The Interactions between Price Discovery, Liquidityand Algorithmic Trading for US-Canadian

Cross-Listed Sharesy

Bart FrijnsIvan Indriawan*

Alireza Tourani-Rad

Auckland University of TechnologyAuckland, New Zealand

This version: September 2016

Abstract

This paper studies the interactions between price discovery, liquidity and algorithmic tradingfor a large sample of Canadian companies cross-listed on the New York Stock Exchange forthe period January 2004 to January 2011. Using daily measures of price discovery, wemodel the interactions between price discovery, relative trading volume, bid-ask spread, andalgorithmic trading activity using a structural vector autoregression to account for laggedand contemporaneous relations among the variables. We observe that over time, the U.S.market is gaining dominance in terms of price discovery. Improvements in liquidity increasea market�s contribution to price discovery, while at the same time, an increase in pricediscovery leads to better liquidity. We �nd that algorithmic trading activity is negativelyrelated to price discovery, which we attribute to the crowding out e¤ect as high-frequencytraders compete aggressively with one another for arbitrage opportunities.

JEL Classi�cation: C32, G15

Keywords: Market Microstructure; Price Discovery; Algorithmic Trading; Cross-Listings.

yWe thank Robert Webb, Yiuman Tse, Robert Fa¤, participants at the 2014 Auckland Finance Meeting, and seminar partic-

ipants at Auckland University of Technology, Massey University, Victoria University of Wellington for helpful comments and

suggestions.

�Corresponding Author. Ivan Indriawan, Department of Finance, Auckland University of Technology,Private Bag 92006, 1020 Auckland, New Zealand, Email: ivan.indriawan@aut.ac.nz.

1 Introduction

One of the central functions of �nancial markets is price discovery, the process by which

prices impound new information (Madhavan, 2000). Price discovery is important because it

re�ects how well a market gathers, interprets, and incorporates new information into prices.

It also emphasizes the importance of obtaining the most current information for decision

making, i.e. when market participants adjust their expectations on an asset�s fundamental

value and update their prices. When an asset is listed in multiple markets, price discovery

plays an even more important role as information can be incorporated into prices in any

market where the security is listed. In such a case, the market which incorporates new

information into prices fastest, has better information processing capacity than other markets

and leads in terms of price discovery. Thus, in a multi-market context, price discovery re�ects

one form of competitiveness of a market relative to others. Such a competitive advantage

may attract more investors to that market leading to an improvement in liquidity in that

market.

Given the importance of price discovery in a multi-market setting, it is crucial for ex-

changes to understand which market contributes more to price discovery, and which factors

lead to improving a market�s contribution to price discovery. Price discovery may shift from

one market to another over time for several reasons, one of them being liquidity. Admati

and P�eiderer (1988) explain that a liquid market attracts liquidity traders and that trading

will become more concentrated. A liquid market also attracts more informed traders because

such market is "thick" and informed traders can exploit their private information without

making large price concessions. At the same time, liquid markets may attract more ana-

lysts which further improves the informational environment. Overall, an increase in liquidity

could thus lead to an improvement in price discovery for that market. An interesting recent

development that can a¤ect price discovery is the upsurge in algorithmic trading (AT). AT

accelerates the speed at which traders can detect and exploit price discrepancies among se-

curities, thus it can potentially enhances price discovery. However, such improvement may

2

come at a cost to some other traders who are disadvantaged in terms of speed. As a conse-

quence, they may opt to trade in the other market, leading to a reduction in price discovery.

These arguments suggest that price discovery will not remain constant, but will vary over

time.

Currently, a clear understanding of how price discovery changes over time and what drives

such dynamics, is lacking. For instance, the questions of whether price discovery is persistent

over time, or whether the dynamics of price discovery is attributable to changes in market

liquidity or AT activity are still to be understood. In addition, whether improvements in price

discovery lead to more market liquidity is not known. To address these questions, studying

price discovery over a longer time period is necessary. Existing studies tend to examine

price discovery over relatively short periods.1 As such, these studies lean towards explaining

cross-sectional di¤erences in price discovery, rather than the dynamics of price discovery

and liquidity over time. The importance of studying price discovery over longer periods is

further emphasized by the changing �nancial market landscape as a result of, for example,

regulatory changes. One such change is the adoption of regulation National Market System

(Reg. NMS) in the U.S. Reg. NMS was intended to improve fairness in price execution,

and to improve the displaying of quotes and access to market data. Such regulation helps

create a more integrated market, and may therefore, a¤ect a market�s contribution to price

discovery.

In this paper, we assess the interactions between price discovery, liquidity and algorithmic

trading for a sample of Canadian stocks traded in Canada and the U.S. Our work contributes

to the literature in several ways. First, by computing daily measures of the Hasbrouck (1995)

information share (IS) and Gonzalo and Granger (1995) permanent-transitory (PT) decom-

position over a long period, we are able to explore trends and persistence in price discovery,

issues that have hardly been explored in a multi-market context. This also allows us to

1For instance, Pascual et al. (2006) study Spanish �rms cross-listed on the NYSE for the year 2000. Eunand Sabherwal (2003) study Canadian �rms cross-listed on the NYSE from February to July 1998, whileChen and Choi (2012) use data from January 1998 to December 2000.

3

examine whether the adoption of Reg. NMS in the U.S. a¤ected the dynamics of price dis-

covery. Second, we assess how measures of price discovery, liquidity, and AT activity interact

with each other over a longer period. Our analyses shed light on what drives price discovery

between markets (i.e. whether changes in relative liquidity and AT activity a¤ect the con-

tribution to price discovery of a market), as well as the importance of price discovery for a

market (i.e. whether an improvement in price discovery a¤ects liquidity and AT activity).2

These �ndings are valuable for exchanges as they indicate what areas they would need to

focus on to improve price discovery. Third, from an empirical perspective, we model the

interactions between price discovery measures, liquidity, and AT activity using a structural

vector autoregression (SVAR). In contrast to the reduced-form Granger causality tests, which

measure predictive relationships, the SVAR allows for the identi�cation of contemporaneous

interactions among the variables, while at the same time, taking into account the possible

endogeneity among them. This is done using the identi�cation through heteroskedasticity

approach developed by Rigobon (2003), which was recently implemented by Chaboud et al.

(2014).3

Applying our model to Canadian stocks listed on the Toronto Stock Exchange (TSX)

and cross-listed on the New York Stock Exchange (NYSE) over the period January 2004 to

January 2011, we document several important �ndings. First, we observe that over time,

the U.S. market is gaining in terms of price discovery. Second, we �nd that several measures

of liquidity are causally related to price discovery. Improvements in liquidity (an increase

2The analysis of the impact of AT activity on price discovery is especially relevant given that AT activityproliferated in the U.S. and Canada at di¤erent times. Hence, price discovery between the two markets mayhave changed over time. In the U.S., HFT, a subset of AT, became especially popular in 2007 and 2008(Rogow, 2009). By 2009, 26 HFTs participate in 68.5% of the dollar volume traded on average (Brogaard,2010). Gibbs (2007) explains that U.S. players will continue to dominate the market because while Canadiantraders ramp up their algorithmic capabilities, they tend to partner with U.S. broker-dealers to leverage theiro¤erings.

3The iden�tication through heteroskedasticity approach was recently applied in several �nance studies.For example, Chaboud et al. (2014) use the approach to identify the contemporaneous causal impact of AT ontriangular arbitrage opportunities. Badshah et al. (2013) use the same approach to assess contemporaneousspillover e¤ects among equity, gold, and exchange rate implied volatility indices. Ehrmann et al. (2011)use a similar model to assess international transmission of shocks between money, bond, equity and foreignexchange markets.

4

in trading volume and a decrease in e¤ective spread) increase an exchange�s contribution to

price discovery, implying that the market which provides better liquidity will become more

important in terms of price discovery. This impact is incorporated instantaneously (within

the same day) as well as with a protracted lag (after several days). Conversely, we �nd

that an increase in price discovery leads to improved liquidity, indicating that the market

which leads in terms of price discovery attracts more liquidity traders. Third, we �nd that in

the case of cross-listed stocks, algorithmic trading activity negatively a¤ects price discovery.

This is in line with the recent literature on negative externalities of high-frequency trading

(HFT). As high-frequency traders compete aggressively with one another to create latency

arbitrage opportunity, they cause a crowding-out e¤ect. As a result, HFT improves the

price discovery for the faster traders, but pushes away the slower traders to another market.

Finally, we �nd that the dynamic relations between price discovery, liquidity and AT activity

persist even after we account for the adoption of Reg. NMS in the U.S. Overall, our �ndings

highlight the importance of liquidity for exchanges in order to improve price discovery, as

well as the importance of price discovery to attract more investors. The impact of HFT on

�nancial markets should be of interest to exchange o¢ cials because while HFT may improve

price discovery for the faster traders, the crowding out e¤ect may hinder the price discovery

of the market as a whole.

The rest of this paper is structured as follows. Section 2 discusses existing studies on the

determinants of price discovery and how our work contributes in this �eld. In Section 3, we

present the data and report descriptive statistics, as well as our measures of liquidity and

AT activity. We discuss our measures for price discovery as well as the models for assessing

dynamics in price discovery in Section 4. In Section 5, we report our �ndings. Section 6

concludes.

5

2 Literature Review

A market�s contribution to price discovery may change over time for various reasons. In

this section, we �rst discuss factors that may contribute to the change in price discovery

over time. We then show how these factors can be modeled to assess the dynamics of price

discovery in a dual-market scenario.

There is a growing literature examining price discovery of cross-listed stocks. The major-

ity of it focuses on the determinants of price discovery, with liquidity playing an important

role. As discussed in Admati and P�eiderer (1988), one of the motives for trade in �nancial

markets is liquidity. Given that investors have discretion over where and when to trade, they

have the tendency to trade in a cheaper and more liquid market, i.e. when the market is

"thick" and their trading has little e¤ect on prices. Such a market may attract more traders,

leading to information clustering and a shift in price discovery.

One type of liquidity, which is important for price discovery, is trading volume. It is often

observed that large trades have persistent price impact, with trade prices lower after large

sales and higher after large purchases. One possible explanation is that increased volume

re�ects a greater likelihood that demand for a stock comes from informed traders (Stickel

and Verrechia, 1994). Consequently, investors interpret high volume as an indication that

the demand underlying a price change is informative, and therefore should get incorporated

into prices. Consistent with this view, Hasbrouck (1995) �nds a positive and statistically

signi�cant relation between the relative trading volume of a sample of 30 Dow stocks and

the NYSE�s contribution to price discovery. He explains that markets di¤er in their ability

to process information such as that coming from trades. A market which has an informative

trading process can shed light on the interpretation of public information, and therefore,

leads in terms of price discovery. Similarly, Pascual et al. (2006) �nd that a market�s

relative contribution to the price discovery process is related to its trading activity. Using

Spanish stocks that are cross-listed on the NYSE, they �nd that the Spanish Stock Exchange

leads in terms of price discovery due to its large trading activity relative to the NYSE as the

6

satellite market.

Another important determinant of price discovery is the relative bid-ask spread. The

trading cost hypothesis predicts that the market with the lower trading costs will react more

quickly to new information, as information-based trades are executed where they produce the

highest net pro�t. As a result, a market�s contribution to price discovery tend to be inversely

related to bid-ask spread. Consistent with this view, Fleming et al. (1996) document that

index future and option price changes lead price discovery in the stock market because the

costs of trading in the index futures and options markets are substantially lower than in

the index stocks. Harris et al. (2002) compare the bid-ask spread and a measure of price

discovery for the years 1988, 1992, and 1995 for 30 Dow stocks. They �nd that the NYSE�s

contribution to price discovery relative to the regional exchanges increases when its spreads

relative to the regional markets decline. With regard to the U.S. and Canadian markets,

Eun and Sabherwal (2003) explain that the lower spread on U.S. exchanges relative to the

TSX represents a competitive threat faced by the TSX liquidity providers from their U.S.

counterpart. The TSX liquidity providers who face more competition from U.S. liquidity

providers are likely to be more responsive to U.S. prices. Chen and Choi (2012) assess

di¤erential private information for Canadian stocks traded in Canada and the U.S. They

document that the TSX has more informed trades and a larger information share. This

cross-border information imbalance is associated with small but positive price premiums in

New York. In addition, Frijns et al. (2015b) �nd that U.S. market�s contribution to price

discovery increases during public news announcements as the bid-ask spread of the U.S.

relative to the Canadian markets decreases.

In addition to liquidity, studies have looked at how algorithmic trading activity a¤ects

stock markets. Earlier studies document positive aspects of AT on price discovery, partic-

ularly on the informativeness of quotes relative to trades. For example, Hendershott et al.

(2011) assess the impact of quote automation in the NYSE from December 2002 through

July 2003. They �nd that for large stocks in particular, AT enhances the informativeness

7

of quotes by more quickly resetting their quotes after news arrivals, but reduces the trade-

related price discovery. Riordan and Storkenmaier (2012) use Deutsche Boerse data from

February to June 2007 to study the e¤ect of a latency reduction on price discovery through

the introduction of Xetra 8.0 trading platform upgrade. They �nd that adverse selection has

reduced dramatically while the contribution of quotes to price discovery has doubled after

the upgrade. Hasbrouck and Saar (2013) use NASDAQ TotalView-ITCH data in the last

quarter of 2007 and �nd that high-frequency trading improves liquidity and price e¢ ciency

of the limit order book.

More recent studies, however, highlight some negative aspects of AT on the market as

a whole. Stein (2009) explains that recent technological advancements resulted in stock

markets being dominated by sophisticated professionals using extensive quantitative �nan-

cial models. Consequently, aggressive investment strategies by these traders have led to

a crowding out e¤ect that pushes prices away from their fundamental values, i.e. prices

becoming less informative. Gai et al. (2014) explain that since U.S. stock markets impose

price, display, and time priority, it is the relative speed, not the absolute speed, that matters.

This induces economic incentives not only to invest in speed but also to slow down other

traders, which is in line with the "quote stu¢ ng" argument of Egginton et al. (2016), where

high-frequency traders submit a profuse number of orders to generate market congestion.

Speci�cally, by submitting large numbers of orders that are canceled very quickly, HFT may

create exploitable latency arbitrage opportunities. Therefore, in contrast to the common

notion that competition improves price e¢ ciency, they �nd that competition through high-

frequency trading limits e¢ ciency and in�ict negative congestion externalities on markets as

a whole.4

It is important to note that in our study, we measure price discovery as a relative term

4Biais et al. (2015) �nd that the improvement in trading speed can either increase or decrease socialwelfare. In line with this argument, Pagnotta and Philippon (2012) explain that the impact of latencyon social welfare depends on the initial level of speed. Particularly, allowing venues to compete on speedimproves welfare if the default speed is relatively low, but decreases welfare once the default speed reachesa certain threshold.

8

between two di¤erent markets. It di¤ers from studies which assess quote and trade informa-

tiveness within a single market (e.g. Hendershott et al., 2011; Riordan and Storkenmaier,

2012; Hasbrouck and Saar, 2013) or those which assess the relative contribution of the faster

traders relative to other traders within the same market (e.g. Brogaard et al., 2015). This is

because in the case of cross-listed stocks, traders have options where to execute their orders

and make use of their information advantage. Brogaard et al. (2015) acknowledge this fea-

ture of cross-listed stocks when comparing the role of HFT and non-HFT on price discovery

in Canada. In their study, they speci�cally select TSX60 stocks which are not cross-listed

in the U.S. because they are unable to precisely measure trading occuring o¤ Canadian ex-

changes. They also note that "it is possible that HFTs�speed and information processing

abilities discourage non-HFTs from submitting limit orders." This implies that while price

discovery for faster traders may have improved due to high-frequency trading, but if there

are more traders getting pushed away from the market due to speed disadvantage, the overall

impact of AT on price discovery of a market could be negative.

While there are currently no studies investigating how AT activity a¤ects price discovery

across markets, there are a few studies which have looked at how liquidity a¤ects price

discovery in a multi-market setting. However, these studies are predominantly cross-sectional

studies. Harris et al. (2002) study price discovery using a sample of 30 Dow stocks for the

years 1988, 1992, and 1995. They calculate di¤erences in price discovery from one year to the

next, and relate these di¤erences to changes in the relative spreads between the NYSE and

the U.S. regional exchanges. Their �ndings suggest that higher NYSE spreads reduce the

NYSE contribution to price discovery. Frijns et al. (2010) measure price discovery annually

for four Australian stocks cross-listed in New Zealand and �ve New Zealand stocks cross-

listed in Australia from 2002 to 2007. They regress Hasbrouck (1995) information share on

several variables such as the log number of trades in each market, the percentage bid-ask

spread in each market, and the log of the market capitalization. They indicate that the

growth in the importance of the Australian market is positively related to the growth in the

9

size of the �rm and negatively related to the size of the percentage spread in the Australian

market. Similarly, Frijns et al. (2015a) measure price discovery annually from 1996 to 2011

for Canadian stocks which are cross-listed on the NYSE, NASDAQ, and AMEX. Their study

examines, in particular, the issue of endogeneity between price discovery and measures of

liquidity and market quality.

Our work extends the above studies by focusing on the dynamics of price discovery.

Speci�cally, we assess, at a daily frequency, how measures of price discovery, trading volume,

bid-ask spread, and AT activity of the U.S. relative to the Canadian markets interact with

each other over longer periods. We acknowledge that these variables may be determined

simultaneously. For instance, improvements in liquidity and AT activity may lead to a

higher contribution to price discovery, while at the same time, higher price discovery may

lead to improvements in liquidity and AT activity. To resolve this endogeneity problem,

we employ a structural VAR. We follow Chaboud et al. (2014) and account for possible

contemporaneous interactions among the VAR variables using the identi�cation through

heteroskedasticity approach originally developed by Rigobon (2003).

3 Data and Descriptive Statistics

Our sample consists of Canadian stocks that are traded on the TSX and NYSE from

January 2004 through January 2011. The end of the sample is chosen to avoid confounding

e¤ects from the new Order Protection Rule in Canada which became e¤ective on February 1,

2011 (see Clark, 2011). Data are collected from the Thomson Reuters Tick History (TRTH)

database maintained by Securities Industry Research Centre of Asia-Paci�c. These Canadian

stocks are traded in both markets throughout the sample period, had no stock splits, and

have data available from TRTH. In total, there are 38 stocks which meet these criteria.5

5We also conduct analysis using a more stringent screening by imposing a minimum message countfollowing the approach of Hasbrouck and Saar (2013). A �rm is excluded from the sample if more than10% of the 10-minute intervals have fewer than 250 messages (trade and quote). This screening reduces thenumber of stocks in the sample to 28. As the results are very similar to those discussed in Section 5 and

10

We collect intraday data on trade price, trade volume, and the bid and ask quotes at

a second and at a millisecond frequency. We use the data at a one-second frequency to

compute price discovery measures and construct liquidity measures and use tick-level data

sampled at a millisecond frequency to construct the AT proxy.6 The tick-level data contains

all activities observed at the top of the order book. This includes transactions and revisions

in bid and ask prices and depths. We omit the �rst and last �ve minutes of the trading day

to avoid capturing any e¤ects from the open and close of the market. For the U.S. market,

we use the national best bid and o¤er (NBBO) quotes and for the Canadian market, we use

quotes posted at the TSX.7 Following Grammig et al. (2005), we use midpoints of quotes

as these are less a¤ected by bid-ask bounce that is normally observed in transaction prices.

We also obtain the intraday Canadian - U.S. Dollar exchange rate quotes from TRTH and

use the midpoint to convert prices into U.S. dollars. This is to facilitate the speci�cation of

the error-term and ensure the comparability of prices between the two markets.

3.1 Liquidity Measures and Algorithmic Trading Proxy

As measures of liquidity, we use the trading volume and the e¤ective spread. To make

inferences about the relations between price discovery and measures of liquidity from both

markets, we employ the trading volume and e¤ective spread of the U.S. market relative to

the Canadian market. Relative trading volume represents the stock�s trading activity and is

de�ned as:

Ratio_V olj =V olUSj

V olUSj + V olCANj

; (1)

presented in Tables 4 - 10, we do not report them, but they are available upon request.6Hasbrouck (1995, 2003) indicates that more powerful tests of market e¢ ciency can be carried out by

sampling at very high frequencies to reduce the contemporaneous correlation in the reduced form residualsbetween markets that is created by time aggregation. Hasbrouck (2003) uses a sampling frequency of 1second, which produces a low contemporaneous residual correlation and a narrow range of informationshares. Similarly, Hendershott and Jones (2005) also sample at 1 second and �nd low residual correlationsin their price discovery study.

7After 2009, the Canadian market fragments considerably. In Section 5.4, we test the robustness of ourresults by taking into account this fragmentation.

11

where V olUSj and V olCANj are the average U.S. and Canadian trading volume on day j,

respectively. The second liquidity measure is the relative e¤ective spread, which measures

trading costs. Hendershott et al. (2011) explain that e¤ective spreads are more meaningful

for the NYSE than quoted spreads because specialists and �oor brokers are sometimes willing

to trade at prices within the quoted bid and ask prices. The e¤ective spread is measured as:

Espreadj =1

x

PTt=12Dt(pt �mt)=mt; (2)

where Dt is a trade indicator which is equal to +1 for buyer-initiated trades and -1 for seller-

initiated trades. We follow the standard trade signing approach of Lee and Ready (1991) and

use contemporaneous quotes to sign trades, following Bessembinder (2003). pt and mt are

the trade price and quote midpoint prevailing at time t, respectively. When aggregating over

a trading day j, we average the e¤ective spreads over x trades. Subsequently, the relative

e¤ective spread is computed as:

Ratio_Espreadj =EspreadUSj

EspreadUSj + EspreadCANj

: (3)

For our AT proxy, we use the negative trading volume in USD100 divided by the total

message tra¢ c number. This is based on the AT measure of Hendershott et al. (2011) and

implemented by Boehmer et al. (2015). The proxy can be expressed as:

AT ij =�(Dollar_V olij)=100Total_messagesij

; (4)

where AT ij is the AT activity for market i on day j, Dollar_V ol is the total dollar trading

volume, and Total_messages is the sum of the number of trade observations and quote

changes.8 This ratio represents the negative dollar volume associated with each trade or

8The total messages used in our study di¤er from the one used by Hendershott et al. (2011), who haveaccess to order-level messages. For our sample, we use observations on the exchange�s best quotes and trades,rather than all order-related messages. Boehmer et al. (2015) explain that this should not be a problembecause the HFT strategies mentioned in the SEC 2010 concept release involve mostly activity at the topof the book, rather than behind it. They also conducted formal comparison between AT measures based on

12

quote update. An increase in this measure re�ects an increase in algorithmic trading activity.

Hendershott et al. (2011) explain that normalization in this case is important because there

may be an increase in trading volume over the same interval. Without normalization, a raw

message tra¢ c measure may just capture the increase in trading rather than the change in the

nature of trading. However, it is important to note that since this AT proxy draws inferences

from total message tra¢ cs, it makes little distinction between high-frequency traders and

slower traders with automated trading systems.9 Since AT ij is negative, relative AT activity

is measured as

Ratio_ATj =ATCANj

ATUSj + ATCANj

: (5)

We calculate the liquidity measures and AT proxy for the 38 cross-listed stocks in our

sample. Table 1 reports the average trading volume, e¤ective spread, number of messages,

and AT activity in both markets, as well as their values in the U.S. relative to Canada.

INSERT TABLE 1 HERE

On average, daily trading volume is higher in the U.S., 1,463,000 shares traded compared

with 1,368,000 shares in Canada. This results in a relative trading volume of 52% for the U.S.

market, suggesting that trading activity is slightly higher in the U.S. relative to Canada. In

terms of e¤ective spread, the U.S. market has a lower spread, 8.5 bps compared to 10.5 bps

in Canada. Relative e¤ective spread for the U.S. market is 45%, indicating that, on average,

trading costs in the U.S. are lower than in Canada. The number of messages per 10-minute

period is similar in both markets. In the U.S., there are 1,159 messages every 10 minutes

and 1,107 messages in Canada, leading to a ratio of 51% for the U.S. market. Algorithmic

order-level data used by Hendershott et al. (2011) and AT measures based on best quotes and trades, and�nd that both measures are highly correlated.

9As alternative AT proxies, we use quote-to-trade ratio as well as ratio of limit order duration (see e.g.Hagstromer and Norden, 2013; Skjeltorp et al., 2015). These proxies re�ect AT activities as strategies usedby algorithmic traders have contributed to a huge increase in the amount of order tra¢ c relative to tradeexecutions, and a decrease in duration between subsequent quote changes. Using either proxies of AT, we�nd similar results.

13

trading activity, on average, is higher (less negative) in the U.S. compared to Canada with a

value of -10.7 and -17.5, respectively. This leads to an AT ratio of 62% for the U.S. relative

to Canada.

One of the key variables in our analysis is the AT proxy. To ensure that this proxy

captures algorithmic trading activity, we compare the distribution of message tra¢ c in Jan-

uary 2004 and in January 2011. Table 2 reports statistics on the message tra¢ cs in the

U.S. and Canada. It reports the daily averages for the number of messages, the number

of quote observations, the number of trades, the quote-to-trade ratio, and the limit order

duration (in seconds), each with a percentage change over the seven year period. We make

several important observations. First, total messages grow exponentially by 1,990% in the

U.S. and by 2,614% in Canada. This growth is consistent with HFT playing an increas-

ingly important role in both markets. Second, we observe that most of the growth in total

messages comes from quotes rather than trades, particularly in Canada. This is re�ected in

the increase in quote-to-trade ratio over the two sample periods by 34% in the U.S., and by

441% in Canada. Third, limit order duration has decreased substantially in both markets,

with the decrease being greater in Canada than in the U.S. Based on these observations, we

conclude that the revision in quotes are more frequent than trades, which is consistent with

Hasbrouck and Saar (2013) who associate high-frequency traders with fast order submissions

and cancellations.

INSERT TABLE 2 HERE

Figure 1 plots the 20-day moving average of trading volume, e¤ective spread, and AT

activity of the U.S., Canada and their relative values. Panel A shows that relative trading

volume, Ratio_V ol, has an upward trend. The increase is notable from 2004 to 2008 prior to

the Global Financial Crisis when U.S. trading volume peaked. The trend steadied between

2009 and 2010, but declined in early 2011.

14

INSERT FIGURE 1 HERE

Panel B plots the relative e¤ective spread, Ratio_Espread over the years. Throughout

the entire sample period, the relative e¤ective spread is lower than 0.50, suggesting that

trading costs in the U.S. are lower than in Canada during our sample period. However,

spreads in both markets have converged over time. Between 2005 to early 2008, the relative

spread was declining due to lower costs of trading in Canada. The spreads in both markets

spiked in the middle of 2008 due to the �nancial crisis. From 2009 onwards, the relative

spread increased due to further lowering of trading costs in Canada.

Panel C plots AT activity of the U.S. relative to Canada. The plot for the Ratio_AT

shows that the trend has been downward sloping over the years. This can be attributed

to the Canadian market increasing its algorithmic trading activity over the recent years,

especially after the emergence of alternative trading systems in mid-2007 to compete with

the TSX (Clark, 2011). Where the U.S. used to report higher AT activity than Canada (ratio

of greater than 0.5) before 2008, it has declined to the point where Canadian AT activity is

higher relative to the U.S. from 2009 onwards.

4 Methodology

4.1 Measuring Price Discovery

The study of price discovery relies on the assumption that when a security is cross-

listed in multiple markets, prices in these markets share a common trend, i.e., prices are

cointegrated. Cointegration implies that prices can deviate from each other in the short-run

due to frictions, but are bound together in the long-run. In our dual-market case, such a

relation can be presented by two I(1) price series, yUSt and yCANt being cointegrated with a

cointegrating vector �0 = ( 1 �1 ). The Engle-Granger Representation Theorem states that

a cointegrated system can be expressed as an error-correction model. Hence, the stationary

15

process, �0yt = yUSt � yCANt , can be applied as an error-correction term for the following

Vector Error-Correction Model (VECM),

�yt = c+ ��0yt�1 +

NXn=1

�n�yt�1 + �t: (6)

where �yt is the (2� 1) vector of log returns, c is a vector of constants, � is a (2� 1) vector

that measures the speed of adjustment to the error-correction term (i.e. � =

0B@ �US

�CAN

1CA),�n are (2 � 2) matrices of AR coe¢ cients, and �t is a (2 � 1) vector of innovations. The

VECM has two parts: the �rst part, �0yt�1; represents the long-run equilibrium between the

price series. The second part,NPn=1

�n�yt�1; represents the short-term dynamics induced by

market imperfections.

We use the above VECM to compute the price discovery measures between two markets.

Our price discovery measures are the Gonzalo and Granger (1995) permanent�transitory

(PT) decomposition, and the Hasbrouck (1995) information share (IS). Both are directly

related and both measures are derived from the VECM.

The PT measure is concerned with permanent shocks that result in a disequilibrium as

markets process news at di¤erent speeds. It measures each market�s contribution to the

common factor, where the contribution is a function of the speed of adjustment coe¢ cients,

�. Hence, the PT can be computed using the following equation,

PTUS =�CAN

(�CAN + j�USj) ; (7)

where �US is negative, and �CAN is positive given our de�nition of �0 = ( 1 �1 ). This ratio

provides an indication of the degree of dominance of one market over the other market. A

higher value of this ratio re�ects a greater feedback or contribution from the US. Therefore,

a PTUS of zero implies that the NYSE does not contribute to the price discovery of the

stocks, whereas a PTUS greater than zero implies feedback from the NYSE to the TSX.

16

PTCAN can be computed as 1� PTUS.

The IS measures the proportion of variance contributed by one market with respect to

the variance of the innovations in the common e¢ cient price. To assess this, note that we

can rewrite Equation (6) as a vector moving average (Wold representation):

�yt = (L)et; (8)

where (L) is a matrix polynomial in the lag operator ((L) = 1 + 1L + 2L2 + � � � ).

Following the Beveridge and Nelson (1981) decomposition, which states that every (ma-

trix) polynomial has permanent and transitory structure, we can write Equation (8) in its

integrated form as:

yt = (1)Pt

s=1es +�(L)et: (9)

where (1) is the sum of all moving average coe¢ cients, and measures the long-run impact

of an innovation to the level of prices. Since prices are cointegrated, �0yt is a stationary

process, which implies that �0(1) = 0, i.e. the long-run impact is the same for all prices. If

we denote = ( US CAN ) as the common row vector in (1), Equation (9) becomes:

yt = � Pt

s=1es +�(L)et: (10)

The increment et in Equation (10) is the component of the price change that is perma-

nently impounded into the price and is due to new information. Hasbrouck (1995) decom-

poses the variance of the common factor innovations, i.e., var( et) = 0. The informa-

tion share of a market is de�ned as the proportion of variance in the common factor that is

attributable to innovations in that market. Since Hasbrouck (1995) uses the Cholesky factor-

ization of = MM 0 to handle contemporaneous correlation, where M is a lower triangular

matrix, the information share of market i is de�ned as:

17

Si =([ M ]i)

2

( 0): (11)

The Cholesky decomposition of orthogonalizes the innovation terms and assigns all

common variance to one market. To account for multiple markets, Hasbrouck (1995) suggests

that di¤erent orderings of the innovation terms be used so that upper and lower information

share bounds can be computed. Speci�cally, we reverse the order of the (1) as well as M

and recompute Equation (11). The midpoint of these bounds is the IS value.

4.2 Modelling Price Discovery Dynamics

Section 2 indicates that factors such as trading volume, bid-ask spread, and algorithmic

trading activity may be related to price discovery. If such relations exist, the ratio of those

variables in one market relative to another may a¤ect the dynamics of price discovery between

the two markets. To examine such dynamics, we use a VAR to model the interactions

between price discovery measures, trading volume, bid-ask spread, and AT activity. We

estimate both a reduced-form and a structural VAR (SVAR) that uses the identi�cation

through heteroskedasticiy approach developed by Rigobon (2003). Doing so, we are able to

assess lagged and contemporaneous interactions among the VAR variables. In this section,

we focus on the mechanics of the identi�cation through heteroskedasticity methodology.

Further details on the methodology are provided in Appendix A.

Given that price discovery measures, trading volume, bid-ask spread, and AT activity may

have contemporaneous e¤ects on each other, and assuming these variables exhibit persistence,

the dynamics of price discovery can be expressed by the following SVAR:

A�Yt = c+

KXk=1

�k�Yt�k + "t; (12)

where �Yt is the (4 � 1) vector of changes in variables, i.e. �Yt = (�ISt, �Ratio_V olt,

�Ratio_Espreadt, �Ratio_ATt)0, �k is a (4�4)matrix of coe¢ cients for the autoregressive

18

terms for lag k, and "t is a vector of error terms. Matrix A captures the structural parameters

and is normalized such that all diagonal elements are equal to 1, and its o¤-diagonal elements

capture the contemporaneous interactions between the variables, i.e.,

A =

0BBBBBBB@

1 a12 a13 a14

a21 1 a23 a24

a31 a32 1 a34

a41 a42 a43 1

1CCCCCCCA:

The o¤-diagonal elements capture the interactions among the variables. For instance,

a12; a13; a14 represent the contemporaneous impact of �Ratio_V ol; �Ratio_Espread and

�Ratio_AT on �IS, while a21; a31; a41 represent the contemporaneous impact of �IS on

�Ratio_V ol; �Ratio_Espread and �Ratio_AT .

Since the contemporaneous relations among the VAR variables are not equal, A is not

symmetric. Consequently, the parameters in A cannot be obtained using OLS. To overcome

this issue, we estimate Equation (12) using the identi�cation through heteroskedasticity

methodology. This approach starts with transforming Equation (12) into its reduced-form

below:

�Yt = A�1c+ A�1KXk=1

�k ��Yt�k + A�1"t

�Yt = ~c+

KXk=1

~�k ��Yt�k + ~"t; (13)

where the residuals ~"t from the reduced-form VAR are related to the residuals "t from the

SVAR through the inverse of A. Here, matrix ~�k allows us to test for Granger causality

among the VAR variables. Since Equation (13) can be estimated by OLS, it serves as the

basis for the heteroskedasticity identi�cation scheme to obtain the parameters in A.

19

5 Empirical Findings

In this section, we begin by showing how price discovery measures for Canadian cross-

listed stocks vary over time. We then present the Granger causality results from the reduced-

form VAR and the results from the structural VAR as formal approaches to assess the

dynamics of price discovery. Finally, we examine whether the adoption of the Reg. NMS

a¤ected the dynamics of price discovery between the U.S. and Canadian markets.

5.1 Price Discovery Over Time

To obtain price discovery estimates over time, the IS and PT are estimated daily for each

�rm.10 The daily estimation eliminates the overnight price jumps which typically generate

excessive noise. Throughout this paper, our price discovery estimates are based on the U.S.

portion of IS and PT. The VECM in Equation (6) is estimated by applying OLS with optimal

lag length suggested by the Schwartz Information Criterion.

INSERT TABLE 3 HERE.

Table 3 reports the descriptive statistics of the PT and IS. Panel A reports the statistics

for the levels. During the entire sample, the average (median) IS for the U.S. market is 52.2%

(55.4%), while for PT, it is 59.0% (60.8%). These �gures indicate that the U.S. contribution

to price discovery tends to be higher than the Canadian contribution. We observe a wide

range in price discovery measures, from 18.5% to 80.8%, and from 29.0% to 84.7% at the

5th and 95th percentile for IS and PT, respectively. Both measures are negatively skewed,

but do not display excess kurtosis. The autocorrelation (AC) for IS and PT are 0.674 and

10Prior to estimating the IS and PT, we conduct the usual procedures of unit root and cointegration tests.First, we perform non-stationarity tests using the Augmented-Dickey Fuller test using SIC to select optimallag length. For all stocks, we cannot reject the presence of a unit root. Subsequently, we conduct Johansen�s(1988) test for cointegration. In all tests, we reject the null of no cointegration in favour of the alternativeof one cointegrating vector. Since the price series in our sample satisfy both conditions, we conclude thateach pair of our sample stocks is cointegrated.

20

0.667 for the �rst lags, and decrease with increasing lags, hence indicating autoregressive

processes. The Augmented Dickey Fuller (ADF) test statistics are insigni�cant, suggesting

that unit roots are present in the IS and PT series.

Panel B reports summary statistics for the �rst di¤erences. The mean values of the

�rst di¤erences are close to zero, although there is quite some variation on a daily basis as

can be seen from the range of the 5th and 95th percentile and the standard deviation. The

series have skewness values close to zero with excess kurtosis, suggesting that observations

occur predominantly around the mean. We do not observe the �rst di¤erences to be serially

correlated as the AC quickly drops to zero after one lag. Furthermore, the ADF test statistics

are highly signi�cant, con�rming that the �rst di¤erence series for IS and PT are stationary.

In Figure 2, we plot IS and PT from January 2004 to January 2011, based on a 20-day

moving average for the 38 stocks in our sample. The IS and PT track each other closely with

the PT being consistently higher than the IS. According to both measures, price discovery

for the U.S. is lower than 50% prior to 2007. This is consistent with earlier studies which

show that the home market for the Canadian-U.S. cross-listed stocks dominate in terms of

price discovery.11 We observe a sharp increase in price discovery around the year 2007. From

2007 onwards, the U.S. market gains dominance with IS and PT greater than 50%. The IS

and PT reach around 80% in 2010. One possible explanation for the increase in the U.S.�s

contribution to price discovery is the implementation of the Reg. NMS which started in 2006

and was �nalised in October 2007, an explanation we examine in Section 5.5.

INSERT FIGURE 2 HERE.

Apart from the slight decrease in IS and PT in late 2008, the increasing trend in price

discovery measures does not seem to be substantially a¤ected by the Global Financial Cri-

sis. Overall, Figure 2 illustrates that price discovery, as measured by IS and PT, exhibits

11See for example, Eun and Sabherwal (2003) Chen and Choi (2012).

21

persistence over time. Once price discovery is gained by a particular market, it tends to stay

in that market. The next section analyzes what drives this dynamics in price discovery.

5.2 Reduced-Form VAR Results

We investigate what drives changes in price discovery over time, i.e. how measures

of price discovery, liquidity, and AT activity interact with each other. To gain prelim-

inary insight about the relation between these measures, we test for correlation among

them. Table 4 presents the correlation matrix among the VAR variables. Correlation

between �IS and �PT is 0.906, which shows the high level of similarity between both

measures. We observe that �Ratio_V ol is positively correlated with �IS and �PT . Both

�Ratio_Espread and �Ratio_AT are negatively correlated with �IS and �PT . Further-

more, �Ratio_AT is also negatively correlated with �Ratio_V ol and positively correlated

with �Ratio_Espread.

INSERT TABLE 4 HERE

To assess the strength and statistical signi�cance of these relations, we start by estimating

the reduced-formVAR of Equation (13) for 38 �rms. The sums of the 5-day lagged coe¢ cients

are reported in Table 5, and the p-values from the Granger causality tests are reported in

parentheses.

Panel A and B of Table 5 report the results of the VAR for the IS and PT, respectively.

The second column in each panel presents the factors which a¤ect the changes in price

discovery measures. We observe that �IS (�PT ) is positively related to the lagged values

of �Ratio_V ol with a coe¢ cient of 0.166 (0.140). A positive change in relative trading

volume between the U.S. and Canada over the previous �ve days leads to a positive change

in IS (PT) in the following day. This is in line with the argument of Stickel and Verrechia

(1994) that high volume indicates that the demand underlying a price change is informative,

and therefore should be incorporated into prices.

22

INSERT TABLE 5 HERE

We also observe that�IS (�PT ) is negatively related to the lagged values of�Ratio_Espread

with a coe¢ cient of -0.144 (-0.172). A decrease in relative e¤ective spread over the past �ve

days leads to a positive change in IS (PT) on the following day. This indicates that as trading

costs decrease, price discovery tends to increase, indicating intermarket competition between

liquidity providers. This is consistent with the cross-sectional �ndings of Eun and Sabherwal

(2003) who suggest that a lower spread in one market represents a competitive threat faced

by liquidity providers in another market. In this case, Canadian liquidity providers become

more responsive to U.S. prices.

The impact of �Ratio_AT on �IS (�PT ) is negative and signi�cant with a coe¢ cient

of -0.057 (-0.007). This implies an increase of AT activity in the U.S. relative to Canada

leads to a lower contribution of the U.S. market to price discovery. We interpret this �nding

as increased algorithmic trading activity limits e¢ ciency and in�icts negative congestion

externalities on �nancial markets. High-frequency traders compete aggressively by gener-

ating market congestion to slow down one another and create exploitable latency arbitrage

opportunities (Gai et al., 2014; Egginton et al., 2016). In the process, they cause a crowd-

ing out e¤ect which pushes away investors who are disadvantaged in terms of speed. As a

consequence, the price discovery of the market as a whole declines.12

The third column in each panel reports the factors which a¤ect the changes in rela-

tive trading volume. We observe that lagged values of �IS (�PT ) have an impact on

�Ratio_V ol with a coe¢ cient of 0.028 (0.051), suggesting that improvements in price dis-

covery lead to an increase in relative trading volume. The coe¢ cients of �Ratio_Espread

on �Ratio_V ol are negative and signi�cant at -0.053 (-0.034) which suggest that as trading

becomes cheaper (relative e¤ective spread decreases), trading volume increases. Further-

12In addition, Abergel et al. (2012) explain that high-frequency traders, in some cases, use their speedadvantage to free-ride on trade-related information (e.g. order �ow, prices, volume, duration between trades)acquired by informed investors. This may reduce investors�incentives to acquire information in the �rst place,leading to lower price discovery.

23

more, we �nd negative coe¢ cients of �Ratio_AT on �Ratio_V ol at -0.074 (-0.079). As

relative AT activity increases, relative trading volume decreases. This �nding again indi-

cates that greater AT activity having negative impact and pushing away other traders in the

market who are disadvantaged in terms of speed.

The fourth column shows that there is an impact of lagged values of �IS (�PT ) on

�Ratio_Espread with a magnitude of -0.001 (-0.0003). The Granger causality tests show

statistically signi�cant results, suggesting that trading costs decrease as a market�s contri-

bution to price discovery increases.

The �fth column shows the factors a¤ecting changes in relative AT activity. We observe

that the impact of �IS (�PT ) on �Ratio_AT is negative and signi�cant with a coe¢ cient

of -0.025 (-0.049). This �nding suggests that algorithmic trading activities increase as a

market�s contribution to price discovery decreases, i.e. as a market becomes less e¢ cient

in processing and incorporating information into its prices. We attribute this �nding to

high-frequency traders exercising arbitrage strategies to exploit price discrepancies among

securities. In line with this argument, the negative coe¢ cients of �Ratio_V ol and positive

coe¢ cients of�Ratio_Espread on�IS (�PT ), respectively, further show that ine¢ ciencies

in the market attract high-frequency trading.

The results in Table 5 suggest that relative increases in liquidity (i.e. higher relative trad-

ing volume and lower e¤ective spread) lead to a greater contribution of a market to price

discovery while an improvement in price discovery leads to greater liquidity. We also observe

that an increase in algorithmic trading activity of a market relative to another market leads

to lower price discovery. Studies such as Hendershott et al. (2011), Riordan and Storken-

maier (2012) and Brogaard et al. (2015) document that high-frequency trading has improved

the informativeness of quotes and increased the price discovery of the faster traders. How-

ever, the increased speed and information processing abilities of the high-frequency traders

may discourage the slower traders from submitting limit orders. In particular, aggressive in-

vestment strategies by the HFTs lead to crowding out e¤ect that pushes slower traders away

24

from the market. To test this assertion, we split our AT variable into U.S. and Canadian

ATs, and re-estimate the reduced-form model of Equation (13). We �nd evidence that com-

petition among AT in one market for latency arbitrage opportunities shift traders to another

market.13 Thus, consistent with Stein (2009) and Egginton et al. (2016), we conclude that

in the process of pursuing a given trading strategy, HFTs in�ict negative externalities which

reduces a market�s contribution to price discovery.

5.3 Structural VAR Results

In addition to lagged e¤ects, we assess the contemporaneous causal relations between

variables using the identi�cation through heteroskedasticity approach (Rigobon, 2003). The

structural parameters in Equation (12) are estimated using GMM for each of the 38 �rms

separately. The coe¢ cients are then averaged while the standard errors are computed cross-

sectionally.

INSERT TABLE 6 HERE

Panel A and B of Table 6 report the results for the contemporaneous relation between the

variables in the structural VAR model. The second column reports the impact of liquidity

and AT activity on price discovery. We observe a signi�cant and positive causal e¤ect of

�Ratio_V ol on�IS with a coe¢ cient of 0.080. There is a strong negative contemporaneous

e¤ect of �Ratio_Espread on �IS (�PT ) with a coe¢ cient of -0.337 (-0.241). The last

row of each Panel indicates a negative contemporaneous interaction of �Ratio_AT on �IS

(�PT ) at -0.084 (-0.153). The fact that these relations are observed in both structural

and reduced-form VAR models suggests that liquidity and AT activity a¤ect price discovery

instantaneously as well as with some lags.

The third column reports the coe¢ cients for the determinants of �Ratio_V ol. We

observe a signi�cant negative relation between �Ratio_Espread and �Ratio_V ol, and13The results can be found in Appendix B.

25

between �Ratio_AT and �Ratio_V ol. However, we do not observe a signi�cant contem-

poraneous causal e¤ect of �IS (�PT ) on �Ratio_V ol. This �nding suggests that price

discovery tends to a¤ect trading volume with lags. Furthermore, the contemporaneous im-

pact of �Ratio_AT on �Ratio_V ol is highly signi�cant at -0.489 (-0.515), indicating that

the impact of AT on relative trading volume is more prevalent contemporaneously, i.e. as

high-frequency traders enter the market, trading activity by the slower traders decreases.

In the fourth column, we observe that �PT negatively a¤ects �Ratio_Espread with a

coe¢ cient of -0.018, suggesting that an increase in PT leads to a decrease in relative spread.

We also observe that �Ratio_AT signi�cantly a¤ects �Ratio_Espread, which was not

observed in Table 4. We interpret this as AT pushing away other traders in the market who

are relatively disadvantaged in terms of speed, hence causing spread to increase.

Finally, in the last column, we observe similar signi�cant relations as previously observed

in Table 5. However, the coe¢ cients of�Ratio_V ol on�Ratio_AT and of�Ratio_Espread

on �Ratio_AT are greater in magnitude at -0.352 (-0.335) and 0.269 (0.391) for the IS (PT)

model, respectively. These results suggest that AT activity reacts strongly to changes in liq-

uidity within the same day. Overall, our results in Table 6 show that there exists not only

lagged, but also contemporaneous relations among relative liquidity, AT activity, and price

discovery.

It is important to note that the Canadian market is fragmented considerably after 2009

with the opening of alternative trading venues such as Alpha Trading, Chi-X and Pure Trad-

ing. Such fragmentation could a¤ect our results. We test the robustness of our �ndings by

reconstructing the variables V olCAN_ALL, EspreadCAN_ALL, and ATCAN_ALL. V olCAN_ALL

and EspreadCAN_ALL are calculated as the total volume traded and the volume-weighted

e¤ective spread across all the exchanges, respectively. ATCAN_ALL is calculated based on

the total messages submitted and the total dollar trading volume across all the Canadian

exchanges. The reduced-form VAR of Equation (13) and the structural VAR of Equation

(12) are then re-estimated using the aggregated data. We observe that the coe¢ cients re-

26

main identical to those reported in Table 5 and 6, suggesting that the dynamic relationships

among the variables in the VAR are not a¤ected by the fragmentation in the Canadian �-

nancial market. A discussion on this fragmentation and results can be found in Appendix

C.

5.4 Price Discovery Dynamics Pre- and Post-Regulation NMS

In a further test, we assess the impact of regulatory changes in the U.S. market. Reg.

NMS was prompted by the Securities and Exchange Commission�s belief that market frag-

mentation reduces liquidity and that the new regulation would help create a more integrated

market.14 Hendershott and Jones (2005) suggest that an increase in market fragmentation

leads to slower price discovery. Hence, regulatory changes to create a more integrated market

should improve price discovery. Furthermore, Barclay et al. (2008) �nd that the consoli-

dation of orders is important for producing e¢ cient prices, especially during times of high

liquidity demand. On the contrary, Chung and Chuwonganant (2012) examine the liquidity

of the U.S. stock markets one month before and after the adoption of Reg. NMS and �nd

that liquidity was reduced in the form of increased quoted and e¤ective spreads, as well as

decreased quoted dollar depth. This evidence indicates that there may be an impact of Reg.

NMS on the dynamics of price discovery.

We �rst show how price discovery, liquidity, and AT activity changed after the Reg.

NMS. We then examine whether the adoption of the Reg. NMS a¤ects the dynamics of

price discovery for cross-listed stocks. We split our data into two sub-periods based on the

completion date of the Reg. NMS on 8 October 2007. The �rst sub-period is from 2 January

2004 to 5 October 2007 as the pre-Reg. NMS period. The second sub-period is from 8

October 2007 to 31 January 2011 as the post-Reg. NMS period.

Table 7 reports the percentage change in price discovery, liquidity, and AT measures14The regulation was intended to improve fairness in price execution, and to improve the displaying of

quotes and access to market data. One of the most in�uential components of the Reg. NMS is the OrderProtection Rule (OPR) which requires that marketplaces enforce policies to ensure consistent price quotationand prevent trading through a better priced order on another market.

27

between pre- and post-Reg. NMS periods. We observe that trading volume in the U.S.

increased signi�cantly by 279% compared to Canada where it only increased by 53%. This

�nding indicates a much larger increase in liquidity in the U.S. compared to Canada after

Reg. NMS. Consequently, relative trading volume increased by 78%. E¤ective spreads, on

the other hand, did not change signi�cantly in either markets. Contrary to Chung and

Chuwonganant (2012), we do not observe a decline in spreads after the adoption of Reg.

NMS, but rather an improvement in trading volume. As for AT activity, the U.S. market

experienced a signi�cant increase of 40%. In Canada, the increase in AT activity is more

substantial at 69%. These �ndings are in line with Panel C of Figure 1, which shows that

the increase in AT activity is much higher in Canada than in the U.S.

INSERT TABLE 7 HERE

We observe that both IS and PT increased signi�cantly by 97% and 53%, respectively,

suggesting that the U.S. contribution to price discovery has increased signi�cantly after the

Reg. NMS. These �ndings are in line with Hendershott and Jones (2005) and Barclay et al.

(2008) who advocate that a new regulation to create a more integrated market would lead to

greater price discovery. Based on the statistics in Table 7, it is evident that price discovery

has increased signi�cantly after the Reg. NMS.

We test the impact of Reg. NMS on price discovery dynamics by examining the relations

between liquidity, AT activity and price discovery measures during the two sub-periods.

Table 8 shows the result of the VAR analysis of Equation (13) for the two sub-periods. For

brevity, we only report the results from IS VAR model.15 Overall, we do not observe any

signi�cant di¤erences from those reported in Table 5. As reported in Panel A and B of Table

8, changes in relative trading volume positively a¤ect the changes in IS as shown by the

highly signi�cant p-values from the Granger causality tests. We also observe that changes

in relative e¤ective spread and relative AT activity are negatively related to changes in IS.

15The PT VAR model yields similar results and these are available upon request.

28

In the opposite direction, we observe that changes in IS lead to positive changes in relative

trading volume as shown by the �rst row of the third column in each Panel. The impact

on changes in relative e¤ective spread remains small and signi�cant for the �rst sub-period,

but insigni�cant for the second sub-period. The coe¢ cients for the changes in relative AT

activity are also negative, despite being signi�cant only in the second sub-period. Based

on these observations, we conclude that while Reg. NMS had a signi�cant impact on the

trading environment in the U.S. and a¤ected the level of price discovery, it did not a¤ect the

underlying relations between price discovery, liquidity and algorithmic trading activity.

INSERT TABLE 8 HERE

Table 9 shows the contemporaneous relations of the VAR variables in Equation (12)

during the two sub-periods. Similar to the results in Table 6, we observe uni-directional

relation between liquidity and price discovery measure. Speci�cally, changes in relative

trading volume contemporaneously and positively a¤ect the changes in IS, while changes in

relative e¤ective spread contemporaneously and negatively a¤ect the changes in IS. The bi-

directional negative relation between AT activity and price discovery measures still persists.

Overall, both Table 8 and 9 show that the relations between price discovery and liquidity

and AT measures persist even after taking into account the regulatory changes in the U.S.

�nancial markets.

INSERT TABLE 9 HERE

6 Conclusion

In this paper, we study price discovery dynamics for a sample of Canadian cross-listed

stocks in the U.S. from January 2004 to January 2011. We compute daily measures of price

29

discovery and assess the causal relations between price discovery, liquidity, and algorith-

mic trading activity. To accommodate both lagged and contemporaneous relations among

the variables, we follow the approach of Chaboud et al. (2014) by estimating a reduced-

form VAR, as well as a structural VAR using the identi�cation through heteroskedasticity

approach developed by Rigobon (2003).

We show that price discovery of the U.S. market relative to Canada exhibits an upward

trend, suggesting that over time, the U.S. market is becoming more dominant in terms of

price discovery for Canadian cross-listed stocks. Assessing the dynamics involved, we �nd

that liquidity is related to price discovery. Improvements in relative liquidity (an increase

in trading volume and a decrease in e¤ective spread in one market relative to another)

increase that market�s contribution to price discovery. This �nding implies that the market

which provides better liquidity will become more important in terms of price discovery. This

impact occurs instantaneously (within the same day) as well as with a protracted lag (after

several days). Conversely, we �nd that an increase in price discovery leads to improved

liquidity, indicating that the market which leads in terms of price discovery attracts more

liquidity. We also �nd that relative algorithmic trading activity is negatively related to price

discovery. This �nding is consistent with the recent literature on negative externalities of

high-frequency trading. Particularly, as high-frequency traders compete aggressively with

one another to create latency arbitrage opportunity, they cause a crowding-out e¤ect which

pushes away investors who are disadvantaged in terms of speed, degrading market quality.

We further observe that while the U.S. market�s contribution to price discovery increased

after the adoption of the Regulation NMS, the dynamic relations between price discovery,

liquidity and algorithmic trading activity do not change, lending support to the robustness

of our results.

30

Appendix A: Identi�cation through Heteroskedasticity

This appendix discusses the identi�cation through heteroskedasticity methodology as em-

ployed in our study. Rigobon (2003) provides the theoretical derivation of the methodology.

The identi�cation through heteroskedasticity methodology is used when measuring con-

temporaneous relationships among the variables in a structural VAR model. Recall the

SVAR equation,

A�Yt = c+

KXk=1

�k�Yt�k + "t; (A.1)

and the reduced-form VAR,

�Yt = A�1c+ A�1KXk=1

�k ��Yt�k + A�1: (A.2)

To assess the contemporaneous interactions of our model, we are interested in estimating

the parameters in matrix A, which represents the structural parameters linking the variables

to each other. There is one issue, however, that is the structural form of Equation (A.1)

cannot be estimated directly using OLS, although the reduced-form of Equation (A.2) can.

Given the relation between the structural and the reduced-form, we can therefore obtain the

parameters in matrix A by �rst estimating the reduced-form model.

In our empirical setting, we obtain the parameters in A through the following procedure.

First, we estimate the reduced-form VAR in Equation (A.2) using OLS. The lag speci�cation

is determined by the Schwartz Information Criterion (SIC), which in our case suggests an

optimal lag-length of 5 days. From this step, we obtain the reduced-form residuals e"t, whichcontain the contemporaneous e¤ects.

Second, from the reduced-form residuals, we de�ne the heteroskedastic regimes. We do

so by computing rolling window variances of 20 observations each, following Ehrmann et

al. (2011). A regime is identi�ed if one variance of a variable exceeds the average variance

of that variable over the sample period plus one standard deviation, while at the same

31

time the variances of the other three variables do not exceed their average variances plus

one standard deviation. Using this approach, we identify 6 regimes in total: 1 regime to

represent a tranquil state where all the four variables do not exhibit elevated conditional

volatility; 4 regimes where only one variable exhibits elevated conditional volatility while the

other three are stable; and 1 regime where at least 2 variables exhibit elevated conditional

volatility.

Third, once the regimes are identi�ed, we estimate the variance-covariance matrices, es,of the reduced-form residuals in variance regime s (s = 1; 2; : : : ; 6). Given that s are

the variance-covariance matrices of the SVAR that we are interested in, and assuming the

following moment conditions hold,

AesA0 = s: (A.3)

the parameters in A and s can be estimated using GMM by minimizing the following

objective function:

min g0g with g = AesA0 � s: (A.4)

Identi�cation is achieved as long as the covariance matrices constitute a system of equa-

tions that is linearly independent. Therefore, the basic idea of the identi�cation through

heteroskedasticity approach is to increase the number of available moments or equations and

obtain matrix A which satis�es Equation (A.3) across di¤erent regime, s. If the variance

of the shocks in the system changes across di¤erent regimes, but the parameters in matrix

A remain constant, the system may be identi�ed. Hence, the shift in variances provides an

extra source of variation needed for identi�cation in the presence of endogeneity, such that

matrix A can be estimated.

There are several important points to note. First, the structural shocks across di¤erent

regimes need to be uncorrelated. If the shocks were correlated and there is no restriction on

32

the variation of such covariance, then every heteroskedastic regime adds as many equations

as unknowns, and the problem of identi�cation cannot be solved. The zero correlation

assumption, therefore, needs to be maintained for the identi�cation to work.

Second, the parameters in matrix A needs to be stable across the di¤erent volatility

regimes. This means that even though exogenous shocks may have changed the conditional

volatility, the structural relationships needs to remain constant. This is slightly harder to

interpret because while in some instances one can point to an event that is likely to have

a¤ected the variances of the shocks, in most cases, the shift in variances is not necessarily

associated with a speci�c event. Thus, heteroskedasticity in the data can still be observed

in the absence of a structural event. As such, a more pragmatic interpretation is to view

the results as conditional on the structural relationship remaining constant. That is, pro-

vided the relationship is constant over time, the method delivers consistent estimates of the

contemporaneous e¤ects.

Table A.1 shows the variances of the reduced-form VAR residuals for Yt; across the

6 di¤erent heteroskedastic regimes. Our benchmark is the variances in regime 1, which

represent the conditional volatility during tranquil period. When we compare the variances in

regime 1 with those in regimes 2 to 6, it is clear that the variances are no longer proportional

to each other. Speci�cally, in the case of regime 2 to 5, one variable exhibits elevated

conditional volatility and the other three are stable, while in the case of regime 6, all 4

variables exhibit elevated conditional volatility. The existence of heteroskedastic regimes

solves the identi�cation problem as they increase the number of Equations (B.3). This is an

important identi�cation requirement, especially to disentangle the dynamics of each of the

variables in the VAR, which normally are highly correlated. As with other studies using this

identi�cation approach, the precise form of the heteroskedasticiy is of no particular interest

(see e.g. Ehrmann et al., 2011; Badshah et al., 2013; Chaboud et al., 2014). What matters is

that the estimates of the coe¢ cients are consistent, regardless of how the heteroskedasticity

is modeled.

33

Table A.1: Variances of the reduced-form VAR residuals

This table reports the variances of the residuals from the reduced-form VAR in Equation (A.2). The residuals

are split into 6 di¤erent regimes based on various elevations in conditional volatility. R1 represents a

tranquil state where all four variables do not exhibit elevated conditional volatility. R2 to R5 represent the

regimes where only one variable exhibits elevated conditional volatility while the other three are stable. R6

represents a regime where at least 2 variables exhibit elevated conditional volatility. The �rst �gure in each

column represents the average variance across our sample. The second �gure (in parantheses) represents the

percentage change from the variance in the tranquil state, R1.

R1 R2 R3 R4 R5 R6

Panel A: IS structural VAR model�IS 0.87 3.40 (290%) 1.01 (16%) 1.26 (45%) 1.29 (49%) 2.44 (181%)�Ratio_V ol 0.54 0.69 (28%) 1.33 (149%) 0.58 (9%) 0.87 (63%) 1.39 (159%)�Ratio_Espread 0.10 0.14 (43%) 0.11 (13%) 0.37 (263%) 0.14 (35%) 0.26 (160%)�Ratio_AT 0.39 0.49 (27%) 0.66 (70%) 0.46 (20%) 1.12 (191%) 1.12 (192%)

Panel B: PT structural VAR model�PT 0.74 2.98 (303%) 0.68 (-8%) 1.06 (44%) 0.99 (34%) 2.11 (187%)�Ratio_V ol 0.54 0.64 (17%) 1.31 (141%) 0.58 (7%) 0.79 (46%) 1.34 (146%)�Ratio_Espread 0.10 0.14 (36%) 0.10 (-4%) 0.35 (233%) 0.13 (24%) 0.27 (158%)�Ratio_AT 0.40 0.47 (19%) 0.63 (58%) 0.47 (19%) 1.11 (181%) 1.11 (179%)

34

Appendix B: The Impact of the U.S. and Canadian AT

Activity

Table B.1: VAR Coe¢ cients accounting for market fragmentation in Canada

This table presents the coe¢ cients of the VAR variables after distinguishing the U.S. and Canadian AT

activities. Panel A reports the results from the IS reduced-form VAR model. Panel B reports the results from

the IS structural VAR model. Figures in brackets are the p-values. *, **, and *** denote signi�cance at the

10%, 5%, and 1% levels, respectively. For presentation, the coe¢ cients for �AT_USt�k and �AT_CANt�kare multiplied with 100.

Panel A: IS VAR analysisDependent Variable

�IS �Ratio_V ol �Ratio_Espread �AT_US �AT_CAN

�ISt�k -2.155 0.031*** -0.001** -0.029*** -0.011[0.000] [0.000] [0.024] [0.002] [0.804]

�Ratio_V olt�k 0.177*** -1.856 -0.006*** -0.045* 0.019[0.000] [0.000] [0.002] [0.060] [0.336]

�Ratio_Espreadt�k -0.133** -0.060*** -2.037 0.032 0.031[0.032] [0.000] [0.000] [0.205] [0.504]

�AT_USt�k -0.017 -0.135*** 0.024 -1.457 0.138***[0.884] [0.003] [0.286] [0.000] [0.000]

�AT_CANt�k 0.119*** 0.060** -0.014*** 0.010*** -1.778[0.000] [0.011] [0.005] [0.009] [0.000]

Adj. R-squared 0.36 0.30 0.34 0.28 0.21

Panel B: PT VAR analysisDependent Variable

�PT �Ratio_V ol �Ratio_Espread �AT_US �AT_CAN

�PTt�k -2.093 0.056*** -0.000** -0.013*** -0.011[0.000] [0.000] [0.024] [0.002] [0.804]

�Ratio_V olt�k 0.125*** -1.857 -0.003*** -0.036* 0.005[0.000] [0.000] [0.002] [0.060] [0.336]

�Ratio_Espreadt�k -0.153** -0.043*** -2.042 0.000 0.033[0.032] [0.000] [0.000] [0.205] [0.504]

�AT_USt�k -0.026 -0.107*** 0.054 -1.546 0.134***[0.884] [0.003] [0.286] [0.000] [0.000]

�AT_CANt�k 0.084*** 0.054** -0.020*** 0.018*** -1.767[0.000] [0.011] [0.005] [0.009] [0.000]

Adj. R-squared 0.35 0.30 0.34 0.28 0.24

35

Appendix C: Fragmentation in the Canadian Financial

Market

The Canadian market fragments considerably after 2009 with the opening of alternative

trading venues such as Alpha Trading (ALP), Chi-X (CXC) and Pure Trading (GO) among

other smaller ones.16 These exchanges were fragmented due to the absence of the consolidated

tape and the Order Protection Rule. As a consequence, dealers were free to decide where

to trade and could carry out orders at a non-optimal price even though a better price was

available on the same exchange or other exchanges. Such fragmentation may explain why

the price discovery is more likely to take place in the U.S and could a¤ect the validity of our

results.

In this section, we provide robustness tests to ensure that our �ndings are not a¤ected by

the fragmentation in the Canadian market. We focus on the four largest Canadian exchanges

(TSX, ALP, CXC, GO) which account for 98.1% of all trades that occur in Canada. We

collect trade and quote data from these exchanges, and use them to reconstruct our VAR vari-

ables, V olCAN_ALL, EspreadCAN_ALL, andATCAN_ALL. V olCAN_ALL andEspreadCAN_ALL

are calculated as the total volume traded and the volume-weighted e¤ective spread across all

the exchanges, respectively. ATCAN_ALL is calculated based on the total messages submitted

and total dollar trading volume across all the exchanges. The reduced-form VAR of Equation

(13) and the structural VAR of Equation (12) are then re-estimated using the aggregated

data. If the fragmentation does a¤ect the dynamics relationship among our variables, then

we can expect our new VAR coe¢ cients to di¤er from those reported in Table 5 and 6.

Table C.1 reports the coe¢ cients from the reduced-form and structural VAR models.

The re-estimated coe¢ cients remain identical to our �ndings thus far, suggesting that the

dynamic relationships among the variables in the VAR hold and are not a¤ected by the

16Clark (2011) �nds that in the year 2010, the TSX accounts for 66% of the total trading volume on allCanadian-listed issues, while Alpha Trading was 23.4%, Chi-X was 6.5%, Pure Trading was 2.2%, and theremaining 1.9% was shared among MATCH Now, Omega, and Liquidnet)

36

fragmentation in the Canadian �nancial market.

Table C.1: VAR Coe¢ cients accounting for market fragmentation in Canada

This table presents the coe¢ cients of the VAR variables after taking into account the fragmentation in the

Canadian �nancial market. Panel A reports the results from the IS reduced-form VAR model. Panel B

reports the results from the IS structural VAR model. Figures in brackets are the p-values. *, **, and ***

denote signi�cance at the 10%, 5%, and 1% levels, respectively.

Panel A: IS reduced-form VAR modelDependent Variable

�IS �Ratio_V ol �Ratio_Espread �Ratio_AT�ISt�k -2.141 0.044*** -0.012* -0.047***

[0.000] [0.000] [0.067] [0.000]�Ratio_V olt�k 0.089*** -1.763 -0.052** -0.300***

[0.002] [0.000] [0.012] [0.000]�Ratio_Espreadt�k -0.088** -0.036*** -1.955 0.023**

[0.047] [0.005] [0.000] [0.039]�Ratio_ATt�k -0.094* -0.073*** -0.026* -1.491

[0.059] [0.000] [0.082] [0.000]Adj. R-squared 0.35 0.31 0.33 0.29

Panel B: IS structural VAR modelDependent Variable

�IS �Ratio_V ol �Ratio_Espread �Ratio_AT�ISt 1 0.034** -0.004 -0.029**

[0.024] [0.309] [0.024]�Ratio_V olt 0.092** 1 -0.020 -0.489***

[0.020] [0.262] [0.000]�Ratio_Espreadt -0.106*** -0.063** 1 0.080***

[0.000] [0.011] [0.000]�Ratio_ATt -0.123*** -0.369*** 0.088*** 1

[0.003] [0.000] [0.000]

37

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42

Table1:SummaryStatistics(by�rm)

Thistableprovidesasummarystatisticsofthe38stocksinoursample.Itreportsthecompanynames,symbols,andmarketcapitalization.Italso

reportstheaveragedailytradingvolume,theaveragedailye¤ectivespread,theaveragenumberofmessagesper10-minuteperiods,andtheaverage

dailyalgorithmictradingactivityinbothmarkets.AlsoreportedaretheratiosofthevariablesintermsoftheU.S.marketrelativetotheCanadian

market.

TradingVolume(�000)

E¤ectiveSpread(bps)

NumberofMessages(10min)

AlgorithmicTradingActivity

No.

Company

US

CAN

RATIO

US

CAN

RATIO

US

CAN

RATIO

US

CAN

RATIO

1BarrickGold

7,061

2,758

72%

4.0

5.7

41%

3,889

3,372

54%

-22.6

-13.8

38%

2Agnico-EagleMinesLimited

2,228

734

75%

5.8

8.8

40%

1,760

1,585

53%

-14.7

-5.8

28%

3AgriumInc.

1,929

806

71%

5.7

8.7

39%

1,806

1,681

52%

-13.4

-7.2

35%

4BCEInc.

634

3,124

17%

5.1

5.9

46%

772

932

45%

-6.1

-29.2

83%

5BankofMontreal

325

1,617

17%

5.6

5.1

52%

879

828

51%

-3.6

-40.8

92%

6BankofNovaScotia

281

2,073

12%

6.9

5.2

57%

796

896

47%

-3.1

-43.5

93%

7Brook�eldO¢ce

1,593

364

81%

7.6

11.6

40%

911

881

51%

-8.5

-2.3

21%

8CamecoCorp.

1,975

1,191

62%

5.9

7.9

43%

1,450

1,475

50%

-17.9

-14.9

45%

9CelesticaInc.

1,181

851

58%

12.7

16.0

44%

460

438

49%

-7.6

-5.1

40%

10CanadianImperialBankCommunication

234

1,295

15%

5.9

5.2

53%

725

703

51%

-3.8

-46.1

92%

11CanadianNationalRailwayCompany

1,047

999

51%

3.7

5.4

41%

1,128

1,090

51%

-15.2

-16.6

52%

12CanadianNaturalResourcesLtd.

1,958

1,830

52%

4.6

6.1

43%

1,864

1,733

52%

-17.4

-24.2

58%

13COTTCorp.

484

286

63%

24.9

34.0

42%

208

222

52%

-6.2

-2.9

32%

14CanadianPaci�c

498

624

44%

5.4

7.3

43%

723

726

50%

-9.7

-14.1

59%

15EncanaCorp.

2,791

2,341

54%

3.6

5.1

42%

2,186

1,988

52%

-22.6

-27.3

55%

16EnbridgeInc.

227

664

25%

6.8

7.4

48%

489

474

51%

-3.8

-15.7

81%

17EnerplusCorp.

585

311

65%

7.8

10.7

42%

438

471

48%

-16.6

-7.2

30%

18GoldcorpInc.

6,489

2,775

70%

5.1

7.1

42%

3,715

3,371

52%

-18.6

-12.2

40%

19CGIGroup

123

968

11%

17.3

17.0

50%

238

223

48%

-1.2

-9.0

88%

20GildanActivewearInc.

497

345

59%

8.8

11.9

42%

449

504

47%

-6.7

-6.2

48%

21KingswayFinancialServicesInc.

45172

21%

36.8

35.1

51%

8876

46%

-0.9

-5.5

86%

22KinrossGoldCorp.

4,436

3,566

55%

10.0

11.8

46%

2,430

2,167

53%

-9.0

-11.4

56%

23ManulifeFinancialCorp.

1,360

3,193

30%

5.0

6.1

45%

1,331

1,448

48%

-11.7

-28.4

71%

24MIDevelopmentsInc.

104

3277%

15.2

23.5

39%

94122

56%

-5.9

-1.1

16%

25NexenInc.

1,540

1,646

48%

6.5

8.0

45%

1,506

1,562

49%

-9.2

-19.0

67%

26PrecisionDrillingTrust

945

738

56%

10.3

13.0

44%

508

476

48%

-12.5

-10.1

45%

27PengrowthEnergyCorp.

966

466

67%

10.8

15.5

41%

330

340

51%

-15.9

-13.9

47%

28PotashCorporationofSaskatchewanInc.

4,334

758

85%

4.1

5.9

41%

3,164

2,691

54%

-37.6

-10.3

22%

29RitchieBrothersAuctioneers

227

5481%

10.7

21.6

33%

217

271

56%

-7.5

-1.9

20%

30RogersCommunicationInc.

328

1,435

19%

5.3

8.4

39%

607

573

51%

-13.7

-25.4

65%

31RoyalBankofCanada

585

2,517

19%

4.7

4.8

49%

1,103

1,204

48%

-5.3

-46.5

90%

32Shaw

CommunicationsInc.

176

771

19%

9.0

11.3

44%

339

350

51%

-3.2

-10.0

76%

33SunLifeFinancial

335

1,240

21%

6.3

7.2

47%

624

662

49%

-4.9

-23.0

82%

34SuncorEnergyIncorporated

4,389

2,672

62%

4.1

5.5

43%

3,074

2,937

51%

-26.5

-21.2

44%

35TransAltaCorp.

36646

5%13.2

11.0

55%

267

219

45%

-0.7

-16.2

96%

36Toronto-DominionBank

677

1,928

26%

4.5

4.7

49%

1,207

1,158

51%

-6.4

-39.7

86%

37TalismanEnergyInc.

2,705

2,990

47%

6.5

8.2

44%

1,784

1,664

52%

-11.0

-17.4

61%

38TransCanadaCorp.

249

1,210

17%

6.0

6.3

49%

483

558

46%

-4.2

-20.8

83%

Mean

1,463

1,368

52%

8.5

10.5

45%

1,159

1,107

51%

-10.7

-17.5

62%

43

Table 2: Descriptive Statistics of the number of quote-change and trade messages

This table reports the percentage change in daily total messages, number of quote changes,number of trades, quote-to-trade ratio, and limit order duration (in seconds) from January2004 to January 2011. The numbers reported are averages across the 38 stocks in oursample. Panel A reports the statistics for the U.S. market. Panel B reports the statisticsfor the Canadian market. Panel C reports the U.S. statistics relative to the total from bothmarkets. *** denotes signi�cance at the 1% level.

Jan-04 Jan-11 %Change t-statPanel A: USTotal messages 3,468 72,497 1,990%*** (9.12)Quote 2,822 61,897 2,093%*** (8.85)Trade 646 10,601 1,541%*** (6.58)Quote-to-trade ratio 4.4 5.8 34%*** (2.58)Limit order duration 11.5 2.4 -79%*** (-15.48)

Panel B: CANTotal messages 3,649 99,047 2,614%*** (9.71)Quote 2,688 92,910 3,356%*** (9.13)Trade 961 6,137 539%*** (7.70)Quote-to-trade ratio 2.8 15.1 441%*** (6.72)Limit order duration 15.0 1.7 -89%*** (-43.38)

Panel C: US/(US+CAN)Total messages 0.49 0.42 -13%*** (-3.04)Quote 0.51 0.40 -22%*** (-4.45)Trade 0.40 0.63 58%*** (5.21)Quote-to-trade ratio 0.61 0.28 -54%*** (-9.63)Limit order duration 0.43 0.59 35%*** (4.90)

44

Table 3: Descriptive Statistics of the Price Discovery Measures

This table reports the descriptive statistics for the price discovery measures. IS and PT areestimated daily from January 2004 to January 2011. The �gures reported are the averagesfor all 38 Canadian cross-listed stocks in the sample. Panel A reports statistics for thelevels, and Panel B reports statistics for the �rst di¤erences. ADF is the t-statistics for theAugmented Dickey-Fuller test. *** denotes signi�cance at the 1% level.

IS PTPanel A: Summary Statistics for levelsMean 0.522 0.5905th 0.185 0.290Median 0.554 0.60895th 0.808 0.847Std. Dev. 0.208 0.179Skewness -0.345 -0.347Kurtosis 2.525 2.732AC 0.672 0.667ADF -2.147 -2.169

Panel B: Summary Statistics for 1st di¤erenceMean 0.00004 0.000085th -0.21854 -0.19921Median 0.00043 0.0000295th 0.21655 0.19747Std. Dev. 0.137 0.125Skewness 0.008 -0.014Kurtosis 5.636 5.326AC -0.450 -0.448ADF -13.619*** -13.422***

45

Table 4: Correlation matrix between VAR variables

This table presents the correlation matrix for the series �IS, �PT , �Ratio_V ol,�Ratio_Espread, and �Ratio_AT . �IS and �PT are the �rst di¤erences in the pricediscovery measures IS and PT , respectively. �Ratio_V ol is the �rst di¤erence in the U.S.trading volume relative to Canada. �Ratio_Espread is the �rst di¤erence in the U.S. ef-fective spread relative to Canada. �Ratio_AT is the �rst di¤erence of the U.S. AT activityrelative to Canada.

�IS �PT �Ratio_V ol �Ratio_Espread �Ratio_AT�IS 1�PT 0.906 1�Ratio_V ol 0.175 0.130 1�Ratio_Espread -0.121 -0.138 -0.103 1�Ratio_AT -0.221 -0.183 -0.702 0.212 1

46

Table 5: VAR Estimation Results

This table presents the sum of the lag coe¢ cients of the VAR in Equation (13). The columnvariable is the dependent variable while the row variable is the explanatory variable. PanelA reports the coe¢ cients from the IS VAR model. Panel B reports the coe¢ cients from thePT VAR model. Figures in brackets are the p-values from the Granger Causality Test. *,**, and *** denote signi�cance at the 10%, 5%, and 1% levels, respectively.

Panel A: IS reduced-form VAR modelDependent Variable

�IS �Ratio_V ol �Ratio_Espread �Ratio_ATP�ISt�k -2.155*** 0.028*** -0.001** -0.025*

[0.000] [0.000] [0.017] [0.078]P�Ratio_V olt�k 0.166*** -1.876*** -0.015 -0.089***

[0.000] [0.000] [0.214] [0.000]P�Ratio_Espreadt�k -0.144** -0.053*** -2.033*** 0.029**

[0.024] [0.006] [0.000] [0.020]P�Ratio_ATt�k -0.057** -0.074*** -0.006 -1.830***

[0.025] [0.000] [0.436] [0.000]Adj. R-squared 0.36 0.30 0.34 0.28

Panel B: PT reduced-form VAR modelDependent Variable

�PT �Ratio_V ol �Ratio_Espread �Ratio_ATP�PTt�k -2.091*** 0.051*** -0.0003* -0.049***

[0.000] [0.000] [0.090] [0.000]P�Ratio_V olt�k 0.140*** -1.885*** -0.014 -0.093***

[0.000] [0.000] [0.250] [0.000]P�Ratio_Espreadt�k -0.172*** -0.034** -2.036*** 0.030**

[0.006] [0.012] [0.000] [0.018]P�Ratio_ATt�k -0.007*** -0.079*** -0.002 -1.842***

[0.003] [0.000] [0.305] [0.000]Adj. R-squared 0.35 0.30 0.34 0.28

47

Figure 1: Trading Volume, E¤ective Spread, and Algorithmic Trading Activity Over Time

This Figure shows time series plots of the U.S. relative daily trading volume, U.S. relativedaily e¤ective spread, and U.S. AT activity. The �gures are the 20-day moving averagescomputed from the mean Ratio_V ol, Ratio_Espread, and Ratio_AT for the 38 �rms inthe sample, respectively. The x-axis represent the sample period from January 2004 toJanuary 2011, while the y-axis represents the value of the levels for each respective variable.

Panel A: Trading Volume

Panel B: E¤ective Spread

Panel C: Algorithmic Trading Activity

48

Figure 2: Price Discovery Measures Over Time

This Figure shows time series plots of the IS and PT for the U.S. market over the sampleperiod January 2004 to January 2011. The �gures are the 20-day moving averages computedfrom the mean IS and PT for the 38 �rms in the sample.

49

Table 6: Contemporaneous Relation between Variables

This table presents the coe¢ cients for the contemporaneous interactions between the VARvariables. Note that the coe¢ cients in this table have the opposite signs to the coe¢ cientsof matrix A because matrix A is on the left-hand side of Equation (12). When taken tothe right-hand side the e¤ects become positive. Subsequently, the column variable is thedependent variable while the row variable is the explanatory variable. Panel A reports theresults from the IS VAR model. Panel B reports the results from the PT VAR model.Figures in brackets are the p-values. *, **, and *** denote signi�cance at the 10%, 5%, and1% levels, respectively.

Panel A: IS structural VAR modelDependent Variable

�IS �Ratio_V ol �Ratio_Espread �Ratio_AT�ISt 1 0.011 -0.008 -0.043***

[0.185] [0.112] [0.000]�Ratio_V olt 0.080*** 1 0.005 -0.352***

[0.003] [0.610] [0.000]�Ratio_Espreadt -0.337*** -0.073* 1 0.269***

[0.000] [0.086] [0.000]�Ratio_ATt -0.084** -0.489*** 0.033** 1

[0.012] [0.000] [0.022]

Panel B: PT structural VAR modelDependent Variable

�PT �Ratio_V ol �Ratio_Espread �Ratio_AT�PTt 1 0.006 -0.018** -0.021*

[0.440] [0.011] [0.063]�Ratio_V olt 0.014 1 0.015 -0.335***

[0.487] [0.115] [0.000]�Ratio_Espreadt -0.241*** -0.041 1 0.391***

[0.001] [0.288] [0.000]�Ratio_ATt -0.153*** -0.515*** 0.030** 1

[0.000] [0.000] [0.024]

50

Table 7: Change in Variables Surrounding Regulation NMS

This table provides the change in price discovery, liquidity, and algorithmic trading activitymeasures for 38 Canadian cross-listed stocks. The �gures reported are the percentage dif-ferences before and after the adoption of Regulation NMS on 8 October 2007. Figures inparentheses are the t-statistics. **, and *** denote signi�cance at the 5%, and 1% levels,respectively.

Di¤ t-statV olUS 279%*** (7.52)V olCAN 84%*** (4.51)Ratio_V ol 78%*** (5.00)

EspreadUS -4% (-0.31)EspreadCAN -10% (-0.89)Ratio_Espread 3%** (2.02)

ATUS 40%*** (7.21)ATCAN 69%*** (33.53)Ratio_AT -19%*** (-8.68)

IS 97%*** (8.50)PT 53%*** (10.75)

51

Table 8: Sub-periods VAR Estimation Results

This table presents the sum of the lag coe¢ cients of the IS VAR in Equation (13) at twosub-periods surrounding Reg. NMS: before and after 8 October 2007. The column variableis the dependent variable while the row variable is the explanatory variable. Panel A reportsthe coe¢ cients from the IS VAR model with the pre-NMS sample. Panel B reports thecoe¢ cients from the IS VAR model with the post-NMS sample. Figures in brackets are thep-values from the Granger Causality Test. *, **, and *** denote signi�cance at the 10%,5%, and 1% levels, respectively.

Panel A: IS reduced-form VAR model (pre Reg. NMS)Dependent Variable

�IS �Ratio_V ol �Ratio_Espread �Ratio_ATP�ISt�k -2.202*** 0.012** -0.003** -0.024

[0.000] [0.018] [0.041] [0.409]P�Ratio_V olt�k 0.160*** -1.881*** -0.024 -0.107***

[0.003] [0.000] [0.342] [0.000]P�Ratio_Espreadt�k -0.095* -0.091** -2.096*** 0.002**

[0.071] [0.018] [0.000] [0.021]P�Ratio_ATt�k -0.088** -0.100*** 0.007 -1.902***

[0.035] [0.000] [0.819] [0.000]Adj. R-squared 0.37 0.31 0.34 0.29

Panel B: IS reduced-form VAR model (post Reg. NMS)Dependent Variable

�IS �Ratio_V ol �Ratio_Espread �Ratio_ATP�ISt�k -2.025*** 0.069*** 0.0035 -0.039***

[0.000] [0.000] [0.276] [0.003]P�Ratio_V olt�k 0.157*** -1.886*** 0.006 -0.076**

[0.000] [0.000] [0.982] [0.037]P�Ratio_Espreadt�k -0.237*** -0.329*** -1.913*** 0.143

[0.001] [0.000] [0.000] [0.145]P�Ratio_ATt�k -0.026*** -0.065*** -0.010* -1.750***

[0.005] [0.000] [0.092] [0.000]Adj. R-squared 0.34 0.30 0.32 0.27

52

Table 9: Sub-periods Contemporaneous Relation Results

This table presents the coe¢ cients for the contemporaneous interactions between the ISVAR variables at two sub-periods surrounding Reg. NMS: before and after 8 October 2007.Note that the coe¢ cients in this table have the opposite signs to the coe¢ cients of matrix Abecause matrix A is on the left-hand side of Equation (12). When taken to the right-handside the e¤ects become positive. Subsequently, the column variable is the dependent variablewhile the row variable is the explanatory variable. Panel A reports the results from the ISVAR model with the pre-NMS sample . Panel B reports the results from the IS VAR modelwith the post-NMS sample. Figures in brackets are the p-values. *, **, and *** denotesigni�cance at the 10%, 5%, and 1% levels, respectively.

Panel A: IS structural VAR model (pre Reg. NMS)Dependent Variable

�IS �Ratio_V ol �Ratio_Espread �Ratio_AT�ISt 1 -0.002 -0.006 -0.032**

[0.832] [0.335] [0.016]�Ratio_V olt 0.123* 1 0.067** -0.392***

[0.084] [0.010] [0.000]�Ratio_Espreadt -0.327*** 0.012 1 0.278***

[0.002] [0.772] [0.000]�Ratio_ATt -0.175** -0.590*** 0.155*** 1

[0.016] [0.000] [0.000]

Panel B: IS structural VAR model (post Reg. NMS)Dependent Variable

�IS �Ratio_V ol �Ratio_Espread �Ratio_AT�ISt 1 0.023 -0.014* -0.032*

[0.309] [0.078] [0.060]�Ratio_V olt 0.087** 1 -0.015 -0.359***

[0.020] [0.100] [0.000]�Ratio_Espreadt -0.150** -0.054 1 0.230***

[0.037] [0.349] [0.001]�Ratio_ATt -0.057* -0.430*** -0.006 1

[0.090] [0.000] [0.657]

53