Rise of the Machines: Algorithmic Trading in the Foreign Exchange Market

Board of Governors of the Federal Reserve System International Finance Discussion Papers Number 980 October 2009 Rise of the Machines: Algorithmic Trading in the Foreign Exchange Market Alain Chaboud, Benjamin Chiquoine, Erik Hjalmarsson, Clara Vega NOTE: International Finance Discussion Papers are preliminary materials circulated to stimulate discussion and critical comment. References in publications to International Finance Discussion Papers (other than an acknowledgment that the writer has had access to unpublished material) should be cleared with the author or authors. Recent IFDPs are available on the Web at www.federalreserve.gov/pubs/ifdp/. This paper can be downloaded without charge from Social Science Research Network electronic library at http://www.ssrn.com/.

Rise of the Machines: Algorithmic Trading in the Foreign Exchange Market Alain Chaboud Benjamin Chiquoine Erik Hjalmarsson Clara Vega (cid:3) September 29, 2009 Abstract We study the impact that algorithmic trading, computers directly interfacing at high frequency with trading platforms, has had on price discovery and volatility in the foreign exchange market. Our dataset represents a majority of global interdealer trading in three major currency pairs in 2006 and 2007. Importantly, it contains precise observations of the size and the direction of the computer-generated and human-generated trades each minute. The empirical analysis provides several important insights. First, we (cid:133)nd evidence thatalgorithmic tradestend to be correlated,suggesting thatthe algorithmic strategies used in the market are not as diverse as those used by non-algorithmic traders. Second, we (cid:133)nd that, despite the apparent correlation of algorithmic trades, there is no evident causal relationship between algorithmic trading and increased exchange rate volatility. If anything, the presence of more algorithmic trading is associated with lower volatility. Third, we show that even though some algorithmic traders appeartorestricttheiractivityintheminutefollowingmacroeconomicdatareleases,algorithmictraders increase their provision of liquidity over the hour following each release. Fourth, we (cid:133)nd that nonalgorithmic order (cid:135)ow accounts for a larger share of the variance in exchange rate returns than does algorithmicorder(cid:135)ow. Fifth,we(cid:133)ndevidencethatsupportstherecentliteraturethatproposestodepart from the prevalent assumption that liquidity providers in limit order books are passive. JEL Classi(cid:133)cation: F3, G12, G14, G15. Keywords: Algorithmictrading;Volatility;Liquidityprovision;Privateinformation. Chaboud, Hjalmarsson, and Vega are with the Division of International Finance, Federal Reserve Board, Mail Stop 20, (cid:3) Washington, DC 20551, USA. Chiquoine is with the Investment Fund for Foundations, 97 Mount Auburn Street, Cambridge MA 02138, USA. Please address comments to the authors via e-mail at alain.p.chaboud@frb.gov, bchiquoine@ti⁄.org, erik.hjalmarsson@frb.govandclara.vega@frb.gov. WearegratefultoTerrenceHendershottandAlbertMenkveldfortheirvaluable insights, to EBS/ICAP for providing the data, and to Nicholas Klagge and James S. Hebden for their excellent research assistance. Wealsobene(cid:133)tedfromthecommentsofGordonBodnar,CharlesJones,LuisMarques,Dag(cid:133)nnRime,AlecSchmidt, John Schoen, Noah Sto⁄man, and of participants in the Spring 2009 Market Microstructure NBER conference, San Francisco AEA2009meetings,theSAISInternationalEconomicsSeminar,theSITE2009conferenceatStanford,andtheBarcelonaEEA 2009 meetings. The views in this paper are solely the responsibility of the authors and should not be interpreted as re(cid:135)ecting the views of the Board of Governors of the Federal Reserve System or of any other person associated with the Federal Reserve System.

1 Introduction The use of algorithmic trading, where computer algorithms directly manage the trading process at high frequency, has become common in major (cid:133)nancial markets in recent years, beginning in the U.S. equity market more than 15 years ago. There has been widespread interest in understanding the potential impact of algorithmic trading on market dynamics, as some analysts have highlighted the potential for improved liquidity and more e¢ cient price discovery while others have expressed concern that it may be a source of increased volatility and reduced liquidity, particularly in times of market stress. A number of articles and opinion pieces on the topic have recently appeared in the press, with most decrying practices used by some algorithmictradersintheequitymarket,andtherehavebeencallsforregulatoryagenciesintheUnitedStates andEuropetobegininvestigations.1 Despitethisinterest,therehasbeenverylittleformalempiricalresearch on algorithmic trading, primarily because of a lack of data where algorithmic trades are clearly identi(cid:133)ed. A notable exception is a recent paper by Hendershott, Jones, and Menkveld (2007), who get around the data constraint by using the (cid:135)ow of electronic messages on the NYSE as a proxy for algorithmic trading. They conclude that algorithmic trading on the NYSE, contrary to the pessimists(cid:146)concerns, likely causes an improvement in market liquidity.2 In the foreign exchange market, there has been no formal empirical research on the subject. The adoption of algorithmic trading in the foreign exchange market is a far more recent phenomenon than in the equity market, as the two major interdealer electronic trading platforms only began to allow algorithmic trades a few years ago. Growth in algorithmic trading has been very rapid, however, and a majority of foreign exchange transactions in the interdealer market currently involve at least one algorithmic counterparty. In algorithmic trading (AT), computers directly interface with trading platforms, placing orders without immediate human intervention. The computers observe market data and possibly other information at very high frequency, and, based on a built-in algorithm, send back trading instructions, often within milliseconds. A variety of algorithms are used: for example, some look for arbitrage opportunities, including small discrepancies in the exchange rates between three currencies; some seek optimal execution of large orders at the minimum cost; and some seek to implement longer-term trading strategies in search of pro(cid:133)ts. Among the most recent developments in algorithmic trading, some algorithms now automatically read and interpret economic data releases, generating trading orders before economists have begun to read the (cid:133)rst line. 1See,forinstance,(cid:147)RewardingBadActors,(cid:148)byPaulKrugman,New YorkTimes,August3,2009,(cid:147)High-FrequencyTrading Grows, Shrouded in Secrecy,(cid:148)Time, August 5, 2009, and (cid:147)Don(cid:146)t Set Speed Limits on Trading,(cid:148)by Arthur Levitt Jr., Wall Street Journal,August 18,2009. 2We also note a paper by Hasbrouck (1996) on program trading,where he analyzes 3 months ofdata where program trades canbeseparatelyidenti(cid:133)edfromothertrades. Heconcludesthatbothtypesofordershaveanapproximatelyequivalentimpact onprices. Algorithmictradingisnotexactlyequivalenttoprogram trading,thoughitisaclosecousin. Inprinciple,aprogram trade could be generated by a trader(cid:146)s computer and then the trade conducted manually by a human trader. Our de(cid:133)nition of AT refersto thedirectinteraction ofa trader(cid:146)scomputerwith an electronictrading platform,thatistheautomated placement ofa trade orderon the platform. 1

The extreme speed of execution that AT allows and the potential that algorithmic trades may be highly correlated, perhaps as many institutions use similar algorithms, have been cited as reasons for concerns that ATmaygeneratelargepriceswingsandmarketinstability. Ontheotherhand,thefactthatsomealgorithms aim for optimal execution at a minimal price impact may be expected to lower volatility. In this paper, we investigate whether algorithmic ((cid:147)computer(cid:148)) trades and non-algorithmic ((cid:147)human(cid:148)) trades have di⁄erent e⁄ectsontheforeignexchangemarket. We(cid:133)rstaskwhetherthepresenceofcomputertradescauseshigheror lower volatility and whether computers increase or reduce liquidity during periods of market stress. We then study the relative importance of human and computer trades in the process of price discovery and re-visit the assumption that liquidity providers are (cid:147)uninformed.(cid:148) We formally investigate these issues using a novel dataset consisting of two years (2006 and 2007) of minute-by-minute trading data from EBS in three currency pairs: the euro-dollar, dollar-yen, and euro-yen. The data represent the vast majority of global spot interdealer transactions in these exchange rates. An important feature of the data is that the volume and direction of human and computer trades each minute are explicitly identi(cid:133)ed, allowing us to measure their respective impacts. We(cid:133)rstshowsomeevidencethatcomputertradesaremorehighlycorrelatedwitheachotherthanhuman trades, suggesting that the strategies used by computers are not as diverse as those used by humans. But the high correlation of computer trades does not necessarily translate into higher volatility. In fact, we (cid:133)nd next that there is no evident causal relationship between AT and increased market volatility. If anything, the presence of more algorithmic trading appears to lead to lower market volatility, although the economic magnitudeofthee⁄ectissmall. Inordertoaccountforthepotentialendogeneityofalgorithmictradingwith regards to volatility, we instrument for the actual level of algorithmic trading with the installed capacity for algorithmic trading in the EBS system at a given time. Next, we study the relative provision of market liquidity by computers and humans at the times of the most in(cid:135)uential U.S. macroeconomic data release, the nonfarm payroll report. We (cid:133)nd that, as a share of total market-making activity, computers tend to pull back slightly at the precise time of the release but then increasetheirpresenceinthefollowinghour. Thisresultsuggeststhatcomputersdo provideliquidityduring periods of market stress. Finally, we estimate return-order (cid:135)ow dynamics using a structural VAR framework in the tradition of Hasbrouck (1991a). The VAR estimation provides two important insights. First, we (cid:133)nd that human order (cid:135)ow accounts for much of the long-run variance in exchange rate returns in the euro-dollar and dollar-yen exchangeratemarkets,i.e.,humansappeartobethe(cid:147)informed(cid:148)tradersinthesemarkets. Incontrast,inthe euro-yen exchange rate market, computers and humans appear to be equally (cid:147)informed.(cid:148)In this cross-rate, we believe that computers have a clear advantage over humans in detecting and reacting more quickly to 2

triangulararbitrageopportunities,wheretheeuro-yenpriceisbrie(cid:135)youtoflinewithpricesintheeuro-dollar and dollar-yen markets. Second, we (cid:133)nd that, on average, computers orhumans that trade on aprice posted byacomputerdonotimpactpricesquiteasmuchastheydowhentheytradeonapricepostedbyahuman. One possible interpretation of this result is that computers tend to place limit orders more strategically than humans do. This empirical evidence supports the literature that proposes to depart from the prevalent assumption that liquidity providers in limit order books are passive.3 The paper proceeds as follows. In Section 2 we introduce the EBS exchange rate data, describing the evolution over time of algorithmic trading and the pattern of interaction between human and algorithmic traders. In Section 3 we study the correlation of algorithmic trades. In Section 4 we analyze the relationship between algorithmic trading and exchange rate volatility. In Section 5 we discuss the provision of liquidity by computers and humans at the time of a major data release. In Section 6 we report the results of the high-frequency VAR analysis. We conclude in Section 7. Some robustness results are presented in the Appendix. 2 Data description Today, two electronic platforms process the vast majority of global interdealer spot trading in the major currency pairs, one o⁄ered by Reuters, and one o⁄ered by EBS.4 These platforms, which are both electronic limit order books, have become essential utilities for the foreign exchange market. Importantly, trading in each major currency pair has over time become very highly concentrated on only one of the two systems. Of the most traded currency pairs, the top two, euro-dollar and dollar-yen, trade primarily on EBS, while the third, sterling-dollar, trades primarily on Reuters. As a result, the reference price at any moment for, say, spot euro-dollar, is the current price on the EBS system, and all dealers across the globe base their customer andderivativequotesonthatprice. EBScontrolsthenetworkandeachoftheterminalsonwhichthetrading isconducted. Traderscanentertradinginstructionsmanually, usinganEBSkeyboard, or, uponapprovalby EBS, via a computer directly interfacing with the system. The type of trader (human or computer) behind each trading instruction is recorded by EBS, allowing for our study.5 We have access to AT data from EBS from 2003 through 2007. We focus on the sample from 2006 and 2007,because,aswewillshow,algorithmictradeswereaverysmallportionoftotaltradesintheearlieryears. 3For example, Chakravarty and Holden (1995), Kumar and Seppi (1994), Kaniel and Liu (2006), and Goettler, Parlour and Rajan (2007) allow informed investors to use both limit and market orders. Bloom(cid:133)eld, O(cid:146)Hara and Saar (2005) argue that informedtradersarenaturalliquidityproviders,andAngel(1994)andHarris(1998)showthatinformedinvestorscanoptimally use limit orders when private information is su¢ ciently persistent. 4EBS has been part ofthe ICAP group since 2006. 5EBS uses the name (cid:147)automated interface(cid:148)(AI) to describe trading activity directly generated by a computer, activity we callAT. 3

In addition to the full 2006-2007 sample, we also consider a sub-sample covering the months of September, October, and November of 2007, when algorithmic trading played an even more important role than earlier in the sample.6 We study the three most-traded currency pairs on the EBS system: euro-dollar, dollar-yen, and euro-yen. Thequotedata,attheone-secondfrequency, consistofthehighestbidquoteandthelowestaskquoteon the EBS system in these currency pairs, from which we construct one-second mid-quote series and compute one-minute exchange rate returns; all the quotes are executable and therefore represent the true price at that moment. The transactions data are at the one-minute frequency and provide detailed information on the volume and direction of trades that can be attributed to computers and humans in each currency pair. Speci(cid:133)cally,thetransactionsvolumedataarebrokendownintocategoriesspecifyingthe(cid:147)maker(cid:148)and(cid:147)taker(cid:148) of the trades (i.e., human or computer), and the direction of the trades (i.e., buy or sell the base currency), foratotalofeightdi⁄erentcombinations. Thatis,the(cid:133)rsttransactioncategorymayspecify,say,theminuteby-minute volume of trade that results from a human taker buying the base currency by (cid:147)hitting(cid:148)a quote postedbyahumanmaker. Wewouldrecordthisactivityasthehuman-humanbuyvolume,withtheaggressor (taker) of the trade buying the base currency. The human-human sell volume is de(cid:133)ned analogously, as are the other six buy and sell volumes that arise from the remaining combinations of computers and humans acting as makers and takers. From these eight types of buy and sell volumes, we can construct, for each minute, trading volume and order (cid:135)ow measures for each of the four possible pairs of human and computer makers and takers: humanmaker/human-taker (HH), computer-maker/human-taker (CH), human-maker/computer-taker (HC), and computer-maker/computer-taker (CC).7 That is, the sum of the buy and sell volumes for each pair gives the volume of trade attributable to that particular combination of maker and taker (which we symbolize as, Vol(HH) or Vol(HC), for example). The di⁄erence between the buy and sell volume for each pair gives us the order (cid:135)ow attributable to that maker-taker combination (which we symbolize simply as HH or HC, for example). The sum of the four volumes, Vol(HH +CH +HC +CC), gives the total volume of trade in the market. The sum of the four order (cid:135)ows, HH +CH +HC +CC, gives the total (market-wide) order (cid:135)ow.8 Throughout the paper, we will use the expression (cid:147)order (cid:135)ow(cid:148)to refer both to the market-wide order (cid:135)ow and to the order (cid:135)ows from other possible decompositions, with the distinction clearly indicated. Importantly, the data allow us to consider order (cid:135)ow broken down by the type of trader who initiated the 6We do not use December2007 in the sub-sample to avoid the in(cid:135)uence ofyear-end e⁄ects. 7Thenaming convention for(cid:147)maker(cid:148)and (cid:147)taker(cid:148)re(cid:135)ectsthefactthatthe(cid:147)maker(cid:148)postsquotesbeforethe(cid:147)taker(cid:148)chooses to trade at that price. Posting quotes is,ofcourse,the traditionalrole ofthe market-(cid:147)maker.(cid:148) 8There is a very high correlation in this market between trading volume per unit of time and the number of transactions per unit of time, and the ratio between the two does not vary much over our sample. Order (cid:135)ow measures based on amounts transacted and those based on numberoftrades are therefore very similar. 4

trade, human-taker order (cid:135)ow (HH +CH) and computer-taker order (cid:135)ow (HC+CC). The main goal of this paper is to analyze the e⁄ect algorithmic trading has on price discovery and volatility in the foreign exchange market. In our exchange rate data as in other (cid:133)nancial data, the net of signedtradesfromthepointofviewofthetakers(themarket-wideorder(cid:135)ow)ishighlypositivelycorrelated with exchange rate returns, so that the takers are considered to be more (cid:147)informed(cid:148)than the makers. Thus, in our analysis of the relative e⁄ects of human and computer trades in the market, we consider prominently the order (cid:135)ow decomposition into human-taker order (cid:135)ow and computer-taker order (cid:135)ow. However, we also consider two other decompositions in our work. We consider the most disaggregated decomposition of order (cid:135)ow (HH;CH;HC;CC), as this decomposition allows us to study whether the liquidity suppliers, who are traditionally assumed to be (cid:147)uninformed(cid:148), are posting quotes strategically. This situation is more likely to arise in our data, which comes from a pure limit order book market, than in data from a hybrid market like the NYSE, because, as Parlour and Seppi (2008) point out, the distinction between liquidity supply and liquidity demand in limit order books is blurry.9 We also decompose the data by maker type (human or computer) in order to study whether computers or humans are providing liquidity during the release of public information, which are periods of high exchange rate volatility and, often, market stress. In our analysis, we exclude data collected from Friday 17:00 through Sunday 17:00 New York time from our sample, as activity on the system during these (cid:147)non-standard(cid:148)hours is minimal and not encouraged by the foreign exchange community. We also drop certain holidays and days of unusually light volume: December 24-December 26, December 31-January 2, Good Friday, Easter Monday, Memorial Day, Labor Day, Thanksgiving and the following day, and July 4 (or, if this is on a weekend, the day on which the U.S. Independence Day holiday is observed). Weshowsummarystatisticsfortheone-minutereturnsandorder(cid:135)owdatainTable1. Thistablecontains a number of noteworthy features. First, order (cid:135)ow, whether in total, broken down by human and computer takers, or broken down into the 4 possible pairs of makers and takers, is serially positively correlated, which is consistent with some informed trading models. For example, Easley and O(cid:146)Hara (1987) model a situation where sequences of large purchases (sales) arise when insiders with positive (negative) signals are present in the market. He and Wang (1995) also show that insiders with good (bad) news tend to buy (sell) repeatedly until their private information is revealed in the prices. The positive serial correlation in order (cid:135)ow is also consistent with strategic order splitting, i.e. a trader willing to buy for informational or non-informational reasonsandsplittinghisordertoreducemarketimpact.Second,thestandarddeviationsofthevariousorder (cid:135)ows di⁄er by exchange rates, by type of taker and across maker/taker pairs. These di⁄erences will be 9ParlourandSeppi(2008)notethatinalimitorderbookinvestorswithactivetradingmotives,someofwhichare(cid:147)informed(cid:148) traders,maychoosetopostlimitordersthataremoreaggresivethanthoseadisinterestedliquidityproviderwouldusebutless aggresive than market orders. 5

important in the interpretation of the upcoming VAR analysis and variance decompositions. We show in Figure 1, from 2003 through 2007 for our three major currency pairs, the fraction of trading volume where at least one of the two counterparties was an algorithmic trader, i.e. Vol(CH+HC+CC) as afractionoftotalvolume.10 Fromitsbeginningin2003,thefractionoftradingvolumeinvolvingATgrewby the end of 2007tonear60% foreuro-dollar, anddollar-yen trading, andtoabout80% foreuro-yen. Figure 2 shows, for our three currency pairs, the evolution over time of the four di⁄erent possible types of trades (i.e. Vol(HH), Vol(CH), Vol(HC), and Vol(CC); as fractions of the total volume). By the end of 2007, in the euro-dollar and dollar-yen markets, human to human trades, in black, accounted for slightly less than half of the volume, and computer to computer trades, in green, for about ten to (cid:133)fteen percent. In euro-dollar and dollar-yen, we note that Vol(HC) and Vol(CH) are about equal to each other, i.e. computers (cid:147)take(cid:148) prices posted by humans, in red, about as often as humans take prices posted by market-making computers, in blue. The story is di⁄erent for the cross-rate, the euro-yen currency pair. By the end of 2007, there were more computer to computer trades than human to human trades. But the most common type of trade was computers trading on prices posted by humans. We believe this re(cid:135)ects computers taking advantage of short-lived triangular arbitrage opportunities, where prices set in the euro-dollar and dollar-yen markets are very brie(cid:135)y out of line with the euro-yen cross rate. In interpreting our results later in the paper, we will keep in mind that trading volume is largest in the euro-dollar and dollar-yen markets, and that price discovery happens mostly in those markets, not in the cross-rate. Our conclusions based on the euro-dollar and dollar-yen markets will then be more easily generalized than those based on the euro-yen market. Table 2tabulatestheaveragesofthevolumefractionsshowninFigures1and2,bothforthefull2006-2007sample and the shorter three-month sub-sample. 3 How Correlated Are Algorithmic Trades and Strategies? We (cid:133)rst investigate the proposition that computers tend to have trading strategies that are more correlated thanthoseofhumans.Sincetheoutsetofthe(cid:133)nancialturmoilinthesummerof2007,articlesinthe(cid:133)nancial press have suggested that AT programs tend to be similarly designed, leading them to take the same side of the market in times of high volatility and potentially exaggerating market movements.11 OnesuchinstancemayhavehappenedonAugust16, 2007, adayofveryhighvolatilityinthedollar-yen market. Onthatday,theJapaneseyenappreciatedsharplyagainsttheU.S.dollararound6:00a.m. and12:00 p.m. (NYtime),asshowninFigure3. The(cid:133)gurealsoshows,foreach30-minuteintervalintheday,computertaker order (cid:135)ow (HC +CC) in the top panel and human-taker order (cid:135)ow (HH +CH) in the lower panel. 10The data in Figures 1 and 2 are 50-day moving averages ofdaily values,highlighting the broad trends overtime. 11See,forinstance,(cid:147)Algorithmic Trades Produce SnowballE⁄ects on Volatility,(cid:148)FinancialTimes,December5,2008. 6

The two sharp exchange rate movements mentioned happened when computers, as a group, aggressively sold dollars and bought yen. We note that computers, during these episodes, mainly traded with humans, not with other computers. Human order (cid:135)ow at those times was, in contrast, quite small, even though the overall trading volume initiated by humans (not shown) was well above that initiated by computers (human takers were therefore selling and buying dollars in almost equal amounts). The (cid:147)taking(cid:148)orders generated by computers during those time intervals were far more correlated than the taking orders generated by humans. After 12:00 p.m., human traders, as a whole, then began to buy dollars fairly aggressively, and the appreciation of the yen against the dollar was partially reversed. This is only a single example, of course, but it leads us to ask how correlated computer trades and strategies have tended to be overall. We do not know precisely the exact mix of the various strategies used by algorithmic traders on EBS. Traders keep the information about their own strategies con(cid:133)dential, including, to some extent, from EBS, and EBS also keeps what they know con(cid:133)dential.12 However, one can get a general sense of the market and of the strategies in conversations with market participants. About half of the algorithmic trading volume on EBS is believed to come from what is often known as the (cid:147)professional trading community,(cid:148) which primarily refers to hedge funds and commodity trading advisors (CTAs). These participants, until very recently, could not trade manually on EBS, so all their trades were algorithmic. Some hedge funds and CTAs seek to exploit short-lived arbitrage opportunities, including triangular arbitrage, often accessing several trading platforms. Others implement lower-frequency strategies, often grouped under the statistical arbitrageappellation,includingcarrytrades,momentumtrades,andstrategiesspanningseveralassetclasses. Only a very small fraction of the trading volume in our sample period is believed to have been generated by algorithms designed to quickly react to data releases. The other half (approximately) of the algorithmic tradingvolumecomesfromforeignexchangedealingbanks,theonlyparticipantsallowedontheEBSsystem until 2003. Some of the banks(cid:146)algorithmic trading is clearly related to activity on their own customer-todealerplatforms,toautomatehedgingactivity,andtominimizingtheimpactoftheexecutionoflargeorders. But a sizable fraction is believed to be proprietary trading implemented algorithmically, likely using a mix of strategies similar to those employed by hedge funds and CTAs. Overall, market participants generally believe that the mix of algorithmic strategies used in the foreign exchange market di⁄ers from that seen in the equity market, where optimal execution algorithms are thought to be relatively more prevalent. The August 16, 2007 episode shown above was widely viewed as the result of a sudden unwinding of the yen-carry trade, with hedge funds and proprietary trading desks at banks rushing to close risky positions and buying yen to pay back low-interest loans. The evidence in this case raises the possibility that many 12EBS requires that new algorithmic traders on its system (cid:133)rst test their algorithms in simulated conditions. EBS then routinelymonitorsthetradingpracticesofitscustomers. Ahighnumberofexcessivelyshort-livedquotes((cid:135)ashing)isdiscouraged, as is a very low ratio oftrades to quotes. 7

algorithmic traders were using fairly similar carry trade and momentum strategies at the time, leading to the high correlation of algorithmic orders and to sharp exchange rate movements. Of course, this is only one episode in our two-year sample. Furthermore, episodes of very sharp appreciation of the yen due to the rapid unwinding of yen carry trades have occurred on several occasions since the late 1990s, some obviously before algorithmic trading was allowed in the market. The sharp move of the yen in October 1998, including a 1-day appreciation of the yen against the dollar of about 7 percent, is the best-known example of such an episode. Next, we investigate whether there is evidence that, over the entire sample, the strategies used by algorithmic traders have tended to be more correlated than those used by human traders. If computers and humans are indi⁄erent between taking or making liquidity at a given point in time, then we should observe that computers and humans trade with each other in proportion to their relative presence in the market. If, on the other hand, computers tend to have more homogeneous trading strategies, we should observe computers trading less among themselves and more with humans. At the extreme, if all computers used the very same algorithms and had the exact same speed of execution, we would observe no trading volume among computers. Therefore, the fraction of trades conducted between computers contains information on how correlated their strategies are.13 To investigate the proposition that computers tend to have trading strategies that are more correlated than those of humans we pursue the following approach. We (cid:133)rst consider a simple benchmark model that assumes random and independent matching of traders. This model allows us to determine the theoretical probabilities of the four possible trades: Human-maker/human-taker, computer-maker/human-taker, human-maker/computer-takerandcomputer-maker/computer-taker. Wethenmakeinferencesregardingthe diversity of computer trading strategies based on how the trading pairs we observe compare to those the benchmark model predicts. Inthebenchmarkmodelthereare H potentialhuman-makers(thenumberofhumansthatarestanding m ready to provide liquidity), H potential human-takers, C potential computer-makers, and C potential t m t computer-takers. For a given period of time, the probability of a computer providing liquidity to a trader is equal to Prob(computer make) = Cm , which we label for simplicity as (cid:11) , and the probability (cid:0) Cm+Hm m of a computer taking liquidity from the market is Prob(computer take) = Ct = (cid:11) . The remaining (cid:0) Ct+Ht t makers and takers are humans, in proportions (1 (cid:11) ) and (1 (cid:11) ), respectively. Assuming that these m t (cid:0) (cid:0) events are independent, the probabilities of the four possible trades, human-maker/human-taker, computer- 13Sto⁄man(2007)usesasimilarmethodtoestimatehowcorrelatedindividualinvestorstrategiesarecomparedtoinstitutional investorstrategies. 8

maker/human-taker, human-maker/computer-taker and computer-maker/computer taker, are: Prob(HH) = (1 (cid:11) )(1 (cid:11) ) m t (cid:0) (cid:0) Prob(HC) = (1 (cid:11) )(cid:11) m t (cid:0) Prob(CH) = (cid:11) (1 (cid:11) ) m t (cid:0) Prob(CC) = (cid:11) (cid:11) : m t These probabilities yield the following identity, Prob(HH) Prob(CC) Prob(HC) Prob(CH); (cid:2) (cid:17) (cid:2) which can be re-written as, Prob(HH) Prob(HC) : Prob(CH) (cid:17) Prob(CC) We label the (cid:133)rst ratio, RH Prob(HH), the (cid:147)human-taker(cid:148)ratio and the second ratio, RC Prob(HC), (cid:17) Prob(CH) (cid:17) Prob(CC) the (cid:147)computer-taker(cid:148)ratio. In a world with more human traders (both makers and takers) than computer traders, each of these ratios will be greater than one, because Prob(HH) > Prob(CH) and Prob(HC) > Prob(CC) i.e., computers take liquidity more from humans than from other computers, and humans take liquidity more from humans than from computers. However, under the baseline assumptions of our randommatching model, the identity shown above states that the ratio of ratios, R RC, will be equal to one. (cid:17) RH In other words, humans will take liquidity from other humans in a similar proportion that computers take liquidity from humans. Turning to the data, under the assumption that potential human-takers are randomly matched with potential human-makers, i.e., that the probability of a human-maker/human-taker trade is equal to the one predictedbyourmodel,Prob(HH)= (Hm+C H m m )(cid:2) (cid:2) H (H t t+Ct) ,wecannowderiveimplicationsfromobservationsof R,ourratioofratios. Inparticular,(cid:133)ndingR>1mustimplythatalgorithmicstrategiesaremorecorrelated than what our random matching model implies. In other words, for R > 1 we must observe that either computerstradewitheachotherlessthanexpected(Prob(CC)< (Hm+C C m m )(cid:2) (cid:2) C (H t t+Ct) )orthatcomputerstrade withhumansmorethanexpected(eitherProb(CH)> (Hm+C C m m )(cid:2) (cid:2) H (H t t+Ct) orProb(HC)> (Hm+C H m m )(cid:2) (cid:2) C (H t t+Ct) ). Our dataset allows us to estimate an ex-post proxy for R. Namely, for each trading day we estimate RH = Vol(HH) and RC = Vol(HC), where Vol(HH) is the daily trading volume between human makers Vol(CH) Vol(CC) and human takers, and so forth. In Table 3 we show the mean of the daily ratio of ratios, R = RC; for d d RH d each currency pair for the full sample and the three-month sub-sample. In contrast to the above theoretical b d 9

prediction that R RC = 1, we (cid:133)nd that for all currency pairs R is statistically greater than one. This (cid:17) RH result is very robust: in euro-dollar, all daily observations of R are above one, and only a very small fraction b of the daily observations are below one for the other currency pairs. The results thus show that computers b do not trade with each other as much as random matching would predict. We take this as evidence that algorithmic strategies are likely less diverse than the trading strategies used by human traders. This(cid:133)nding,combinedwiththeobservedgrowthinalgorithmictradingovertime,mayraisesomeconcerns abouttheimpactofATonvolatilityintheforeignexchangemarket. Asmentionedpreviously,someanalysts have pointed to the possible danger of having many algorithmic traders take the same side of the market at the same moment. However, it is not a foregone conclusion that a high correlation of algorithmic strategies should necessarily lead to higher volatility or large swings in exchange rates. Both the high correlation of trading strategies and the widespread use of de-stabilizing strategies may need to be present to cause higher volatility. For instance, if many algorithmic traders use similar triangular arbitrage strategies, the high correlation of those strategies should have little impact on volatility, and may even lower volatility as it improves the e¢ ciency of the price discovery process. Strategies designed to minimize the price impact of trades should also, a priori, not be expected to increase volatility. In contrast, if the high correlation re(cid:135)ects a large number of algorithmic traders using the same carry trade or momentum strategies, as in the August 2007 example shown at the beginning of this section, then there may be some reasons for concern. However, as noted earlier, episodes of sharp movements in exchange rates similar to that example have occurred in the past on several occasions, including well before the introduction of algorithmic trading in the foreign exchange market, suggesting that such episodes are a result of the dramatic unwinding of certain trading strategies, regardless of whether these strategies are implemented through algorithmic trading or not. In the next section, we explicitly investigate the relationship between the presence of algorithmic trading and market volatility. 4 The impact of algorithmic trading on volatility In this section, we study whether the presence of algorithmic trading is associated with disruptive market behavior in the form of increased volatility. In particular, taking into account the potential endogeneity of algorithmictradingactivity,wetestforacausalrelationshipbetweenthefractionofdailyalgorithmictrading relative to the overall daily volume, and daily realized volatility. 10

4.1 A (cid:133)rst look We (cid:133)rst take an informal look at the data. Figure 4 shows monthly observations of annualized realized volatility(basedon1-minutereturns)andofthefractionofalgorithmictrading(thefractionoftotaltrading volumeinvolvingatleastonecomputertrader)foreachofourcurrencypairs. Asdiscussedearlier, thereisa clear upward trend in the fraction of AT in the three currency pairs over 2006 and 2007. Realized volatility in euro-dollar, dollar-yen, and euro-yen declines slightly until mid-2007, and then rises in the second half of 2007, particularly sharply in the yen exchange rates, as the (cid:133)nancial crisis begins. In Figure 5, we study whether days with high market volatility are also days with a higher-than-usual fractionofalgorithmictrading,andvice-versa. Usingdailyobservations,we(cid:133)rstsortthedataintoincreasing decilesofrealizedvolatility(thedecilemeansareshownasbarsinthegraphsontheleft).14 Wethencalculate themeanfractionofATforthedaysineachofthesedeciles(shownaslinesinthesamegraphs). Toaccount for the sharp upward trend in algorithmic participation over our sample, the daily fraction of algorithmic tradingisnormalized: wedivideitbya20-daymovingaveragecenteredonthechosenobservation(amoving average from day t 10 through day t+10, excluding day t). Next, we repeat the exercise, now sorting (cid:0) the daily data into increasing deciles of the normalized fraction of AT (the decile means are shown as bars in the graphs on the right) and calculating mean realized volatility for the days in each of these deciles (shown as lines in the same graphs). The results in Figure 5 (both the graphs on the left and the graphs on the right) show little or no relationship between the level of realized volatility on a particular day and the normalized fraction of AT on that same day. The highest decile in the euro-dollar currency pair may be the onlypossibleexception,withaslightuptickevidentinbothvolatilityandATactivity. Finally, wenotethat, in untabulated results, for each of the three currency pairs, not one of the top 10 days in realized volatility is associated with a top ten day in the share of (normalized) AT. The simple analysis in Figure 5 does not point to any substantial systematic link between AT activity andvolatility. However,thisanalysisignoresthepossible,andlikely,endogeneityofalgorithmicactivitywith regards to volatility, and therefore does not address the question of whether there is a causal relationship between algorithmic trading and volatility. In the remainder of this section, we attempt to answer this question through an instrumental variable analysis. 4.2 Identi(cid:133)cation The main challenge in identifying a causal relationship between algorithmic trading and volatility is the potential endogeneity of algorithmic trading. That is, although one may conjecture that algorithmic trading 14With498dailyobservations,the(cid:133)rst9decileseachinclude50observations,andthehighestdecilecontains48observations. 11

impacts volatility, it is also plausible that algorithmic trading activity may be a function of the level of volatility. For instance, highly volatile markets may present comparative advantages to automated trading algorithmsrelativetohumantraders,whichmightincreasethefractionofalgorithmictradingduringvolatile periods. In contrast, however, one could also argue that a high level of volatility might reduce the informativeness of historical price patterns on which some trading algorithms are likely to base their decisions, and thus reduce the e⁄ectiveness of the algorithms and lead them to trade less. Thus, one can not easily determine in what direction the bias will go in an OLS regression of volatility on the fraction of algorithmic trading. To deal with the endogeneity issue, we adopt an instrumental variable (IV) approach as outlined below. We are interested in estimating the following regression equation, 22 RV =(cid:11) +(cid:12) AT +(cid:13) (cid:28) + (cid:14) RV +(cid:15) ; (1) it i i it 0i it i it k it (cid:0) k=1 X where i = 1;2;3 represents currency pairs and t = 1;:::;T, represents time. RV is (log) realized daily it volatility, AT is the fraction of algorithmic trading at time t in currency pair i, (cid:28) is either a time trend or it it a set of time dummies that control for secular trends in the data, and (cid:15) is an error term that is assumed it to be uncorrelated with RV , k 1, but not necessarily with AT . The large number of lags of volatility, it k it (cid:0) (cid:21) which covers the business days of the past month, is included to control for the strong serial correlation in volatility (e.g. Andersen, Bollerslev, Diebold, and Labys, 2003 and Bollerslev and Wright, 2000). The exact de(cid:133)nitions of RV , AT , and (cid:28) are given below. it it it The main focus of interest is the parameter (cid:12) , which measures the impact of algorithmic trading on i volatility in currency pair i. However, since AT and (cid:15) may be correlated, due to the potential endogeneity it it discussed above, the OLS estimator of (cid:12) may be biased. In order to obtain an unbiased estimate, we i will therefore consider an instrumental variable approach. Formally, we need to (cid:133)nd a variable, or set of variables, z , that is uncorrelated with (cid:15) (validity of the instrument) and correlated with AT (relevance it it it of the instrument). The instrument we propose to use is the fraction of trading (cid:135)oors equipped to trade algorithmically on EBS relative to the total number of trading (cid:135)oors linked to the EBS system.15 That is, in order to place algorithmic trades on EBS, a special user interface is required, and the total number of trading (cid:135)oors with such user interfaces thus provides a measure of the overall algorithmic trading (cid:147)capacity(cid:148)in the market. The ratio of these algorithmic trading (cid:135)oors to the total number of trading (cid:135)oors provides a measure of the 15More precisely, we actually observe a time series of the number of EBS (cid:147)deal codes(cid:148)of each type over our sample period. Generally speaking, EBS assigns a deal code to each trading (cid:135)oor equipped with at least one of its terminals, and records whetherthey are equipped to trade algorithmically ornot. These data are con(cid:133)dential. 12

potentialfractionofalgorithmictrading. Sincesettingupanalgorithmictradingoperationlikelytakesseveral months,thenumberoftrading(cid:135)oorsofeachtypeisclearlyexogenouswithregardstodailymarketvolatility; the fraction of AT trading (cid:135)oors is therefore a valid instrument. In addition, it is positively correlated with the fraction of algorithmic trading, and it provides a relevant instrument as seen from the tests for weak instruments discussed below. Under the breakdown provided by EBS, there are three types of trading (cid:135)oors linked to the EBS system: purely algorithmic trading (cid:135)oors, purely manual trading (cid:135)oors, and dual trading (cid:135)oors, those equipped to handle both manual and algorithmic trades. We consider two natural instrumental variables: the fraction of pure AT trading (cid:135)oors over the total number of trading (cid:135)oors (including pure AT, manual, and dual ones), andthefractionofthesumofpureATand dualtrading(cid:135)oorsoverthetotalnumber. Sinceitisnotobvious which variable is the better instrument, we use both simultaneously.16 ThedataonATtrading(cid:135)oorsareprovidedonamonthlybasis,whereasthedataonrealizedvolatilityand algorithmic trading are sampled on a daily frequency. We therefore transform the trading (cid:135)oor data to daily data by repeating the monthly value each day of the month. Although this leads to a dataset of two years of daily data, the number of daily observations (498) overstates the e⁄ective number of observations, since the coe¢ cient on AT participation will be identi(cid:133)ed from monthly variations in the instrumental variables. Transforming the instruments to a daily frequency is, however, more e¢ cient than transforming all data to a monthly frequency, since the daily data help to identify the monthly shifts. The instrumental variable regressions are estimated using Limited Information Maximum Likelihood (LIML), and we test for weak instruments by comparing the (cid:133)rst stage F statistic for the excluded instru- (cid:0) ments to the critical values of Stock and Yogo(cid:146)s (2005) test of weak instruments. We use LIML rather than two-stage least squares since Stock and Yogo (2005) show that the former is much less sensitive to weak instruments than the latter (see also Stock et al., 2002). 4.3 Variable de(cid:133)nitions 4.3.1 Realized Volatility Volatility is measured as the daily realized volatility obtained from one minute returns; that is, the volatility measure is equal to the square root of the daily sum of squared one minute log-price changes. The use of realized volatility, based on high-frequency intra-daily returns, as an estimate of ex-post volatility is now well established and generally considered the most precise and robust way of measuring volatility. Although 16RegressionsnotreportedhereshowthatusingthefractionofpureATtrading(cid:135)oorsasasingleinstrumentgivesqualitatively similar results to those presented below based on both instruments. Using the fraction of the sum of both pure and dual AT trading (cid:135)oors as a single instrument also leads to the same qualititative conclusion,but with more signs ofweak instruments. 13

many older studies relied on (cid:133)ve minute returns in order to avoid contamination by market microstructure noise (e.g. Andersen et al., 2001), recent work shows that sampling at the one-minute frequency, or even higher frequencies, does not lead to biases in liquid markets (see, for instance, the results for liquid stocks in Bandi and Russel, 2006, and the study by Chaboud et al., 2007, who explicitly examine EBS data on the euro-dollar exchange rate during 2005 and (cid:133)nds that sampling frequencies upwards of once every 20 seconds does not lead to noticeable biases). Here, we restrict ourselves to using minute-by-minute data.17 Following the common conventions in the literature on volatility modelling (e.g. Andersen, Bollerslev, Diebold, and Labys, 2003), the realized volatility is log-transformed to obtain a more well behaved time-series. 4.3.2 Algorithmic trading Weconsidertwomeasuresofthefractionofalgorithmictrading,AT ,inagivencurrencypair: thecomputerit participation fraction and the computer-taker fraction. The (cid:133)rst is simply the percent of the overall trading volume that includes an algorithmic trader as either a maker or a taker (Vol(CH +HC +CC)); that is, the percent of trading volume where a computer is involved in at least one side of the trade. In addition, we also consider an alternative measure de(cid:133)ned as the fraction of overall trading volume that is due to a computer-taker (Vol(HC+CC)). 4.3.3 Time controls AsseeninFigure4,thereisaclearseculartrendinthecomputer-participationfraction,18 whichisnotpresent inrealizedvolatility. Euro-dollar,dollar-yen,andeuro-yenvolatilityistrendingdownatthebeginningofthe period and starts to trend up in the summer of 2007. In order to control for the trend in algorithmic trading in the regression, we include either a (cid:147)linear quarterly(cid:148)time trend or a full set of year-quarter dummies, one for each year-quarter pair in the data (8 dummies). That is, the linear quarterly time trend stays constant withineachquarterandincreasesbythesameamounteachquarter,whereastheyear-quarterdummiesallows for a more (cid:135)exible trend speci(cid:133)cation that can shift in arbitrary fashion from year-quarter to year-quarter. Both secular trend speci(cid:133)cations are thus (cid:133)xed within each quarter. This restriction is imposed in order to preserve the identi(cid:133)cation coming from the monthly instrumental variables. Using monthly, or (cid:133)ner, time dummies would eliminate the variation in the instrument and render the model unidenti(cid:133)ed. Although it is theoreticallypossibletoincludeamonthlytimetrend,thiswouldleadtoveryweakidenti(cid:133)cationempirically. 17Using realized volatility based on (cid:133)ve-minute returns leads to results that are very similar to those reported below for the one-minute returns,and the qualitative conclusions are identical. 18The same is true forthe computer-takerfraction,not shown in the (cid:133)gure. 14

4.4 Empirical results The regression results are presented in Table 4. We present OLS and LIML-IV results, with either the quarterly trend or the year-quarter dummies included. We show in Panels A and B the results for the computer-participation volume, and in Panels C and D the results for computer-taker volume. We report results for the sample starting in January 2006 and ending in December 2007. In order to save space, we only show the estimates of the coe¢ cients in front of the fraction of algorithmic trading volume variables. TheOLSresults,whicharelikelytobebiasedduetotheaforementionedendogeneityissues,showafairly clear pattern of a positive correlation between volatility and AT participation, with several positive and statisticallysigni(cid:133)cantcoe¢ cients. TheR2sarefairlylarge,re(cid:135)ectingthestrongserialcorrelationinrealized volatility, which is picked up by the lagged regressors. There are also no systematic di⁄erences between the quarterly trend and quarterly dummies speci(cid:133)cations. TurningtothemoreinterestingIVresults,whichcontrolfortheendogeneitybias,thecoe¢ cientestimates changefairlydramatically. Allpointestimatesarenownegativeandsomeofthemarestatisticallysigni(cid:133)cant. Thus,ifthereisacausal relationshipbetweenthefractionofalgorithmictradingandthelevelofvolatility,all evidencesuggeststhatitisnegative,suchthatincreasedATparticipationlowersthevolatilityinthemarket. The stark di⁄erence between the IV and OLS results shows the importance of controlling for endogeneity when estimating the causal e⁄ect of AT on volatility; the opposite conclusion would have been reached if one ignored the endogeneity issue. The evidence of a statistically signi(cid:133)cant relationship is fairly weak, however,withmostcoe¢ cientsstatisticallyindistinguishablefromzero. Themorerestrictivequarterlytrend speci(cid:133)cation suggests a signi(cid:133)cant relationship for the euro-dollar and dollar-yen, but this no longer holds if one allows for year-quarter dummies. To the extent that the estimated coe¢ cients are statistically signi(cid:133)cant, it is important to discuss the economic magnitude of the estimated relationship between AT and volatility. The regression is run with log volatility rather than actual volatility, which makes it a little less straightforward to interpret the size of the coe¢ cients. However, some back-of-the-envelope calculations can provide a rough idea. Suppose that the coe¢ cient on computer participation is about 0:01, which is in line with the coe¢ cient estimates for the (cid:0) euro-dollar. The average monthly shift in computer participation in the euro-dollar is about 1.5 percentage pointsandtheaveragelog-volatilityintheeuro-dollarisabout3:76(withreturnscalculatedinbasispoints), which implies an annualized volatility of about 6:82 percent. Increasing the computer participation fraction by1.5percentagepointsdecreaseslog-volatilityby0:015andresultsinanannualizedvolatilityofabout6:72. Thus, a typical change in computer participation might change volatility by about a tenth of a percentage point in annualized terms, a small e⁄ect. 15

The(cid:133)rststageF statisticsfortheexcludedinstrumentsintheIVregressionsarealsoreportedinPanels (cid:0) B and D. Stock and Yogo (2005) show that this F statistic can be used to test for weak instruments. (cid:0) Rejection of the null of weak instruments indicates that standard inference on the IV-estimated coe¢ cients can be performed, whereas a failure to reject indicates possible size distortions in the tests of the LIML coe¢ cients. The critical values of Stock and Yogo (2005) are designed such that they indicate a maximal actual size for a nominal sized (cid:133)ve percent test on the coe¢ cient. Thus, in the case considered here with two excluded instruments and one endogenous regressor, a value greater than 8:68 for this F statistic indicates (cid:0) thatthemaximalsizeofanominal5percenttestwillbenogreaterthan10percent, whichmightbedeemed acceptable; avaluegreaterthan5:33fortheF statisticindicatesamaximalsizeof15percentforanominal (cid:0) 5 percent test. In general, the larger the F statistic, the stronger the instruments. As is evident from the (cid:0) table, there are no signs of weak instruments in the speci(cid:133)cation with a quarterly trend. There are, however, signsofweakinstrumentsinthecasewithyear-quarterdummies,fortheeuro-yen. Thisisnottoosurprising given that the instruments only change on a monthlyfrequency, and the year-quarter dummies therefore put a great deal of strain on the identi(cid:133)cation mechanism. Importantly, though, the results for the two major currencypairsarerobusttoanyweak-instrumentproblemsandthereportedcoe¢ cientsandstandarderrors are unbiased. To sum up, the evidence of any causal e⁄ect of algorithmic trading on volatility is not strong, but what evidence there is points fairly consistently towards a negative relationship. There is thus no systematic statistical evidence to back the often-voiced opinion that AT leads to increased levels of market volatility. If anything, the contrary appears to be true. 5 Who provides liquidity during the release of public announcements? In the previous section we discuss one of the major concerns regarding algorithmic trading, namely, whether AT causes exchange rate volatility. We now examine another major concern, whether AT improves or reduces liquidity during stress periods, when it is arguably needed the most. To answer this question, we cannot simply regress computer-maker volume, a proxy for liquidity provided by computers, on exchange rate volatility, a proxy for stress periods, because, as we discussed in the previous section, algorithmic volume and volatility are endogenous variables. In contrast to the previous section we do not estimate an IV regression, as there are no obvious instruments for volatility.19 Instead, we follow the event study literature 19One could consider macroeconomic news announcements as potential instruments for volatility. However, macroeconomic news announcements are exogeneous variables that cause both foreign exchange rate volatility and liquidity changes. Since we cannot assume that the e⁄ect macroeconomic news announcements have on liquidity is only due to the e⁄ect macroeconomic 16

and compare the liquidity provision by humans and computers during U.S. nonfarm payroll announcements, a period of exogenously heightened volatility, to the liquidity provision by both types of agents during nonannouncement days. This comparison will help us determine who provides relatively more liquidity during stress periods. We note that, when we consider liquidity provision by humans and computers following other important macroeconomic news announcements, the results are qualitatively similar. However, we focus in this section on the nonfarm payroll announcement only, as it routinely generates the highest volatility of all US macroeconomic announcements.20 We consider two liquidity provision estimates: a one-minute estimate and a one-hour estimate. The oneminuteestimateiscalculatedusingvolumeobservationsfrom8:30a.m. to8.31a.m. ET(whenU.S.nonfarm payroll is released), while the one-hour estimate is calculated using observations from 8:25 am to 9:24 am ET. We de(cid:133)ne the one-minute (one-hour) liquidity provision by humans, LH, as the sum of human-maker volume,Vol(HH+HC),dividedbytotalvolumeduringthatperiod,andtheone-minute(one-hour)liquidity provisionbycomputers,LC,asthesumofcomputer-makervolume,Vol(CC+CH),dividedbytotalvolume during that period. Similar to the liquidity provision measures, we de(cid:133)ne the one-minute volatility as the squared 1-minute return from 8:30 a.m. to 8.31 a.m. ET and the one-hour volatility as the sum of squared 1-minute returns from 8:25 am to 9:24 am ET. To compare liquidity provision by humans and computers during announcement times to liquidity provisionduring(moretranquil)non-announcementtimes,wecouldestimatetheaverageliquidityprovisionduring announcementtimesandcompareittotheaverageliquidityprovisionduringnon-announcementtimes, with both means taken over the entire sample period. However, as we discussed previously, exchange rate trading volumesandthesharesofliquidityprovisionbyhumansandcomputersexhibitcleartrendsoveroursample, making the comparison of the two di⁄erent means problematic. Alternatively, and this is the methodology we follow, on each announcement day we estimate the ratio of liquidity provision on that day relative to the liquidityprovisionondayssurroundingtheannouncement. Thisamountstousinganon-parametricapproach to detrend the data. The time series of these ratios will be stationary, and we can then test the hypothesis that the ratio is greater than one. Speci(cid:133)cally, we divide the one-minute (one-hour) liquidity provision by humans, LH , and computers, LC , estimated on announcement day t by the one-minute (one-hour) a a liquidity provision by humans, LH , and computers, LC , respectively, estimated during the surrounding n n non-announcement day period, de(cid:133)ned as 10 business days before and after a nonfarm payroll release date t. The liquidity provision measures on the non-announcement days are calculated in the same manner as on the announcement days, using data only for the periods 8:30 a.m. to 8.31 a.m. ET or 8:25 am to 9:24 news announcements have on volatility,the exclusion restriction required by IV estimation is violated. 20AndersenandBollerslev(1998),amongothers,refertothenonfarmpayrollreportasthe(cid:147)king(cid:148)ofannouncements,because ofthe signi(cid:133)cant sensitivity ofmost asset markets to its release. 17

am ET, for the one-minute and one-hour measures, respectively.21 We follow the same procedure with our one-minute and one-hour volatility estimates. Consistent with previous studies, we show in Table 5 Panel A that the one-hour volatility on nonfarm payroll announcement days is 3 to 6 times larger than during non-announcement days. The one-minute volatility is 15 to 30 times larger during announcement days compared to non-announcement days. As expected, given the fact that we focus on a U.S. data release, the volatility increase is smaller in the crossrate, the euro-yen exchange rate, than in the euro-dollar and yen-dollar exchange rates. Focusing on the statistically signi(cid:133)cant estimates, we show in Table 5 Panel B that, as a share of total volume, humanmakervolumetendstoincreaseduringtheminuteoftheannouncement(theone-minuteratio LHa isgreater LHn than one), while computer-maker volume tends to decrease (the one-minute ratio LCa is less than one). LCn Interestingly, this pattern is reversed when we focus on the one-hour volume estimates for the euro-dollar and euro-yen exchange rate markets. In relative terms, computers do not increase their provision of liquidity as much as humans do during the minute following the announcement. However, computers increase their provision of liquidity relatively more than humans do over the entire hour following the announcement, a period when market volatility remains quite elevated. We note that, over our sample period, the U.S. nonfarm payroll data releases were clearly the most anticipated and most in(cid:135)uential U.S. macroeconomic data releases. They often generated a large initial sharp movement in exchange rates, followed by an extended period of volatility. The behavior of computer traders observed in the (cid:133)rst minute could re(cid:135)ect the fact that many algorithms are not designed to react to the sharp, almost discrete, moves in exchange rates that often come at the precise moment of the data release. Some algorithmic traders may then prefer to pull back from the market a few seconds before 8:30 a.m. ET on days of nonfarm payroll announcements, resuming trading once the risk of a sharp initial price movement has passed. But the data show that algorithmic traders, as a whole, do not shrink back from providing liquidity during the extended period of volatility that follows the data releases. 6 Price Discovery In the previous three sections, we analyze questions that are primarily motivated by practical concerns regarding algorithmic trading, such as whether computer traders induce volatility or reduce liquidity. In this section we turn to questions that are driven more by the market microstructure literature, but that also lead 21Forsimplicity,welabelthe10businessdaysbeforeandafterthenonfarmpayrollannouncementasnon-announcementdays. However, during this 20-day period there are both days with no macroeconomic news and days with news. For instance, every Thursday, including the day before the monthly nonfarm payroll number is released, initial jobless claims are released. Thus, our estimation will likely be biased towards not (cid:133)nding statistically di⁄erent behavior across the two periods. As we show in Table 5,volatility is,on average,much lowerduring this 20-day period than on nonfarm payrolldays,and therefore the period stillserves as a good benchmark. 18

to interesting practical insights regarding the e⁄ects and nature of algorithmic trading. In particular, we study price discovery within a vector autoregressive framework, which enables us to evaluate to what extent humans or computers represent the (cid:147)informed(cid:148)traders in the market. Our (cid:133)ndings reveal several interesting features regarding the impact of algorithmic trades and the order placement behavior of computer traders. 6.1 Who are the (cid:147)informed(cid:148)traders, humans or computers? We (cid:133)rst investigate whether human or computer trades have a more (cid:147)permanent(cid:148)impact on prices. To this end, we estimate return-order (cid:135)ow dynamics in a structural vector autoregressive (VAR) framework in the tradition of Hasbrouck (1991a), where returns are contemporaneously a⁄ected by order (cid:135)ow, but order (cid:135)ow is not contemporaneously a⁄ected by returns. Similar to Hasbrouck(cid:146)s (1996) decomposition of program and nonprogram order (cid:135)ow, we decompose order (cid:135)ow into two components: human-taker OF(ht) =HH +CH and computer-taker OF(ct) =HC+CC , and thus we estimate for each currency(cid:0)i one return equation(cid:1) and two order (cid:135)ow eq(cid:0)uations. In light of E(cid:1)vans and Lyons (2008) (cid:133)ndings, we estimate the structural VAR with U.S. macroeconomic news surprises as exogenous variables that a⁄ect both returns and order (cid:135)ow. Speci(cid:133)cally, we estimate the following system of equations for each currency i, J J J K r = (cid:11)r+ (cid:12)r r + (cid:13)rctOF(ct) + (cid:13)rhtOF(ht) + (cid:14)r S +"r; (2) it ij it j ij it j ij it j ik kt it (cid:0) (cid:0) (cid:0) j=1 j=0 j=0 k=1 X X X X J J J K OF(ht) = (cid:11)OF + (cid:12)OF r + (cid:13)OF(ht) OF(ht) + (cid:13)OF(ct) OF(ct) + (cid:14)OF S +"OF(ht) ; it ht ijht it j ijht it j ijht it j ikht kt it (cid:0) (cid:0) (cid:0) j=1 j=1 j=1 k=1 X X X X J J J K OF(ct) = (cid:11)OF + (cid:12)OFr + (cid:13)OF(ct) OF(ct) + (cid:13)OF(ht) OF(ht) + (cid:14)OFS +"OF(ct) : it ct ijct it j ijct it j ijct it j ikct kt it (cid:0) (cid:0) (cid:0) j=1 j=1 j=1 k=1 X X X X Herer isthe1-minuteexchangeratereturnforcurrencyiattimet;OFhtisthecurrencyihuman-takerorder it it (cid:135)owattimet;OFct isthecurrencyicomputer-takerorder(cid:135)owattimet;andS isthemacroeconomicnews it kt announcement surprise for announcement k at time t de(cid:133)ned as the di⁄erence between the announcement realizationanditscorrespondingmarketexpectation. WeuseBloomberg(cid:146)sreal-timedataontheexpectations and realizations of K = 28 U.S. macroeconomic fundamentals to calculate S . The 28 announcements we kt consideraresimilartothoseinAndersenetal. (2003, 2007)andPasquarielloandVega(2007).22 Sinceunits ofmeasurementvaryacrossmacroeconomicvariables,westandardizetheresultingsurprisesbydividingeach 22OurlistofU.S.macroeconomicnewsannouncementsisthesameasthelistofannouncementsinAndersenetal. (2007)and PasquarielloandVega(2007)withtheadditionofthreeannouncements: unemploymentrate,corePPIandcoreCPI.Andersen et al. (2007) and Pasquariello and Vega (2007) use International Money Market Services (MMS) data on the expectations of U.S. macroeconomic fundamentals. In contrast, we use Bloomberg data because the MMS data are no longer available after 2003. Bloomberg provides survey data similarto those MMS previously provided. 19

of them by their sample standard deviation. Economic theory suggests that we should also include foreign macroeconomic news announcements in equation (2). However, previous studies (cid:133)nd that exchange rates do not respond much to non-U.S. macroeconomic announcements, even at high frequencies (e.g. Andersen et al., 2003), so we expect the omitted variable bias in our speci(cid:133)cation to be small. The underlying economic model is based on continuous time, and we thus estimate the VAR using the highest sample frequency available to us, minute-by-minute data. The estimation period is restricted to the 2006 2007sample,andthetotalnumberofobservationsforeachcurrencypairis717;120inthefullsample (cid:0) and 89;280 in the three-month sub-sample (September, October and November of 2007). In both samples, 20 lags are included in the estimated VARs, i.e. J =20. Our speci(cid:133)cation in equation (2) does not allow human-taker order (cid:135)ow to contemporaneously a⁄ect computer-taker order (cid:135)ow or vice-versa. The advantage of this approach is that we can estimate the impulse response functions without giving more importance to a particular type of order (cid:135)ow, i.e., we do not need to assumeaparticularorderingofthehuman-takerandcomputer-takerorder(cid:135)owintheVAR.Thedisadvantage is that the human-taker and computer-taker order (cid:135)ow shocks may not be orthogonal. However, in our estimation this does not appear to be a problem, as our residuals are found to be approximately orthogonal (the correlation between the human-taker and computer-takerequation residuals are -0.001, -0.1 and -0.1 for theeuro-dollar,yen-dollar,andeuro-yenexchangeratesrespectively). Asarobustnesscheck,wealsoestimate the VAR with two di⁄erent orderings. We (cid:133)rst assume human-taker order (cid:135)ow a⁄ects computer-taker order (cid:135)ow contemporaneously, and then assume the opposite ordering. This latter approach allows us to compute upper and lower bound impulse responses. These results are presented in the Appendix, and show that the results presented here are not sensitive to alternative identi(cid:133)cation schemes in the VAR. Beforeconsideringtheimpulseresponsefunctionsandthevariancedecompositions,webrie(cid:135)ysummarize the main lessons from the estimated coe¢ cients in the VAR. Focusing on the return equation, we (cid:133)nd that minute-by-minute returns tend to be negatively serially correlated, with the coe¢ cient on the (cid:133)rst own lag varying between 0:08 and 0:15; there is thus some evidence of mean reversion in the exchange rates at (cid:0) (cid:0) these high frequencies, which is a well-know empirical (cid:133)nding. Both order (cid:135)ows are signi(cid:133)cant predictors of returns. The price impact of the lagged order (cid:135)ows range from around 4 to 18 basis points per billion units of order (cid:135)ow (denominated in the base currency), as compared to a range of approximately 28 100 basis (cid:0) points in the contemporaneous order (cid:135)ow. As theory would predict, we (cid:133)nd that U.S. macroeconomic news announcementsa⁄ectlesstheeuro-yenexchangerate(i.e.,theR2 ofregressingtheeuro-yenexchangerateon macroeconomic news surprises and restricting the sample to announcement-only observations is 23%) than the euro-dollar and dollar-yen exchange rates (i.e., the R2s of an announcement-only sample are 60% and 59%, respectively). However, U.S. macroeconomic news announcements still have an e⁄ect on the cross-rate 20

to the extent that the U.S. economy is more or less correlated with the Japanese or the Euro-area economy. Focusing on the order-(cid:135)ow equations, we (cid:133)nd that the (cid:133)rst own lag in both order (cid:135)ow equations is always highly signi(cid:133)cant, and typically around 0:1 for all currency pairs. There is thus a sizeable (cid:133)rst-order autocorrelation in the human-taker and computer-taker order (cid:135)ows. The coe¢ cients on the (cid:133)rst order crosslags in the order (cid:135)ow regressions are most often substantially smaller than the coe¢ cient on the own lag and vary in signs. Lagged returns have a small but positive impact on order (cid:135)ow, suggestive of a form of trend chasing by both computers and humans in their order placement. We note that despite the strongly signi(cid:133)cant estimates that are recorded in the VAR estimations, the amount of variation in the order (cid:135)ow and return variables that is captured by their lagged values is very limited. The R2 for the estimated equations with only lagged variables are typically around three to ten percent for the order (cid:135)ow equations, and between one and three percent for the return equations. This can be compared to an R2 of 20 to 30 percent when one includes contemporaneous order (cid:135)ow. 6.2 Impulse Response Function and Variance Decomposition Results As originally suggested by Hasbrouck (1991b), we use the impulse response functions to assess the price impact of various order (cid:135)ow types, and the variance decompositions to measure the relative importance of the variables driving foreign exchange returns. In Table 6 Panel A, we show the results from the impulse response analysis based on the estimation of equation (2), using the full sample for 2006-2007 and the threemonthsub-sample,whenthesizeoftheshockisthesameacrossthedi⁄erenttypesoforder(cid:135)ow: aonebillion base currency shock to order (cid:135)ow. We also show the results when the size of the shock varies according to the average size shock: a one standard deviation base currency shock to order (cid:135)ow (Table 6 Panel B). We show both the short-run (instantaneous) impulse responses, the long-run cumulative responses, and the di⁄erence between the two responses. The long-run statistics are calculated after 30-minutes, at which point the cumulative impulse responses have converged and can thus be interpreted as the long-run total impact of the shock. All the responses are measured in basis points. The standard errors reported in the tables are calculated by bootstrapping, using 200 repetitions. Starting with a hypothetical shock of one billion base currency order (cid:135)ow, the results in Table 6 Panel A, show that the immediate response of prices to human-taker order (cid:135)ow is often larger than the immediate responsetocomputer-takerorder(cid:135)ow. Thismaypartiallybeattributedtothefactthatsomeofthealgorithmic trading is used for the optimal execution of large orders at a minimum cost. Algorithmic trades appear tobe successfulin thatendeavor, withcomputers likelybreakingupthelargerorders and timingthe smaller trades to minimize the impact on prices. We emphasize, though, that the di⁄erences in price impact, which 21

rangefrom1to8basispoints,arenotverylargeineconomicterms. Furthermore,we(cid:133)ndthattheresultcan be reversed in the long-run and in the three-month sub-sample. For example, the euro-dollar human-taker price impact is larger than the computer-taker price impact in the short-run, but the opposite is true in the long-run and in the three-month sub-sample. In contrast to these results, the response to a hypothetical one standard deviation shock to the di⁄erent order (cid:135)ows (Table 6 Panel B) consistently shows that in the euro-dollar and dollar-yen markets, humans have a bigger impact on prices than computers and the di⁄erences are relatively large. For example, a one standard deviation shock to human-taker order (cid:135)ow in the yen-dollar exchange rate market has an average long-run e⁄ect of 0.9 basis points compared to an average e⁄ect of 0.3 basis points for computer-taker order (cid:135)ow. Interestingly, the di⁄erence in price impact in the cross-rate, the euro-yen exchange rate, is very small. Inthismarket, computers haveaclearadvantageoverhumansindetectingandreactingmorequickly to triangular arbitrage opportunities so that a large proportion of algorithmic trading contributes to more e¢ cient price discovery. It is then not so surprising that in this market computers and humans, on average, appear to be equally (cid:147)informed.(cid:148) In Table 7 we report the fraction of the total (long-run) variance in returns that can be attributed to innovations in human-taker order (cid:135)ow and computer-taker order (cid:135)ow.23 Following Hasbrouck (1991b), we interpretthisvariancedecompositionasasummarymeasureoftheinformativenessoftrades,andthus,inthe current context, a comparison of the relative informativeness of the di⁄erent types of order (cid:135)ow. Consistent withtheresultsfromtheimpulseresponsefunctionsbasedonaonestandarddeviationshocktoorder(cid:135)ow,we (cid:133)ndthatintheeuro-dollaranddollar-yenexchangeratemarketshuman-takerorder(cid:135)owexplainsmuchmore ofthetotalvarianceinreturnsthancomputer-takerorder(cid:135)ow. Speci(cid:133)cally, human-takerorder(cid:135)owexplains about 30 percent of the total variance in returns compared to only 4 percent explained by computer-taker order (cid:135)ow. Thefactthathuman-takerorder(cid:135)owexplainsabiggerportionoftotalvarianceinreturnsisnotsurprising becausehuman-takervolumeisabout75percentoftotalvolumeinthesetwomarketsinthefullsampleperiod andabout65percentoftotalvolumeinthethree-monthsub-sample(seeTable2). Moreoverlargebuy(sell) orders tend to be human-taker orders, i.e. we show in Table 1 that the standard deviation of human-taker order (cid:135)ow is twice as big as that of the computer-taker order (cid:135)ow. But, do computers tend to contribute (cid:147)disproportionately(cid:148)littletothelong-runvarianceinreturnsrelativetotheirtradingvolume? Toanswerthis question we do a back-of-the-envelope calculation. We compute the relative share of the explained variance that is due to computer-taker order (cid:135)ow as the percent of total variation in returns explained by computer- 23The variance decompositions are virtually identical in the short- and long-run and thus we only show the long-run decomposition results. 22

taker order (cid:135)ow divided by the percent of total variation in returns explained jointly by both human-taker and computer-taker order (cid:135)ow. For example, this relative share is 14% = 100 4:74 (Table 7) in the euro- (cid:2) 34 dollar market. We can then compare this relative share to the fraction of overall trading volume that is due to computer-taker volume, which we show in Table 2. In the full 2006-2007 sample for the euro-dollar and the dollar-yen currency pairs, the fraction of volume due to computer-takers is about twice as large as the fraction of the explained long-run variance that is due to computer-taker order (cid:135)ow. In the euro-yen, the fractions are approximately equal. These results are fairly similar in the three-month sub-sample, although the fraction of explained variance has increased somewhat compared to the volume fraction. Thus, in the two major currency pairs, there is evidence that computer-taker order (cid:135)ow contributes relatively less to the variation in returns than one would infer from just looking at the proportion of computer-taker volume. 6.3 Are liquidity providers (cid:147)uninformed(cid:148)? We now turn to examine whether liquidity providers post quotes strategically. To this end we augment equation (2) and decompose order (cid:135)ow into four components. Speci(cid:133)cally, we estimate the following system of equations for each currency i; J L J K r = (cid:11)r+ (cid:12)r r + (cid:13)rlOF(l) + (cid:14)r S +"r; (3) it ij it j ij it j ik kt it (cid:0) (cid:0) j=1 l=1j=0 k=1 X XX X J L J K OF(l) = (cid:11)OF + (cid:12)OFr + (cid:13)OF(l) OF(l) + (cid:14)OFS +"OF(l) : it l ijl it j ijl it j ikl kt it (cid:0) (cid:0) j=1 l=1j=1 k=1 X XX X where r is the 1-minute exchange rate return for currency i at time t; L = 4, OF(1) = OFHH is the it it it currency i human-maker/human-taker order (cid:135)ow at time t; OF(2) = OFCH is the currency i computerit it maker/human-taker order (cid:135)ow at time t; OF(3) = OFHC is the currency i human-maker/computer-taker it it order (cid:135)ow at time t; OF(4) =OFCC is the currency i computer-maker/computer-taker order (cid:135)ow at time t; it it S is the macroeconomic news announcement surprise for announcement k at time t.24 kt In addition to identifying whether traders, on average, have a more permanent impact on prices when trading with humans than with computers, this speci(cid:133)cation also allows us to observe the e⁄ect order (cid:135)ow hasonpriceswhen,forinstance,nopartyhasaspeedadvantage,i.e. bothpartiesarehumansorbothparties are computers, and when either the maker has a speed advantage, CH, or the taker has a speed advantage, HC. This distinction may be particularly useful when analyzing the cross-rate, where computers likely have 24In the Appendix, we analyze the robustness of this structural VAR by also estimating impulse responses and variance decompositions from allpossible triangularidenti(cid:133)cation schemes,only imposing that returns are ordered last in the VAR. 23

a clear advantage over humans in detecting short-lived triangular arbitrage opportunities. Starting with a hypothetical shock of one billion base currency order (cid:135)ow, the results in Table 8 Panel A showthatthereisnoclearpatterninwhichorder(cid:135)owimpactspricesthemost. However,thedynamicsofthe VAR system help reveal an interesting (cid:133)nding: There is a consistent and often large short-run over-reaction to CC and CH shocks. That is, as seen in Table 8, the short run response to a CC or CH order (cid:135)ow shock is always larger than the long-run response, and sometimes substantially so. The euro-dollar in the sample covering September, October, and November of 2007 provides an extreme case where the initial reaction to a one billion dollar CC shock is a 22 basis point move, but the long-run cumulative reaction is just 6 basis points. Interestingly, the opposite pattern is true for the HH order (cid:135)ow shocks, where there is always an initial under-reaction in returns. To the extent that an over-reaction of prices to order (cid:135)ow is suggestive of the presence of liquidity traders, these impulse response patterns suggest that computers provide liquidity when the probability of trading with an informed trader is low.25 The response to a hypothetical one standard deviation shock to the di⁄erent order (cid:135)ows consistently shows that HH order (cid:135)ow has a bigger impact on prices than CC order (cid:135)ow (Table 8 Panel B) and that the di⁄erences are large. In particular, a one standard deviation shock to HH order (cid:135)ow has an average long-run e⁄ect of 0.6 basis points across currencies compared to a one standard deviation shock to CC order (cid:135)ow, which has an average e⁄ect of 0.1 basis points. Interestingly, we observe that when humans trade with other humans they in(cid:135)uence prices more than when they trade with computers (the impact of HH on prices is bigger than the impact of CH on prices), and when computers trade with other computers they in(cid:135)uence priceslessthanwhentheytradewithhumans(theimpactofCC onpricesissmallerthantheimpactofHC onprices). Ourinterpretationisthatcomputersprovideliquiditymorestrategicallythanhumans,sothatthe counterparty cannot a⁄ect prices as much. This interpretation is consistent with the over-reaction of prices to CC and CH order (cid:135)ow described above: Computers appear to provide liquidity when adverse selection costs are low. This (cid:133)nding relates to the literature that proposes to depart from the prevalent assumption that liquidity providers in limit order books are passive.26 We also (cid:133)nd that the price response to order (cid:135)ow varies across currencies as these markets di⁄er along several dimensions. Trading volume is largest in the euro-dollar and dollar-yen markets, compared to the euro-yen market, and price discovery clearly happens mostly in the two largest markets. In the cross-rate 25Dynamic learning models with informed and uninformed investors predict that prices will temporarily over-react to uninformed order (cid:135)ow and under-react to informed order (cid:135)ow (e.g., Albuquerque and Miao, 2008). We note that the over- and under-reactionofpricestoaparticulartypeoforder(cid:135)owisdi⁄erentfrom theover-andunder-reactionofpricestopublicnews, whicharebothconsideredasignofmarketine¢ ciency. Order(cid:135)ow typesarenotpublicknowledge,sothatagentscannottrade on this information. 26For example, Chakravarty and Holden (1995), Kumar and Seppi (1994), Kaniel and Liu (2006), and Goettler, Parlour and Rajan (2007) allow informed investors to use both limit and market orders. Bloom(cid:133)eld, O(cid:146)Hara and Saar (2005) argue that informedtradersarenaturalliquidityprovidersandAngel(1994)andHarris(1998)showthatinformedinvestorscanoptimally use limit orders when private information is su¢ ciently persistent. 24

market, the euro-yen, computers have a speed advantage over humans in pro(cid:133)ting from triangular arbitrage opportunities, where prices set in the euro-dollar and dollar-yen markets are very brie(cid:135)y out of line with the euro-yen rate. Consistent with this speed advantage we observe that human-maker/computer-taker order (cid:135)ow has a larger price impact in the cross-rate market than in the other two markets. Inadditiontotheimpulseresponsefunctions,wealsoreportthelong-runforecastvariancedecomposition of returns in Table 9 for both the full sample and the three-month sub-sample. Consistent with the impulse responsefunctionstoaonestandarddeviationshocktoorder(cid:135)ow,theHH order(cid:135)owmakesupthedominant part of the variance share in the euro-dollar and dollar-yen exchange rate markets. In the last three months of the sample, this share has generally decreased. The share of variance in returns that can be attributed to the CC order (cid:135)ow is surprisingly small, especially in the latter sub-sample, given that this category of trades represents a sizeable fraction of overall volume of trade during the last months of 2007, as seen in Table 2. The mixed order (cid:135)ow (CH and HC order (cid:135)ow) typically contributes with about the same share to the explained variance in the euro-dollar and dollar-yen exchange rate markets. In contrast, in the euro-yen exchange rate market HC order (cid:135)ow makes up the dominant part of the variance share, which is consistent with our discussion of computers taking advantage of triangular arbitrage opportunities in this market. Overall, about 15 to 35 percent of the total variation in returns can be attributed to shocks to the four order (cid:135)ows. However, in most currency pairs, very little of this ultimate long-run price discovery that occurs via order (cid:135)ow does so via the CC order (cid:135)ow. Similar to Table 7, we also report in Table 9 the fraction of the explained share of the return variance that can be attributed to the di⁄erent order (cid:135)ow combinations. Comparingthesetothefractionofoverallvolumethatisduetothesecombinationsofcomputersandhumans, reportedinTable2,givesanideaofwhetherthedi⁄erentorder(cid:135)owcombinationscontributeproportionately to the variance in returns. It is clear that CC order (cid:135)ow tends to contribute disproportionately little to the long-run variance of returns, and that HH order (cid:135)ow often contributes disproportionately much. 7 Conclusion Using highly-detailed high-frequency trading data for three major exchange rates over 2006 and 2007, we analyzetheimpactofthegrowthofalgorithmictradingonthespotinterdealerforeignexchangemarket. We focus on the following questions: (i) Are the algorithms underlying the computer-generated trades similar enough to result in highly correlated strategies, which some fear may cause disruptive market behavior? (ii) Does algorithmic trading increase volatility in the market, perhaps as a result of the previous concern? (iii) Do algorithmic traders improve or reduce market liquidity at times of market stress? (iv) Are human or computer traders the more (cid:147)informed(cid:148)traders in the market, i.e. who has the most impact on price 25

discovery? (v) Is there evidence in this market that the liquidity providers (the (cid:147)makers(cid:148)) and not just the liquidity(cid:147)takers(cid:148),areinformed,anddocomputermakerspostordersmorestrategicallythanhumanmakers? The (cid:133)rst three questions directly address concerns that have been raised recently in the (cid:133)nancial press, especially in conjunction with the current crisis, while the last two questions relate more to the empirical market microstructure literature on price discovery and order placement. Together, the analysis of these questions brings new and interesting results to the table, both from a practical and academic perspective, in an area where almost no formal research has been available. Our empirical results provide evidence that algorithmic trades are more correlated than non-algorithmic trades, suggesting that the trading strategies used by the computer traders are less diverse than those of their human counterparts. Although this may cause some concerns regarding the disruptive potential of computer-generatedtrades,wedonot(cid:133)ndevidenceofapositivecausalrelationshipbetweentheproportionof algorithmictradinginthemarketandthelevelofvolatility;ifanything,theevidencepointstowardsanegative relationship, suggesting that the presence of algorithmic trading reduces volatility. As for the provision of marketliquidity,we(cid:133)ndevidencethat,comparedtonon-algorithmictraders,algorithmictradersreducetheir share of liquidity provision in the minute following major data announcements, when the probability of a pricejumpisveryhigh. However,theyincreasetheirshareofliquidityprovisiontothemarketovertheentire hour following these announcements, which is almost always a period of elevated volatility. This empirical evidence thus suggests that computers do provide liquidity during periods of market stress. To address the last two questions (price discovery and order placement), we use a high-frequency VAR framework in the tradition of Hasbrouck (1991a). We (cid:133)nd that non-algorithmic trades account for a substantially larger share of the price movements in the euro-dollar and yen-dollar exchange rate markets than would be expected given the sizable fraction of algorithmic trades. Non-algorithmic traders are the (cid:147)informed(cid:148)traders in these two markets, driving price discovery. In the cross-rate, the euro-yen exchange rate market, we (cid:133)nd that computers and humans are equally (cid:147)informed,(cid:148)likely because of the large proportion of algorithmic trades dedicated to search for triangular arbitrage opportunities. Finally, we (cid:133)nd that, on average, computer takers or human takers that trade on prices posted by computers do not impact prices as much as they do when they trade on prices posted by humans. One interpretation of this result is that computers place limit orders more strategically than humans do. This (cid:133)nding dovetails with the literature on limit order books that relaxes the common modeling assumption that liquidity providers are passive. Overall, this study therefore provides essentially no evidence to bolster the widespread concerns about thee⁄ectofalgorithmictradingonthefunctioningof(cid:133)nancialmarkets. Thelessonwetakefromouranalysis of algorithmic trading in the interdealer foreign exchange market is that it is more how algorithmic trading is used and what it is predominantly designed to achieve that determines its impact on the market, and not 26

primarily whether or not the order (cid:135)ow reaching the market is generated at high frequency by computers. In the global interdealer foreign exchange market, the rapid growth of algorithmic trading has not come at the cost of lower market quality, at least not in the data we have seen so far. Given the constant search for execution speed in (cid:133)nancial markets and the increasing availability of algorithmic trading technology, it is likely that, absent regulatory intervention, the share of algorithmic trading across most (cid:133)nancial markets will continue to grow. Our study o⁄ers hope that the growing presence of algorithmic trading will not have a negative impact on global (cid:133)nancial markets. Appendix: Robustness check of the VAR results The impulse responses and variance decompositions in the above VAR analyses are derived under the assumption that there are no contemporaneous interactions between the di⁄erent order (cid:135)ow components. This identifying assumption is appealing because it treats the order (cid:135)ow components symmetrically and ensures that the results are not driven by the ordering of the order (cid:135)ows in the VAR. On the other hand, it cannot be ruled out that one order (cid:135)ow component a⁄ects another one contemporaneously within the one-minute timespanoverwhicheachobservationissampled. Ifthisisthecase,theVARspeci(cid:133)cationthatweuseabove would be too restrictive and the resulting impulse responses and variance decompositions would likely be biased. As discussed above, given the fairly low correlation that we observe in the VAR residuals for the di⁄erent order (cid:135)ow equations, this does not appear to be a major concern, but since these correlations are not identical to zero it is still possible that other identi(cid:133)cation schemes would lead to di⁄erent conclusions. In this section we therefore perform a comprehensive robustness check of the VAR results by calculating upper and lower bounds on the impulse responses and variance decompositions. In particular, we consider all possible orderings of the order (cid:135)ows in the VARs, while imposing a triangular structure. That is, we still assume that returns are ordered last in the VAR and are thus a⁄ected contemporaneously by all order (cid:135)ow components, but we then consider all possible orderings for the di⁄erent order (cid:135)ows. In the case where we split order (cid:135)ow into human and computer order (cid:135)ow, this results in just two di⁄erent speci(cid:133)cations(cid:151)one where computer order (cid:135)ow a⁄ects human order (cid:135)ow contemporaneously but contemporaneous human order (cid:135)ow has no impact on computer order (cid:135)ow, and the opposite speci(cid:133)cation where human order (cid:135)ow a⁄ects computer order (cid:135)ow contemporaneously. In the case with four di⁄erent order (cid:135)ows, there are 24 di⁄erent orderings, when one allows for all possible triangular identi(cid:133)cation schemes, only imposing that returns are ordered last. From each of these speci(cid:133)cations, we calculate impulse responses and variance decompositions. The minimum and maximum of these over all speci(cid:133)cations are reported in Tables A1 and A2 for the two order (cid:135)ow case and in Tables A3 and A4 in the four order (cid:135)ow case. 27

Starting with the simpler case with order (cid:135)ow split up into human or computer order (cid:135)ow, Tables A1 and A2 con(cid:133)rm our conjecture that the low correlation in the VAR residuals render the VAR speci(cid:133)cation very robust to the ordering of the order (cid:135)ows. The min-max intervals shown in the two tables are generally very tight and all of our earlier qualitative conclusions that we draw from our preferred structural VAR speci(cid:133)cation holds also under these alternative orderings. Turning to the VAR analysis with four separate order (cid:135)ow, the number of possible orderings increases dramaticallyto24. Thislargenumberofpossiblespeci(cid:133)cationsinevitablyresultsinwidermin-maxintervals, even though the correlations in the VAR residuals are generally small. In order to usefully interpret these results,wecheckwhetherourmainqualitativeconclusionsfromourpreferredstructuralspeci(cid:133)cationanalyzed above also holds up, in a min-max sense, under all possible orderings. Our (cid:133)rst main result in the above analysiswasthatthereisaninitialover-reactiontoCC andCH shocksandaninitialunder-reactiontoHH shocks. As seen in Table A3, these (cid:133)ndings are mostly supported by the min-max results as well. The only exceptions recorded are for the euro-yen cross rate, where the under-reaction to CC and CH shocks is also much weaker in the original results in Table 8. It is also evident from Table A3, Panel B, that the min-max results support the (cid:133)nding that a one standard deviation shock to HH has a substantially bigger impact on returnsthanaCC shock. Inaddition,TableA3,PanelB,alsoshowsthattheimpactoftheHH shocktends to be larger than the CH impact, and the CC impact tends to be smaller than the HC impact. Finally, the results in Table A3 also mostly support the (cid:133)nding that the reactions to HC order (cid:135)ow are greater in the euro-yen cross currency than in the two main currency pairs, although some overlap is seen for the one standard deviation shock in Panel B. Table A4 shows the corresponding min-max results for the variance decomposition. Again, our main conclusions are mostly supported in a min-max sense. HH makes up the largest share of the explained variance in the two main currency pairs in the full sample, although in the three-month sub-sample there is some overlap between the min-max intervals for the HH order (cid:135)ow and the HC order (cid:135)ow. CC always contributesaverysmallshareoftheexplainedvarianceandHC alwayscontributesafairlysubstantialshare in the cross currency. Insummary,theserobustnesschecksshowthatourmainVARusedforexaminingpricediscovery(equation (2)), using human and computer order (cid:135)ows, is not particularly sensitive to the exact identi(cid:133)cation scheme that is used. The results presented in Tables 6 and 7 thus appear tobe robust to alternative orderings in the VAR. Our second VAR speci(cid:133)cation (equation (3)), which we use to analyze strategic liquidity provision, is a little more sensitive to the exact identi(cid:133)cation scheme used, but the min-max results are still overall very supportive of our main conclusions. 28

Table A1: Min-max impulse responses from the VAR speci(cid:133)cation with human-taker and computer-taker order (cid:135)ow. The table shows the minimum and maximum triangular impulse responses for returns as a result of shocks to the human-taker order (cid:135)ow (HH +CH) or computer-taker (CC +HC) order (cid:135)ow, denoted H-taker and C-taker in the table headings, respectively. In Panel A we show the return response, in basis points,toaone-billionbase-currencyshocktooneoftheorder(cid:135)ows. InPanelBweshowthereturnresponse, in basis points, to a one standard deviation shock to one of the order (cid:135)ows. We show the results for the full 2006-2007 sample and for the three-month sub-sample, which only uses data from September, October, and November of 2007. For each currency pair we show the short-run (immediate) response of returns; the correspondingcumulativelong-runresponseofreturns,calculatedasthecumulativeimpactoftheshockafter 30 minutes; and the di⁄erence between the cumulative long-run response in returns minus the immediate responseofreturns,i.e.,weprovidetheextentofover-reactionorunder-reactiontoanorder(cid:135)owshock. There are a total of 717;120 minute-by-minute observations in the full two-year sample and 89;280 observations in the three-month sub-sample. Full 2006-2007 sample 3-month sub-sample H-taker C-taker H-taker C-taker Panel A: One billion base-currency shock USD/EUR Short run [28:05;28:06] [26:84;26:94] [23:11;23:20] [24:89;25:22] Long run [27:85;27:87] [32:26;32:35] [24:06;24:16] [31:04;31:38] Di⁄erence [ 0:20; 0:20] [5:42;5:42] [0:94;0:96] [6:14;6:16] (cid:0) (cid:0) JPY/USD Short run [44:96;46:76] [28:92;39:81] [44:99;48:02] [33:45;44:88] Long run [45:50;47:50] [33:21;44:27] [46:80;49:54] [28:83;40:63] Di⁄erence [0:54;0:74] [4:29;4:46] [1:52;1:81] [ 4:62; 4:25] (cid:0) (cid:0) JPY/EUR Short run [90:18;99:32] [90:50;102:71] [109:04;124:02] [101:74;115:52] Long run [98:30;108:07] [96:57;109:85] [116:54;132:53] [108:54;123:26] Di⁄erence [8:12;8:75] [6:07;7:14] [7:50;8:51] [6:79;7:74] Panel B: One standard deviation shock USD/EUR Short run [0:6613;0:6616] [0:2630;0:2639] [0:6023;0:6045] [0:3139;0:3180] Long run [0:6566;0:6570] [0:3161;0:3170] [0:6269;0:6296] [0:3914;0:3957] Di⁄erence [ 0:0047; 0:0046] [0:0531;0:0531] [0:0246;0:0251] [0:0775;0:0777] (cid:0) (cid:0) JPY/USD Short run [0:8370;0:8660] [0:2375;0:3251] [0:9594;1:0158] [0:3798;0:5056] Long run [0:8470;0:8796] [0:2727;0:3616] [0:9980;1:0480] [0:3274;0:4577] Di⁄erence [0:0100;0:0137] [0:0352;0:0364] [0:0322;0:0386] [ 0:0524; 0:0479] (cid:0) (cid:0) JPY/EUR Short run [0:5060;0:5541] [0:4318;0:4874] [0:6671;0:7532] [0:6725;0:7581] Long run [0:5515;0:6030] [0:4608;0:5213] [0:7130;0:8049] [0:7174;0:8089] Di⁄erence [0:0455;0:0488] [0:0289;0:0339] [0:0459;0:0517] [0:0449;0:0508] 29

Table A2: Min-max variance decompositions from the VAR speci(cid:133)cation with human-taker and computertaker order (cid:135)ow. The table shows the minimum and maximum triangular long-run variance decomposition of returns, expressed in percent and calculated at the 30 minute horizon. That is, the table shows the proportion of the long-run variation in returns that can be attributed to shocks to the human-taker order (cid:135)ow (HH +CH) and the computer-taker (CC+HC) order (cid:135)ow, denoted H-taker and C-taker in the table headings,respectively. Foreachcurrencypairweshowtheactualvariancedecomposition,andtheproportion of the explained variance in returns that can be attributed to each order (cid:135)ow type. That is, we re-scale the variance decompositions so that they add up to 100 percent. We show results for the full 2006-2007 sample and for the three-month sub-sample, which only uses data from September, October, and November of 2007. There are a total of 717;120 minute-by-minute observations in the full two-year sample and 89;280 observations in the three-month sub-sample. Full 2006-2007 sample 3-month sub-sample H-taker C-taker H-taker C-taker USD/EUR Variance decomposition [29:25;29:28] [4:71;4:74] [25:78;25:96] [7:08;7:26] Proportion of explained share [86:04;86:14] [13:86;13:96] [78:02;78:58] [21:42;21:98] JPY/USD Variance decomposition [27:71;29:67] [2:31;4:28] [26:03;29:19] [4:21;7:37] Proportion of explained share [86:63;92:77] [7:23;13:37] [77:94;87:40] [12:60;22:06] JPY/EUR Variance decomposition [10:15;12:16] [7:37;9:39] [9:94;12:67] [10:15;12:88] Proportion of explained share [51:93;62:27] [37:73;48:07] [43:55;55:53] [44:47;56:45] 30

elbat ehT .snoitanibmoc wo(cid:135) redro rekat/rekam-retupmoc/namuh ruof lla htiw noitac(cid:133)iceps RAV eht morf sesnopser eslupmi xam-niM :3A elbaT ,)HH( wo(cid:135) redro rekat-namuh/rekam-namuh eht ot skcohs fo tluser a sa snruter rof sesnopser eslupmi ralugnairt mumixam dna muminim eht swohs ,)CC(wo(cid:135)redrorekat-retupmoc/rekam-retupmocro ,)CH(wo(cid:135)redrorekat-retupmoc/rekam-namuh ,)HC(wo(cid:135)redrorekat-namuh/rekam-retupmoc ew A lenaP nI .atad etunim-yb-etunim gnisu ,)3( noitauqe fo noitamitse no desab era stluser ehT .sgnidaeh elbat eht ni noitaton suoivbo ni detoned ni ,esnopser nruter eht wohs ew B lenaP nI .swo(cid:135) redro eht fo eno ot kcohs ycnerruc-esab noillib-eno a ot ,stniop sisab ni ,esnopser nruter eht wohs htnom-eerht eht rof dna elpmas 7002-6002 lluf eht rof stluser eht troper eW .swo(cid:135) redro eht fo eno ot kcohs noitaived dradnats eno a ot ,stniop sisab esnopser)etaidemmi(nur-trohsehtwohsewriapycnerruchcaeroF .7002forebmevoNdna,rebotcO,rebmetpeSmorfatadsesuylnohcihw,elpmas-bus eht dna ;setunim 03 retfa kcohs eht fo tcapmi evitalumuc eht sa detaluclac ,snruter fo esnopser nur-gnol evitalumuc gnidnopserroc eht ;snruter fo ronoitcaer-revofotnetxeehtedivorpew ,.e.i ,snruterfoesnopseretaidemmiehtsunimsnruterniesnopsernur-gnolevitalumucehtneewtebecnere⁄id snoitavresbo082;98dnaelpmasraey-owtllufehtnisnoitavresboetunim-yb-etunim021;717folatotaeraerehT .kcohswo(cid:135)redronaotnoitcaer-rednu .elpmas-bus htnom-eerht eht ni elpmas-bus htnom-3 elpmas 7002-6002 lluF /rekam-C /rekam-H /rekam-C /rekam-H /rekam-C /rekam-H /rekam-C /rekam-H rekat-C rekat-C rekat-H rekat-H rekat-C rekat-C rekat-H rekat-H kcohs ycnerruc-esab noillib enO :A lenaP RUE/DSU ]85:83;66:21[ ]85:24;10:71[ ]75:74;94:71[ ]96:72;12:02[ ]14:25;94:02[ ]58:54;62:51[ ]17:35;36:81[ ]23:33;33:72[ nur trohS ]01:62;27:4 [ ]15:94;46:52[ ]86:24;05:7[ ]77:03;80:42[ ]46:74;71:21[ ]80:05;80:22[ ]65:64;12:8[ ]38:43;98:92[ nur gnoL (cid:0) ]46:11 ;18:71 [ ]34:9;13:4[ ]17:4 ;51:01 [ ]55:4;62:2[ ]65:3 ;31:9 [ ]02:7;96:2[ ]50:7 ;84:01 [ ]88:2;50:1[ ecnere⁄iD (cid:0) (cid:0) (cid:0) (cid:0) (cid:0) (cid:0) (cid:0) (cid:0) DSU/YPJ ]49:98;61:16[ ]48:46;80:32[ ]06:49;02:04[ ]40:45;15:14[ ]46:38;39:15[ ]02:06;14:91[ ]56:59;45:93[ ]88:15;11:34[ nur trohS ]56:17;38:44[ ]73:95;69:91[ ]86:09;41:63[ ]25:75;94:64[ ]96:77;69:34[ ]32:36;20:52[ ]90:98;22:92[ ]42:45;86:64[ nur gnoL ]58:51 ;34:81 [ ]28:2 ;50:7 [ ]95:1 ;14:7 [ ]89:4;84:3[ ]27:4 ;54:8 [ ]18:5;57:1[ ]74:6 ;24:01 [ ]17:3;52:2[ ecnere⁄iD (cid:0) (cid:0) (cid:0) (cid:0) (cid:0) (cid:0) (cid:0) (cid:0) (cid:0) (cid:0) RUE/YPJ ]07:101;10:68[ ]12:731;01:09[ ]84:741;10:03[ ]04:871;59:831[ ]91:311;99:99[ ]21:121;23:87[ ]90:231;32:03[ ]08:321;33:201[ nur trohS ]27:201;85:68[ ]58:441;81:69[ ]17:641;51:02[ ]31:891;80:951[ ]62:501;01:19[ ]27:921;28:48[ ]33:631;25:52[ ]08:731;68:511[ nur gnoL ]76:1;35:0[ ]18:7;64:4[ ]77:0 ;68:9 [ ]34:12;06:81[ ]78:7 ;98:8 [ ]37:8;41:6[ ]72:4;57:4 [ ]95:41;73:31[ ecnere⁄iD (cid:0) (cid:0) (cid:0) (cid:0) (cid:0) kcohs noitaived dradnats enO :B lenaP RUE/DSU ]8941:0;1840:0[ ]9644:0;3281:0[ ]4464:0;9371:0[ ]9385:0;5983:0[ ]4541:0;1550:0[ ]3973:0;6721:0[ ]1244:0;5451:0[ ]7946:0;6094:0[ nur trohS ]4101:0;9710:0 [ ]7515:0;7472:0[ ]4614:0;6470:0[ ]9846:0;1464:0[ ]1231:0;7230:0[ ]3414:0;7481:0[ ]2383:0;1860:0[ ]1976:0;5635:0[ nur gnoL (cid:0) ]2540:0 ;7760:0 [ ]9201:0;2340:0[ ]0640:0 ;8001:0 [ ]9190:0;8640:0[ ]9900:0 ;6420:0 [ ]9060:0;4120:0[ ]0850:0 ;8680:0 [ ]7350:0;2020:0[ ecnere⁄iD (cid:0) (cid:0) (cid:0) (cid:0) (cid:0) (cid:0) (cid:0) (cid:0) DSU/YPJ ]3543:0;6032:0[ ]4295:0;4222:0[ ]6687:0;7243:0[ ]8309:0;4846:0[ ]3402:0;4421:0[ ]8014:0;5931:0[ ]4895:0;0452:0[ ]0208:0;3726:0[ nur trohS ]1572:0;0961:0[ ]4245:0;3291:0[ ]0457:0;0803:0[ ]9169:0;1627:0[ ]8981:0;3501:0[ ]5134:0;9971:0[ ]4755:0;7781:0[ ]4838:0;3976:0[ nur gnoL ]7950:0 ;8070:0 [ ]2720:0 ;3360:0 [ ]3410:0 ;6750:0 [ ]7770:0;1850:0[ ]6110:0 ;3020:0 [ ]8140:0;8110:0[ ]5040:0 ;9660:0 [ ]7450:0;7430:0[ ecnere⁄iD (cid:0) (cid:0) (cid:0) (cid:0) (cid:0) (cid:0) (cid:0) (cid:0) (cid:0) (cid:0) RUE/YPJ ]0952:0;1912:0[ ]0077:0;0335:0[ ]3015:0;4801:0[ ]2057:0;5955:0[ ]5571:0;9451:0[ ]8105:0;9543:0[ ]5153:0;7480:0[ ]6535:0;1824:0[ nur trohS ]6162:0;6022:0[ ]8218:0;0965:0[ ]6705:0;8270:0[ ]2338:0;5046:0[ ]2361:0;2141:0[ ]4735:0;6473:0[ ]8263:0;5170:0[ ]3695:0;7484:0[ nur gnoL ]3400:0;4100:0[ ]6640:0;4420:0[ ]7200:0 ;6530:0 [ ]4880:0;5770:0[ ]2210:0 ;8310:0 [ ]2630:0;0520:0[ ]4110:0;3310:0 [ ]0260:0;5650:0[ ecnere⁄iD (cid:0) (cid:0) (cid:0) (cid:0) (cid:0) 31

ehT .snoitanibmoc wo(cid:135) redro rekat/rekam-retupmoc/namuh ruof lla htiw noitac(cid:133)iceps RAV eht morf snoitisopmoced ecnairav xam-niM :4A elbaT etunim 03 eht ta detaluclac dna tnecrep ni desserpxe ,snruter fo noitisopmoced ecnairav nur-gnol ralugnairt mumixam dna muminim eht swohs elbat rekat-namuh/rekam-namuhehtotskcohsotdetubirttaebnactahtsnruterninoitairavnur-gnolehtfonoitroporpehtswohselbateht,sitahT .noziroh -retupmoc/rekam-retupmoc dna ,)CH( wo(cid:135) redro rekat-retupmoc/rekam-namuh ,)HC( wo(cid:135) redro rekat-namuh/rekam-retupmoc ,)HH( wo(cid:135) redro eht fo snoitroporp eht dna ,noitisopmoced ecnairav lautca eht wohs eW .sgnidaeh elbat eht ni noitaton suoivbo ni detoned ,)CC( wo(cid:135) redro rekat ot pu dda yeht taht os snoitisopmoced ecnairav eht elacs-er ew ,si tahT .epyt wo(cid:135) redro hcae ot detubirtta eb nac taht snruter ni ecnairav denialpxe dna,rebotcO,rebmetpeSmorfatadsesuylnohcihw,elpmas-bushtnom-eerhtehtrofdnaelpmas7002-6002llufehtrofstlusertneserpeW .tnecrep001 htnom-eerhtehtnisnoitavresbo082;98dnaelpmasraey-owtllufehtnisnoitavresboetunim-yb-etunim021;717folatotaeraerehT .7002forebmevoN .elpmas-bus elpmas-bus htnom-3 elpmas 7002-6002 lluF /rekam-C /rekam-H /rekam-C /rekam-H /rekam-C /rekam-H /rekam-C /rekam-H rekat-C rekat-C rekat-H rekat-H rekat-C rekat-C rekat-H rekat-H RUE/DSU ]36:1;32:0[ ]42:41;05:2[ ]72:51;22:2[ ]92:42;09:01[ ]24:1;12:0[ ]17:9;61:1[ ]60:31;46:1[ ]82:82;51:61[ .pmoced ecnairaV ]58:4;96:0[ ]34:24;64:7[ ]25:54;16:6[ ]14:27;05:23[ ]71:4;36:0[ ]15:82;24:3[ ]63:83;08:4[ ]50:38;24:74[ noitroporP DSU/YPJ ]04:3;25:1[ ]40:01;15:1[ ]54:71;43:3[ ]81:32;00:21[ ]56:1;16:0[ ]77:6;58:0[ ]61:41;75:2[ ]74:52;16:51[ .pmoced ecnairaV ]19:9;44:4[ ]92:92;04:4[ ]49:05;47:9[ ]56:76;40:53[ ]01:5;09:1[ ]29:02;46:2[ ]47:34;49:7[ ]07:87;22:84[ noitroporP RUE/YPJ ]05:1;70:1[ ]13:31;14:6[ ]38:5;92:0[ ]85:21;20:7[ ]22:1;59:0[ ]59:9;37:4[ ]98:4;92:0[ ]83:11;92:7[ .pmoced ecnairaV ]94:6;66:4[ ]76:75;97:72[ ]72:52;62:1[ ]45:45;04:03[ ]42:6;78:4[ ]78:05;91:42[ ]89:42;94:1[ ]81:85;52:73[ noitroporP 32

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Table1: Summarystatisticsfortheone-minutereturnandorder(cid:135)owdata. Themeanandstandarddeviation, as well as the (cid:133)rst-order autocorrelation, (cid:26), are shown for each variable and currency pair. The returns are expressedinbasispointsandtheorder(cid:135)owsinmillionsofthebasecurrency. Thesummarystatisticsaregiven for both the full 2006-2007 sample, as well as for the three-month sub-sample, which only uses observations from September, October, and November of 2007. The (cid:133)rst two rows for each currency show the summary statistics for returns and the total market-wide order (cid:135)ow. The following two rows give the results for the order (cid:135)ows broken down into human-takers and computer-takers and the last four rows show the results for the order (cid:135)ow decomposed into each maker-taker pair. There are a total of 717;120 observations in the full two-yearsampleand89;280observationsinthethree-monthsubsample. Weshowthestatisticalsigni(cid:133)cance of the (cid:133)rst order autocorrelation. The , , and represent signi(cid:133)cance at the 1, 5, and 10 percent level, (cid:3)(cid:3)(cid:3) (cid:3)(cid:3) (cid:3) respectively. Full 2006-2007 Sample 3-month sub sample Variable Mean Std. dev. (cid:26) Mean Std. dev. (cid:26) USD/EUR Returns 0:0030 1:2398 0:005(cid:3)(cid:3)(cid:3) 0:0080 1:2057 0:007(cid:3)(cid:3) (cid:0) Total order (cid:135)ow (HH+CH+HC+CC) 0:0315 25:9455 0:150(cid:3)(cid:3)(cid:3) 0:0937 29:7065 0:174(cid:3)(cid:3)(cid:3) (cid:0) H-taker (HH+CH) 0:0413 23:977 0:155(cid:3)(cid:3)(cid:3) 0:0796 26:8096 0:189(cid:3)(cid:3)(cid:3) (cid:0) C-taker (HC+CC) 0:0099 9:9363 0:127(cid:3)(cid:3)(cid:3) 0:0140 12:8900 0:115(cid:3)(cid:3)(cid:3) (cid:0) (cid:0) H-maker/H-taker (HH) 0:1425 19:9614 0:177(cid:3)(cid:3)(cid:3) 0:0327 21:9211 0:209(cid:3)(cid:3)(cid:3) C-maker/H-taker (CH) 0:1012 8:8970 0:166(cid:3)(cid:3)(cid:3) 0:1123 10:7649 0:215(cid:3)(cid:3)(cid:3) (cid:0) (cid:0) H-maker/C-taker (HC) 0:0123 8:9232 0:152(cid:3)(cid:3)(cid:3) 0:0483 11:5856 0:150(cid:3)(cid:3)(cid:3) C-maker/C-taker (CC) 0:0222 2:7939 0:053(cid:3)(cid:3)(cid:3) 0:0623 3:9477 0:072(cid:3)(cid:3)(cid:3) (cid:0) (cid:0) JPY/USD Returns 0:0007 1:6038 0:010(cid:3)(cid:3)(cid:3) 0:0045 1:9110 0:007(cid:3)(cid:3) (cid:0) (cid:0) (cid:0) Total order (cid:135)ow (HH+CH+HC+CC) 0:1061 20:0980 0:189(cid:3)(cid:3)(cid:3) 0:3439 23:6359 0:211(cid:3)(cid:3)(cid:3) (cid:0) H-taker (HH+CH) 0:0853 19:1127 0:190(cid:3)(cid:3)(cid:3) 0:2088 22:0344 0:204(cid:3)(cid:3)(cid:3) (cid:0) C-taker (HC+CC) 0:0209 8:3941 0:170(cid:3)(cid:3)(cid:3) 0:1351 11:5877 0:158(cid:3)(cid:3)(cid:3) (cid:0) H-maker/H-taker (HH) 0:1037 15:9972 0:209(cid:3)(cid:3)(cid:3) 0:1203 17:4612 0:226(cid:3)(cid:3)(cid:3) (cid:0) C-maker/H-taker (CH) 0:0184 6:9030 0:172(cid:3)(cid:3)(cid:3) 0:0885 9:1773 0:162(cid:3)(cid:3)(cid:3) (cid:0) (cid:0) H-maker/C-taker (HC) 0:0198 7:5686 0:198(cid:3)(cid:3)(cid:3) 0:0901 10:1673 0:191(cid:3)(cid:3)(cid:3) (cid:0) C-maker/C-taker (CC) 0:0011 2:4556 0:032(cid:3)(cid:3)(cid:3) 0:045 3:8751 0:026(cid:3)(cid:3)(cid:3) (cid:0) JPY/EUR Returns 0:0024 1:5976 0:053(cid:3)(cid:3)(cid:3) 0:0036 2:1398 0:017(cid:3)(cid:3)(cid:3) (cid:0) (cid:0) Total order (cid:135)ow (HH+CH+HC+CC) 0:0648 7:0941 0:152(cid:3)(cid:3)(cid:3) 0:1574 8:5978 0:147(cid:3)(cid:3)(cid:3) (cid:0) (cid:0) H-taker (HH+CH) 0:0497 5:7006 0:150(cid:3)(cid:3)(cid:3) 0:1216 6:2074 0:125(cid:3)(cid:3)(cid:3) (cid:0) (cid:0) C-taker (HC+CC) 0:0151 4:8409 0:146(cid:3)(cid:3)(cid:3) 0:0358 6:7000 0:131(cid:3)(cid:3)(cid:3) (cid:0) (cid:0) H-maker/H-taker (HH) 0:0172 4:4203 0:159(cid:3)(cid:3)(cid:3) 0:0600 4:3106 0:157(cid:3)(cid:3)(cid:3) (cid:0) (cid:0) C-maker/H-taker (CH) 0:0325 2:8912 0:129(cid:3)(cid:3)(cid:3) 0:0616 3:7197 0:092(cid:3)(cid:3)(cid:3) (cid:0) (cid:0) H-maker/C-taker (HC) 0:0095 4:5331 0:173(cid:3)(cid:3)(cid:3) 0:0264 6:0968 0:161(cid:3)(cid:3)(cid:3) (cid:0) (cid:0) C-maker/C-taker (CC) 0:0056 1:5558 0:023(cid:3)(cid:3)(cid:3) 0:0095 2:5621 0:001 (cid:0) (cid:0) (cid:0) 36

Table 2: Summary statistics for the fractions of trade volume attributable to di⁄erent trader combinations. The table shows the fraction of the total volume of trade that is attributable to di⁄erent combinations of makers and takers. Results for the full 2006-2007 sample as well as for the three-month sub-sample, which only uses data from September, October, and November of 2007, are shown. We show the average of the daily fractions, calculated by summing up across all minutes within a day, and the standard deviations of those daily fractions. For each currency, the (cid:133)rst row shows the fraction of the total volume of trade where a computer was involved on at least one side of the trade (i.e. as a maker or a taker). The second row shows thefractionofthetotalvolumewhereahumanactedasataker,thethirdrowshowsthefractionofthetotal volume where a computer acted as a taker, and the following four rows shows the fractions broken down by each maker-taker pair. Full 2006-2007 Sample 3-month sub sample Variable Mean Std. dev. Mean Std. dev. USD/EUR C-participation (Vol(CH+HC+CC)) 0:4163 0:1135 0:5386 0:0355 H-taker (Vol(CH+HH)) 0:7810 0:0791 0:6864 0:0331 C-taker (Vol(HC+CC)) 0:2190 0:0791 0:3136 0:0331 H-maker/H-taker (Vol(HH)) 0:5837 0:1135 0:4614 0:0355 C-maker/H-taker (Vol(CH)) 0:1973 0:0398 0:2251 0:0144 H-maker/C-taker (Vol(HC)) 0:1710 0:0514 0:2304 0:0205 C-maker/C-taker (Vol(CC)) 0:0480 0:0290 0:0831 0:0150 JPY/USD C-participation (Vol(CH+HC+CC)) 0:4242 0:1065 0:5652 0:0364 H-taker (Vol(CH+HH)) 0:7585 0:0805 0:6461 0:0311 C-taker (Vol(HC+CC)) 0:2415 0:0805 0:3539 0:0311 H-maker/H-taker (Vol(HH)) 0:5758 0:1065 0:4348 0:0364 C-maker/H-taker (Vol(CH)) 0:1827 0:0304 0:2114 0:0126 H-maker/C-taker (Vol(HC)) 0:1860 0:0498 0:2486 0:0154 C-maker/C-taker (Vol(CC)) 0:0555 0:0321 0:1052 0:0193 JPY/EUR C-involved (Vol(CH+HC+CC)) 0:6186 0:1154 0:7907 0:0410 H-taker (Vol(CH+HH)) 0:5557 0:1018 0:4037 0:0467 C-taker (Vol(HC+CC)) 0:4443 0:1018 0:5963 0:0467 H-maker/H-taker (Vol(HH)) 0:3814 0:1154 0:2093 0:0410 C-maker/H-taker (Vol(CH)) 0:1743 0:0360 0:1944 0:0164 H-maker/C-taker (Vol(HC)) 0:3337 0:0473 0:3734 0:0193 C-maker/C-taker (Vol(CC)) 0:1106 0:0673 0:2229 0:0464 37

Table3: EstimatesoftheratioR=RC=RH. ThetablereportsthemeanestimatesoftheratioR=RC=RH, where RC = Vol(HC)=Vol(CC) and RH = Vol(HH)=Vol(CH). Vol(HH) is the daily trading volume betweenhuman-makersandhuman-takers,Vol(HC)isthedailytradingvolumebetweenhuman-makersand computer-takers, Vol(CH) is the daily trading volume between computer-makers and human-takers, and Vol(CC) is the daily trading volume between computer-makers and computer-takers. We report the mean of the daily ratio R and the standard errors are shown in parantheses below the estimate. We also show the number of days that had a ratio that was less than one. We report the results for the full 2006-2007 sample and the three-month sub-sample, which only uses data from September, October, and November of 2007. The , , and represent a statistically signi(cid:133)cant deviation from one at the 1, 5, and 10 percent level, (cid:3)(cid:3)(cid:3) (cid:3)(cid:3) (cid:3) respectively. Full 2006-2007 sample 3-month sub sample USD/EUR Mean of daily R= RC/RH 1:4463(cid:3)(cid:3)(cid:3) 1:3721(cid:3)(cid:3)(cid:3) Standard Error (0:0063) (0:0099) No. of days with R<1 0 0 No. of obs 498 62 JPY/USD Mean of daily R= RC/RH 1:2619(cid:3)(cid:3)(cid:3) 1:1719(cid:3)(cid:3)(cid:3) Standard Error (0:0074) (0:0142) No. of days with R<1 15 4 No. of obs 498 62 JPY/EUR Mean of daily R= RC/RH 1:6886(cid:3)(cid:3)(cid:3) 1:6242(cid:3)(cid:3)(cid:3) Standard Error (0:0154) (0:0250) No. of days with R<1 4 0 No. of obs 498 62 38

Table 4: Regressions of realized volatility on the fraction of algorithmic trading. The table shows the results from estimating the relationship between daily realized volatility and the fraction of algorithmic trading, using daily data from 2006 and 2007. Robust standard errors are given in parentheses below the coe¢ cient estimates. The left hand side of the table shows the results with a quarterly time trend included in the regressions and the right hand side of the table shows the results with year-quarter time dummies (i.e., eight time dummies, one for each quarter in the two years of data) included in the regressions. Panels A and B show the results when the fraction of algorithmic trading is measured as the fraction of the total trade volume that has a computer involved on at least one side of the trade (i.e. as a maker or a taker). Panels C and D show the results when only the fraction of volume with computer taking is used. In addition to the fraction of algorithmic trading and the control(s) for secular trends, 22 lags of volatility are also included in every speci(cid:133)cation. In all cases, only the coe¢ cient on the fraction of algorithmic trading is displayed. Panels A and C show the results from a standard OLS estimation, along with the R2. Panels B and D show the results from the IV speci(cid:133)cation estimated with Limited Information Maximum Likelihood (LIML). In Panels B and D, the Stock and Yogo (2005) F test of weak instruments are also shown. The critical values (cid:0) for Stock and Yogo(cid:146)s (2005) F-test are designed such that they indicate a maximal actual size for a nominal sized (cid:133)ve percent test on the coe¢ cient in the LIML estimation. Thus, in order for the actual size of the LIML test to be no greater than 10% (15%), the F-statistic should exceed 8:68 (5:33). There are a total of 498 daily observations in the data. The , , and represent signi(cid:133)cance at the 1, 5, and 10 percent level, (cid:3)(cid:3)(cid:3) (cid:3)(cid:3) (cid:3) respectively. With quarterly time trend With year-quarter time dummies USD/EUR JPY/USD JPY/EUR USD/EUR JPY/USD JPY/EUR Panel A. Fraction of volume with any computer participation, OLS estimation Coe⁄. on AT 0:0029 0:0018 0:0034(cid:3)(cid:3)(cid:3) 0:0078(cid:3)(cid:3)(cid:3) 0:0030 0:0065(cid:3)(cid:3)(cid:3) (cid:0) (0:0024) (0:0021) (0:0012) (0:0027) (0:0024) (0:0016) R2(%) 53:44% 61:13% 71:90% 56:73% 62:57% 73:33% Panel B. Fraction of volume with any computer participation, IV estimation Coe⁄. on AT 0:0121(cid:3) 0:0186(cid:3)(cid:3) 0:0022 0:0078 0:0101 0:0128 (cid:0) (cid:0) (cid:0) (cid:0) (cid:0) (cid:0) (0:0062) (0:0089) (0:0039) (0:0061) (0:0069) (0:0175) F-Stat 29:58 19:46 32:18 38:17 20:89 2:25 Panel C. Fraction of volume with computer-taking, OLS estimation Coe⁄. on AT 0:0037 0:0027 0:0015 0:0094(cid:3)(cid:3) 0:0034 0:0032(cid:3)(cid:3) (cid:0) (cid:0) (0:0036) (0:0024) (0:0012) (0:0038) (0:0027) (0:0016) R2(%) 53:39% 61:17% 71:56% 56:43% 62:55% 72:66% Panel D. Fraction of volume with computer-taking, IV estimation Coe⁄. on AT 0:0160(cid:3)(cid:3) 0:0215(cid:3)(cid:3) 0:0007 0:0072 0:0122 0:0182 (cid:0) (cid:0) (cid:0) (cid:0) (cid:0) (cid:0) (0:0080) (0:0109) (0:0028) (0:0070) (0:0082) (0:0291) F-Stat 39:99 17:63 64:81 55:45 21:20 1:04 39

Table 5: We report the mean ratio of the exchange rate volatility (Panel A) and liquidity provision by humans and by computers (Panel B) estimated during announcement days relative to that estimated during non-announcementdays. Theone-hourmeasureisestimatedusingobservationsfrom8:25amto9:24amET andtheone-minutemeasureisestimatedusing8:30amto8:31amETobservations. Announcementdaysare de(cid:133)ned as nonfarm payroll announcement days and non-announcement days are de(cid:133)ned as 10 business days before and after the nonfarm payroll announcement. In each panel, we report the chi-squared and p-value of the Wald test that the ratio is equal to 1. In Panel C we report the chi-squared and p-value of the Wald test that the liquidity provision of humans during announcement days relative to non-announcement days is similar to the liquidity provision of computers. The statistics are estimated using data in the full sample from 2006 to 2007 and there are 23 observations (April 6, 2007 nonfarm payroll announcement is missing because it falls on Good Friday, when trading in the foreign exchange market is limited). Human liquidity provision, LH, is de(cid:133)ned as the sum of human-maker/human-taker volume plus human-maker/human-taker volume divided by total volume. Computer liquidity provision, LC, is de(cid:133)ned as the sum of computermaker/computer-taker volume plus computer-maker/human-taker volume divided by total volume. The , (cid:3)(cid:3)(cid:3) , and represent signi(cid:133)cance at the 1, 5, and 10 percent level, respectively. (cid:3)(cid:3) (cid:3) USD/EUR JPY/USD JPY/EUR Hour Minute Hour Minute Hour Minute Panel A: Volatility (cid:27) (cid:27) n a 6:236(cid:3)(cid:3)(cid:3) 21:704(cid:3)(cid:3)(cid:3) 5:595(cid:3)(cid:3)(cid:3) 24:812(cid:3)(cid:3)(cid:3) 3:697(cid:3)(cid:3)(cid:3) 14:403(cid:3)(cid:3) (cid:31)2 (H :(cid:27) =(cid:27) ) 69:86 18:76 33:34 15:45 19:37 5:96 0 a n p-value 0:0000 0:0003 0:0000 0:0008 0:0002 0:0235 Panel B: Liquidity Provision Liquidity provision by humans, L L H H n a 0:964(cid:3)(cid:3)(cid:3) 1:062(cid:3)(cid:3)(cid:3) 1:023 1:183(cid:3)(cid:3)(cid:3) 0:888(cid:3)(cid:3)(cid:3) 0:980 Liquidity provision by computers, L L C C n a 1:132(cid:3)(cid:3)(cid:3) 0:871(cid:3)(cid:3)(cid:3) 0:974 0:652(cid:3)(cid:3)(cid:3) 1:227(cid:3)(cid:3)(cid:3) 1:151 (cid:31)2 (H :LH =LH orLC =LC ) 16:56 9:04 2:71 31:91 25:19 0:5 0 a n a n p-value 0:0005 0:0067 0:1143 0 0:0001 0:487 Panel C: Comparison of Liquidity Provision between Humans and Computers L L H H n a (cid:0) L L C C n a (cid:0) 0:168(cid:3)(cid:3)(cid:3) 0:191(cid:3)(cid:3) 0:049 0:532(cid:3)(cid:3)(cid:3) (cid:0) 0:339(cid:3)(cid:3)(cid:3) (cid:0) 0:171 (cid:31)2 H : LHa = LCa 19:24 5:91 1:50 36:07 25:21 0:66 0 LHn LCn p-va(cid:16)lue (cid:17) 0:0003 0:0241 0:2339 0:0000 0:0001 0:4245 40

Table 6: Impulse responses from the VAR speci(cid:133)cation with human-taker and computer-taker order (cid:135)ow. The table shows the impulse responses for returns as a result of shocks to the human-taker order (cid:135)ow (HH +CH) or computer-taker (CC+HC) order (cid:135)ow, denoted H-taker and C-taker in the table headings, respectively. The results are based on estimation of equation (2), using minute-by-minute data. In Panel A we show the return response, in basis points, to a one-billion base-currency shock to one of the order (cid:135)ows. InPanelBweshowthereturnresponse,inbasispoints,toaonestandarddeviationshocktooneoftheorder (cid:135)ows. We show the results for the full 2006-2007 sample and for the three-month sub-sample, which only uses data from September, October, and November of 2007. For each currency pair we show the short-run (immediate) response of returns; the corresponding cumulative long-run response of returns, calculated as the cumulative impact of the shock after 30 minutes; and the di⁄erence between the cumulative long-run response in returns minus the immediate response of returns, i.e., we provide the extent of over-reaction or under-reaction to an order (cid:135)ow shock. There are a total of 717;120 minute-by-minute observations in the full two-year sample and 89;280 observations in the three-month sub-sample. We show in parenthesis the standard errors of the di⁄erence between the short-run and long-run response. These standard errors are calculated by bootstrapping, using 200 repetitions. Full 2006-2007 sample 3-month sub-sample H-taker C-taker H-taker C-taker Panel A: One billion base-currency shock USD/EUR Short run 28:06 26:94 23:20 25:22 Long run 27:87 32:35 24:16 31:38 Di⁄erence 0:20 5:42 0:96 6:16 (cid:0) (0:29) (0:67) (0:72) (1:36) JPY/USD Short run 46:77 39:81 48:02 44:89 Long run 47:50 44:27 49:54 40:63 Di⁄erence 0:74 4:46 1:52 4:26 (cid:0) (0:48) (1:08) (1:36) (2:35) JPY/EUR Short run 99:32 102:71 124:02 115:52 Long run 108:07 109:85 132:53 123:26 Di⁄erence 8:75 7:14 8:51 7:74 (1:50) (1:67) (4:79) (4:76) Panel B: One standard deviation shock USD/EUR Short run 0:6617 0:2639 0:6045 0:3181 Long run 0:6570 0:3170 0:6296 0:3957 Di⁄erence 0:0046 0:0531 0:0251 0:0777 (cid:0) (0:0068) (0:0065) (0:0189) (0:0172) JPY/USD Short run 0:8706 0:3269 1:0241 0:5098 Long run 0:8843 0:3635 1:0565 0:4614 Di⁄erence 0:0137 0:0366 0:0324 0:0483 (cid:0) (0:0090) (0:0089) (0:0289) (0:0267) JPY/EUR Short run 0:5572 0:4901 0:7587 0:7636 Long run 0:6063 0:5242 0:8108 0:8148 Di⁄erence 0:0491 0:0341 0:0520 0:0512 (0:0085) (0:0080) (0:0294) (0:0314) 41

Table 7: Variance decompositions from the VAR speci(cid:133)cation with human-taker and computer-taker order (cid:135)ow. The table provides the long-run variance decomposition of returns, expressed in percent and calculated at the 30 minute horizon, based on estimation of equation (2), using minute-by-minute data. That is, the tableshowstheproportionofthelong-runvariationinreturnsthatcanbeattributedtoshockstothehumantaker order (cid:135)ow (HH +CH) and the computer-taker (CC +HC) order (cid:135)ow, denoted H-taker and C-taker in the table headings, respectively. For each currency pair we show the actual variance decomposition, and the proportion of the explained variance in returns that can be attributed to each order (cid:135)ow type. That is, we re-scale the variance decompositions so that they add up to 100 percent. We show results for the full 2006-2007 sample and for the three-month sub-sample, which only uses data from September, October, and November of 2007. There are a total of 717;120 minute-by-minute observations in the full two-year sample and 89;280 observations in the three-month sub-sample. We show in parenthesis the standard errors calculated by bootstrapping, using 200 repetitions. Full 2006-2007 sample 3-month sub-sample H-taker C-taker H-taker C-taker USD/EUR Variance decomposition 29:27 4:74 25:92 7:25 (0:95) (0:19) (0:79) (0:42) Proportion of explained share 86:06 13:94 78:14 21:86 (2:79) (0:56) (2:38) (1:27) JPY/USD Variance decomposition 29:31 4:22 28:59 7:22 (0:35) (0:11) (0:50) (0:33) Proportion of explained share 87:41 12:59 79:84 20:16 (1:04) (0:33) (1:40) (0:92) JPY/EUR Variance decomposition 12:03 9:28 12:47 12:67 (0:21) (0:20) (0:38) (0:38) Proportion of explained share 56:45 43:55 49:60 50:40 (0:99) (0:94) (1:51) (1:51) 42

Table 8: Impulse responses from the VAR speci(cid:133)cation with all four human/computer-maker/taker order (cid:135)ow combinations. The table shows the impulse responses for returns as a result of shocks to the human-maker/human-taker order (cid:135)ow (HH), computer-maker/human-taker order (cid:135)ow (CH), humanmaker/computer-taker order (cid:135)ow (HC), or computer-maker/computer-taker order (cid:135)ow (CC), denoted in obviousnotationinthetableheadings. Theresultsarebasedonestimationofequation(3),usingminute-byminutedata. InPanelAweshowthereturnresponse,inbasispoints,toaone-billionbase-currencyshockto one of the order (cid:135)ows. In Panel B we show the return response, in basis points, to a one standard deviation shock to one of the order (cid:135)ows. We report the results for the full 2006-2007 sample and for the three-month sub-sample, which only uses data from September, October, and November of 2007. For each currency pair we show the short-run (immediate) response of returns; the corresponding cumulative long-run response of returns, calculated as the cumulative impact of the shock after 30 minutes; and the di⁄erence between the cumulative long-run response in returns minus the immediate response of returns, i.e., we provide the extent of over-reaction or under-reaction to an order (cid:135)ow shock. There are a total of 717;120 minute-by-minute observations in the full two-year sample and 89;280 observations in the three-month sub-sample. We show in parenthesis the standard errors of the di⁄erence between the short-run and the long-run response. These standard errors are calculated by bootstrapping, using 200 repetitions. Full 2006-2007 sample 3-month sub-sample H-maker/ C-maker/ H-maker/ C-maker/ H-maker/ C-maker/ H-maker/ C-maker/ H-taker H-taker C-taker C-taker H-taker H-taker C-taker C-taker Panel A: One billion base-currency shock USD/EUR Short run 27:64 29:66 26:57 32:19 20:58 30:94 28:94 21:74 Long run 30:13 20:47 29:89 24:92 24:18 23:35 34:64 5:94 Di⁄erence 2:49 9:19 3:32 7:26 3:60 7:59 5:70 15:80 (cid:0) (cid:0) (cid:0) (cid:0) (0:35) (0:88) (0:83) (2:42) (0:97) (2:03) (1:79) (4:64) JPY/USD Short run 43:48 58:94 40:34 61:57 41:96 64:63 46:08 67:65 Long run 47:01 49:53 42:61 54:37 46:83 57:24 40:33 51:81 Di⁄erence 3:53 9:41 2:27 7:20 4:87 7:39 5:75 15:85 (cid:0) (cid:0) (cid:0) (cid:0) (cid:0) (0:59) (1:57) (1:30) (3:38) (1:62) (3:43) (2:89) (7:39) JPY/EUR Short run 102:61 92:16 100:91 102:04 139:33 103:92 114:01 94:47 Long run 116:12 91:24 107:18 93:41 159:46 96:85 118:47 95:20 Di⁄erence 13:51 0:92 6:27 8:63 20:13 7:07 4:46 0:74 (cid:0) (cid:0) (cid:0) (1:98) (3:18) (1:94) (4:98) (7:25) (9:35) (5:78) (10:70) Panel B: One standard deviation shock USD/EUR Short run 0:5389 0:2575 0:2318 0:0893 0:4342 0:3211 0:3228 0:0845 Long run 0:5875 0:1777 0:2608 0:0692 0:5101 0:2424 0:3864 0:0231 Di⁄erence 0:0486 0:0798 0:0290 0:0202 0:0760 0:0788 0:0636 0:0614 (cid:0) (cid:0) (cid:0) (cid:0) (0:0069) (0:0076) (0:0072) (0:0067) (0:0203) (0:0211) (0:0200) (0:0180) JPY/USD Short run 0:6721 0:3968 0:2962 0:1506 0:7019 0:5801 0:4544 0:2607 Long run 0:7267 0:3334 0:3129 0:1330 0:7834 0:5137 0:3976 0:1997 Di⁄erence 0:0546 0:0634 0:0167 0:0176 0:0815 0:0663 0:0567 0:0611 (cid:0) (cid:0) (cid:0) (cid:0) (cid:0) (0:0091) (0:0106) (0:0096) (0:0083) (0:0274) (0:0307) (0:0284) (0:0284) JPY/EUR Short run 0:4440 0:2629 0:4481 0:1583 0:5859 0:3829 0:6809 0:2409 Long run 0:5024 0:2603 0:4760 0:1449 0:6706 0:3568 0:7076 0:2428 Di⁄erence 0:0584 0:0026 0:0279 0:0134 0:0847 0:0260 0:0266 0:0019 (cid:0) (cid:0) (cid:0) (0:0086) (0:0091) (0:0086) (0:0077) (0:0306) (0:0344) (0:0345) (0:0273) 43

Table 9: Variance decompositions from the VAR speci(cid:133)cation with all four human/computer-maker/taker order (cid:135)ow combinations. The table provides the long-run variance decomposition of returns, expressed in percent and calculated at the 30 minute horizon, based on estimation of equation (3), using minuteby-minute data. That is, the table shows the proportion of the long-run variation in returns that can be attributedtoshockstothehuman-maker/human-takerorder(cid:135)ow(HH),computer-maker/human-takerorder (cid:135)ow (CH), human-maker/computer-taker order (cid:135)ow (HC), and computer-maker/computer-taker order (cid:135)ow (CC), denoted in obvious notation in the table headings. We show the actual variance decomposition, and the proportions of the explained variance in returns that can be attributed to each order (cid:135)ow type. That is, we re-scale the variance decompositions so that they add up to 100 percent. We present results for the full 2006-2007 sample and for the three-month sub-sample, which only uses data from September, October, and November of 2007. There are a total of 717;120 minute-by-minute observations in the full two-year sample and 89;280 observations in the three-month sub-sample. We show in parenthesis the standard errors, which are calculated by bootstrapping, using 200 repetitions. Full 2006-2007 sample 3-month sub-sample H-maker/ C-maker/ H-maker/ C-maker/ H-maker/ C-maker/ H-maker/ C-maker/ H-taker H-taker C-taker C-taker H-taker H-taker C-taker C-taker USD/EUR Variance decomp. 20:71 4:73 3:89 0:58 14:19 7:68 7:86 0:59 (0:89) (0:24) (0:21) (0:04) (0:75) (0:48) (0:43) (0:09) Proportion 69:24 15:81 13:01 1:94 46:80 25:33 25:92 1:95 (2:98) (0:80) (0:70) (0:13) (2:47) (1:58) (1:42) (0:30) JPY/USD Variance decomp. 18:62 6:48 3:70 0:93 14:47 9:78 6:12 2:00 (0:33) (0:15) (0:11) (0:04) (0:46) (0:41) (0:31) (0:13) Proportion 62:63 21:80 12:45 3:13 44:70 30:21 18:91 6:18 (1:11) (0:50) (0:37) (0:13) (1:42) (1:27) (0:96) (0:40) JPY/EUR Variance decomp. 7:84 2:74 7:94 0:99 7:72 3:32 10:47 1:30 (0:16) (0:12) (0:19) (0:06) (0:29) (0:20) (0:42) (0:11) Proportion 40:18 14:04 40:70 5:07 33:84 14:56 45:90 5:70 (0:82) (0:61) (0:97) (0:31) (1:27) (0:88) (1:84) (0:48) 44

100 80 60 40 20 0 Jan-03 Jan-04 Jan-05 Jan-06 Jan-07 Jan-08 Figure 1: 50-day moving averages of participation rates of algorithmic traders )tnecreP( noitapicitraP USD/EUR JPY/USD JPY/EUR

JPY/EUR 100 80 60 40 20 0 Jan-03 Jan-04 Jan-05 Jan-06 Jan-07 Jan-08 Figure 2: 50-day moving averages of participation rates broken down into four maker-taker pairs )tnecreP( noitapicitraP USD/EUR 100 80 60 40 20 0 Jan-03 Jan-04 Jan-05 Jan-06 Jan-07 Jan-08 )tnecreP( noitapicitraP JPY/USD 100 80 60 40 20 0 Jan-03 Jan-04 Jan-05 Jan-06 Jan-07 Jan-08 )tnecreP( noitapicitraP H-Maker/H-Taker C-Maker/H-Taker H-Maker/C-Taker C-Maker/C-Taker

Computer-Taker Order Flow $ Millions Yen/$ 1500 Order Flow 117 Dollar-Yen 1000 116 500 115 0 -500 114 -1000 113 -1500 112 -2000 -2500 111 6 12 6 12 6 12 6 12 PM AM AM PM PM AM AM PM Human-Taker Order Flow $ Millions Yen/$ 1500 117 Order Flow Dollar-Yen 1000 116 500 115 0 -500 114 -1000 113 -1500 112 -2000 -2500 111 6 12 6 12 6 12 6 12 PM AM AM PM PM AM AM PM Figure 3: Dollar-Yen Market on August 16, 2007

USD/EUR Percent Percent 90 Share of Algorithmic Trading* 18 80 Realized Volatility** 15 70 60 12 50 9 40 30 6 20 3 10 0 0 2 0 0 6 2 0 0 7 JPY/USD Percent Percent 90 18 80 15 70 60 12 50 9 40 30 6 20 3 10 0 0 2 0 0 6 2 0 0 7 JPY/EUR Percent Percent 90 18 80 15 70 60 12 50 9 40 30 6 20 3 10 0 0 2 0 0 6 2 0 0 7 Figure 4: Volatility and Algorithmic Market Participation *Daily realized volatility is based on 1-minute returns. We show monthly observations **Share of algorithmic trading is at a monthly frequency

18% USD/EUR 1.2 18% USD/EUR 1.2 16% 1.15 16% 1.15 1.1 1.1 14% 14% 1.05 1.05 12% 12% 1 1 10% 10% 0.95 0.95 8% 8% 0.9 0.9 6% 0.85 6% 0.85 4% 0.8 4% 0.8 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10 DECILES OF REALIZED VOLATILITY DECILES OF NORMALIZED AT PARTICIPATION 18% JPY/USD 1.2 18% JPY/USD 1.2 16% 1.15 16% 1.15 1.1 1.1 14% 14% 1.05 1.05 12% 12% 1 1 10% 10% 0.95 0.95 8% 8% 0.9 0.9 6% 0.85 6% 0.85 4% 0.8 4% 0.8 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10 DECILES OF REALIZED VOLATILITY DECILES OF NORMALIZED AT PARTICIPATION 18% JPY/EUR 1.2 18% JPY/EUR 1.2 16% 1.15 16% 1.15 1.1 1.1 14% 14% 1.05 1.05 12% 12% 1 1 10% 10% 0.95 0.95 8% 8% 0.9 0.9 6% 0.85 6% 0.85 4% 0.8 4% 0.8 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10 DECILES OF REALIZED VOLATILITY DECILES OF NORMALIZED AT PARTICIPATION annualized volatility normalized AT participation normalized AT participation annualized volatility Figure 5: Deciles of Realized Volatility and AT Participation