The impact of arbitrage on market liquidity

Transcription

1 The impact of arbitrage on market liquidity Dominik M. Rösch a a Rotterdam School of Management, Erasmus University First draft: May 2013 Abstract The notion that arbitrageurs improve liquidity is based on the assumption that arbitrage opportunities arise because of demand shocks. If, however, arbitrage opportunities reflect informational differences, arbitrageurs create adverse selection and deteriorate liquidity. I test these competing hypotheses in the Depositary Receipts market, where arbitrage is frequent and almost risk-free. As inverse measures of arbitrage activity I use price deviations across both markets based on simultaneous trades, and quotes, and further the velocity at which deviations increase before simultaneous trades. Using 16 years of international tick-by-tick data I find that (i) 70% of all arbitrage opportunities arise because of demand shocks, and (ii) greater arbitrage activity predicts a decrease in order imbalance and an increase in liquidity. These findings suggest that arbitrageurs trade against market order imbalance, and thereby improve market integration and liquidity. Keywords: liquidity, efficiency, fragmentation, arbitrage, market integration I thank Dion Bongaerts, Tarun Chordia, Ruben Cox, Nicolae Gârleanu, Amit Goyal, Andrew Karolyi, Albert Kyle, Pamela Moulton, Avanidhar Subrahmanyam, Raman Uppal, Dimitrios Vagias, Mathijs van Dijk, Manuel Vasconcelos, Kumar Venkataraman, Axel Vischer, Avi Wohl, and participants at the 2013 Liquidity Conference (Rotterdam), and at seminars at Erasmus University, and Cornell for valuable comments. This work was carried out on the National e- infrastructure with the support of SURF Foundation. I thank SURFsara, and in particular Lykle Voort, for technical support, and OneMarket-Data for the use of their OneTick software. I also gratefully acknowledge financial support from the Vereniging Trustfonds Erasmus Universiteit Rotterdam. address: drosch@rsm.nl (Dominik M. Rösch) November 4, 2013

2 Abstract The impact of arbitrage on market liquidity The notion that arbitrageurs improve liquidity is based on the assumption that arbitrage opportunities arise because of demand shocks. If, however, arbitrage opportunities reflect informational differences, arbitrageurs create adverse selection and deteriorate liquidity. I test these competing hypotheses in the Depositary Receipts market, where arbitrage is frequent and almost risk-free. As inverse measures of arbitrage activity I use price deviations across both markets based on simultaneous trades, and quotes, and further the velocity at which deviations increase before simultaneous trades. Using 16 years of international tick-by-tick data I find that (i) 70% of all arbitrage opportunities arise because of demand shocks, and (ii) greater arbitrage activity predicts a decrease in order imbalance and an increase in liquidity. These findings suggest that arbitrageurs trade against market order imbalance, and thereby improve market integration and liquidity.

3 Inefficiencies in financial markets can have effects on the real economy. For example, in a financial market in which the law of one price is violated perhaps the purest 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 arbitrageurs can also impact liquidity. According to the limits of arbitrage literature the role of the arbitrageur is to eliminate mispricings and provide liquidity (Gromb and Vayanos, 2010). However, the assumed impact arbitrage has on liquidity is opposite in the Depositary Receipts literature where with arbitrage present, the adverse selection costs of domestic dealers increase, so that... liquidity falls (Domowitz, Glen, and Madhavan, 1998) and trading costs are higher... due to greater adverse selection associated with arbitrageurs (Bacidore and Sofianos, 2002). Indeed, theoretical models suggest that the impact of arbitrage on market liquidity depends on the underlying reason for the arbitrage opportunity to arise. The notion that arbitrageurs provide liquidity is mainly based on the assumption that arbitrage opportunities arise due to non-fundamental demand shocks, such as fire sales by mutual funds, and hence arbitrageurs increase market-making capacity by trading against net market demand (Grossman and Miller, 1988; Holden, 1995; Gromb and Vayanos, 2010; Rahi and Zigrand, 2012; Foucault, Pagano, and Röell, 2013). But in informationally fragmented markets, where arbitrage opportunities can reflect informational differences, arbitrageurs might create adverse selection and deteriorate liquidity (Kumar and Seppi, 1994; Domowitz, Glen, and Madhavan, 1998). Several papers provide evidence that information production varies 1

4 across markets (e.g. Grossman (1988)) which can lead to predictabilities across both markets (Chan, Chan, and Karolyi, 1991; Cremers and Weinbaum, 2010). The impact of arbitrageurs on market liquidity does not need to be contemporaneous alone, but could have persistent effects. O Hara and Oldfield (1986) and Comerton-Forde, Hendershott, Jones, Moulton, and Seasholes (2010) provide theoretical and empirical evidence that overnight inventories affect future liquidity. If arbitrageurs trade against net market order imbalance, a decrease in arbitrage activity might lead to higher order imbalance, which could predict future illiquidity. So far the literature mainly focused on the important impact of high frequency trading (HFT) and algorithmic trading (AT) on market quality. While the general impact of HFT and AT is important, it is equally important to understand the impact of particular trading strategies that require HFT or AT. For example, while Chaboud, Chiquoine, Hjalmarsson, and Vega (2013) show that increased AT decreases arbitrage opportunities, and improves price efficiency in the foreign exchange market, they do not find a relation between the correlation of algorithmic traders actions and market efficiency, and interpret this to provide support for Foucault (2012): The effect of algorithmic trading on the informativeness of prices may ultimately depend on the type of strategies used by algorithmic traders, not on the presence of algorithmic trading per se. One such particular trading strategy is arbitrage, which so far has been mainly investigated in the content of the limits-of-arbitrage literature (e.g. Mitchell, Pulvino, and Stafford (2002); De Jong, Rosenthal, and van Dijk (2009); Gagnon and Karolyi (2010b); Ben-David, Franzoni, and Moussawi (2012).) The limitsof-arbitrage literature can explain why arbitrage opportunities persist, but not why arbitrage opportunities arise. Similarly, the limits-of-arbitrage literature can 2

5 explain how liquidity impacts arbitrage activity, but not how arbitrage impacts liquidity. Schultz and Shive (2010) do provide first empirical evidence that arbitrage opportunities between shares issued by the same company and trading on the same exchange mainly arise from non-fundamental demand shocks and Lou and Polk (2013) look at arbitrage activity in momentum strategies and ask whether arbitrageurs can have a destabilizing effect, but both papers do not investigate the impact on liquidity. Roll, Schwartz, and Subrahmanyam (2007) and Choi, Getmansky, and Tookes (2009) empirically investigate liquidity and arbitrage activity directly. Choi, Getmansky, and Tookes (2009) find empirical evidence in favour 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 activity 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 (2007) find opposite evidence, that arbitrageurs in the futures-cash basis deteriorate liquidity. It remains an open empirical question whether the notion that arbitrage activity improves liquidity is supported by empirical evidence. Motivated by these observations, in this paper, I investigate why arbitrage opportunities arise and the impact of arbitrageurs on market liquidity. Of course, the effects of cross-sectional market making (Holden, 1995) and adverse selection are not exclusive. If, for example, both effects are equally strong, and cancel each other out, arbitrage activity will not have a visible effect on the spread set by local market-makers. This forms the null hypothesis. Alternatively, if the 3

6 effect of increased adverse selection dominates, arbitrageurs deteriorate liquidity. This forms the first alternative hypothesis. But if arbitrage opportunities arise because of demand shocks, arbitrageurs trade against local net market demand, and increase the market-making capacity. If this effect is stronger than potential adverse selection arbitrageurs should improve liquidity. This forms the second alternative hypothesis. My focus is the American Depositary Receipts (ADR) market. As laid out by Gagnon and Karolyi (2010b) ADR s represent claims against the home-market shares, and offer identical cash-flows as the ordinary share in the home market (albeit in USD), and hence should trade at the same price. Further, the authors state that in the ADR market, institutions exist to facilitate arbitrage (making arbitrage almost risk-free) and elaborate on the mechanics of arbitrage. Especially 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 suitable to study arbitrage. Despite this the authors provide comprehensive empirical evidence that arbitrage opportunities occur frequently and can be sizeable. Conversations with employees of BNY Mellon (the world s largest depositary for ADR s) confirm that arbitrage is frequent in the ADR market. I examine intraday bid and ask quotes and trade prices 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 I construct two measures of price deviations. First, the difference between the best bid and the best ask prices across both markets, which measures opportunity profits. Second, the difference between simultaneous trade prices, which measures traded profits. Inspired by Schultz and Shive (2010), I first investigate if arbitrage opportunities 4

7 arise due to a non-fundamental demand shock where the asset that creates the arbitrage is also the asset that closes down the arbitrage. I then compare opportunity profits and liquidity around simultaneous trades across both markets. I distinguish between simultaneous trades that occur during (18 million trades) and outside (11 million) positive opportunity profits. I then construct two (inverse) proxies for daily arbitrage activity, namely the daily maximum opportunity profit and the average daily traded profit. I extend the analysis by a third (inverse) measure of arbitrage activity, the velocity at which opportunity profits increase before a simultaneous trade occurs. Using these three stock-day measures of arbitrage activity I estimate vector autoregressions and impulse response functions from detrended and expunged from other calendar regularities arbitrage activity, and both home market and ADR liquidity. I further estimate impulse response functions using net market order imbalance (absolute difference between buyer- and seller-initiated trades), in addition to liquidity measures. To address the concern of an omitted variable bias, I estimate a fixed-effect panel vector autoregression and further the effect of opportunity profits on the difference between illiquidity during and outside overlapping trading hours, i.e. when both the ADR and the home market share are trading. The intraday analysis reveals that in the ADR market more than 70% of all arbitrage arise due to a non-fundamental demand shock. And for simultaneous trades that occur during positive opportunity profits I find that opportunity profits peak at the time the trade occurs with on average 21% higher opportunity profits than its two minute average around the trade. This provides justification for interpreting these trades as motivated by arbitrage. 5

8 Using the daily measures I find that the average daily maximum opportunity profit is around 0.9% (as a percentage of the home-market share price) and the average daily traded profit is around 0.6%, both similar to the cost-adjusted, absolute end-of-day price deviations reported by Gagnon and Karolyi (2010b) of 1.12%. The velocity at which opportunity profits increase before a simultaneous trade occurs is 5BP per minute, on average. Impulse response functions indicate that a positive shock to arbitrage activity predicts an increase in liquidity and a decrease in net market order imbalance. And further that an increase in arbitrage activity does not predict a general improvement in liquidity, but rather that it predicts a stronger increase in liquidity when arbitrageurs are active, i.e. during overlapping trading times, than outside, i.e. when arbitrageurs are not active. The main contribution is to provide empirical evidence that arbitrageurs improve liquidity. I provide empirical evidence that most arbitrage opportunities arise because of a demand shock and that an increase in arbitrage activity predicts a decrease in net market order imbalance. Both indicates that arbitrageurs trade against net market demand, and hence improve international market integration by shifting excess demands across markets. Further I provide evidence that an increase in arbitrage activity predicts an increase in liquidity. A likely explanation is that because net market order imbalance has a persistent effect on liquidity, and arbitrageurs trade against net market order imbalance, arbitrageurs do improve liquidity. My secondary contribution is to extend the ADR literature. First, I use intraday data over a long time span from both the ADR and the home market stock from five different exchanges and document large opportunity profits of almost 1% 6

9 averaged over the whole sample. Second, by showing that an increase in arbitrage activity decreases the gap between liquidity during and outside overlapping trading times I join two distinct research streams in the Depositary Receipts literature, where one focuses on explaining deviations from the law of one price (e.g. Gagnon and Karolyi (2010b)) and the other explains liquidity differences during and outside overlapping trading hours (e.g. Werner and Kleidon (1996); Moulton and Wei (2009)). I consider the finding that arbitrageurs improve liquidity important for at least four reasons. First, the findings provide empirical justification for the assumption underlying the limits of arbitrage theory. Especially, that the benefits of arbitrageurs trading against net market demand outweigh a potential increase in adverse selection, even in emerging markets which are in general less informationally integrated (Bacidore and Sofianos, 2002). Second, the findings help to understand how policy changes that hinder arbitrage activity (e.g. short-sell bans, or transaction taxes), negatively impact not only the efficiency of the financial market, but also its liquidity. For example, in January 2014 eleven European member states plan to introduce a transaction tax on financial instruments of at least 0.1%. The results of this paper suggest that the transaction tax will negatively impact liquidity, because of a decrease in arbitrage activity, which will increase the cost of capital for firms (Amihud and Mendelson, 1986). Third, the results add to the debate about how recent changes to the trading environment, seemingly helping arbitrageurs, affect market quality. 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 7

10 trading, algorithmic trading, and liquidity) individually improves market liquidity and informational efficiency (O Hara and Ye, 2011; Menkveld, 2012; Hendershott, Jones, and Menkveld, 2011; Chordia, Roll, and Subrahmanyam, 2008). This paper indicates that arbitrageurs might play an important role in these findings. Fourth, the results can provide an explanation for time-variation in liquidity differences during and outside overlapping trading times. Where Werner and Kleidon (1996) find that quoted spreads of ADR s in 1991 are higher during than outside overlapping trading times, using data from 2003 Moulton and Wei (2009) find the opposite. The increase in arbitrage activity provides one explanation for these different findings. This paper is organized as follows. In section 1 I discuss data and sample construction. Section 2 discusses the construction of the intraday price deviations based on trade and quote data and provides evidence that arbitrage opportunities arise because of demand shocks, and that simultaneous trades around positive opportunity profits are driven by arbitrage motivations. Section 3 discusses the construction of three daily measures of arbitrage activity, and measure of liquidity, and order imbalance. Section 4 shows that an increase in arbitrage activity predicts an increase in liquidity on an individual stock-level using time-series and panel vector autoregressions. Section 5 provides evidence that arbitrage activity predicts liquidity and net market order imbalance at a market level. Section 6 concludes. 1. Data, and sample construction I focus on arbitrage opportunities in the American Depositary Receipts market (ADR), because here arbitrage is frequent and almost risk-free as outlined by (Gagnon and Karolyi, 2010b). For a detailed explanation and a comprehensive in- 8

11 troduction to the ADR market I refer to Karolyi (1998). For a survey about recent developments in the ADR market I refer to Gagnon and Karolyi (2013), chapter 11, which is based on Gagnon and Karolyi (2010a). The feature of convertibility in the ADR market, 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. Convertibility 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 (which not necessarily needs to be the same, see e.g. Aulerich, Fishe, and Harris (2011)). As the following example shows, convertibility allows to interpret price differences between bid and ask prices at the time an arbitrageur opens the arbitrage position as profits an actual arbitrageur could make. For example, if the currency adjusted bid price of the home market stock is higher than the ask price of the ADR an arbitrage opportunity exists to simultaneously short sell the home market stock at the bid price, convert the proceeds from the short-sale into USD, and buy the ADR at the NYSE at the ask price. 1 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 1 Note that this example is for illustrative purposes only. In real markets short-selling is capital intensive, and an initial margin requirement of 150% is required (in the US, Regulation T), which then also creates exchange rate risk. 9

12 Navigator), or the actual depositary 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 After the conversion the home-market share can be delivered to close down the short position, resulting in a USD profit equal to the difference between the bid of the home market and the ask of the ADR at the time the arbitrage position was opened. This indicates that actual realized profits (excluding fixed costs) after the arbitrage position is closed cannot be lower than profits at the time the arbitrage position was opened. To construct my sample of ADR s and their respective home market shares I use standard sources in the DR literature: Datastream, Bank of New York Complete Depositary Receipt Directory ( and Deutsche Bank Depositary 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 Depositary 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 matched home-market/adr pairs and construct my sample based on the five home-market exchanges with the most identified ADR/home-market pairs, and with overlapping trading times to the NYSE. This results in 69 ADR/home-market pairs across the following five exchanges: the London Stock Exchange (England, with 27 stocks), Sao Paolo Stock Exchange (Brazil, 12 stocks), Bolsa Mexicana de Valores (Mexico, During a meeting BNY Mellon mentioned that conversion often takes place within the same day and that conversion costs range from 0 to 5 cents a share. 10

13 12 stocks), XETRA (Germany, 9 stocks), and Euronext Paris (France, 9 stocks). For all matched ADR/home-market 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 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. Most of the analysis requires comparing prices across the ADR and the homemarket stock. To have valid, tradable quotes for both the ADR and the homemarket stock most of the analysis is based on overlapping trading times, i.e. when both the home-market as well as the NYSE are in their continuous trading session. Figure 1 shows the continuous trading times for all five exchanges in the sample on 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. 3 Day 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 exchanges are varying within the year, but in general are 2, 6, and 6.5 hours between Europe, Brazil, and Mexico and the NYSE, respectively (as depicted in Figure 1). 11

14 2. Intraday arbitrage opportunities and simultaneous trades 2.1. Do arbitrage opportunities arise due to demand shocks or information differences? If arbitrage opportunities arise because of non-fundamental demand shocks arbitrageurs will act as cross-sectional market makers (Holden, 1995) and improve liquidity. However, if arbitrage opportunities arise because of different information sets, arbitrageurs will likely be perceived as informed traders, increasing adverse selection costs and deteriorating liquidity. Because the reason behind an arbitrage opportunity to arise partly determines the impact arbitrageurs have on liquidity I first follow Schultz and Shive (2010) and study how arbitrage opportunities arise. To measure opportunity profits profit i,s of stock i in second s I calculate the relative difference between the bid on the home-market (ADR) and the ask on the ADR (home-market), i.e. profit i,s is calculated as: profit i,s = max( bid.home i,s ask.adr i,s, bid.adr i,s ask.home i,s, 0) (1) mid.home i,s mid.home i,s where, mid.home i,s is the last mid-quote price of stock i in second s, and bid.home i,s (ask.home i,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.adr i,s (ask.adr i,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). To make results comparable among stocks I scale each second s arbitrage 12

15 profit by the mid-quote of the home-market share. 4 If for one particular stock i at time x 1 opportunity profits are zero, but at time x opportunity profits are positive, at least one bid or ask quote of at least one asset had to change from time x 1 to time x (this asset is denoted the First mover, either the ADR, the home-market stock, or the respective currency pair). Similar, if opportunity profits are positive till time y 1 > x, but zero at time y at least one bid or ask quote of at least one asset had to change. In this case I say that an arbitrage opportunity arises for stock i at time x and disappears at time y (to reduce potential noise I ignore any arbitrage opportunity that last less than one second, so that y > x.) 5 For each stock i, and for each arbitrage opportunity a I consider the maximum opportunity profit within the arbitrage opportunity as the profit opportunity of a. The first three rows of Panel A of Table 1 report the average across all 69 stocks in the sample of the daily average number of arbitrage opportunities, their daily average (time-weighted) maximum opportunity profit in per cent, and the daily average time the arbitrage opportunity persists in seconds. The rest of Panel A report these statistics by exchange. Panel B of Table 1 report these three statistics over two different time intervals, namely 1996 to 2000 and 2001 to The time intervals are chosen as in later parts I focus on data from 2001 to 2011 to mitigate issues arising from infrequent trading and stocks entering the sample. 4 Because this might lead to spurious results in later regressions, where both the independent as well as the dependent variable are scaled by the mid-quote, I also use opportunity profit in USD, which qualitatively yields the same result (unreported). 5 In case the day opens with an arbitrage opportunity, I consider the asset which market opened last as the First mover. On the other hand if an arbitrage opportunity exists and either of the markets closes I drop this arbitrage opportunity from the analysis in this section, as I do not know which asset closes down the arbitrage. Both cases are infrequent and do not impact the main results in this section. 13

16 Following Schultz and Shive (2010) I consider an arbitrage opportunity to arise because of a non-fundamental demand shock if the same asset is responsible for the arbitrage opportunity to arise and to disappear. However, if any of the other two assets moves and the arbitrage opportunity disappears, the shock to the First mover was persistent, reflecting potential differences in information. The table reports all statistics across which asset created the arbitrage opportunity (First mover), namely the respective currency in which the home-market stock is quoted in (Forex), the ADR (ADR), the home-market ordinary stock (ORD), and if both the ADR and the home-market stock move together (BOTH ). 6 For each First mover I distinguish between arbitrage opportunities that arise because of a transitory change in the asset (Transitory), potentially due to a non-fundamental demand shock, or because of a persistent change in the asset (Persistent), potentially due to information. On average around 61 arbitrage opportunities arise per day, of which 43 (over 70%) arise because of price pressure, over the whole sample but also with similar ratios in each of the five exchanges reported in Panel A of Table 1, and in each of the two time periods reported in Panel B of Table 1. On average arbitrage opportunities profits decreased from 0.50% in the early years to 0.24% in the later years of the sample. Also the time arbitrage opportunities last decreased from around 10 minutes to 5 minutes in the later years. Arbitrage opportunities are particular short lived if the arbitrage opportunity arises because of a transitory change in the currency pair (81 seconds), with particular low opportunity profits (0.05%). This indicates that demand shocks in the currency market do not play 6 In the case that the currency pairs moves together with any of the other assets, the arbitrage opportunity is considered to arise or to disappear, because of a movement in the other asset. 14

17 a major role in explaining the ADR arbitrage. However, on average, three times a day, the currency market does seem to lead the other markets creating sizeable opportunity profits of 0.20%, on average. Table 1 provides evidence that the majority of all arbitrage opportunities arise because of a demand shock in either the ADR or the home-market stock, and hence that arbitrageurs trade against net market demand and act as cross-sectional market makers (Holden, 1995) most of the time Are simultaneous trades during positive opportunity profits driven by arbitrage? I now turn to estimate absolute price differences between simultaneous trades and provide empirical evidence that during positive opportunity profits these trades are motivated by arbitrage and behave like arbitrage trades. In particular I show that opportunity profits increase (decrease) before (after) simultaneous trades during positive opportunity profits. To measure trade profits trade.profit i,t of stock i for simultaneous trade t I calculate the relative difference between the trade prices of the ADR and the home market stock, i.e. trade.profit i,t is calculated as: trade.profit i,t = trade.home i,t trade.adr i,t1 mid.home i,t (2) where, trade.home i,t is the currency adjusted trade price for trade t of the homemarket stock, and trade.adr i,t1 is the bundling adjusted trade price for trade t 1 of the ADR, such that t 1 minimizes the distance to t and both trades occur within two seconds, i.e. t t 1 < 2. With 27 million simultaneous trades in total they occur frequently over the 15

18 whole sample, and explain a large fraction of all ADR trades during the overlapping trading times (27%). Further, despite that I match trades that can be up to 2 seconds apart, the average time between trades on the ADR and homemarket share is just 0.27 seconds. The number of simultaneous trades increased significantly from 1996 to 2011 and is not only driven by the increase in total trades in later years. For example, in 2000 the average number of ADR trades per stock-month for German stocks (during the overlapping trading times) is 900, and in 2001 it is 1300 (i.e. on average one ADR trade every two minutes), but the amount of simultaneous trades increased from 200 to over 600 per month (more than tripled), so that for Xetra in 2001 almost half of all trades on ADR s occur within two seconds of a trade on the home market. In the spirit of an event study (where the event is a simultaneous trade) I now look at opportunity profits before and after the event. For each stock-day I average opportunity profits per second from one minute before till one minute after a simultaneous trade occurs across all simultaneous trades within the day. For each stock i and each day d I get 121 observations n with 60 <= n <= 60 denoted profit i,d (n), where the first (last) observation is the average opportunity profit one minute before (after) a simultaneous trade occurs. I then run regressions as depicted in Eq. 3 for each stock-day to explain the time variation of opportunity 16

19 profits around simultaneous trades. 7 profit i,d (n) = α i,d +β 1,i,d Before n +β 2,i,d T ime n +β 3,i,d T ime n Before n +ɛ i,d,n (3) where, α i,d is the intercept, Before n is a dummy variable which is set to 1 before the event, T ime n is a linear time trend, and T ime n Before n is a time trend before the event. Table 2 reports the results from stock-day regressions as in Eq. 3. In the first two columns the dependent variable is profit i,d (n) (Profit opportunity (%)). In the next and last two columns the dependent variable is constructed as before, but instead of averaging opportunity profits, I average proportional quoted spread of the ADR (ADR PQSPR (%)) and home-market ordinary stock (ORD PQSPR (%)), respectively. The proportional quoted spread is defined as the difference between the ask and the bid quote, divided by the mid quote. For each of the three different dependent variables I report two different regressions. In column 1, 3, and 5 (In) the event is a simultaneous trade with positive opportunity profits (i.e. profit i,d (0) > 0). While column 2, 4, and 6 (Out) report results using simultaneous trades with zero opportunity profits as the event (i.e. profit i,d (0) = 0). For each independent variable I report the pooled average estimated slope coefficient. Estimated coefficients for both time trends are scaled by 60, and hence 7 On days with more than one simultaneous trade, regressions are estimated using Weighted- Least-Square, with weights equal to one over the standard deviation of the average opportunity profit in second n. Using OLS only marginally changes the results, indicating that the standard deviation of the average opportunity profit at second n only marginally varies across the 2-minute interval. Further, to address concerns of overlapping events, which can cause autocorrelations, and to adjust for heteroskedasticity I report Newey-West t-statistics. 17

20 measure the change per minute. I further report the pooled average Newey-West t-stat (t-stat avg) (which are capped at -100, and +100), the percentage of coefficients that are positive (% positive), the percentage of coefficients that are positive and significant at the 5% level (% + significant), and the percentage of coefficients that are negative and significant at the 5% level (% - significant). Further for each regression I report the average R 2 and the number of regressions over which the averages are taken (# regressions). The number of regressions indicates that for around 130K (100K) stock-days a simultaneous trade occurs inside (outside) positive opportunity profits. This is a big fraction of the total number of stock-days of around 166K in the whole sample, but still significantly less than the number of stock-days with positive opportunity profits (98%, as shown later in Table 3). First, the average R 2 slightly varies across different regressions, but is always above 51% and in the majority around 60%. This indicates that the proposed functional form captures most of the 2-minutes time variation in opportunity profits, and liquidity around simultaneous trades. Second, the average opportunity profit around simultaneous trades inside positive opportunity profits are much higher than outside, it is around 35BP and 5BP, respectively. 8 This provides evidence that both trades indeed occur within very different situations and are likely driven by very different motivations. More importantly the opportunity profit is higher before a simultaneous trade occurs within positive opportunity profits (measured by Before), and in this case is also strictly increasing (decreasing) before (after) the event (measured by Time and Time*Before, respectively). The opportunity profit 8 A large difference is also visible between the average traded profit (from Eq. 2) during and outside positive opportunity profits, which is 54BP and 24BP, respectively. 18

21 at the time the trade occurs is on average 43BP ( ( )), which is around 21% higher than the average opportunity profit (the estimated intercept of 35BP). The results further indicate that while liquidity slightly decreases from 60 seconds before to 60 seconds after the trade, the magnitude is similar across both kinds of trades, but with very different dynamics. For simultaneous trades outside positive opportunity profits liquidity is pretty much constant before the trade and then worsens with the trade and slowly recovers. On the other hand, in the case of simultaneous trade which occur inside positive opportunity profits liquidity improves before the trade, indicated by the negative and statistical significant coefficient for Time*Before (explaining the increase in opportunity profits) and then reverts back indicated by the positive coefficient for Time and the fact that the absolute magnitude for Time is less than for Time*Before. In fact the quoted spread for the home market stock (ADR) before the event is 3 BP (5 BP) lower than the overall average. In total for both the ADR and the home-market stock the quoted spread is on average around 8 BP lower, which is roughly the same magnitude as the increase in opportunity profits. In unreported tests I consider the 97K stock-days in which both simultaneous trades occur within and outside positive opportunity profits. I run regressions as before, but as dependent variables I consider the difference in opportunity profits (quoted spread) between simultaneous trades within and outside positive opportunity profits. In all cases the absolute average t-statistic is above 2, indicating that the dynamics around simultaneous trades within and outside positive opportunity profits are significantly different from each other. Because opportunity profits rise (fall) before (after) simultaneous trades dur- 19

22 ing positive opportunity profits, I interpret these trades as driven by arbitrage. Of course taking the average across all simultaneous trades with positive opportunity profits will wrongly classify many trades as arbitrage trades and potentially miss out several arbitrage trades. However, the finding of a statistically and economically significant increase (decrease) in opportunity profits from one minute before (after) the actual trade justifies the interpretation that these trades are at least partly driven by arbitrage motivations. And indicates that simultaneous trades at times during positive opportunity profits behave like arbitrage trades, in the sense that an increase in opportunity profits predicts arbitrage trades and that on the other hand arbitrage trades predict a decrease in opportunity profits. One concern might be that I use all simultaneous trades, and not only signed simultaneous trades, i.e. simultaneous trades for which the trade for one market is buyer and the other market is seller initiated. However, this would not allow arbitrageurs to use limit orders, a potentially unrealistic restriction. Chaboud, Chiquoine, Hjalmarsson, and Vega (2013) find that improvement in the informational efficiency of prices... seems to come predominantly from an increase in the trading activity of algorithmic traders when they are.. posting quotes which are hit. Using a datset provided by Nasdaq in which trades are identified as coming from high-frequency traders (HFT), and if the HFT is on the passive (limit order) or active (market-order) side, Brogaard, Hendershott, and Riordan (2013) find that HFT are passive on around half of their trades. Further, Menkveld (2013) finds that for one particular high-frequency trader that employs a cross-market strategy... four out of five of its trades are passive. This indicates that at least high-frequency and algorithmic traders (and potentially arbitrageurs) significantly rely on limit-orders. The build-up of opportunity profits and that arbitrage op- 20

23 portunities last in average for several minutes (Table 1), indicates that profits an arbitrageur could make are more important than speed. For example, under position limits the arbitrageur solves an optimal stopping problem and will not enter the arbitrage immediately (Brennan and Schwartz, 1990). Therefore it stands to reason that arbitrageurs could also make use of limit orders, to increase potential profits beyond what is available by trading immediately using market-orders. Of course, the arbitrageur would only use a limit-order for one asset, and use a market-order for the other asset as soon as the limit-order was hit. 9 So far I have provided empirically evidence that most arbitrage opportunity arise because of demand shocks (Table 1). While this indicates that arbitrageurs likely act as cross-sectional market makers (Holden, 1995) by trading against net market demand, and hence provide liquidity, most of the time, the overall effect of arbitrageurs on liquidity is not clear yet. Many arbitrage opportunities arise because of information differences (Table 1 indicates around 30%) and hence the overall effect of arbitrageurs on liquidity might still be negative. To study the overall effect I now turn to proxy arbitrage activity, and investigate the joint dynamics between arbitrage activity and market liquidity in the following sections. 9 In unreported robustness tests I use signed trades, and find that the main results are unchanged. However, signed trades occur less frequent, but still in total more than 5 million times, and the average difference between trade prices is only around half the size using signed trades instead of all simultaneous trades during positive opportunity profits. A similar argumentation does not apply for measuring opportunity profits. When constructing opportunity profits I ignore the use of limit orders, to ensure that the estimated profits are actively tradable using market orders. 21

24 3. Daily measures of arbitrage activity, liquidity, and order imbalance 3.1. Daily measures of arbitrage activity A potential channel of how arbitrageurs might impact liquidity is through order imbalance. If arbitrage opportunities mainly arise because of demand shocks (as indicated by Table 1), arbitrageurs will trade against, and not cause, a high absolute market order imbalance (OIB). Chordia, Roll, and Subrahmanyam (2002) provide evidence that high OIB reduces liquidity, contemporaneously, and both O Hara and Oldfield (1986) and Comerton-Forde, Hendershott, Jones, Moulton, and Seasholes (2010) provide theoretical and empirical evidence that overnight OIB affect future liquidity. Hence, a lack of arbitrage activity might increase OIB, which affects current and future liquidity. Following Roll, Schwartz, and Subrahmanyam (2007) I focus on daily data. Using daily data ensures that the time is short enough (compared to lets say weekly data) for example to measure the effect of OIB (as empirically found by Comerton-Forde, Hendershott, Jones, Moulton, and Seasholes (2010) using daily data), but on the same time long enough (compared to intraday data) to capture more persistent effects. 10 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 10 However, estimating impulse response functions per stock-day based on 4-minute intervals, leaves the main results qualitatively unchanged. 22

25 arbitrageurs are not active 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) 11, and return correlations (Lou and Polk, 2013). 12 Motivated by these observations I construct two daily measures of arbitrage activity based on intraday absolute price differences. First, the stock-day maximum observable opportunity profit within the day (from Eq. 1). And second, the stock-day average trade profit across all arbitrage trades (defined as simultaneous trades that occur during positive opportunity profits, from Eq. 2). The motivation for using the daily maximum opportunity profit is the following. In general opportunity profits are lower than or equal to what arbitrageurs see as a suitable compensation (i.e. risk-, and transaction-cost adjusted profits) for pursuing the trade. Opportunity profits cannot be much higher than the compensation 11 I note that Roll, Schwartz, and Subrahmanyam (2007) interpret end-of-day absolute price differences (the basis) as a direct measure of arbitrage activity, so that if the basis widens on a particular day, arbitrage forces on subsequent days... increase. In contrast, I interpret absolute price differences derived from intraday data as an inverse measure of arbitrage activity. The different interpretations are due to differences 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. Second, I also look at price deviations across simultaneous trades. And third, in the ADR market arbitrage opportunities are short lived (Table 1 indicates that in average they vanish after several minutes). 12 Alternatively, previous literature used the excess amount of short-selling to measure arbitrage activity (Choi, Getmansky, and Tookes, 2009; Hanson and Sunderam, 2011), but this measure is not feasible for arbitrage positions that are open for less than three business days (as is the case in the market I look at). Equity transaction (in the US) settle T+3, i.e. traders are required to settle the transaction within three business days, if the short-position is open less than three business days it will likely not show up in any statistic. Another potential measure of arbitrage activity in the ADR market is changes in shares outstanding. If for example the home-market stock is converted into the ADR as part of closing down the arbitrage position this will affect the number of shares outstanding. However, as confirmed by BNY Mellon, a lot of arbitrage positions are not actually closed by converting the shares, but rather by trading in the opposite directions, which yields more profits because the asset that is overvalued often becomes the asset that is undervalued, even within the same trading day. 23

26 required by arbitrageurs, because before profits would have reached this level an arbitrageur would step in and drive prices back to fundamentals. The daily maximum opportunity profit within a day should hence be around the compensation required by arbitrageurs. Following this interpretation one would expect that the average of traded profit within the day is of a similar magnitude as the maximum opportunity profit (which is what I find in Table 3). One concern with these measures might be that arbitrage activity might vary purely because of variations in the costs associated with arbitrage. While the opportunity profit is adjusted for varying transaction costs (i.e. the bid-ask spreads), it is not adjusted for fixed costs, such as transaction fees, or the cost of maintaining the required infrastructure, which also vary over time but at a much slower pace. Another concern might be that both measures of arbitrage activity do not take into account the time it takes for an arbitrageur to become active. Despite a large opportunity profit, if an arbitrageur quickly trades on it, arbitrage activity is still relatively high. To address concerns that arbitrage activity is purely driven by time variation in these costs (that go beyond what is captured in detrending the series as in Eq. 4), and to address the notion of time it takes an arbitrageur to trade I construct another (inverse) measure of arbitrage activity based on Table 2. The sum of both time-trends reported from stock-day regressions in Table 2 measures the velocity at which opportunity profits increase before an arbitrage trade occurs, and hence measure how fast an arbitrageur steps in. For example, Table 2 shows that the average velocity at which opportunity profits increase before an arbitrage trade is on average 5BP per minute (more than 13% of the average 24

27 estimated intercept). If the slope is small this indicates that either a small gradual rise or a sudden bigger jump in opportunity profit is enough for an arbitrageur to step in and trade. On the other hand if the slope is large, it indicates that arbitrageurs wait for an extended time for the opportunity profit to increase before they trade. The latter case indicates that arbitrageurs are less active than in the former. And hence the slope can be interpreted as an inverse measure of arbitrage active. Table 3 presents daily summary statistics for all three measures of arbitrage activity by exchange (Panel A) as well as by time (Panel B). The first three rows in Panel A report cross-sectional summary statistics (the mean, minimum, maximum, and the 25%, 50% (median), and 75% percentile) of the time-series averages of the daily maximum opportunity profit, the average traded profit, and the velocity at which opportunity profit increase before an arbitrage trade across all the 69 stock pairs in the sample. The rest of Panel A reports these cross-sectional summary statistics across all stock pairs from a given exchange. Panel B of Table 3 shows cross-sectional statistics across all stock pairs during two different time periods, namely 1996 to 2000 and 2001 to In all cases the first column (#Stocks) indicates the number of stocks over which the cross-sectional summary statistics are computed, and the second column (%Days+) indicates the percentage of stock-days with a positive opportunity profit, traded profit or velocity. For the majority of all stock-days both traded profits (83%) and opportunity profits (98%) are nonzero, with the exception of the early years (1996 to 2000) in which the trade profit cannot be computed for every two out of five stockdays, because of missing arbitrage trades. While both opportunity profits and 25