Essays in empirical market microstructure

This dissertation is composed of three essays in empirical market microstructure. My first two essays study market quality issues related to High-frequency Trading (HFT) using a dataset provided by NASDAQ that identifies the activity of high-frequency traders (HFTs). My first essay studies the systematic effects of HFT on market quality. I find only small effects of HFT participation on spreads and adverse selection costs, and I find evidence that HFT trades improve price efficiency. I also examine HFT trading strategies, and show that HFTs engage in successful intraday market timing. My second essay studies HFT in extreme market conditions, focusing on whether it has a stabilizing or destabilizing effect. I find that HFTs buy during mini-flash crashes, sell during price spikes, and provide more liquidity than they consume during both types of events. These results suggest HFTs play a stabilizing role during extreme return events, but their net trading volumes are low so these effects are probably small. I also examine returns around large HFT order imbalances, and find only economically small evidence of the price momentum that these imbalances have been hypothesized to cause. Finally, I study HFT activity around sustained market order flow imbalances, termed "toxic order flow" by Easley, Lopez de Prado, and O'Hara (2011), and find that HFT participation levels decrease as order flow toxicity increases. Overall, in my first two essays, I find evidence of beneficial and neutral roles played by HFTs, both in normal and extreme market conditions, but no significant evidence for any of the detrimental impacts they are thought to have. My third essay compares corporate bond trading costs in a market that provides pretrade transparency (the NYSE) with those in a market that is opaque (the OTC market). I find that trading costs are dramatically lower in the market with pretrade transparency, and that pretrade transparency is the most likely explanation for the difference. I also advance a likely explanation for the puzzle of why bond trading costs are lower for larger trades, and introduce a new statistical procedure for assessing trade signing errors in microstructure data with stale quotes.

ESSAYS IN EMPIRICAL MARKET MICROSTRUCTURE by Allen Mario Carrion A dissertation submitted to the faculty of The University of Utah in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Business Administration David Eccles School of Business The University of Utah August 2012 Copyright © Allen Mario Carrion 2012 All Rights Reserved Th e Uni v e r s i t y o f Ut a h Gr a dua t e S cho o l STATEMENT OF DI SSERTATION APPROVAL Th e di s s e r t a t i o n o f Al l en Ma r i o Ca r r i o n h a s be en a ppr o v ed by th e f o l l owi ng s up e r v i s o r y c ommi t t e e memb e r s : Hen dr i k Be s s emb i n de r , Co -Cha i r 4 / 2 6 / 2 0 1 2 D a t e A p p r o v e d Mi c ha e l J . Co o p e r , Co -Cha i r 4 / 2 6 / 2 0 1 2 D a t e A p p r o v e d Mi c ha e l Ha l l i ng , Memb e r 4 / 2 6 / 2 0 1 2 D a t e A p p r o v e d Ra c he l Ha y e s , Memb e r 4 / 2 6 / 2 0 1 2 D a t e A p p r o v e d Kuma r Ven ka t a r ama n , Memb e r 4 / 2 6 / 2 0 1 2 D a t e A p p r o v e d a nd by Wi l l i am He s t e r l y , Cha i r o f t h e Depa r tme n t o f Da v i d Ec c l e s Sc ho o l o f Bus i n e s s a nd by Cha r l e s A. Wi g h t , De a n o f The Gr a d ua t e S c ho o l . ABSTRACT This dissertation is composed of three essays in empirical market microstructure. My first two essays study market quality issues related to High-frequency Trading (HFT) using a dataset provided by NASDAQ that identifies the activity of high-frequency traders (HFTs). My first essay studies the systematic effects of HFT on market quality. I find only small effects of HFT participation on spreads and adverse selection costs, and I find evidence that HFT trades improve price efficiency. I also examine HFT trading strategies, and show that HFTs engage in successful intraday market timing. My second essay studies HFT in extreme market conditions, focusing on whether it has a stabilizing or destabilizing effect. I find that HFTs buy during mini-flash crashes, sell during price spikes, and provide more liquidity than they consume during both types of events. These results suggest HFTs play a stabilizing role during extreme return events, but their net trading volumes are low so these effects are probably small. I also examine returns around large HFT order imbalances, and find only economically small evidence of the price momentum that these imbalances have been hypothesized to cause. Finally, I study HFT activity around sustained market order flow imbalances, termed "toxic order flow" by Easley, Lopez de Prado, and O'Hara (2011), and find that HFT participation levels decrease as order flow toxicity increases. Overall, in my first two essays, I find evidence of beneficial and neutral roles played by HFTs, both in normal and extreme market conditions, but no significant evidence for any of the detrimental impacts they are iv thought to have. My third essay compares corporate bond trading costs in a market that provides pretrade transparency (the NYSE) with those in a market that is opaque (the OTC market). I find that trading costs are dramatically lower in the market with pretrade transparency, and that pretrade transparency is the most likely explanation for the difference. I also advance a likely explanation for the puzzle of why bond trading costs are lower for larger trades, and introduce a new statistical procedure for assessing trade signing errors in microstructure data with stale quotes. I dedicate this dissertation to my family, especially my wife Traci, my children Dean and Natali, my parents Mario and Sally, and my in-laws Ronald and Dana. TABLE OF CONTENTS ABSTRACT ....................................................................................................................... iii ACKNOWLEDGEMENTS ............................................................................................. viii 1. INTRODUCTION .......................................................................................................... 1 2. VERY FAST MONEY: HIGH-FREQUENCY TRADING ON THE NASDAQ.......... 4 2.1 Abstract ..................................................................................................................... 4 2.2 Introduction ............................................................................................................... 5 2.3 Data ......................................................................................................................... 12 2.4 HFT Activity Levels ............................................................................................... 15 2.5 Trading Costs .......................................................................................................... 18 2.6 Market Efficiency ................................................................................................... 29 2.7 Trading Behavior .................................................................................................... 37 2.8 Conclusion .............................................................................................................. 49 2.9 References ............................................................................................................... 51 3. HIGH-FREQUENCY TRADING IN EXTREME MARKET CONDITIONS ............ 77 3.1 Abstract ................................................................................................................... 77 3.2 Introduction ............................................................................................................. 78 3.3 Data ......................................................................................................................... 83 3.4 Mini-flash Crashes and Price Spikes ...................................................................... 87 3.5 Price-destabilizing HFT Order Imbalances ............................................................ 94 3.6 Resiliency ................................................................................................................ 98 3.7 Toxic Order Flow .................................................................................................. 102 3.8 Conclusion ............................................................................................................ 107 3.9 References ............................................................................................................. 108 4. PRETRADE TRANSPARENCY AND CORPORATE BOND TRADING COSTS: EVIDENCE FROM THE NYSE AND OTC MARKETS ............................................. 122 4.1 Abstract ................................................................................................................. 122 4.2 Introduction ........................................................................................................... 123 vii 4.3 Corporate Bond Trading in the NYSE and OTC Markets .................................... 127 4.4 Data Description ................................................................................................... 131 4.5 Methodology ......................................................................................................... 136 4.6 Full Sample Empirical Results ............................................................................. 144 4.7 Dealer Trade Sample Empirical Results ............................................................... 147 4.8 Robustness to Stale Quote Errors ......................................................................... 149 4.9 Conclusions ........................................................................................................... 151 4.10 References ........................................................................................................... 154 ACKNOWLEDGEMENTS I would like to acknowledge the support I have received in researching and writing this dissertation. I am particularly grateful to my co-chairs, Hendrik Bessembinder and Michael Cooper, for their guidance and generosity with their time. I also wish to thank my other committee members, Michael Halling, Kumar Venkataraman, and Rachel Hayes. Others who have provided insightful feedback include Shmuel Baruch, Jonathan Brogaard, Marios Panayides, Nitish Sinha, Jeff Smith, Chris Stanton, and Laura Tuttle. I have also received helpful comments from seminar participants at the University of Utah, Lehigh University, CFTC, FDIC, and SEC and attendees at the 2010 EFA and 2010 MFA conferences. I thank NASDAQ and Frank Hatheway for supplying the HFT data. Finally, I have greatly enjoyed the camaraderie and support of my fellow doctoral students at the University of Utah, especially Madhuparna Kolay. 1. INTRODUCTION This dissertation is composed of three essays in empirical market microstructure. Market microstructure is defined by Hasbrouck as "the study of the trading mechanisms used for financial securities."1 This field deals with issues such as liquidity, pricing efficiency, trading under information asymmetry, trading strategies, and market design. Empirical market microstructure utilizes highly granular market data to reveal insights on these topics, and often involves processing large volumes of individual trades and quotes. My first two essays study issues related to High-frequency Trading (HFT). HFT is a recent development where a small group of market participants has developed a dramatic speed advantage over other traders and participates in a large share of the trading volume. Their effects on the functioning of the markets are controversial and not well understood. I provide new evidence on this issue using a proprietary dataset provided by the NASDAQ that identifies the trades and quotes of high-frequency traders (HFTs). My first essay studies the systematic unconditional effects of HFT on market quality. I find that spreads are slightly wider in trades where HFTs provide liquidity and tighter in trades where they demand liquidity, but the differences are small and liquidity is plentiful in this sample regardless of HFT participation. I find that, contrary to 1 See Joel Hasbrouck, Empirical Market Microstructure, (New York: Oxford University Press, 2007), 3. 2 theoretical predictions, HFTs do not impose high adverse selection costs on other traders when demanding liquidity, and they seem to improve price efficiency when they trade. I also provide evidence regarding HFT trading strategies, showing that HFTs engage in successful intraday market timing but do not seem to trade on cross-sectional return predictability. My second essay studies HFT in extreme market conditions, with a focus on whether it has a stabilizing or destabilizing effect. I find that HFTs buy during mini-flash crashes, sell during price spikes, and provide more liquidity than they consume during both types of events. These results suggest HFTs play a stabilizing role during extreme return events, but their net trading volumes are low so these effects are probably small. I also examine returns around large HFT order imbalances, and find only economically small evidence of the price momentum that these imbalances have been hypothesized to cause. Finally, I study HFT activity around sustained market order flow imbalances, termed "toxic order flow" by Easley, Lopez de Prado, and O'Hara (2011), and find that HFT participation levels decrease as order flow toxicity increases. This finding holds for both liquidity-supplying and liquidity-demanding participation, which is inconsistent with predictions that HFTs increase their liquidity demand at high toxicity levels. Overall, in my first two essays, I find evidence of beneficial and neutral roles played by HFTs, both in normal and extreme market conditions, but no significant evidence for any of the detrimental impacts they are thought to have. My only results that could arguably be considered consistent with negative impacts are findings of decreased participation around some extreme events, but these effects are not dramatic. My third essay compares corporate bond trading costs in a market that provides pretrade transparency (the NYSE) with those in a market that is opaque (the OTC 3 market). I find that trading costs are dramatically lower in the market with pretrade transparency, and that pretrade transparency is the most likely explanation for the difference. I also advance a likely explanation for the puzzle of why bond trading costs are lower for larger trades. An important theme, in both this dissertation and the field of empirical market microstructure in general, is how specific trading arrangements affect market quality from an investor's perspective. This topic is relevant for investors deciding where to trade, for markets designers interested in how best to organize their trading mechanisms to attract traders, and for regulators formulating market rules. In the first two essays, the trading arrangements of interest are the market structure, technology, and regulations that have allowed high-frequency trading to exist and flourish. In the third essay, the trading arrangement of interest is pretrade transparency. Other contributions I make in this dissertation include tests of a variety of academic theories and informal hypotheses advanced by market participants and the financial press, new empirical facts that can guide future theoretical research, and a new statistical procedure for assessing trade signing errors in microstructure data with stale quotes. 2. VERY FAST MONEY: HIGH-FREQUENCY TRADING ON THE NASDAQ 2.1 Abstract I provide large-sample evidence regarding High-frequency Trading (HFT) strategies and market quality, using a proprietary sample of NASDAQ trades and quotes that identifies HFT participation. Spreads are slightly wider for trades where HFTs provide liquidity and slightly tighter when HFTs take liquidity, suggesting that HFTs provide liquidity when it is scarce and consume liquidity when plentiful. Prices incorporate information from order flow and market-wide returns more efficiently on days when HFT participation is high. This effect is driven by HFT demand-side participation, implying that HFTs improve price efficiency when demanding liquidity. I also provide evidence regarding HFT trading strategies, showing that HFTs engage in successful intraday market timing, but do not seem to trade on cross-sectional return predictability at the horizons I study. The new evidence in this paper is relevant to the ongoing HFT-related policy debates and can potentially provide guidance to theoretical researchers seeking to model HFT behavior and market quality impacts. 5 2.2 Introduction High-frequency trading has become a pervasive feature of the equity markets in a relatively short period of time. Estimates of high-frequency trading activity levels vary, but are large. For example, a 2009 article in Advanced Trading estimates that high frequency trading is responsible for 73% of the of U.S. equity trading volume. The developments in market structure (such as decimalization, REG NMS, and automated electronic limit order books) that have created the circumstances for HFT to flourish are relatively recent. Our understanding of the impact of high-frequency trading on market quality is in its infancy, partly due to its sudden emergence and also the scarcity of high quality data. There are diverse views among market participants and regulators on whether HFT is beneficial, neutral, or detrimental. Reflecting this uncertainty, proposals to both restrict and encourage high-frequency trading are simultaneously being debated. In a letter to the SEC, Senator Charles Schumer writes: I have come to believe that HFT provides less of the benefits to our markets than its adherents claim, and does so at a greater cost to long-term investors ... The SEC should identify market participants who frequently engage in these practices, and require exchanges and other trading venues to slow down those market participants [in times of stress] … the Commission should consider imposing a minimum quote duration, so that orders could not be sent and cancelled within a fraction of a second.2 Conversely, the Joint SEC-CFTC Advisory Committee recommends: the Commission should consider encouraging, through incentives or regulation, persons who regularly implement market maker strategies to maintain best buy and sell quotations which are ‘reasonably related to the market' … We recognize that many High Frequency Traders are not even 2 Sen. Schumer's letter available at http://schumer.senate.gov/Newsroom/record_print.cfm?id=327487. 6 broker-dealers and therefore their compliance with quoting requirements would have to be addressed primarily through pricing incentives.3 The differing views regarding the impact of HFT on market quality partly stem from the lack of consensus on the nature of their trading practices. A common view is that they have taken over the market-making function. Under this scenario, they generally benefit the market by increasing competition to provide liquidity, but there are still concerns that they lack the affirmative obligations that bound traditional market makers and could cause disruptions by exiting the market at their discretion. They are also thought to engage in high-frequency arbitrage, which may have the beneficial effect of making prices more efficient. The alternate perspective is that the liquidity they provide is unreliable, and is outweighed by disruptive practices they are alleged to employ such as order spoofing, predatory trading, herding, or overloading market infrastructure with excessive messages. Aside from the views of market participants and regulators, there are theoretical reasons to suspect that HFT may affect market quality. In the classic market microstructure models, the major sources of trading frictions are information asymmetry, inventory risk, and order processing costs. HFTs are likely to differ from the intermediaries they have replaced in all of these dimensions. As pointed out in Jovanovic and Menkveld (2011) and Biais, Foucault, and Moinas (2011), the speed advantage of HFTs could allow them to react more quickly to public news than other traders, which would reduce the adverse selection costs they face when providing liquidity while making limit orders riskier for slower traders. Similarly, Stoll (2000) argues that speed 3 The Joint SEC-CFTC Advisory Committee Report is available at http://www.sec.gov/spotlight/sec-cftcjointcommittee/ 021811-report.pdf 7 differentials play a role in informational frictions, and that increasing the speed parity among traders could reduce spreads under certain conditions. Inventory costs may also play a greater role than in the past. High-frequency traders generally seek to end the day flat. In models such as Garman (1976) and Ho and Stoll (1981), inventory adjustment motives affect liquidity,4 and recent evidence is supportive (see Naik and Yadav 2003, Panayides 2007, Comerton et al. 2010). Several studies have shown evidence of market maker inventory adjustment taking place relatively slowly,5 and if HFTs manage inventory more aggressively, we might expect the effects on liquidity to increase. Order processing costs should be reduced for HFTs because of their large trading volumes. Rebates for adding liquidity are tiered by volume, and their fixed costs will be spread over more transactions. While the classic microstructure literature has implications for HFT, there has also been a recent growth in HFT-specific theoretical literature. Jovanovic and Menkveld (2011) develop a model where the information asymmetry effects can generate either beneficial or negative impacts, and derive the conditions where each outcome is in effect. Biais, Foucault, and Moinas (2011), Cvitanic and Kirilenko (2010), and Jarrow and Protter (2011) present theoretical models where HFTs can play disruptive roles. The mechanisms are overinvestment, adverse selection, and the crowding out of slower traders in Biais, Foucault, and Moinas (2011), order sniping in Cvitanic and Kirilenko (2010), and a type of herding behavior in Jarrow and Protter (2011). 4 To be more precise, inventory affects midquotes, effectively reducing liquidity for trades that increase inventory imbalances while improving liquidity for inventory rebalancing trades. 5 Hasbrouck and Sofianos (1993) find cases where inventory takes long periods to revert to apparent target levels. In a more recent sample, Hendershott and Menkveld (2010) reported inventory half-lives of 0.55- 2.11 days. 8 Despite the emerging theoretical literature and ongoing policy debates concerning HFT, there is little empirical evidence on the market quality impacts and trading behaviors of HFT. The empirical studies include Brogaard (2011, 2012a, 2012b), Menkveld (2012), Jovanovic and Menkveld (2011), Hasbrouck and Saar (2011), and Kirilenko, Kyle, Samadi, and Tuzun (2011) (KKST (2011) hereafter). Of these, KKST (2011) focus on an extreme event (the 2010 Flash Crash6), and Jovanovic and Menkveld (2011) and Menkveld (2012) study a single high-frequency trader, and Brogaard (2012b) focuses on trading strategies instead of market quality effects, leaving only three papers that address the collective effects of HFT in normal market conditions. 7 Brogaard (2011, 2012a) studies a sample of NASDAQ trades and quotes with HFT participation identified by the exchange, and finds that HFT is generally beneficial or benign. Brogaard (2011, 2012a) finds that they provide a large share of the liquidity in the market and play an important role in the price discovery process. Brogaard (2012) finds HFT activity dampens volatility. Hasbrouck and Saar (2011) also study recent NASDAQ data and use the intensity of order placements and cancellations, which they call strategic runs, to identify periods when HFTs are active in a stock. They find that high-frequency trading "lowers short-term volatility, reduces quoted spreads and total price impact of trades, and increases depth in the limit order book" (p. 3). There is a related thread of empirical studies on algorithmic trading (AT). HFT is generally considered a subset of AT, but HFTs and non-HFT AT are very different. 6 The Flash Crash is the popular name for an event that occurred on May 6, 2010, where within a half hour period, the major U.S. equity indexes dropped more than 5% and quickly reversed most of the losses. Volatility in some ETFs and individual stocks was even greater. See KKST (2011). 7 Arguably, Jovanovic and Menkveld (2011) could fall into this category as well. In part of their analysis, they study the introduction of an HFT-friendly trading venue on market quality, but they do not clearly claim that this measures the impact of HFT. 9 Hasbrouck and Saar (2011) explain the distinction clearly. They divide algorithmic traders into agency algorithms and proprietary algorithms. Agency algorithms are "employed to minimize trading costs of buy-side managers" (p. 2). These can be thought of as engaging in activities such as splitting large orders or alternating between providing and taking liquidity with the goal of meeting a longer term trading need while minimizing its price impact. Proprietary algorithmic traders encompass the subset of AT that I am referring to as HFT. They trade their own capital, turn over positions rapidly, have technology and infrastructure to trade at very high speeds (2-3 milliseconds, according to Hasbrouck and Saar 2011), and are reluctant to hold inventory overnight. The AT literature does not study HFT directly, but often touches on related issues or includes HFT in AT samples. The empirical AT studies that address market quality issues include Chaboud, Chiquoine, Hjalmarsson, and Vega (2009), Hendershott and Riordan (2009), and Hendershott, Jones, and Menkveld (2011).8 Chaboud et al. (2009) study algorithmic trading in foreign exchange markets and find that AT trades contribute less to price discovery than human trades in two of the three currencies in their sample, AT limit orders seem to be strategically placed (face less adverse selection costs), AT reduces liquidity provision before the NFP report and increases afterwards, and there is some evidence that AT lowers volatility. Hendershott and Riordan (2009) examine AT in the DAX stocks on the Deutsche Boerse's Xetra platform. They find that ATs are more likely to demand liquidity when it is cheap and supply when it is expensive, and that ATs contribute more to price discovery than human traders. Hendershott, Jones, and Menkveld (2011) examine market quality measures on the NYSE and find that AT 8 There is also a somewhat large AT literature that studies algorithmic trading strategies and trading costs for users of algorithms. 10 improves liquidity for large capitalization stocks, makes quotes more informative, and reduces the adverse selection costs of trades. Chaboud et al. (2009) and Hendershott and Riordan (2009) study data that explicitly identify algorithmic trader participation, while Hendershott, Jones, and Menkveld (2011) uses message traffic as a proxy for AT activity and utilize an infrastructure improvement to establish causality. I contribute to this literature by examining the market quality impacts of HFT and testing several hypotheses regarding HFT behavior in a proprietary sample of NASDAQ trades and quotes that identifies HFT participation. This is the same dataset used in Brogaard (2011, 2012a), but I focus on a different set of questions and market quality dimensions. The market quality tests I conduct suggest that HFTs play a neutral or beneficial role. Trading costs are unconditionally very low, but spreads are slightly wider for trades where HFTs provide liquidity and slightly tighter when HFTs take liquidity, suggesting that HFTs provide liquidity when it is scarce and consume liquidity when plentiful. These results hold whether HFT participation is defined as being on the aggressive side, the passive side, or either, and are robust to controls for stock and trade characteristics and market conditions. To the best of my knowledge, this is the first large sample trading cost analysis performed in data that explicitly identify HFT trades.9 Prices are more efficient on days when HFTs are more active in a given stock, in the sense that it takes less time for stock prices to incorporate information from order flow and market index returns. This result is driven by HFT liquidity-demanding trades. I also provide new evidence on the trading behavior of HFTs. Their trading performance 9 Hasbrouck and Saar (2011) are not able to identify HFT participation in specific trades. Jovanovic and Menkveld (2011) and Menkveld (2010) study a single HFT. Other similar studies examine AT instead of HFT. 11 as measured in a VWAP analysis is consistent with successful intraday market timing, but I find no evidence that their trades predict the cross section of short-term expected returns. These results should be interpreted with some caution. As discussed in more detail below, the sample does not identify the activity of all high-frequency traders, and contains only NASDAQ continuous trading activity in the sample stocks. The sample stocks are traded in multiple venues, and are presumably traded by the sample HFTs in other venues. Also, the NASDAQ exchange is organized as a virtual electronic limit order book with price and time priority, pretrade and posttrade transparency, anonymity, and a maker-taker fee model. It is not clear that any conclusions drawn in this sample will necessarily generalize to markets that are organized differently. These concerns are somewhat mitigated by the facts that the sample contains an economically large amount of trading activity, both in absolute terms and as a share of volume in the sample firms, and the identified HFT firms account for a large share of the observed volume. In addition, although I find only benign or beneficial effects of HFT in this paper, my analysis focuses on their systematic effects and does not rule out the possibility that there are certain circumstances where HFT can have negative impacts. In particular, the data do not distinguish between individual HFTs, so I can only observe their aggregated activity. Therefore, while this is useful in studying their behavior on balance and their overall impact on the market, it is possible that individual HFTs follow disruptive strategies that are hidden by the level of aggregation in the data. Nevertheless, I believe the evidence provided in this paper should advance our understanding of HFT market quality impacts and trading behavior. 12 The rest of this paper is organized as follows. Section 2.3 describes the data. Section 2.4 examines the level of HFT participation in the sample. Section 2.5 studies trading costs and how they vary with HFT participation. Section 2.6 presents price efficiency tests. Section 2.7 analyzes HFT trading behavior and performance. Section 2.8 concludes. 2.3 Data 2.3.1 Overview The primary data source employed is a proprietary dataset provided by NASDAQ consisting of trades and quotes for a sample of 120 stocks. The stock sample was chosen by Terrence Hendershott and Ryan Riordan. See Table 2.1 for a list of sample stocks. It is stratified by market capitalization,10 and is evenly split by NASDAQ and NYSE listing. The sample period covers all of 2008 and 2009 and one week in 2010.11 The trade sample consists of all trades executed on the exchange in continuous trading, excluding crosses and NASDAQ TRF-reported trades. Trades are time stamped to the millisecond and signed to indicate whether they were initiated by a buyer or seller. The trade signs are high quality, and are based on records of rebate payments.12 NASDAQ Inside Quotes (BBOs) are provided for subsamples of the data. These subsamples cover the first full trading week in each quarter, the week of Oct 6-10, 2008 (the week of the Lehman collapse), and the week of Feb 22-26, 2010. The BBO data are time stamped to the millisecond and does not have the problems with timestamp discrepancies that are 10 With 40 large, 40 medium, and 40 small stocks. 11 There is one day, October 10, 2008, missing from the dataset which may become available in the future. 12 Rebate payments are payments made to the liquidity supplier in a maker-taker market. These are partial rebates of the fees collected by the exchange from the trade initiator. 13 present in alternate sources. The only filter applied to the full trade sample was the removal of trades before 9:30 am and after 4:00 pm. A subsample used for trading cost analysis also required a usable quote before and after each trade. For some analyses, additional filters were applied, and specifics are provided in the relevant sections. A unique feature of this dataset is that high-frequency participation is identified in the data. NASDAQ has manually identified 26 high-frequency trading firms and flagged their activity. Specifically, trades contain a field with the following codes: HH, HN, NH, or NN. H identifies a high-frequency trader and N identifies a non-HFT. The first term in a pair classifies the liquidity taker, and the second term classifies the liquidity provider. For example, a trade marked HN would mean a high-frequency trader took liquidity from a non-HFT on that trade. Similarly, HFT quotes are flagged in the limit order book snapshots and a subsample of quotes. The identities of the HFT firms are not provided. The selection process was manual and apparently somewhat subjective. The principles are described in Brogaard (2012a) as follows: The characteristics of firms identified as being HFTs are the following: They engage in proprietary trading… They use sponsored access providers whereby they have access to the co-location services and can obtain large-volume discounts and reduce latency. They tend to switch between long and short net positions several times throughout the day…. Orders by HFT firms are of a shorter time duration than those placed by non-HFT firms. Also, HFT firms normally have a lower ratio of trades per orders placed than non-HFT firms. (p. 7) Brogaard (2012a) and Hasbrouck and Saar (2011) note that the selection process excludes certain types of firms that engage in HFT, such as firms whose primary business is not HFT but sometimes engage in HFT or HFT firms that route trades through a non- HFT firm. This concern is valid but is somewhat mitigated by the large percentage of 14 trading volume that the sample firms participate in, which is described in further detail in Section 2.4. It is also worth repeating that the level of aggregation in the data does not allow individual HFTs to be studied in isolation. I also obtain supplemental data from CRSP and TAQ. I use CRSP data for the sample stock descriptive statistics only. For several tests, I employ midpoint returns, and in some cases, I consider it preferable to use an NBBO midpoint constructed from the TAQ CQ tape instead of the NASDAQ midpoint. The NBBO includes price data from other market centers, and is available on dates when NASDAQ Inside Quotes are not provided. In addition to the larger sample size available with NBBO quotes, my main considerations in choosing a quote source for a particular application are that TAQ quotes are only time stamped to the second, while NASDAQ quotes are timestamped to the millisecond, and whether I am primarily interested in liquidity and prices across all markets or on the exchange where the sample trades occur. I also use TAQ to obtain SPY midpoints to construct a proxy for the market return, and I use trade data from the CT to assess NASDAQ's volume shares in sample stocks.13 2.3.2 Descriptive Statistics Table 2.2 presents trade summary statistics. The second column reports values for the full sample. The full sample covers 509 days and contains 550,118,372 trades for approximately 106 billion shares and a total dollar volume of $3.9 trillion. The daily average share volume in the sample is 208 million shares and the dollar volume is $7.7 billion. There is substantial variation in the daily trading activity. On the 10th percentile 13 SPY is the ticker symbol for an ETF that tracks the S&P 500. 15 day, there is $4.4 billion traded, while on the 90th percentile day, $11.9 billion is traded. The trade size is of particular interest because there is a common perception that trade sizes are much smaller than in the past. They are in fact small in this sample: the average size is 192.3 shares, the median is 100 shares, and the 90th percentile is 400 shares. The third column reports values for the subsample where matching NASDAQ pretrade and posttrade quotes are available. This subsample contains 61,272,712 trades for 11.6 billion shares and $444 billion dollars. By comparing the two columns, we can informally assess whether the quote subsample is reasonably representative. The days with quotes have somewhat more trading activity, but in general appear similar. The subsample covers roughly 10% of the trading days in the full sample, and the aggregate trades, share volume, and dollar volume are around 11% of the full sample values. The daily mean share volume and dollar volume in the subsample are 14% and 18% higher than the full sample means. The trade size distributions are very close. 2.4 HFT Activity Levels In this section, I examine the extent of HFT activity as a share of total dollar trading volume. I construct three measures of the HFT participation share that differ in how each trade is classified as an HFT or non-HFT trade. The first counts trades where an HFT participates on either side of a trade (All), the second only uses trades where an HFT is the liquidity demander (Demand), and the third only uses trades where an HFT is the liquidity supplier (Supply). Trades where HFT are on both sides are counted in all three measures. The denominator is all trading volume in the NASDAQ sample only, 16 which is consistent because the numerator does not include HFT from other trading venues. Brogaard (2012b) performs a similar analysis. This section complements the material in that paper by reporting additional pooling/weighting schemes designed to show time-series and cross-sectional variation, and by introducing a measure of stock-specific time variation in HFT participation that I use as an explanatory variable in several analyses that follow in this paper. Table 2.3 summarizes the main findings. Across the full sample, HFTs participate in 68.3% of all dollar trading volume, demand liquidity in 42.2%, and supply liquidity in 41.2%. From the daily results with trades pooled across all stocks, the mean participation shares are similar and little time variation is evident, with standard deviations ranging from 2.4% to 3.6%. These levels are strikingly high and are of a similar order of magnitude to those reported by Brogaard. The third section of Table 2.3 calculates participation shares by stock-day and reports sample statistics equally weighting across stock-days. This removes the extra weight implicitly given to stock-days with more trades in the previous sections. Here we see much lower mean participation levels (48.3%, 32.5%, and 23.2% for All, Demand, and Supply, respectively), suggesting HFTs are participating more heavily in stock-days with more trading activity. We also see more variability, with standard deviations from 15.4% to 20.5%. A natural question is whether the variability in HFT participation across stock-days is determined by temporary market conditions and or by persistent stock characteristics. To gain some insight into this question, the fourth section of Table 2.3 first takes the means of the daily participation shares for each stock, and then reports summary statistics across stocks. This analysis shows that there is substantial variation in 17 long-run mean HFT participation across stocks. For example, the 90th percentile stock has a mean daily HFT (All) share of 72.6%, while the 10th percentile stock has a share of 25.1%. This is consistent with an analysis of HFT participation by stock-day in Brogaard (2012b), which finds that some persistent stock characteristics such as market capitalization and market-to-book are determinants of HFT activity. For some of the tests I wish to conduct later, I will need to identify days with high HFT intensity. In light of the observations above, a stock-specific measure that controls for the normal level of HFT activity in that stock is desirable. For each of the three types of HFT participation, I construct indicator variables that take a value of 1 for each stock-day where the dollar volume participation share is in the highest tercile for that stock across all sample days and 0 otherwise. The choice of terciles is somewhat arbitrary, but seems to be a reasonable tradeoff between sample size and extremity. Before using the HFT participation indicator variables, I address three potential concerns regarding their suitability. First, they must capture sufficient time variation in HFT activity within a given stock. Hasbrouck and Saar (2011) show that stock-specific HFT quoting intensity varies greatly over short intervals, but it is necessary to verify that this time variation is also present in trading activity and is not dampened at the daily horizon. The last section of Table 2.3 reports summary statistics on the differences between the dollar volume HFT participation levels on days when the indicator variable is 1 (high participation days) and other days (normal participation days). The mean differences are 16.6%, 16.1%, and 12.5% for All, Demand, and Supply, respectively, and their 10th percentile values are 9.4%, 10.9%, and 8.2%. Second, given the growth in HFT over time, it is possible that these variables are proxies for time trends, and any 18 effects they capture could be attributable to time trends in market quality unrelated to HFT. To investigate this, on each day in the sample, I count the number of stocks where each of these variables show high HFT participation levels. These counts are plotted over time in Figure 2.1. Given that the indicator variables take the value of 1 in each stock's high-participation tercile, if these variables only captured a trend, we would expect to see no stocks experiencing high-HFT days in the first two-thirds of the sample and all 120 stocks with high-HFT days in the last one-third of the sample (with some noise). This is not the case. Figure 2.1 does show some signs of a trend but with strong time variability from day to day. A third concern is that HFT liquidity demand and supply may be highly correlated, and using all three variables would be redundant. Visually, there appears to be some correlation, but also periods with significant divergences. The correlation coefficients confirm that there is high correlation but also independent information. The correlation between the daily demand and supply indicator variable counts is .203, and the mean stock-specific correlation between the daily raw dollar volume shares is .147, with a 10th percentile value of -.068 of and a 90th percentile value of .385. Overall, it seems reasonable to use these indicators in further analyses. 2.5 Trading Costs 2.5.1 Methodology In this section, I compare the trading costs between trades with HFT participation to those without. The primary metrics I use are effective spreads, price impacts, and realized spreads. I also report quoted spreads but, because they are conditional on a trade occurring, in this context, they are more useful in understanding when HFTs trade than as 19 an actual measure of trading costs. All spreads are measured as percentages of the midpoint price prior to the trade, and I follow the convention of reporting half spreads to reflect one-way rather than round trip costs. For this analysis, I use the subsample of trades where both pre- and posttrade quotes are available. I also convert spreads to total dollar costs for selected cases. Effective spreads measure the difference between a trade's execution price and the pretrade midpoint. Effective spreads compensate liquidity providers for adverse selection costs when trading with informed traders (as in Glosten and Milgrom 1985) and are expected to contain a residual component that covers inventory risk, order processing costs, and market maker rents. An established empirical decomposition method separates the effective spreads into the price impact (adverse selection component) and realized spread (residual component). See Huang and Stoll (1996) and Bessembinder and Kaufman (1997a, 1997b) for a discussion of this methodology and examples of its implementation. The following formulas are used on every trade where quotes are available: (2.1) Effective Spread = 100Q(P - M0)/ M0 (2.2) Price Impact = 100Q(MT - M0)/ M0 (2.3) Realized Spread = 100Q(P - MT)/ M0 = Effective Spread - Price Impact where Q is a trade sign indicator variable equal to 1 for buys and -1 for sells, P is the trade price, M0 is the pretrade quote midpoint, and MT is midpoint T minutes after the trade. Reported decompositions are computed with T set to 1-minute, and untabulated 20 robustness tests use 5-minutes and 30-minutes. The last midpoint of the regular trading hours is used when trades are within T minutes of the close. Aside from the traditional interpretations of this decomposition, there are additional reasons why it is of particular interest when combined with the HFT identification. If HFTs systematically profit from naïve market-making, we should observe high realized spreads on their liquidity-providing trades. Otherwise, if HFTs profit from these trades, it must be through some other mechanism, such as rebates or superior exit timing (i.e., beating the 1-minute benchmark used in the decomposition). If the realized spreads on these trades are much higher than on those where others provide liquidity, this suggests that HFTs have skill in choosing when to offer liquidity to the market. When taking liquidity, if HFTs are trading on information, we should observe high price impacts, while if they are simply re-balancing, we should not. To compare trading costs in trades with HFT participation to those without, I regress these measures of trading costs on indicator variables that capture whether a HFT participated in a trade and control for stock and trade characteristics and market conditions. The regressions are variations on two models. In the first set of regressions, the effect of HFT participation is constrained to be constant across all trade types. The following specification is used: (2.4) SPREADitn = αit + β1 HFT + β2j SIZEj + β3 BUY + β4 SELL + ε where i indexes stocks, t indexes day-half hour intervals, n indexes trades, and j indexes trade size groups. SPREAD is either an effective spread or price impact. HFT is an 21 indicator variable equal to 1 if a trade had HFT participation and 0 otherwise. Different versions of the model define HFT participation by trade side (liquidity-demanding or supplying). I include fixed-effects intercepts for every stock-day-half hour to control for stock characteristics and market conditions. Trade size groups are defined as SMALL (< 500 shares), MEDIUM (>=500 shares, < 1000 shares), and LARGE (> 1000 shares). BUY and SELL indicate which side of the trade took liquidity. SMALL and SELL are dropped from the estimation, so in these cases, the fixed-effects intercepts capture the trading costs for small sells, and the coefficients on the other indicator variables must be interpreted as spread differences from small sells. The second set of models allows the effects of HFT participation to vary with trade characteristics: (2.5) SPREADitn = αit + β1j (HFT x SIZEj) + β2 (HFT x BUY) + β3 (HFT x SELL) + ε where the variable definitions are identical to the constrained version. Again, SMALL and SELL are dropped from the estimation. I also estimate variations of the constrained model one day at a time and one stock at a time to examine how these relationships vary over time and across stocks. 2.5.2 Results Means and medians of the spread and price impacts are reported in Table 2.4. These are tabulated for the full sample and for all counterparty type combinations in the data. For the full sample, mean effective spreads are 2.7 bps, mean price impacts are 3.9 22 bps, and realized spreads are -0.9 bps. These trading cost measures are strikingly low compared to historical estimates. For example, Bessembinder (2003) finds mean effective spreads of 28.9 bps and realized spreads of 17.2 bps in his postdecimalization NASDAQ sample.14 Many other studies have noted reductions in trading costs over time (see Angel, Harris, and Spatt 2010, and Chordia, Roll, and Subrahmanyam 2008, 2011), so the low costs in this sample are not entirely unexpected. It is surprising, however, that mean realized spreads are negative for the full sample and all counterparty combinations, and medians are negative in the full sample and negative or zero for all counterparty categories. This observation holds in robustness tests using both 5-minute and 30-minute realized spreads. This means that effective spreads do not fully compensate the liquidity provider for adverse selection costs. It does not necessarily mean that liquidity providers lose money to informed traders on average, because the absolute values are small and at least partially offset by liquidity rebates. It is also possible that some liquidity providers are able to beat the 1-minute posttrade benchmarks built into these measures, which I explore in Section 2.7.1. Nevertheless, it does mean the compensation for liquidity provision is very low based on these widely-used measures. I am not aware of any prior study showing negative realized spreads in any market. I offer two possible explanations. First, it is possible that increased competition between liquidity providers has driven compensation for liquidity provision down to a level close to the liquidity rebate. Second, it is possible that disintermediation has increased to a degree where a large proportion of the trades we observe are now between traders seeking liquidity with varying degrees of patience, as opposed to trades between an impatient liquidity 14 Originally reported as round trip spreads, converted to half spreads here to facilitate comparison with my results. 23 demander and a professional liquidity provider. This does not rule out the low or negative realized spreads we observe in the NH and HH categories, because if HFTs expect some small profit from a trade, they may be willing to quote aggressively to compete with patient liquidity demanders. However, these are only conjectures that I am not able to test in these data. In all of the trading costs measures in Table 2.4, we do see some variation across the HFT participation categories, but it is generally small. Across all measures and categories, the largest difference is 1.6 bps when comparing median realized spreads between HH trades and NH or NN trades. Differences in means and medians may mask important differences that would emerge when controlling for other factors that influence trading costs, however, so I consider the regression results below to be more informative. Table 2.5 reports the results from the regressions constraining the effect of HFT participation to be constant. In Panel A, the dependent variable is the effective spread. Models 1 and 2 define the HFT participation indicator based on the liquidity demander, and Models 3 and 4 use the liquidity provider. Models 1 and 3 include only the HFT participation indicator and stock and day-half hour fixed effects, while Models 2 and 4 include the trade size and sign controls. The controls add very little explanatory power beyond the fixed effects. The coefficient estimates show that effective spreads are 0.7 bps lower on trades where an HFT demands liquidity and 0.3 bps higher on trades where an HFT supplies liquidity. This suggests that HFTs provide liquidity when it is scarce and consume liquidity when plentiful. In Panel B, the dependent variable is 1-minute price impact, and the regression models are otherwise identical to those in Panel A. The coefficient estimates in Panel B show that 1-minute price impacts are 0.1 bps higher on 24 trades where an HFT demands liquidity, and 0.1 bps lower on trades where an HFT supplies liquidity. All estimates on the HFT indicator variables are significant at the 1% level. Table 2.6 reports regressions that interact the HFT participation indicators with trade characteristics to determine if the impact of HFT participation varies across trade types. In Panel A, the dependent variables are effective spreads. In Model 1, the impact of HFT demand participation is statistically smaller (less negative) for medium and large trades than for small trades, but the differences are only 0.1 bps. In Model 3, the impact of HFT supply is also smaller for medium trades and is roughly cancelled out for large trades. In Models 2 and 4, the differences in impact across buys and sells are statistically significant but are only 0.1 bps or less. In Panel B, the dependent variables are 1-minute price impacts. Here we observe more variation with characteristics, but magnitudes of the differences are still small. From Model 1, the price impacts of liquidity-demanding HFT trades of all sizes are 0.1 bps higher than similar non-HFT trades. From Model 2, the price impact of HFT liquidity-demanding sell trades is 0.1 bps higher than similar trades, and for buy trades, there is almost no effect. From Model 3, the price impacts of small trades where HFTs provide liquidity are almost indistinguishable from similar trades, while they are 0.4 bps lower for medium trades and 0.8 bps lower for large trades. From Model 4, for sell trades where HFTs provide liquidity, the price impacts are 0.2 bps lower than those of similar trades, while for buy trades, the price impacts are about the same as for similar trades. Overall, the estimated impacts of their trades on effective spread and price impacts statistically vary with characteristics, but are unconditionally small and do not become dramatically large for any particular category I have examined. 25 The strongest stylized fact from this analysis is that HFTs avoid more informed larger trades. Figures 2.2 and 2.3 show how the effects of HFT on effective spreads and 1- minute price impacts vary over time and across stocks. These are plots of the coefficients on the HFT indicator variable in Equation (2.4) with all controls, estimated one day at a time or one stock at a time. From the effective spread coefficient plots in Figure 2.2 Panel A and C, we see the coefficients do vary over time, but within an economically small range. For example, in Panel A, we see the lowest value for HFT_demand is -1.5 bps, and the highest is -0.2 bps. Panels B and D show how the coefficients vary by stock, with stocks sorted by their coefficient values. These show little variation except in the tails, and by inspection, the tails tend to hold small stocks. The graphs for price impact shown in Figure 2.3 are similar, with economically small time variation in price impacts over time, and little variation across stocks except for the tails. It is also of interest to compare the price impact regression estimates with the price discovery analysis in Brogaard (2011). Brogaard finds that when demanding liquidity, HFT trades bring information into the market, and when supplying liquidity they avoid trading with informed traders. The regression models employed in this paper provide an alternate perspective on these questions. These models test whether the price impacts of trades with HFT participation are significantly different from price impacts of other trades, after controlling for other factors described previously. The results in Table 2.5 Panel B Models 1 and 2 show that trades where HFTs demand liquidity do have very slightly higher price impacts than trades where they do not. The results in Models 3 and 4 show that trades where HFTs supply liquidity have slightly lower price impacts. The 26 results in Table 2.6 Panel B suggest that these conclusions are somewhat trade-characteristic dependent, however. For example, from Panel B Model 3, we see that when HFTs supply liquidity in medium and large trades, the price impact is 0.4 - 0.8 bps lower than predicted by fixed effects and trade characteristics, but for small trades, the model predicts no difference between HFT and non-HFT trades. It is worth noting that these differences are all small, and small trades are more prevalent so the small trade differences probably deserve the most weight. I interpret these results as weakly supportive of the conclusion that HFT liquidity-demanding trades are more informed, but they suggest that the conclusion HFTs avoid providing liquidity to informed traders is not robust across methodologies. It is also useful to convert some of the spread measures presented above to total dollar costs to estimate how much HFTs earned or paid in spreads on their NASDAQ trades. I report values for the 49-day subsample where sufficient data are available for this analysis. In this sample, the total dollar volume traded is $443,996 million. The total dollar effective spread paid to complete these trades amounted to $98 million.15 The total dollar effective spread earned by HFTs is $42 million, and the total dollar effective spread paid by HFTs is $34 million, for a net dollar effective spread earned by HFTs of $8 million.16 The total effective spreads paid by non-HFT liquidity demanders is $64 million, and the total earned by non-HFT liquidity suppliers is $56 million, for a net dollar effective spread paid by non-HFTs of $8 million. In addition to dollar effective 15 Total dollar effective spreads are calculated as Q(P-M0) x share volume for each trade, and summed over all trades in the category of interest. Total dollar price impacts are calculated analogously. 16 The total paid in effective spreads by HFTs is the sum over trade categories HH and HN. The total earned is the sum over trade categories HH and NH. The other total dollar spread calculations in this section follow the same pattern. 27 spreads, it is of particular interest to examine dollar price impacts because one of the detrimental impacts of HFTs predicted by the theoretical literature is high adverse selection costs imposed by HFTs on non-HFTs when demanding liquidity. The total dollar price impact imposed on liquidity providers over all trades is $135 million, of which $53 million is borne by HFTs, and $82 million is borne by non-HFTs. Of the $82 million borne by non-HFTs, $48 million is imposed by other non-HFTs and $34 million is imposed by HFTs. HFTs impose a total dollar price impact of $54 million on other traders when demanding liquidity (the $34 million on non-HFTs and another $20 million on HFT counterparties), only slightly more than what they bear when providing liquidity. Using Model 4 in Panel B of Table 2.4 to estimate the effect of HFT on price impacts, without HFT demand participation, non-HFT liquidity suppliers would be projected to face only $1 million less in price impact, for a total of $81 million. Taken together, these calculations suggest that HFTs earn about $9 million in realized spreads in this sample, or $47.5 million annualized across the 120 sample stocks. It is noteworthy that this is much less than the total HFT profits estimated in Brogaard (2012b), suggesting that HFTs derive a significant part of their income from sources other than the spread.17 I interpret the total dollar price impact estimates as confirming the initial observations that the price impact effects of HFT are economically small, and as suggesting that concerns regarding excessive adverse selection costs imposed by HFTs on non-HFTs are probably overblown. 17 Brogaard (2012b) estimates total daily HFT profits of $298,000 in this dataset, which would annualize to $75 million. Brogaard does not require quote data for the total HFT profit calculations, so this estimate is based on a larger sample than mine. 28 Overall, the results from the regressions confirm the initial observations from the summary statistics. HFT participation explains statistically significant differences in trading cost measures, but these differences are economically small. These results must be interpreted with some caution, however. We cannot assign causality to HFT for the small differences in trading costs I report. First, it is possible that causality runs in the opposite direction. It is likely that HFTs condition their trading behavior on expected trading costs. Second, even if HFTs do not participate in a given trade, their presence in the market could still affect the cost of that trade through competition or adverse selection. In the model of Jovanovic and Menkveld (2011), the "presence in the wings" (p. 28) of an HFT can change the behavior of other market participants. Despite this qualification, it is still informative to observe that the market does not deteriorate or improve drastically on average for trades with any combination of counterparties. In particular, the adverse selection costs imposed by HFT on slower traders in the models of Jovanovic and Menkveld (2011) and Biais, Foucault, and Moinas (2011) are empirically not much higher than those imposed by other slow traders. These results also suggest that the trading cost reductions during bursts of HFT activity found by Hasbrouck and Saar (2011) may not be simply explained by more trades being executed with HFT counterparties during these bursts. The results of this analysis may help inform the debate about affirmative obligations for HFT liquidity provision. It appears that there is little compensation for unsophisticated liquidity provision in this market, and it may not be sufficient to induce HFTs to provide liquidity without being selective in which trades they take and in which market conditions they will operate. 29 2.6 Market Efficiency Pricing efficiency is widely considered to be an important dimension of market quality. Fama (1970) describes an efficient market as one where "security prices at any time ‘fully reflect' all available information" (p. 383). Chordia, Roll, and Subrahmanyam (2008) (CRS (2008) hereafter) note that the empirical literature has shown that intraday inefficiencies can exist in markets that are efficient at longer horizons, because it takes investors time to process and react to information. They further state that "the determinants of this short horizon predictability deserve a thorough investigation by finance scholars" (p. 249). It is an open question whether high-frequency trading makes prices more efficient. Theory provides little direct guidance. There is no consensus on how to describe HFT behavior, so it is not clear whether they should be modeled as discretionary market makers, arbitrageurs, predators, or some combination. The HFT-specific models such as Jovanovic and Menkveld (2011) and Jarrow and Protter (2011) describe a variety of mechanisms that could make prices more or less efficient. Empirically, Brogaard (2011) finds that HFTs are an important part of the price discovery process, but this is not equivalent to showing that their activity makes prices more efficient and no direct efficiency tests on the time series of prices were performed. Also, Brogaard (2012a) and Hasbrouck and Saar (2011) find evidence that HFT reduces volatility, which is often informally considered an inverse measure of efficiency. However, total volatility is composed of fundamental volatility and excess volatility. While reducing excess volatility makes prices more efficient, these studies only deal with total volatility. 30 Finally, Hasbrouck and Saar (2011) find that HFT increases liquidity and CRS (2008) find that liquidity improves market efficiency. In this section, I will further investigate this question by comparing the results of direct tests of price efficiency during days with high HFT activity to normal days. A common type of efficiency test measures whether prices are efficient with respect to a specific information set, and I use lagged order imbalances and market returns in this role. 2.6.1 Methodology First, I apply tests loosely inspired by Chordia, Roll, and Subrahmanyam (2005) (CRS (2005) hereafter) and CRS (2008) to examine the incorporation of information from lagged order flows.18 These tests exploit the concept that efficient prices will follow a random walk, and ex-ante conditioning information will not have explanatory power for future returns. CRS (2005) show that order flow imbalances in individual stocks from one period can predict returns in the next period over some short horizons. CRS (2008) show that the predictive value of lagged order flow imbalance increases on days when liquidity is low, and presents a test specification that I adapt to test the effects of HFT on efficiency. The basic form of the model I use is: (2.6) Rt = α + β1OIBt-1 + β2(OIBt-1 x HFT) + β3MKTt + ε 18 This efficiency test is also used in Chung and Hrazdil (2010a, 2010b). 31 where Rt is the midpoint return calculated from TAQ midpoints, OIBt-1 is the lagged order imbalance, HFT is an indicator variable that identifies high-HFT participation days, and MKT is the SPY S&P 500 ETF midpoint return calculated from TAQ. I use midpoint returns instead of trade returns because predictability in transaction prices due to bid-ask bounce is not generally considered evidence of informational inefficiency. The HFT indicator in my model replaces the illiquid day indicator variable in CRS (2008), and is defined and discussed in Section 2.4. In different versions of this test, HFT participation is alternately calculated using all HFT trades, liquidity-demanding trades only, or liquidity supplying trades only. Following CRS (2008), I use 5-minute intervals to measure returns and order imbalances. I also use 1-minute intervals because CRS (2008) show that the 5-minute horizon predictability has diminished over time, and because HFT effects may be more pronounced at shorter horizons. OIB is defined as (Buyer Initiated Dollar Volume - Seller Initiated Dollar Volume) / Total Dollar Volume. OIB is measured over the same interval length as returns. MKTt is included to reduce the correlation in the residuals across stocks. The regression is estimated one stock at a time, and the time series coefficients are averaged across stocks in a reverse of the Fama- MacBeth procedure. T-statistics are corrected for correlation in the regression residuals across stocks using the method in CRS (2008). This method adjusts the measured standard errors upwards by [1+ (N - 1)ρ]1/2, where N is the number of individual regressions and is the mean pair-wise correlation across the residuals. If the relationship found in CRS (2005, 2008) holds in this sample, β1 will be positive. If the market is more efficient when HFT activity is high, then the sum of β1 and β2 will be lower in absolute value than β1, regardless of whether the CRS finding of a positive β1 holds. 32 I employ a second set of efficiency tests using the price delay measures from Hou and Moskowitz (2005). While the CRS tests measure the incorporation of information in past order flow, price delay measures the incorporation of information from market index returns. There are at least two reasons to suspect HFT may affect the incorporation of index return information into individual stock prices. First, index returns are a plausible input variable to HFT strategies and index arbitrage is frequently mentioned in informal descriptions of suspected HFT behavior. Second, Jovanovic and Menkveld (2011) find that HFT activity is positively correlated to the explanatory power of the market index for a stock's returns. They attribute this effect to increased HFT activity when hard information has more value, but causality could run the other way as well. Hou and Moskowitz (2005) refine procedures used earlier by Brennan, Jegadeesh, and Swaminathan (1993) and Mech (1993). While Hou and Moskowitz (2005) use price delay based on weekly data as a stock characteristic in asset pricing tests, I calculate price delay with 1-minute and 5-minute midpoint returns and employ it as an efficiency measure. To measure price delay, I first estimate the regressions: (2.7) Rt = α + β1MKTt + δ1MKTt-1 + δ 2MKTt-2 … + δ 6MKTt-6 + ε (2.8) Rt = α + β1MKTt + ε where returns are defined as in Equation (2.6), and six lags of MKT are used. As in the order flow imbalance tests, I use both 5-minute and 1-minute intervals. These regressions are estimated one stock at a time, separately for high-HFT participation days and normal days. I refer to Equation (2.7) as the unrestricted model and Equation (2.8) as 33 the restricted model. Then for each stock, I calculate the following price delay measures, separately on high-HFT participation days and normal days: (2.9) D1 = 1 - (R2 rest/R2 unrest) (2.10) D2 = (δ1 + 2 δ2 + 3 δ3 … + 6 δ6)/ (β1 + δ1 + 2 δ2 + 3 δ3 … + 6 δ6) (2.11) D3 = ( T(δ1) + 2 T(δ2 )+ … + 6T(δ6))/ (T(β1) + T(δ1) + 2 T(δ2) … + 6T(δ6)) where R2 rest is the R2 from Equation (2.8), R2 unrest is R2 the from Equation (2.7), T(.) is the t-statistic on the coefficient in Equation (2.7), and other terms are as defined in Equation (2.7). D1 is based on the procedure in Mech (1993) and can be interpreted as the additional explanatory power from the lagged returns as proportion of the total explanatory power of the unrestricted regression. Coefficient ratios similar to D2 and D3 were used in Brennan, Jegadeesh, and Swaminathan (1993), but the weightings were introduced by Hou and Moskowitz (2005). D2 gives more weight to coefficients on more distant lags of the market return. D3 is similar to D2 but gives more weight to coefficients that are estimated more precisely. Higher values of price delay reflect slower adjustment. For each stock, I calculate each price delay measure separately for high HFT days and normal days, defined as in the order imbalance tests above. Then within each stock, I subtract price delay measures on high HFT days from normal days, and average these differences across stocks. If stock prices incorporate market-wide information more efficiently on days when HFT activity is high, then price delay should be lower on these days and the mean differences will be negative. When testing whether the mean differences are significantly 34 different from zero, it is not clear that the differences can be considered independent observations. The inputs to the price delay measures are coefficients estimated from regressions on returns in the same sample period. For each stock, two regressions are run in separate subsamples, with different days entering the subsamples for each stock based on stock-specific HFT activity. If there are market-wide mechanisms that cause simultaneous price delays across multiple stocks, there will be some cross-sectional dependence in the differences because there is correlation between high-HFT days across stocks. To correct for this, I use the same standard error adjustment as in the order imbalance tests calculated from residuals on the unrestricted regression estimated over the full sample (not divided by HFT participation category). I believe this is a conservative approach because the sample splitting procedure should reduce the dependence relative to that in the order imbalance tests. I am not aware of any prior studies that address this issue. 2.6.2 Results The results from the order flow imbalance tests are shown in Table 2.7. The mean coefficients on lagged order imbalance are positive and significant in all models except for the specification using 5-minute returns and liquidity-supplying HFT participation, where it is still positive and marginally significant. The number of stocks with positive and significant coefficients on lagged order imbalance in the individual regressions is higher than the number of stocks with negative significant coefficients, and often much higher. This is consistent with the findings in CRS (2008) for most of their models and subsamples. For both 5-minute and 1-minute returns, the explanatory power 35 of lagged order imbalance is reduced on high-HFT days when HFT activity is defined using all HFT participation or liquidity-demanding HFT participation. As an illustration, consider the 5-minute returns with all HFT participation. The mean coefficient on lagged order imbalance is 0.0960. The mean coefficient on lagged order imbalance interacted with the HFT indicator is -0.0704. This means on high-HFT days, the predicted effect of lagged order imbalance is .0255 (0.0960 - .0704) compared to 0.0960 on normal HFT days, and the t-statistic of -2.69 on the coefficient on the interaction term is the test against the null that the difference in lagged OIB effect between the high and normal days is 0. There are 37 (out of 120) individual stock interaction coefficients that are significantly negative, while only are 2 significantly positive. The results for all specifications using all HFT participation or HFT liquidity-demanding participation are qualitatively similar, but are stronger for liquidity-demanding participation and with 5- minute returns. For example, the predictive power of order flow is reduced by roughly 20% on high-HFT demand days for 1-minute intervals, but it is almost completely removed for 5-minute intervals. In both specifications using HFT liquidity-supplying participation, the mean interaction terms are not significantly different from 0 and there is no strong pattern in individual coefficients. The results from the price delay tests are shown in Table 2.8. Price delay is lower on high-all HFT participation days and high-HFT demand participation days in all specifications, and the effects using HFT supply participation days are weaker. This pattern is similar to the lagged order flow test results. For all participation and demand participation, the price delay difference point estimates are all negative and significant using raw t-statistics. Using the conservative t-statistics adjustment described above, the 36 5-minute differences all become insignificant. 1-minute differences are significant at the 10% level for D1 with HFT participation defined using all trades and are insignificant using HFT demand trades. For D2, the differences remain statistically significant at the 5% level in both specifications. For D3, the difference is significant at the 10% level using all HFT participation and significant at the 5% level using HFT demand participation. With participation defined using HFT liquidity supply, D2 and D3 differences are significantly negative at 5-minute horizons before the adjustment, and none are significant after. Differences are insignificant in other specifications before the adjustment and the point estimates are of mixed signs. Overall, these results suggest prices are more efficient when HFT activity is high. Prices tend to reflect more of the information in past order flows and past market returns on high-HFT activity days, and the effect is stronger when they are demanding liquidity. Based on the evidence presented here alone, we cannot conclude that HFT activity causes market efficiency increases, only that there is a positive correlation. However, if HFTs possess comparative advantages in profitably exploiting pricing inefficiencies, it seems unlikely that HFTs choose to trade more and demand liquidity more when the market is more efficient. Also, the fact that the improvements in measured efficiency are observed primarily when HFT demand is high is relevant to a claim made in CRS (2008). They conjecture that the short-term predictive power of order imbalances is due to the limited ability of market makers to absorb the imbalances without causing price pressure. They argue that liquidity improves efficiency in this setting because arbitrage traders are more likely to trade on this predictability when liquidity is high, and they do so by submitting market orders or marketable limit orders. My results are consistent with a version of this 37 story where HFTs play the role of arbitrageur, and inconsistent with a version where HFTs are enhancing efficiency by improving liquidity. It is also informative to interpret these results in the context of the finding in Brogaard (2012b) that HFTs tend to trade in the same direction as past order flow. The predictive relationship, when present, is that buying pressure in one interval predicts positive returns in the next and vice-versa. If HFT trading weakens this relationship, this would suggest that HFTs either trade with the contemporaneous order flow, against the lagged order flow, or both. Brogaard's results are inconsistent with the second mechanism and do not address the first. However, Brogaard studies order flow at shorter intervals so this result is not directly comparable. Price delay reductions on high-HFT days are generally larger at 1-minute horizons than at 5-minute horizons, and this is different from what we observed in the lagged order flow tests. This could be interpreted as supporting the conjecture in Jovanovic and Menkveld (2011) that HFTs trade more aggressively on hard information, as it is easier to envision updating a stock's fair value after observing an index return than after an order flow imbalance. 2.7 Trading Behavior 2.7.1 Timing The trading costs reported in Section 2.5 can, with some assumptions, be interpreted as trading profits earned by HFT. This is somewhat intuitive, and a related analysis is performed in Menkveld (2012). From Table 2.4, using the 5-minute decomposition, we could estimate that HFTs on average lose 0.3 bps per trade when providing liquidity to non-HFTs, and earn 1.0 bps per trade when demanding liquidity 38 from non-HFTs (before rebates and fees).19 Two of the required assumptions for this calculation may be incorrect in this application, however. First, we only observe a subset of HFT trades in the sample stocks. We miss trades that occur in crosses or in other trading venues. While the working assumption is that HFTs end the day flat or close to it, inspection of the data shows that the trades in the sample often add up to substantial apparent positions at the end of the day. It is not possible to tell if these positions were offset out of view or are actual overnight positions. And if they were offset, it is difficult to estimate at what price. The offsetting trades could have been done at the opening cross, the closing cross, or any price traded in sufficient size on any other trading venue. The second assumption is that positions are exited at the 5-minute (or 30-minute in the alternate decomposition) posttrade benchmark on average. These are useful benchmarks from a market quality perspective, but we do not expect that HFTs typically offset their positions mechanically after a fixed interval. If HFTs have trading skills that allow them to strategically time the reversal of their positions, then realized spreads would understate their profits. I attempt to determine whether HFTs have trade timing skills for two main reasons. First, the estimates from the realized spreads are very small and suggest that HFTs are willing to trade for miniscule profits. If they are in fact doing this, they are providing liquidity for little compensation beyond the rebate and bringing very granular information into prices when they take liquidity. If they are instead trading based on superior price forecasts, these interpretations would be an overly optimistic description of their trading behavior and the apparent liquidity they provide could be overstated. Under 19 These approximations ignore the fact that price impact is not incurred on exits. 39 that scenario, the liquidity provided by HFT in the sample trades was only available to counterparties trading against their price forecasts, and was not offered because they perceived the measured spreads to be an adequate incentive to provide liquidity. This distinction has implications for the affirmative obligation proposals. If their profits did not really come from very small per-trade amounts scaled over very large volumes, would HFTs be economically viable if they were forced to trade less selectively? Second, little is known about the intraday predictability of stock prices. Analogous to the search for signs of longer horizon predictability in the asset manager performance literature, HFT trading performance and behavior is a natural setting to search for signs of short-term predictability. In this section, I attempt to shed light on this question by measuring their trading performance using VWAP (Volume-Weighted Average Price) analysis. 20 By comparing the VWAPs of their buys and sells against the day's VWAP and each other, I can measure the performance of the trades in this sample against a useful benchmark without making any assumptions about the prices or times of the unobserved trades. When subtracting the VWAP of HFT buys from HFT sales, this provides an intuitive measure of their trading performance over a day and is unaffected by their impact on the market VWAP. I also calculate these separately for liquidity-demanding and liquidity-providing trades. This approach is related to the floor trader performance measure from Manaster and Mann (1996) and the traded spread from Stoll (2000). The results of this analysis are presented in Table 2.9. All VWAP differences are signed so a positive number indicates positive trading performance (i.e., market VWAP - 20 See Berkowitz, Logue, and Noser (1988). 40 HFT buy VWAP will be positive if HFTs buy below the market VWAP). The basic VWAP calculations and each difference calculation are performed daily for each stock and summarized across stock-days, sample days, and stocks. Panel A reports summary statistics averaged across all stock-days. The mean of the difference between HFT sell VWAP and HFT buy VWAP is 6.5 bps. Positive skewness is evident, as the median difference is only 2.3 bps. Buys and sells contribute about equally (3.3 bps below market VWAP and 3.2 bps above market VWAP, respectively). This performance is driven by liquidity-providing trades. For liquidity-providing HFT trades, the mean sell VWAP - buy VWAP difference is 12.8 bps, while it is only 2.3 bps for liquidity-demanding trades. The VWAP differences relate to performance on round trips, while the performance implied by realized (half) spreads mentioned above is for a one-way transaction. A comparison with the realized spreads doubled suggests that realized spreads understate HFT trading performance for liquidity-demanding trades somewhat and understate their performance when providing liquidity dramatically.21 Note that this comparison is not entirely clean because it is based on different samples, as I compute realized spreads only on days where quotes are available and VWAP measures for all sample days, and there are also weighting differences.22 In Panel B, the VWAP differences for each stock are averaged over each sample day, and the resulting daily values are then averaged to produce a time series of daily measures. The standard deviation and skewness observed in Panel A decrease, which is 21 The difference is more dramatic when correcting for 1-way price impacts. Assuming no-timing ability, using effective spreads from Table 4 and considering price impacts on entries but not on exits, implied Sell VWAP - VWAP Buy differences are 2.5 bps for liquidity-providing round trip trades and -1.1 bps for liquidity-demanding round trip trades. 22 A possible next step is to analyze a subsample of VWAP differences on days where there are quotes available, and use benchmarks based on volume-weighted mean spreads calculated by stock day to correct the weighting issues. 41 not surprising because I am essentially creating an equal-weighted portfolio of all the sample stocks every day. The consistency of the HFT liquidity-providing trade performance over time becomes apparent. On the 10th percentile day, the mean sell VWAP - buy VWAP difference across all stocks is positive 2.7 bps. In Panel C, the differences are averaged over all sample days for each stock, and then summarized across stocks. These results highlight another dimension of HFT liquidity-provision performance consistency. In the 10th percentile stock, the sell VWAP - buy VWAP difference is positive 1.9 bps. The information in Panel B and C is shown graphically in Figure 2.4. In Panel A, we see that there are some very high-performance days, and high-performance days outnumber low-performance days. From Panel C, we observe that overall performance is distributed relatively evenly across stocks, and liquidity-demanding performance is negatively correlated with liquidity-supplying performance. One final note on Table 2.9: all of the mean differences in the table indicate positive performance and all are significantly different from 0 at the 5% level or higher, with the exception of sell VWAP - market VWAP in Panel C. At what horizon do HFTs have market timing ability? We might expect this ability to be concentrated at the shortest horizons based on their investments in very low-latency technology and various assertions in the press. This relates to questions about the nature of intraday return predictability, whether HFTs are willing to risk their capital on expected price changes that take longer to play out, and also on HFTs potential effects on price formation. I investigate this issue in two ways. First, I decompose the sell VWAP - buy VWAP differences reported in Table 2.9 into shorter term and longer term components. I replace the price on each HFT trade with the market VWAP for the 5- 42 minute interval in which the trade occurred, and recalculate daily HFT buy and sell VWAPS for each stock using these transformed prices. I call these HFT positioning VWAPS, and refer to the sell HFT positioning VWAP - HFT buy positioning VWAP difference as HFT positioning performance. This procedure removes the effects of HFT market timing within 5-minute intervals, and leaves only the effect of HFTs' choices of how much to buy or sell in a given 5-minute interval. If HFT market timing performance is only due to their short-term timing ability, then their positioning performance should be close to zero. I also measure the difference between the actual sell HFT VWAP - HFT buy VWAP and the HFT positioning performance on each stock-day, and call this the HFT short-term timing performance. Given the similar results across weighting schemes in Table 2.9, I only conduct this analysis with stock-day weighting. For my second test, for every stock-day, I rank each 5-minute interval by market VWAP and observe the variation in HFT activity across groups of intervals. This is designed to reveal how their trading activity differs across lower and higher price periods, and the use of 5-minute VWAPs as the measure of price focuses the test on positioning performance and away from fleeting prices. There are 78 5-minute intervals in the trading day, so I rank the intervals into 13 groups, giving each group six 5-minute intervals. The HFT activity measures I consider are net normalized HFT dollar volume and HFT order imbalance. I define net normalized HFT dollar volume as HFT buy dollar volume less HFT sell dollar volume divided by total HFT dollar volume traded. HFT order imbalance is calculated with the same formula but uses only trades where HFTs demand liquidity, and is identical to the order imbalance used in Section 2.6 with only HFT trades. If HFT market timing skill is concentrated at very high frequencies, then there should be little or 43 no difference in their activity between low-price and high-price 5-minute intervals. This approach also reveals whether the HFT positioning performance observed above comes from trades at the extreme prices of the day or is shown more continuously across the distribution of prices, and whether this differs across liquidity-demanding and supplying trades. The results of the decomposition analysis are presented in Table 2.10. The overall stock-day-weighted HFT sell-buy VWAP differences from Table 2.9 are repeated in Panel A for convenience. Panel B reports summary statistics on HFT positioning performance. For all trades, 5.0 bps of the 6.5 bps overall mean sell-buy VWAP difference is attributable to positioning performance. For liquidity-demanding trades, their positioning performance of 2.8 bps is actually higher than their 2.3 bps sell - buy VWAP difference. For liquidity-demanding trades, 8.1 bps of their 12.8 bps mean sell - buy VWAP difference is attributable to positioning performance. All of the positioning performance estimates are highly statistically significant. HFT positioning performance also seems to inherit much of the positive skewness in their overall sell-buy VWAP differences. Panel C reports summary statistics on HFT short-term timing performance. These are the component of HFT sell - buy VWAP difference that is not explained by their positioning performance, and can be interpreted as a measure of HFT's ability to time the market within 5-minute intervals. HFT short-term timing performance for all trades and liquidity-demanding trades is positive, while it is negative for liquidity-demanding trades. All of the short-term timing performance estimates are highly statistically significant. HFT short-term timing performance is also positively skewed, but less so than positioning performance. It is noteworthy that HFT short-term timing 44 performance on liquidity-demanding trades is negative. This suggests that without HFT's positioning skill, their short-term timing ability in these trades is not sufficient to overcome the bid-ask spread. Overall, these results are striking. HFTs would retain most of their market timing ability if they transacted at the market VWAPs for the 5-minute intervals in which their trades occur. HFT positioning performance is greater than short-term timing performance for all trade categories. This even holds for their liquidity-providing trades, where we might expect most of their performance to come from earning the spread when it is wide. Despite the attention paid to HFT investments in the arms race to achieve the lowest possible latencies, it seems that their pricing models could be more important than their speed. The results of the HFT activity analysis across intervals ranked by VWAP within each stock day are presented in Table 2.11. Based on the positioning performance results in Table 2.10, we can expect HFTs to buy more than they sell in 5-minute intervals when prices are low, and vice-versa. This is in fact what we observe, both for their overall trading (HFT Net Dollar Volume Ratio) and liquidity-demanding trades (HFT Order Imbalance). In addition to confirming the results in Table 2.10, this analysis also sheds light on whether this is solely driven by trading behavior at the extreme prices or is more continuous. The difference in HFT Net Dollar Volume Ratio between Group 13 (high prices) and Group 1 (low prices) is -.074 and is highly significant. Similarly, the difference in HFT Order Imbalance between Group 13 and Group 1 is -.042 and is also highly significant. This confirms that at least part of the HFT positioning performance shown previously is driven by trading in the correct direction during the extreme price intervals of the day. Further inspection shows evidence that this positioning performance 45 is relatively continuous as well. In Groups 1-5 (the five 5-minute intervals of the day with the lowest prices), HFT net buying is significant, and in Groups 7-13 (the seven 5- minute intervals of the day with the highest prices), HFT net selling is significant. Similarly, in Groups 1-6, HFT Order Imbalance is significantly positive, and in Groups 11-13, HFT Order Imbalance is significantly negative. Across groups as prices move from low to high, HFT Net Dollar Volume Ratios are monotonically decreasing, and HFT Order Imbalances are near-monotonically decreasing. This continuous pattern reveals insights about the nature of intraday return predictability, but there is another arguably more important implication. If HFTs were systematically profiting from pushing prices to their extremes and then reversing their positions, we would expect to see very different patterns, such as selling pressure in the intervals in Group 2 or buying pressure in Group 12. While I cannot rule out that this behavior occurs sporadically or at horizons I do not study, I find no signs of it in this analysis. I interpret these results in this section as suggesting that HFTs possess intraday market timing skills, buying when prices are temporarily low and selling when prices are temporarily high. This suggests that there is economically significant predictability in intraday prices. These timing skills are not driven by very short-term signals, and are not limited to trades made during the periods with the extreme prices of the day. Finally, HFT liquidity-providing trades outperform their liquidity-demanding trades. This raises the question why they engage in so many liquidity-demanding trades. As discussed in Section 2.4, half or more of HFT dollar trading volume is liquidity-demanding. It is possible that some of these trades are motivated by inventory rebalancing or other risk considerations instead of profits. It is also possible that HFT liquidity-demanding trades 46 are motivated by more time-sensitive information than their liquidity-supplying trades, or that they are in the position of having employed as much capital as possible in liquidity provision and have excess capital they are willing to employ in less attractive (but still profitable) liquidity-demanding strategies. 2.7.2 Predictive Positioning Do the positions HFTs take predict short-term cross-sectional stock returns? This is of interest for some of the same reasons that motivated the study of timing in the previous section. If the stocks that HFTs are holding or actively buying in one period outperform the stocks they are short or actively selling, that would suggest there is short-term predictability in the cross section of returns. It would also give us insights into how they allocate their capital. If HFTs trade in and out of stocks based on short-term signals, then it is unlikely that we can expect them to consistently dedicate market-making capital to specific stocks. There are several reasons to suspect HFTs may trade based on relative expected returns. First, the results from the price delay tests in Section 2.6 are consistent with relative value trading. Second, studying longer horizons, the empirical asset pricing literature has found stronger evidence of cross-sectional predictability than time-series predictability. If this is true at shorter horizons as well, it is likely that HFTs would take advantage of this. Third, by actively balancing their long and short positions, HFTs can reduce market risk, and to the extent they are able to predict relative returns, it would be natural for them to incorporate this information into their hedging choices. Finally, in various informal descriptions, HFTs are thought to engage in relative value trading, pairs trading, or "arbitrage." 47 In this test, I form decile portfolios based on HFTs' stock-specific trading activity and compare the 1-minute and 5-minute midpoint returns on the portfolios they have bought to those on the portfolios they have sold. I use two measures of their buying and selling activity. First, as a proxy for their overall positions at the start of each interval, I measure their cumulative net trading volume in each stock from the start of the day until the end of the prior interval. Second, as a proxy for their recent trading, I calculate the lagged position change as the cumulative net volume in each stock over the prior interval. This measure may be more informative if HFTs are not agile enough to move their entire portfolios in the direction of predicted future returns over a short period of time but do start trading in the correct direction, or if the first measure contains too much accumulated error from trades on other venues over the course of the day, as discussed in Section 2.7.1. Position changes are also measured with error but, because the errors accumulate over the measurement horizon, the position change errors should be smaller than the position errors. At the beginning of each interval, stocks are ranked into deciles based on the HFT positions and position changes, and returns are calculated for each decile and a 10-1 spread portfolio. Variations of this procedure are common in the empirical asset pricing literature to test whether a category of investor's holdings or change in holdings are related to future returns. See Yan and Zhang (2009) for an example that tests whether short-term institutional investor's equity trades are informed. The results are shown in Table 2.12. The stocks HFTs hold or bought actively in the prior period tend to underperform the stocks they are short or sold actively. The spread portfolio returns are all negative, and are statistically significant with the exception of the position portfolios at 5-minute holding periods. They range from -0.05 48 bps for the 1-minute position decile spread portfolio to -0.70 bps for the 5-minute position change decile spread portfolio. As a robustness test, I ran Fama-Macbeth regressions of returns on the positions and position changes (unreported). These show qualitatively similar results: the coefficients on the positions and position changes are either significantly negative or insignificant. Table 2.12 also reports information on the mean positions and position changes in each portfolio. This helps understand the typical magnitudes of HFT positions in each stock, how fast they change, and whether there are tendencies towards net long or short position or if positions tend to offset across stocks. The mean estimated HFT short position for a stock in the 5-minute decile 1 portfolio is -$4,576,538 and the long position in the decile 10 portfolio is $4,426,550. One-minute portfolios are similar. For the 5- minute position change portfolios, there is $347,750 of selling for the average stock in decile 1 and of $352,802 of buying for the average stock in decile 10. For the 1-minute position change portfolios, there is $129,778 of selling in decile 1 and of $130,409 of buying in decile 10. However, it is not correct to interpret this as evidence that HFTs almost completely offset their long positions with short positions, and their buying with selling, because this sample does not include the whole universe of their trades and these are unconditional mean values. A more informative approach is to divide the absolute value of their net positions (position changes) by their gross positions (position changes). Performing this analysis on 5-minute positions, the mean of this ratio is 29%, and the 90th percentile ratio is 58%. Similarly, for 5-minute position changes, the mean of this ratio is 30%, and the 90th percentile ratio is 60%. There are occasionally periods when HFT positions or position changes appear very directional, however. For example, there are 49 500 1-minute intervals in the sample where the net position changes are 95% or more of the gross. To the extent this sample is representative, it appears HFTs tend to offset some but not all of their long and short positions (position changes), and occasionally trade very directionally. The magnitudes of the negative spread portfolio returns are small, and are within the mean quoted bid-ask spreads. The strongest conclusion I can draw is that I do not find evidence that their positions or trades positively predict relative returns at these horizons. This should not be interpreted as meaning they are losing money. We do not expect them to trade at the midpoints or exactly at these frequencies. It is also important to note these 120 stocks are presumably a small sample of the assets they trade. The most likely explanation for the small negative returns seems to be liquidity effects. We may be observing the effect of small reversals after the positions HFTs actively take create price pressure. The use of midpoint returns is intended to mitigate this effect, but does not necessarily do so perfectly. 2.8 Conclusion In this paper, I analyze market quality and HFT trading behavior using a large sample of NASDAQ trades and quotes with HFT participation explicitly identified. I find that trading costs are unconditionally low in this market, but spreads are slightly wider for trades where HFTs provide liquidity and slightly tighter when HFTs take liquidity. This suggests that HFTs provide liquidity when it is scarce and consume liquidity when plentiful. Prices incorporate information from order flow and market-wide returns more efficiently on days when HFT participation is high. This effect is 50 driven by HFT demand-side participation, implying that HFTs improve price efficiency when demanding liquidity. I also find that HFTs seem to possess intraday market timing ability, but I find no evidence that they trade to exploit predictability in cross-sectional expected returns at the horizons I study. The new evidence in this paper is relevant to the ongoing HFT-related policy debates and can potentially provide guidance to theoretical researchers seeking to model HFT behavior and market quality impacts. Of particular interest, the trading cost and market timing analysis have implications for the proposals to impose affirmative obligations to provide liquidity on HFTs. The trading costs I document indicate that there is little compensation in the spread for naïve liquidity provision in this market. The evidence on HFT intraday market timing suggests that HFT profits are not driven by spreads alone, and it is not clear that their strategies would be economically viable if affirmative obligations prevented them from exercising discretion in when to trade. The results in this study suggest that HFTs play a beneficial or neutral role in the market. However, it is important to note that my data are limited to NASDAQ continuous trading and my focus is on unconditional systematic effects. These issues and other limitations of this study are discussed in more detail in previous sections. 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Yan, Xuemin S., and Zhe Zhang. "Institutional investors and equity returns: Are short-term institutions better informed?" Review of financial Studies 22, no. 2 (2009): 893-924. 54 Table 2.1 Sample Stocks Sample was selected for NASDAQ by Terrence Hendershott and Ryan Riordan. Sample period is January 2008 - December 2009 and February 22, 2010 - February 26, 2010. Listing venue, price, and market capitalization are from CRSP as of February 26, 2010. Dollar trading volumes are from TAQ for trades between 9:30 am and 4:00 pm and are averaged over all days in sample for each name. Stocks are sorted in descending order by market capitalization. Avg. Dollar Trading Volume Ticker Name Listing Market Cap (billions) Price Nasdaq CT NASDAQ Share AAPL APPLE INC NASDAQ 185.548 204.62 1,654.244 4,229.780 38.2% PG PROCTER & GAMBLE CO NYSE 183.803 63.28 186.570 889.604 20.7% GE GENERAL ELECTRIC NYSE 171.357 16.06 350.167 1,710.448 19.4% PFE PFIZER INC NYSE 141.635 17.55 190.253 908.159 20.4% CSCO CISCO SYSTEMS INC NASDAQ 139.305 24.33 544.225 1,216.373 43.7% GOOG GOOGLE INC NASDAQ 128.612 526.80 976.411 2,197.014 43.5% HPQ HEWLETT PACKARD NYSE 119.564 50.79 168.456 762.414 21.6% INTC INTEL CORP NASDAQ 113.408 20.53 557.855 1,285.776 42.6% DIS DISNEY WALT CO NYSE 60.590 31.24 81.993 377.655 20.9% MMM 3M CO NYSE 57.045 80.15 65.307 329.624 19.3% AMGN AMGEN INC NASDAQ 55.438 56.61 243.441 532.812 45.6% AMZN AMAZON COM INC NASDAQ 52.715 118.40 306.855 727.308 42.9% AXP AMERICAN EXPRESS CO NYSE 45.703 38.19 111.628 493.304 22.1% GILD GILEAD SCIENCES NASDAQ 42.952 47.61 200.488 435.583 45.7% CMCSA COMCAST CORP NASDAQ 33.884 16.44 192.761 417.744 45.8% DOW DOW CHEMICAL CO NYSE 32.565 28.31 60.744 293.240 20.6% HON HONEYWELL INTERNATIONAL NYSE 30.704 40.16 54.990 242.639 22.2% EBAY EBAY INC NASDAQ 29.903 23.02 159.904 363.127 43.7% PNC P N C FINANCIAL SERVICES GRP INC NYSE 27.792 53.76 51.977 303.458 17.3% GLW CORNING INC NYSE 27.483 17.63 63.275 276.531 22.1% CELG CELGENE CORP NASDAQ 27.363 59.52 130.188 281.530 45.9% COST COSTCO WHOLESALE CORP NASDAQ 26.850 60.97 144.949 330.337 43.5% ESRX EXPRESS SCRIPTS NASDAQ 26.445 96.01 89.624 193.355 46.2% MOS MOSAIC COMPANY NYSE 25.993 58.39 110.995 519.619 19.5% DELL DELL INC NASDAQ 25.911 13.24 200.338 464.816 41.8% KMB KIMBERLY CLARK NYSE 25.286 60.74 27.274 163.386 16.4% ADBE ADOBE SYSTEMS NASDAQ 18.211 34.65 115.867 245.726 46.5% AGN ALLERGAN INC NYSE 17.763 58.43 23.249 124.567 18.2% CB CHUBB CORP NYSE 16.753 50.46 29.610 168.466 17.5% AMAT APPLIED MATERIALS INC NASDAQ 16.442 12.24 150.360 339.454 43.4% GENZ GENZYME CORP NASDAQ 15.221 57.20 102.936 220.846 46.9% BIIB BIOGEN IDEC INC NASDAQ 15.120 55.01 86.319 193.493 44.7% BHI BAKER HUGHES INC NYSE 14.946 47.92 64.653 275.455 22.8% GPS GAP INC NYSE 14.835 21.50 40.019 170.821 23.6% SWN SOUTHWESTERN ENERGY CO NYSE 14.726 42.55 44.165 214.302 20.7% KR KROGER COMPANY NYSE 14.363 22.10 39.537 191.461 20.4% CTSH COGNIZANT TECHNOLOGY SOLS NASDAQ 14.322 48.13 63.043 145.206 43.7% 55 Table 2.1 Continued Avg. Dollar Trading Volume Ticker Name Listing Market Cap (billions) Price Nasdaq CT NASDAQ Share BRCM BROADCOM CORP NASDAQ 13.737 31.32 128.856 295.870 43.3% AA ALCOA INC NYSE 13.570 13.30 90.068 410.228 21.4% ISRG INTUITIVE SURGICAL INC NASDAQ 13.516 347.14 99.863 220.226 45.3% CSL CARLISLE COMPANIES NYSE 2.064 34.30 2.569 14.552 17.1% AINV APOLLO INVESTMENT CORP NASDAQ 2.055 11.66 8.404 19.069 42.2% LECO LINCOLN ELECTRIC HOLDINGS INC NASDAQ 2.034 47.70 9.476 17.911 52.4% SFG STANCORP FINANCIAL GROUP NYSE 2.030 42.98 2.975 17.587 16.9% FL FOOT LOCKER INC NYSE 2.030 12.97 5.874 30.986 19.2% ERIE ERIE INDEMNITY CO NASDAQ 2.029 39.62 2.739 4.706 57.2% LSTR LANDSTAR SYSTEM NASDAQ 2.004 39.89 15.164 31.165 47.6% CNQR CONCUR TECHNOLOGIES INC NASDAQ 1.943 39.34 12.837 27.586 46.9% EWBC EAST WEST BANCORP INC NASDAQ 1.927 17.52 8.506 19.787 42.2% JKHY HENRY JACK & ASSOC INC NASDAQ 1.908 22.58 8.708 17.120 49.8% FCN F T I CONSULTING NYSE 1.904 36.74 9.878 50.463 20.3% CBT CABOT CORP NYSE 1.899 29.06 2.247 12.376 17.6% PNY PIEDMONT NATURAL GAS INC NYSE 1.895 25.83 2.057 12.067 16.2% GAS NICOR INC NYSE 1.884 41.65 4.612 23.929 18.6% BRE B R E PROPERTIES NYSE 1.860 33.71 5.196 36.006 14.5% CR CRANE CO NYSE 1.855 31.67 2.130 11.512 17.7% FMER FIRSTMERIT CORP NASDAQ 1.838 21.13 10.510 20.940 49.8% COO COOPER COMPANIES INC NYSE 1.832 40.06 3.291 19.065 16.6% ISIL INTERSIL CORP NASDAQ 1.826 14.84 23.484 53.516 43.5% MELI MERCADOLIBRE NASDAQ 1.815 41.14 11.878 28.770 40.0% ROC ROCKWOOD HOLDINGS INC NYSE 1.782 23.99 2.556 13.784 18.5% CSE CAPITALSOURCE NYSE 1.777 5.50 5.377 30.523 15.2% CHTT CHATTEM INC NASDAQ 1.774 93.48 12.617 27.768 46.3% ARCC ARES CAPITAL NASDAQ 1.737 13.07 4.232 9.884 42.6% CKH SEACOR HOLDINGS NYSE 1.727 76.38 3.585 18.195 19.1% NSR NEUSTAR INC NYSE 1.726 23.18 3.201 15.541 19.8% PTP PLATINUM UNDERWRITERS HLDGS LTD NYSE 1.710 37.39 2.958 20.932 14.2% CPWR COMPUWARE CORP NASDAQ 1.703 7.49 11.685 26.184 44.2% FULT FULTON FINANCIAL CORP PA NASDAQ 1.697 9.62 7.652 15.745 47.2% AYI ACUITY BRANDS NYSE 1.692 38.98 4.146 22.083 18.6% SF STIFEL FINANCIAL NYSE 1.689 54.70 2.434 14.160 17.5% 56 Table 2.1 Continued Avg. Dollar Trading Volume Ticker Name Listing Market Cap (billions) Price Nasdaq CT NASDAQ Share NUS NU SKIN ENTERPRISES INC NYSE 1.676 26.72 1.120 6.844 14.9% BARE BARE ESCENTUALS NASDAQ 1.674 18.18 5.483 14.289 36.3% LPNT LIFEPOINT HOSPITALS INC NASDAQ 1.673 30.50 11.012 25.294 44.2% CRI CARTERS INC NYSE 1.664 28.66 3.179 18.992 16.9% AMED AMEDISYS INC NASDAQ 1.630 57.65 16.055 37.936 44.7% BXS BANCORPSOUTH NYSE 1.625 19.47 2.892 17.268 16.3% LANC LANCASTER COLONY CORP NASDAQ 1.623 57.54 3.880 7.474 52.6% CETV CENTRAL EUROPEAN MEDIA ENT LTD NASDAQ 1.513 26.99 10.819 23.362 46.5% MANT MANTECH INTERNATIONAL CORP NASDAQ 1.106 49.38 7.760 15.189 50.8% NXTM NXSTAGE MEDICAL NASDAQ 0.498 10.65 0.449 1.013 43.6% CTRN CITI TRENDS INC NASDAQ 0.438 29.74 2.481 5.538 45.9% RVI RETAIL VENTURES NYSE 0.438 8.94 0.210 1.410 13.4% MAKO MAKO SURGICAL NASDAQ 0.436 13.21 0.283 0.703 37.4% MOD MODINE MANUFACTURING NYSE 0.435 9.40 0.554 2.924 16.3% ROG ROGERS CORP NYSE 0.433 27.45 0.898 4.084 18.8% KTII K TRON INTL INC NASDAQ 0.424 149.46 0.684 1.369 49.8% KNOL KNOLOGY INC NASDAQ 0.421 11.45 0.798 1.723 47.3% PPD PRE PAID LEGAL SERVICES INC NYSE 0.418 41.64 0.633 3.928 14.7% DCOM DIME COMMUNITY BANCSHARES NASDAQ 0.418 12.14 1.679 3.339 49.7% BW BRUSH ENGINEERED MATERIALS INC NYSE 0.416 20.54 1.160 5.631 19.4% SJW S J W CORP NYSE 0.415 22.44 0.585 2.416 17.6% MRTN MARTEN TRANSPORT LTD NASDAQ 0.412 18.84 1.310 2.900 46.2% FPO FIRST POTOMAC REALTY TRUST NYSE 0.411 13.68 0.395 2.884 13.2% IPAR INTERMEDIATE PARFUMS INC NASDAQ 0.410 13.58 0.751 1.540 48.9% FRED FREDS INC NASDAQ 0.407 10.35 2.383 5.271 44.9% MDCO MEDICINES COMPANY NASDAQ 0.407 7.70 4.613 10.934 42.7% MIG MEADOWBROOK INSURANCE GROUP NYSE 0.405 7.08 0.212 1.697 12.7% ANGO ANGIODYNAMICS NASDAQ 0.402 16.26 1.305 2.790 44.9% PBH PRESTIGE BRANDS HOLDINGS INC NYSE 0.402 8.03 0.334 2.309 14.2% BZ BOISE INC NYSE 0.401 4.75 0.224 2.256 13.0% 57 Table 2.1 Continued Avg. Dollar Trading Volume Ticker Name Listing Market Cap (billions) Price Nasdaq CT NASDAQ Share CDR CEDAR SHOPPING CENTERS INC NYSE 0.400 6.59 0.388 2.843 12.9% APOG APOGEE ENTERPRISES INC NASDAQ 0.400 14.29 2.545 5.498 46.3% MFB MAIDENFORM BRANDS INC NYSE 0.399 17.22 0.276 1.982 14.0% EBF ENNIS INC NYSE 0.397 15.37 0.228 1.731 13.7% FFIC FLUSHING FINANCIAL CORP NASDAQ 0.395 12.69 1.000 1.975 49.8% CPSI COMPUTER PROGRAMS & SYSTEMS INC NASDAQ 0.394 35.94 1.946 4.217 47.5% RIGL RIGEL PHARMACEUTICALS NASDAQ 0.392 7.55 4.175 9.221 43.0% ABD A C C O BRANDS NYSE 0.391 7.17 0.406 2.973 13.3% DK DELEK U S HOLDINGS INC NYSE 0.390 7.27 0.426 2.433 16.8% CRVL CORVEL CORP NASDAQ 0.389 32.20 0.826 1.527 52.7% CBZ CBIZ INC NYSE 0.389 6.23 0.284 2.235 13.4% AZZ A Z Z INC NYSE 0.388 31.41 1.118 6.523 16.9% CCO CLEAR CHANNEL OUTDOOR HLDGS NYSE 0.387 9.52 0.618 4.114 15.1% BAS BASIC ENERGY SERVICES INC NYSE 0.385 9.45 1.075 5.781 17.4% IMGN IMMUNOGEN INC NASDAQ 0.379 6.61 0.895 2.269 41.4% MXWL MAXWELL TECHNOLOGIES INC NASDAQ 0.366 13.86 1.130 2.476 45.4% CBEY CBEYOND INC NASDAQ 0.360 12.41 3.403 7.301 45.2% ROCK GIBRALTAR INDUSTRIES INC NASDAQ 0.353 11.68 2.079 4.423 46.2% NC NACCO INDUSTRIES NYSE 0.313 46.80 0.437 2.549 17.0% 58 Table 2.2 Trade Summary Statistics Trade and Inside Quote (BBO) data provided by NASDAQ. Trade sample period is January 2008 - December 2009 and February 22, 2010 - February 26, 2010. Trades are missing on October 10, 2008. Quote sample period is the first full week of each quarter during 2008 and 2009, September 15, 2008 - September 19, 2008 (the week of Lehman's failure), and February 22, 2010 - February 26, 2010. Only trades between 9:30 am and 4:00 pm are used. Descriptive Statistics Full Sample Matched w/ quotes Days in Sample 509 49 Number of Trades 550,118,372 61,272,712 Total Share Volume (millions) 105,772 11,642 Total Dollar Volume (millions) 3,919,037 443,996 Trade size Mean 192.3 190.0 Std Dev 449.2 447.3 10th %ile 50 58 Median 100 100 90th %ile 400 398 Num of Trades/Day Mean 1,080,783 1,250,464 Std Dev 393,491 570,385 10th %ile 691,279 634,906 Median 1,009,167 1,091,299 90th %ile 1,575,009 2,263,314 Daily Share Volume (millions) Mean 208 238 Std Dev 73 97 10th %ile 130 132 Median 197 209 90th %ile 298 396 Daily Dollar Volume (millions) Mean 7,699 9,061 Std Dev 3,147 4,158 10th %ile 4,439 4,537 Median 6,892 7,740 90th %ile 11,912 15,076 59 Table 2.3 HFT Participation Dollar Volume Shares HFT participation shares are measured as dollar volume of sample trades with HFT participation divided by total dollar volume of sample trades. Three versions of participation shares are calculated, differing in whether HFT participation is defined as trades where an HFT participates in any side (All), the liquidity-demanding side (Demand), or the liquidity-supplying side (Supply). Trades where an HFT participates in both sides are used in all three measures. Trade data provided by NASDAQ. Trade sample period is January 2008 - December 2009 and February 22, 2010 - February 26, 2010. Trades are missing on October 10, 2008. Only trades between 9:30 am and 4:00 pm are used. HFT Participation Definition All Demand Supply Full Sample Pooled 68.3% 42.2% 41.2% Daily Pooling N 509 509 509 Mean 68.5% 42.7% 41.1% Std Dev 2.8% 3.6% 2.4% 10th %ile 65.2% 37.9% 38.2% Median 68.3% 42.7% 41.1% 90th %ile 72.3% 47.8% 44.1% Stock-Day Pooling N 61,014 61,014 61,014 Mean 48.3% 32.5% 23.2% Std Dev 20.5% 15.4% 16.8% 10th %ile 19.9% 10.9% 5.5% Median 49.2% 33.2% 17.9% 90th %ile 75.0% 52.6% 50.5% Stock Pooling N 120 120 120 Mean 48.3% 32.5% 23.2% Std Dev 17.7% 11.9% 15.0% 10th %ile 25.1% 15.4% 10.2% Median 46.4% 34.2% 15.7% 90th %ile 72.6% 47.1% 49.4% Within-Stock Variation (differences between means on high participation and normal participation days for each stock) N 120 120 120 Mean 16.6% 16.1% 12.5% Std Dev 5.4% 4.1% 3.6% 10th %ile 9.4% 10.9% 8.2% Median 16.7% 16.1% 12.0% 90th %ile 23.4% 21.7% 16.9% 60 Table 2.4 Mean and Median Spread and Price Impact Summary All spreads and price impacts are measured as a percent of the pretrade midpoint. Trades signs are provided by NASDAQ based on payments to liquidity providers. Uses trade subsample where both a pretrade and posttrade midpoint are available. The first letter in each trade category label refers to the liquidity taker and the second refers to the liquidity provider. H signifies that the counterparty is an HFT, N signifies a non-HFT. 1-minute decomposition Category N Quoted Spread Effective Spread Price Impact Realized Spread All 61,272,712 0.036 0.027 0.036 -0.009 HH 11,631,186 0.032 0.023 0.035 -0.012 HN 14,837,559 0.036 0.021 0.034 -0.013 NH 19,581,587 0.033 0.028 0.032 -0.004 NN 15,222,380 0.043 0.035 0.042 -0.007 All 61,272,712 0.026 0.022 0.025 -0.002 HH 11,631,186 0.026 0.023 0.029 -0.016 HN 14,837,559 0.026 0.018 0.024 -0.010 NH 19,581,587 0.026 0.024 0.023 0.000 NN 15,222,380 0.026 0.023 0.024 0.000 61 Table 2.5 Regression Estimates of Effective Spread and Price Impacts on HFTs Participation Variables and Controls The regression model is: SPREADitn = αit + β1 HFT + β2j SIZEj + β3 BUY + β4 SELL + ε where i indexes stocks, t indexes day-half hours, n indexes trades, and j indexes trade size groups. The regression is estimated with stock and day-half hour fixed-effects. HFT is an indicator variable that takes a value of 1 if an HFT participated in the trade and 0 otherwise. Different models define HFT based on the liquidity-demanding or liquidity-providing side of the trade. Trade size groups are defined as SMALL (< 500 shares), MEDIUM (>=500 shares, <=1,000 shares), and LARGE (> 1,000 shares). BUY and SELL are dummies indicating the aggressive side of the trade. Panel A: Effective Spreads Model Explanatory Variable (1) (2) (3) (4) HFT Participation HFT_demand -0.007 -0.007 (<.0001) (<.0001) HFT_supply 0.003 0.003 (<.0001) (<.0001) Trade Size Medium 0.000 0.001 (<.0001) (<.0001) Large 0.001 0.003 (<.0001) (<.0001) Trade Sign 0.000 0.000 Buy (<.0001) (<.0001) R2 27.60% 27.60% 27.41% 27.41% 62 Table 2.5 Continued Panel B: 1-minute Price Impacts Model Explanatory Variable (1) (2) (3) (4) HFT Participation HFT_demand 0.001 0.001 (<.0001) (<.0001) HFT_supply -0.001 -0.001 (<.0001) (<.0001) Trade Size Medium 0.005 0.004 (<.0001) (<.0001) Large 0.008 0.008 (<.0001) (<.0001) Trade Sign Buy 0.003 0.003 (<.0001) (<.0001) R2 2.44% 2.44% 2.44% 2.44% 63 Table 2.6 Regression Estimates of Effective Spread and Price Impacts on HFT Participation Variables, Controls, and Interactions The regression model is: SPREADitn = αit + β1j (HFT x SIZEj) + β2 (HFT x BUY) + β3 (HFT x SELL) + ε where i indexes stocks, t indexes day-half hours, n indexes trades, and j indexes trade size groups. The regression is estimated with stock and day-half hour fixed-effects. HFT is an indicator variable that takes a value of 1 if an HFT participated in the trade and 0 otherwise. Different models define HFT based on the liquidity-demanding or liquidity-providing side of the trade. Trade size groups are defined as SMALL (< 500 shares), MEDIUM (>=500 shares, <=1,000 shares), and LARGE (> 1,000 shares). BUY and SELL are dummies indicating the aggressive side of the trade. Panel A: Effective Spreads Model Explanatory Variable (1) (2) (3) (4) HFT Participation HFT_demand -0.007 -0.007 (<.0001) (<.0001) HFT_demand x Medium 0.001 (<.0001) HFT_demand x Large 0.001 (<.0001) HFT_demand x Buy 0.000 (<.0001) HFT_ supply 0.004 0.003 (<.0001) (<.0001) HFT_supply x Medium -0.002 (<.0001) HFT_supply x Large -0.004 (<.0001) HFT_ supply x Buy 0.000 (<.0001) Trade Size Medium 0.000 0.000 0.002 0.001 (<.0001) (<.0001) (<.0001) (<.0001) Large 0.001 0.001 0.004 0.003 (<.0001) (<.0001) (<.0001) (<.0001) Trade Sign Buy -0.001 -0.001 (<.0001) (<.0001) R2 27.60% 27.60% 27.41% 27.41% 64 Table 2.6 Continued Panel B: 1-minute Price Impacts Model Explanatory Variable (1) (2) (3) (4) HFT Participation HFT_demand 0.001 0.001 (<.0001) (<.0001) HFT_demand x Medium 0.000 (0.119) HFT_demand x Large 0.000 (0.4015) HFT_demand x Buy -0.001 (<.0001) HFT_ supply 0.000 -0.002 (<.0001) (<.0001) HFT_supply x Medium -0.004 (<.0001) HFT_supply x Large -0.008 (<.0001) HFT_ supply x Buy 0.002 (<.0001) Trade Size Medium 0.005 0.005 0.006 0.004 (<.0001) (<.0001) (<.0001) (<.0001) Large 0.008 0.008 0.011 0.008 (<.0001) (<.0001) (<.0001) (<.0001) Trade Sign Buy 0.003 0.002 (<.0001) (<.0001) R2 2.44% 2.44% 2.44% 2.44% 65 Table 2.7 Regressions of 5-minute and 1-minute Returns on Contemporaneous Market Returns, Lagged Order Imbalances, and Lagged Order Imbalance Interacted with a Dummy Variable for HFT Participation Regimes Returns are from TAQ and are calculated using the last midpoint in each interval. SPY ETF returns are used as the market proxy. OIB$t-1 is the dollar value of buyer-initiated trades less the dollar value of seller-initiated trades divided by the total dollar volume during interval t-1. A stock is defined as having a high-HFT participation day when its participation share is in its highest tercile for that stock over the entire sample. Participation share is defined as HFT dollar volume divided by the stock's total dollar volume. Three versions of participation shares are calculated, differing in whether HFT participation is defined as trades where an HFT participates in any side (All), the liquidity-demanding side (Demand), or the liquidity-supplying side (Supply). Trades where an HFT participates in both sides are used in all three measures. The regressions are estimated separated for each stock, and cross-sectional means of coefficients across all stocks are reported. T-statistics test the null that the mean is 0. Adjusted t-statistics are corrected for cross-correlation in the residuals. The numbers of positive significant and negative significant coefficients in the individual stock regressions are reported, with significance defined as a t-statistic greater than 2 in absolute value. The sample contains 120 stocks. All coefficients are multiplied by 1000. Panel A: 5-minute returns t-statistic HFT Participation Definition Variable Coefficient Raw Adjusted Num pos sig Num neg sig All Intercept 0.0066 3.34 1.38 9 2 MKT 825.0872 36.52 15.07 120 0 OIB$t-1 0.0960 6.62 2.73 59 12 OIB$t-1 x HFT -0.0704 -6.51 -2.69 2 37 Demand Intercept 0.0066 3.33 1.37 9 2 MKT 825.0813 36.52 15.06 120 0 OIB$t-1 0.1098 7.42 3.06 59 10 OIB$t-1 x HFT -0.1175 -9.73 -4.01 4 57 Supply Intercept 0.0066 3.36 1.39 9 2 MKT 825.1111 36.52 15.07 120 0 OIB$t-1 0.0651 4.38 1.81 47 24 OIB$t-1 x HFT 0.0249 2.52 1.04 17 6 Panel B: 1-minute returns All Intercept 0.0004 0.91 0.39 6 2 MKT 691.5641 31.78 13.60 120 0 OIB$t-1 0.1047 14.48 6.20 112 1 OIB$t-1 x HFT -0.0193 -5.55 -2.37 7 53 Demand Intercept 0.0004 0.92 0.39 7 2 MKT 691.5636 31.78 13.60 120 0 OIB$t-1 0.1066 14.71 6.29 114 1 OIB$t-1 x HFT -0.0244 -6.75 -2.89 8 64 Supply Intercept 0.0004 0.95 0.41 6 2 MKT 691.5649 31.78 13.60 120 0 OIB$t-1 0.0992 13.58 5.81 111 3 OIB$t-1 x HFT -0.0024 -0.79 -0.34 19 23 66 Table 2.8 Comparisons of Price Delay Measures across High and Normal HFT Participation Regimes Price Delay measures use regressions of a stock's return on contemporaneous and lagged market returns (unrestricted regression) compared to regressions on contemporaneous returns only (restricted regression) to measure the speed with which market information is incorporated into the stock's price. D1 is derived from R2 from the restricted and unrestricted regressions. D2 uses ratios of lagged coefficients to all coefficients and gives more weight to longer lags. D3 is similar to D2 but uses t-statistics instead of coefficients, down weighting less precise estimates. Higher values indicate greater delays. Six lags of market returns are used. Returns are from TAQ and are calculated using the