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.
1
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.
2
(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
3
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,
4
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-
5
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
6
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).
7
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
8
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.
10
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
11
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)
14
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 (%)
#Stocks avg min 25% Median 75% max
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
Arbitrage Profits (%) 53 0.75 0.47 0.27 0.53 0.52 0.40
Seconds in Arbitrage 53 1,752 560 237 825 778 457
2005 to 2008
# of Arbitrage 66 19 36 3 9 9 3
Arbitrage Profits (%) 66 0.34 0.19 0.13 0.22 0.20 0.17
Seconds in Arbitrage 66 1,219 237 157 575 289 337
2009 to 2011
# of Arbitrage 65 22 41 5 10 12 5
Arbitrage Profits (%) 65 0.47 0.22 0.20 0.26 0.22 0.24
Seconds in Arbitrage 65 1,746 194 324 679 220 494
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 DOM PQSPR FOR PQSPR
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 DOM PQSPR FOR PQSPR
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
#Stocks avg min 25% Median 75% max
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.
50
DOM_PQSPR FOR_PQSPR
0%2%4%6%8%
10%
0%1%2%3%4%5%6%
0.0%
0.5%
1.0%
1.5%
2.0%
0.0%0.5%1.0%1.5%2.0%2.5%
0%
2%
4%
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.
51
Brazil England France Germany Mexico
0%
50%
100%
150%
0%
50%
100%
150%
DO
M_P
QS
PR
FO
R_P
QS
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.
52
Brazil England France Germany Mexico
0%
50%
100%
150%
0%
50%
100%
150%
DO
M_P
ES
PR
FO
R_P
ES
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.
53
Brazil England France Germany Mexico
−40%
−20%
0%
20%
40%
60%
−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%
20%
40%
60%
0%
20%
40%
60%
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.
55
Brazil England France Germany Mexico
0%
20%
40%
0%
20%
40%
DO
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
Brazil England France Germany Mexico
−40%
−30%
−20%
−10%
0%
10%
20%
−40%
−30%
−20%
−10%
0%
10%
20%
DO
M_P
QS
PR
FO
R_P
QS
PR
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).
58