THE JOURNAL OF FINANCE VOL. LVIII, NO. 2 APRIL 2003
Cross-Border Listings and Price Discovery:
Evidence from U.S.-Listed Canadian Stocks
CHEOL S. EUN and SANJIV SABHERWAL n
ABSTRACT
We examine the contribution of cross-listings to price discovery for a sample
of Canadian stocks listed on both the Toronto Stock Exchange (TSE) and a
U.S. exchange. We ¢nd that prices on the TSE and U.S. exchange are cointegrated and mutually adjusting. The U.S. share of price discovery ranges from
0.2 percent to 98.2 percent, with an average of 38.1 percent. The U.S. share is
directly related to the U.S. share of trading and to the ratio of proportions of
informative trades on the U.S. exchange and the TSE, and inversely related to
the ratio of bid-ask spreads.
WITH THE ENHANCED GLOBALIZATION of ¢nancial markets, the number of non-U.S.
¢rms cross-listing shares on a U.S. exchange has substantially increased. Attracting non-U.S. listings is now a top priority of the U.S. stock exchanges. At
the end of 2000, 420 non-U.S. ¢rms were listed on the New York Stock Exchange
(NYSE).The number of foreign ¢rms listed on Nasdaq was even higher.The popularity of international cross-listings has prompted many academic studies on the
topic.1 Most of these studies focus on the bene¢ts of international cross-listings,
including the reduced cost of capital and the enhanced liquidity of a ¢rm’s stock.
Studies such as Alexander, Eun, and Janakiramanan (1987, 1988) and Foerster
and Karolyi (1993) suggest that the cost of capital declines because the portion of
the risk premium that compensates for cross-border investment barriers dissipates. Miller (1999) and Foerster and Karolyi (1999) propose increased investor
recognition as another possible explanation. Several studies examine changes in
trading volume and costs due to international cross-listing. Foerster and Karolyi
(1998) ¢nd that the bid-ask spreads in Canada decrease after the cross-listing of
Canadian stocks in the United States. Domowitz, Glen, and Madhavan (1998) suggest that the impact of cross-listing is complex and depends on the degree of
quote transparency, that is, the extent to which price information is observable
in the two markets. Smith and So¢anos (1997) examine if cross-listing is a zerosum game, with increased trading in the United States being o¡set by reduced
n
Eun is at Georgia Institute of Technology and Sabherwal is at the University of Rhode
Island. We thank Rick Green (the editor), Ajay Khorana, Cli¡ord Lee, Henry Oppenheimer,
Stephen Sapp, and Steve Smith for helpful comments and Shih-Ching Jeng for research assistance. We are especially grateful to an anonymous referee for detailed and insightful comments. All errors are our own.
1
Karolyi (1998) provides a useful survey of international cross-listing.
549
550
The Journal of Finance
trading in the home market. They ¢nd that the home-market value of trading increases substantially after foreign ¢rms list on the NYSE. The aforementioned
studies, however, have not addressed the following important question: Do international cross-listings of stocks contribute to the price discovery of these stocks?
One objective of this study is to examine the extent to which the U.S. stock exchanges contribute to the price discovery of non-U.S. securities cross-listed on
these exchanges. In particular, we look at the price discovery of Canadian stocks
listed on the U.S. exchanges. Price discovery, described by Schreiber and
Schwartz (1986) as the search for an equilibrium price, is a key function of a stock
exchange. Previously, Bacidore and So¢anos (2002) and Solnik (1996) have suggested that price discovery should mostly take place in the home market. In view
of the increasing popularity of international cross-listings, the extent to which
the U.S. stock exchange is contributing to the price discovery of the non-U.S.
stocks is of considerable importance.2
Studies such as Harris et al. (1995) and Hasbrouck (1995) have examined the
relative contribution of the NYSE and regional exchanges to the price discovery
of U.S. stocks trading on these exchanges. Whether or not all exchanges contribute to the price discovery of a U.S. stock trading on multiple exchanges within
the United States is an interesting issue. However, the question becomes more
intriguing when a non-U.S. stock is cross-listed in the United States, and thus
trades on exchanges in di¡erent countries. For a U.S. stock trading on multiple
U.S. exchanges, one may expect that the established exchange, such as the NYSE,
would dominate the regional exchanges, such as Cincinnati and Paci¢c, in terms
of price discovery.When a non-U.S. security trades on an established exchange in
the United States, what to expect is not as obvious in regard to the relative extent
of price discovery. On the one hand, the non-U.S. stock exchange is likely to contribute substantially to price discovery as it is in the security’s home market
where substantial information is expected to be produced. On the other hand,
the dominance of the U.S. stock exchanges as among the largest and most liquid
exchanges in the world suggests that they are also likely to contribute signi¢cantly to price discovery. The following quote from a report produced by the Toronto Stock Exchange (TSE) Board of Governors (The Toronto Stock Exchange,
1998) illustrates the competitive threat that the non-U.S. exchanges perceive
from the U.S. exchanges: ‘‘The TSE cannot a¡ord to have the U.S. markets become
the price discovery mechanism for Canadian interlisted stocks.’’ One could thus
expect that the U.S. market provides signi¢cant feedback to the home market of
the cross-listed non-U.S. security and contributes to its price discovery.
2
The following quote (our italics) in PR Newswire, April 15, 1988, suggests that this contribution could be perceived as an important bene¢t of cross-listing. This quote is from James H.
Foreman, President and CEO of Pegasus Gold, a Canadian company listed on the Toronto
Stock Exchange (TSE) that also listed its shares on the American Stock Exchange (AMEX)
on April 21, 1988: ‘‘A listing on the American Stock Exchange would increase liquidity in the
company’s shares, tighten quotation spreads, allow direct linkage between the TSE and
AMEX to achieve the best price for our dually traded stock, as well as increase overall sponsorship of the company in the investment community.’’
Cross-Border Listings and Price Discovery
551
Another objective of our study is to analyze the factors that a¡ect the extent of
the U.S. stock exchange’s contribution to price discovery. Studies examining
price discovery in a purely domestic context provide some evidence of the factors
that a¡ect the NYSE’s contribution to price discovery relative to the regional exchanges. For a sample of the 30 Dow stocks, Hasbrouck (1995) ¢nds a positive and
statistically signi¢cant correlation between the NYSE contribution to price discovery and its market share by trading volume. Hasbrouck also ¢nds that the
NYSE’s contribution is signi¢cantly positively correlated with its trading volume
market share in medium-size trades but not with its shares in small and large
trades. This is consistent with the argument that the medium-size trades move
prices. Also for a sample of the 30 Dow stocks, Harris, McInish, and Wood
(2002) ¢nd evidence that the NYSE contribution to price discovery increases
when its bid-ask spreads decline relative to the regional exchanges. In contrast
to these studies, which examined the above factors a¡ecting the contribution to
price discovery in a purely domestic context, we look at whether these factors
a¡ect the contribution of a U.S. exchange relative to a non-U.S. exchange. Also,
unlike these studies, we perform a cross-sectional regression analysis of the factors a¡ecting price discovery. Finally, we examine additional factors, such as the
exchange on which a ¢rm is listed in the United States and the duration of listing
in the United States.
Our econometric approach to assessing the contribution of U.S. exchanges to
the price discovery of cross-listed securities is similar to the approach used by
Harris et al. (1995). In this approach, price discovery is concerned with the adjustments to prices due to cross-market information £ows. Using an error correction
model for IBM’s prices, Harris et al. ¢nd that not only do prices on the Paci¢c and
Midwest exchanges respond to deviations from NYSE prices, but NYSE prices
also respond to deviations from prices on regional exchanges, though the magnitude of adjustment on NYSE is smaller than those on regional exchanges. They
interpret their ¢ndings as evidence that some price discovery takes place on regional exchanges as well. In our international context, if the prices on a non-U.S.
exchange adjust to the U.S. prices, then the U.S. exchange is contributing to the
price discovery of cross-listed stocks, and the magnitudes of the adjustment coef¢cients may be used to assess its contribution.
In this study, we examine TSE-listed Canadian stocks that are also listed in the
United States on the NYSE, American Stock Exchange (AMEX), or Nasdaq. The
TSE represents about 90 percent of the traded value in Canada. Our choice of
Canadian stocks is motivated by several reasons. First, the Canadian stocks
represent the largest group of stocks listed in the United States from a single
country.Therefore, their study provides the best opportunity for a cross-sectional
analysis of the determinants of relative price adjustments in the home and U.S.
markets, while holding the nationality of shares constant. Second, many of them
trade actively in both the United States and Canada, which is essential for conducting intraday analyses. Third, the TSE trading time coincides with the U.S.
trading time (9:30 a.m. to 4:00 p.m. Eastern time). Since we need prices observed
at the same time in the two markets, the Canadian securities o¡er a distinct bene¢t over cross-listed securities from Europe or Asia for which there is little or no
552
The Journal of Finance
overlap time between the home market and the U.S. market. Finally, Canadian
securities are listed in the United States as ordinary shares, whereas securities
from other countries are usually listed as American depositary receipts (ADRs).
The ADRs are U.S. dollar (US$) denominated receipts issued by U.S. depository
banks. The receipts represent claims to a speci¢c number of the home market
shares held in trust by the depository. As explained in detail in Pulatkonak and
So¢anos (1999), Canadian ordinaries trading in the United States and global registered shares are more fungible with the home market security than the
ADRs.3 Our sample consists of 62 TSE-listed securities, of which 38 are crosslisted on the NYSE, 3 on the AMEX, and 21 on the Nasdaq. Our sample period is
the six-month period of February to July 1998.
An analysis of a cross-listed stock can be based on either transaction prices or
quoted prices. The use of the most recent transaction prices is likely to su¡er
from autocorrelation problems induced by infrequent trading. Since quotes can
be updated in the absence of trades, we perform the analysis in this study using
regularly spaced quotes. For each sample stock, we form two price series by selecting the midpoint of the last bid and ask quotes appearing in each market at
10 -minute intervals. We similarly create a series of exchange rates that are used
to convert the U.S. prices to Canadian dollars (C$). This facilitates the speci¢cation of the error correction term in error correction models and the assessment of
equality of prices in the United States and Canada.
The main ¢ndings of our study are as follows. First, prices on the TSE and the
U.S. exchange are nonstationary with a unit root. However, they are cointegrated, with equality of prices holding as an equilibrium relationship.Thus, when
there are deviations from this relationship, the Toronto and/or U.S. prices must
adjust to restore equality. Second, the adjustments that maintain equality of
prices occur on both exchanges. That is, not only do the U.S. prices adjust to the
TSE prices, but they also provide feedback so that the TSE prices adjust to the
U.S. prices. Thus, the U.S. market also contributes to the price discovery of sample stocks. In general, the U.S. prices adjust more to the TSE prices than vice versa. The proportion of adjustment that occurs on the TSE ranges from 0.2 percent
to 98.2 percent, with an average of 38.1 percent. Although the TSE is dominant for
a majority of the ¢rms, there are many ¢rms for which the U.S. exchange’s contribution to price discovery is more than that of the TSE.Third, regression analysis
indicates that theTSE share of total adjustment in prices is directly related to the
U.S. share of total trading in a stock and to the ratio of proportions of informative
(medium-size) trades on the U.S. exchange and the TSE, and inversely related to
the ratio of bid-ask spreads on the U.S. exchange and the TSE.
The rest of the paper is organized as follows. Section I discusses the main features of the TSE and the U.S. exchanges and the nature of TSE cross-listings in
3
This seems to suggest that the U.S. and TSE prices of Canadian cross-listed stocks are
likely to move more closely to each other than the prices of ADRs from other countries and
their home-market securities. However, ADRs are also fairly close substitutes of the underlying securities. Though in a di¡erent context, the analysis of DaimlerChrysler Global Registered Share (GRS) in Karolyi (1999) suggests that the stock performance of a cross-listed
¢rm could not be attributed to how it is cross-listed.
Cross-Border Listings and Price Discovery
553
the United States. In Section II, we discuss the data sources and the sample details. In Section III, we perform the preliminary data analysis, including unit
root and cointegration tests. We discuss the error correction models in Section
IV. In SectionV, we provide the details of the cross-sectional analysis. In particular, we discuss our measure of the U.S. feedback to the TSE based on the estimates in the previous section, our hypotheses regarding the determinants of the
extent of this feedback, and the results of the regression analysis used to test
these hypotheses. Concluding comments are provided in Section VI.
I. TSE and U.S. Exchanges
In this section, we brie£y compare the features of the TSE with those of the U.S.
exchanges.4 We also discuss the nature of cross-listings of the TSE stocks in the
United States.
The TSE was incorporated in 1878, and it is the main stock exchange in Canada. As per the TSE annual report (1998), more than 1,400 ¢rms are listed on the
TSE. Almost 27 billion shares were traded on the TSE in 1998, representing 90
percent of the traded value in Canada. On average, more than C$2 billion worth
of stock trades are made every day on the TSE. Like the NYSE and AMEX, the
TSE is an auction market. Each stock listed on the TSE is assigned to a registered trader who acts as the market maker.The registered trader’s duties include
providing a minimum guaranteed ¢ll, maintaining minimum spread, and providing for orderly trading. The system of a single registered trader for each stock at
the TSE resembles the specialist system at the NYSE and AMEX.
The regular trading hours of the TSE are the same as those of the U.S. exchanges, from 9:30 a.m. to 4:00 p.m. Eastern time. The trading environment at
the TSE is £oorless and completely electronic. All trading takes place through
the Computer Assisted Trading System (CATS). During 1998, the U.S. exchanges
had fractional trading and the tick for most stocks was US$1/16, or 6.25 cents.The
TSE had already switched to decimal trading, with a tick of ¢ve cents for most
stocks.5 The TSE listing requirements do not di¡er much from those of Nasdaq
or AMEX, thus making it easy for a Canadian company already listed on the TSE
to list on Nasdaq or AMEX. However, the standards and costs of the NYSE substantially exceed those of the TSE, AMEX, and Nasdaq. Generally, the blue-chip
Canadian ¢rms are listed on both the TSE and NYSE. Among the foreign stocks
listed in the United States, Canadian listings constitute the largest group of
stocks from a single country. For the NYSE, Pulatkonak and So¢anos (1999) point
out that at the end of 1998, Canadian issues accounted for 16 percent of all
non-U.S. issues. Canadian stocks are listed in the United States as ordinary
4
See Smith, Turnbull, and White (2000) for a detailed discussion of the institutional similarities and di¡erences between the TSE and NYSE. Smith, Turnbull, and White (2001) provide
details of order execution on the TSE.
5
Gri⁄ths et al. (1998a) examine the switch to £oorless trading on the TSE, and Gri⁄ths
et al. (1998b) examine the switch to decimal trading on the TSE.
554
The Journal of Finance
shares; most other non-U.S. stocks are listed as American depositary
receipts (ADRs). The certi¢cate traded in the United States for a cross-listed Canadian stock is identical to the one traded in Canada. Investors do not face legal
restrictions on cross-border ownership and trading, and there are no conversion
fees.
II. Data Sources and Sample Details
A. Sources of Data
The intraday data used in this study are from three sources. The trade and
quote data for the TSE are from the TSE daily equity trades database. It contains
all equity trades and quotes for the day, sorted by symbol and stamp time. The
intraday data for trading on the U.S. exchanges (NYSE, AMEX, and Nasdaq)
are from the Trade and Quote (TAQ) database. For the intraday exchange rates,
we use the data collected by Olsen & Associates, Switzerland. This dataset consists of all the quotes that appear on the interbank Reuters network. Each quote
contains a bid and an ask price along with the time to the nearest even second.
Some of the other data, such as the date of listing in the United States and the
market capitalization, are from the web sites of exchanges and the Center for
Research in Security Prices (CRSP). Some of the trading in sample stocks occurs
on regional exchanges and Electronic Communication Networks (ECNs). The
data on the percentage of trading in regionals and ECNs are from the TAQ database and the Nasdaq academic liaison.
B. Sample Details
This study covers the six-month period from February 2 to July 31, 1998. The
markets do not seem to be particularly noteworthy during this period, and show
a general upward trend consistent with the stock market performance during the
1990s. The six-month study period has 124 days for which data are available on
both the TAQ and TSE intraday databases.We analyze those Canadian stocks that
are listed on the TSE in Canada and on the NYSE, AMEX, or Nasdaq in the United States
We begin our sample selection with all those Canadian ¢rms that traded on the
TSE and either the NYSE, AMEX, or Nasdaq throughout the study period, and
had a minimum trading history of three months preceding the study period. To
provide su⁄cient observations for intraday analysis and inference, we exclude
thinly traded stocks. We consider thinly traded stocks as those with fewer than
2,000 trades during the six-month study period on either the TSE or the U.S. exchange. Since the stock splits in the United States and Canada can di¡er by a few
days, we exclude the stocks that split during the study period. We also exclude a
stock in which the TSE trades were not settled using the usual continuous net
settlement method. Our ¢nal sample consists of 62 ¢rms, with 38 of them listed
on NYSE, 21 on Nasdaq, and 3 on AMEX.
Cross-Border Listings and Price Discovery
555
The basic details of the sample ¢rms indicate that a maximum of 12 are in
mining followed by 5 each in oil and gas and software.6 Typically, the Canadian
¢rms listed on Nasdaq include many of Canada’s leading high-tech ¢rms, such as
Cognos, as well as small to medium-size industrial or oil or mineral ¢rms, such as
Methanex and Abacan Resource. In general, the blue-chip Canadian ¢rms, such
as Canadian Paci¢c and Royal Bank of Canada, trade at the NYSE.There is a large
variation in the extent of trading in the United States.7 The U.S. share of trading
volume ranges from a low of about three percent to a high of about 88 percent, with
an average of about 42 percent. Consistent with Pulatkonak and So¢anos (1999),
who ¢nd that U.S trading in stocks from the ¢nancial services sector is signi¢cantly lower than that of similar stocks from other industries, the three banks in
the sample have the lowest proportion of trading in the United States
Table I provides summary statistics for the entire sample and for the NYSE/
AMEX and Nasdaq subsamples. As expected, ¢rms listed on the NYSE/AMEX
are much larger and have much higher prices than those on Nasdaq. Stocks listed
on the NYSE/AMEX are more heavily traded in both Canada and the United
States than those listed on Nasdaq. Collectively, the TSE faces sti¡ competition
from the U.S. exchanges, with the median value of the percentage of shares
traded in the United States being 43.6 percent.
III. Preliminary Data Analysis: Unit Root and Cointegration Tests
In this section, we ¢rst provide the basic details of the prices used in the time
series analyses. We then perform unit root tests for prices of each stock to establish that price series are nonstationary and integrated of order one, denoted as
I(1). Subsequently, we use the Johansen (1988) method to con¢rm the cointegration of prices for each stock.
A. Price Series forAnalysis
An analysis of a cross-listed stock trading in two markets can be based on
either transaction prices or quoted prices.The use of the most recent transaction
prices is likely to su¡er from an autocorrelation problem induced by infrequent
trading. Since quotes can be updated in the absence of trades, we perform the
analysis in this study using regularly spaced quotes. In particular, for each sample stock, we form the two price series for analysis by selecting the midpoint of
the last bid and ask quotes in each market at 10 -minute intervals.8 Consequently,
6
Details of the sample ¢rms are available upon request.
Prior studies, such as Gould and Kleidon (1994), point out that trades among dealers are
included in reported trading volume on Nasdaq. These studies suggest that trades by public
investors on Nasdaq are 50 to 65 percent of the reported volume. The Nasdaq trading volumes
used in our study are 50 percent of the reported trading volumes.
8
We also perform the analysis using transaction prices. For each sample stock, we form two
price series by using the minimal span procedure outlined in Harris et al. (1995). We form
synchronous pairs of transaction prices for each stock by selecting those trades on the TSE
and U.S. exchange that chronologically follow one another. There is no qualitative change in
results when these transaction prices are used.
7
556
The Journal of Finance
Table I
Summary Statistics of Sample Firms
Market capitalization is as on December 31, 1997, as reported in the TSE Factbook, 1997. Price is
the average (weighted by the number of shares traded) price paid on all trades on the TSE during the six-month study period of February 2 to July 31, 1998. Number of shares traded is the total
number of shares traded during this period. Percentage of shares traded in the U.S. is the number
of shares traded on the U.S. exchange as a percentage of the total number of shares traded on
the U.S. exchange and the TSE. The intraday data is obtained from the TSE intraday database
and the TAQ database.
NYSE/AMEX
(41 Firms)
319
1,319
3,876
6,407
25,099
Nasdaq
(21 Firms)
Market
capitalization
(C$ million)
5th percentile
25th percentile
Median
75th percentile
95th percentile
Price (C$)
5th percentile
25th percentile
Median
75th percentile
95th percentile
Number of shares
traded on the TSE
(million)
5th percentile
25th percentile
Median
75th percentile
95th percentile
6.2
19.2
49.4
81.1
177.2
2.6
3.3
8.3
11.2
52.0
2.8
8.6
23.4
58.7
131.7
Number of shares
traded in the U.S.
(million)
5th percentile
25th percentile
Median
75th percentile
95th percentile
3.0
8.7
22.2
50.1
163.4
3.0
3.3
5.4
11.5
18.4
3.0
5.2
12.3
36.7
143.3
Percentage of shares
traded in the U.S.
5th percentile
25th percentile
Median
75th percentile
95th percentile
5.54
18.27
29.14
55.68
85.52
3.9%
22.6%
42.5%
54.6%
78.6%
40
137
228
418
1,457
All
(62 Firms)
1.54
3.69
10.56
18.27
38.02
12.4%
29.0%
45.1%
58.9%
75.0%
111
348
1,428
4,963
17,701
2.96
8.97
21.19
41.00
2.96
7.9%
24.3%
43.6%
58.3%
78.6%
we have 39 prices per day in each market for each stock, or 4,836 observations for
the 124 trading days in our sample.
In the error correction models that we estimate later in this paper, we also include the returns on the market.We use the return on HIPs (TSE 100 index participation units) as a proxy for the return on the Canadian stock market. HIPs
traded on the TSE (symbol: HIP) and were designed to track the TSE 100 index.
The TSE 100 index includes the larger and more liquid issues within the broader
TSE 300 index. We use the return on SPDRs (Standard & Poor’s depositary receipts) as a proxy for the return on the U.S. stock market. SPDRs trade on the
Cross-Border Listings and Price Discovery
557
AMEX (symbol: SPY) and are designed to track the S&P 500 index. Similar to our
method with the sample stocks, we construct price series of quotes for both HIPs
and SPDRs.
The intraday prices on the TSE are from the TSE intraday database. The intraday prices on the U.S. exchanges are from the TAQ database. We ¢lter the prices
for errors, requiring that the price of a stock on an exchange be a multiple of the
tick size for that stock on that exchange. Further, for the TSE data, we exclude
closing quotes and quotes £agged as odd lots, pre-open, or halted. For TAQ data,
we exclude quotes £agged as closing quotes, trading halts, non¢rm quotes, and
pre-opening indications.
After forming the series of prices in Canada and the United States, we convert
the U.S. prices to Canadian dollars. Our analyses in this paper are based on the
price series for each ¢rm in the same currency (C$).This facilitates the speci¢cation of the error correction term in error correction models, as well as the assessment of equality of prices in the United States and Canada.9 The exchange rate
dataset that we use is from Olsen & Associates, Switzerland, and consists of all
the quotes that appear on the interbank Reuters network. There are 57,569 valid
exchange rate quotes appearing from 9:30 a.m. to 4:00 p.m. on the 124 days for
which both the TSE and the U.S. exchanges were open during the study period,
implying an average of 1.2 quotes per minute. From these quotes, we form a series
of exchange rates by selecting the midpoint of the last bid and ask quotes that
appear at every 10 -minute interval. During the six-month study period, the exchange rate was fairly stable. The C$ initially appreciated with respect to the
US$ from C$1.45/US$ to C$1.41/US$, but depreciated to C$1.51/US$ by the end
of the period.The average exchange rate was C$1.44/US$.The standard deviation
based on daily exchange rates was C$0.026/US$.
B. Unit Root Tests
Our ¢rst objective now is to test whether or not the TSE and U.S. price series
are cointegrated. The concept of cointegration becomes relevant when the time
series being analyzed are nonstationary. In particular, two time series xt and yt
are both integrated of order one, denoted as I(1), if they are both nonstationary
but their changes are stationary.Then, xt and yt are cointegrated if there exists a
linear combination zt 5 yt Axt, which is stationary, denoted as I(0). Therefore,
before analyzing cointegration between prices of our sample stocks in Canada
and the United States, we check if the two price series for each stock are I(1).We
also check if the HIP and SPYprice series are I(1).
We use the augmented Dickey^Fuller (1981) test, which includes lagged ¢rst
di¡erences of the price series in the equation, to check for the presence of a unit
root. For each price series, we consider the following three regression equations.
The di¡erences among the three regression equations are concerned with the
presence of a drift term and a linear time trend. The null hypothesis in all three
9
We also perform the analyses using unconverted prices. We do not ¢nd any qualitative
change in results when we treat the US$/C$ exchange rate as a separate variable.
558
The Journal of Finance
cases is that d equals zero; if the null cannot be rejected, the {xt} price series contains a unit root:
Dxt ¼ dxt1 þ
p
X
fi Dxti þ et
ð1Þ
i¼1
Dxt ¼ c0 þ dxt1 þ
p
X
fi Dxti þ et
ð2Þ
i¼1
Dxt ¼ c0 þ dxt1 þ c1 t þ
p
X
fi Dxti þ et
ð3Þ
i¼1
We use the Schwarz Bayesian criterion (Schwarz (1978)) to determine p, the number of lags in the model.We estimate the above equations for the two price series
for each ¢rm and the HIP and SPYprice series, and then test the null that d equals
zero. The critical values of the t-statistics depend on the equation being estimated. Using the critical values as per Enders (1995), we ¢nd that at the ¢ve percent level, the null is rejected only for Inco Ltd. in equation (1), Cognos in
equation (2), and for no ¢rm in equation (3). The null cannot be rejected for any
of the price series in any equation at the one percent level.The Dickey and Pantula (1987) extension of the basic procedure con¢rms the absence of more than one
unit root. Overall, we conclude that both price series for the sample stocks and
the HIP and SPYprice series are I(1).
C. CointegrationTests
Though the U.S. and TSE prices of a Canadian cross-listed stock are nonstationary, we do not expect them to diverge without bound from each other, because
they are the prices of the same security trading at two locations. Formally, we
expect the price series for each stock to be cointegrated. Since we are including
HIP and SPY prices in the error correction model, we need to see if PtHIP , PtSPY ,
TSE
US
and the two price series for each stock j, Pj;t
and Pj;t
, are cointegrated.10 This
HIP
SPY
TSE
US
>would be true if Pt , Pt , Pt , and Pt are I(1), which we have already con¢rmed, and if there exists a vector b 5 (bTSE, bUS, bHIP, bSPY) such that
bTSE PtTSE þ bUS PtUS þ bHIP PtHIP þ bSPY PtSPY is I(0). Since there are four price
series for each stock, there may be more than one cointegrating vector for a stock.
In the error correction models that we estimate later in this paper, we will need
to include as many error correction terms as the number of cointegrating vectors.
We now use the Johansen (1988) method to test for the cointegration of the four
price series for each stock and the number of cointegrating vectors if the prices
are indeed cointegrated.
In this method, a pth order autoregressive
process, xt 5 A1xt 11A2xt 21
P
y1Apxt p1et, is rewritten as Dxt ¼ p1
P
Dx
i
ti þ Pxtp þ et , where, D is the
i¼1
¢rst-di¡erence lag operator, xt is a (n 1) vector of I(1) time-series variables, et is
10
We now drop the subscript j for ease of reading.
Cross-Border Listings and Price Discovery
559
a zero mean n-dimensional white noise vector, Pi are (n n) matrices of parameters, and P is a (n n) matrix of parameters whose rank is equal to the number
of independent cointegrating vectors. The hypothesis, that the number of cointegrating vectors
Pis at most r, is tested using either ltrace(r) or lmax^(r, r11), where
ltrace ðrÞ ¼ T ni¼tþ1 ln ð1 ^
lt Þ and lmax ðr; r þ 1Þ ¼ T lnð1 lrþ1 Þ, with T
being the number of usable observations and ^li being the estimated value of the
characteristic root (eigenvalue) obtained from the estimated P matrix. The statistic ltrace(r) tests the null hypothesis that the number of distinct cointegrating
vectors is less than or equal to r against a general alternative.The statistic lmax(r,
r11) tests the null that the number of cointegrating vectors is r against the alternative of r11 cointegrating vectors. Both lmax and ltrace statistics follow nonstandard distributions. Their critical values are provided in Johansen and Juselius
(1990). In our study, n equals four, corresponding to the four series
PtHIP ; PtSPDR ; PtTSE and PtUS . The 99 percent critical values are 32.6, 26.2, 18.8,
and 11.6 for lmax, and 55.6, 37.3, 22.0, and 11.6 for ltrace, corresponding to r of zero,
one, two, or three, respectively.
We determine the number of lags in the model by using the multivariate version
of the Schwarz Bayesian criterion (Schwarz (1978)), and then test for cointegration and the number of cointegrating vectors. For each of our sample stocks, we
¢nd that PtHIP , PtSPY , PtTSE, and PtUS are cointegrated, and there is, in fact, a single cointegrating vector.11 For example, for Abacan Resource Corporation, lmax
for the null hypothesis that r equals zero is 533.8, which is greater than the 99
percent critical value of 32.6. Therefore, we reject the null of no cointegration in
favor of the alternative of one cointegrating vector. We now test the null that r
equals one. We cannot reject this null, as lmax is 13.5, which is less than the 99
percent critical value of 26.2. So, we conclude that there is a single cointegrating
vector.12 The same conclusion is reached for this ¢rm as well as the other sample
¢rms, when ltrace is used instead of lmax.
IV. Error Correction Models
As mentioned earlier, our approach to assessing the contribution of U.S. exchanges to price discovery is similar to the error correction approach used by
Harris et al. (1995). An alternative to this approach is the Hasbrouck (1995) approach. Hasbrouck’s starting point also is that if a security trades in two di¡erent
markets, its prices in the two markets should be cointegrated. This means that
the price series have a common stochastic trend. A market’s contribution to price
discovery is measured as the market’s relative contribution to the variance of the
11
The detailed results are not included for the sake of space. They are available upon request.
12
When we perform the augmented Dickey^Fuller (1981) tests, we do not ¢nd evidence of
signi¢cant deterministic terms. So, the results reported in the illustration are for the model
with no deterministic terms. We also perform cointegration tests for models with deterministic components, and ¢nd that our result of the existence of one cointegrating vector is robust
across di¡erent models.
560
The Journal of Finance
innovations in the common trend.This contribution is termed the market’s‘‘information share.’’13
We chose the error correction approach because it is more conducive to our
study. The Hasbrouck approach involves Choleski factorization of the covariance
matrix of the innovations in prices on di¡erent exchanges, which requires that
the prices be ordered. Consequently, the information shares are not unique as
they depend on the ordering of the prices. Nonuniqueness of the information
shares would pose a major problem if we use this approach. Since we perform
cross-sectional regressions using the U.S. contribution to price discovery as the
dependent variable, we need a unique value of the U.S. contribution instead of its
upper and lower bounds. We have reason to believe that the divergence between
upper and lower bounds in our study may be substantial. To facilitate the crosssectional analysis, we use a fairly large sample.There is considerable diversity in
how actively the ¢rms are traded. So, we use prices sampled at a 10 -minute interval, which is not a particularly high frequency as compared to the one-second
interval in Hasbrouck (1995). Other studies that have used the Hasbrouck approach for prices sampled at frequencies comparable to ours have found a wide
divergence in the upper and lower bounds (e.g., Booth et al. (2002) and Huang
(2002)).14
In the previous section, we con¢rmed that there is a single cointegrating vector for the four price series for each of our sample stocks. In view of the
relative absence of capital controls between the U.S. and Canadian markets,
we expect that the prices of the U.S.-listed Canadian stocks in the two markets
will be very close to one another. Accordingly, in the cointegrating vector
(bTSE, bUS, bHIP, bSPY), we expect the normalized values of bTSE and bUS to be
one and negative one, respectively, and the values of bHIP and bSPY to be close to
zero. We use the Johansen methodology to estimate the cointegrating vector for
each ¢rm, and report a summary of the normalized estimates (bTSE equals one) in
Panel A of Table II. The estimates are as expected. Also, the TSE and U.S.
prices of the NYSE-listed ¢rms tend to move more closely together than those
of the Nasdaq-listed ¢rms. Overall, the median of the normalized estimates
for the sample ¢rms is (1, 1, 0, 0). These results con¢rm that the prices of
Canadian cross-listed securities tend to be equal in Canada and the United
States.
13
In contrast to the approach in Harris et al. (1995) and Harris et al. (2002), which employs
the permanent-transitory decomposition of the cointegrated system, the information shares
in the Hasbrouck (1995) approach are extracted from a variance decomposition in the vector
moving average representation of the error correction model. For further discussion of the
methodologies, please see Hasbrouck (1995, 2000) and Harris et al. (1995, 2002).
14
Booth et al. (2002) study price discovery in the Finnish upstairs and downstairs markets.
Using trading intervals of approximately 30 minutes, they ¢nd the average upper and lower
bounds for the downstairs market to be 99.2 percent and 13.0 percent, respectively. Huang
(2002) studies price discovery among the various Nasdaq quote participants using one-minute
intervals. For July 1998, he ¢nds the upper and lower bounds of Island (an electronic communication network) for Dell Computer Corporation to be 83.2 percent and 24.5 percent, respectively.
Cross-Border Listings and Price Discovery
561
Table II
Error Correction Models
We estimate the following error correction model for each ¢rm. Multivariate Schwarz Bayesian
criterion is used to determine the number of lags p (i, j, k, l 5 1,..., p).
TSE
US
HIP
SPY
þ aTSE ðPt1
þ bUS Pt1
þ bHIP Pt1
þ bSPY Pt1
Þ
DPtTSE ¼ aTSE
0
p
p
p
p
X
X
X
X
TSE
US
HIP
SPY
gi DPti
þ
di DPti
þ
ui DPti
þ
zi DPti
þ eTSE
þ
t
i¼1
i¼1
i¼1
i¼1
US
TSE
US
HIP
SPY
DPtUS ¼ aUS
ðPt1
þ bUS Pt1
þ bHIP Pt1
þ bSPY Pt1
Þ
0 þa
p
p
p
p
X
X
X
X
TSE
US
HIP
SPY
gj DPtj
þ
dj DPtj
þ
uj DPtj
þ
zj DPtj
þ eUS
þ
t
j¼1
j¼1
j¼1
j¼1
TSE
US
HIP
SPY
DPtHIP ¼ aHIP
þ aHIP ðPt1
þ bUS Pt1
þ bHIP Pt1
þ bSPY Pt1
Þ
0
p
p
p
p
X
X
X
X
TSE
US
HIP
SPY
gk DPtk
þ
dk DPtk
þ
uk DPtk
þ
zk DPtk
þ eHIP
þ
t
k¼1
k¼1
k¼1
k¼1
TSE
US
HIP
SPY
DPtSPY ¼ aSPY
þ aSPY ðPt1
þ bUS Pt1
þ bHIP Pt1
þ bSPY Pt1
Þ
0
p
p
p
p
X
X
X
X
TSE
US
HIP
SPY
gl DPtl
þ
dl DPtl
þ
ul DPtl
þ
zl DPtl
þ eSPY
þ
t
l¼1
l¼1
l¼1
l¼1
The values of b obtained using the Johansen cointegration methodology are reported in Panel
A. Summary statistics of estimated values of a are reported in Panel B. The percentiles for aTSE
are computed using the absolute values.
Panel A: Estimated Values of b (Normalized, so that bTSE Equals One)
NYSE/AMEX (41 Firms)
b
5th percentile
25th percentile
Median
75th percentile
95th percentile
US
HIP
b
1.009
1.002
1.000
0.999
0.997
0.015
0.002
0.000
0.003
0.009
b
SPY
0.006
0.002
0.000
0.001
0.017
Nasdaq (21 Firms)
b
US
b
HIP
b
All 62 Firms
SPY
US
bHIP
b
bSPY
1.022 0.035 0.069 1.019 0.030 0.059
1.009 0.013 0.044 1.004 0.005 0.003
1.002 0.003
0.002 1.000
0.000
0.000
0.999
0.060
0.012 0.999
0.004
0.003
0.983
0.102
0.025 0.994
0.084
0.022
Panel B: Estimated Values of a
NYSE/AMEX (41 Firms)
a
5th percentile
25th percentile
Median
75th percentile
95th percentile
TSE
0.02
0.08
0.16
0.22
0.35
US
a
a
HIP
a
SPY
Nasdaq (21 Firms)
a
TSE
a
US
0.10 0.02 0.01 0.03 0.04
0.18
0.00
0.00 0.05 0.07
0.29
0.00
0.00 0.07 0.11
0.49
0.01
0.01 0.15 0.14
0.72
0.07
0.05 0.20 0.20
HIP
SPY
a
a
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
All 62 Firms
TSE
a
aUS
aHIP
aSPY
0.03
0.06
0.13
0.18
0.30
0.06 0.01 0.01
0.11
0.00 0.00
0.18
0.00 0.00
0.37
0.00 0.01
0.71
0.03
0.03
We now estimate the following generalized error correction models, which include the lagged changes of prices. Multivariate Schwarz Bayesian criterion is
used to determine the number of lags p (i, j, k, l 5 1,y, p), which is set uniformly
across the four equations. This reveals optimal lags to be one or two for the
562
The Journal of Finance
sample ¢rms.The values of betas in the following are as per the vectors estimated
above, with bUS values typically close to negative one, and bHIP and bSPY values
typically close to zero:
TSE
US
HIP
SPY
DPtTSE ¼ aTSE
þ aTSE ðPt1
þ bUS Pt1
þ bHIP Pt1
þ bSPY Pt1
Þ
0
þ
p
X
TSE
gi DPti
þ
p
X
i¼1
US
di DPti
þ
i¼1
p
X
HIP
ui DPti
þ
i¼1
p
X
SPY
zi DPti
þ eTSE
t
ð4Þ
i¼1
US
TSE
US
HIP
SPY
ðPt1
þ bUS Pt1
þ bHIP Pt1
þ bSPY Pt1
Þþ
DPtUS ¼ aUS
0 þa
p
X
TSE
gj DPtj
j¼1
þ
p
X
US
dj DPtj
þ
j¼1
p
X
HIP
uj DPtj
þ
j¼1
p
X
SPY
zj DPtj
þ eUS
t
ð5Þ
j¼1
TSE
US
HIP
SPY
DPtHIP ¼ aHIP
þ aHIP ðPt1
þ bUS Pt1
þ bHIP Pt1
þ bSPY Pt1
Þ
0
þ
p
X
TSE
gk DPtk
þ
k¼1
p
X
US
dk DPtk
þ
k¼1
p
X
HIP
uk DPtk
þ
k¼1
p
X
SPY
zk DPtk
þ eHIP
ð6Þ
t
k¼1
TSE
US
HIP
SPY
þ aSPY ðPt1
þ bUS Pt1
þ bHIP Pt1
þ bSPY Pt1
Þ
DPtSPY ¼ aSPY
0
þ
p
X
l¼1
TSE
gl DPtl
þ
p
X
l¼1
US
dl DPtl
þ
p
X
l¼1
HIP
ul DPtl
þ
p
X
SPY
zl DPtl
þ eSPY
t
ð7Þ
l¼1
The estimates of alphas indicate the extent to which the price series respond to a
deviation from the equilibrium relationship. There is clearly no reason to expect
that the prices of HIP and SPY will respond signi¢cantly to the individual stock
prices and therefore we expect aHIP and aSPY to be close to zero. However, either or
both PtTSE and PtUS must respond to the magnitude of the departure. On the one
hand, as the TSE is the home-market of the sample stocks, we expect prices in the
United States to respond to prices on the TSE, and adjust to some extent to the
departure. On the other hand, as the United States is a leading ¢nancial center in
the world and an important business venue for the Canadian ¢rms, we expect
some feedback from the United States to the TSE.
As per the above discussion, the coe⁄cients of main interest are aTSE and aUS.
TSE
US
Consider the situation in which Pt1
4Pt1
. One likely way in which the gap between the two prices could reduce is that, at time t, PTSE declines and PUS
increases.15 Accordingly, aTSE should be negative and aUS should be positive. The
TSE
US
same signs would be expected in the situation in which Pt1
oPt1
. Panel B of
Table II provides a summary of the estimates of the coe⁄cients for the error correction term. For the sake of space, only a summary is reported here, although we
brie£y discuss ¢rm-speci¢c results below.
15
Other less likely possibilities include (a) PTSE increases but PUS increases more, and (b)
decreases but PUS decreases less.
TSE
P
Cross-Border Listings and Price Discovery
563
As expected, aHIP and aSPY are almost always close to zero. Our main results
regarding the estimates of aTSE and aUS are as follows. First, all coe⁄cients have
the expected signs: aTSE values are negative and aUS values are positive. Second,
for 61 of the 62 sample ¢rms, aUS is statistically signi¢cant at the one percent
level. Thus, the U.S. prices of all the ¢rms except one respond to deviations from
the Canadian prices. The sole exception is Biovail Corporation International, for
which 83 percent of the total trading takes place in the United States. Third, for
all but four of the sample ¢rms, aTSE is statistically signi¢cant at the one percent
level.Thus, the Canadian prices of 58 of the 62 sample ¢rms respond to deviations
from the U.S. prices.The four ¢rms whose Canadian prices are not a¡ected by the
U.S. prices include BCE Inc. and the three banks in the sample, namely, the Bank
of Montreal, the Royal Bank of Canada, and The Toronto Dominion Bank. On
average, only 5.5 percent of the total trading in these four ¢rms takes place in
the United States. Overall, the results imply that, in general, both prices respond
to a departure from equality. Thus, both the TSE and the U.S. exchange contribute to price discovery.
Finally, we compare the magnitudes of aUS and jaTSE j.We perform a likelihood
ratio test, with a chi-square distributed test statistic, using the Johansen (1988)
cointegration methodology to check if aUS equals jaTSE j. For 50 of the 62 ¢rms, we
can reject the null of equality at the 95 percent level of signi¢cance. For a majority
of the ¢rms (45 out of 62), aUS is greater than jaTSE j. As indicated in Panel B of
Table II, the median value for aUS is 0.18 as compared to 0.13 for jaTSE j. In Figure 1,
we plot aUS versus jaTSE j for the 62 sample ¢rms. Most observations are substantially o¡ the vertical axis, implying that the U.S. exchange makes a contribution
to price discovery.Though a majority of the ¢rms are above the 451 line, implying
that for these ¢rms aUS is greater than jaTSE j, there is a signi¢cant number of
¢rms (17) below the line for which aUS is less than jaTSE j.
In contrast to the purely domestic studies on price discovery, which ¢nd that
the NYSE consistently dominates the regionals, the above results indicate that
although the TSE is dominant for a majority of the ¢rms, there are many ¢rms for
which the U.S. exchange is dominant. As re£ected in the median values of aUS and
jaTSE j for the sample, the extent to which theTSE prices respond to the U.S. prices
is substantial. Overall, there is strong evidence that considerable price discovery
for the U.S.-listed Canadian stocks takes place not only in their home market but
in the United States as well.16
16
This has an interesting implication for order execution. In a letter to the U.S. Securities
and Exchange Commission (SEC) on March 9, 1999, the TSE suggested that the SEC re¢ne the
interpretation of a U.S. broker’s best execution obligation for foreign stocks listed in the United States. In particular, the TSE suggested that for the U.S.-listed Canadian ¢rms, the U.S.
brokers should be obligated to check the Canadian prices also. Our ¢nding that the TSE is the
main price discovery mechanism for a majority of the U.S.-listed Canadian stocks provides
support for the suggested change. However, the ¢nding that the U.S. exchanges serve as the
primary price discovery mechanism for some Canadian stocks, while making a signi¢cant
contribution to the price discovery of other stocks, suggests that the Canadian brokers should
also be required to check the U.S. prices of the Canadian stocks cross-listed in the United
States.
564
The Journal of Finance
Figure 1. Plot of aUS versus jaTSEj for the 62 sample ¢rms. The variables aTSE and aUS
are the coe⁄cients of the error correction terms in the TSE and the U.S. equation, respectively, in the error correction model estimated separately for each stock. The estimates of
jaTSEj and aUS can be interpreted as the average adjustment of each series towards the
other to restore equality of the two prices.
V. Cross-sectional Analysis
We have seen that the extent of feedback provided by the United States to the
TSE varies considerably across ¢rms. In this section, we analyze the determinants
of the variation.We ¢rst discuss our measure of the U.S. feedback to theTSE, which
is later used as the dependent variable in the cross-sectional regressions.We then
discuss our explanatory variables and the associated hypotheses, followed by the
summary statistics of explanatory variables and the regression results.
A. DependentVariable
The coe⁄cients jaTSE j and aUS of the error correction terms, estimated in the
previous section, can be interpreted as the average adjustment of each series towards the other in order to restore the equality of the two prices. As an example,
consider Alcan Aluminum Limited. The coe⁄cients aHIP and aSPY are 0.02 each,
and are insigni¢cant. The two coe⁄cients of main interest, aTSE and aUS, are
0.232 and 0.436, respectively, and are signi¢cant at the one percent level. So, if
Cross-Border Listings and Price Discovery
565
PtTSE is greater than PtUS by one percent, price adjustments take place such that
PtTSE declines by 0.232 percent and PtUS increases by 0.436 percent. Though a majority of the total adjustment occurs in the United States, there is a signi¢cant
error correction that takes place on the TSE as a result of the feedback provided
by the U.S. prices.
The proportion of the total adjustment that occurs at the TSE can be considered a measure of the price adjustment that takes place due to the trading of the
security on the U.S. exchange. We de¢ne this variable as TseAdj ¼
jaTSE j=ðjaTSE j þ aUS Þ. A higher value of this ratio re£ects a greater feedback or
contribution from the United States. If there is no feedback from the United
States, then aTSE is zero, and TseAdj is zero. In this case, the U.S. market is not
contributing to price discovery. Borrowing the terminology ¢rst used in Garbade
and Silber (1982), the U.S. exchange is a‘‘pure satellite’’of the TSE, since only the
U.S. prices move toward the TSE prices.Values of TseAdj greater than zero imply
feedback from the United States to the TSE.We use TseAdj as our dependent variable.The averageTseAdj across our 62 sample ¢rms is 38.1 percent and the median
is 36.2 percent.
B. ExplanatoryVariables
B.1. U.S. Share of TradingVolume
In a study of the NYSE contribution to price discovery relative to the
regional exchanges for a sample of the 30 Dow stocks, Hasbrouck (1995)
¢nds a positive and statistically signi¢cant correlation between the NYSE contribution to price discovery and its market share by trading volume. We
expect TseAdj, the TSE share of total adjustment in prices in response to deviations from equality between the TSE and U.S. prices, to be directly related to the
U.S. proportion of total trading.The TSE market makers for stocks with a greater
fraction of trading in the United States would be more concerned about the U.S.
prices. Foerster and Karolyi (1998) ¢nd that the bid-ask spreads on the TSE decline after cross-listing on a U.S. exchange, and the decrease in spreads is concentrated in those stocks for which the U.S. exchange is able to capture a
relatively large proportion of total trading volume. They interpret this
result as the TSE market makers’competitive response to the additional presence
of the U.S. market makers. Werner and Kleidon (1996) examine the British
cross-listings on NYSE and AMEX. They ¢nd that when both the U.K. and U.S.
markets are open, the London dealers in cross-listed stocks are concerned
about the added competition for order £ow represented by New York trading
activity.
Another reason to expect the above relationship is that the higher the U.S.
share of trading in a stock, the more informative the U.S. trading is likely to be
relative to the TSE. The e⁄ciency of the U.S. market relative to the TSE would
increase as the U.S. share of total trading volume increases. Stickel and Verrecchia (1994) suggest that investors interpret high volume as an indication that the
demand underlying a price change is informative.
566
The Journal of Finance
B.2. Relative Trading Costs in the United States
We expect TseAdj to be inversely related to the relative trading cost in the United States. Since bid-ask spread represents a major portion of the trading costs,
our testable hypothesis is that there is an inverse relationship between TseAdj
and the ratio of spreads on the U.S. exchange and the TSE.We expect the inverse
relationship because the lower the ratio of spreads on U.S. exchange and the TSE,
the greater the competitive threat faced by the TSE market makers from the U.S.
market makers.The TSE market makers who face more competition from the U.S.
market makers are likely to be more responsive to the U.S. prices.
The above is also consistent with earlier studies relating price discovery to
trading costs, such as Fleming, Ostdiek, and Whaley (1996). These authors suggest that more informed trading, and therefore price discovery, will occur in the
market with lower trading costs. One of their empirical ¢ndings is that index
future and option price changes lead price changes in the stock market. They argue that this is due to the costs of trading the market through index futures and
options being substantially lower than the costs of executing market trades in
the index stocks. Jones and Seguin (1997) document that volatility decreased
after commissions were deregulated on U.S. markets in 1975. These authors suggest that lower trading costs allow informed traders to act on their information
more e¡ectively, thereby keeping prices better in line with fundamentals and reducing volatility. For a sample of the 30 Dow stocks, Harris et al. (2002) ¢nd evidence that the NYSE contribution to price discovery relative to the regional
exchanges increases when its spreads relative to the regionals decline.
B.3. Ratio of Proportions of Shares Traded in the United States and
on the TSE in Medium-Sized Lots
Barclay and Warner (1993) provide evidence consistent with the argument that
informed trades are concentrated in the medium-size category. Hasbrouck (1995)
¢nds that the information share of NYSE (relative to regional exchanges) is
signi¢cantly positively correlated with NYSE’s share of trading activity in
medium-size trades. He suggests that the lack of a relationship between NYSE’s
information share and small-size trades re£ects the low information content of
these trades, and the lack of a relationship between NYSE’s information share
and large-size trades is consistent with Seppi’s (1990) analysis that the block
trade market supports uninformed trading.Therefore, we expect the price discovery in the United States relative to Canada to be directly related to the ratio of
proportions of shares traded in the United States and on the TSE in mediumsized lots.17
B.4. OtherVariables
Our sample ¢rms are listed on di¡erent U.S. exchanges. In recent years, researchers have focused on some of the Nasdaq features that appear to indicate
17
We are grateful to an anonymous referee for suggesting this point.
Cross-Border Listings and Price Discovery
567
that Nasdaq is less competitive. During the early to mid-1990s, some studies suggested that the Nasdaq dealers collude (e.g., Christie and Schultz (1994)). Some
other studies, such as Demsetz (1997), suggest that there is less competition on
Nasdaq because of an ine⁄cient market structure and/or institutional procedures. Such studies led to an increased scrutiny of Nasdaq that resulted in a series of reforms. In January 1997, the SEC began a phased implementation of
reforms that provide some auction market characteristics to Nasdaq. Barclay et
al. (1999) study the e¡ects of these reforms for the ¢rst 100 stocks phased in and
¢nd that many of the objectives of the SEC have been met. Nonetheless, due to the
practice of preference trading on Nasdaq and its fragmented structure, it may
contribute less to price discovery than the NYSE. Bloom¢eld and O’Hara (1998)
¢nd evidence that increasing the proportion of trading that is preferenced can
reduce the informational e⁄ciency of prices. Biais (1993) argues that fragmented
markets such as Nasdaq are less transparent since deals are often the outcome of
bilateral transactions negotiated on the phone. Kim, Lin, and Slovin (1997) ¢nd
that the prices of NYSE stocks incorporate private information contained in analyst recommendations much faster than prices of Nasdaq stocks. In view of these
studies, it seems desirable to control for the exchange.18
We examine the duration for which a ¢rm has been listed in the United States.
Seasoning of the issue in the United States could a¡ect factors such as analyst
coverage, media attention, and the interest from U.S. investors, which could explain the extent to which the United States contributes to price discovery. We
also examine the proportion of U.S. trading that occurs on the primary exchange
in the United States (NYSE/AMEX/Nasdaq). Hasbrouck (1995) suggests that the
trading on a primary exchange is more informative than that on regional exchanges. Also, primary exchanges may be more conducive to price discovery than
ECNs, which are fragmented markets whose participants often do not know the
prices quoted on other networks. To ensure that our results are not driven by any
possible e¡ect of a ¢rm’s size, we also control for the ¢rm size, as proxied by a
¢rm’s market capitalization. It is possible that the home market may have superior access to information for ¢rms in a particular industry. Therefore, we also
control for the industry e¡ects through dummy variables.
C. Summary Statistics of the ExplanatoryVariables
Table III provides a summary of the explanatory variables. The U.S. share of
total trading in a stock, UsVol, is measured as the number of shares traded in
the United States as a percentage of the total number of shares traded in that
stock on the TSE and the U.S. exchange during the six-month study period. We
measure transaction costs on the TSE and in the United States as quoted spread:
Spread 5 (Ask Bid)/[(Ask1Bid)/2]. The variables UsSpread and TseSpread are
percentage quoted spreads on the U.S. exchange and the TSE, respectively, and
SpreadRatio is the ratio of UsSpread and TseSpread.The variable MediumTrade is
18
As only three of our sample ¢rms are listed on the AMEX, whose market structure is
similar to that of NYSE, we combine them with the NYSE ¢rms.
568
The Journal of Finance
Table III
Cross-Sectional Regression Related Variables
The U.S. share of total trading in a stock, UsVol, is measured as the number of shares traded in the United
States as a percentage of the total number of shares traded in that stock on the TSE and the U.S. exchange
during the six-month study period. We measure spreads as (Ask Bid)/((Ask1Bid)/2). The variables UsSpread and TseSpread are percentage spreads on the U.S. exchange and the TSE, respectively, and SpreadRatio is the ratio of these spreads. The variable MediumTrade is the ratio of the proportion of number of shares
traded in the United States in medium-sized lots (2,501 to 10,000 shares) and the proportion of number of
shares traded on the TSE in medium-sized lots. The variable YearsListed is the number of years for which a
¢rm has been listed in the United States through February 1, 1998; MktCap is the market capitalization on
December 31, 1997; and Primary is the percentage of trading in the United States that occurs on the NYSE
for NYSE-listed stocks, on AMEX for AMEX-listed stocks, and on Nasdaq for Nasdaq-listed stocks.The data
sources are the TSE intraday database, the TAQ database, the Nasdaq academic liaison, web sites of exchanges, and CRSP.
NYSE/AMEX (41 Firms)
Nasdaq (21 Firms)
All (62 Firms)
UsVol
5th percentile
25th percentile
Median
75th percentile
95th percentile
3.9%
22.6%
42.5%
54.6%
78.6%
12.4%
29.0%
45.1%
58.9%
75.0%
7.9%
24.3%
43.6%
58.3%
78.6%
UsSpread
5th percentile
25th percentile
Median
75th percentile
95th percentile
0.3%
0.4%
0.6%
1.2%
2.6%
1.0%
1.5%
1.7%
3.3%
5.4%
0.3%
0.5%
1.0%
1.7%
5.0%
TseSpread
5th percentile
25th percentile
Median
75th percentile
95th percentile
0.2%
0.3%
0.5%
0.9%
1.8%
0.6%
1.2%
1.5%
2.2%
3.2%
0.2%
0.4%
0.8%
1.3%
2.9%
SpreadRatio
5th percentile
25th percentile
Median
75th percentile
95th percentile
0.70
1.03
1.45
1.74
2.52
0.73
1.00
1.20
1.93
2.37
0.70
1.02
1.44
1.82
2.51
MediumTrade
5th percentile
25th percentile
Median
75th percentile
95th percentile
0.65
1.02
1.38
1.81
2.21
0.83
1.04
1.20
1.40
1.88
0.65
1.03
1.33
1.66
2.20
YearsListed
5th percentile
25th percentile
Median
75th percentile
95th percentile
0.98
1.84
3.60
15.02
62.21
0.59
2.64
3.78
5.63
9.28
0.86
2.18
3.71
10.57
47.10
MktCap
5th percentile
25th percentile
Median
75th percentile
95th percentile
Primary
5th percentile
25th percentile
Median
75th percentile
95th percentile
319
1,319
3,876
6,407
25,099
70.4%
82.0%
87.7%
92.9%
94.6%
40
137
228
418
1,457
93.9%
95.9%
97.1%
98.1%
99.5%
111
348
1,428
4,963
17,701
72.3%
85.0%
92.4%
95.9%
98.4%
Cross-Border Listings and Price Discovery
569
the ratio of the proportion of U.S. shares traded in medium-sized lots and the
proportion of TSE shares traded in medium-sized lots. It is measured as
Number of shares traded in the U:S: in medium-sized lots=
Total number of shares traded in the U:S:
Medium Trade ¼
Number of shares traded on the TSE in medium-sized lots=
Total number of shares traded on the TSE
where medium size refers to 2,501 to 10,000 shares.19 The variable YearsListed is
the number of years for which a ¢rm has been listed in the United States through
February 1, 1998; MktCap is the market capitalization on December 31, 1997; and
Primary is the percentage of trading in the United States that occurs on the
NYSE for NYSE-listed stocks, on AMEX for AMEX-listed stocks, and on Nasdaq
for Nasdaq-listed stocks.
Table III shows that the sample stocks are quite actively traded in both the United States and Canada. The median value of the U.S. share of trading is 43.6 percent. Consistent with previous studies examining spreads for the TSE securities
cross-listed in the United States (for example, Foerster and Karolyi (1998)), we
¢nd that the TSE spreads are lower than U.S. spreads. Across the U.S. exchanges,
the median spread on Nasdaq (1.7 percent) is considerably more than the median
spread on NYSE (0.6 percent). One reason for this is the di¡erence in characteristics, such as the market capitalization of Nasdaq- and NYSE-listed stocks. Consistent with such di¡erences, the average spread on the TSE of NYSE-listed
stocks (0.5 percent) is also much lower than the average spread on the TSE of
Nasdaq-listed stocks (1.5 percent).The median value of MediumTrade is more than
one, implying that a greater proportion of the U.S. trading is in medium-sized
lots than the proportion of the TSE trading. For our sample, the median duration
of listing in the United States at the beginning of the study period is 3.7 years.
D. Regression Analysis
Since the dependent variable, TseAdj, is a bounded fraction ranging from zero
to one, we use the logistic transformation, ln(x/(1 x)), where x is TseAdj, as the
dependent variable. This logistic transformation ensures that the predicted regression values lie between zero and one.We present the estimates of alternative
regression models in Table IV. In general, the results support our hypotheses.
D.1. Variables of Main Interest
The coe⁄cient of UsVol is positive and statistically signi¢cant at the one percent level, implying that the greater the U.S. proportion of total trading, the
greater the price discovery in the United States. The coe⁄cient of SpreadRatio
is negative and signi¢cant at the ¢ve percent level, which is consistent with the
19
Barclay and Warner (1993) consider medium size as 500 to 9,900 shares, and Hasbrouck
(1995) considers two separate medium-size categories, 501 to 2,500 shares and 2,501 to 10,000
shares. As mentioned later, we consider alternative speci¢cations of medium-size trades, but
report results based on the 2,501 to 10,000 speci¢cation.
570
The Journal of Finance
Table IV
Regression Results
The dependent variable is the logistic transformation of TseAdj, the TSE share of total adjustment in prices in response to deviations from equality between the TSE and U.S. prices.We measure ¢rm size, LMktCap, as the log of market capitalization. The U.S. share of total trading in a
stock, UsVol, is measured as the number of shares traded in the United States as a percentage of
the total number of shares traded in that stock on the TSE and the U.S. exchange during the sixmonth study period. The variable SpreadRatio is the ratio of quoted spreads on the U.S. exchange and the TSE. The variable MediumTrade is the ratio of proportions of shares traded in
the United States and on the TSE in medium-sized lots of 2,501 to 10,000 shares; Exchange is a
dummy variable that takes a value of one for the NYSE/AMEX-listed ¢rms and zero for the
Nasdaq-listed ¢rms; YearsListed is the number of years for which a ¢rm has been listed in
the United States; and Primary is the percentage of trading in the United States that occurs
on the primary market. We classify sample ¢rms in ¢ve industry groups. Mining, Manufacturing, Finance, and Utility are dummies corresponding to four of these groups.The ¢fth industry
group includes service ¢rms and the only trading ¢rm in the sample. Adjusted t-statistics based
on the heteroskedasticity-consistent covariance matrix as per White (1980) are in parentheses
below the coe⁄cients. Two-tailed signi¢cance at the 1, 5, and 10 percent levels is indicated by
nnn nn
, , and n, respectively.
Intercept
LMktCap
UsVol
SpreadRatio
(1)
(2)
(3)
(4)
(5)
(6)
1.84 n n n
(3.21)
0.25 n n n
( 4.17)
2.07 n n n
(3.27)
1.03 n n n
( 4.13)
0.49
( 0.52)
0.24 n n n
( 4.16)
3.09 n n n
(4.28)
0.55 n n
( 2.16)
0.75 n n n
(2.67)
0.25
( 0.25)
0.27 n n n
( 3.45)
3.06 n n n
(4.28)
0.57 n n
( 2.27)
0.71 n n
(2.41)
0.19
(0.45)
0.44
( 0.43)
0.31 n n n
( 3.39)
3.13 n n n
(4.32)
0.56 n n
( 2.25)
0.81 n n n
(2.64)
0.19
(0.71)
0.15 n
(1.72)
2.22
( 1.45)
0.37 n n n
( 4.46)
3.22 n n n
(4.88)
0.53 n n
( 2.29)
0.76 n n n
(2.59)
0.59 n n
(2.08)
0.15 n
(1.78)
2.15 n
(1.82)
3.15 n n
( 2.28)
0.30 n n n
( 3.74)
2.78 n n n
(4.70)
0.57 n n
( 2.42)
0.69 n n
(2.51)
0.64 n n
(2.51)
0.05
(0.60)
3.16 n n n
(3.36)
0.23
(1.43)
0.17
(0.84)
0.81
( 1.29)
0.17
( 0.74)
73.35
MediumTrade
Exchange
YearsListed
Primary
Mining
Manufacturing
Finance
Utility
Adjusted R2 (%)
65.39
70.98
70.67
71.75
72.54
argument that lower transaction costs in the United States imply a greater competitive threat to the TSE, resulting in a greater adjustment by the TSE prices in
response to the U.S. prices. Also, as the transaction costs in the United States
decline vis-a'-vis the TSE, there is more informed trading in the United States,
Cross-Border Listings and Price Discovery
571
and consequently more price discovery. Finally, the coe⁄cient of MediumTrade is
positive and statistically signi¢cant, implying that the greater the proportion of
U.S. shares traded in medium-sized lots relative to the TSE, the greater the price
discovery in the United States.20 However, if we use a broader de¢nition of medium-sized lots as 501 to 10,000 shares, the statistical signi¢cance of the positive
relationship is not robust across alternative regression models.
As we have used a logistic transformation of the dependent variable, it is di⁄cult to directly interpret the magnitude of the estimated coe⁄cients. To get an
idea of the impact of the main variables of interest on the relative contribution
of the U.S. exchange to price discovery, we focus on speci¢cation (2), which includes the main variables, and controls for the ¢rm size. First, we estimate the
U.S. contribution for the benchmark case, in which we set the value of each explanatory variable to its sample median. For the benchmark case, in which Market
capitalization is C$1,428 million, UsVol is 43.6 percent, SpreadRatio is 1.44, and
MediumTrade is 1.33, the U.S. contribution to price discovery is 34.2 percent.
Then, we increase one variable at a time by a quarter of its respective median
value above, holding the other three constant.We ¢nd that a 25 percent increase
in Market capitalization (from C$1,428 million to C$1,785 million) leads to a 1.2
percent decrease in the U.S. contribution to price discovery (from 34.2 percent
to 33.0 percent). Similarly, a 25 percent increase in UsVol, SpreadRatio, and MediumTrade leads to a 7.9 percent increase, a 4.3 percent decrease, and a 5.8 percent
increase, respectively, in the U.S. contribution.
D.2. OtherVariables
The coe⁄cient for the percentage of trading in the United States that occurs
on the primary exchange is positive and statistically signi¢cant. This is consistent with the argument that trading on the primary U.S. exchanges is more informative than trading on regional exchanges and ECNs.The coe⁄cient for ¢rm size
is negative and signi¢cant, suggesting that ceteris paribus, price discovery in the
United States relative to Canada is greater for smaller ¢rms.21 The dummy variable for di¡erentiating between the NYSE and Nasdaq is positive, and it is significant when we include Primary as an explanatory variable, which suggests that
the NYSE is more conducive to price discovery. This is consistent with the ¢ndings of past studies that the NYSE is more transparent and the prices on it are
informationally more e⁄cient. As expected, the coe⁄cient for the duration of
listing in the United States is positive. However, it is not consistently signi¢cant.
20
Similar to the ratio MediumTrade, we also measure the ratios SmallTrade and LargeTrade,
where small size refers to up to 2,500 shares, and large size refers to more than 10,000 shares.
We estimate a speci¢cation that includes all three ratios. The coe⁄cients of SmallTrade and
LargeTrade are estimated to be 0.06 each, and are statistically insigni¢cant at the 10 percent level (t-statistics of 0.32 and 1.21, respectively). The coe⁄cient of MediumTrade is 0.76,
and is statistically signi¢cant at the one percent level (t-statistics of 2.63).
21
We checked for the existence of any clientele patterns that could explain this result. However, an analysis of transaction size data and informal conversations with traders on Wall
Street did not suggest any clientele patterns that could explain this puzzling result.
572
The Journal of Finance
So, the evidence that the U.S contributes more to the price discovery of longer
listed ¢rms is weak.The coe⁄cients on the industry dummies are not signi¢cant.
D.3. Robustness of the Results of Cross-Sectional Analysis
We examine if the results of cross-sectional analysis are robust. We ¢rst see if
any outlier extremes are driving these results. Using alternative diagnostics
such as Studentized residuals and Cook’s distance, we identify three to ¢ve outliers and rerun the regressions without these outliers.We do not ¢nd any change
in results. We also do not ¢nd any change in results when we exclude the three
banks with a very low U.S. share of trading volume.
As indicated earlier, we include in the sample only those ¢rms with at least
2,000 trades during the six-month study period. We examine the robustness of
our results when we impose stricter criteria for inclusion. First, we exclude four
more ¢rms that have more than 2,000 but fewer than 2,500 trades on at least one
of the two exchanges. We do not ¢nd any qualitative change in results when we
perform regression analysis for this smaller sample of 58 ¢rms.We then impose a
yet stricter criterion, raising the cuto¡ point to 3,000 trades, and consequently
excluding nine ¢rms.There is no change in results for the variables of main interest when we perform regression analysis for this sample of 53 ¢rms. There is also
no change in results for the other variables, except that the exchange dummy is
no longer statistically signi¢cant. Thus, one should be cautious in interpreting
our result regarding NYSE’s greater conduciveness to price discovery.
We also estimate the speci¢cations in Table IV, using a Tobit model with the
nontransformed TseAdj as the dependent variable and the left and right censoring points at zero and one, respectively. We do not ¢nd any qualitative change in
results. Our results are also robust to the use of the Newey^West (1987) covariance matrix. To examine nonlinear dependence between the U.S. and the TSE
prices, we explore the possibility of employing the generalized autoregressive
conditional heteroskedasticity (GARCH) setup as in Karolyi (1995) and Racine
and Ackert (2000). We adopt a similar bivariate GARCH model, though we di¡er
in the inclusion of an error correction term and in the use of intraday data instead of daily data. We are unable to obtain convergence of the maximum likelihood estimates of model parameters, regardless of the conditional variance
process and the lag structure employed.We are not aware of any study that examines conditional heteroskedasticity with error correction terms for intraday
data, and it would be worth focusing on this issue in future research.
VI. Conclusions
In this study, we examine the contribution of the U.S. stock exchange to the
price discovery of non-U.S. stocks cross-listed in the United States. Using a sample of 62 Canadian stocks listed on the TSE that are also listed in the United
States on the NYSE, AMEX, or Nasdaq, we ¢nd that price adjustments due to
cross-market information £ows take place not only on the U.S. exchange but also
Cross-Border Listings and Price Discovery
573
on the TSE.Thus, the U.S. exchange also contributes to price discovery. For a majority of the stocks, the U.S. prices adjust more to the TSE prices than vice versa.
We also examine the factors that a¡ect the extent to which the U.S. exchange
contributes to price determination. Our regression results are consistent with
the argument that the greater the competition o¡ered by the United States, the
greater the U.S. contribution to price discovery. First, a larger U.S. share of trading suggests greater competition from the United States as well as greater informativeness of the U.S. trading relative to the TSE trading, and we ¢nd that the
adjustment by the TSE prices to the U.S. prices is more for stocks with a higher
U.S. share of total trading. Second, a smaller ratio of spreads on the U.S. exchange and the TSE implies a larger competitive threat from the United States,
as well as more informed trading in the United States, and we ¢nd that the TSE
share of total adjustment in prices is inversely related to the ratio of spreads on
the U.S. exchange and theTSE.Third, consistent with the argument that the medium-size trades have a higher information content than small- and large-size
trades, we ¢nd that the U.S. contribution to price discovery increases as the proportion of medium-size trades in the U.S. relative to the TSE increases.
It may be noted that our conclusions are based solely on a sample of Canadian
stocks that are cross-listed on the U.S. exchanges. These stocks trade as ‘‘ordinaries’’ and there is a perfect overlap of trading times in the two markets, which
makes them di¡erent from cross-listings from many other countries. It would be
useful to examine stocks from other countries as well in order to learn more
about price discovery for cross-listed stocks. In a contemporaneous study, Grammig, Melvin, and Schlag (2000) ¢nd signi¢cant feedback from the NYSE to Frankfurt for three German ADRs. As discussed in Pulatkonak and So¢anos (1999),
there is a signi¢cant variation in the U.S. share of trading volume for cross-listings from di¡erent countries. It would be interesting to analyze how the U.S. contribution to price discovery varies across di¡erent countries. We leave this
analysis for future research.
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