High-Frequency Market Making to Large Institutional Trades

Transcription

1 High-Frequency Market Making to Large Institutional Trades Robert A. Korajczyk Northwestern University Dermot Murphy University of Illinois at Chicago First Draft: November 30, 2014 This Draft: May 24, 2016 Abstract We study high-frequency trader (HFT) marker maker behavior in the presence of large trade packages. HFTs lose money on trading and make money from liquidity rebates. HFT liquidity provision is significantly reduced for large stressful trades with this reduction being more pronounced when an HFT assumes the designated market maker role. Over the life of a large trade, HFTs initially accommodate the order but switch to competing with the order. This is due to both inventory management and order anticipation. Average implementation shortfall for non-stressful (stressful) trades is 11 (35) basis points and is significantly affected by HFT liquidity provision. We thank the Investment Industry Regulatory Organization of Canada (IIROC) for providing us with access to the data used for this study and Victoria Pinnington and Helen Hogarth of IIROC for answering our innumerable questions regarding the data and Canadian market structure details. We also thank Torben Andersen, Rob Battalio, Oleg Bondarenko, Jonathan Brogaard, Kevin Crotty, Robert Ferstenberg, Mark Grinblatt, Hans Heidle, Sean Kersey, Maja Kos, Hanh Le, Katya Malinova, Ioanid Roşu, Gideon Saar, Andriy Shkilko, Brian Weller, Avi Wohl, Mao Ye, and seminar participants at DePaul University, European Finance Association, IIROC/Capital Markets Institute High Frequency Trading Forum, Inquire-Europe, Multinational Finance Society, Notre Dame Conference on Current Topics in Financial Regulation, Tel Aviv University, University of British Columbia, University of Geneva, University of St. Gallen, and Wilfrid Laurier University for helpful comments. Kellogg School of Management, Northwestern University, 2001 Sheridan Road, Evanston, IL, ; tel: (847) ; r-korajczyk@kellogg.northwestern.edu. University of Illinois at Chicago, College of Business, Department of Finance, 601 South Morgan Street, Chicago, IL, ; tel: (312) ; murphyd@uic.edu.

2 1 Introduction An increased prevalence of high-frequency trading is often associated with improvements in market quality in the form of reduced quoted bid ask spreads and greater efficiency in the price discovery process. 1 High-frequency traders, in particular those that have largely taken on a market-making role but without the obligations of a traditional market maker, compete with one another to turn over shares quickly, which naturally results in a lower equilibrium bid ask spread. On the surface, it appears that high-frequency traders greatly contribute to a more liquid market. This argument, however, does not readily apply to large institutional traders that demand more liquidity than is posted at the best bid or offer price. Although we have known since Scholes (1972) and Kraus and Stoll (1972) that large institutional trades command higher premia, 2 relatively little is known about how today s market makers, who are predominantly in the highfrequency trading domain, dynamically interact with such orders and what this ultimately means for the transactions costs of these orders. This is further complicated by the fact that most large institutional orders are executed piecewise over time. Large parent orders placed by portfolio managers are often split into many child orders to avoid detection by other market participants; otherwise, the portfolio managers will receive inferior prices for their total orders. While markets may appear liquid, a concern is that high-frequency market makers, with the ability to eventually detect such a large order, will modify their standing limit orders to avoid the potential adverse price movements and possibly trade in advance of the remaining child orders. Therefore, while markets might appear liquid, based on bidask spreads, portfolio managers sometimes think of this as phantom liquidity, due to its tendency to disappear when needed. 3 It is particularly important to examine larger institutional-sized orders because they are the most likely to be affected by the disappearance of liquidity. We study liquidity provision of HFTs during execution of a sample of over 180,000 large institutional-sized trading packages, or parent orders (which we will typically call large trades ), 1 See, for example, Jovanovic and Menkveld (2015), Menkveld (2013), Hagströmer and Norden (2013), and Brogaard, Hendershott, and Riordan (2014). 2 See also Chan and Lakonishok (1993) and Chan and Lakonishok (1995). 3 See, for example, an article by the Financial Post entitled Pressure grows for crackdown on high-frequency trading from October

3 on Canadian equities exchanges. The Investment Industry Regulatory Organization of Canada (IIROC) provides us with access to order-level data for all Canadian equities for the period from January 2012 to June For each message, we are provided with a broker ID and a client ID, so we can track the order and trade activity for any client ID across time, stocks, and exchanges. We are unable, however, to link client accounts when a client uses multiple brokers or when the client uses multiple client IDs for the same broker. HFTs lose money on trading and make money from liquidity rebates, on average. The negative average trading profits suggest that order anticipation strategies, or back-running (Yang and Zhu (2015)) are not the primary source of profitability for HFTs. The positive profits from maker fees suggests that quote-matching strategies are a larger source of profits for the HFTs. We define a stressful large trade as one for which the parent trade size, as a percentage of total volume in that stock day, is in the upper quartile of all large trades. Within high-volume stocks, HFTs provide percent of liquidity to the aggressive component (the marketable order component) of large, non-stressful, trades. In lower-volume stocks, HFTs provide a lower percentage of liquidity (12.69 percent), which is consistent with other studies which find that HFTs provide more liquidity in more frequently traded stocks. 4 However, liquidity provision substantially changes when the large trade is classified as stressful. For high-volume firms, HFTs provide percent of liquidity to the aggressive component of the large stressful trade, which represents a percentage reduction of 25.5 percent. We also find a modest decrease in HFT liquidity provision for stressful trades in lower-volume firms. We also examine how HFTs dynamically interact with large institutional trades. When the large trade is considered stressful, we find that HFTs are initially accommodating of the order, but eventually switch to trading in the same direction as that order. For example, as a large stressful buy order is executed over time, the abnormal buying activity of the HFTs substantially increases relative to their selling activity. We also find that their abnormal order submission activity on the bid side of the limit order book also substantially increases relative to order submission activity on the ask side. 4 See Anand and Venkataraman (2016) and Tong (2015). 2

4 If HFTs are initially accommodating of a large institutional order, then it is possible that they eventually trade in the same direction of that order because they are managing their inventory risk, as in the inventory models of Amihud and Mendelson (1980) and Ho and Stoll (1981). However, it is also possible that HFTs exploit their technological and speed advantages to predict large trade order flow and compete with that order. There is theoretical support for this argument: Baldauf and Mollner (2016) show that fast traders utilize an order anticipation strategy to avoid adverse selection by cancelling mispriced quotes, while Yang and Zhu (2015) show that a fast trader back-runs large orders by eventually competing with the order. Examining dynamic HFT order imbalances relative to their short-term and longer-term inventory changes and the predicted component of large trade volume, we find support for both inventory control and order anticipation strategies. Our evidence shows that while HFTs trade in the direction of large trades to adjust the inventory positions, their trading is also related to the predictable component of large trade volume. The HFTs passive order imbalance reacts more to the predictable component of large trades than their aggressive order imbalance, which is consistent with the model of Baldauf and Mollner (2016). We also examine an interesting event that occurred on November 26, 2012, in which one HFT became the designated market maker for 24 stocks. We suspect that this HFT was motivated to take on a DMM role because of the Integrated Fee Model regulation that was introduced by IIROC on April 1, 2012, according to which DMMs would now receive a discount of 70 percent on fees charged to traders by the exchange, with these fees typically based on the proportion of message traffic originating from that trader. 5 Budish, Cramton, and Shim (2015) and Baldauf and Mollner (2016) suggest that an upgrade in HFT speed, whatever the cost, should theoretically lead to an increased rate of cancellation of orders that would otherwise be adversely selected, thus leading to a reduction in HFT liquidity provision to large orders that move prices. We interpret the HFT-to- DMM switch as a de-facto upgrade in speed for the designated market maker in that stock; indeed, we find that in some of our 24 stocks, the orders submitted by the DMM increased by a factor exceeding 1,000. Large institutional trades are likely to lead to short-term price movements, and we 5 This regulation also stipulated that fees would now be charged for all market messages and not just trades as before. Malinova, Park, and Riordan (2013) focus on this regulatory change and find that trades, quotes, and cancellations fell while bid ask spreads increased following the introduction of this regulation. 3

5 examine how HFT liquidity provision to large trades changes following the HFT-to-DMM change. We find that while HFT liquidity provision to large trades is higher following this change, the reduction in liquidity provision to large stressful trades in the HFT-as-DMM regime is higher than before the regime change, thereby strengthening our identification that HFT liquidity provision is reduced in response to large stressful trades. Finally, we find that the cost of executing an institutional-sized parent trade is significantly influenced by HFT behavior. We estimate the implementation shortfall (IS) for large trade packages, which is cost of a large trade due to price impact. IS averages 11 basis points for large non-stressful trades and 35 basis points for large stressful trades. IS is significantly negatively related to HFT liquidity provision. If HFTs provide 10 percentage points less liquidity to the aggressive component of a large trade, then IS is 2.5 basis points higher. There is considerable interest in the effect of high-frequency traders (HFTs) on the the trading costs of other market participants. For example, Hirschey (2013) finds evidence consistent with HFTs trading in anticipation of future order flow by non-hfts. Brogaard, Hendershott, and Riordan (2014) find that HFTs trade in the direction of permanent price movements and in the opposite direction of transitory pricing errors using aggressive orders. Carrion (2013) finds that spreads are higher when HFTs supply more liquidity and narrower when HFTs demand more liquidity, and that price efficiency is higher when HFT participation is higher. Breckenfelder (2013) finds that when HFTs compete for trades, liquidity deteriorates and short-term volatility rises. Hagströmer and Norden (2013) use a tick-size change on NASDAQ OMX Sweden to show that HFT market makers mitigate short-term volatility. Finally, Kirilenko, Kyle, Samadi, and Tuzun (2015) find that while HFTs were not responsible for the Flash Crash of May 2010, they did exacerbate market volatility. Van Kervel and Menkveld (2016) study the interaction between high-frequency traders on NASDAQ and 6,000 institutional trades in Swedish stocks from four large Swedish institutional investors. In contrast, the IIROC database provides us with access to over 180,000 large institutional trades that originate in Canada, which represents a significant global market that is highly correlated with US markets. Similar to our results, they find that HFTs initially trade with the wind but eventually trade against the wind as the large trade progresses, and that this behavior 4

6 is a significant determinant of the implementation shortfall of the large trade. Anand and Venkataraman (2016) examine whether stock exchanges should impose marketmaker obligations. Using a similar transaction-level data set with masked trader identity from the TSX for the year 2006, they find that endogenous liquidity providers provide different levels of liquidity based on their trading profits, inventory risks, and capital commitments and based on different market conditions, such as large-price-movement days and high-volatility days. In contrast, our primary focus is on large institutional trades, how market making HFTs dynamically interact with them, and what this ultimately means for the costs of these large trades. Finally, Tong (2015) examines aggregated HFT trading activity on a sample of NASDAQ stocks and how this relates to execution price for large institutional trades. The information provided in our database allows us to directly examine HFT liquidity provision to large trades, along with the trading characteristics of all market-making HFTs. 2 Data and Canadian Market Structure For this study, we are provided with access to detailed order-level data by the Investment Industry Regulatory Organization of Canada (IIROC), a Canadian national self-regulatory organization that regulates securities dealers in Canada s equity markets. IIROC carries out its regulatory responsibilities through setting and enforcing rules regarding the proficiency, business and financial conduct of dealer firms and their registered employees, and through setting and enforcing market integrity rules regarding trading activity on Canadian equity marketplaces. 6 Through the monitoring of the Canadian equities markets, IIROC collects detailed records on all orders submitted to Canadian exchanges. IIROC provides us with access to a data set that contains all trades, orders, order cancellations, and order amendments for the period from January 1, 2012 to June 30, Each record contains a masked identification for the trader submitting that order. In the case of trades, we are given masked identification for both the buyer and the seller, in addition to the party submitting the market or marketable limit order (henceforth, we will use marketable limit order to denote a marketable limit order or market order). Altogether, 6 This information and additional details can be found at 5

7 the data set comprises approximately 60 billion observations. For the purposes of our study, we make extensive use of the following data fields: Security ID, date, time of order (reported to the one-thousandth of a second), price of order, share quantity of order. User ID: this is the masked identification for the trader submitting the order. In the case of trades, the User IDs for both the buyer and seller are provided. Event: this field specifies whether an observation is a trade, order, order cancellation, order amendment, trade cancellation (typically due to data error), or off-market trade, among other event types. Bid price and ask price: we can determine whether a submitted order originates from a buyer or seller, depending on which of these data fields is nonempty. Active and passive indicators for trades: these determine which side of the trade submits the marketable limit order (thus making trade-direction inference algorithms, such as the Lee and Ready (1991) algorithm, unnecessary). The data set allows us to classify high-frequency traders that act as market makers on Canadian markets and to identify large institutional trade packages. Our ultimate goal is to determine how high-frequency traders dynamically interact with large institutional trade packages, and how this influences market quality. According to the World Federation of Exchanges, as of 2013, the total market capitalization of stocks listed with the TMX group (which operates the two national exchanges of Canada the Toronto Stock Exchange (TSX), which serves the senior equity market, and the TSX Venture Exchange (TSX-V), which serves the public venture equity market) is equal to about $2 trillion USD, while the total market capitalization of stocks listed with the New York Stock Exchange (NYSE) or NASDAQ, is equal to about $24 trillion USD. This makes the TMX group the seventh-largest exchange in the world by total market capitalization. 7 The dollar turnover of shares in 2013 for shares traded with the TMX exchanges is about $1.3 trillion USD, and for the NYSE 7 The six largest exchanges by market capitalization in 2013, from largest to smallest, are NYSE, NASDAQ OMX, Japan Exchange Group, Euronext, Hong Kong Exchanges, and Shanghai SE. 6

8 and NASDAQ it is about $21.5 trillion USD. In 2013, TMX had 3,810 stocks listed domestically, while NYSE and NASDAQ together had 4,180. The Canadian dollar and U.S. dollar were typically close to parity over the sample period, which makes their respective dollar values comparable. The monthly returns of an index fund representing the S&P/TSX 60 (a stock market index of 60 large companies listed on the TSX) and the monthly returns of an index fund representing the S&P 500 have a correlation of 0.79, which is based on the period from late 1999 to late Given that Canada and the U.S. are strong trading partners with close geographical proximity, this high correlation is not surprising. Finally, we make note of a few specifics of the Canadian market structure. As mentioned above, the two national stock exchanges of Canada are the TSX and TSX-V, which are both completely electronic stock exchanges in which orders are submitted to their respective limit order books. Both are owned and operated by the TMX Group. In addition, the TMX Group operates the TMX Information Processor, which provides a central source of consolidated Canadian equity market data that meets standards approved by regulators. Also, in 2011, the Canadian Securities Administrators (CSA) implemented the Order Protection Rule, which is designed to ensure that all accessible, visible, better-priced limit orders are executed before inferiorly priced limit orders. The Order Protection Rule differs from Regulation NMS in the United States in that it protects the full depth of the visible limit order book as opposed to just the top of the limit order book. For example, if Marketplace 1 has two standing sell limit orders with different prices and Marketplace 2 has one standing sell limit order with a price that is inferior to both limit orders from Marketplace 1, then the Order Protection Rule ensures that a large buy will first execute against both limit orders from Marketplace 1. This is unlike Regulation NMS, which would ensure that a large marketable limit order first executes against the best immediate quotes in both marketplaces, resulting in a total execution price that is inferior to that under the Order Protection Rule. Altogether, there are 13 distinct Canadian stock exchanges identified in our sample like the traders, these exchanges also have masked identification. 7

9 3 Classifying HFTs The first step in our analysis is to classify high-frequency traders that act as market makers (henceforth, HFTs). Our methodology for identifying HFTs in a given stock is as follows. First, we define a trader as an HFT for a given stock day if the following four conditions hold: 1. The trader is in the highest quintile of the number of trades as a percentage of all trades on that stock day relative to all other traders within that stock day. 2. The trader has traded at least 50 times during that stock day. 3. The trader has a net daily trading position, as a percentage of its volume of shares traded, for that stock day of 10 percent or less. 4. The trader has an order-to-trade ratio that is greater than 5. HFTs tend to trade much more than other traders and close the day with close-to-zero net trading positions, which motivates our requirements (1), (2), and (3). Requirement (4) ensures that we only include traders that have high order-to-trade ratios, which is a common feature for HFTs. Traders are identified as HFTs for a given stock day if they meet these four requirements. We define traders as HFTs for a given stock if they additionally satisfy the following two requirements: 1. The traders are identified as HFTs for at least 75 percent of stock days in which they trade at least once. 2. The traders are identified as HFTs for at least 20 active stock days. Altogether, this classification methodology yields 19 distinct HFTs. Panel A of Table 1 contains information about each of these 19 HFTs. In Panel B, we partition these HFTs into three groups: (1) Super HFTs, which are identified as HFTs in at least 50 stocks; (2) Major HFTs, which are identified as HFTs in at least 10 stocks and less than 50 stocks; and (3) Minor HFTs, which are identified as HFTs in less than 10 stocks. There are 3 Super HFTs, 8 Major HFTs, and 8 Minor HFTs. According to Panel B, on average, a Super HFT is classified as an HFT in 132 stocks, is 8

10 involved in percent of all trades, has an order-to-trade ratio of 22.99, and percent of its share volume is executed via marketable limit orders (and thus, percent of its share volume is executed via passive limit orders). Super HFTs tend to close the day with an absolute inventory position, as a percentage of share volume, of 4.00 percent. Finally, they are classified as HFTs on 88.2 percent of all stock days in which they are active. On average, Major HFTs and Minor HFTs are classified as HFTs in 22 stocks and 4 stocks, respectively. Relative to the Super HFTs, the fraction of trades in which they are involved is lower (7.87 and 5.25 percent), their order-to-trade ratios are comparable (21.71 and 25.99), the percentage of share volume executed via marketable limit orders is lower (17.67 percent and percent), and their closing net trading positions are similar (3.32 percent and 3.38 percent). Finally, Major and Minor HFTs are classified as HFTs on 86.9 and 80.1 percent of all active stock days, respectively. There are 190 stocks with at least one active HFT in our sample. Because our ultimate goal is to analyze HFT marking making activity relative to large institutional-sized trade packages, we will focus exclusively on these stocks. We also partition these stocks into average daily dollarvolume terciles over the sample period. On average, a high-volume stock has $78.3 million in dollar volume, 10,467 trades, and 207,655 orders per day. A medium-volume stock has $13.9 million in dollar volume, 3,566 trades, and 72,362 orders per day. Finally, a low-volume stock has $3.4 million in dollar volume, 1,970 trades, and 26,003 orders per day. The highest-volume stock in our sample has, on average, $242.8 million in dollar volume, 20,284 trades, and 334,079 orders per day. Volume information can be found in Panel B of Table 2. Panel A of Table 2 summarizes HFT market making activity within each volume tercile. For stocks in the highest-volume tercile, an average of 2.79 HFTs are trading on any stock day. In addition, these HFTs together submit 20.6 percent of all orders, provide liquidity to 15.2 percent of all dollar volume, and actively take liquidity for 3.3 percent of all dollar volume. 8 On average, 16.3 percent of HFT dollar volume is due to aggressive orders, while the remaining 83.7 percent is due to passive orders that are counterparty to other traders aggressive trades. These HFTs are 8 To provide liquidity or passively trade means to execute against marketable limit orders using passive limit orders that are standing on the limit order book. To actively take liquidity or aggressively trade means to submit a marketable limit order that executes against passive standing limit orders. 9

11 clearly taking on a market-making role via passive liquidity provision, but they do also trade using aggressive orders. Within the medium-volume and low-volume stocks, there is an average of 1.44 and 0.98 HFTs present on any stock day, respectively, which is much lower than the HFT presence in the high-volume stocks (2.79). HFTs provide slightly less passive liquidity within these terciles than for high-volume stocks (11.8 percent and 14.3 percent). We also include information for the five highest-volume securities, where it is apparent that the HFTs are especially active. The highest-volume stock, which we denote Stock 1, has an average of 5.84 active HFTs on any stock day, and together these HFTs submit 35.8 percent of all orders, passively provide liquidity to 30.5 percent of all dollar volume, and actively take liquidity for 9.1 percent of all dollar volume. To put the HFT passive liquidity provision into context, Stock 1 has an average daily dollar volume of $242.8 million, meaning that HFTs provide liquidity to approximately 30.5% $242.8 million = $74.05 million of aggressive volume per day. Information on the remaining four highest-volume securities (Stocks 2 to 5) can also be found in both panels of Table 2. 4 Classifying Large Institutional-Sized Trades A major issue raised by many institutional traders regards the concept of phantom liquidity, in which displayed liquidity tends to disappear when a trader attempts to execute its trade, either in full or in part. Large trades (parent orders) are generally executed over the course of hours or even days (through smaller child orders and trades). To examine phantom liquidity and how it might affect the cost of a large trade, we must first identify these large trades. Fortunately, the IIROC database allows us to track any trader (whose identification is masked) over time, meaning we can identify large trades that are executed via many smaller trades over the course of the day. We define a large trade as follows: For high-volume stocks, an aggregate dollar volume of at least $1 million that comes from a single account; 10

12 For stocks that are not in the high-volume tercile, an aggregate dollar volume of at least $500,000 that comes from a single account; The aggregate dollar volume must consist of either 100 percent buys or 100 percent sells. We allow large trades to span multiple days in our sample. When a client trades the same asset in the same direction on consecutive days, we treat this as a single parent trade package if there are child trades in both the last half hour of the first day and the first half hour of the following day. Otherwise, these are treated as separate parent trades. A large trade is defined as a stressful trade if its total dollar volume, as a percentage of total volume for that stock/day, is in the upper quartile relative to other large trades; otherwise, the large trade is considered non-stressful. We filter out any large trade that execute less than 10 percent of its total order using aggressive trades we are interested in examining liquidity provision to large trades, so we require a reasonable number of aggressive orders to be contained in these large trades. This classification results in 181,346 parent orders. Table 3 provides details about the large non-stressful and stressful trades identified in our database. There are 136,212 large non-stressful trades in our sample of 190 stocks. On average, a large non-stressful trade is for $2.22 million and comprises 2.5 percent of trading volume in that stock. A parent trade is executed using an average of 327 child trades, with 469 child orders submitted. About 62.7 percent of the total trade is executed via marketable limit orders and 37.3 percent of the total trade is executed via passive limit orders. A large, non-stressful trade takes about 4.5 hours to completely execute, on average. There are 45,134 large stressful trades in our sample of 190 stocks. On average, a large stressful trade is for $3.26 million. It is executed using 604 child trades, with 782 orders submitted percent of the total trade is executed via marketable limit orders and 37.0 percent of the total trade is executed via passive limit orders. The average large stressful trade takes about 5.4 hours to completely execute. Additional information regarding quantile cutoffs for large non-stressful and stressful trades can also be found in Table 3. We also compute the implementation shortfall (IS) for every large trade. Implementation shortfall is measured as the total cost of a trade relative to the pre-trade bid ask midpoint. For 11

13 example, suppose there is a buy order for 100,000 shares executed throughout the course of the day and the buyer ended up paying $1.02 million for these shares. Suppose also that, at the initiation of this trade, the bid ask midpoint was equal to $10. If there was no price impact, then the trader would have paid $10 100, 000 = $1.0 million for the 100,000 share purchase. However, because of price impact, the trader pays $1.02 million $1.0 million = $20, 000 more for its trade. Therefore, its implementation shortfall equals $20, 000/$1.0 million = 2 percent. Assume a large trade t in stock i of X it total shares is executed using N smaller child trades. Let p n,it and x n,it denote the price and share volume, respectively, of the n-th child trade within large trade t for shares in stock i. Also denote m 0,it as the bid ask midpoint at the initiation of the large trade. The implementation shortfall for large trade t is calculated as: IS it = N n=1 p n,itx n,it m 0,it X it m 1,it X it IS it = m 0,itX it N n=1 p n,itx n,it m 0,it X it for large buys, and for large sells. Note that it is possible for the implementation shortfall to be negative a negative IS would be good for the trader. For example, if the implementation shortfall for a large buy order is negative one percent, the large trader paid one percent less than it would have paid if it had bought all shares at the initial bid ask midpoint. Table 3 provides statistics regarding the implementation shortfall for large trades. The mean IS for a large non-stressful trade is 11 basis points while the tenth and ninetieth percentiles are -67 and 93 basis points. Some large trades that are buys (sells) will occasionally benefit from contemporaneous downward (upward) market movements, while others will be more costly due to contemporaneous upward (downward) market movements. We adjust for contemporaneous market movements in our analysis of IS later in the paper. Large stressful trades generally have a higher IS: the mean, tenth percentile, and ninetieth percentile are 35, -57, and 156 basis points, respectively. We summarize HFT profitability for days containing non-stressful large trades and and compare it to days containing stressful large trades. We calculate stock day HFT trade profitability by subtracting the value of shares bought from the value of shares sold while marking to market 12

14 any inventory held at the end of the day. We also account for liquidity taking-fees and liquidityproviding rebates by crediting $ per share for each share passively supplied by the HFT and subtracting $ per share for each share actively demanded by the HFT via marketable limit orders. 9 Total HFT profits are calculated as the sum of HFT trade profits and rebate profits. Profit per share is calculated as the total HFT profit divided by the maximum of the number of shares bought by the HFT and the number of shares sold. The summary statistics for HFT profitability are reported in Table 4. According to Panel A, in which we examine HFT profitability on days without stressful trades, an HFT loses about $100 per stock day from trading and this is similar across volume subgroups. However, HFTs more than make up for this via liquidity rebates. On average, an HFT makes $380 per stock day in liquidity rebates (net of liquidity-taking fees). This number is highest in the high-volume stocks, which is expected, since the HFTs are turning over more shares in these stocks. Specifically, HFTs make $634 per stock day in rebates within high-volume stocks and make $182 per stock day in low-volume stocks. On average, HFT profit per share traded is $0.0023, and this is higher in the high-volume stocks ($0.0027). Standard deviation in profit per share is also highest in the highvolume stocks. 10 The negative average trading profits suggest that order anticipation strategies, or back-running (Yang and Zhu (2015)) are not the primary source of profitability for HFTs, although it is likely that the average losses could be even greater without using these strategies. The positive profits from maker fees suggests that quote-matching strategies are likely to be a larger source of profits for the HFTs. In Panel B, we examine HFT profitability on stock days in which there was at least one stressful trade. We find that trade profits are similarly negative and rebate profits are generally lower (with the exception of the low volume subgroup), which suggests that HFTs are providing less liquidity during times of stress. Profit per share statistics are also similar, which implies that HFTs are trading fewer shares on those days since total profit statistics are comparable to those reported in Panel A. 9 This is the rebate schedule for stocks that trade above one dollar on the TSX and TSX-V. Because a very large portion of volume is traded on these exchanges, we use this rebate schedule to approximate rebate profits. 10 The result that average trading profits are negative while average net liquidity rebates are positive and greater in magnitude is consistent with Battalio, Corwin, and Jennings (2015), which states that a broker cannot maximize both execution quality and liquidity rebates (that is, they cannot have it all ). 13

15 5 HFT Liquidity Provision to Large Trades We wish to determine what influences HFT liquidity provision for large trades. Earlier, we discussed phantom liquidity the concept that traders, particularly HFTs, might withdraw liquidity if they anticipate that prices will move against them when holding a position in a stock. Large trades, for example, tend to move prices, so it would be rational for an HFT to withdraw liquidity and either reoffer it at a costlier price or not reoffer it at all to the large trader. One possible explanation is that the HFT adjusts prices as compensation for the adverse selection detected in the large trade. Another possible explanation is that the HFT adjusts its prices all large trades, including those that are liquidity-motivated (and hence with no adverse-selection concerns), because of the possibility of permanent price impact from an information-based large trade or a transitory price impact from a liquidity-motivated trade that persists for longer than the HFT is willing to hold that stock position. Our dependent variable of interest is HFT liquidity provision for the aggressive component of large trades. For example, suppose there is a large buy in a particular stock for $10 million and that 50 percent of this order is executed using aggressive orders. If HFTs together provide liquidity to $2 million of the $5 million aggressive order, then they provide 40 percent of liquidity to the aggressive component of the large trade. Specifically, we define our dependent variables as follows: HF T LIQ it = HFT Passive Dollar Volume it Large Trade Aggressive Dollar Volume it We are interested in the determinants of HFT liquidity provision to large trades. Specifically, our goal is to measure the extent to which HFTs in particular might reduce their liquidity provision to large trades when those trades exert more stress on the marketplace. As previously mentioned, we identify a large trade as stressful if it is in the highest quartile of large-trade dollar volume, as a percentage of total dollar volume for that stock day (the stress indicator variable equals one in this case and zero otherwise). HFTs should be more active in high-volume stocks because of the ability to turn over 14

16 shares more quickly. Indeed, according to Table 2, we see that HFTs provide more liquidity in these stocks. We are particularly interested in the extent to which HFTs might reduce their liquidity provision within these stocks when a stressful event occurs, as there is potential for bigger losses if prices move against their positions. Therefore, we will also interact the stress indicator variable with an indicator variable that equals one if the large trade is in a high-volume stock and zero otherwise. Finally, we include control variables that could also plausibly affect HFT liquidity provision. We include the percentage of dollar volume for the large trade that is executed using aggressive orders (AGG), the number of hours it takes to fully execute the trade (T IME), the dollar volume of the large trade (T SIZE, in millions of dollars), and the squared dollar volume of the large trade (T SIZE2) to account for potential nonlinearities in the price impact of the trade. To examine the determinants of HFT liquidity provision, we estimate the following regression: HF T LIQ it = α + γ d + β 1 ST RESS it + β 2 HIGHV OL i + β 3 (ST RESS it HIGHV OL i ) + γ X it + ε it, where γ d represents date fixed effect controls and X it is a vector of control variables that includes AGG it, T IME it, T SIZE it, and T SIZE2 it. In this regression and all other regression in this paper, standard errors are clustered at the firm level. The regression results for HFT liquidity provision are reported in Table 5. According to regression column (3), for lower-volume firms, HFTs provide liquidity to percent of the aggressive component of large trades, and this is reduced by 1.21 percentage points (to percent) if the large trade is considered stressful. This reduction is much more pronounced for highvolume firms: in this case, HFTs provide liquidity to percent of the aggressive component of large trades, and this is reduced by 6.67 percentage points (to percentage points) if the large trade is stressful. Compared to non-stressful large trades, HFTs provide 8.1 percent less liquidity to stressful large trades in lower volume firms, and 29.4 percent less liquidity to stressful large trades 15

17 in high volume firms (both of these results are statistically significant at the one percent level). 11 For convenience, Figure 1 summarizes these results graphically. The coefficients for the control variables are as expected. HFTs provide less liquidity to more aggressive large trades, since the aggressiveness of the trade implies more price impact, thus increasing the likelihood that the HFT s orders will be adversely selected. There is no significant relationship between HFT liquidity provision and the time it takes to complete the trade, most likely because an HFT is unable to easily infer this information. We also find that HFTs provide more liquidity to larger trades, and the negative coefficient on the squared dollar trade size term indicates that this liquidity provision is nonlinear and decreasing in trades that are especially large. 12 When DMMs Become HFT-DMMs HFTs provide a lower percentage of liquidity to stressful trades, especially within high-volume stocks. However, it is possible that there is an omitted variable that causes both the stressful trade to occur and the HFT liquidity provision to be lower. To address this endogeneity issue, we examine an interesting event that increased HFT presence in 24 stocks in our sample. Prior to November 26, 2012, a variety of non-hft DMMs were assigned to 24 specific stocks. The behavior of these DMMs is typical few orders per day and many trades relative to those orders. DMMs have the right to execute against odd lot orders without placing any orders of their own, which is why we observe a low number of DMM orders relative to their trades. Starting on November 26, 2012, these 24 stocks were all assigned the same, new DMM. This new DMM clearly exhibits behaviors of an HFT in particular, this DMM submits many more orders and executes many more trades (in some stocks, more than 1,000 times the number of orders than before), has a high order-to-trade ratio, and also has much higher dollar volume. 11 Because our HFTLIQ variable is bounded below by zero and above by one, we also run an alternative regression where we apply logistic transformation to this variable. We get similarly significant results (in this regression and subsequent regressions using HFT liquidity provision) if we use this logistic transformation. To ease interpretation of the coefficients, we report the results of the linear probability model. 12 In Tables A1 and A2 of the Internet Appendix, we provide summary statistics and similar regression results for Designated Market Makers (DMMs). DMMs are assigned to TSX stocks and are required to continuously post bids and offers such that their spread does not exceed a pre-specified threshold. We find that DMMs provide an average of about 2 percent of liquidity, and that their liquidity provision does not significantly change relative to large stressful trades. Their behavior is mostly inconsequential to our analysis, with the exception of an event in which an HFT took on the DMM role in several stocks. This event will be discussed in the next section. 16

18 This change can be seen as a de-facto upgrade in speed for the designated market maker. Budish, Cramton, and Shim (2015) and Baldauf and Mollner (2016) present theoretical models suggesting that an upgrade in HFT speed, whatever the cost, leads to a more efficient cancellation of orders that would otherwise be adversely selected, thus implying a reduction in HFT liquidity provision to large orders that move prices. We examine liquidity provision to large institutional trades following the aforementioned DMM change; an implication of their model is that the reduction in HFT liquidity provision to large stressful trades, which are more likely to exert short-term price movements, will become more pronounced following the change of a DMM to an HFT-DMM. Table 6 provides additional details about the DMM change observed in our data. Many of the 24 stocks have high dollar volume and market capitalization. We report four of the highestvolume stocks, which, in the interest of confidentiality, we will name Stocks A D. The DMM for Stock A, for example, submits an average of 10 orders per day in the five days before November 26, 2012 and approximately 18,000 orders per day in the five days starting November 26, 2012, indicating an approximate 180,000 percent increase. Average daily trades increased from approximately 600 to 2,900, and average daily dollar volume increased from approximately $1.9 million to $19 million. Similarly large relative increases in orders, trades, and dollar volume are also observed for the remaining 20 stocks. The new DMMs are clearly operating at a higher speed. We have some conjectures for why this event occurred. Effective April 1, 2012, IIROC implemented its Integrated Fee Model, in which designated market makers would now receive a 70 percent discount on marketplace fees. These fees are based on the proportion of message traffic (orders and trades) originating from that trader, although before the Integrated Fee Model (IFM) was implemented, the fees were only based on the proportion of message traffic due to trades and not orders. HFTs that are not DMMs do not qualify for this 70 percent discount. Given that HFTs constitute a significant portion of submitted orders and trades, a 70 percent discount would be highly beneficial, particularly because fees under the Integrated Fee Model are charged based on order activity. However, the date on which the DMMs in those 24 stocks all become the single HFT-DMM is November 26, 2012, which is approximately 8 months after the implementation of the Integrated Fee Model. While it is clear that HFTs would now have greater incentive to take on a DMM role, we do not believe that HFTs could instantaneously become DMMs following the 17

19 new regulation the application process and approval process by the TSX Allocation Committee for DMMs presumably take time, and 8 months seems like a reasonable time frame. Therefore, we have identified an event in which HFT presence in these particular stocks has increased, via the DMM channel, and is independent of the arrival of stressful trades. To examine how this event might influence liquidity provision to large trades, we first define a new variable indicating liquidity provision to large trades by HFTs and the DMM combined: HDLIQ it = HF T LIQ it + DMMLIQ it. Henceforth, HDLIQ liquidity provision will denote the liquidity provision provided to large trades by HFTs and the DMM combined. As in the previous section, we will examine the potential determinants of this liquidity provision using the same independent variables as the previous regressions. However, we will now also include an indicator variable that equals one (NEW DMM = 1) when the large trade is executed on a day in which the HFT is assigned as a DMM in one of the 24 stocks discussed above. This indicator variable will be interacted with the stress indicator, the high-volume stock indicator, and the cross product of the stress and high-volume stock indicators. Specifically, we estimate the following regression model: HDLIQ it = α + γ d + β 1 ST RESS it + β 2 HIGHV OL i + β 3 (ST RESS it HIGHV OL i ) + β 4 NEW DMM it + β 5 (NEW DMM it ST RESS it ) + β 6 (NEW DMM it HIGHV OL i ) + β 7 (NEW DMM it ST RESS it HIGHV OL i ) + γ X it + ε it. Unconditionally, we expect HFT liquidity provision to be higher following the introduction of the HFT-DMM, as this increases the presence of HFTs in those stocks. However, in the case of large stressful trades, we expect the reduction in HFT liquidity provision to be more pronounced (compared to large non-stressful trades) due to the increased presence of HFTs that are betterequipped to forecast short-term price movements, as in Foucault, Hombert, and Roşu (2016). 18

20 The regression results are reported in Table 7. According to the regression in column (3), for high-volume firms in the pre HFT-DMM period, a stressful trade leads to a 29.8 percent reduction in liquidity (22.36 = percent for non-stressful trades versus = percent for stressful trades). In contrast, for high-volume firms in the post HFT-DMM period, a stressful trades leads to a 42.3 percent reduction in liquidity (26.7 percent for non-stressful trades versus 15.4 percent for stressful trades), which is consistent with our prediction that the de facto speed upgrade leads to a greater reduction in liquidity for stressful trades. Finally, we find that the percent of liquidity provided by HFTs significantly increases in the HFT-DMM period for nonstressful trades, although it does not significantly change for stressful trades. Our results indicate that HFT liquidity withdrawal for stressful trades becomes especially pronounced when the HFT takes over the DMM role. For convenience, Figure 2 summarizes these results graphically. In Tables A3 to A5 of the Internet Appendix, we provide additional robustness results showing that HFTs reduce their liquidity provision for other stressful periods. Table A3 provides evidence that HFTs lower their liquidity provision when their profits in the previous week have been abnormally low, which is consistent with evidence provides in Comerton-Forde, Hendershott, Jones, Moulton, and Seasholes (2010). Table A4 provides evidence that HFT liquidity provision is even lower when there are multiple concurrent stressful trades in the same direction. Finally, Table A5 provide evidence that HFTs liquidity provision is lower on days when stock price movements are extreme, although it is possible that they still act as net providers of liquidity on these days (Brogaard, Carrion, Moyaert, Riordan, Shkilko, and Sokolov (2015)). 6 Dynamic HFT Liquidity Provision In this section, we delve into more detail about how HFTs dynamically interact with large institutional trades. In the last section, we provided evidence that the percentage of liquidity provided by HFTs to large stressful trades is much lower than that for stressful trades. Is this because HFTs are dynamically adapting their behavior to these trades, or because of increased competition from other liquidity suppliers? We can address this question by examining HFT abnormal order submission and trading activity over the course of these large trades. Further, we can use our detailed data to 19

21 understand the nature of this liquidity withdrawal. Are HFTs withdrawing liquidity because their speed provides them with an ability to better-predict order flow, or is it simply because HFTs are managing their inventory risk? As a first step, we provide graphical representations of how HFT activity evolves over the course of large trades by dividing those large trades into time deciles. For example, if a large trade is executed over the course of five hours, then the first time decile of this large trade denotes the first thirty minutes of that trade. This way, we normalize time progression for all large trades with different times to total execution. To ensure that each time decile covers a reasonable window of time, and to reduce noise, we examine large trades that are executed over a minimum of 2.5 hours, which ensures that each time decile is at least 15 minutes in length, and in only high-volume stocks, to ensure that there is enough HFT activity within each time decile (this restriction is only for the upcoming figures and does not apply to the regression results reported later). We calculate HFT activity within each of the time deciles specifically, their net trading activity, abnormal buying and selling activity, and abnormal order submission activity. First, we calculate HFT net passive trading activity (NP T ) within each large trade time decile as the difference between HFT total shares purchased and sold using passive trades divided by the sum of shares purchased and sold. HFT net active trading activity (NAT ) is similarly calculated, but only uses shares actively bought and sold by HFTs. To account for time-of-day effects, we demean these variables using their average values in the previous sixty days at that same time of day. We report the the mean NAT and NP T within each time decile across all stressful large trades in Figure 3. We find that within the first time decile, HFTs have slightly positive NP T for large stressful sells (significant at the 10% level) and slightly negative N P T for large stressful buys (although this is below significance at the 10% level), indicating that HFTs are initially providing liquidity to the large trade, or at the very least are not strongly trading in either direction. However, for later time deciles, we see that this result substantially reverses. For large stressful buys, HFTs consistently have positive NP T and NAT for time deciles greater than one, indicating that HFTs are engaged in proportionally more buying activity when a large stressful parent trade that is a buy is being executed (similar results hold for large stressful sells). 20

22 Trade imbalances, however, do not tell the full story. It is possible that both HFT buying and selling activity have substantially increased, which could still be beneficial to a large trader even if the imbalance were in the same direction as the large order. Therefore, we also examine abnormal HFT buying and selling activity within each time decile for stressful and non-stressful large buys and large sells. Specifically, for each large trade, we calculate abnormal HFT passive buying activity (AP B) as the total number of shares passively bought in decile d divided by its sixty-day moving average within the same time-of-day window. Abnormal HFT passive selling activity (AP S) is defined similarly. Following this, we calculate the mean AP B and AP S across all large non-stressful buys, non-stressful sells, stressful buys, and stressful sells. This way, we can observe how HFTs abnormally trade during stressful buys and sells over time, and how this compares to their behavior during non-stressful buys and sells. The results for HFT abnormal buying and selling activity (AP B and AP S) during large institutional buys (stressful and non-stressful) are reported in Figure 4. First, we find that HFT abnormal buying and selling activity is higher for non-stressful buys than it is for stressful buys, indicating that HFT activity is comparatively scaled back for the stressful buys. Second, we find a significant gap between HFT buying and selling activity for stressful buys, but not for nonstressful buys. This is reflective of the order-imbalance results we reported earlier: HFTs appear to be focusing more on buying activity, as opposed to selling activity, during these stressful buys. Finally, we find that HFT activity is higher during the beginning and end of any large buy it is likely higher during the beginning because the HFT has not completely inferred yet that a large trade with potential price impact is underway, while it is likely higher during the end because HFTs have previously pulled back their sell orders (or aggressively bought the shares contained in other traders sell orders) and are now offering the same shares through passive orders. At the bottom of this figure, we also include the share density of these large institutional buys. It is apparent that the density follows a U shape, meaning that more of the shares executed in a large-buy order are concentrated at the beginning and (especially) the end of the large trade program. Figure 5 similarly reports HFT abnormal buying and selling activity, but for large institutional sells. The results are similar, in that HFTs provide substantially less liquidity to stressful sell orders, focus more on selling activity for large stressful sell orders, and are most active at the beginning and end 21

23 of the large sell order. We also examine abnormal HFT order submission activity over the life of these trades and find similar results, which are reported in Figures 6 and 7. This indicates that for large stressful trades, HFTs are both trading and submitting orders at abnormally high levels in the same direction as the trade. Order Anticipation or Inventory Management? The previous section provides evidence that HFTs are somewhat accommodating to large stressful trades at the beginning of the parent trade, but subsequently switch to trading in the same direction of the large trade. However, it is still unclear why HFTs dynamically interact with these orders in this way. One possibility is that HFTs use their speed advantage to employ an order anticipation strategy that allows them to anticipate large order flows that likely originate from institutional traders. Baldauf and Mollner (2016), for example, provide a theoretical model showing that faster traders avoid adverse selection by cancelling mispriced quotes, while Yang and Zhu (2015) theoretically show that a fast trader back-runs large orders by eventually competing with the order. Our evidence so far is consistent with this possibility of eventual order anticipation by the HFT. However, a second possibility is that HFTs are simply managing their inventory risk, as in the inventory market making models of Amihud and Mendelson (1980) and Ho and Stoll (1981). HFTs that initially accommodate a large trade in its early stage will likely end up with a large inventory position that must be worked off, thus causing the HFT to trade in the same direction as the large trade in its later stages. Inventory management would lead to the HFT reducing the competitiveness of their limit orders on the opposite side of the limit order book to the large trade, which could also explain our earlier result showing that HFTs provide a lower percentage of liquidity to large stressful trades. The purpose of this section is to examine whether HFT liquidity withdrawal over the life of a large trade can be explained by order anticipation, inventory management, or some combination of the two. We proceed with this analysis by dividing each trading day into fifteen-minute periods. For each stock, we focus on the primary HFT that is active in that stock, as measured by their average daily dollar volume. We first measure HFT short-term and longer-term inventory variation at 22

24 fifteen-minute intervals. To capture HFT order anticipation, we calculate the net shares demanded by large trades within each of these periods and estimate the predicted component of this net measure using stock order imbalance and price change information in recent periods. Following this, we examine the relationship between current HFT order imbalance relative to short-term and longer-term inventory variation and the predicted component of large institutional net trading volume. Specifically, our dependent variable of interest is HFT order imbalance in fifteen-minute period t and stock i. We normalize this variable by dividing it by the HFT maximum absolute inventory position in the previous week. This way, we capture the net trading activity of HFTs relative to their typical inventory tolerance level: HF T OIB it = HFT Shares Bought it HFT Shares Sold it Max Absolute Inventory Position in Previous Week it. Short-term inventory management implies that HF T OIB will be negatively correlated with its lagged value. We also take longer-term inventory management into consideration by calculating the total number of shares bought minus the total number of shares sold by the HFT in the past week (also normalized by their maximum absolute position in the past week) (HF T INV it ). The lagged value of this variable should also be negatively correlated with current HFT order imbalance. Finally, we interact HF T INV with a variable representing the inverse of number of periods left in the day to account for the possibility that HFT inventory management might change as the trading day comes to an end (denoted (HF T INV/T M)). If HFTs adjust inventory more aggressively the closer to the market close, the coefficient on this interaction tern should be negative. We are particularly interested in examining how HF T OIB is related to the predicted component of net large institutional trading volume, after controlling for HFT inventory dynamics. To estimate the predicted component of net large institutional trading volume, we calculate actual net large institutional trading volume within each period t and stock i (normalized by total trading volume and denoted N I) and examine its relationship with public information such as lagged order imbalance and price movements within each stock. Specifically, we test the following regression 23

25 model: 8 8 NI it = α + βi k SOIB i,t k + λ k i r i,t k + γ i,t OD + δ i,dow + ε it, k=1 k=1 where SOIB is the total number of shares bought minus the total number of shares sold divided by total volume in stock i in period t, r is the stock return calculated using the bid ask midpoint, γ i,t OD represents time-of-day fixed effects, and δ i,dow represents day-of-week fixed effects. We estimate the regression coefficients β k and λ k (k = 1,..., 8) and fixed effect coefficients for each stock. In unreported results, we find that there is a significant relation between past stock order imbalance and net institutional trading volume, and a similarly significant relation between past stock returns and net institutional trading volume. We use the estimates from these stock-level regressions to calculate the predicted value of NI for each period t and stock i (denoted we also obtain the unpredicted residual component from this regression (denoted ˆε). ˆ NI), and With our inventory and order anticipation variables defined, we estimate the following regression to determine if HFT order imbalances are driven by inventory management (lagged HF T OIB and HF T INV ), order anticipation (predicted NI), or some combination of both: HF T OIB i,t = α + β 1 ˆ NIi,t + β 2 ˆε i,t + β 3 HF T OIB i,t 1 + β 4 HF T INV i,t 1 + β 5 (HF T INV/T M) i,t 1 + e i,t. The results are reported in Table 8, with Panel A reporting results using the predicted value of net non-stressful large trades as the NI independent variable, and with Panel B using the predicted value of net stressful large trades as the N I independent variable. According to the first column of Panel A, HFT order imbalance is positively associated with the predicted component of large non-stressful trade volume, and negatively associated with the unpredicted component. This is consistent with the hypothesis that HFTs are following an order anticipation strategy, although they appear to be accommodating to the unpredicted component of the large trade net order flow. We find that HFT order imbalance is negatively associated with its lagged value, indicating that HFTs seem to be engaging in short-term inventory management. In addition, we find that HFT order imbalance is negatively associated with their longer-term inventory, indicating that HFTs are 24

26 more aggressive with reverting their inventory to the near-zero position when inventory levels are closer to their maximum tolerance levels. Finally, we find that when there is less time remaining in the day, HFTs become more aggressive in closing their inventory position. Overall, these results indicate that HFTs are actively managing their inventory positions, but also trade in the direction of anticipated large trade order flow. The second and third columns report results for HFT order imbalances using only their passive trades and active trades, respectively. When the predicted component of signed large trade volume is one percentage point higher, HFT passive order imbalance is 0.38 percentage points higher, while HFT aggressive order imbalance is 0.13 percentage points higher. That is, HFTs are using both passive and active orders to trade in the same direction as predicted large trade volume, although the relationship is about three times stronger for passive order imbalance compared to active order imbalance. This indicates that HFTs are aggressively pricing their limit orders such that they primarily trade in the same direction as predicted signed large trade volume. For the unexpected component of signed large trade volume, HFTs primarily trade in the opposite direction to this volume using passive orders (with a regression coefficient of versus a marginally significant for HFT aggressive order imbalance), indicating that their standing limit orders are picked off relative to the component of large trade volume that remains unpredicted. Finally, we find that the coefficients on past HFT order imbalance and inventory are much higher in magnitude in the HFT passive order imbalance regression, indicating that HFTs primarily manage their inventories by aggressively pricing their limit orders such that their inventory position reverts to zero. Panel B reports the results when using the predicted values of net stressful large trades as the NI independent variable. The main point to note here is that the coefficients on the Predicted Large Trade variable are larger in magnitude relative to the results reported in Panel A across all three columns. This indicates that HFTs are more aggressive when trading in the same direction of large stressful trades. Because large stressful trades are more likely to move prices, HFTs are more likely to be more aggressive about trading in the same direction as these trades. 25

27 7 Implementation Shortfall and Liquidity Provision So far, we have shown that HFTs provide a lower percentage of liquidity to large institutional trades that are considered stressful, and that HFTs eventually trade in the same direction of large institutional orders; this can partially be explained by the management of their inventories, but also by their ability to anticipate the order as it progresses. In this section, we examine the implications of this HFT reduction in liquidity provision on the overall cost of these large institutional trades. Recall that we calculated the implementation shortfall (IS) for each large parent trade in our sample this represents the cost of a trade due to price impact. For example, if IS equals 20 basis points for a large buy order, this means that the buyer paid 20 basis points more than it would have paid had there been unlimited liquidity at the initial bid ask midpoint for this large buy order. If the buyer was interested in purchasing $10 million worth of shares, it would have paid $10.02 million due to price impact. Our dependent variable of interest is the implementation shortfall for large trades. We examine how this variable is related to HFT liquidity provision (HF T LIQ), as defined in Section 5. We expect that IS will be negatively related to the HF T LIQ variable, in that lower HFT liquidity provision will be associated with costlier trades. We use the same control variables introduced in Section 5: the aggressiveness of the trade (AGG), the time to trade completion (T IME), the size of the total trade (T SIZE), and its squared value (T SIZE2). We expect that more aggressive trades will be more costly because they demand more liquidity, thus causing more price impact. Trades with a longer time to completion should be associated with a lower IS since they are more likely to be liquidity-based trades that are not based short-lived information. Larger trades are more likely to have a higher IS because they exert more price pressure on one side of the limit order book. We also control for the contemporaneous market return (interacted with a buy or sell indicator for that large trade) to account for market movements that occur while the trade is being executed. Finally, we use indicator variables to control for high-volume (HIGHV OL) and medium-volume firms (MIDV OL), as IS will typically be lower for firms with more trading activity. Specifically, we examine the determinants of large trade implementation shortfall by 26

28 running the following regression: IS it = α + ξ d + β HF T LIQ it + ξ Y it + u it, where Y represents a vector of the control variables described above and ξ d represents day fixed effects. The regression results are reported in Table 9. We find that HFT liquidity provision is negatively related to the IS of a large trade, which is consistent with our predictions. Importantly, we are also able to quantify the average effect of a reduction in HFT liquidity provision on IS. According to the regression in column (3), if HFTs provide 10 percentage points less liquidity to the active component of a large trade, the IS of the trade is 2.5 basis points higher. The coefficients on the control variables in this regression are as expected. Large trades that are executed with more aggressive orders have a higher IS. If a large trade takes a longer time to execute, then the IS is lower, possibly because the trader is more successful in hiding the information content contained in the total order (or because the large trade contains less information and thus the trader can choose a longer execution time). IS is increasing in total trade size but decreasing in total trade size squared, indicating a concave relationship between trade size and cost. IS is lower in medium-volume stocks and even lower in high-volume stocks. Finally, IS is higher for large buys when market returns are positive and higher for large sells when market returns are negative. 8 Conclusion High-frequency traders operate with a speed advantage over other market participants, allowing them to quickly adapt to new information and other public signals such as short-term changes in the stock price and order flow. As market makers, HFTs benefit from this speed advantage by dynamically adjusting their liquidity provision to market conditions, managing their inventory with greater efficiency, and avoiding having their orders adversely selected by large institutional traders. 27

29 In this paper, we examine how HFT market makers dynamically interact with large institutional trades. When a large trade is stressful, the percentage of liquidity provided to that trade by HFTs is much lower. We find that HFTs are accommodating to large institutional trades in their early life, but switch to trading in the same direction of those trades as they progress. Our evidence suggests that HFTs eventually trade in the same direction as these large institutional trades for two reasons: (1) to revert an inventory position that was built up in the early life of the large trade, and (2) because the HFTs anticipate additional orders in the same direction, which is consistent with the theoretical models of order anticipation in Baldauf and Mollner (2016) and Yang and Zhu (2015). We find that a 10 percentage point reduction in HFT liquidity provision to large stressful trades leads to an implementation shortfall increase of 2.5 basis points. The theoretical models in Budish, Cramton, and Shim (2015) and Baldauf and Mollner (2016) suggest that an upgrade in HFT speed leads to a reduction in HFT liquidity provision to large orders that move prices in the short-term. The institutional trades identified in our sample provide a good source of short-term price pressures, and we do indeed find that the HFTs, who operate at high speeds by definition, trade in the same direction as these institutional trades. Further, we find that when an HFT takes on the designated market maker role, which implies a de facto upgrade in speed for the market makers in those stocks, the reduction in liquidity provision to the large stressful trades becomes even greater. Most large parent orders are broken into smaller child orders in order to reduce the price impact of the trade. HFTs can use their speed advantage to back-run large institutional-sized trades by detecting those trades and submitting competing orders. They can also use their speed advantage to gain priority in the limit order queue and receive liquidity rebates. We find that HFT net trading activity is significantly related to forecasted trading imbalances from large trade packages, after controlling for their inventory position. This is consistent with back-running. However, our finding that HFTs lose money on trading and make money from liquidity rebates suggests that back-running cannot be their main source of revenue. We also find that HFT trading is significantly influenced by their inventory position. They respond to inventory accumulation by trading in the opposite direction, an implication of many models. HFT behavior and trade characteristics have significant effects on the implementation shortfall of large trades. Implementation shortfall is 28

30 11 (35) basis points for non-stressful (stressful) trades and significantly negatively related to HFT liquidity provision. References Amihud, Y., and H. Mendelson, 1980, Dealership market: Market-making with inventory, Journal of Financial Economics 8, Anand, A., and K. Venkataraman, 2016, Market conditions, fragility, and the economics of market making, Journal of Financial Economics, forthcoming. Baldauf, M., and J. Mollner, 2016, Fast traders make a quick buck: The role of speed in liquidity provision, Working Paper. Battalio, R., S. Corwin, and R. Jennings, 2015, Can brokers have it all? On the relation between make take fees and limit order execution quality, Working Paper. Breckenfelder, J., 2013, Competition between high-frequency traders and market quality, Working Paper. Brogaard, J., A. Carrion, T. Moyaert, R. Riordan, A. Shkilko, and K. Sokolov, 2015, High-frequency trading and extreme price movements, Working Paper. Brogaard, J., T. Hendershott, and R. Riordan, 2014, High frequency trading and price discovery, Review of Financial Studies 27, Budish, E., P. Cramton, and J. Shim, 2015, The high-frequency trading arms race: Frequent batch auctions as a market design response, Quarterly Journal of Economics 130, Carrion, Allen, 2013, Very fast money: High-frequency trading on the NASDAQ, Journal of Financial Markets pp Chan, Louis K. C., and J. Lakonishok, 1993, Institutional trades and intraday stock price behavior, Journal of Financial Economics 33,

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32 Tong, L., 2015, A blessing or a curse? The impact of high frequency trading on institutional investors, Working Paper. Van Kervel, V., and A. Menkveld, 2016, High-frequency trading around large institutional orders, Working Paper. Yang, L., and H. Zhu, 2015, Back-running: Seeking and hiding fundamental information in order flows, Working Paper. 31

33 Figure 1: HFT Liquidity Provision for Stressful and Non-Stressful Trades. This graph plots HFT liquidity provision (as a percentage of total liquidity provision to the aggressive component of the large trade) for large trades that are stressful and large trades that are non-stressful, within both high-volume firms and lower volume firms. A trade is stressful if its total dollar volume, as a percentage of total dollar volume for that stock day, is in the upper quartile relative to all large trades. A firm is high-volume if it is in the upper tercile of average daily dollar volume. Otherwise, it is a lower-volume firm. Numbers are based on the coefficients from the HFT liquidity provision-regression from Table 5. 32

34 Figure 2: HD Liquidity Provision Before and After DMM Becomes HFT-DMM. This graph plots HFT and DMM combined liquidity provision (as a percentage of total liquidity provision to the aggressive component of the large trade) for 24 stocks in which each DMM became the same HFT-DMM on November 26, We examine HFT and DMM combined liquidity provision before and after this date, and for stressful trades and non-stressful trades, for high-volume firms. Numbers are based on the coefficients from the HD liquidity provision-regression from Table 7. 33