THE ROLE OF U.S. TRADING IN PRICING INTERNATIONALLY CROSS-LISTED STOCKS

Transcription

1 THE ROLE OF U.S. TRADING IN PRICING INTERNATIONALLY CROSS-LISTED STOCKS by Joacim Grammig a, Micael Melvin b, and Cristian Sclag c Abstract: Tis paper addresses two issues: 1) were does price discovery occur for firms tat are traded simultaneously in te U.S. and in teir ome markets and 2) wat explains te differences across firms in te sare of price discovery tat occurs in te U.S? Te answer to te first question is tat te ome market is typically were te majority of price discovery occurs, but tere are significant exceptions to tis rule and te nature of price discovery across international markets during te time of trading overlap is ricer and more complex tan previously realized. For te second question, te results provide strong support tat liquidity is an important factor. For a particular firm, te greater te liquidity of U.S. trading relative to te ome market, te greater te role for U.S. price discovery. a Faculty of Economics, University of Tübingen, joacim.grammig@uni-tuebingen.de, ++49 (7071) b Barclays Global Investors, Micael.melvin@barclaysglobal.com, c Faculty of Economics and Business Administration, Goete-University Frankfurt, sclag@finance.uni-frankfurt.de, ++49 (69) June 2007 Preliminary & incomplete draft for Stanford conference discussion

2 THE ROLE OF U.S. TRADING IN PRICING INTERNATIONALLY CROSS-LISTED STOCKS I. INTRODUCTION Wen a firm s stock is traded simultaneously in bot te United States and anoter country, wat sould we expect regarding te role of U.S. trading in price discovery? If te evidence indicates tat tere is a bigger role for U.S. price discovery for some firms tan oters or for stocks of some countries tan oters, wat determines tis different role for different stocks? Tere is only a small literature on te topic of price discovery for internationally cross-listed firms, and te evidence regarding were price discovery occurs is mixed. Tere is some support for an important role for bot te ome and foreign market and tere is also support for te ome market dominating price discovery. Studies using ig-frequency intradaily data include Ding, Harris, Lau, and McInis (1999), Hupperets and Menkveld (2002), Eun and Saberwal (2003); and Pylaktis and Korczak (2004). All four papers find support for significant price discovery in bot te ome and te foreign market. Grammig, Melvin, and Sclag (2005) study German and U.S. trading and find support for te ome market dominating. Studies based upon lower frequency daily data include Kim, Szakmary, and Matur (2000) wo find a small role for U.S. price discovery in te case of firms from Japan, te Neterlands, te U.K., Sweden, and Australia. Lau and Diltz (1994) detect two-way causality between Japanese and U.S. prices of Japanese firms cross-listed in te U.S., wile Lieberman, Ben-Zion, and Hauser (1999), studying Israeli firms also traded in te U.S., find tat price discovery occurs in Israel wit te exception of Teva, were 2

3 te U.S. price leads te Israeli price. Wang, Rui, and Firt (2002) and Agarwal, Liu, and Ree (fortcoming) conclude tat for Hong Kong stocks listed in London, Hong Kong is te dominant market, wereas von Furstenberg and Tabora (2004) find two-way causality for two Mexican firms also traded in te U.S. One major purpose of te present study is to contribute new evidence on te location of price discovery. Specifically, te analysis focuses on te overlap of trading for firms from Canada, France, Germany, and te U.K. wit te U.S. Models of te information sares from eac market are estimated for te major traded firms. So in contrast to most of te oter studies, our paper as a multi-country perspective, and we are also able to see if tere are structural differences between firms from different countries. Tis is of special interest wit respect to a comparison of Frenc, Britis, and German firms to Canadian firms, since te equity of te latter is traded in te U.S. via ordinary sares and te overlap wit NYSE trading times is longest. Our empirical results indicate tat te sare of price discovery of te ome market (and, analogously, for te foreign market) can vary considerably across stocks. For example, in our sample tere are stocks wit a ome market information sare of almost 100 percent, wile for oter firms tis number is less tan 50 percent. Interestingly, te Canadian firms are by no means tose for wic te relative importance of te U.S. price is largest. U.S. information sares for te five firms listed in Toronto and New York vary from rougly 10 percent to around 55 percent and, tus, are covered by te full range of values obtained for firms from oter countries. Tese findings are te motivation for a subsequent cross-section analysis, were we try to identify te important determinants of tis variation in information sares. 3

4 Teory suggests tat te sare of price discovery in a given market is closely linked to te relative liquidity of tis market compared to te oter market, and tis intuition is te guideline for our coice of variables for te regression analysis. As it turns out, te differences in realized bid-ask spreads between te ome and te foreign market and te ratio of turnover on te foreign and te domestic market can almost perfectly explain differences in information sares across stocks. As sown in te literature review, te frequency of te data employed in te empirical study is of crucial importance for te results. Te time-series evidence on price discovery in our paper comes from ig-frequency data sampled at 10-second intervals. Sampling at lower frequencies (even 1-minute intervals), as is commonly done in te literature, can result in rater wide bounds on te information sares of different markets so tat te true causality is blurred. Our metodology differs from tat used in oter studies also wit respect to te treatment of te excange rate. In most cases first one stock price is converted from foreign into domestic currency (or vice versa) using te current excange rate, and ten te analysis is done in terms of just te two stock prices. Tis approac may introduce some problems in inferring price discovery as te effect of excange rate cange is incorrectly being ascribed to te stock price incorporating te excange rate, as sown via Monte Carlo simulation in Grammig, Melvin, and Sclag (2005). Intuitively, tis effect becomes more pronounced wit an increasing volatility of te excange rate. As a consequence, if te goal is to infer price discovery of te two trading locations, a tree variable system wit te excange rate, te ome market price, and te foreign market price sould be modeled. We follow suc a strategy to allow a clear focus on te 4

5 contribution of eac market to price discovery. A by-product of tis estimation strategy is tat we can estimate te adjustment of te two market locations to excange rate socks, wic is an interesting result by itself. To summarize te main findings of our analysis, te estimated models reveal tat for most stocks price discovery largely occurs in te ome market wit a relatively small role for U.S. trading. However, results differ substantially across firms and some firms cast a larger role for U.S. tan ome market price discovery. Te cross-sectional analysis contains a very ig degree of explanatory power and indicates tat te differences between firms are driven by differences in te relative liquidity of te U.S. market versus te ome market. Te more liquid is U.S. trading in a stock, te larger te role for U.S. price discovery relative to te ome market. Wit respect to te excange rate effects, it appears tat te adjustment to excange rate socks mostly takes place via te U.S. price rater tan te ome market price. Te bottom line of our paper, terefore, is tat te dynamics of international price discovery are more complex tan previously tougt. Te study is organized as follows: section II provides information on eac of te stock markets studied and teir trading mecanisms along wit information on te firms in te sample. Section III describes te data to be used for estimation. Section IV offers a description of ypotesized equilibrium relationsips and te econometric metodology employed. Estimation results and discussion are presented in section V. A conclusion and summary is given in te final section VI. II. TRADING VENUES AND FIRMS 5

6 Tis study involves data on stocks traded on five different excanges in five different countries. Te excanges and countries are: te New York Stock Excange (NYSE)/United States; Te Toronto Stock Excange (TSE)/Canada; te Xetra system operated by te Deutsce Börse/Germany; te London Stock Excange (LSE)/Great Britain; and te Paris Bourse/France. Tese locations are cosen for analysis because tey ave trading ours tat overlap U.S. trading ours and ig-frequency intra-daily quote data are available. As mentioned in te introduction te goals of tis study require data sampled at very ig frequencies to reveal te causality present in te data (if any). Daily data, wic is available for all excanges, would not be useful. In addition, only tose firms wic are most actively traded can be usefully included in a study of price discovery as infrequent trading would result in eiter many data oles wit igfrequency sampling or else a level of time aggregation tat blurs te true causality in te data. <Table 1 goes ere> A brief summary of eac trading venue is provided in Table 1. It can be seen tat most firms listing teir sares in te United States do so wit an American Depositary Receipt (ADR). ADRs are issued by a depositary bank accumulating sares of te underlying foreign stock. ADRs are issued at a fixed multiple relative to te underlying sares (like 5 ADRs per underlying sare of Alcatel or 1 ADR per 6 underlying sares of BP Amoco). Tey tend to trade in a very limited range around te price of te underlying sare, excange-rate adjusted. ADRs and underlying sares are close, but not perfect, substitutes. Gagnon and Karolyi (2003) ave an extensive discussion of differences between ADRs and underlying sares and te issues involved in arbitraging tis market. 6

7 Focusing on a different but related issue Moulton and Wei (2005) provide evidence of ow NYSE specialist beavior is affected by te presence of te underlying sares in Europe as substitutes for New York trading. DaimlerCrysler (DCX) is a special case in our sample, since it trades in te United States as a global registered sare (GRS). Tis is a single security tat is traded globally altoug it is quoted and settled in te respective local currency. GRSs differ from ADRs in tat tey do not involve a depositary intermediary and ave no issues of conversion between different forms since te same security is traded internationally. A GRS sould terefore be an even closer, albeit still not perfect, substitute for te underlying stock across international markets as it allows all stockolders to participate in corporate matters (dividends, distributions, and control issues) regardless of teir location. As mentioned above Canadian firms traded in te United States are listed as ordinary sares. One migt terefore tink tat Canadian ordinary sares trading in te United States may be more fungible wit te ome market tan ADRs since te certificates traded in bot countries are identical and tere are no conversion fees. Our empirical work below will provide evidence on te degree to wic U.S. and Canadian prices move togeter relative to prices of oter countries sares. III. DATA For te purpose of tis study, we focus on bid and ask quotes submitted during te period of continuous trading in eac market. Table 1 indicates tat te intersection of te 7

8 continuous trading ours of all excanges is from 9:30-11:00 New York time. As a result, te empirical work will focus on tis common interval of time for all markets. Te sample contains 85 firms from te TSE, 15 from te Paris Bourse, 11 from Xetra/Deutsce Börse, and 28 firms from te LSE. Tese were te top-traded firms from eac ome market and tere was a fairly steep drop-off in trading volume at te next lower firms. In 2004, te total number of firms listed on te NYSE from tese countries was: Canada,; U.K.,; France,; and Germany,. Wile Canadian trading overlaps te entire New York trading day, te European markets only overlap te New York morning. We use te same sample period for all firms so tat we ave te same number of observations and old everyting constant oter tan te firm used for estimation. Te New York data are from te TAQ data set available from te NYSE. Frankfurt data are proprietary data from te XETRA trading system of te Deutsce Börse. London data are te tick data set available from te London Stock Excange. Paris trade and quote data were privately obtained, wile Toronto data are te Equity Trades and Quotes data set from te Toronto Stock Excange. Te intradaily excange rates were obtained from Olsen Data in Zuric and are indicative quotes as posted by Reuters. Table 2 lists te firms in our sample along wit information on bid-ask spreads in te ome market and te NYSE. Te first column lists te NYSE stock symbols for eac firm. Te second column provides te conversion ratios between ADRs and te underlying ome-market sares at te beginning of our sample. For instance, 4 SAP ADRs are equivalent to 1 sare of SAP in Frankfurt during our sample period. An asterisk denotes firms for wic no ADRs, but ordinary sares or a GRS (in te case of 8

9 DCX) are traded on te NYSE. In te empirical work tat follows, te NYSE prices are adjusted by te appropriate conversion rate to be comparable to te underlying sare prices. Te tird column of Table 2 lists te ome market of eac firm. Te next two columns sow te average relative spreads at ome and on te NYSE. Tese are computed by taking sample averages of te spreads relative to te mid-quotes over te first 1.5 ours of New York trading. Volume and turnover data are reported in te remaining columns of Table 2. Tis average daily information is reported for te ome market and te NYSE and for te overlap period of te New York morning as well as all day. Note tat in te majority of cases te relative spread is larger on te NYSE tan on te ome market, and tat te degree to wic te NYSE spread exceeds tat of te ome market varies considerably across firms. However, tere are also firms for wic te relative spread on te ome market is iger tan on te NYSE (). Turnover is expressed in U.S. dollars using te sample average excange rates to convert ome market trades into dollars. For most firms, ome market trading is eavier tan New York trading. However, Canadian firms trade more in New York tan at ome. Wit 90 minutes te joint overlap of all markets under consideration in our analysis migt seem sort, given tat a full trading day can last up to 8 or 9 ours. It is terefore of some interest to see if te overlap period is sufficiently representative. Based on te values in table 2, te ratios of NYSE to ome market volume and of NYSE to ome market turnover for te overlap and for te full trading day exibit nearly perfect correlations wit values greater tan Altoug tis does not constitute a full test it neverteless yields strong support for te ypotesis tat te overlap period is not too special. 9

10 <Table 2 goes ere> In summary, table 2 provides a portrait of te ome market as te primary market (in terms of trading activity) for most firms. However, one can see tat te difference between New York and ome market trading activity differs greatly across firms. Next we turn to a more detailed description of te sampling metodology. All asset price series are in logaritms of te average of te bid and ask prices. As mentioned above, te asset prices were sampled at 10-second intervals to assemble te basic data set. A preliminary analysis was conducted over alternative sampling frequencies and we cose 10 seconds as being suitable relative to lower frequencies like 1 minute or 10 minutes. Estimates using 1-minute sampling revealed an increase in te information sare for New York prices tat is misleading in tat te New York price cange includes bot te effects of NYSE price socks as well as te effects of te NYSE price adjusting to excange rate socks. At an even lower sampling frequency like 10 minutes, te contemporaneous correlation results in estimation bounds on te information sares so wide tat one cannot clearly identify were price discovery occurs. At iger sampling frequencies tan 10 seconds tere was no gain in terms of reducing significant contemporaneous correlation, but tere is a trade-off wit microstructural issues like nonsyncronous quoting or oter sources of microstructure noise. Since our econometric model also involves lagged values of te price variables and te excange rate, an additional sampling issue is wit regard to overnigt returns and lags. In our sample no overnigt returns were used and no lags reaced back to prior days. For instance, if te model calls for tree lags in te variables, te data used for estimation begin wit te fourt observation on eac day. Te initial observation eac 10

11 day for eac stock is determined by te first 10-second interval following te NYSE open containing a quote in bot markets. 11

12 IV. PRICE FORMATION AND DETERMINANTS: METHODOLOGY IV.A. Liquidity and te price discovery in internationally cross listed stocks A recent paper by Baruc, Karolyi, and Lemmon (fortcoming) provides a teoretical model and empirical support for trading volume of cross-listed firms to be concentrated in te market wit te igest correlation of cross-listed asset returns wit oter asset returns in tat market. As te autors point out, te determination of suc asset returns remains to be explained. Our expectation is tat te relative liquidity of eac market sould be a major factor in determining location of price discovery. As Harris (2003, p. 243) states: How informative prices are depends on te costs of acquiring information and on ow muc liquidity is available to informed traders. If information is expensive, or te market is not liquid, prices will not be very informative. Te relation between informativeness of price and liquidity is also supported by finance teory as seen in papers like Admati and Pfleiderer (1988) or Hong and Rady (2002). In suc models, price innovations are smaller, te deeper or more liquid te market. So any given cange as a larger information component in te more liquid market. Models like Foucault (1999) or Foucault, Kadan, and Kandel (2003) ave limit orders of liquidity traders priced wit wider spreads as te uncertainty regarding information increases. Te market location were information is embedded in price sould ave greater liquidity tan te oter market. Harris, McInis, and Wood (2003) make a connection between liquidity, information, and ome bias in international investment. Domestic investors may be better informed about and better able to monitor local firms tan foreign firms. Tey point to 12

13 studies by Low (1993), Brennan and Cao (1997), and Coval (1996) as offering support for suc information-based ome bias. Te following simple model in wic liquidity influences price discovery in internationally cross listed stocks is similar to te one presented in Grammig, Melvin and Sclag (2005). Assume tat te log of te excange rate at time t, E t, is exogenous wit respect to U.S. and ome-market sares and evolves as a random walk wit wite noise innovationε : E t E t e t e t = 1 + ε. (1) Te log of te ome-market sare price, P t, may follow a random walk and, tereby, introduce te innovation or random-walk component in te intrinsic value of te firm. Alternatively, it may follow te last observed log of te U.S. price, u P t, adjusted by te excange rate. In te most general setting, P t represents a weigted average of tese two prices, were te weigt venues: l is determined by te relative liquidity of te two trading t P u = lpt + ( 1 l)( Pt 1 Et 1) t 1 + ε. (2) wit ε t as te wite noise innovation associated wit te ome market. Similarly, te log of te U.S. price, u P t, evolves as: u u Pt = l Et 1 + Pt 1) + (1 l) Pt 1 + were u t ( ε (3) u ε t is te wite noise innovation associated wit te U.S. market. In te one extreme case were l = 1 te ome market price and te excange rate are completely determined by teir own innovations, and te long run development of te U.S. price 13

14 depends on te ome market and te excange rate innovations. Te U.S. market innovations exert only a transitory effect on te U.S. price. In tis situation te ome market is te primary and te U.S. market te derivative market. Put differently, price discovery for te stock is exclusively taking place in te ome market. In te oter extreme case, were U.S. market and te excange rate innovations wic determine te long run development of te ome market price. l = 0, te ome market is te derivative market, and it is only te In our empirical model, we allow te innovations of bot ome market price, excange rate, and U.S. market price to exert permanent effects on te two price series and te excange rate. Te magnitude and composition of te permanent effects are allowed to be different and estimated empirically so tat te data will reveal were price discovery occurs. Te estimate of te information sare of innovations of te ome market for te foreign market ten represents an indirect estimate of te parameter l. Arbitrage would force te two stock prices, denominated in te same currency, to move closely togeter over time. Subtracting te log of te U.S. price from te log of te dollar value of a ome-market sare we get u e u Et + Pt Pt = ε t + εt ε t, (4) i.e. te linear combination of te log excange rate, log ome-market price, and log U.S. price is a linear combination of tree stationary variables. In oter words,,, and u P t are cointegrated wit te single (normalized) cointegrating vector A = (1,1, 1) '. E t P t 14

15 IV.B. Estimation of information sares for internationally cross-listed stocks One of te key contributions of tis paper is to address te relative importance of te innovations in te ome and te U.S. market price and tose in te excange rate for te long-run development of te price series. Te metodology employed to address te issue of price discovery in internationally cross listed stocks is based on, but in some important aspects different from, te metodology introduced by Hasbrouck (1995). 1 Te differences are caused by te fact tat an asset is traded in dollars in te U.S. market and in local currency in te ome market, so tat te concept of a single efficient price for an asset tat is traded simultaneously on n markets as to be re-tougt if tere is variation in te excange rate. It is assumed (and will be tested empirically) tat tere is a single cointegrating u relation between,, and wit normalized cointegrating vector A = 1, 1, 1 '. E t P t P ( ) t Te dynamics of ome market price, U.S. market price and excange rate can be represented in a non-stationary vector autoregression (VAR), and te model outlined in equations (1)-(3) is a special case of suc a VAR. Te Granger Representation Teorem (Engle and Granger, 1987) ten implies tat we can write te cointegrated tree variable system in vector error (or equilibrium) correction form (VECM). Te stationary vector process of te innovations { ε e, ε, ε u } is assumed to ave zero mean, contemporaneous t t t covariance matrix Ω, and to be serially uncorrelated. Using Joansen s (1991) maximum likeliood metodology one can estimate te VECM parameters and test for te number 1 An alternative metod for inferring price discovery follows Gonzalo and Granger s (1995) common factor approac. A special issue of te Journal of Financial Markets is devoted to discussion and estimation of te two different metods (see Lemann, 2002, for furter elaboration). 15

16 of linearly independent cointegrating vectors. We expect only one cointegrating relation, but tere could also be eiter none or two. In bot of te latter cases te validity of te model would be questionable. Te bootstrap metodology for cointegrated systems proposed by Li and Maddala (1997) is applied to estimate te standard errors (in fact te wole joint distribution) of te VECM parameter estimates and also of te derived statistics discussed below. A very useful representation of te cointegrated tree variable system is its infinite-order vector moving average (VMA) representation. Summing up te VMA weigts and adding te identity matrix, we obtain a matrix Ψ, te elements of wic e represent te permanent impact of a one unit innovation in ε, ε and u ε on te two price series and te excange rate. Economic common sense suggests tat te impact of bot price series on te excange rate sould be small in magnitude, as te excange rate is expected to be exogenous in our system. It was Hasbrouck s (1995) insigt to interpret a variance decomposition of te permanent impact on te efficient price of an asset tat is cross-listed in n different (national) markets as a means to assign an information sare to eac of te n markets. Te transfer of te idea to internationally cross-listed stocks is straigtforward, once te effect of te excange rate is properly accounted for. In te case of uncorrelated innovations, te information sare of te U.S. market for te ome market would ten simply be equal to te sare of te total variance of te permanent impact attributable to te U.S. price, and analogous computations would yield te information sares of te ome market and te excange rate innovations. A decomposition of te variance of te permanent impact on te U.S. price and on te excange rate could be conducted in te 16

17 same fasion. Due to contemporaneous correlation of te innovations (i.e., Ω will not be diagonal), te computation of information sares is a bit more involved. Te Colesky factorization of te innovation covariance matrix Ω is te standard solution to tis problem. A potential problem of tis metod is tat te ordering of te variables can influence te results, since te innovation ordered first in te Colesky decomposition is assigned te igest information sare, wile te one ordered last receives te smallest sare. Te larger te contemporaneous correlation of te innovations, te wider te bounds of te information sares generated by different orderings of te variables. In our empirical application, we terefore permute te ordering of te variables in te Colesky factorization and assess te consequences of te ordering on te results. It turns out tat coosing te appropriate sampling frequency is te key to reducing te contemporaneous correlation of te innovations suc tat te ordering becomes practically irrelevant. Furtermore, we also report te average of te igest and te lowest information sares wic result from te different orderings. Te bootstrap metodology adopted in tis paper furter allows us to compute standard errors for tese (averaged) information sares. Collecting te information sares in a matrix yields e ε I e = ε IS I e ε I E P P u I I I ε E ε P ε P u I I I ε E u ε P u u ε P u. For example, u I ε P denotes te information sare (averaged over igest and lowest) of te (ortogonalized) U.S. market innovation wit respect to te ome market 17

18 price. By construction, te rows of te matrix IS sum to one. If te excange rate is exogenous, ten we expect tat te estimates of bot E I ε and u E I ε are close to zero. IV.C. Determinants of information sares Our second main objective is to study, in a cross sectional analysis, te determinants of te information sares, and especially to test te ypotesis tat liquidity is an important factor explaining te information sare of te U.S. market for internationally cross listed stocks. For tis purpose we focus on explaining te information sare of te U.S. market innovations wit respect to te ome market price. Having estimated tese information sares for a sample of NYSE listed international firms we estimate a cross sectional logistic regression, were te dependent variable is transformed to take into account te fact tat, by construction, te information sares are bounded between 0 and 1: u ε P Ii u ε P 1 Ii = xi ln β (5) + ui x i denotes a vector of explanatory variables serving as proxies for te relative liquidity of te ome and te U.S. market of firm i. β is a vector of parameters to be estimated, and u a firm specific disturbance, were E( u ) = 0. Te variables used to proxy for liquidity i i are te difference between te U.S. market and ome market realized bid-ask spreads and te ratio of U.S. to ome market value and volume of traded stocks per day. We are aware tat if tese variables appear on te rigt and side of equation (5) we ave to deal wit te problem of endogenous regressors, as te information sare, in turn, may explain te (relative) liquidity for a stock. Endogeneity implies tat OLS estimation would 18

19 produce inconsistent parameter estimates. We terefore use instruments wic are assumed to be uncorrelated wit te disturbances u i, but correlated wit te endogenous liquidity proxies. Tese instruments are a) te number of U.S. analysts following firm i, b) te ratio of U.S. to non-u.s. fund oldings of NYSE-listed sares and c) te ratio of foreign to total sales of firm i. Standard GMM inference is employed to estimate te parameters β and to compute parameter standard errors. If te ypotesis is true tat te more liquid te U.S. market is relative to te ome market, te iger te information sare of te U.S. market, ten we would expect statistically and economically significant parameter estimates for te liquidity proxies and considerable explanatory power of te regressors. V. ESTIMATION RESULTS V.A. Information Sares in Price Discovery: Time-Series Evidence Augmented Dickey-Fuller tests reveal unit roots in te log of eac asset price and te variables are identified as being integrated of order one. Te results of Joansen cointegration tests clearly support te ypotesis of one cointegrating vector among te tree variables. Wit te variables ordered as excange rate, ome-market price, and U.S. price, te estimated cointegrating vectors are close to te vector A = (1,1, 1) ' indicated by teory. Due to te number of firms in te sample, estimates of te cointegration models are not reported. Instead, we focus on te estimates of te VECM equation and te associated information sares. Te coice of lag lengt is determined by te Scwarz Information Criterion (SIC). We start wit 18 lags, wic represent tree minutes in a 19

20 sample wit observations at 10-second intervals. Ten, using te same set of observations tat was used for te estimation of te model wit 18 lags, we estimate te VECM at eac sorter lag lengt down to one lag to determine te lag structure tat minimizes te SIC. As explained above, te Colesky factorization of te innovation variancecovariance matrix results in an upper bound on te estimated information sare for te variable tat comes first in te ordering and a lower bound on te information sare for te variable tat comes last in te ordering. We report te averages between te two after permuting te order to obtain bot extreme bounds. First, an ordering of excange rate, ome-market price, and U.S. price is used to estimate te information sares and ten a reordering wit excange rate, U.S. price, and ome-market price is used and te average of te two information sares is reported in Appendix 1 for eac firm in te sample. Table 3 summarizes te information by averaging across firms in eac country. Table 3 reports information sares for excange rates, ome market prices, and US prices. Te country summaries report cross-firm mean, median, minimum, maximum, standard deviations, 5 t and 95 t percentile, and average lower and upper bounds associated wit te permutation of te ordering of variables. To interpret te results, let s focus on Frenc stocks first in table 3a. Excange rates Te first set of results in te table reports te information sare of innovations in te excange rate (FX) on te excange rate, te ome market price (HOME), and te U.S. price (NYSE). Te data confirm tat te excange rate may be considered exogenous wit respect to te stock prices, as tere is a very small role for eiter 20

21 country s stock prices in explaining te evolution of te excange rate as, on average, percent of te total variance of te excange rate is explained by excange rate innovations. Looking to te rigt in Table 3a, we see tat te average ome- and U.S.- market information sares are just 0.27 and 0.75 percent, respectively for te excange rate. A glance at te oter countries in Table 3 indicate similar findings: te innovations in te excange rate do not depend upon te stock price innovations. Te excange rate innovations account for essentially all price discovery in te excange rate wit te stock prices contributing essentially noting. Tis is consistent wit te excange rate being exogenous wit respect to te two stock prices and is reflected in te information sare of te excange rate in explaining te variance of excange rate innovations equaling one wile te information sares for te ome-market and U.S. prices are essentially zero. Tis exogeneity of te excange rate is supported across all firms. Stock prices Turning next to te information sares for te stock price innovations, starting again wit te Frenc stocks in Table 3a, we see tat tere is no significant role for excange rate innovations in explaining ome-market stock prices, as te average information sare of te excange rate innovations is 0.74 percent. Most price discovery for ome-market firms occurs in te ome market. Te average information sare for ome-market innovations is percent, wile te average for NYSE innovations is percent. A look at te results for te oter countries reveal an even greater omemarket price discovery effect for Germany, but a smaller effect for Canada. Te average ome-market information sare is just percent in Canada wit an NYSE information sare of percent. Even more striking is a comparison of te reported 21

22 Min statistics. Te smallest ome-market information sare for France is percent, wile for Germany it is percent. However, in Canada, te minimum ome-market information sare is 0.79 percent. Correspondingly, te maximum NYSE information sare is percent for Canadian stocks. Clearly, in te case of Canada tere are some firms were price discovery largely occurs in te United States. Finally, we consider te information sares wit regard to price discovery for NYSE trading. Focusing first on France in Table 3, we see tat tere is some role for te excange rate. Te mean information sare for te excange rate is 9.19 percent. However, te overwelming majority of te price discovery comes from te ome market (mean of percent). NYSE trading just contributes an information sare of percent. Results for German stocks are similar. Tere is a moderate role for te excange rate (12.81 percent), and te NYSE (10.13 percent), but te dominant information sare is te ome market (77.05 percent). Te Canadian sample exibits a smaller role for te excange rate (2.33 percent) but a larger role for te NYSE (35.76 percent), wit te ome market once again dominant (61.90). A look at te Max statistics for te NYSE information sare indicates no case were te NYSE dominates price discovery for New York trading in Frenc or German firms. But for Canadian firms te Max statistic of suggests tere are some Canadian firms were price discovery occurs in New York. In summary, Table 3 clearly sows te dominance of te ome market price in price discovery. Te information sares for U.S. price innovations are seen to be somewat of a mirror image of te ome-price information sares. Te iger te 22

23 information sare of te ome-market price innovations in explaining ome-market price, te lower te U.S. information sares. Table 3 clearly indicates tat, for te average firm, te ome market is te primary market and te U.S. is te derivative market. However, some firms ave a sizeable role for U.S. price discovery. Te interesting question of wat explains suc differences across firms will be addressed in te cross-section analysis below. As already mentioned, te excange rates appear to be exogenous as tere is no economically significant role for te stock prices in excange rate price discovery. Yet ow do te stock prices adjust to excange rate socks? To avoid arbitrage and restore te law of one price, te stock prices must cange following a cange in te excange rate. Comparing te excange rate information sares for ome-market and U.S. prices in Table 3, it is clear tat generally te U.S. price bears te burden of adjustment to an excange rate sock as te values of te excange rate information sares in explaining U.S. prices are significantly greater tan tose for ome-market prices in all but a few cases. Te exceptions wit significantly more adjustment of te ome-market price to an excange rate sock are seen in Appendix 1 as a few Canadian firms. Tis is consistent wit te U.S. being te primary market for tese stocks. One migt expect Canadian firms to be essentially U.S. firms, since te two markets are so close geograpically, and bot trading volume and turnover are larger on te NYSE tan on te TSE for all Canadian firms (for bot te overlap and te wole trading day). Appendix 1 indicates tat some Canadian firms are, indeed, like U.S. firms in terms of price discovery. In fact, some Canadian firms ave, essentially, all price discovery occurring in New York wit no role for Canadian trading. Firms wit an NYSE 23

24 information sare for ome market pricing close to 100 percent include BR (98.38), FS (90.51), LAF (94.92), RBA (92.02), TRA (89.24), and VTS (93.76). However, many more Canadian firms ave te majority of price discovery occur at ome. Tis sows tat pure geograpical proximity is not a reliable predictor for te informational content of a foreign listing, wic is an interesting result per se in an international finance context. So te cross-sectional variation in information sares still remains an open issue, and in te next section we will focus on explanations based on microstructure arguments. V.B. Information Sares in Price Discovery: Cross-Firm Evidence As sown in Appendix 1, te U.S. information sares for ome market prices range from 0.36 percent (BGM) to about percent (BR). In between tese extremes, we see tat in some cases, tere is a sizeable role for U.S. price innovations in ome market price discovery wile in oter cases, tere is but a small role. We now analyze te determinants of tese cross-firm differences using te logistic regression model tat was described above in equation (5). Te focus is on assembling a data set tat would include measures of liquidity in bot stock markets. However, since endogeneity issues arise in a regression of information sares on measures of liquidity we also assembled data on additional variables tat could reasonably serve as instruments. An extensive searc for data on instrumental variables was undertaken. Tese variables include te extent to wic a firm is mainly a domestic firm rater tan a multinational, and te U.S. following tat firms ave. Data on te following measures of liquidity were obtained for te time period of te NYSE and ome market trading overlap: 24

25 NYSE and ome market turnover (from NYSE and ome market) NYSE and ome market volume (from NYSE and ome market) NYSE and ome market realized bid-ask spreads (from NYSE and ome market). Te realized spread is computed as twice te absolute difference between te transaction price at time t and te midquote at t+5 minutes. 2 Relative realized spreads were ten calculated as te realized spread divided by te midquote at time t. Te realized spread is preferred to te quoted spread at t as quoted spreads include an informational aspect tat is purged wen using realized spreads. As stated in Boemer (2004, p. 13) Realized spreads can be interpreted as a market s inerent execution cost, because tey exclude te effects of te information content of order flow. 3 To serve as instruments, data on te following variables were obtained: te ratio of foreign to total sales (from Worldscope) U.S. analysts following (from I/B/E/S) 4 U.S. and non-u.s. fund oldings of NYSE listed sares (from Tompson Financial Spectrum). Te dependent variable in te regression is te information sare in ome market prices tat is attributed to innovations in New York prices. Tese data are found in te section labeled Info sare attributable to US market innovations (ome market)) in Figure 1. Estimation is carried out using Generalized Metod of Moments (GMM). Te 2 Te spreads were calculated for medium-sized trades, wit a dollar value of $50,000-$300,000, in order to capture normal spreads. Small and, particularly, large trades are more subject to idiosyncratic deals. 3 Since November 2000, te U.S. Securities and Excange Commission requires market centers to publis montly data on realized spreads and effective spreads along wit execution speed as indicators of market quality. See Boemer (2004) and te American Stock Excange website for furter discussion of realized spreads. 4 Specifically, tis is te number of U.S. analysts making a recommendation on a stock in Jennifer Juergens provided valuable advice in identifying te firms and locations of analysts. 25

26 GMM ortogonality conditions are tat te instruments are uncorrelated wit te residuals of te specified model of information sares as a linear function of a constant and te liquidity indicators. Te weigting matrix used is Wite s eteroskedasticityconsistent covariance matrix. Initial analysis indicates tat, not surprisingly, tere is considerable collinearity among te tree measures of liquidity. In particular, turnover and volume essentially convey practically te same information. Since turnover as marginally greater explanatory power, it is employed (in logs) in te reported estimations along wit te difference of te realized relative spreads. Estimation results are reported in Table 4. Bot measures of liquidity ave te expected effect on information sares and bot ave statistically significant coefficient estimates. Te results support te following inference: te greater te NYSE trading activity relative to te ome market, te greater te sare of price discovery in New York; and te larger te realized spread on a firm s sares in New York trading relative to te ome market, te lower te New York price discovery. Te evidence is consistent wit liquidity playing an important role in understanding te link between U.S. trading and price discovery for internationally cross-listed firms. In addition, te model developed ere is able to explain a large proportion of te cross-firm variation in information sares as reflected in te R 2 of Finally, te J-statistic of 0.21 reported in Table 4 as an associated p-value of Terefore, we cannot reject te null ypotesis tat te moment conditions are correct at any reasonable significance level. <Table 4 goes ere> Given te positive impact of relative turnover on U.S. information sares, te results for te Canadian stocks deserve closer attention. As discussed above te ratio of 26

27 NYSE to ome market turnover is large (greater tan one) for all Canadian stocks, so tat based on just tis variable te logistic regression would predict a generally larger U.S. information sare for tese firms. However, a detailed analysis of te differences in realized spreads between te NYSE and te TSE for te Canadian firms sows tat tis cost of trading is always iger on te NYSE tan on te TSE, wereas we observe eiter te opposite sign of te difference (for UK firms) or mixed signs for te German and Frenc stocks. So te effect of a iger relative turnover of te NYSE relative to te ome market is outweiged by iger implicit transaction costs, and as a result te average Canadian firm is not substantially different from, e.g., te typical UK firm. VI. SUMMARY AND CONCLUSIONS Tis paper addresses two issues: 1) Were does price discovery occur for firms tat are traded simultaneously in New York and in oter markets in oter countries and 2) wat explains te differences across firms in te sare of price discovery tat occurs in New York? Te sort answer to te first question is tat most firms ave te largest fraction of price discovery occur at ome, wit New York taking a smaller role. However, te data reveal important exceptions to tis finding. It is simply not true tat New York trading always lags te ome market and tere is no significant role for price discovery to occur in New York. Te estimates for te information sare of U.S. prices for ome market prices range from almost zero to more tan 98 percent. Te answer to te second question is found by modeling te information sare of New York trading in price discovery of ome-market prices across firms as a function of variables related to 27

28 New York liquidity relative to liquidity in te ome market. Te data strongly support liquidity as an important factor in understanding te role of te U.S. in price discovery. For a particular firm, te greater te liquidity of U.S. trading relative to te ome market, te greater te role for NYSE price discovery for tat firm. An additional issue of interest arises from our modeling strategy of allowing an independent effect for te excange rate, wic is different from oter studies in te same area. Te results indicate strong support for te excange rate as an exogenous variable in te cross-country pricing of a firm s stock. Furtermore, our results indicate tat te NYSE price usually bears te burden of adjustment to te law of one price following an excange rate sock. Tis is interpreted as furter evidence tat te NYSE is typically te derivative market for non-u.s. firms and te ome market is te primary market. However, it is important to realize tat tis is not a universal trut. For tose firms were te NYSE as te dominant price discovery role, te excange rate adjustment comes more from te ome market tan te NYSE. Tus, it is not always true tat an ADR provides exposure to currency fluctuations for a U.S. investor. For tose ADRs wit greater liquidity in U.S. trading tan at ome, we would find little price response to an excange rate cange. Overall, te results indicate tat te nature of price discovery across international markets during te time of trading overlap is ricer and more complex tan previously realized. Wile te ome market is typically were te majority of price discovery occurs, tere are significant exceptions to tis rule. 28

29 REFERENCES Admati, A.R., and P. Pfleiderer, 1988, A Teory of Intraday Patterns: Volume and Price Variability, Review of Financial Studies, 1, Agarwal, S., C. Liu, and S.G. Ree, fortcoming, Were Does Price Discovery Occur for Stocks Traded in Multiple Markets? Evidence from Hong Kong and London, Journal of International Money and Finance. Baruc, S., A. Karolyi, and M.L. Lemmon, fortcoming, Multi-Market Trading and Liquidity: Teory and Evidence, Journal of Finance. Boemer, E., 2004, Dimensions of Execution Quality: Recent Evidence for U.S. Equity Markets, Working Paper, Texas A&M University. Brennan, M.J., and H.H. Cao, 1997, International Portfolio Investment Flows, Journal of Finance, 52, Coval, J., 1996, International Capital Flows wen Investors Have Local Information, Working Paper, University of Micigan. Ding, D.K., F.H. deb. Harris, S.T. Lau, and T.H. McInis, 1999, An Investigation of Price Discovery in Informationally-Linked Markets: Equity Trading in Malaysia and Singapore, Journal of Multinational Financial Management, 9, Eun, C.S., and S. Saberwal, 2003, Price Discovery for Internationally Traded Securities: Evidence from te U.S.-Listed Canadian Stocks. Journal of Finance, 58, Foucault, T., 1999, Order Flow Composition and Trading Costs in a Dynamic Limit Order Market, Journal of Financial Markets, 2,

30 Foucault, T., O. Kadan, and E. Kandel, 2003, Limit Order Book as a Market for Liquidity, Working Paper, HEC Scool of Management. Gagnon, L., and G.A. Karolyi, 2003, Multi-Market Trading and Arbitrage. Working Paper, Oio State University. Grammig, J., M. Melvin, and C. Sclag, 2005, Internationally Cross-Listed Stock Prices During Overlapping Trading Hours: Price Discovery and Excange Rate Effects, Journal of Empirical Finance, 12, Harris, F., T. McInis, and B. Wood, 2003, DCX Trading in New York and Frankfurt: Corporate Governance Affects Trading Costs Across International Dual-Listings, Working Paper, Wake Forest University. Harris, L, 2003, Trading and Excanges, Oxford: Oxford University Press. Hong, H., and S. Rady, 2002, Strategic Trading and Learning About Liquidity, Journal of Financial Markets, 5, Hupperets, E.C.J., and A.J. Menkveld, 2002, Intraday Analysis of Market Integration: Dutc Blue Cips traded in Amsterdam and New York, Journal of Financial Markets, 5, Kim, M., A.C. Szakmary, and I. Matur, 2000, Price Transmission Dynamics between ADRs and Teir Underlying Foreign Securities, Journal of Banking and Finance 24, Kato, K., S. Linn, and J. Scalleim, 1990, Are Tere Arbitrage Opportunities in te Market for American Depository Receipts? Journal of International Financial Markets, Institutions, and Money 1,

31 Lau, S.T., and J.D. Diltz, 1994, Stock Returns and te Transfer of Information Between te New York and Tokyo Stock Excanges, Journal of International Money and Finance 13, Lemann, B.N., 2002, Some Desiderata for te Measurement of Price Discovery Across Markets, Journal of Financial Markets 5, Lieberman, O, U. Ben-Zion, and S. Hauser, 1999, A Caracterization of te Price Beavior of International Dual Stocks: an error correction approac, Journal of International Money and Finance 18, Low, Aaron, 1993, Essays on Asymmetric Information in International Finance, unpublised dissertation, UCLA Anderson Scool. Moulton, P.C. and L. Wei, 2005, A Tale of Two Time Zones: Cross-Listed Stocks Liquidity and te Availability of Substitutes, Working Paper, New York Stock Excange. Paruolo, P., 1997a, Asymptotic Inference on te Moving Average Impact Matrix in Cointegrated VAR Systems, Econometric Teory 13, Paruolo, P., 1997b, Standard Errors for te Long Run Variance Matrix, Econometric Teory 14, Pylaktis, K. and P. Korczak, 2004, Price Discovery Process in International Cross- Listings: Evidence from US-Listed Britis and Frenc Companies, Working Paper, Cass Business Scool. Sleifer, A. and R.W. Visny, 1997, Te Limits of Arbitrage, Journal of Finance 52, von Furstenberg, G.M. and C.B. Tabora, 2004, Bolsa or NYSE: price discovery for 31