the impact of arbitrageurs on market liquidity€¦ · surfsara, and in particular lykle voort, for...

The impact of arbitrageurs on market liquidity.I

Dominik M. Roscha

aRotterdam School of Management, Erasmus UniversityFirst draft: May 2013

Abstract

Do arbitrageurs act as cross-market liquidity providers helping local market-makers

to cope with temporary order imbalances or are they perceived as informed traders

thereby increasing adverse selection costs? Using 5,620,997,653 currency adjusted

bid and ask quotes on 69 US cross-listed and their 69 home market stocks across 5

different countries and over 16 years I find the following. A decrease in arbitrage

profits (an indication of greater arbitrage activity) predicts an increase in liquidity

and a decrease in order imbalance in the home and in the cross-listed market. Fur-

ther, a decrease in arbitrage profits predicts a stronger increase in liquidity during

than outside overlapping trading hours (the time in the day when arbitrageurs are

active), indicating that arbitrage profit do not predict general liquidity changes.

These findings suggest that arbitrageurs improve liquidity and financial market

integration by trading against local net market demand.

Keywords: liquidity, efficiency, fragmentation, arbitrage, market integration

II thank Dion Bongaerts, Tarun Chordia, Ruben Cox, Nicolae Garleanu, Amit Goyal, Avanid-har Subrahmanyam, Raman Uppal, Dimitrios Vagias, Mathijs van Dijk, Manuel Vasconcelos,Axel Vischer and seminar participants at Erasmus University for valuable comments. This workwas carried out on the National e-infrastructure with the support of SURF Foundation. I thankSURFsara, and in particular Lykle Voort, for technical support, and OneMarket-Data for theuse of their OneTick software.

Email address: [email protected] (Dominik M. Rosch)

July 17, 2013

1. Introduction

Inefficiencies in financial markets have real effects on the economy. For example,

in a financial market in which the law of one price is violated – perhaps the

strongest indication that the financial market is less than perfectly efficient – prices

do not reflect fundamentals hampering efficient resource allocation and the ability

to learn from prices for market-makers and decision makers alike.

While liquidity encourages arbitrage activity, which enforces the law of one

price, there are good reasons to believe that vice versa, arbitrageurs impact liquid-

ity. Theoretical models suggest that the impact of arbitrage on market liquidity

depends on the underlying reason for the arbitrage to arise. If the arbitrage arises

due to a non-fundamental demand shock, such as fire sales by mutual funds, arbi-

trageurs increase the market-making capacity and hence improve liquidity (Holden,

1995; Gromb and Vayanos, 2010). However, if the arbitrage arises from different

information sets, arbitrageurs have an informational advantage to other traders

and might create adverse selection. Hence, in informationally fragmented markets

arbitrageurs might deteriorate liquidity (Kumar and Seppi, 1994; Domowitz, Glen,

and Madhavan, 1998).

The impact of arbitrageurs on market liquidity does not need to be contem-

poraneous alone, but could have persistent effects, too. First, arbitrageurs could

predict changes in liquidity and in anticipation of an increase in illiquidity step out

of the market (Shleifer and Vishny, 1997). Second, O’Hara and Oldfield (1986)

show that overnight inventories can affect liquidity in the next day. If arbitrageurs

trade against net order imbalance, a decrease in arbitrage activity might hence

lead to higher order imbalances, which could predict future illiquidity.

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The current consensus seems to be to assume that arbitrage arise because of

non-fundamental demand shocks and to conclude that arbitrageurs improve liq-

uidity (Gromb and Vayanos, 2010; Rahi and Zigrand, 2012; Foucault, Pagano, and

Roell, 2013). This was not always the case. Historically, arbitrageurs were partly

blamed for the 1987 market crash and index arbitrage was viewed to destabilize

markets (Kumar and Seppi, 1994). The paradigm shift on the role of arbitrageurs

in the financial market occured despite scarce and mixed empirical evidence.

Many insightful studies exist that study arbitrage or liquidity, but to the best

of my knowledge only two empirical studies look at the joint dynamics of arbitrage

and liquidity.1 Choi, Getmansky, and Tookes (2009) find empirical evidence in

favor of a positive impact of arbitrageurs on liquidity. However, this evidence of a

positive impact of arbitrage on liquidity is based on measures of the hedging activ-

ity of arbitrageurs, rather than on measures of the actual arbitrage activity itself.

Hedging clearly has less possible information than the arbitrage trade itself, and

the above mentioned tension, between “cross-sectional market making” (Holden,

1995) and adverse selection does not arise. Roll, Schwartz, and Subrahmanyam

1A short (and incomplete) list of papers studying arbitrage or liquidity is given in the follow-ing. Amihud and Mendelson (1986) show that illiquidity explains cross-sectional variations inreturns, Amihud (2002) shows that investors demand a premium for holding illiquid stocks, andPastor and Stambaugh (2003) give empirical evidence for illiquidity as a priced state variable.Chordia, Roll, and Subrahmanyam (2000); Hasbrouck and Seppi (2001); Karolyi, Lee, and vanDijk (2012) empirically analyze common components and co-movements in liquidity. Empiricalevidence of why arbitrage persists is given by Mitchell, Pulvino, and Stafford (2002); Garveyand Murphy (2006); De Jong, Rosenthal, and van Dijk (2009); Gagnon and Karolyi (2010);Ben-David, Franzoni, and Moussawi (2012) in general confirming the theoretical limits of ar-bitrage theory, e.g. (Pontiff, 2006; Gromb and Vayanos, 2010). Schultz and Shive (2010) giveempirical evidence that arbitrage between shares issued by the same company mainly arise fromnon-fundamental demand shocks, but do not link this to liquidity. Further Lou and Polk (2013)look at arbitrage activity in momentum strategies, but do not link this to liquidity. To the bestof my knowledge only Roll, Schwartz, and Subrahmanyam (2007); Choi, Getmansky, and Tookes(2009) empirically investigate liquidity and arbitrage jointly.

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(2007) find opposite evidence, that arbitrageurs in the futures-cash basis deterio-

rate liquidity. It remains an open empirical question whether the consensus view

that arbitrage activity improves liquidity is supported by empirical evidence.

Motivated by these observations, in this paper, I investigate the impact of arbi-

trageurs on market liquidity in the American Depository Receipt (ADR) market.

The feature of conversion, in which the ADR can be converted to the home

market share, and the other way around, makes the ADR market particular suit-

able to study arbitrage, because it allows to measure arbitrage profits and interpret

it as an inverse proxy for arbitrage activity. For example, if the bid price of the

home market stock is USD 101 and the ask of the ADR is USD 99, an arbitrage

exists to buy the ADR and short sell the home market stock. Because the ADR

can now be converted to the home market stock, the short position can be closed,

giving a profit of USD 2. The realized (ex post) profit (excluding transaction costs)

is equal to the profit (ex ante), the difference in the prices of when the arbitrage

was opened.

I examine intraday bid and ask quotes for 69 ADRs and currency adjusted

prices for the home market stock from Brazil, England, France, Germany, and

Mexico over a long time frame from 1996 till 2011. I first document large price

deviations with average daily maximum arbitrage profits of 1%. I then provide

empirical evidence that in the ADR market more than 70% of all arbitrage arise

due to a non-fundamental demand shock where the asset that causes the arbitrage

to arise is also the asset that closes down the arbitrage after a few minutes. This

provides initial evidence that arbitrageurs likely act as liquidity providers in the

ADR market.

I then estimate vector autoregressions and impulse response functions from

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detrended and expunged from other calendar regularities arbitrage profit, and

both home market and ADR liquidity. I find that a positive shock to arbitrage

profit (an inverse measure for arbitrage activity) predicts an increase in illiquidity.

This provides further evidence that arbitrageurs act as liquidity providers.

To address concerns that unobserved variables explain above results, I further

estimate the effect of arbitrage profits on the difference between illiquidity during

and outside overlapping trading hours and find a positive relation. This indicates

that arbitrage profit does not forecast general movements in illiquidity, but rather

differences in liquidity provision during and outside overlapping trading hours, i.e.

when arbitrageurs are active and when not. I then explore a potential channel how

arbitrageurs act as liquidity providers and show that arbitrageurs trade against net

market order imbalance (absolute difference between buyer- and seller-initiated

trades). Last I estimate impulse response functions for each stock-day in the

sample and find a positive response in home market quoted spread to a positive

shock in arbitrage profit across almost every stock, and for almost every day. For

most ADRs the response has a positive trend over time. Again this indicates that

above results are not driven by endogeneity concerns, or by a common unobserved

variable.

My primary contribution is to investigate the impact of arbitrageurs on liquid-

ity. I provide empirical evidence that arbitrageurs improve liquidity (to the best

of my knowledge the first of its kind). Further, compared to both previous studies

investigating the impact of arbitrageurs on liquidity, I look at liquidity changes in

both markets affected by the arbitrage. I find that arbitrageurs improve liquidity

in both markets and not merely shift liquidity from one market to the other. I

provide empirical evidence that arbitrageurs trade against net market demand,

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and hence improve international market integration by shifting excess demands

across markets. My secondary contribution is to extend the ADR literature. Very

few studies in the ADR market look at intraday data from the home market, an

exception is Hupperets and Menkveld (2002) who look at intraday data for 7 Dutch

stocks, but only over one year. First I document large arbitrage profits of almost

1% averaged over the whole sample using intraday data over a long timespan from

both the ADR and the home market stock from five different exchanges. Second I

join two distinct research streams in the Depository Receipt literature, where one

focuses on explaining arbitrage profits (e.g. Gagnon and Karolyi (2010)) and the

other explains liquidity differences during and outside overlapping trading hours,

i.e. when both the DR and the home market share are trading (e.g. Werner and

Kleidon (1996); Moulton and Wei (2009)).

Understanding the impact of arbitrageurs on liquidity improves understanding

of how frictions impeding arbitrage might impact liquidity. My findings indicate

that arbitrageurs improve liquidity and hence that shocks to frictions impeding

arbitrage could deteriorate liquidity. For example in January 2014 eleven European

member states plan to introduce a transaction tax on financial instruments. The

tax will be at least 0.1% of the purchase price for equity transactions (European

Commission, 2013), thereby significantly increasing the barrier for an arbitrage

to be profitable. The results of this paper suggest that the transaction tax will

negatively impact liquidity, because of a decrease in arbitrage activity. A decrease

in liquidity will increase the cost of capital for firms (Amihud and Mendelson,

1986) and ultimately influence managers decision to cross-list their stock.

The beneficial effect of arbitrage activity on liquidity is consistent with prior

studies, in which arbitrageurs are assumed (but are not investigated) to create posi-

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tive liquidity externalities by enforcing the law of one price. First, arbitrageurs cre-

ate a substitute which increases competition between market-makers and thereby

improves liquidity (Moulton and Wei, 2009). Second, market participants can learn

from the price of the other market again improving liquidity (Cespa and Foucault,

2012). Third, trust in the price discovery is build up, which otherwise might de-

teriorate and stop traders to trade, decreasing price efficiency and liquidity (Rahi

and Zigrand, 2012).

Recent changes to the trading environment, seemingly helping arbitrageurs,

make this study particular relevant. Markets are not only more fragmented than

ever before allowing arbitrage opportunities to arise, it is also possible to trade on

these opportunities in milliseconds using computer based algorithms with very low

transaction costs. Looking at all four changes (i.e. fragmentation, high frequency

trading, algorithmic trading, and liquidity) individualy improves market liquidity

and informational efficiency (O’Hara and Ye, 2011; Menkveld, 2012; Hendershott,

Jones, and Menkveld, 2011; Chordia, Roll, and Subrahmanyam, 2008), but the

likely contribution of arbitrageurs’ impact on market liquidity is largely ignored.

2. The setting

To estimate the impact of arbitrage activity on liquidity I first construct a

measure of arbitrage activity from intraday bid and ask quotes. Unfortunately, a

direct measure of arbitrage activity is not available, but a possible indirect (inverse)

measure is absolute price difference. Arbitrageurs’ function in the financial market

is to trade on arbitrage opportunities and thereby to enforce the law of one price.

Hence, if arbitrageurs are very active, absolute price differences should be low. On

the other hand, failing to align prices indicates that arbitrageurs are not active

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enough. In a similar way previous literature measured arbitrage activity by the

outcome of arbitrage activity, such as the absolute price difference (Roll, Schwartz,

and Subrahmanyam, 2007)2, and return correlations (Lou and Polk, 2013).3

The feature of convertibility in the American Depository Receipt (ADR) mar-

ket, where an ADR can be converted to the home market share, and the other way

around, makes the ADR a particular suitable setting to study arbitrage.4 Con-

vertibility is a rare feature that distinguishes the ADR arbitrage from many other

arbitrage opportunities, for example from arbitrage on Exchange Traded Funds,

which can only be converted by “authorized participants” (Ben-David, Franzoni,

and Moussawi (2012)) or from arbitrage on price differences between (cash-settled)

derivatives and spot prices, which profit at expiry depends on the difference of the

final settlement price of the derivative and the price the underlying could be traded

at. As the following example shows, convertibility allows to interpret price differ-

ences between bid and ask prices at the time an arbitrageurs opens the arbitrage

as profits an actual arbitrageur could make.

2I note that Roll, Schwartz, and Subrahmanyam (2007) interpret absolute price differences(the basis) as a direct measure of arbitrage activity, so that “if the basis widens on a particularday, arbitrage forces on subsequent days ... increase.” In contrast, I interpret absolute pricedifferences as an inverse measure of arbitrage activity. The different interpretations are due todifferences in the measure as well as differences in the underlying market. First Roll, Schwartz,and Subrahmanyam (2007) use end-of-day price deviations, whereas I use intraday prices, andsecond in the ADR market arbitrage opportunities are short lived (as discussed later, they nor-mally vanish after several minutes). As such it makes it difficult to argue that in the ADR marketarbitrageurs would get active tomorrow, while they could exploit the arbitrage today, especiallyconsidering that arbitrage opportunities are short lived in the ADR market.

3Alternatively, previous literature used the excess amount of short-selling to measure arbitrageactivity (Choi, Getmansky, and Tookes, 2009; Hanson and Sunderam, 2011), but this measureis not feasible for arbitrage positions that are only open for one or two business days (as is thecase in the market I look at). Equity transaction settle “T+3”, i.e. traders are required to settlethe transaction within three business days, if the short-position is open less than three businessdays it will likely not show up in any statistic.

4For a detailed explanation and a comprehensive introduction to the ADR market I refer toKarolyi (1998).

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Figure 1 shows an example of an arbitrage where the bid price of the home

market stock is higher than the ask price of the ADR. To profit from this arbitrage

first short sell the home market stock for the bid price, convert the proceeds from

the short-sell into USD, and buy the ADR at the NYSE for the ask price.5 After

that the ADR can be converted into the home-market stock either through a

broker (e.g. Interactive Brokers), a crossing platform (e.g. ADR Max, or ADR

Navigator), or the actual depository bank, which (in general) is obliged to provide

the home market share for the ADR and vice-versa. According to Interactive

Brokers such conversion takes around one to two business days, and according to

wallstreetandtech.com costs 2 to 3 cents a share in 2006.6 After the conversion took

place the home-market share can be delivered to close down the short position,

resulting in a profit equal to the difference between the bid of the home market

and the ask of the ADR at the time the arbitrage was opened (indicated by the

shaded area in Figure 1).

Hence, in general my measure of arbitrage profit is lower or equal to what an

arbitrageur sees as a suitable compensation (i.e. profits, adjusted for costs and

risks) for providing her services (enforcing the law of one price). For these reasons

I denote price differences between the bid price of one market and the ask price

of the other market, as arbitrage profit and interpret it as an inverse measure of

arbitrage activity.

To construct my sample of ADRs and their respective home market share I use

standard sources in the DR literature: Datastream, Bank of New York Complete

5Note: that this example is for illustrative purposes only. In real markets short-selling iscapital intensive, and an initial margin requirement of 150% is required (Regulation T).

6http://ibkb.interactivebrokers.com/node/1834; http://www.wallstreetandtech.com/automating-adrs/189401872

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Depositary Receipt Directory (www.adrbnymellon.com) and Deutsche Bank De-

positary Receipts Services (adr.db.com). Details about the sample construction

can be found in the appendix. I focus on the NYSE as the cross-listed market as

it is and was the world leading exchange in terms of listed Depository Receipts

(DR) and together with NASDAQ captures almost 90% of the worldwide total

trading in the DR market of USD 3.5 trillion in 2010 (Cole-Fontayn, 2011). I

identify 69 matched home-market/ADR pairs from five different home market ex-

changes, specifically the London Stock Exchange (England, with 27 stocks), Sao

Paolo Stock Exchange (Brazil, 12 stocks), Bolsa Mexicana de Valores (Mexico, 12

stocks), XETRA (Germany, 9 stocks), and Euronext Paris (France, 9 stocks).

For all matched home-market/ADR pairs I obtain intraday data on quotes and

trades (time-stamped with microsecond precision) as well as their respective sizes

from Thomson Reuters Tick History (TRTH) over the sample period Jan-1996

(the earliest date available in TRTH) till the end of 2011. Similarly, I obtain

intraday quotes on the currency pairs required to convert local prices into USD,

the currency in which the ADR is quoted in. Quote and trade data is filtered as

described in the Appendix (Data filters). After the filtering 5,620,997,653 quotes

remain, with roughly 50% from ADRs. Further 804,602,677 trades remain, with

around 25% on ADRs.

The main analysis is based on a daily measure (following Roll, Schwartz, and

Subrahmanyam (2007)) derived from intraday data.7 More specifically the focus of

the main analysis are the hours in the day in which arbitrageurs are active. This is

the time when both the home-market as well as the NYSE are in their continuous

7As a robustness test, I also estimate the results per stock-day, based on 4-minute intervals.

9

trading session called the overlapping trading hours (for details I refer to the Ap-

pendix, sample construction). Unless otherwise specified, all of the following daily

measures are calculated only from quote and trade data during the overlapping

trading hours.

2.1. The measures: arbitrage profit as an inverse measure of arbitrage activity

In general, arbitrage profit profiti,s of stock i in second s is calculated as the

maximum relative difference between the bid on the home market (ADR) and the

ask on the ADR (home market), i.e. profiti,s is calculated as:

profiti,s = max(bid.homei,s − ask.adri,s

mid.homei,s,bid.adri,s − ask.homei,s

mid.homei,s, 0) (1)

where, mid.homei,s is the last mid-quote price of stock i in second s, and bid.homei,s

(ask.homei,s) is the last bid (ask) of stock i in second s converted to USD using

the prevailing bid (ask) of the respective currency pair, i.e. BRL for Brazil, GBP

for England, EUR for Germany and France (after 1-Jan-1999, and before DEM

and FRF, respectively), and MXN for Mexico. Further bid.adri,s (ask.adri,s) is

the last bid (ask) in second s of the ADR trading at the NYSE associated to stock

i, adjusted for the respective bundling ratio as described in the Appendix (Data

filters). Note that to make results comparable among stocks I scale each seconds

arbitrage profit by the mid-quote of the home-market share.8

To derive a stock-day measure of arbitrage profits, I take the one second with

the highest profit within the day, i.e. arbitrage profits of stock i on day d is given

8While this might create spurious results later on because both the independent as well as thedependent variable are scaled by the mid-quote, in the given setup this might be less of an issue,as each variable is also explained by lagged versions of itself. However, to avoid any doubt resultshave been replicated using arbitrage profits in USD: qualitatively yielding the same results.

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by the maximum of profiti,s over all seconds s within the day d.

profiti,d = maxs∈d

(profiti,s) (2)

While using a time weighted average across all observable profit within a day

gives qualitatively similar results, the motivation for using the daily maximum

is the following. Observable arbitrage profits in general are lower or equal to

what arbitrageurs see as suitable risk-, and transaction-cost adjusted profits for

pursuing the trade. If arbitrageurs are very active this barrier will be close to

zero, indicating that there are hardly any frictions impeding arbitrage. However,

arbitrage profits might be very low due to other reasons than arbitrage activity.

Looking at time-variations in the daily maximum observable arbitrage profit hence

makes it more likely that the measure captures the time-variations of the barrier

of when an observable arbitrage profit is also perceived as such from an actual

arbitrageur, i.e. leads to a risk-, and transaction-cost adjusted profit.

Table 1 presents summary statistics for arbitrage profits by exchange (Panel A)

as well as by time (Panel B). The first two row in Panel A report cross-sectional

summary statistics (the mean, minimum, maximum, and the 25%, 50% (median),

and 75%, percentile across the 69 stock pairs in the sample) of the time-series

averages. The average of the daily maximum arbitrage profit is around 1%, with

a maximum of 3.4% for one Brazilian stock (with RIC CPFE3.SA). The rest of

Panel A reports these cross-sectional summary statistics across all stock pairs from

a given exchange. Variation in the arbitrage profit across exchanges is relatively

minor, with the exception of Brazil and Germany. For England the median stock

has an arbitrage profit of 0.70%, whereas for France it is 0.73% and for Mexico

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0.83%. It might appear surprising to see both England, and Mexico, one developed

and one emerging market, having similar arbitrage profits, but these profits are

adjusted for the bid-ask spread. Mexico has a proportional quoted spread of 1.4%

for its average home-market stock, and 1% for the average ADR across the whole

sample, this is roughly 3 to 7 times the size of the proportional quoted spread for

the average stock from England of 0.2% and 0.4% (see also Figure 3).

Panel B of Table 1 shows cross-sectional statistics across all stock pairs during

three different time periods. Average arbitrage profit declines from around 1% in

1996 to 2004, to 0.7% in 2005 to 2008, and rises slightly to 0.8% in the last period

(from 2009 to 2011). To further explore time-variations in arbitrage profit, I now

report the daily time-series development.

Figure 2 presents the daily time-series development of market-wide, i.e. equally

weighted average across all stocks from a given exchange, average, high, and low

arbitrage profit. Each of the five rows refers to one of the five exchanges considered

in the sample. In all five cases the high in arbitrage profits is decreasing over time,

indicating that markets are getting more efficient. This is consistent with findings

by Chordia, Roll, and Subrahmanyam (2005), who show that efficiency for US

stocks increased over time.

2.2. The measures: liquidity and order imbalance

I now use filtered trade and quote data to calculate the following three liquidity

measures. First, proportional quoted spread is the daily time-weighted average of

the difference in the ask and the bid price, scaled by the mid-quote price (PQSPR).

Second, proportional effective spread is the daily average of the absolute difference

between the logarithm of the trade price and the logarithm of the mid-quote price

12

of the prevailing quote (PESPR). Third, quoted depth is defined as the daily time-

weighted average of the sum of the number of shares available for both the best bid

and the best ask prices. To get a comparable statistic across stocks the number

of shares available are then converted into a USD volume using the time-weighted

average mid-quote price converted to USD across the trading time. In the following

I use the logarithm of the USD quoted depth and refer to it simply as depth. All

three measures have been widely used as measures of illiquidity before (or in the

case of depth, liquidity), for example Roll, Schwartz, and Subrahmanyam (2007);

Moulton and Wei (2009). While other measures of illiquidity are available (e.g.

Amihud (2002)) these are often not easily constructed on a stock-day level.

I further construct a measure for buying or selling pressure. First I sign every

trade in both the home market and the ADR using the Lee and Ready (1991)

algorithm.9 Second, to derive a daily order imbalance measure for each stock I

take the difference between the number of buyer- and seller-initiated trades in a

given day. As deviations can be positive as well as negative I then take the absolute

value as a measure for order imbalance (OIB).

Figure 3 plots the daily time-series development of market-wide, i.e. equally

weighted average across all stocks from a given exchange, proportional quoted

spread (PQSPR). In the left (right) column the development of PQSPR for the

average home-market stock (ADR) is shown, each of the five rows refers to one of

the five exchanges considered in the sample. In all ten cases graphs are downward

9A trade is classified as buyer- (seller-) initiated if it is closer to the ask (bid) of the prevailingquote. A trade at the midpoint of the quote is classified as buyer- (seller-) initiated if the previousprice change is positive (negative). Lee and Radhakrishna (2000) and Odders-White (2000) giveevidence that this algorithm is quite accurate for NYSE stocks, indicating that at least for theADRs misclassification’s should be minimal.

13

sloping, indicating a decrease in illiquidity over time. In the early years of the

sample (1999) average PQSPR in Brazil was around 2.4% for the home-market

stock and 1.4% for the associated ADR. Eight years later (2007) these numbers

dropped to 0.5% and 0.2%, respectively. A similar decline in PQSPR is visible

for stocks from developed markets, albeit from a much lower starting level. For

example average PQSPR in England in 2007 was 0.1% for both the home-market

stock and the ADR, down from 0.3% and 0.8%, respectively. These declines in

PQPSR follow general trends for markets to become more liquid, for example

Chordia, Roll, and Subrahmanyam (2001, 2011) show these trends for US stocks.

Note, that as the market can consists of as little as one stock (e.g Germany in

1997) variation in the marketwide time-series, as depicted in Figure 2 and Figure 3,

is partly also due to cross-sectional variation.

2.3. The methodology: Vector autoregressions and impulse response functions

To give evidence for how arbitrageurs impact market liquidity, I first present

simple correlations between daily measures of liquidity and daily arbitrage activity.

Then I give evidence for two way Granger causality, where both arbitrage activ-

ity Granger causes liquidity, and the other way around. To address endogeneity

issues arising from contemporaneous regressions and correlations, I use vector au-

toregressions (VAR) in the following. Vector autoregression (VAR) regress each

variable on lagged versions of itself and of lagged versions of all other variables in

the system. For example a first-order VAR of arbitrage profit (πt) and proportional

quoted spread (λt) consists of two equations as given below.

πt = α1 + β11 ∗ πt−1 + β12 ∗ λt−1 + ε1t (3)

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λt = α2 + β21 ∗ πt−1 + β22 ∗ λt−1 + ε2t (4)

The order of the VAR has been chosen by the Akaike information criteria.

I especially focus on impulse response functions (IRF), which track the reponse

on one variable (referred to as the effect) from an impulse to another variable

(referred to as the cause). Because estimated VAR innovations are correlated

across equations I use Cholesky composition to calculate orthogonalized impulse

responses. As using Cholesky composition makes the results sensitive to the or-

dering of the input variables, the order has been fixed to arbitrage profit, home

market liquidity, and last ADR liquidity. All VARs are also estimated using all of

the other 5 possible permutations of the order of the input variables, qualitatively

leaving the results unchanged.

Similar to Roll, Schwartz, and Subrahmanyam (2007) all variables entering the

VAR are first expunged of deterministic time-trends and other calendar regular-

ities. This is to ensure that regression results are not spurious and driven by a

common trend, or by other common calendar regularities.

3. The evidence

3.1. Arbitrage arises because of non-fundamental demand shocks

If arbitrage opportunities arise because of non-fundamental demand shocks ar-

bitrageurs will act as “cross-sectional market” makers (Holden, 1995) and improve

liquidity. However, if arbitrage opportunities arise because of different information

sets, arbitrageurs are likely perceived as informed traders, increasing adverse selec-

tion costs and deteriorating liquidity. Because the reason of why arbitrage arises

partly determines the impact arbitrageurs have on liquidity I start (where Schultz

15

and Shive (2010) stop) by estimating the frequency of how arbitrage arises.

Panel A of Table 2 reports the averages across all 69 stocks in the sample

of the daily average number of arbitrage, their average profit in USD, and the

average time the arbitrage persist in seconds. Panel B of Table 2 report these three

statistics over different time intervals. The statistics are reported by the reason of

why the arbitrage arises. If the bid and ask quotes of all three assets (the currency

pair, the ADR, and the home market stock) are such that no-arbitrage exists, it

takes one asset (the First mover) to move first to create an arbitrage. Similar, it

takes any of the three assets to move to make the arbitrage disappear. If the same

asset moves and the arbitrage disappears as the one that created the arbitrage, the

arbitrage occured because of a non-fundamental demand shock. However, if any

of the other two assets moves and the arbitrage disappears, the shock to the First

mover was permanent, reflecting differences in information. The table reports all

statistics across if the arbitrage arises because of a non-fundamental demand shock

(Price Pressure) or because of information (Information), and further by the asset

that created the arbitrage (First mover).

On average around 61 arbitrage opportunities arise per day, of which over 70%

arise because of price pressure, over the whole sample but also with similar ratios

in each of the three time periods reported in Panel B of Table 2 and in each of the

five exchanges (untabulated). Note, that arbitrage that arise or vanish because

both the ADR and the home market stock move at the same time are ignored,

because this happens relatively infrequent and gives a similar picture, that the

majority arise because of a non-fundamental demand shock.

Hence, Table 2 provides first support that arbitrageurs in the ADR market

likely act as “cross-sectional market” makers (Holden, 1995) and hence likely im-

16

prove liquidity.

3.2. Correlations, and Granger causality as initial evidence

Using stock-day estimates of arbitrage profit and illiquidity from tick-by-tick

data, I now present correlation and Granger causality results as initial evidence

for the joint dynamics of these variables.

Panel A of Table 3 reports Pearson correlations between daily estimates of

arbitrage profit and proportional quoted spreads per individual stock. The average

stock has a correlation between arbitrage profits and proportional quoted spread

of the home market (ADR) over the whole sample of around 24.17% (25.22%), of

which 83% (87%) of all individual stock estimates are statistically significant at

the 1% level.

Panel B of Table 3 reports pairwise Spearman rank correlations for individual

stock estimates, as before. The average rank correlation between arbitrage profits

and proportional quoted spread of the home market (ADR) over the whole sample

is around 36.39% (35.47%) and statistically significant at the 1% level in around

93% (93%).

Further Granger causality indicates that both are interrelated, both Granger

causing the other. Panel C of Table 3 reports the percentage of all stocks where the

null hypothesis, that the row variable does not Granger cause the column variable

is rejected at a 5% significance level.10 At first sight it might seem surprising

that in around 40% of all cases illiquidity (Dom PQSPR, For PQSPR) Granger

10For example, arbitrage profit Granger causes quoted spread if a Wald test rejects the hy-pothesis that the R2 of the unrestricted model (in which quoted spread are explained by laggedquoted spread and lagged arbitrage profit) is equal to the R2 of the restricted model (in whichquoted spread is only explained by lagged quoted spreads).

17

causing arbitrage profits could be rejected. But a change in illiquidity does not

necessary change arbitrage profits. Mechanical and ceteris paribus an increase in

illiquidity in one market will lead to a decrease in arbitrage profits, but as the

correlation coefficient indicates average correlation between both variables is in

general positive. However, the impact liquidity has on arbitrage has been well

established (e.g. Roll, Schwartz, and Subrahmanyam (2007)). The focus in this

study is the other way around, the impact of arbitrageurs on liquidity: For 71%

(71%) I cannot reject that arbitrage profit Granger causes quoted spread on home

market stocks (ADRs).

In summary, Table 3 indicates positive and significant (statistically and eco-

nomically) correlations between both arbitrage profit and quoted spread, as well

as that both Granger cause each other. Although this is evidence that arbitrage

profits and illiquidity are jointly determined, this could be purely because of com-

mon time trends, or because of other calendar regularities.11 For example, as

Roll, Schwartz, and Subrahmanyam (2007) mention, arbitrage activity might be

lower on Fridays, due to additional costs or risk of holding open positions over the

weekend. But this argumentation is as valid for arbitrageurs as for local market-

makers, hence Friday might also be characterised by lower liquidity. To address

these concerns I detrend arbitrage profits, and all liquidity variables.

Table 4 (Table 5) reports results of individual-stock regressions of daily ar-

bitrage profits, proportional quoted spread, order imbalances, and differences in

proportional quoted spread during and outside overlapping trading hours (propor-

tional effective spread, and USD quoted depth) on a time-trend and other calendar

11However, this is not the case. In unreported Granger causality tests on the adjusted series(as explained later on) similar results are achieved.

18

regularities. In detail, each variable is regressed on a linear and quadratic time-

trend, 4 day-of-the-week, and 11 month dummies (similar to Roll, Schwartz, and

Subrahmanyam (2007)). Further to address sudden changes in USD quoted depth I

include a dummy variable for stocks and their cross-listed counterpart from France

(Mexico), which is set to 1 after 2007-02-17 (2009-09-28).12

All reported estimated slope coefficients are averaged across all individual-stock

regressions and reported separately for the home-market (DOM) and for the ADRs

(FOR). As can be seen, arbitrage profit is indeed higher on Friday (i.e. arbitrageurs

are less active) than on any other weekday (the average slope coefficient for the

Friday dummy is: 0.03%). However, liquidity during the overlapping time period

on Friday seems lower for the home market stock (the average slope coefficient for

the Friday dummy is: -0.009%), and higher for the ADR (0.006%), but in both

cases not statistically significantly different from the benchmark case (Mondays).

Further Table 4 and Table 5 report the average test statistic for a Dickey-Fuller

test for finding a unit root in the residuals of the individual stock regression. In

all cases the existence of a unit root is rejected at the 1% level.

Instead of using the stock-day estimate of arbitrage profit or proportional

quoted spread, the residuals from the individual stock regressions on a time trend

and other calendar regularities (as described above) are used in the following and

for brevity referred to as adjusted series. While above correlation and Granger

causality results might be influenced by the deterministic time trend, a more se-

12Unreported graphs show sudden jumps in USD depth for the home-market stocks fromFrance, and Mexico. Suddenly after 28-Sep-2009 depth for all stocks in Mexico increased by afactor of 100, likely due to a change in reporting conventions. The sudden drop in depth on andaround 27-Feb-2007 for France, does not seem to be related to reporting conventions, becausestocks were differently influenced. In this case it seems rather related to a merger from EuronextParis and NYSE on 04-Apr-2007.

19

rious concern is endogeneity. I address this by estimating vector autoregressions

(VARs) using the adjusted series in the next subsection.

3.3. Stock level: Arbitrage activity predicts liquidity

Vector autoregression (VAR) regress each variable on lagged version of itself and

of lagged versions of all other variables in the system, and hence treat every variable

as endogenous. Input series for each VAR are daily estimates of arbitrage profits,

home market and ADR proportional quoted spreads. All three series are detrended,

and other calendar regularities have been removed, i.e. residuals from regressions

reported in Table 4 are used. Further these series are winsorized at the 1% level,

i.e. for each stock the lowest (highest) 1% are set to the 1% (99%) percentile.13

To make results comparable across stocks, after winsorizing the adjusted series the

series is further standardized, i.e. from each observation the time series mean over

each day in the sample is subtracted and each observation is divided by the series

standard deviation. For parsimony the order for each VAR is fixed to 5.14

Panel A of Table 6 reports correlations in VAR innovations (residuals). For

the average (similar median) stock innovations from regressing arbitrage profits

on lagged arbitrage profit, home market and ADR quoted spreads have a corre-

lation of around 12% (8%) to innovations from regressing home market (ADR)

quoted spreads on lagged arbitrage profit, home market and ADR quoted spreads.

This gives further evidence for the joint dynamics between arbitrage profits and

13Using non-winsorized data does not affect results for developed home markets (England,France, and Germany) and results for emerging markets (Brazil, and Mexico) remain qualitativelyunchanged.

14The order was chosen by first letting Akaike information criteria chose the order separatelyfor each stock. this yield an order between 1 and 10 days. A good choice seems 5-days, which isaround the median order, and one working week

20

illiquidity.

The results from the VAR estimation are now used to construct impulse re-

sponse functions (IRF).

An IRF tracks the shock of one standard deviation to one of the variables

through the system and through time. Because VAR are estimated on standardized

data the IRF effect is also measured in standard deviations.

Panel B of Table 6 reports the cumulative impulse response after 5-days (the

order of the VAR) to a one standard deviation shock to the causal variable.

It is tempting to make comparisons within IRF results, for example to argue

that home market quoted spread has a stronger impact on ADR quoted spread,

than the other way around, and hence give further evidence for the “gravitational

pull of the ... domestic market” Halling, Pagano, Randl, and Zechner (2007).15

However, this has to be done with caution. Because for each estimated VAR in-

novations are correlated across equations I use Cholesky composition to calculate

orthogonalized impulse responses. As using Cholesky composition makes the re-

sults sensitive to the ordering of the input variables, the order has been fixed to

arbitrage profit, home market liquidity, and last ADR liquidity in Table 6 and

later on. For example if IRF are estimated for the order ADR proportional quoted

spread, arbitrage profit, and last home market proportional quoted spread, this ef-

fect reverses and the effect of a shock to ADR illiquidity forecasts a higher change

in home market illiquidity, than the other way around. However, estimating all

other 5 possible permutations of the three input variables yields qualitatively simi-

15A shock of one standard deviation to home market quoted spread forecasts an even biggershock to ADR quoted spread of in average 1.58 standard deviations, which is much stronger thanthe other way around (0.38).

21

lar results for the responses in illiquidity to a shock to arbitrage profit. For example

with the default order in 75% of all stocks a shock to arbitrage profit yields a sta-

tistically significant effect (at the 5% level) to home market proportional quoted

spread. Changing the order to ADR liquidity, arbitrage profits, and last home

market liquidity yields that 63% of all estimates are statistically significant.

For the average stock a positive shock of one standard deviation to arbitrage

profits predicts an increase in home market and ADR illiquidity by 0.95 and by

0.54 standard deviations, respectively. Further a shock to arbitrage profits results

in a cumulative impulse response in home market (ADR) illiquidity that is statis-

tically significant at the 5% level for 75% (55%) of all stocks. Note that statistical

significance can be found for stocks across all five different exchanges, for example

40% of all stocks from Mexico show a statistically significant response to home

market illiquidity from a shock to arbitrage profit.

To study IRF in more depth, I now construct a “market” index for each ex-

change. This not only simplifies analysis of the impulse response functions by

reducing the amount from 69 (stock-ADR pairs) to 5 (home-market exchanges), it

also sheds light on if these effects are purely idiosyncratic (i.e. stock specific) or if

a common component exists.

3.4. Market level: Arbitrage activity predicts liquidity

In this section I estimate VAR on the market level for each exchange. Input se-

ries for each VAR are the same as in the previous section, i.e. adjusted, winsorized,

and standardized arbitrage profit and home market and ADR proportional quoted

spreads, however in this section I take equally weighted averages across all stocks

from a given exchange, before standardizing the series. To reduce variations in any

22

of the input variables due to stocks added to the “market” I only use data starting

from 2001, this ensures that every day the market consist of at least four stocks

(Germany in 2011), and that the timeseries average over all days in the sample of

the number of stocks in the market is at least 7.5 (Germany).

Figure 4 shows the cumulative impulse response from a one standard deviation

shock to arbitrage profit to home market (ADR) proportional quoted spread in

the upper (lower) row (bold line), as well as bootstrapped 95% confidence bands

around the estimate. For parsimony Figure 4 only reports IRFs from shocks to ar-

bitrage profit. These impulse response functions have been estimated by exchange

(column). The x-axis tracks the response through time starting from 1 (the con-

temporaneous effect) till the n-th day, the order of the VAR, which was chosen

by Akaike information criteria individually for each exchange and varies from 18

for Brazil to 30 for England. It is visible that all impulse response functions are

upward sloping, indicating that an increase in arbitrage profits predicts an increase

in illiquidity. And all of them are statistically significant at the 5% level. Further

the economic significance is substantial. Across all exchanges a one standard de-

viation shock to arbitrage profit predicts an increase in illiquidity (both for the

home as well as the cross-listed market) of around 0.5 standard deviations.

Further note that most IRFs are flattening out, indicating previous Dickey-

Fuller tests that reject the existence of a unit-root at significance level below 1%

(see Table 4).

Similar plots are given for impulse response functions estimated from VAR us-

ing proportional effective spreads (Figure 5), and quoted depth (Figure 6). In each

case input series are first detrended, winsorized, and standardized as in the bench-

mark case (i.e. using the proportional quoted spreads). Results are in line with

23

previous once: an increase to arbitrage profits predicts an increase in illiquidity.

A positive shock to arbitrage profit predicts an statistically significant increase in

PESPR for both the home market, as well as the cross-listed market, and for all

five different exchanges. Further a positive shock to arbitrage profit predicts a

decrease in quoted depth in all except one case (home market depth in France).

However, in only half of the cases the effect is statistically significant (and of the

right sign). The low significance for England is likely driven by the fact that depth

is only observed for three years starting from 2009.

A snapshot of these impulse response functions is given in Panel A, Panel

B, and Panel C of Table 7, i.e. Table 7 reports the 5-day cumulative responses

to a one standard deviation shock to arbitrage profit. Results indicate that a

one standard deviation positive shock to arbitrage profits predicts an increase in

illiquidity (quoted spread, effective spread, and quoted depth) in all cases, except

for home market depth in France. Further results are significant at the 5% level

in 22 out of 30 cases.16 Panel D and Panel E of Table 7 also report a snapshot of

an IRF. These IRF are the focus of the two following sections.

So far the evidence in this paper indicates that an increase in arbitrage profits

(an inverse measure of arbitrage activity) predicts an increase in illiquidity, proxied

by proportional quoted spreads, proportional effective spread, as well as USD

quoted depth. These findings are robust for either using individual stocks, or an

exchange specific “market”.

16Note again that results are sensitive to the ordering of the input variables. However, esti-mating all 5 possible permutations of the order yields qualitatively similar results. For example,ordering the input variables such that arbitrage profits is last and home market illiquidity first(second), indicates that a positive shock to arbitrage profits predicts an increase in illiquidity(quoted spread, effective spread, and quoted depth) in 26 (26) out of 30 cases and 15 (14) ofthese are significant at the 5% level.

24

The question now arises whether arbitrageurs are predicting changes in liquidity

and in anticipation of an increase in illiquidity, or funding constrains step out of the

market (e.g. Shleifer and Vishny (1997)), or whether they directly (e.g. through

cross-sectional market making Holden (1995)) or indirectly (e.g. by creating a

substitute Moulton and Wei (2009)) positively influence liquidity.

To answer this question I focus on liquidity provision during and outside over-

lapping trading hours in the next section.

3.5. Arbitrage activity not merely predicts, but influences liquidity

In the depository receipt market the same stock can often be observed during

and outside times in which arbitrage takes place (i.e. during and outside overlap-

ping trading hours, as depicted by Figure 10). However, for Mexico and Brazil

the opening hours of the home market almost exactly overlap with the opening

hours of the cross-listed market (NYSE) and hence are both not considered in the

following.

For the home market I now examine differences in proportional quoted spread

during the overlapping time and from 12 UTC (to avoid the general effects of the

opening period) till the cross-listed market opens (for example 13:30 UTC on 15-

Oct-2008). In a similar way I look at differences in proportional quoted spread

during the overlapping time and afterwards for the cross-listed market. Like in

the previous section these series are first adjusted for time trends and calendar

regularities, i.e. residuals from individual stock regressions provided in Table 4

are used. The adjusted series are then winsorized and averaged across all stocks

(ADRs) from a given exchange to yield the input series for the VAR.

By using the residuals of regressing the differences in illiquidity during and

25

outside overlapping trading hours on an intercept, a time trend and other calendar

regularities, I especially remove any general differences in illiquidity across the

same day. Hence, if arbitrageurs would predict a general decline in liquidity and

in anticipation withdraw from the markets, differences in liquidity across the same

day would be around 0. However, if arbitrageurs indeed have a direct or indirect

effect on liquidity the difference between illiquidity between overlapping and non-

overlapping trading hours should increase.

This is indeed what impulse response functions indicate as shown in Figure 7.

Figure 7 shows the cumulative impulse response from a one standard deviation

shock to arbitrage profit to differences between illiquidity during and outside over-

lapping trading hours for both the home-market and the ADR (similar to Figure

4). In all cases the slope of the IRF is positive, indicating that a positive shock to

arbitrage profits predicts an increase in the difference between illiquidity during

and outside overlapping trading hours. Further most of the slopes are statistically

(at the 5% level) as well as economically significant (except for the cross-listed

stocks from England). A shock of one standard deviation to arbitrage profits

predicts an increase of around 0.2 standard deviations in the difference between

illiquidity during and outside overlapping trading hours.

In segmented markets one would expect illiquidity of both the home as well

as the cross-listed market to be higher during the overlap than outside. This is

because illiquidity in general follows a U-shaped intraday pattern, and the overlap

for the home market coincides with the closing period, whereas the overlap of the

cross-listed market overlaps with its opening period. If however, both markets were

integrated the opposite effect should be visible, i.e. both the U-shaped pattern of

home market and cross-listed market illiquidity should converge to a big U-shaped

26

pattern spanning the whole trading time of when the home market opens till when

the cross-listed market closes (compare Figure 2 of Werner and Kleidon (1996)).

In this case differences in illiquidity during or outside overlapping trading hours

should be minimal.

Because previous results show that if arbitrageurs are getting less active differ-

ences in illiquidity increase, these results indicate that arbitrageurs are improving

market integration.

3.6. Arbitrageurs are trading against net market demand

To further understand possible mechanisms of how arbitrageurs might improve

market liquidity, I now estimate impulse response functions with order imbalance

instead of illiquidity measures.17 If arbitrageurs trade against net market demand

and thereby improve liquidity, a decrease in arbitrage activity should increase net

order imbalances. Figure 8 shows impulse response functions estimated from vector

autogregressions on arbitrage profits, and home and ADR order imbalance. As

before, for each individual stock all three series are first detrended (i.e. residuals

from regressions from Table 5 are used), and then winsorized at the 1% level.

Finally I take the equal weighted average across all stocks from a given exchange

and then standardize each series. These series on market arbitrage profit, home

market and ADR order imbalance are the input series for the VAR. In all 10

cases the IRF is upward sloping, and in 6 out of 10 cases the effect is statistically

significant at the 5% level. This indicates that a positive shock to arbitrage profits

17I note that order imbalance and liquidity are related as well (e.g. Chordia, Roll, and Sub-rahmanyam (2002)). I hence also estimate vector autoregression and impulse response functionsusing both adjusted series of daily proportional quoted spread and order imbalance together.Estimating the effect on quoted spread and order imbalance to a shock to arbitrage profit jointly,results in similar effects as if the effects are estimated separately (as done in the main text).

27

predicts an increase in order imbalance. The economic significance is substantial.

A one standard deviation shock to arbitrage profits predicts an increase in order

imbalance of around 0.1 to 0.2 standard deviations. This gives rise to one possible

way of how arbitrageurs might improve liquidity. Arbitrageurs trade against net

market demand, and thereby increase market-making capacity and hence improve

liquidity.

3.7. Intraday: Arbitrageurs improve market liquidity for most stocks, most of the

time

Tests in Section 3.5 already partially address endogeneity concerns, for example

an omitted variable bias might arise because frictions to arbitrage might also im-

pact liquidity. A good example is funding liquidity (Brunnermeier and Pedersen,

2008), a decrease in funding liquidity will likely impact arbitrage activity as well as

market liquidity. Omitted variables will likely affect illiquidity equally across the

day, and hence will have no effect on the illiquidity differences during and outside

overlapping trading hours. But in Section 3.5 I find that arbitrage profits predict

a higher increase in illiquidity during than outside overlapping trading hours: at

odds with a general decline in liquidity. However, to further address this concern I

estimate all VARs from previous sections with two additional input variables: the

home market and ADR illiquidity before and after the overlapping trading time,

respectively (results of these IRFs are unreported and are available upon request).

The concept of these additional variables is that they proxy for any change in the

general trading environment, such as changes in funding liquidity. Adding these

two additional variables to the VAR underlying each IRF does not change the

results.

28

To further address this concern I now run IRF based on intraday data. While

frictions such as funding liquidity might change interday it seems less likely that

they often change intraday.

I estimate an IRF for each stock-day on which both the home market as well

as the cross-listed market have at least 50 quote messages during the overlapping

trading period based on a VAR of order 5. Input series to each VAR are maximum

arbitrage profit, and average proportional quoted spread for the home market

and the ADR over a 4-minute interval. On the one hand the intraday horizon

needs to be long enough to not pick up short-term order balance management by

market-makers (for example Chordia, Roll, and Subrahmanyam (2005) show that

5-minute returns are predictable from past order flow in 2002). On the other hand

the intraday horizon needs to be short enough to allow sufficient observations and

hence meaningful regressions within the day. Using 4-minute intervals seems a

reasonable tradeoff. Due to similar reasons as before all series are detrended using

a linear and quadratic timetrend for each stock-day and then the residuals are

used as input to the VAR. As the overlapping period for European markets in

general is 2 hours, each VAR is based on 115 intervals, 5 intervals are lost due to

the need for lagged observations. For both emerging markets (Brazil, and Mexico)

the overlapping period is substantially longer as shown in Figure 10.

Figure 9 shows yearly box plots of the 20-minutes cumulative impulse response

to a one standard deviation shock to arbitrage profit per exchange. It is striking to

see that the yearly average response to home market illiquidity is positive across

most years and across almost all stocks (except for Mexico). This is in line with

previous results. Further the response on illiquidity of the ADR indicates a positive

trend reaching its top around 2007, 2008. Back then most ADRs have a positive

29

response to a shock in arbitrage profit. However, this trend seems to brake down

after 2008, potentially influenced by the financial crisis.

All in all, evidence that previous results are not significantly driven by endo-

geneity issues.

4. Conclusion

The answer to the question of how arbitrageurs impact market liquidity helps

to understand how frictions impeding arbitrage might impact liquidity. In this

paper I provide empirical evidence that is in line with the interpretation of ar-

bitrageurs as “cross-sectional market” makers (Holden, 1995). Arbitrageurs are

improving liquidity and are indeed trading against net market demand, or as Fou-

cault, Pagano, and Roell (2013) put it, arbitrageurs are “leaning against the wind”

(p. 336). The limits of arbitrage literature in general assumes that arbitrage

opportunities arise because of non-fundamental (liquidity) shocks or investor sen-

timent and hence assumes that arbitrageurs are improving liquidity (Gromb and

Vayanos, 2010; Foucault, Pagano, and Roell, 2013). This was not always the case.

Historically arbitrageurs were partly blamed for the 1987 market crash, and arbi-

trage was considered to be de-stabilizing. To the best of my knowledge the broad

evidence for the positive role of arbitrageurs presented in this paper is the first

that empirically supports this paradigm shift.

These results shed additional light on possible consequences of frictions imped-

ing arbitrage, such as short-selling bans, or transaction taxes and hence might be

of interest for policy makers. To curb excessive trading eleven European member

states plan to introduce a transaction tax in January 2014. This tax will be at least

0.1% of the purchase price, which is two times the proportional quoted spread for

30

the average stock (in my sample) at Xetra in 2011. Further an increase in trans-

action costs of 0.1% will likely affect arbitrage profits in a similar magnitude. For

the average stock at Xetra in 2011 arbitrage profit is around 0.1%, with a daily

standard deviation of 0.2%. The transaction tax planned for January 2014 hence

is of the same magnitude as average arbitrage profits in 2011 and equals a shock

of half a standard deviation. Likely this will have an adverse effect on liquidity

and hence might make cross-listing for companies less attractive.

Finding opposing results for the impact of arbitrageurs on liquidity in the ADR

market compared to the findings by Roll, Schwartz, and Subrahmanyam (2007)

for the future-cash market, are likely because both the ADR and the home-market

are viewed as substitutes and hence no specific clientele effect arises. Indeed, a

survey in 2003 by JPMorgan among 102 institutional investors revealed that 24%

of all investors are indifferent between investing in the home-market share or its

respective ADR, but rather depend their decision on liquidity (JPMorgan, 2003).

However, the important question of how generalizable these results are, remains

unanswered. Empirical evidence indicates that arbitrageurs not always improve

liquidity, but might also harm it. For example Roll, Schwartz, and Subrahmanyam

(2007) show that in the future-cash basis increased arbitrage activity predicts a

decrease in liquidity. Further using impulse response functions estimated per stock-

day indicate a positive time trend in how arbitrageurs impact liquidity in the cross-

listed market. In the early years their impact seems more in the direction of the

findings from Roll, Schwartz, and Subrahmanyam (2007), whereas in the latter

years their impact is similar to their impact on the home market illiquidity, i.e.

in general arbitrageurs are improving liquidity provision. A potential explanation

is given by Domowitz, Glen, and Madhavan (1998), who show (theoretical, and

31

empirical) that ”if intermarket price information is freely available, cross-listing

... increases liquidity in both markets.”, while on the other hand if ”intermarket

information linkages are extremely poor, cross-listing reduces liquidity.” The time-

series of how arbitrageurs impact liquidity in the cross-listed market, might hence

indicate improvements in market integration upto 2008.

32

Appendix A: Sample construction

This appendix describes details of the sample construction. I first retrieve all dead

and alive American and global depository receipts (DRs) from Datastream which

returns (in Dec-12) 7700 different DRs of which around 10% (732) are traded at

the New York Stock Exchange (NYSE), the focus in this study.

The home market share, associated to any of the ADRs, can be identified using

data from adrbnymellon.com or adr.db.com. Both websites offer a list of DRs and

an ISIN code for the home market share.

As the analysis requires intraday data for which I use the Thomson Reuters

Tick History (TRTH) database, I filter out any DR for which no RIC identifier

(the primary identifier in TRTH) could be established for either the DR or the

home-market stock. Upon request Datastream provides a RIC field, however this

field is empty for around 50% of all DRs. In the case of a missing RIC field for

the ADR or for the home market shares I use the TRTH API to search for a RIC

code by ISIN.

For every ISIN the RIC from the major exchange of the home market country

is chosen. This way 199 out of the 732 stocks remain. A possible reason for this

significant drop in identified home-market/ADR pairs is that either the ADR got

delisted from the NYSE, or that the home-market share got delisted from the

home-market exchange before 1996, the beginning of the TRTH database.

A similar setup (i.e. using intraday data from TRTH for ADRs, albeit for an

event study) is considered by Berkman and Nguyen (2010), who are able to identify

277 ADR-home market pairs, but of which only 44 trade at NYSE. Berkman and

Nguyen (2010) use a matching based on country of origin, name, stock type, and

33

price rather than on the RIC code itself. Further Gagnon and Karolyi (2010)

identifies 506 ADR-home market pairs using Datastream, but the ADR can be

listed on either NYSE, Amex, or Nasdaq. The above matching results in 199 pairs

where the ADR is traded at the NYSE.

I now proceed to use the top five home market exchanges, in terms of having

the most identified cross-listed ADRs trading in NYSE and having an overlapping

trading time with the NYSE (to avoid non-synchronous prices). These exchanges

are the London Stock Exchange (England, with 29 stocks), Sao Paolo Stock Ex-

change (Brazil, 20 stocks), Bolsa Mexicana de Valores (Mexico, 14 stocks), XETRA

(Germany, 9 stocks), and Euronext Paris 18 (France, 9 stocks). Of these 81 stocks

I filter out 6, because I could not find intraday data for either the home market

or the cross-listed ADR for at least 100 days. Further 6 stocks from Brazil and

Mexico dropped from the sample because prices of the home market could not be

aligned to prices of the ADR, as described in more detail on page 35.

Figure 10 shows the continuous trading times for all five exchanges in the

sample on 2008-10-15.19 The opening and closing time at the NYSE is indicated

by the left and right vertical line, respectively. The area within the vertical lines,

in which the home-market is open, refers to the overlapping trading hours for this

specific exchange.

18Note that Euronext and NYSE merged on 04-Apr-200719Day light saving time (DST) does not follow the same rule in the USA and the other countries

in the sample. Hence, overlapping trading hours between the NYSE and the other exchangesare varying within the year, but in general are 2, 6, and 6.5 hours between Europe, Brazil, andMexico and the NYSE, respectively (as depicted in Figure 10). However, for example, on 28th,March 2000 overlapping trading hours between France and the NYSE are from UTC 13:30 tillUTC 14:30, because European countries enter summer time on 26th, March, while the UnitedStates enters summer time one week later, on 2nd, April.

34

Appendix B: Data filters

This appendix describes the quote and trade data filters. I discard non-positive

bid and ask quotes (in total 24,583 quotes), quotes where the ask is lower or equal

to the bid quote (1,072,514 quotes), and quotes outside the continuous trading

session (26,866,555 quotes). Further, outliers are removed (904,455 quotes). An

outlier is defined as a bid (ask) quotes that differs by more than 10% of the average

of the 10 surrounding bid (ask) quotes, where the ask price is more than USD (or

the respective home-currency, i.e. EUR, GBP, ...) 5 different from the bid price,

or where the ratio of the difference of the ask and bid price to the mid quote is

higher than 25%. In a similar way trade prices are filtered.

To make prices comparable between the home market stock and the ADR, bid

and ask quotes of the ADR are converted according to the bundling ratio which I

got from either adrbnymellon.com or adr.db.com. Unfortunately, bundling ratios

can be time-varying and both websites only report the latest bundling ratio (Dec-

2012). To adjust the bundling ratio over time, I first plot daily currency adjusted

mid-quote ratios for each stock in the sample (unreported). If the ratio varies

around one the current bundling ratio is assumed to be correct for the whole

sample, if a clear step function can be identified bundling ratios are adjusted

accordingly, and if the resulting plot does neither resemble a line around one nor a

step function the stock is dropped from the sample. As such six stocks from Brazil

and Mexico dropped from the sample because prices of the home market could not

be aligned to prices of the ADR.

For 20 ADRs the bundling ratio changed over the sample, with a maximum

of three changes for one ADR with RIC ICA.N referring to a stock in Mexico

35

(Empresas ICA).

To further ensure that stocks are mapped properly and prices are adjusted

correctly I drop any stock-day if arbitrage profit is higher than USD 10 at any

second. For 48 out of the 69 stocks the highest profit on every day is below USD

10, and further these 48 stocks also have a reasonable low average percentage profit

with the highest average across the 48 stocks of around 3.3%. This indicates that

the majority of all stocks are mapped correctly to their ADR and that ADR prices

are correctly adjusted for the bundling ratio across the whole sample.

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41

5. Tables & Figures

Table 1 – Cross-sectional summary statistics of time-series averages, 69 ADR-ORD pairs, 1996 - 2011This table reports the cross-sectional minimum (min), maximum (max), average (avg), and the 25%, 50% (median), and75%, percentile of the time-series average by stock of the daily highest observable arbitrage profit (Arbitrage profits.)If the currency adjusted home-market bid (ask) price is higher (lower) than the bundling adjusted cross-listed shareask (bid) price an arbitrage opportunity exists. And I measure arbitrage profits as the absolute difference between thehome-market bid (ask) price and the cross-listed share ask (bid) price relative to the home-market mid-quote price.Ask (bid) quotes from the home market are converted to USD using prevailing tick-by-tick ask (bid) quotes from therespective currency pair. An example for available arbitrage profit is indicated by the shaded area in Figure 1. The firstcolumn (#Stocks) indicates the number of stocks over which the summary statistics are computed. Panel A reportsthese summary statistics for the whole sample as well as by all five exchanges in the sample. Panel B reports thesesummary statistics by time. All data underlying the computations are from TRTH.

Panel A: Arbitrage profits by exchange (%)

#Stocks avg min 25% Median 75% max

All 69 0.922 0.124 0.521 0.796 1.174 3.375

Brazil 12 1.712 1.021 1.313 1.461 1.836 3.375

England 27 0.743 0.181 0.515 0.695 0.931 1.469

France 9 0.923 0.217 0.616 0.729 0.843 2.780

Germany 9 0.345 0.124 0.220 0.382 0.433 0.584

Mexico 12 0.966 0.517 0.645 0.831 1.197 1.902

Panel B: Arbitrage profits by year (%)


1996 to 2004 53 1.077 0.297 0.699 1.011 1.280 2.740

2005 to 2008 66 0.739 0.149 0.334 0.602 0.997 2.513

2009 to 2011 65 0.800 0.099 0.278 0.458 0.989 6.413

42

Table 2 – Average daily arbitrage and reasons of why they arise, 69 ADR-ORD pairs, 1996 - 2011This table presents the average daily number of arbitrage opportunities (# of Arbitrage), the average associated profit(Arbitrage Profits (%)) and the average time in seconds it takes till the arbitrage disappears (Seconds in Arbitrage). Allthree statistics are calculated on a stock-day level and are then averaged for each stock across all days. All statisticsare reported by the asset (Forex, ADR, or ORD) that created the arbitrage (”First mover”) and whether the arbitragedisappears because the same asset that created the arbitrage also makes it vanish (”Price pressure”) or not (”Informa-tion”). Panel A reports averages across all stocks in the sample. Panel B reports averages over three different timespans. The first column (#Stocks) indicates the number of stocks over which the summary statistics are computed. Alldata underlying the computations are from TRTH.

Panel A: All

# Stocks Price Pressure Information

First mover: Forex ADR ORD Forex ADR ORD

# of Arbitrage 69 17 24 3 7 7 3

Arbitrage Profits (%) 69 0.55 0.32 0.20 0.36 0.33 0.27

Seconds in Arbitrage 69 1,570 363 231 702 462 423

Panel B: By year

# Stocks Price Pressure Information

First mover: Forex ADR ORD Forex ADR ORD

1996 to 2004

# of Arbitrage 53 12 5 2 3 2 2



2005 to 2008

# of Arbitrage 66 19 36 3 9 9 3



2009 to 2011

# of Arbitrage 65 22 41 5 10 12 5



43

Table 3 – Correlations and Granger causality tests, 69 ADR-ORD pairs, 1996 - 2011This table presents pairwise correlation and Granger causality tests between individual stock daily arbitrage profit(Profit), home-market proportional quoted spread (DOM PQSPR), and cross-listed proportional quoted spread (FORPQSPR). All measures are computed during overlapping trading hours only, i.e. when both the home market as well asthe cross-listed market (NYSE) are open. Panel A (Panel B) reports Pearson (Spearman rank) correlation coefficientsaveraged across all individual stock estimates and in parenthesis the percentage of how many estimates are significant atthe 1% level. Panel C reports Granger causality tests. Given is the percentage of all stock individual Granger tests wherethe null hypothesis that the row variable does not Granger cause the column variable is rejected at the 5% confidencelevel. All data underlying the computations are from TRTH.

Panel A: Pearson correlations

Profit DOM PQSPR FOR PQSPR

Profit 22.46 (82.61) 25.30 (85.51)

DOM PQSPR 22.46 (82.61) 59.13 (98.55)

FOR PQSPR 25.30 (85.51) 59.13 (98.55)

Panel B: Spearman rank correlations


Profit 36.32 (92.75) 35.49 (91.30)

DOM PQSPR 36.32 (92.75) 66.97 (98.55)

FOR PQSPR 35.49 (91.30) 66.97 (98.55)

Panel C: Granger causality


Profit 71.01 71.01

DOM PQSPR 55.07 94.20

FOR PQSPR 57.97 89.86

44

Table 4 – Regressions to detrend arbitrage profits and liquidity measures, 69 ADR-ORD pairs, 1996 -2011This table presents the results of individual stock time-series regressions to remove time-trends and other time regularitiesfrom arbitrage profit (Profit), proportional quoted spread (PQSPR), absolute order imbalance (OIB), and difference inproportional quoted spread during and outside overlapping trading hours (DIFF ). Regression results for PQSPR, OIB,and DIFF are reported separately for the home market stock (DOM ), and the cross-listed ADR (FOR). All measuresare computed during overlapping trading hours only (except DOM DIFF, and FOR DIFF ), i.e. when both the homemarket as well as the cross-listed market (NYSE) are open. Each individual stock measure is regressed on a linear timetrend (Trend), a squared time trend (sqr Trend), 11 month dummies (February till December), 4 day-of-the week dummy(Tuesday till Friday), as well as two exchange specific dummies: A dummy for stocks and their cross-listed counterpartfrom France (Mexico), which is set to 1 after 2007-02-17 (2009-09-28). Estimated slope coefficients, R-squared (R2),adjusted R-squared (adj. R2), and number of observations (# Obs.) obtained from all individual stock time-seriesregressions are averaged across all regressions (# Regressions). Cross-sectional t-statistics are in parentheses belowthe coefficients. Further the table reports the average Dickey-Fuller unit-root test statistic (UR Residuals). All dataunderlying the computations are from TRTH.

Dependent: Profitd (%) PQSPRd (%) OIBd DIFF d (%)

DOM FOR DOM FOR DOM FOR

intercept 1.095 0.827 0.787 41.372 20.737 -0.878 0.004(5.48) (5.57) (7.94) (5.10) (3.12) (-4.17) (0.10)

France2007 -0.638 0.031 0.120 14.430 10.356 -0.002 0.008(-22.73) (10.04) (8.59) (5.74) (4.34) (-6.01) (1.70)

Mexico2009 -0.373 0.031 -0.205 -3.266 -26.679 1.537(-3.37) (0.33) (-1.21) (-0.49) (-5.99) (9.93)

Trend -0.002 -0.000 -0.000 -0.052 0.021 0.000 0.000(-1.42) (-2.52) (-0.92) (-0.46) (0.54) (1.55) (0.78)

sqr Trend 0.000 0.000 0.000 0.000 0.000 -0.000 -0.000(1.27) (0.27) (1.09) (0.90) (0.77) (-1.34) (-0.96)

Tuesday 0.005 -0.018 -0.004 3.609 2.113 0.103 -0.000(0.64) (-3.83) (-2.09) (1.64) (2.39) (3.57) (-0.10)

Wednesday -0.010 -0.019 -0.000 5.131 2.544 0.113 -0.001(-0.87) (-3.11) (-0.18) (2.89) (3.34) (3.73) (-0.83)

Thursday 0.002 -0.012 -0.000 2.967 1.400 0.116 0.002(0.21) (-1.71) (-0.17) (2.76) (1.42) (3.50) (0.65)

Friday 0.030 -0.008 0.005 2.435 -0.728 0.103 0.007(4.18) (-1.15) (1.21) (1.75) (-1.32) (3.28) (1.08)

February 0.004 -0.018 0.002 1.183 0.330 -0.000 0.004(0.14) (-1.69) (0.37) (0.52) (0.20) (-0.00) (1.52)

March -0.017 -0.012 0.003 6.743 5.534 -0.026 0.012(-0.64) (-0.87) (0.22) (1.48) (1.99) (-0.88) (1.26)

April -0.007 -0.026 -0.021 0.615 0.231 0.048 0.009(-0.19) (-2.01) (-2.87) (0.16) (0.10) (1.17) (2.11)

May 0.152 -0.021 0.002 3.854 6.990 0.118 0.010(0.98) (-1.78) (0.08) (0.76) (1.92) (3.04) (2.14)

June 0.023 -0.025 0.018 3.023 0.406 0.061 0.032(0.30) (-2.19) (0.30) (0.62) (0.19) (1.59) (1.18)

July -0.034 -0.014 0.001 3.198 -0.569 0.042 0.027(-0.83) (-1.09) (0.03) (0.56) (-0.22) (1.67) (1.08)

August -0.039 -0.023 -0.006 0.040 -2.351 0.046 0.032(-1.37) (-2.02) (-0.26) (0.01) (-0.99) (2.02) (1.13)

September -0.039 -0.020 -0.000 6.548 1.355 0.018 0.017(-1.55) (-1.46) (-0.01) (1.31) (0.52) (0.67) (1.08)

October 0.079 0.029 0.051 9.897 1.486 -0.049 0.005(2.82) (3.23) (3.71) (3.11) (0.76) (-1.68) (0.37)

November -0.000 0.002 0.022 0.636 -2.086 -0.026 -0.005(-0.01) (0.29) (2.06) (0.30) (-1.05) (-1.04) (-0.44)

December 0.010 0.018 0.006 -11.107 -7.083 0.005 -0.002(0.39) (2.33) (0.88) (-4.16) (-4.36) (0.28) (-0.32)

UR Residuals -10.35 -8.39 -6.70 -15.97 -14.44 -15.47 -13.09

R2 23.58 53.89 60.36 16.69 18.75 9.29 9.40

adj. R2 22.77 53.38 59.93 15.75 17.83 8.30 8.43

# Obs. 2,281 2,410 2,410 2,305 2,305 2,097 2,193

# Regressions 69 69 69 69 69 68 56

45

Table 5 – Regressions to detrend effective spread, and quoted depth 69 ADR-ORD pairs, 1996 - 2011This table presents the results of individual stock time-series regressions to remove time-trends and other time regularitiesfrom proportional effective spread for the home (DOM PESPR) and for the cross-listed stock (FOR PESPR), as well asUSD quoted depth for the home (DOM DEPTH ) and the cross-listed stock (FOR DEPTH ). All measures are computedduring overlapping trading hours only, i.e. when both the home market as well as the cross-listed market (NYSE) areopen. Each individual stock measure is regressed on a linear time trend (Trend), a squared time trend (sqr Trend),11 month dummies (February till December), 4 day-of-the week dummy (Tuesday till Friday), as well as two exchangespecific dummies: A dummy for stocks and their cross-listed counterpart from France (Mexico), which is set to 1 after2007-02-17 (2009-09-28). Estimated slope coefficients, R-squared (R2), adjusted R-squared (adj. R2), and number ofobservations (# Obs.) obtained from all individual stock time-series regressions are averaged across all regressions (#Regressions). Cross-sectional t-statistics are in parentheses below the coefficients. Further the table reports the averageDickey-Fuller unit-root test statistic (UR Residuals). All data underlying the computations are from TRTH.

Dependent: PESPRd (%) DEPTH d

DOM FOR DOM FOR

intercept 1.090 0.766 2.334 0.460(1.46) (4.29) (1.86) (2.32)

France2007 0.009 0.417 -2.670 -0.072(2.70) (3.05) (-7.98) (-4.72)

Mexico2009 -0.017 0.022 0.088 -0.093(-0.25) (0.29) (9.19) (-4.04)

Trend -0.000 -0.000 0.003 -0.000(-1.37) (-3.18) (1.22) (-2.24)

sqr Trend 0.000 0.000 -0.000 0.000(0.51) (1.67) (-2.03) (0.73)

Tuesday -0.018 -0.005 0.108 0.004(-4.49) (-2.52) (2.34) (5.48)

Wednesday -0.016 -0.003 0.072 0.005(-3.51) (-1.39) (2.95) (5.14)

Thursday -0.010 -0.001 0.093 0.003(-2.45) (-0.66) (2.05) (4.37)

Friday -0.005 0.001 0.112 0.002(-1.01) (0.43) (2.17) (2.53)

February -0.012 -0.005 -0.003 0.000(-2.13) (-1.50) (-0.02) (0.17)

March -0.004 0.002 -0.011 -0.001(-0.41) (0.23) (-0.14) (-0.47)

April -0.019 -0.009 0.047 0.002(-2.00) (-1.72) (0.60) (0.44)

May -0.017 -0.006 0.113 0.001(-1.74) (-0.90) (0.62) (0.28)

June -0.023 -0.006 -0.062 0.002(-2.45) (-0.63) (-0.44) (0.50)

July -0.010 -0.006 -0.300 -0.000(-0.90) (-0.82) (-2.11) (-0.09)

August -0.022 0.000 -0.580 -0.010(-1.96) (0.01) (-2.34) (-2.42)

September -0.010 0.016 -0.649 -0.005(-1.02) (1.34) (-2.27) (-1.25)

October 0.017 0.030 -0.414 -0.006(2.17) (4.47) (-1.61) (-1.72)

November 0.009 0.009 -0.176 -0.004(1.22) (1.82) (-1.42) (-1.06)

December 0.011 0.013 -0.138 -0.005(1.43) (2.15) (-1.44) (-1.47)

UR Residuals -9.92 -8.59 -6.61 -8.49

R2 50.17 58.44 46.22 38.92

adj. R2 49.66 58.09 45.13 37.85

# Obs. 2,539 2,642 1,801 1,953

# Regressions 69 69 67 66

46

Table 6 – Individual stock VAR results from daily data, 69 ADR-ORD pairs, 1996 - 2011This table reports results from per stock vector autoregressions. Vector autoregressions are estimated per stock usingadjusted (i.e. the residuals from table 4) time-series of daily arbitrage profits, and home and cross-listed illiquidity.For parsimony each individual VAR is estimated using 5-lags. Panel A presents the cross-sectional average (avg),minimum (min), maximum (max), and the 25%, 50% (median), and 75%, percentile of the pairwise correlations of theVAR innovations. Panel B presents the cross-sectional average (avg), minimum (min), maximum (max), and the 25%,50% (median), and 75%, percentile of the 5-day cumulative, estimated impulse responses to a Cholesky one standard-deviation shock. The first three rows of Panel B report the responses in standard-deviations to a shock to arbitrageprofits (Profit), the next three rows to a shock to home market quoted spread (DOM PQSPR), and the last three rowsto cross-listed quoted spread (FOR PQSPR). The first column (#Stocks) indicates the number of stocks over which thesummary statistics are computed. In panel B the second column (%Sig+) gives the percentage of how many estimatesare positive, and significant at the 5% level (based on bootstrapped error bands from 1000 runs). All data underlyingthe computations are from TRTH.

Panel A: Correlations in VAR innovations


Profit, DOM PQSPR (%) 69 12.45 -16.03 7.60 11.18 18.76 30.79

Profit, FOR PQSPR (%) 69 7.56 -22.28 0.93 8.57 15.75 33.97

DOM PQSPR, FOR PQSPR (%) 69 21.67 -4.71 14.25 21.92 27.75 47.10

Panel B: 5-day cumulative IRF responses

#Stocks %Sig+ avg min 25% Median 75% max

effect of shock to Profit on:

Profit 69 100 7.25 4.15 6.90 7.42 7.76 9.22

DOM PQSPR 69 78 1.02 -0.31 0.57 1.13 1.41 2.44

FOR PQSPR 69 56 0.55 -1.18 0.02 0.57 1.13 1.89

effect of shock to DOM PQSPR on:

Profit 69 34 0.25 -1.03 -0.01 0.19 0.57 1.32

DOM PQSPR 69 100 6.89 3.92 6.43 7.24 7.55 8.41

FOR PQSPR 69 92 1.63 0.13 1.25 1.63 2.05 2.89

effect of shock to FOR PQSPR on:

Profit 69 47 0.27 -1.75 0.13 0.29 0.49 1.41

DOM PQSPR 69 63 0.41 -0.64 0.19 0.40 0.59 1.59

FOR PQSPR 69 100 6.05 3.16 5.19 6.23 6.97 8.30

47

Table 7 – Market VAR results from daily data, 69 ADR-ORD pairs, 2001 - 2011This table reports results from per market vector autoregressions. Vector autoregressions are estimated per exchange(i.e. equally weighted averages across all stocks in a given exchange) using adjusted (i.e. the residuals from table 4)time-series of daily arbitrage profits, home and cross-listed illiquidity. Panel A, B, C, D, and E present 5-day cumulative,estimated impulse responses to a Cholesky one standard-deviation shock to arbitrage profit both to the home market(DOM) and the cross-listed market (FOR). Panel A reports responses in proportional quoted spread (PQSPR). PanelB reports responses in proportional effective spread (PESPR). Panel C reports responses in quoted depths (DEPTH).Panel D reports responses in absolute order imbalance (OIB). And Panel E reports responses in the difference betweenproportional quoted spread during and outside overlapping trading hours (DIFF). All responses are measured in standard-deviations. Significance at the 5% level is indicated by two stars (based on bootstrapped error bands from 1000 runs).All data underlying the computations are from TRTH.

Brazil England France Germany Mexico

Panel A: 5-day cumulative responses in quoted spread to shocks to arbitrage profits

DOM PQSPR 0.348 ** 0.321 ** 0.216 ** 0.445 ** 0.067

FOR PQSPR 0.248 ** 0.081 ** 0.072 0.435 ** 0.124 **

Panel B: 5-day cumulative responses in effective spread to shocks to arbitrage profits

DOM PESPR 0.385 ** 0.432 ** 0.215 ** 0.481 ** 0.190 **

FOR PESPR 0.280 ** 0.154 ** 0.146 ** 0.444 ** 0.219 **

Panel C: 5-day cumulative responses in quoted depth to shocks to arbitrage profits

DOM DEPTH -0.039 -0.057 0.327 ** -0.125 ** -0.031

FOR DEPTH -0.022 -0.197 -0.151 ** -0.205 ** -0.019

Panel D: 5-day cumulative responses in absolute order imbalance to shocks to arbitrage profits

DOM OIB 0.039 0.215 ** 0.083 0.201 ** 0.115 **

FOR OIB 0.208 ** 0.122 ** 0.050 0.181 ** 0.163 **

Panel E: 5-day cumulative responses in differences in quoted spread during and outside overlap to shocks to arbitrage profits

DOM DIFF 0.111 ** 0.098 ** 0.220 **

FOR DIFF 0.066 0.177 ** 0.254 **

48

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13:29 13:30 13:31 13:32 13:33 13:34 13:35

SYMBOL_NAME ● ●VOD.L VOD.N

Figure 1 – Bid, ask and arbitrage profits for Vodafone trading at LSE and its respective cross-listedADR, 2008-10-15This figure shows the bid and ask prices for both the currency adjusted home market share traded at the LSE (withRIC: VOD.L) as well as the cross-listed NYSE share (with RIC: VOD.N) on 2008-10-15 for six minutes around the timethe NYSE market starts the continuous trading session (13:30 UTC). In both cases the ask (bid) price is the upper(lower) line of the two lines belonging to the same share (with the same colour). The x-axis shows the time in UTC.The y-axis shows the bid and ask quotes in USD. Trades are indicated by dots in the colour on which stock the tradeoccurred. Any arbitrage opportunity is indicated by a shaded area and the respective average profit is the size of theshaded area. All data underlying the computations are from TRTH.

49

0%1%2%3%4%5%

0%1%2%3%4%5%

0%1%2%3%4%5%

0%1%2%3%4%5%

0%1%2%3%4%5%

Brazil

England

France

Germ

anyM

exico

1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012

LOW TWAP HIGH

Figure 2 – Daily time-variation in market arbitrage profits, 69 ADR-ORD pairs, 1996 - 2011This figure shows daily market-wide, i.e. equally weighted average across the stocks in the sample, time variation inthe average time-weighted (TWAP), maximum (HIGH), and minimum (LOW) arbitrage profit of the currency adjustedhome and the cross-listed share across all stocks in our sample by exchange (row). All observations above 5% are cutoff. All data underlying the computations are from TRTH.

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DOM_PQSPR FOR_PQSPR

0%2%4%6%8%

10%

0%1%2%3%4%5%6%

0.0%

0.5%

1.0%

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0%

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6%

8%

Brazil

England

France

Germ

anyM

exico

1999 2003 2007 2011 1999 2003 2007 2011

Figure 3 – Daily time-variation in market proportional quoted spread, 69 ADR-ORD pairs, 1996 - 2011This figure shows daily market-wide, i.e. equally weighted average across the stocks in the sample, time variation in theproportional quoted spread (PQSPR) during overlapping trading times, i.e. when both the home market as well as thecross-listed exchange is in their continuous trading session. The left (right) column shows the spread measure calculatedfor home market (cross-listed) shares by exchange (row). All data underlying the computations are from TRTH.

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0%

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M_P

QS

PR

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R_P

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PR

0 5 10 15 20 25 300 5 10 15 20 25 300 5 10 15 20 25 300 5 10 15 20 25 300 5 10 15 20 25 30

coef lower upper

Figure 4 – Cumulative responses from shocks to arbitrage profit on home and cross-listed quoted spread,69 ADR-ORD pairs, 2001- 2011This figure shows impulse response functions (IRF) from vector autoregression (VAR) estimated on market-wide (i.e.equally-weighted averages across all stocks in the sample from a given exchange) adjusted (i.e. the residuals of regressionsin Table 4) daily arbitrage profits (Profit), average quoted spread in the home market, and average quoted spread in thecross-listed market. The lag length of each VAR is chosen individually (for each exchange) by the Akaike informationcriterion. IRF are estimated for each different exchange (in columns) separately. All IRF show cumulative responses instandard deviations measured to Cholesky one standard-deviation shocks to arbitrage profit. All variables are measuredduring the overlapping trading time, i.e. when both the home market and the cross-listed market are in their continuoustrading session. Each figure shows bootstrapped 95% confidence bands based on 1000 runs (lower, upper). All dataunderlying the computations are from TRTH.

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0%

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DO

M_P

ES

PR

FO

R_P

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PR

0 5 10 15 20 25 0 5 10 15 20 25 0 5 10 15 20 25 0 5 10 15 20 25 0 5 10 15 20 25

coef lower upper

Figure 5 – Cumulative responses from shocks to arbitrage profit on home and cross-listed effective spread,69 ADR-ORD pairs, 2001- 2011This figure shows impulse response functions (IRF) from vector autoregression (VAR) estimated on market-wide (i.e.equally-weighted averages across all stocks in the sample from a given exchange) adjusted (i.e. the residuals of regressionsin Table 5) daily arbitrage profits (Profit), average effective spread in the home market, and average effective spread inthe cross-listed market. The lag length of each VAR is chosen individually (for each exchange) by the Akaike informationcriterion. IRF are estimated for each different exchange (in columns) separately. All IRF show cumulative responses instandard deviations measured to Cholesky one standard-deviation shocks to arbitrage profit. All variables are measuredduring the overlapping trading time, i.e. when both the home market and the cross-listed market are in their continuoustrading session. Each figure shows bootstrapped 95% confidence bands based on 1000 runs (lower, upper). All dataunderlying the computations are from TRTH.

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−40%

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−50%−40%−30%−20%−10%

0%10%

DO

M_D

EP

TH

FO

R_D

EP

TH

5 10 15 5 10 15 5 10 15 5 10 15 5 10 15

coef lower upper

Figure 6 – Cumulative responses from shocks to arbitrage profit on home and cross-listed quoted depth,69 ADR-ORD pairs, 2001- 2011This figure shows impulse response functions (IRF) from vector autoregression (VAR) estimated on market-wide (i.e.equally-weighted averages across all stocks in the sample from a given exchange) adjusted (i.e. the residuals of regressionsin Table 5) daily arbitrage profits (Profit), average quoted depth in the home market, and average quoted depth in thecross-listed market. The lag length of each VAR is chosen individually (for each exchange) by the Akaike informationcriterion. IRF are estimated for each different exchange (in columns) separately. All IRF show cumulative responses instandard deviations measured to Cholesky one standard-deviation shocks to arbitrage profit. All variables are measuredduring the overlapping trading time, i.e. when both the home market and the cross-listed market are in their continuoustrading session. Each figure shows bootstrapped 95% confidence bands based on 1000 runs (lower, upper). All dataunderlying the computations are from TRTH.

54

England France Germany

0%

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80%

DO

M_D

IFF

FO

R_D

IFF

0 5 10 15 20 25 30 0 5 10 15 20 25 30 0 5 10 15 20 25 30

coef lower upper

Figure 7 – Cumulative responses from shocks to arbitrage profit on improvement to home and cross-listedquoted spread, 69 ADR-ORD pairs, 2001- 2011This figure shows impulse response functions (IRF) from vector autoregression (VAR) estimated on market-wide (i.e.equally-weighted averages across all stocks in the sample from a given exchange) adjusted (i.e. the residuals of regressionsin Table 4) daily arbitrage profits (Profit), difference in average quoted spread during overlapping trading time and beforein the home market as well as in the cross-listed market. The lag length of each VAR is chosen individually (for eachexchange) by the Akaike information criterion. IRF are estimated for each different exchange (in columns) separately.All IRF show cumulative responses in standard deviations measured to Cholesky one standard-deviation shocks toarbitrage profit. All variables are measured during the overlapping trading time, i.e. when both the home market andthe cross-listed market are in their continuous trading session. Each figure shows bootstrapped 95% confidence bandsbased on 1000 runs (lower, upper). All data underlying the computations are from TRTH.

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0%

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40%

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M_O

IBF

OR

_OIB

0 5 10 15 20 250 5 10 15 20 250 5 10 15 20 250 5 10 15 20 250 5 10 15 20 25

coef lower upper

Figure 8 – Cumulative responses from shocks to arbitrage profit on home and cross-listed order imbalance,69 ADR-ORD pairs, 2001- 2011This figure shows impulse response functions (IRF) from vector autoregression (VAR) estimated on market-wide (i.e.equally-weighted averages across all stocks in the sample from a given exchange) adjusted (i.e. the residuals of regressionsin Table 4) daily arbitrage profits (Profit), average absolute net order imbalance in the home market, and average absolutenet order imbalance the cross-listed market. The lag length of each VAR is chosen individually (for each exchange) bythe Akaike information criterion. IRF are estimated for each different exchange (in columns) separately. All IRF showcumulative responses in standard deviations measured to Cholesky one standard-deviation shocks to arbitrage profit.All variables are measured during the overlapping trading time, i.e. when both the home market and the cross-listedmarket are in their continuous trading session. Each figure shows bootstrapped 95% confidence bands based on 1000runs (lower, upper). All data underlying the computations are from TRTH.

56


−40%

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2001 2005 2009 2001 2005 2009 2001 2005 2009 2001 2005 2009 2001 2005 2009

Figure 9 – Boxplots of yearly liquidity responses to Choleski one standard-deviation shock to arbitrageprofits, 69 ADR-ORD pairs, 2001 - 2011This figure shows yearly boxplots of the yearly average of the daily estimated average 20-minute cumulative effect ofa Cholesky one standard-deviation shock to arbitrage profit on domestic proportional quoted spreads (DOM PQSPR)and on NYSE proportional quoted spreads (FOR PQSPR) for all stocks in the sample. The impulse response functionis estimated from a stock-day vector autoregression of 4-minute intervals within the day. The 25th, 50th (median), and75th percentile of the impulse response of a Choleski one standard-deviation shock to arbitrage profit on home-market(DOM PQSPR) and cross-listed market (FOR PQSPR) proportional quoted spread across the 69 stocks in the sampleis indicated by the bottom, middle, and top line of the boxes in the left (right) chart, respectively. The highest (lowest)individual stock estimate below (above) the 75th (25th) percentile plus (minus) 1.5 times the interquartile range, i.e.the end of the whiskers, is indicated by the top (bottom) of the line above (below) the boxes. Observations above theend of the top whisker and below the end of the bottom whisker are not shown (in total 34 observations). All dataunderlying the computations are from TRTH.

57

Mexico

Germany

France

England

Brazil

07 08 09 10 11 12 13 14 15 16 17 18 19 20 21

Figure 10 – Appendix: Continuous trading sessions per exchange 2008-10-15This figure shows the hour of the day (x-axis) in which each of the five exchanges (y-axis) is in their continuous tradingsession on one specific date, 2008-10-15 (horizonal lines). The vertical lines in the figure depict the opening (left) andclosing (right) time of the continuous trading session at the cross-listed market (NYSE). The x-axis shows the hour ofthe day in Coordinated Universal Time (UTC).

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the impact of arbitrageurs on market liquidity€¦ · surfsara, and in particular lykle voort, for...

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