Beyond he issue of perfec subsiuabiliy, here may also exis limis of arbirage in he sense of Shleifer and Vishny (1997). In his seing noise raders generae deviaions of prices from fundamenal values ha may persis for some ime. Such deviaions are no easily exploied by arbiragers risking oher peoples capial and 5 Karolyi (2003) provides a good review of he differences beween ADRs, GRSs, and home marke shares. 8

9 subjec o shor-erm performance consrains. However, in our seing of wo socks raded simulaneously for he same firm, an arbirage sraegy is sraighforward and relaively easy o implemen. Therefore, in normal imes we expec (and observe) he law of one price holding for ADRs and home-marke socks. Only in exreme circumsances, such as during a financial crisis as discussed in Melvin (forhcoming), do we ever see persisen deviaions from he law of one price for ADRs and home-marke shares. In such cases, arbirage is ineffecive in he manner discussed by Shleifer and Vishny. 9

10 3. INTERNATIONAL EQUITY TRADING AND EQUILIBRIUM RELATIONSHIPS Equilibrium in he marke for U.S.-raded shares and he underlying home-marke shares involves he dollar price of he ADR or GRS, he home-marke price of he underlying shares, and he exchange rae. We moivae he empirical analysis by firs presening a simple microsrucure model where price discovery is assumed o occur in he home marke. We assume ha he log of he exchange rae a ime, E, is exogenous wih respec o U.S. and home-marke shares and evolves as a random walk wih innovaion u : E = E + u (1) 1 The log of he home-marke share price,, follows a random walk and inroduces he innovaion or random-walk componen in he inrinsic value of he firm as v: h h 1 h P P = P + v (2) The log of he U.S. share price, u P, adjuss o he las observed exchange rae and homemarke price and also includes a random erm, w, o reflec any U.S.-based randomness ha may be due o ick-size, liquidiy orders, or any oher idiosyncraic source: P E P + w u h = (3) The innovaions u, v, and w are assumed o be boh serially and conemporaneously uncorrelaed wih zero mean. Though arbirage would resul in he U.S. price closely following he exchangerae-adjused home marke price during he ime of day when he wo markes overlap, i is no necessary ha he wo values be equal a every poin in ime. There should be a noarbirage band due o ransacion coss, and for ADRs, ime lags and associaed exchange 10

11 rae risk involved in conversions of home-marke shares ino ADRs or he flow-back conversions in he opposie direcion. 6 However, he wo sock prices, denominaed in he same currency, should move closely ogeher over ime. If we subrac he log of he U.S. price from he log of he dollar value of a home-marke share we have: E P P E u P v E P h u h h + = = + (4) w u v w Since he linear combinaion of he log exchange rae, log home-marke price, and log U.S. price is saionary, E, P h, and P u are coinegraed wih coinegraing vecor A =[1 1 1]. I is easily seen ha in he simple model of equaions (1)-(3) only he home marke innovaions u and he exchange rae innovaions v deermine he long run developmen of he U.S. price. Boh home marke price and exchange rae are compleely deermined by heir own innovaions, whereas he U.S. marke innovaions w exer only a ransiory effec on he U.S. price and do no influence he home marke price and he exchange rae a all. In oher words, price discovery for he sock is exclusively aking place in he home marke. In our empirical model, however, we allow he innovaions of boh home marke price, exchange rae, and U.S. marke price o exer permanen effecs on all hree price series. However, he magniude of he permanen effecs are allowed o be differen and esimaed empirically. Noe ha in he simple model oulined above he permanen effec of an innovaion is eiher 100 percen (innovaion u on E and P u, respecively and innovaion v on P h and P u, respecively) or zero (innovaion w on all price series). For he general model employed in our empirical analysis, we mainain he assumpion of he exisence of one coinegraing relaion beween E, P h, and P u wih 6 Miller and Morey (1996) sudy he price of Glaxo-Wellcome sock during he overlap of rading beween London and New York and show ha he differences beween he ADR and he London price do no exceed he ransacion coss ha would be associaed wih arbirage. 11

12 coinegraing vecor A =[1 1 1]. We furher assume ha he vecor P,P h,p u = ( E )' can be represened by a nonsaionary vecor auoregression of he form: P = β + φ1 P 1 + φ2 P φq P q + ε (5) where ε is zero-mean whie noise wih covariance marix Ω. From he Granger Represenaion Theorem (Engle and Granger, 1987) we know ha if here are coinegraing relaions among he elemens of P, here exiss an error correcion represenaion of he form: P + = α + BZ 1 + δ 1 P 1 + δ 2 P P q+ 1 ε (6) where Z 1 = A' P CONTRIBUTIONS TO PRICE DISCOVERY In order o esimae he conribuion of each marke o price discovery, we adap he mehod proposed by Hasbrouck (1995), and wrie he coinegraed sysem in a vecor moving average (VMA) represenaion: P = Ψ ( L ) ε = ε + ψ1ε 1 + ψ 2ε (7) Coinegraion of he hree price series wih coinegraing vecor A implies ha A ' Ψ (1) = 0, where Ψ ( 1) = I + ψ 1 + ψ The esimaion of he Ψ (1) marix is he cornersone of he analysis since his marix conains informaion abou he magniude of he permanen effec ha each of he innovaions exers on he long run dynamics of he hree prices. The economeric mehodology o esimae Ψ (1) involves hree seps. Firs, he Schwarz informaion crierion (SIC) is employed o idenify he appropriae lag lengh in equaion (6). In he second sep we esimae a VEC model wih he idenified lag lengh, which is hen used in a dynamic simulaion o esimae he VMA parameers in 12

13 (7) and he elemens of he Ψ (1) marix. 7 Once Ψ (1) is esimaed, we can infer he share of informaion associaed wih innovaions o each marke by using a mehod similar o Hasbrouck (1995). 8 In conras o Hasbrouck s analysis, however, our model conains wo common rends ha can be naurally associaed wih he efficien exchange rae and he efficien sock price. Hasbrouck s price discovery sudy of inner-u.s. markes implies one common rend (he efficien sock price) and N-1 coinegraing relaions (wih N he number of parallel markes), whereas in our model of inernaional price discovery here is room only for one coinegraing vecor. From Sock and Wason s (1988) common rends represenaion of a coinegraed sysem i can be seen ha he permanen impac of innovaions on he hree asse prices is given by he vecor Ψ ( 1) ε. I is useful o wrie he componens of his vecor explicily as: ψ 11 (1) ε = ψ 21 ψ 31 ψ 12 ψ 22 ψ 32 ψ e 13 ε ψ ε h 23 u ψ 33 ε Ψ. (8) For example, wih he elemens in P being ordered as E, P h, and P u, he firs row of e 11 h 12 u 13 Ψ ( 1) ε, ψ ε + ψ ε + ψ ε, gives he long-run componen of he innovaions ha is permanenly impounded in he exchange rae. The permanen impac of a one uni innovaion in price j on price i is given by ψ ij. For insance, ψ 12 is he long-run impac of a one-uni innovaion in he home-marke price on he exchange rae random walk. Given our prior beliefs regarding inernaional price discovery, we expec he Ψ (1) 7 See Hamilon (1994) p for a discussion of his mehod. 8 An alernaive mehod for inferring price discovery follows Gonzalo and Granger s (1995) common facor approach. In a special issue of he Journal of Financial Markes, papers by Lehmann (2002), Baillie, Booh, Tse, and Zaboina (2002), DeJong (2002), Hasbrouck (2002), and Harris, McInish, and Wood (2002), provide a deailed analysis of he wo approaches. One imporan difference arises in he possible imprecision of he informaion shares approach if here exiss subsanive cross-correlaion across markes. In our applicaion, he residual correlaions across markes are so small ha imprecision is no a pracical issue. 13

14 marix o have a specific form. In paricular, we expec: ψ =ψ = 0, ψ, = ψ 32 and ψ =ψ. Inuiively, ψ and ψ equaling zero means ha he exchange rae is unaffeced by home and U.S. marke innovaions. Furhermore, he assumed symmeric response o innovaions coming from he home and he U.S. marke (implied by ψ 22 =ψ 32 and ψ =ψ ) follows from he resricions imposed by coinegraion, i.e., A ' Ψ (1) = 0 and a coinegraing vecor of A' = [ 1 1 1]. We have no prior belief wih regard o ψ and ψ, as he wo sock prices may have differen responses o exchange rae innovaions. The esimaion resuls repored below will provide an empirical es of hese priors. To find he informaion shares aribuable o each marke, we decompose he variance of long-run impacs var( ψ ε e h u + ψ ε i1 i2 + ψ ε i3 ), i=1,2,3. These variances can be found on he diagonal of he marix ψ Ωψ'. The informaion shares are obained by a decomposiion of each of he hree variances ino he conribuions of each marke. In case of conemporaneous correlaion among he innovaions, i is no possible o idenify an independen informaion share for each asse wihou furher resricions. To circumven his problem, we follow he sandard approach by using he Cholesky facorizaion of Ω. This provides a lower riangular marix C, where Ω = C' C. The Cholesky facorizaion is creaing an orhogonalizaion by which one could, for example, firs isolae he impac of he exchange rae innovaion, hen he home-marke innovaion condiioned on he exchange rae innovaion, and hen he U.S. innovaion, condiioned on boh of he oher markes. In his recursive seing, one may hink of he orhogonalized innovaion in he U.S. marke as being he residual of a regression of he 14

15 U.S. innovaion on he innovaions in he exchange rae and home-marke price. 9 Wih a given ordering of markes, one now may compue he informaion share of marke j wih respec o price series i, S ij, as: S 2 ij ([ ψc ] ij ) /( ψωψ' ) ii =. (10) This normalizaion guaranees ha he informaion shares sum o uniy for each price series. The Cholesky facorizaion will resul in providing an upper bound on he share for he marke ordered firs and a lower bound for he share of he marke ordered las. Hence, he resuling informaion shares will depend upon a specific ordering of he markes, and i is imporan o check ha he qualiaive resuls are robus across alernaive orderings. There are a couple of ways in which his issue may be addressed. We could appeal o direced acyclic graph analysis as discussed in Swanson and Granger (1997) o moivae a paricular ordering of he variables (which would suppor a choice of he order we acually use: exchange rae, home-marke price, and U.S. price). However, given our high frequency sample, we will demonsrae in our empirical applicaion ha he esimaed upper and lower bounds for he informaion shares lie in a very igh range regardless of he ordering so ha he issue is relaively unimporan in our case. 5. DATA AND ESTIMATION RESULTS 5.1. Daa and Informal Evidence We sudy he relaionship beween U.S. and German rading over he common rading ime overlap each day for he period Augus 1 o Ocober 31, The overlap beween Frankfur and New York rading is from 14:30 o 16:00 GMT (or 9:30-11:00 New York ime) unil Sepember 20, On his day, he XETRA opening and closing hours were shifed forward by 30 minues so ha he overlap is from 14:30 o 16:30 GMT 9 Hamilon, p has a good discussion of his issue. 15

16 for he remainder of he sample. The exchange rae daa are ick-by-ick quoes on he dollar price of he euro as repored on he Reuers indicaive quoing screen. The daa were obained from Olsen & Associaes, Zurich. See Danielsson and Payne (2002) for an insrucive discussion of indicaive exchange rae quoes compared o he quoes on an elecronic brokerage. Since he indicaive quoes are from individual dealers bu he brokerage repors he inside spread (he bes bid and ask across all conribuing dealers), indicaive quoes end o be more volaile and exhibi higher negaive auocorrelaion han he bes bid and ask quoes from he brokerage. However, quoes from he brokerage are no public informaion and only indicaive quoes are available for our sample. The NYSE quoe daa are aken from he TAQ daa se available from he NYSE. The XETRA quoe daa are proprieary daa provided by he Frankfur Sock Exchange for his sudy. Boh quoe series represen firm quoes a which rades may occur. Table 1 liss summary saisics for each firm and each marke. The firs wo columns provide average bid and ask prices. XETRA quoes are in euro while NYSE quoes are in dollars. The dollar price of he euro was greaer han 1 during his period, wih a mean of for he bid price, so dollar prices exceed euro prices on he same firm. The SAP ADR represens 1/12 of a share of SAP sock as issued in Germany. In Table 1 and he empirical work ha follows, he NYSE prices are muliplied by 12 o be comparable o he home-marke shares. The hird column shows ha XETRA quoing is more inense han NYSE. XETRA quoes range from 3.4 imes he NYSE quoes for DCX o 3.9 imes he NYSE quoes for DT. Number of shares raded is also higher on XETRA han for he NYSE. The fourh column shows he average daily rading volume in each marke and i is seen ha he raio of XETRA volume o NYSE volume ranges from 3.0 for SAP o 20.5 for DT. The las column repors he average daily urnover as measured in euro for XETRA and dollars for he NYSE. In German rading, DCX generaes he 16

17 highes volume, followed by DT and hen SAP. Analyzing he share of volume we see ha he NYSE share is larges for SAP, followed by DCX and DT. <Table 1 goes here> Figure 1 plos he sock prices and he exchange rae, all measured as he average of bid and ask prices, over he 3-monh period we sudy. The difference beween he wo prices reflecs he exchange rae, which is seen in he final graph o move in a fairly narrow range over he sample period. The acual dollar/euro exchange rae raded wihin a range of o over he Augus Ocober period sudied. The fac ha he exchange rae was close o 1 over he period resuls in he XETRA euro price and he NYSE dollar price moving closely ogeher over ime. <Figure 1 goes here> The volume and urnover daa presened in Table 1 end o confirm he noion ha XETRA provides he primary marke and U.S. rading is in he derivaive asse. Addiional informal evidence may be seen in plos of he quoing inensiy of each marke. Figure 2 presens plos of he average number of quoe updaes per second for each 5- minue inerval over he rading day. The period of overlap beween New York and Frankfur is he peak period of aciviy during he day. Noe how quoing inensiy rises in Frankfur wih he New York opening and how quoing inensiy falls in New York wih he Frankfur close. This effec seems mos pronounced for DT and we shall see below how he informaion shares indicae ha DT seems much more a German firm han an inernaional firm. The spike in Frankfur quoing ha occurs a 13:30 is associaed wih he close of floor rading. Overall, Figure 2 is consisen wih he New York rading being derived from Frankfur, bu i is also suggesive of synergies beween he wo markes as quoing inensiy in Frankfur rises when New York opens. 10 <Figure 2 goes here> 10 An examinaion of similar plos for rades insead of quoes reveals he same synergies exising beween Frankfur and New York 17

18 5.2. Economeric Model Specificaion and Esimaion The informal evidence presened in Table 1 and Figure 2 is useful and provocaive, bu is only suggesive of he inerdependencies beween he markes. We now urn o he formal economeric evidence regarding he relaionship beween U.S. and home-marke rading. Firs, we discuss addiional issues relaed o daa and sampling and hen we develop he esimaes in line wih he discussion in Secions III and IV. All asse price series are in logarihms of he average of he bid and ask prices. We use he midpoin of he quoes raher han he bid or ask as our basic uni of observaion for wo reasons. Firs, his is he mos frequen mehodology used in he lieraure. Second, using midpoins minimizes he possibiliy ha quoes are being revised jus on one side of he marke or he oher o reflec posiions. I is unlikely ha he choice of midpoin versus bid or ask prices will have any subsanive effec on he resuls. The asse prices were sampled a 10-second inervals o assemble he basic daa se. The choice of sampling inerval was made wih he issue of conemporaneous correlaion in mind. There can be one-way causaliy exising among variables a a high sampling frequency ha dissolves ino conemporaneous correlaion a higher levels of emporal aggregaion. 11 We examined he correlaions among he residuals of our hreeequaion VEC sysem over alernaive sampling frequencies and chose 10 seconds as being suiable relaive o lower frequencies like 1 minue, as he 1 minue frequency yielded much more evidence of significan conemporaneous correlaion. A sampling frequencies higher han 10 seconds here was no gain in erms of reducing significan conemporaneous correlaions, bu here is a radeoff wih issues such as nonsynchronous quoing or oher sources of microsrucure noise ha makes 10 seconds preferable. An addiional sampling issue is wih regard o overnigh reurns and lags. 11 See Granger (1988) for discussion of relaed issues. 18

19 We creaed a daa se ha sared each day wih observaions on he dependen variables and lags so ha no overnigh reurns were used and no lags reached back o prior days. For insance, if he model calls for 3 lags in he VEC, he dependen variable begins wih he fourh observaion of each day. The iniial observaion each day for each sock was deermined by he firs 10-second inerval following he NYSE open conaining a quoe in boh markes. Augmened Dickey-Fuller ess revealed uni roos in he log of each asse price and he variables were idenified as being I(1). Johansen coinegraion ess were performed and he resuls clearly suppor he hypohesis of one coinegraing vecor among he 3 variables (see Table 2). The nex sep is o esimae he VEC equaion (7). The choice of lag lengh was deermined by he Schwarz Informaion Crierion (SIC). We sared wih 18 lags, which is 3 minues in a sample wih observaions a 10-second inervals. Then, holding he number of observaions consan, we esimaed he VEC a each shorer lag lengh down o 1 lag o deermine he lag srucure ha minimized he SIC. This revealed 3 lags as opimal for SAP and DT and 4 lags as opimal for DCX. The coinegraing relaions of he esimaed VECs are repored in Table 2. Wih he variables ordered as exchange rae, home-marke price, and U.S. price, he esimaed coinegraing vecors are close o he vecor A =[1 1 1] indicaed by heory. For each securiy, summary saisics are given on he order of coinegraion in Table In all 3 cases, he daa suppor one coinegraing vecor. <Table 2 goes here> The esimaion precision is assessed by employing he boosrap mehod suggesed by Li and Maddala (1997). In order no o disor he dynamic properies of he coinegraed sysem we choose o boosrap from he residuals of our esimaed VEC 12 See Johansen (1991) for discussion of he es saisics. 19

20 models raher han from he acual daa. 13 More precisely, he esimaed residuals are resampled by drawing observaions randomly wih replacemen and hen building a new vecor of observaions on he daa from he innovaions and he lagged values of he dependen variables. From he new se of observaions, parameers are re-esimaed. This process is repeaed 1,000 imes o generae he empirical disribuions for he parameers of ineres. The boosrap procedure offers he chance o obain parameer sandard errors (and in fac esimaes of he whole disribuion) when hey are no available analyically. We hus overcome he drawback ha he precision regarding esimaes of he long run impac marix and he informaion shares canno be assessed analyically. All sandard errors repored in ables 3 (long run impacs) and 4 (informaion shares) as well as he densiy esimaes of he informaion shares in figure 3 are based on he boosrap samples. 14 By a dynamic simulaion of he VECMs we find he VMA parameer marices in equaion (8) and, by summing up, he esimaes of he Ψ(1) marix. As a byproduc, his procedure also enables us o plo impulse response funcions (IRFs) which illusrae he impac of a one-uni innovaion in he XETRA price, he NYSE price, and he exchange rae. The values o which he IRFs converge are he respecive elemens of he Ψ(1) marix. IRF plos of he funcions are given in Figure 3 and esimaes of he Ψ(1) marix are repored in Table 3. Focusing firs on he NYSE innovaions, one can see ha here is a larger impac on XETRA prices for DCX and SAP han for DTE. In addiion, here is no apparen effec on he exchange rae. Similarly, a shock o he XETRA price has no effec on he exchange rae, bu a considerable effec on he NYSE price. Finally, exchange rae innovaions are seen o have a large impac on he NYSE price bu a very 13 Given he dynamic srucure of he model, boosrapping he dependen variables would disor he rue relaionships when lagged dependen variables appear on he righ-hand-side of he equaion. See Sapp (2000) for a similar boosrap applicaion o high-frequency exchange rae daa. 14 Asympoic inference on he long-run impac marix and he informaion shares is provided by Paruolo (1997a, 1997b). 20

21 small effec on he XETRA price. The effecs jus deailed anicipae he price-discovery findings o be repored below. In erms of he ime required for he sysem o converge o a new equilibrium, he impulse responses are ploed for unis represening 10-second inervals. While resuls differ somewha across he various plos in Figure 3, i appears ha convergence o he new equilibrium occurs wihin abou 200 inervals, or 33 minues, following a 1-uni innovaion in he various prices. <Figure 3 goes here> The esimaes of he Ψ(1) marices mee our prior expecaions as discussed in he previous secion: he exchange rae appears o be unaffeced by innovaions in he sock prices (for insance, he DCX impac of a uni shock o he XETRA price on he exchange rae of wih a sandard error of 0.011); he long-run impac of a shock o he XETRA price is abou he same on boh XETRA and NYSE prices (noe he DCX impacs of a uni shock o he XETRA price equal o and on XETRA and NYSE prices, respecively); and he long-run impac of a shock o he NYSE price is abou he same on boh XETRA and NYSE prices (DCX impacs of and for NYSE shock effecs on XETRA and NYSE prices, respecively). In addiion, Table 3 repors esimaes of parameers for which we had no prior beliefs: he long-run impac of a shock o he XETRA price is greaer han he long-run impac of a shock o he NYSE price (compare o for he DCX XETRA price) and shocks o he exchange rae have a greaer impac on he NYSE price han he XETRA price (compare o for DCX). The greaer impac of XETRA prices compared o NYSE prices is consisen wih a view ha price is discovered in Frankfur and hen New York follows wih he derivaive marke. <Table 3 goes here> The fac ha he NYSE price appears o accommodae mos of he adjusmen o an exchange rae shock while he XETRA price is relaively unaffeced by such shocks is 21

22 imporan new evidence on how inernaional equiy prices evolve. One migh hink ha, given a shif in he exchange rae, boh prices would end o adjus o a new equilibrium defined by he new exchange rae. For insance, if he dollar depreciaes agains he euro, we migh expec arbirage forces o resul in a rise in he NYSE price and a simulaneous fall in he XETRA price in order for he law of one price o hold in he inernaional equiy marke. Insead, he evidence indicaes ha almos all of he adjusmen o a new exchange rae comes hrough changes in he NYSE price. There is a small and saisically significan negaive effec of he exchange rae innovaion on he XETRA price ha is roughly he same magniude for DCX and SAP bu much smaller for DT. However, he NYSE effec is abou 3 imes he XETRA effec for DCX and SAP and abou 12 imes he XETRA effec in he case of DT. 15 The fac ha he NYSE price does mos of he adjusmen o an exchange rae shock is addiional evidence ha he ADR is priced as he derivaive asse. Given he home-marke price, a change in he exchange rae requires a change in he NYSE price in order o follow he XETRA price. In order o preven arbirage opporuniies, i is no surprise ha here is a very quick adjusmen in he sock prices following an exchange rae change. This dynamic paern of adjusmen o an exchange rae change across inernaional equiy markes would be los in an analysis a a low ime series frequency Informaion Shares As explained above, he riangularizaion of he innovaion variance-covariance marix resuls in an upper bound on he esimaed informaion share for he variable ha 15 The exchange rae evidence is also suggesive ha our overall resuls are no driven by he fac ha here is more frequen quoing on XETRA han he NYSE. I does no appear o be he case ha XETRA seems o be he firs mover jus because hey have more frequen quoes. The NYSE quoes do mos of he adjusing o he exchange rae while XETRA quoes appear o be relaively unaffeced by exchange rae changes. The differences in our esimaes across firms (even hough all hree have abou he same raios of XETRA o NYSE quoes) is corollary evidence ha he resuls may reflec real economic phenomena and are no jus an arifac of quoe frequency. 22

23 comes firs in he ordering and a lower bound on he informaion share for he variable ha comes las in he ordering. We will laer address his issue by esimaing he upper and lower bounds of informaion shares. Firs, an ordering of exchange rae, homemarke price, and U.S. price is used o esimae he informaion shares. We use his order in compuing he informaion shares repored in Table 4. <Table 4 goes here> Table 4 conains esimaes and sandard errors of informaion shares. For insance, consider he firs row of informaion shares for DCX. The exchange rae innovaions accoun for essenially all price discovery in he exchange rae wih he sock prices conribuing essenially nohing. This is consisen wih he exchange rae being exogenous wih respec o he wo sock prices. The same paern is seen for he oher wo socks as well. Figure 3 conains esimaes of he kernel densiies associaed wih he informaion shares. The figure provides a more deailed look a he differences across he firms han he sandard errors repored in Table 4. <Figure 3 goes here> Analyzing he informaion shares relaed o he XETRA prices, we find ha he exchange rae innovaions conribue less han 1 percen for all hree firms. The XETRA price innovaions are shown o be mos imporan wih informaion shares ranging from for DT o for SAP. The NYSE innovaions have an informaion share of approximaely zero for DT, abou 9 percen for DCX, and abou 20 percen for SAP. The informaion shares relaed o NYSE prices indicae ha he exchange rae accouns for shares ranging from abou 5 percen for DT o abou 7 percen for DCX. XETRA price innovaions have he larges informaion share of abou 84 percen for DCX, 94 percen for DT, and 75 percen for SAP. The NYSE price innovaions accoun for an informaion share of abou zero for DT, 9 percen for DCX, and 19 percen for SAP. Noe ha he esimaion precision is high as indicaed by he small sandard errors. 23

24 The op wo graphs of Figure 4 emphasize he resul ha he exchange rae innovaions have an effec on NYSE prices ha is markedly differen han he effec on he XETRA prices. If one superimposed he XETRA figure on he NYSE, no even he exreme ails would overlap. On he oher hand, i is seen in he four lower figures ha he effecs of XETRA price innovaions and NYSE price innovaions are similar for socks in boh rading locaions. The kernel densiies look quie similar for XETRA innovaion effecs on XETRA and NYSE prices and NYSE innovaion effecs on XETRA and NYSE prices. An overview of he resuls repored in Table 4 and Figure 3 offers a clear inerpreaion of he findings: a) he exchange rae is exogenous wih respec o he sock prices; b) exchange rae innovaions are more imporan in undersanding he evoluion of NYSE prices han XETRA prices; and c) mos of he fundamenal or random walk componen of he value of he 3 firms is deermined in Frankfur. There are sriking differences across he hree firms, especially beween he DT and SAP resuls. The XETRA price innovaion share is above 99 percen for he XETRA price of DT. The same informaion share for SAP is abou 75 percen. There is almos a 20 percen informaion share for he NYSE innovaion in boh he XETRA and NYSE prices for SAP. Why does DT have such a large informaion share for XETRA relaive o SAP and DCX? In conras o DCX and SAP, DT appears o be more of a German firm han a mulinaional firm. This is borne ou in he revenue daa as U.S.-based revenue accouns for less han 1 percen of DT revenue, a lile more han 50 percen of DCX revenue, and a lile less han 50 percen of SAP revenue. 16 Even more descripive of he differences beween he mulinaional naure of SAP shares relaive o DT is he U.S. versus non-u.s. locaion of muual fund holders of each sock. The shares of he NYSE 16 An examinaion of each firm s web homepage indicaed he following recen daa: DCX, oal revenue in he 3 rd quarer of 1999 was 36.3 billion euro wih 19.3 billion euro from he U.S.; DT, oal revenue in 1999 was 35.5 billion euro wih 161 million euro from he U.S.; SAP, oal revenue in he 3 rd quarer of 1999 was 1.1 billion euro wih 492 million euro from he U.S. 24

25 raded socks held by U.S. versus non-u.s. muual funds in January, 2001 are: DCX, 9,152,343/132,084,720; DT, 693,933/24,173,898; and SAP, 7,969,826/958, U.S. muual funds own more han 8 imes as many SAP ADRs as non-u.s. funds. However, only 3 percen of DT ADRs are owned by U.S. muual funds. The larges owners of SAP end o be large U.S. insiuions (he op 5 being INVESCO Funds Group, Inc., INVESCO Capial Managemen, Inc., MFS Invesmen Managemen, Smih Barney Asse Managemen, and Kayne Anderson Rudnick Invesmen Managemen, LLC) while he larges owners of DT end o be non-u.s. funds (he op 5 includes Brandes Invesmen Parners, LP, Frankfur Trus, Union Bank of Swizerland-Asse Managemen, Ciadel Invesmen Managemen, LP, and UBS Warburg). I is clear ha SAP has a much sronger following in he Unied Saes han DT. DCX, on he oher hand, lies beween he resuls found for DT and SAP. While DCX and SAP boh have similar U.S. revenue shares, heir ownership paerns are quie differen. DCX ownership is more similar o DT wih U.S. muual funds holding only abou 7 percen of he shares. So DCX lies in beween SAP and DT in erms of he srengh of is U.S. following. Beyond he obvious differences in erms of he geographic disribuion of ownership, here may be some addiional facors ha help explain he fac ha SAP has a larger share of price discovery for he NYSE han DT or DCX. Firs, SAP is considered a new economy sock and he U.S. marke focus on hose firms may accoun for he larger informaion share of he NYSE. Second, SAP s bigges rivals are U.S. firms. So U.S. news may be more relevan for SAP han DCX, who has major rivals in Europe and Asia, or DT, who essenially does business in Europe only. The ordering of variables underlying Table 4 was moivaed by our priors on he likely recursive ordering of he conemporaneous correlaion. However, one can furher explore he sensiiviy of resuls over he alernaive possible orderings. We do so in 17 Muual fund ownership is lised on he J.P. Morgan ADR web sie: 25

26 order o demonsrae ha he bounds for informaion shares are quie small. By permuing he order of variables in he Cholesky decomposiion, we find he bounds for informaion shares given in Table 5. In many cases, he bounds are so igh ha he upper and lower values round o he same 3 decimal places. In oher cases, here is less han 1 percenage poin difference. Given he igh bounds ha exis over alernaive orderings, i is clear ha he informaion shares and associaed inferences are unaffeced in any subsanive manner by he ordering of variables. <Table 5 goes here> As a final robusness check, we re-esimaed he sysem using one-minue sampling inervals insead of he 10-second inervals employed above. The resuls change lile. The mos noable difference is for DCX. A he lower one-minue frequency here is a larger (smaller) informaion share for NYSE (XETRA) innovaions on prices in boh markes and a larger (smaller) impac of exchange rae innovaions on XETRA (NYSE) prices. We conjecure ha his has o do wih DCX being a globally regisered share wih a narrower no-arbirage band han in he case of he ADRs. Consider he effecs of an exchange rae shock. The NYSE price adjuss quickly o resore he law of one price while he XETRA price moves very lile. This is as found a he 10-second frequency. However a a lower frequency, he rue relaionships become blurred as he NYSE informaion share is oversaed as i includes boh he effecs of NYSE price shocks as well as he exchange rae shocks o which he NYSE price has already adjused Simulaion of Bivariae and Trivariae Models I is imporan o emphasize ha informaion shares may be sensiive o he mehodology chosen wih respec o he exchange rae. Prior sudies have used he exchange rae o conver one sock price ino he same currency unis as he oher and 26

27 hen esimae a wo-variable, or bivariae, sysem. We allow he exchange rae o ener he analysis separaely and esimae a hree-variable, or rivariae, sysem. To explore he sensiiviy of informaion shares o model specificaion, a simulaion sudy is conduced. Specifically, a daa generaing process (DGP) is simulaed o find he informaion shares of NYSE innovaions wih respec o he XETRA price and XETRA innovaions wih respec o he NYSE price. The variance of he exchange rae innovaions is allowed o ake five differen values. Then he rivariae model, as pu forward in his paper, is compared o he bivariae model. The laer is esimaed boh in erms of he NYSE price convered o euros and he XETRA price convered o dollars. The exac parameerizaion of he model is given in Table 6. We generae 1,000 daases of 40,000 observaions each using he model specified in Table 6 for each of he exchange rae variance values. Table 6 repors he average informaion shares over he 1,000 replicaions for each DGP. <Table 6 goes here> The rivariae model repors exchange rae informaion shares for home and U.S. sock prices. As expeced, he greaer he volailiy of he exchange rae, he greaer he exchange rae informaion shares. Of greaer ineres, however, is he sock price informaion shares. The rue DGP implies ha he informaion shares associaed wih each sock price should be equal, or heir raio should equal 1. As shown in Table 6, his is basically he resul found in he rivariae case. However, he bivariae models reveal ha he greaer he exchange rae variance, he greaer he informaion share of he sock marke incorporaing he exchange rae and he smaller he informaion share of he oher marke. For insance, wih an exchange rae variance of 2, if he U.S. price is convered o euros, hen he U.S. informaion share is while he home informaion share is Bu if he home price is convered o dollars, hen he resuls are jus reversed. The simulaions clearly reveal ha he bivariae approach can be quie misleading wih a 27

28 bias owards oversaing he informaion share of he marke whose price is convered ino he foreign currency. The more volaile are exchange raes, he greaer he bias. 6. SUMMARY AND CONCLUSIONS We now reurn o he iniial quesions ha moivaed his sudy: where does price discovery occur for inernaionally-raded firms and how do inernaional sock prices adjus o an exchange rae shock? Our approach o answering hese quesions involves an analysis of he high-frequency quoes on hree blue-chip German firms during he daily overlap of rading in Frankfur on XETRA and New York on he NYSE. While he resuls suppor he noion ha price discovery occurs largely in he home marke, resuls differ across our hree firms. In order of he informaion shares aribued o Frankfur rading in explaining XETRA (NYSE) price innovaions we have DT, wih 99 (94) percen; DCX, wih 91 (84) percen; and SAP, wih 80 (75) percen. The high share for DT is likely a resul of he fac ha almos all DT revenue is earned in Germany and DT ADR ownership is concenraed ouside he U.S. DCX and SAP boh have subsanial U.S. revenue sources and SAP ADR ownership is concenraed inside he U.S. I makes inuiive sense ha mulinaional firms would have more room for inernaional price discovery han firms ha are essenially operaing only in heir home marke. An addiional quesion of ineres relaed o he firs quesion is: how do inernaional sock prices adjus o an exchange rae shock? We find ha he New York prices bear almos all of he adjusmen o exchange rae changes. For each of our firms, he informaion shares aribued o he exchange rae in explaining XETRA prices are approximaely zero. For NYSE prices, he exchange rae innovaions have an informaion share of a leas 5 percen. Thus, he NYSE invesor is subjec o exchange 28