Examination of High Frequency Trading

Electronic copy available at: http://ssrn.com/abstract=1641387

HIGH FREQUENCY TRADING AND ITSIMPACT ON MARKET QUALITY

Jonathan A. Brogaard ∗

Northwestern UniversityKellogg School of Management

Northwestern University School of [email protected]

August 25, 2010

∗I would like to thank my advisors, Tom Brennan, Robert Korajczyk, Robert McDonald, andAnnette Vissing-Jorgensen, for the considerable amount of time and energy they have spent dis-cussing this topic with me; the Zell Center for Risk Research for their financial support; and themany other professors and Ph.D. students at Northwestern University’s Kellogg School of Man-agement and at Northwestern’s School of Law for assistance on this paper. Please contact theauthor before citing this preliminary work.

1


Abstract

This paper examines the impact of high frequency traders (HFTs) onequities markets. I analyze a unique data set to study the strategies utilizedby HFTs, their profitability, and their relationship with characteristics of theoverall market, including liquidity, price efficiency, and volatility. I findthat in my sample HFTs participate in 77% of all trades and that they tendto engage in a price-reversal strategy. I find no evidence suggesting HFTswithdraw from markets in bad times or that they engage in abnormal front-running of large non-HFTs trades. The 26 high frequency trading (HFT)firms in the sample earn approximately $3 billion in profits annually. HFTsdemand liquidity for 50.4% of all trades and supply liquidity for 51.4% ofall trades. HFTs tend to demand liquidity in smaller amounts, and tradesbefore and after a HFT demanded trade occur more quickly than other trades.HFTs provide the inside quotes approximately 50% of the time. In additionif HFTs were not part of the market, the average trade of 100 shares wouldresult in a price movement of $.013 more than it currently does, while atrade of 1000 shares would cause the price to move an additional $.056.HFTs are an integral part of the price discovery process and price efficiency.Utilizing a variety of measures introduced by Hasbrouck (1991a, 1991b,1995), I show that HFTs trades and quotes contribute more to price discoverythan do non-HFTs activity. Finally, HFT reduces volatility. By constructinga hypothetical alternative price path that removes HFTs from the market, Ishow that the volatility of stocks is roughly unchanged when HFT initiatedtrades are eliminated and significantly higher when all types of HFT tradesare removed.

2


1 Introduction

1.1 Motivation

Financial markets continuously evolve. Whenever a change in the market com-position occurs, it is important to study the impact of the new development. Inthe 1980’s the pertinent issues were program trading (Harris et al., 1994) and theexpansion of option markets (Skinner, 1989); In the 1990’s it was the relaxation ofthe order book (Barclay et al., 1999); In the early 2000’s it was algorithmic trading(Hendershott et al., 2008), the decimalization of prices (Chung et al., 2004), andthe introduction of electronic communication networks (Huang, 2002). Today it ishigh frequency trading (HFT; and I use HFTs to refer to high frequency traders).HFT has changed the composition of the market and has brought concerns withit. The fact that HFT is a new breed of trading with no trade-by-trade human in-teraction that can execute dozens of transactions faster than a blink of an eye isconcerning and makes it important to understand the impact it is having on themarket. HFT has come to make up a large portion of the U.S. equity markets, yetthe academic analysis of its role in the financial markets is non-existence. Thispaper aims to fill the gap.

Widespread interest exists in understanding the impact of HFT on marketquality: HFTs argue they improve liquidity, enhance price discovery, and reducevolatility, while others express concern that HFT may exacerbate volatility, con-sume liquidity, and profit at the expense of more traditional investors. Despitethese empirically verifiable claims this paper appears to be the first formal aca-demic study of HFT, primarily because the data necessary for such a study haspreviously been unavailable.

In the press HFT has received an increasing amount of attention with mostof it emphasizing the concerns with HFT. For example, on May 6, 2010 the DowJones Industrial Average dropped over 1,000 points in intraday trading in what hascome to be known as the “flash crash”. The next day, some media blamed HFTsfor driving down the market (Krudy, June 10, 2010). Others in the media blamedthe temporary withdrawal of HFTs from the market as causing the precipitous fall(Lee, August 10, 2010).1

Congress and regulators have begun to take notice and vocalize concern withHFT. The SEC issued a Concept Release regarding the topic on January 14, 2010requesting feedback on how HFTs operate and what benefits and costs they bringwith them (Securities and Commission, January 14, 2010). The Dodd Frank Wall

1To date, the true cause of the flash crash has not been determined.

3

Street Reform and Consumer Protection Act calls for an in depth study on HFT(Section 967(2)(D)). The CFTC has created a technology advisory committee toaddress the development of high frequency trading. Talk of regulation on HFThas already begun. Given the lack of empirical findings for such regulation, theframework for regulation is best summarized by Senator Ted Kaufman, ”When-ever you have a lot of money, a lot of change, and no regulation, bad things hap-pen” (Kardos and Patterson, January 18, 2010). There has been a proposal (HouseResolution 1068) to impose a per-trade tax of .25%. Some have suggested imple-menting fees when the number of canceled orders by a market participant exceedsa certain level, or limit the number of canceled orders. While others have recom-mended requiring quotes to have a minimum life before they can be canceled orrevised. Before discussing regulation to restrict HFT it is useful to know whetherHFT is harming or benefiting markets.

In this paper I examine the empirical consequences of HFT on market func-tionality. I utilize a unique dataset that distinguishes HFT from non-HFT quotesand trades. This paper provides an analysis of HFTs behavior and their impacton financial markets. Such an analysis is necessary since to ensure properly func-tioning financial markets the SEC, CFTC, Congress and exchanges must set ap-propriate rules for traders. These rules should be based on the actual behavior andimplications of market participants. It is equally important that investors under-stand whether or not new market developments, like the rise of HFT, benefit orharm them.

This paper studies HFT from a variety of viewpoints and hopes to answer twofundamental questions. First, what are the activities of HFTs? Specifically, whatcategory of trader do HFTs relate to, what type of trading behavior do they follow,how profitable are they, and what are the determinants of their market partici-pation? Second, how does HFT impact market quality? Using research designtechniques that overcome data limitations I ask whether HFT affects liquidity,contributes to the price discovery process, and generates or dampens volatility.

To answer these questions, the paper first describes the activities of HFTs,showing that HFTs make up a large percent of all trading and that they both pro-vide and demand liquidity. Their activities tend to be stable over time and acrossmarket conditions. Second, it examines HFTs strategy and profitability. HFTsgenerally engage in a price reversal strategy, buying after price declines and sell-ing after price gains. They are profitable, making around $3 billion each year ontrading volume of $28.3 trillion dollars. Third, it considers the impact of HFTon the market, focusing on three areas - liquidity, price discovery, and volatility.HFT accounts for a significant portion of inside quotes and their presence reduce

4

the price impact of trades by a noticeable amount. Using a variety of Hasbrouckmeasures, the data show HFT adds to the efficiency of the markets. Finally, thedata show HFT tends to decrease volatility.

Given these results, HFTs appear to be a new form of market makers and theyappear to make markets operate better (i.e. increase liquidity and price efficiency,and reduce volatility) for all market participants.

HFT is a recent phenomenon. It was brought to the general public’s attentionon July 23, 2009 in a New York Times article (Duhigg, July 23, 2009). Not untilMarch 2010 did Wikipedia have an entry for HFT. Tradebot, a large player in thefield who frequently makes up over 5% of all trading activity and was one of theearliest HFTs, has only been around since 1999. Whereas only recently an aver-age trade on the NYSE took ten seconds to execute, (Hendershott and Moulton,2007), now some firms’ entire trading strategy is to buy and sell stocks multipletimes within a mere second. The acceleration in speed has arisen for two main rea-sons: First, the change from stock prices trading in eighths to decimalization hasallowed for more minute price variation. This smaller price variation makes trad-ing with short horizons less risky as price movements are in pennies not eighths ofa dollar. Second, there have been technological advances in the ability and speedto analyze information and to transport data between locations. As a result, a newtype of trader has evolved to take advantage of these advances: the high frequencytrader. Because the trading process is the basis by which information and risk be-come embedded into stock prices it is important to understand how HFT is beingutilized and its place in the price formation process.

The rest of the paper is as follows: Section 2 describes the related literatureand provides definitions of relevant terms. Section 3 discusses the data. Section 4provides descriptive statistics. Section 5 analyzes HFTs investment strategy, mar-ket activity, and profitability. Section 6 analyzes HFT impact on market quality,in order of liquidity, price discovery, and finally volatility. Section 7 concludes.

2 Literature ReviewHFT has received little attention to date in the academic literature. This is be-cause until recently the concept of HFT did not exist. In addition, data to conductresearch in this area has not been available. The only academic paper regardingHFT is one by Kearns, Kulesza, and Nevmyvaka (2010), and this paper showsthat the maximum amount of profitability that HFT can make based on TAQ dataunder the implausible assumption that HFT enter every transaction that is prof-itable. The findings suggest that an upper bound on the profits HFT can earn per

5

year is $21.3 billion. HFT touches on a variety of related fields of research, themost relevant being algorithmic trading (AT).

In principal AT is similar to HFT except that the holding period can vary. Itis also similar to HFT in that data to study the phenomena are difficult to obtain.Nonetheless several papers have studied AT.

Hendershott and Riordan (2009) use data from the firms listed in the DeutscheBoerse DAX index. They find that AT supply 50% of the liquidity in that mar-ket. They find that AT increase the efficiency of the price process and that ATcontribute more to price discovery than does human trading. Also, they find apositive relationship between AT providing the best quotes for stocks and the sizeof the spread. Regarding volatility, the study finds little evidence between anyrelationship between it and AT.

Hendershott, Jones, and Menkveld (2008) utilize a dataset of NYSE electronicmessage traffic, and use this as a proxy for algorithmic liquidity supply. Thetime period of their data surrounds the start of autoquoting on NYSE for differentstocks and so they use this event as an exogenous instrument for AT. The studyfinds that AT increases liquidity and lowers bid-ask spreads.

Chaboud, Hjalmarsson, Vega, and Chiquoine (2009) look at AT in the foreignexchange market. Like Hendershott and Riordan (2009), they find no evidenceof there being a causal relationship between AT and price volatility of exchangerates. Their results suggest human order flow is responsible for a larger portion ofthe return variance.

Gsell (2008) takes a simple algorithmic trading strategy and simulates the im-pact it would have on markets. He finds that the low latency of algorithmic tradersreduces market volatility, but that the large volume of trades increases the impacton market prices.

Together these papers suggest that algorithmic trading as a whole improvesmarket liquidity and does not impact, or may even decrease, price volatility. Thispaper fits in to this literature by decomposing the AT type traders into short-horizon traders and others and focusing on the impact of the short-horizon traderson market quality.

The author is unaware of any theoretical work conducted that directly ad-dresses HFT. Some work has been conducted to understand what the impact onmarket quality will be of having investors with different investment time horizons.However, these papers that distinguish traders based on their investment horizondo not try and define the horizons. With that caveat, two papers directly addressthe scenario when there are short and long term investors in a market: “Herd onthe Street: Informational Inefficiencies in a Market with Short-Term Speculation”

6

(Froot, Scharfstein, and Stein, 1992); and “Short-Term Investment and the Infor-mational Efficiency of the Market” (Vives, 1995).

Froot, Scharfstein, and Stein (1992) find that short-term speculators may puttoo much emphasis on some (short term) information and not enough on funda-mentals. The result being a decrease in the informational quality of asset prices.Although the paper does not extend its model in the following direction, a de-crease in the informational quality suggests a decrease in price efficiency and anincrease in volatility.

Vives (1995) obtains the result that the market impact of short term investorsdepends on how information arrives. The informativeness of asset prices is im-pacted differently based on the arrival of information, “with concentrated arrivalof information, short horizons reduce final price informativeness; with diffuse ar-rival of information, short horizons enhance it” (Vives, 1995). The theoreticalwork on short horizon investors suggest that HFT may be beneficial to marketquality or that it may be harmful to it.

2.1 Definitions

To date there lacks a clear definition for many of the terms in rapid trading andin computer controlled trading. Even the Securities and Exchange recognizes thisand says that high frequency trading “does not have a settled definition and mayencompass a variety of strategies in addition to passive market making” (Securitiesand Commission, January 14, 2010). HFT is a type of strategy that is engaged inbuying and selling shares rapidly, often in terms of milliseconds and seconds.This paper takes the definition from the SEC: HFT refers to, “professional tradersacting in a proprietary capacity that engages in strategies that generate a largenumber of trades on a daily basis” (Securities and Commission, January 14, 2010).By some estimates HFT makes up over 50% of the total volume on equity marketsdaily (Securities and Commission, January 14, 2010; Spicer, December 2, 2009).

Other terms of interest when discussing HFT, although not the focus of thispaper, include “pinging” and “algorithmic trading.”

The SEC defines pinging as, “an immediate-or-cancel order that can be usedto search for and access all types of undisplayed liquidity, including dark poolsand undisplayed order types at exchanges and ECNs. The trading center thatreceives an immediate-or-cancel order will execute the order immediately if it hasavailable liquidity at or better than the limit price of the order and otherwise willimmediately respond to the order with a cancelation” (Securities and Commission,January 14, 2010). The SEC goes on to clarify, “[T]here is an important distinctionbetween using tools such as pinging orders as part of a normal search for liquidity

7

with which to trade and using such tools to detect and trade in front of largetrading interest as part of an ‘order anticipation’ trading strategy” (Securities andCommission, January 14, 2010).

A type of trading that is similar to HFT, but fundamentally different is algo-rithmic trading (AT). AT is defined as “the use of computer algorithms to automat-ically make trading decisions, submit orders, and manage those orders after sub-mission” (Hendershott and Riordan, 2009). AT and HFT are similar in that theyboth use automatic computer generated decision making technology. However,they differ in that AT may have holding periods that are minutes, days, weeks, orlonger, whereas HFT by definition hold their position for a very short horizon andtry to close the trading day in a neutral position. Thus, HFT must be a type of AT,but AT need not be HFT.

3 Data

3.1 Standard Data

The data in this paper comes from a variety of sources. It uses in standard fash-ion CRSP data when considering daily data not included in the Nasdaq dataset.Compustat data is used to incorporate firm characteristics in the analysis.

3.2 Nasdaq High Frequency Data

The unique data set used in this study has data on trades and quotes on a groupof 120 stocks. The trade data consists of all trades that occur on the Nasdaq ex-change, excluding trades that occurred at the opening, closing, and during intradaycrosses. The trade data used in this study includes those from all of 2008, 2009and from February 22, 2010 to February 26, 2010. The trades include a millisec-ond timestamp at which the trade occurred and an indicator of what type of trader(HFTs or not) is providing or taking liquidity.

The Quote data is from February 22, 2010 to February 26, 2010. It includesthe best bid and ask that is being offered by HFTs and by non-HFTs at all timesthroughout the day.

The Book data is from the first full week of the first month of each quarterin 2008 and 2009, September 15 - 19, 2008, and February 22 - 26, 2010. Itprovides the 10 best price levels on each side of the market that are available onthe Nasdaq book. Along with the standard variables for limit order data, the datashow whether the liquidity was provided by HFTs or non-HFTs, and whether theliquidity was displayed or hidden.

The Nasdaq dataset consists of 26 traders that have been identified as engaging

8

primarily in high frequency trading. This was determined based on known infor-mation regarding the different firms’ trading styles and also on the firms’ websitedescriptions. The characteristics of HFT firms that are identified are the follow-ing: They engage in proprietary trading; that is, the firms do not have customersbut instead trade their own capital. The HFT firms use sophisticated trading toolssuch as high-powered analytics and computing co-location services located nearexchanges to reduce latency. The HFT firms engage in sponsored access providerswhereby they have access to the co-location services and can obtain large-volumediscounts. The HFT firms tend to switch between long and short net positionsseveral times throughout the day, whereas non-HFT firms rarely switch from longto short net positions on any given day. Orders by HFT firms are of a shorter timeduration than those placed by non-HFT firms. Also, HFT firms normally have alower ratio of trades per orders placed than do non-HFT firms.

Firms that others may define as HFTs are not labeled as HFT firms here if theysatisfy one of the following: brokerage firms who provide direct market access andother powerful trading tools to its customers; proprietary trading firms that are adesk of a larger, integrated firm, like a large Wall Street bank with multiple tradingdesks; an independent firm that is engaged in HFT activities, but who routes itstrades through a MPID of a non-HFT type firm; firms that engage in HFT activitiesbut are small.

The data is for a sample of 120 Nasdaq stocks whose ticker symbols are listedin table 1. These sample stocks were selected by a group of academics. Thestocks consist of a varying degree of market capitalization, market-to-book ratios,industries, and listing venues.

4 Descriptive StatisticsBefore entering the analysis section of the paper, as HFT data has not been iden-tified before, I first provide the basic descriptive statistics of interest. I look at liq-uidity and trading statistics of the HFT sample and show they are typical stocks,I then compare the firm characteristics to the Compustat database and show theyare on average larger firms, but otherwise a relatively close match to an averageCompustat firm. Finally, I provide general statistics on the percent of the mar-ket trades in which HFT is involved, considering all types of trades, supplyingliquidity trades, and demanding liquidity trades.

Table 2 describes the 120 stocks in the Nasdaq sample data set. These statisticsare taken for the five trading days from February 22 to February 26, 2010. Thistable shows that these stocks are quite average and provide a reasonable subsample

9

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10

of the market. The price of the stocks is on average 39.57 and ranges between 4.6and 544. The daily trading volume on Nasdaq for these stocks averages 1.064million shares, and ranges from as small as 2,000 shares to 14 million shares.This is done on average over 5,150 trades, whereas some stock trade just 8 timeson a given day while others trade as many as 59,799 times. The 120 stocks arequite liquid. Quoted half-spreads are calculated when trades occur. the averagequoted half-spread of 1.82 cents is comparable to large and liquid stocks in othermarkets. The average trade size, in shares is 139.6. The average depth of theinside bid and ask, measured by summing the depth at the bid and at the ask timestheir respective prices, dividing by two and taking the average per day, is $71,550.

Table 2: Summary Statistics. Summary statistics for the HFT dataset from February 22,2010 to February 26, 2010.

Variable Mean Std. Dev. Min. Max.Price 39.573 60.336 4.628 544.046Daily Trading Volume (Millions) 1.064 2.137 0.002 14.857Daily Number of Trades per Day 5150.983 7591.812 8 59799Quoted Half Spread (cents) 1.838 4.956 0.5 42.5Trade Size 139.617 107.631 37 1597Depth (Thousand Dollars) 71.55 196.421 1.161 2027.506

N 600

Table 3 describes the 120 stocks in the HFT database compared to the Com-pustat database. The table shows that the average HFT database firm is larger thenthe average Compustat firm. The Compustat firms consist of all firms in the Com-pustat database with data available and that have a market capitalization of greaterthan $10 million in 2009. The Compustat database statistics include the firmsthat are found in the HFT database. The data for both the Compustat and the HFTfirms are for fiscal year end on December 31, 2009. If a firm’s year-end is on a dif-ferent date, the fiscal year-end that is most recent, but prior to December 31, 2009,is used. Whereas the average Compustat firm has a market capitalization of $2.6billion, the average HFT database firm has a market capitalization of $17.59 bil-lion. However the sample does span a large variation of firm sizes, from the verysmall with a market capitalization of only $80 million, to the the very large witha market capitalization of $175.9 billion. Compustat includes many very smallfirms that reduce its mean market capitalization, making the HFT sample appearoverweighted with larger firms. The market-to-book ratio also differs between

11

Compustat and the HFT sample. Whereas HFT have a mean market-to-book of2.65, the Compustat data has one of 10.9. Based on industry, the HFT sample is arelatively close match to the Compustat database. The industries are determinedbased on the Fama-French 10 industry designation from SIC identifiers. The HFTdatabase tends to overweight Manufacturing, Telecommunications, Healthcare,and underweight Energy and Other. The HFT firms are all listed on the NYSE orNasdaq exchange, with half of the firms listed on each exchange. Whereas aboutone-third of Compustat firms are listed on other exchanges.2 The HFT databaseprovides a robust variety of industries, market capitalization, and market-to-bookvalues.

Table 4 looks at the prevalence of HFT in the stock market. It captures thisin a variety of ways: the number of trades, shares, and dollar-volume that haveHFT involved compared to trades where no HFT participates. The table providessummary statistics for the involvement of HFT in the market. Three differentstatistics are calculated for each split of the data. The column “Trades” reportsthe number of trades, “Shares” reports the number of shares traded, and “Dollar”reports the dollar value of those shares traded. Panel A - HFT Involved In AnyTrade splits the data based on whether HFT was involved in any way in a trade ornot. The results show that HFT make up over 77% of all trades. HFTs tend to tradein smaller shares as per-share traded they make up just under 75%. Finally, basedon a dollar-volume basis of trade, they make up 73.8% of the trading volume.

The next two panels separate HFT transactions into what side of the trade it ison based on liquidity. Panel B - HFT Involved As Liquidity Taker groups tradesinto the HFT category only when the HFT is on the liquidity demanding side ofthe transaction. HFTs takes liquidity in 50.4% of all trades, worth a dollar amountof just about the same percentage of all transactions on a dollar basis. They makeup only 47.6% of shares trading, suggesting they provide liquidity in stocks thatare slightly higher priced. There is nothing inconsistent with HFTs being marketmakers and also demanding liquidity as Chae and Wang (2003) and Van der Wel(2008) find market makers frequently take liquidity, make informational-basedtrades, and make a significant portion of there profits from their non-liquidityproviding activities.

Panel C - HFT Involved As Liquidity Supplier groups trades into HFT onlywhen the supply of liquidity in a transaction is coming from HFT. The amount of

2Comparing Compustat firms that are listed on NYSE or Nasdaq reduces the number of firmsto 5050 with an average market capitalization of $3.46 billion, and with the industries more closelymatching those in the HFT dataset.

12

Tabl

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13

liquidity supplied is only slightly more than that demanded by HFTs at 51.4% ofall trades having their liquidity provided by HFT. Based on number of shares thisvalue falls to 50.8% of all shares traded; and based on dollar-volume, it drops to45.5% of all trades.

5 HFT StrategyBefore analyzing HFT impact on market quality, it is insightful to understandmore about what drives HFT activity. To research this, I use an ordered logitregression to show HFTs trading strategy is heavily dependent on past returns. Ifurther identify that they engage in a price reversal strategy, whereby they tend tobuy stocks at short-term troughs and they tend to sell stocks at short-term peaks.This is true regardless of whether they are supplying or demanding liquidity. Also,HFT tends to occur in larger, value firms, with lower volume and lower spreadsand depth. Finally, based on their trading activities at the aggregate level I estimateHFTs earn approximately $3 billion a year.

5.1 Investment Strategy

HFTs do not readily share their trading strategies. However, the descriptive statis-tics (and upcoming section 6.2 results) suggest they essentially partake in marketmaking activities by providing liquidity and a continuous market into which otherinvestors can trade. What is known regarding HFTs is that they tend to buy andsell in very short time periods. Therefore, rather than changes in firm fundamen-tals, HFTs must be basing their decision to buy and sell from short term signalssuch as stock price movements, spreads, or volume.

I begin the analysis by performing an all-inclusive ordered logit regression intothe potentially important factors; thereafter I analyze the promising strategies inmore detail. There are three decisions a high frequency trader (HFTr, singular ofHFTs) makes at any given moment: Does it buy, does it sell, or does it do nothing.This decision making process occurs continuously. I model this setting by usinga three level ordered logit. The ordered logit is such that the lowest decision is tosell, the middle option is to do nothing, and the highest option is to buy.

Before getting to the ordered logit, I summarize the theoretical reason for whyan ordered logit is appropriate in this setting, as first discussed by Hausman, Lo,and MacKinlay (1992).

HFTs trading behavior consist of a sequence of actionsZ(t1), Z(t2), . . . , Z(tη)observed at regular time intervals t0, t1, t2, . . . , tη. Let Z∗

k be an unobservable con-

14

Table 4: HFT Aggregate Activity. The table provides summary statistics for the involve-ment of HFT in the market. Three different statistics are calculated for each split of thedata. The column Trades reports the number of trades, Shares reports the number of sharestraded, and Dollar reports the dollar value of those shares traded. Panel A - HFT InvolvedIn Any Trade splits the data based on whether HFT was involved in any way in a trade ornot. Panel B - HFT Involved As Liquidity Taker groups trades into HFT only when theliquidity demand of a transaction comes from HFT. Panel C - HFT Involved As LiquiditySupplier groups trades into HFT only when the supply of liquidity in a transaction comesfrom HFT.

Panel A - HFT Involved In Any Trade

Type of Trader Trades(Sum)

Trades (%) Shares(Sum)

Shares (%) Dollar(Sum)

Dollar (%)

HFT 2,387,851 77.3% 477,944,435 74.9% $19,427,424,121 73.8%Non HFT 702,739 22.7% 160,337,476 25.1% $6,879,817,754 26.2%Total 3,090,590 100.0% 638,281,911 100.0% $26,307,241,875 100.0%

Panel B - HFT Involved As Liquidity Taker

HFT 1,556,766 50.4% 303,971,478 47.6% $13,169,044,493 50.1%Non HFT 1,533,824 49.6% 334,310,433 52.4% $13,138,197,383 49.9%Total 3,090,590 100.0% 638,281,911 100.0% $26,307,241,875 100.0%

Panel C - HFT Involved As Liquidity Supplier

HFT 1,588,157 51.4% 324,221,557 50.8% $11,959,264,046 45.5%Non HFT 1,502,433 48.6% 314,060,354 49.2% $14,347,977,829 54.5%Total 3,090,590 100.0% 638,281,911 100.0% $26,307,241,875 100.0%

15

tinuous random variable where

Z∗k = X

′

kβ + εk, E[εk|Xk] = 0, εk i.n.i.d. N(0, σ2k) (1)

where ‘i.n.i.d.’ stands for the assumption that the εk’s are independent but notidentically distributed, and Xk is a q × 1 vector of predetermined variables thatsets the conditional mean of Z∗

k . Whereas Hausman, Lo, and MacKinlay (1992)deal with tick by tick stock price data, the scenario in this paper deals with HFTstrade behavior data that is aggregated into ten second intervals. Therefore, thesubscripts are used to denote ten second period, not transaction time.

The essence of the ordered logit model is the assumption that observed HFTsbehavior Zk are related to the continuous variable Z∗

k in the following mapping:

Zk =

s1 if Z∗

k ∈ A1,s2 if Z∗

k ∈ A2,...

...sm if Z∗

k ∈ Am,

where the sets Aj form a partition of the state space ζ∗ of Z∗k . The partition

will have the properties that ζ∗ =∪m

j=1Aj and Ai∩Aj = ∅ for i ̸= j, and the sj’sare the discrete values that comprise the state space ζ of Zk. The ordered logitspecification allows an investigator to understand the link between ζ∗ and ζ andrelate it to a set of economic variables used as explanatory variables that can beused to understand the HFT trading strategy. In this application the sj’s are Sell,Do Nothing, Buy. Note, the observable actions could also be split into size, forexample, Sell 1000 + shares, Sell 500 - 1000, etc., but I restrict the ζ partition tothese three natural breaks. The alternative fine tuned separation, for instance, bysubdividing the buys and selling into the number of shares exchanged, is beyondthe needs of this analysis.

I assume the error terms in εk’s in equation 1 are conditionally independently,but not identically, distributed, conditioned on the Xk’s and the other explanatoryvariables, Wk, that are omitted from equation 1, which allows for heteroscedas-ticity in σ2

k.The conditional distribution of observed return changes Zk, conditioned on

Xk and Wk, is determined by the partition boundaries calculated from the orderedlogit regression. As stated in Hausman, Lo, and MacKinlay (1992), for a Gaussianεk, the conditional distribution is

16

P (Zk = si|Xk,Wk)

= P (X′

kβ + εk ∈ Ai|Xk,Wk)

=

P (X

′

kβ + εk ≤ α1|Xk,Wk) if i = 1P (αi−1 < X

′

kβ + εk ≤ αi|Xk,Wk) if 1 < i < m,P (αm−1 < X

′

kβ + εk|Xk,Wk) if i = m,(2)

=

Φ(

α1−X′kβ

σk) if i = 1

Φ(αi−X

′kβ

σk)− Φ(

αi−1−X′kβ

σk) if 1 < i < m,

1− Φ(αm−1−X

′kβ

σk) if i = m,

(3)

where Φ(·) is the standard normal cumulative distribution function.The intuition for the ordered logit model is that the probability of the type of

behavior by HFTs is determined by where the conditional mean lies relative to thepartition boundaries. Therefore, for a given conditional mean X ′

kβ, shifting theboundaries will alter the probabilities of observing each state, Sell, Do Nothing,or Buy. The order of the outcomes could be reversed with no real consequenceexcept for the coefficients changing signs as the ordered logit only takes advantageof the fact there is some natural ordering of the events. The explanatory variablesthen allow one to analyze the different effects of relevant economic variables tounderstand HFT behavior . As the data determines where the partition boundariesthe ordered logit model creates an empirical mapping between the unobservableζ∗ state space and the observable ζ state space. Here, the empirical relationshipbetween HFTs behavior can be analyzed with respect to the economic variablesXk and Wk.

I divide the time frames in to ten second intervals throughout the trading day.3 For each ten second interval I utilize a variety of independent variables. The

3I also tried other time intervals, such as 250 milliseconds, one second and 100 second periods.The results from these alternative suggestions are similar in significance to the results presentedin that where a ten second period shows significance, so does the one second interval for tenlagged period’s worth, and similarly where ten lagged ten second intervals show significance, sodoes the one lagged one hundred second interval. The ten second intervals has been adopted afterattempting a variety of alterations but finding this one the best for keeping the results parsimoniousand still being able to uncover important results.

17

regression I run is as follows:

HFTi,t = α +β1−11 ×Retlagi,0−10 +β12−22 ×Depthbidlagi,0−10

+β23−33 ×Depthasklagi,0−10 +β34−44 × Spreadlagi,0−10

+β45−55 × Tradeslagi,0−10 β56−66 ×Dollarvlagi,0−10.

Each explanatory variable has a subscript 0-10. This represents the num-ber of lagged time periods away from the event occurring in the time t depen-dent variable. Subscript 0 represents the contemporaneous value for that vari-able. For example, retlag0 represents the return for the particular stock dur-ing time period t. And, the return for time period t is defined as retlagi,0 =(pricei,t − pricei,t−1)/pricei,t−1. Thus the betas represent row vectors of 1x11and the explanatory variables column vectors of 11x1. Depthbid is the averagetime weighted best bid depth for stock i in that time period. Depthask is the av-erage time weighted best offer depth for stock i in that time period. Spread is theaverage time weighted spread for company i in that time period, where spread isthe best ask price minus the best bid price. Trades is the number of distinct tradesthat occurred for company i in that time period. DollarV is the dollar-volume ofshares exchanged in transactions for company i in that time period. The dependentvariable, HFT , is -1, 0 or 1. It takes the value -1 if during that ten second periodHFTs were on net selling shares for stock i, it is zero if the HFTs performed notransaction or its buys and sell exactly canceled, and it is 1 if on net HFTs werebuying shares for stock i. Firm fixed effects are implemented.

From this ordered logit model one may expect to see a variety of potentialpatterns. A handful of different strategies have been suggested in which HFTsengage. For instance, momentum trading, price reversal trading, trading in highvolume markets, or trading in high spread markets. It could be they base their trad-ing decisions on the spread and so the Spread variables would have considerablepower in explaining when HFTs buy or sell. If HFTs are in general momentumtraders, then I would expect to see them buy after prices rise, and to sell afterprices fall. If HFTs are price reversal traders, then I would expect to observe thembuying when prices fall and to sell when prices are rising. Table 5 shows theresults.

The results reported in table 5 are the marginal effects at the mean for theordered logit. From the ordered logit regression’s summarized results in table 5,there is sporadic significance in all but one place, the lagged values of companyi’s stock returns. There is a strong relationship with higher past returns and the

18

Table 5: HFT Ordered Logit - Exploratory Regression. This table includes several explanatory variables in order touncover in which strategies HFTs are engaged. Each explanatory variable is followed by a number between 0 and 10. Thisrepresents the number of lagged time periods away from the event occurring in the time t dependent variable. Subscript 0represents the contemporaneous value for that variable. For example, retlag0 represents the return for the particular stockduring time period t. And, the return for time period t is defined as retlagi,0 = (pricei,t − pricei,t−1)/pricei,t−1.Depthbid is the average time weighted best bid depth for stock i in that time period. Depthask is the average timeweighted best offer depth for stock i in that time period. Spread is the average time weighted spread for company i inthat time period, where spread is the best ask price minus the best bid price. Trades is the number of distinct tradesthat occurred for company i in that time period. DollarV is the dollar-volume of shares exchanged in transactions forcompany i in that time period. The dependent variable, HFT , is -1, 0 or 1. It takes the value -1 if during that ten secondperiod HFTs were on net selling shares for stock i, it is zero if the HFTs performed no transaction or its buys and sellexactly canceled, and it is 1 if on net HFTs were buying shares for stock i. The regression uses firm fixed effects.

Variable Coefficient T-Stat Variable Coefficient T-Statretlag0 7.461 (0.49) depthasklag1 -8.72e-13 (-1.01)retlag1 5.017∗∗ (3.22) depthasklag2 -5.15e-13 (-1.22)retlag2 4.577∗∗∗ (4.14) depthasklag3 3.49e-13 (0.69)retlag3 5.744∗∗∗ (5.63) depthasklag4 -2.97e-13 (-0.65)retlag4 4.405∗∗∗ (4.35) depthasklag5 -5.88e-13 (-1.19)retlag5 4.176∗∗∗ (5.04) depthasklag6 -5.81e-13 (-1.18)retlag6 4.254∗∗∗ (5.65) depthasklag7 5.55e-13 (1.21)retlag7 2.724∗∗∗ (3.82) depthasklag8 -2.03e-13 (-0.55)retlag8 1.423∗ (2.29) depthasklag9 -1.58e-13 (-0.34)retlag9 2.245∗∗ (3.08) depthasklag10 1.79e-13 (0.36)retlag10 1.216∗ (2.24) depthasklag0 1.68e-12 (1.42)spreadlag1 0.00528 (0.69) tradeslag1 -0.000184 (-1.38)spreadlag2 0.00199 (0.50) tradeslag2 0.00000749 (0.07)spreadlag3 -0.00549 (-1.19) tradeslag3 0.000203∗∗ (2.69)spreadlag4 -0.000316 (-0.05) tradeslag4 -0.000165∗ (-1.97)spreadlag5 0.000114 (0.03) tradeslag5 0.000169∗ (2.31)spreadlag6 0.00456 (0.79) tradeslag6 -0.0000886 (-0.95)spreadlag7 0.00254 (0.30) tradeslag7 0.0000884 (1.17)spreadlag8 -0.00960 (-1.56) tradeslag8 -0.000176∗ (-1.99)spreadlag9 0.00126 (0.30) tradeslag9 -0.00000946 (-0.08)spreadlag10 0.00870 (1.31) tradeslag10 0.0000171 (0.14)spreadlag0 -0.00332 (-0.47) tradeslag0 0.000208 (1.18)depthbidlag1 7.07e-13 (0.86) dvolumelag1 -4.09e-14 (-0.06)depthbidlag2 8.71e-13∗∗ (2.74) dvolumelag2 3.61e-13 (0.29)depthbidlag3 6.21e-13 (1.38) dvolumelag3 -1.68e-12∗ (-2.05)depthbidlag4 6.82e-13 (1.75) dvolumelag4 8.88e-13 (1.31)depthbidlag5 9.16e-13 (1.10) dvolumelag5 -1.37e-12∗ (-2.16)depthbidlag6 -5.30e-13 (-0.98) dvolumelag6 5.47e-13 (0.70)depthbidlag7 -2.33e-14 (-0.06) dvolumelag7 -3.29e-13 (-0.47)depthbidlag8 6.43e-13 (1.77) dvolumelag8 2.19e-13 (0.26)depthbidlag9 -1.22e-13 (-0.21) dvolumelag9 2.73e-13 (0.15)depthbidlag10 -1.75e-12∗ (-2.50) dvolumelag10 -3.70e-13 (-0.26)depthbidlag0 -1.80e-12 (-1.30) dvolumelag0 -3.99e-13 (-0.33)N 1281695

Marginal effects; t statistics in parentheses∗ p < 0.05, ∗∗ p < 0.01, ∗∗∗ p < 0.001

19

likelihood the HFTs will be selling (and with low past returns and the likelihoodthe HFTs will be buying). There is some statistical significance in other locations,however no where is it consistent like that of the return coefficients. This suggeststhat past spread size, depth, and volume are not primary factors in HFTs tradingdecisions. Of the strategies discussed above, these results are consistent with aprice reversal trading strategy. To further understand this potential price reversalstrategy I focus on analyzing the lag returns influence on HFTs’ trading behavior.

It appears that HFTs engage in a price reversal strategy. To analyze this further,I examine HFTs buy and sell logits separately, focusing on the lagged returnssurrounding HFTs’ buying or selling stocks and decomposing the differences indemanding versus supplying liquidity activity.

To better understand HFTs trading strategy I run logit regressions on differentdependent variables. I consider a total of six different regressions: HFTs selling,HFTs selling when supplying liquidity, HFTs selling when demanding liquidity,HFTs buying, HFTs buying when supplying liquidity, and HFTs buying whendemanding liquidity. The results found in table 6 are the marginal effects at themean and the logit incorporates firm fixed effects. The first column is the resultsfor HFT Sell, all types. The results show the strong relationship between pastreturns and HFTs decision to sell. prior to HFTs executing a sale of a stock,the stock tend to rise, with statistically significance up to 90 seconds prior to thetrade, barring time period 8. This finding suggests HFTs in general engage in aprice reversal strategy.

The next column has as the dependent variable a one if HFTs were on netsupplying liquidity to the market and selling during a given ten second intervaland a zero otherwise. The results are similar to the previous results, except thatthe magnitude and statistical significance is not as strong. There appears to bemore scattered significance of past returns.

The third column in table 6 has as the dependent variable a one if HFTs wereon net taking liquidity from the market and selling during the ten second intervaland a zero otherwise. There is still strong statistical significance from the ten pastreturn periods, barring the ninth one. The signs are the same as before, which isconsistent with a price reversal strategy. One large difference is the fact that thecontemporaneous period return coefficient is large and negative. It is not clearfrom the logit model whether this means that HFTs initiate a sale once prices havestarted to fall, or that after they start selling prices fall. This cannot be determinedfrom this regression as the contemporaneous return will include within its time pe-riod HFTs transactions, but I cannot determine whether HFTs were selling beforeprices fell or after they fell within this ten second increment.

20

Table 6: Regressions of the Sell decision, split based on Liquidity Type. This tablereports the results from running a logit with dependent variable equal to 1 if (1) HFTson net sell in a given ten second period, (2) HFTs on net sell and supply liquidity, and(3) HFTs on net sell and demand liquidity, (4) HFTs on net buy in a given ten secondperiod, (5) HFTs on net buy and supply liquidity, and (6) HFTs on net buy and demandliquidity, and 0 otherwise. Each explanatory variable is followed by a number between 0and 10. This represents the number of lagged time periods away from the event occurringin the time t dependent variable. Subscript 0 represents the contemporaneous value forthat variable. For example, retlag0 represents the return for the particular stock duringtime period t. And, the return for time period t is defined as retlagi,0 = (pricei,t −pricei,t−1)/pricei,t−1. Firm fixed effects are used. The reported coefficients are themarginal effects at the mean.

(1) (2) (3) (4) (5) (6)HFT S - A HFT S - S HFT S - D HFT B - A HFT B - S HFT B - D

retlag0 4.925 16.35∗∗∗ -16.48∗∗∗ -2.793 -48.10∗∗∗ 53.48∗∗∗

(0.66) (3.69) (-8.38) (-0.37) (-14.21) (18.93)retlag1 5.145∗∗ -0.934 7.594∗∗∗ -6.490∗∗∗ -4.910∗∗∗ -0.874

(3.13) (-0.96) (9.80) (-3.87) (-4.25) (-0.69)retlag2 5.230∗∗∗ 1.179 4.619∗∗∗ -5.763∗∗∗ -4.533∗∗∗ -1.408

(3.87) (1.44) (5.54) (-4.44) (-4.38) (-1.80)retlag3 6.521∗∗∗ 2.684∗∗∗ 4.276∗∗∗ -7.460∗∗∗ -4.257∗∗∗ -2.906∗∗

(5.87) (4.03) (6.03) (-6.29) (-6.80) (-2.89)retlag4 4.881∗∗∗ 1.234 4.209∗∗∗ -6.291∗∗∗ -2.802∗∗∗ -3.202∗∗∗

(4.13) (1.60) (5.41) (-5.25) (-3.75) (-3.84)retlag5 4.194∗∗∗ 2.038∗ 2.498∗∗∗ -6.384∗∗∗ -2.572∗∗∗ -3.023∗∗∗

(3.82) (2.46) (3.45) (-6.34) (-3.32) (-4.32)retlag6 5.098∗∗∗ 2.278∗∗∗ 2.989∗∗∗ -6.110∗∗∗ -3.042∗∗∗ -2.766∗∗∗

(4.91) (3.65) (4.26) (-6.14) (-4.28) (-3.85)retlag7 3.380∗∗∗ 0.497 3.439∗∗∗ -3.260∗∗ -2.001∗∗ -1.022

(3.84) (0.83) (4.21) (-3.13) (-2.67) (-1.45)retlag8 0.923 0.0277 1.087 -2.274∗ -1.553∗ -0.226

(0.99) (0.04) (1.68) (-2.43) (-2.50) (-0.28)retlag9 2.521∗ 0.270 2.610∗∗ -2.770∗∗ -1.513∗ -1.395∗

(2.53) (0.43) (3.14) (-2.77) (-2.08) (-2.01)retlag10 0.351 -0.854 1.603∗ -2.049∗ -1.908∗∗ 0.445

(0.39) (-1.28) (2.22) (-2.26) (-2.88) (0.67)N 1377798 1377798 1343177 1377798 1366278 1377798Marginal effects; t statistics in parentheses∗ p < 0.05, ∗∗ p < 0.01, ∗∗∗ p < 0.001

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The Buy regressions are also shown in table 6. The fourth column is the resultfor HFT Buy, all types. The results show the strong relationship between pastreturns and HFTs decision to buy. Prior to HFTs executing a purchase of a stock,the stock tend to fall, with statistically significance up to 100 seconds prior to thetrade.

The fifth column has as the dependent variable a one if HFTs were on netsupplying liquidity to the market and buying during a given ten second interval anda zero otherwise. The results in the lag returns are similar to the previous results,except that the magnitude of the coefficients are smaller. There is an especiallylarge relationship with the contemporaneous period return and the HFTs decisionto supply liquidity and buy in a trade.

The last column in table 6 has as the dependent variable a one if HFTs wereon net taking liquidity from the market and buying during the ten second intervaland a zero otherwise. There is still some statistical significance from the ten pastreturn periods, but only in time periods 0 and 3 - 6. The signs for the lag returnsare negative as expected, except for the contemporaneous period return, which islarge and positive. Like in the HFT Sell - Demand scenario, it is not clear fromthis logit model how to interpret this.

The results in table 6 show that HFT are engaged in a price reversal strategy.This is true whether they are supplying liquidity or demanding it.

5.1.1 Front Running

A potential investing strategy of which HFTs have been claimed to be engaged inis front running. Some charge HFTs with detecting when other market participantshope to move a large number of shares in a company and that the HFTs entersinto the same position just before the other market participant. It is in this contextwhere pinging, as defined in section 2.1, and the SEC’s concern with it apply. Thatis, some claim HFTs ping stock prices to detect large orders being executed. Ifthey detect a large order coming through they may increase their trading activity.The result of such an action by HFTs would be to drive up the cost for non-HFTsto execute the desired transaction.

To see whether or not this is occurring on a systematic basis I perform thefollowing exercise: For each stock over the database time series I create twentybins based on trade size for trades initiated by non-HFTs. Each bin has roughlythe same number of observations. Next, I look at the average percent of tradesthat were initiated by HFTs for different number of trades prior to a non-HFTrinitiated trades (for prior trades 1 - 10).

I graph the results in figure 1. The x-axis is the 20 different non-HFTr initiated

22

trade size bins; the y-axis is the fraction of trades for different non-HFTr trade sizebins for different prior trade periods that were initiated by HFTs; the z-axis is thedifferent prior trade periods.

Figure 1: HFT Front Running. The graph shows the percent of trades initiated by HFTsfor different prior time periods that precede different size non-HFTr initiated trades. Thex-axis is the 20 different non-HFTr initiated trade size bins; the y-axis is the fraction oftrades for different non-HFTr trade size bins for different prior trade periods that wereinitiated by a HFTr; the z-axis is the different prior trade periods.

The figure suggests front running by HFTs before large orders is not system-atically occurring. In fact, it appears that larger trades, relative to each stock, tendto be preceded by fewer HFTr initiated trades. The non-HFTr trades that are pre-ceded by the highest number of HFTr initiated trades are those that are small andthose that are of moderate size. Also, it is interesting that the immediately preced-ing trades tend to have fewer HFTr initiated trades than those further out. As willbe shown later, trades initiated by one type of market participant have a greaterprobability of being preceded by the same type of market participant, which mayexplain why the graph’s pattern occurs.

5.1.2 HFT Market Activity

In addition to understanding the trading behavior of HFTs at the trade by tradelevel, it is informative to understand what drives HFTs to trade in certain stocks

23

on certain days. Table 7 shows the variation in HFT market makeup in differentstocks on different days. Panel A is the percent of trading variation of non-HFTand HFT in a certain stock on a given day. Panel B is the percent of tradingvariation of HFT and non-HFT in supplying liquidity for a particular stock on agiven day. Panel C is the percent of trading variation of HFT and non-HFT indemanding liquidity for a particular stock on a given day.

Panel A shows that HFT share of the market varies a great deal depending onthe stock and the day. Its percent of all trades varies from 10.8% to 93.6%, basedon number of trades. They average being involved in 61.8% of all trades, which,compared to the numbers seen in the descriptive statistics from table 4, suggeststhey trade more in stocks that trade frequently, as they make up 77% of all tradesin the entire market.

Panel B looks at HFT supplying liquidity. HFT supply liquidity in 35.5% oftrades in the average stock per day. This number is substantially smaller than the50% they were found to supply in the market as a whole in table 4. Thus, HFTmust supply liquidity in stocks that trade more frequently. Also, notice the widevariation in the supply of liquidity, in some stocks they provide no liquidity, whilein others they supply 74%.

Panel C looks at HFT demanding liquidity. HFT demand liquidity in 39.6% oftrades in the average stock per day. So HFT must be taking liquidity in stocks thattrade more frequently. Also, the HFT demand for liquidity varies substantiallyranging from 3.6% to 79.9%, but less than when they supply liquidity.

The results in table 7 show there is a large variation in the degree of HFT indifferent stocks over time, the next step is to consider which determinants result inan increase or decrease in HFT activity. Before doing so, however, I briefly showthe summary statistics of HFT quote changes.

5.1.2.1 HFT Quote Revisions and Cancelations This section provides sum-mary statistics on HFTs quote revision and cancelation behavior. Analysis ofliquidity will be provided in detail in section 6.2. Quote cancelations and revi-sions have been found to have net economically significant benefits by reducingthe non-execution cost that would otherwise occur (Fong and Liu, 2010). I lookat the frequency of quote changes at the inside bid and ask for HFT and non-HFTquotes. I examine the data in three ways. The results are in table 8. In Panel A Isum up the total number of quote changes for each stock on each day. With thisas the denominator, in the HFT row the numerator is the number of those changeswhich where for HFT quotes, in the Non-HFT row the numerator is the number ofthose changes which where for non-HFT quotes. These results, and those in Pan-

24

Table 7: HFT Market Participation Summary Statistics. This table shows the variationin HFT market makeup. Panel A is the percent of trading variation of non-HFT and HFTin a certain stock on a given day. Panel B is the percent of trading variation of HFTand non-HFT in supplying liquidity for a particular stock on a given day. Panel C is thepercent of trading variation of HFT and non-HFT in demanding liquidity for a particularstock on a given day.

Panel A - HFT Involved In A Stock

Trades SharesType of Trader Mean Median Std.

Dev.Min Max Mean Median Std.

Dev.Min Max

HFT 61.8% 64.0% 18.25 10.8% 93.6% 58.4% 59.4% 17.99 7.8% 90.9%Non HFT 39.3% 37.1% 19.24 6.4% 92.2% 42.7% 41.6% 18.83 9.1% 93.1%Total 100.0%100.0% 100.0%100.0%

Panel B - HFT Involved In A Stock As Liquidity Supplier

HFT 36.8% 35.5% 15.99 0% 74.4% 33.4% 32.7% 14.54 0.2% 66.4%Non HFT 64.1% 65.3% 16.63 25.6% 100.0%67.5% 67.9% 15.13 33.6% 100.0%Total 100.0%100.0% 100.0%100.0%

Panel C - HFT Involved In A Stock As Liquidity Taker

HFT 39.6% 40.3% 16.43 3.6% 79.9% 37.8% 37.7% 16.49 2.6% 78.9%Non HFT 61.1% 60.3% 16.70 20.1% 96.4% 62.8% 62.7% 16.73 21.1% 97.4%Total 100.0%100.0% 100.0%100.0%

25

els B and C show the minimum, 25th, median, 75th, and maximum quote changes.An alternative approach which directly compares HFT and non-HFT quote changebehavior is to look at the ratio of changes. Panel B does this, where HFT

Non−HFT=

the fraction of HFT quote changes divided by non-HFT quote changes for eachfirm day. Observing the data this way emphasizes the higher frequency at whichHFT change their quotes; the HFT quote changes occur about 50% more oftenthan do non-HFT quote changes. Panel C uses the same HFT

Non−HFTvariable, but

splits it into two groups based on the median market capitalization of the data.In large market cap firms, those in which HFT tend to trade more in, HFT makequote changes almost twice as frequent as do non-HFT.

Table 8: Quote Change Frequency. This table examines the frequency of quote changesby HFT and non-HFT. In Panel A I sum up the total number of quote changes for eachstock on each day. With this as the denominator, in the HFT row the numerator is thenumber of those changes which where for HFT quotes, in the Non-HFT row the numeratoris the number of those changes which where for non-HFT quotes. These results, and thosein Panels B and C show the minimum, 25th, median, 75th, and maximum changes. Analternative approach which directly compares HFT and non-HFT quote change behavioris to look at the ratio of changes. Panel B does this, where HFT

Non−HFT = the fractionof HFT quote changes divided by non-HFT quote changes for each firm day. Panel Cuses the same HFT / Non-HFT variable, but splits it into two groups based on the medianmarket capitalization of the data.

Panel AType Mean Min. p25 p50 p75 Max. NHFT 0.549 0.005 0.454 0.555 0.676 0.901 595.000Non-HFT 0.451 0.099 0.324 0.445 0.546 0.995 595.000

Panel BHFT / Non-HFT 1.559 0.005 0.830 1.247 2.089 9.093 595.000

Panel CLow Market Cap. 1.016 0.009 0.683 0.969 1.322 3.258 297.000High Market Cap. 1.926 0.005 1.073 1.770 2.538 9.093 298.000Total 1.559 0.005 0.830 1.247 2.089 9.093 595.000

26

5.1.3 HFT Market Activity Determinants

Table 9 examines which determinants drive HFT trading. I perform an OLS re-gression with the dependent variable being the percent of share volume in whichHFT were involved in for a given company on a given day. I run the followingregression:

Hi,t = α+MCi ∗ β1 +MBi ∗ β2 +NTi,t ∗ β3 +NVi,t ∗ β4 +Depi,t ∗ β5 + V oli,t ∗ β6 + ACi,t ∗ β7 + ϵi,t,

where i is the subscript representing the firm, t is the subscript for each day, His the percent of share volume in which HFT are involved out of all trades, MC isthe log market capitalization as of December 31, 2009, MB is the market to bookratio as of December 31, 2009, which is winsorized at the 99th percentile, NT isthe number of non HFT trades that occurred, scaled by market capitalization, NVis the volume of non HFT dollars that were exchanged, scaled by market capital-ization, Dep is the average depth of the bid and of the ask, equally weighted, V olis the ten second realized volatility summed up over the day, AC is the absolutevalue of the Durbin-Watson score minus two from a regression of returns over thecurrent and previous ten second period.

Table 9 reports the standardized regression coefficients in column (1). Thatis, instead of running the typical OLS regression on the regressors, the variables,both dependent and independent, are de-meaned, and are divided by their respec-tive standard deviations so as to standardize all variables. The coefficients reportedcan be understood as signaling that when there is a one standard deviation changein an independent variable, the coefficient is the expected change in standard de-viations that will occur in the dependent variable. This makes the regressors un-derlying scale of units irrelevant to interpreting the coefficients. Thus, the largerthe coefficient, the more important its role in impacting the dependent variable.Column two reports the normal coefficients.

The results in the full regression, columns (1) and (2) show that market capital-ization is very important and has a positive relationship with HFT market activity.The market to book ratio is slightly statistically significant, but with a very smallnegative coefficient, suggesting HFT tends to occur slightly more often in valuefirms. Also statistically significant and with moderate economically significantis the dollar volume of non HFT, which is interpreted as HFTs preferring to tradewhen there is less volume, all else being equal. The spread and depth variables are

27

statistically significant and both have medium economically significance. HFTsprefer to trade when there is less depth and lower spreads between bids and asks,all else being equal. Volatility, autocorrelation, and the number of non HFT tradesare not statistically significant.

Many of the explanatory variables may be endogenously determined and asa result the OLS estimator may be a biased. Thus, I run the same regression butonly keeping Market Capitalization and Market to Book. The results are also intable 9, with column (3) reporting the standardized beta coefficients and column(4) reporting the standard OLS coefficient results. This restricted regression in-creases the magnitude of both explanatory variables to a degree, but otherwise theeconomic impact is roughly the same.

5.1.4 HFT Market Activity Time Series

A concern surrounding the May 6 “flash crash” was that the regular market par-ticipants, such as HFTs, stopped trading. Although the database I have does notinclude the May 6, 2010 data, it does span 2008 and 2009, which were volatiletimes in U.S. equity markets. To see whether HFT percent of market trades variessignificantly from day to day, and especially around time periods when the U.S.market experienced large losses, I look at each trading day and count the fractionof activity in which HFT was involved. The results are shown in figure 2. Thereare three graphs. The first is a time series of the fraction of trades were HFTwas involved in during 2008 and 2009. The second graph looks at the fraction ofshares in which HFT was involved during this period. The final graph looks at thefraction of dollar volume in which HFT was involved during this period. In eachgraph there are three lines. The line labeled “All HFT” represents the fractionof exchanges in which HFT was involved either as providing liquidity or as tak-ing liquidity; the line labeled “HFT Liquidity Supplied” represents the fraction oftransactions in which HFT was providing liquidity; the line “HFT Liquidity De-manded” represents the fraction of trades in which HFT was demanding liquidity.All three graphs have minimal volatility among the three measures. Especially ofnote, there is no abnormally large drop, or increase, in HFT participation in thesample data as a whole occurring in September of 2009, when the U.S. equitymarkets were especially volatile.

5.1.5 A Closer Look at Volatility

What has been shown so far has dealt mostly with means, but a major concernis that HFTs are around during normal times, but during extreme market condi-tions, for example when volatility increases, HFTs reduce their trading activity.

28

Table 9: Determinants of HFT Percent of the Market This table shows the result of thefollowing OLS regression: Hi,t = α +MCi ∗ βi +MBi ∗ βi + NTi,t ∗ βi,t + NVi,t ∗βi,t + Depi,t ∗ βi,t + V oli,t ∗ βi,t + ACi,t ∗ βi,t, where i is the subscript representingthe firm, t is the subscript for each day, H is the percent of share volume in which HFTare involved out of all trades, MC is the log market capitalization as of December 31,2009, MB is the market to book ratio as of December 31, 2009, which is winsorized atthe 99th percentile, NT is the number of non HFT trades that occurred, scaled by marketcapitalization, NV is the volume of non HFT dollars that were exchanged, scaled bymarket capitalization, Dep is the average depth of the bid and of the ask, equally weighted,V ol is the ten second realized volatility summed up over the day, AC is the absolute valueof the Durbin-Watson score minus two from a regression of returns over the current andprevious ten second period. Column one shows the standardized beta coefficients, columntwo shows the regular coefficients, column three shows the standardized beta coefficientsfor the regression excluding explanatory variables that may be endogenously determined,and column four shows the regular coefficients.

(1) (2) (3) (4)Economic Impact OLS Coef. Economic Impact OLS Coef.

Market Cap. 0.722∗∗∗ 0.0682∗∗∗ 0.757∗∗∗ 0.0725∗∗∗

(19.51) (19.51) (25.85) (25.85)Market / Book -0.063∗ -0.00609∗ -0.122∗∗∗ -0.0119∗∗∗

(-2.13) (-2.13) (-4.16) (-4.16)$ of Non HFT Volume -0.138∗∗∗ -0.0000239∗∗∗

(-3.82) (-3.82)Average Spread -0.111∗∗∗ -0.0000426∗∗∗

(-3.88) (-3.88)Average Depth -0.132∗∗∗ -2.95e-11∗∗∗

(-4.79) (-4.79)Volatility -0.031 -0.00195

(-1.07) (-1.07)Autocorrelation -0.017 -0.000932

(-0.62) (-0.62)# of Non HFT Trades 0.042 0.0194

(0.98) (0.98)Constant 0.0823∗ 0.0309

(2.54) (1.41)Observations 590 590 590 590Adjusted R2 0.575 0.575 0.533 0.533Standardized beta coefficients in (1) and (3); t statistics in parentheses∗ p < 0.05, ∗∗ p < 0.01, ∗∗∗ p < 0.001

29

Figure 2: Time Series of HFT Market Participation The first graph is a time series ofthe fraction of trades in which HFT was involved in during 2008 and 2009. The secondgraph looks at the fraction of shares in which HFT was involved. The final graph looksat the fraction of dollar volume in which HFT was involved. In each graph three linesappear. One line represents whether HFT was involved as either a liquidity provider or aliquidity taker; another line represents transactions in which HFT was providing liquidity;the final line represents when HFT was demanding liquidity.

3040

5060

7080

01 Jan 08 01 Jul 08 01 Jan 09 01 Jul 09 01 Jan 10sas_date

HFT Liquidity Demanded Trades All HFT TradesHFT Liquidity Supplied Trades

2040

6080


HFT Liquidity Demanded Shares All HFT SharesHFT Liquidity Supplied Shares

3040

5060

7080


HFT Liquidity Demanded DVolume All HFT DVolumeHFT Liquidity Supplied DVolume

30

An alternative concern is that HFT induces heightened levels of volatility, whichis specifically addressed in Section 6.3. To study how HFTs behaves in differentlevels of volatility I implement a quantile regression. The OLS regression deter-mines coefficients based on the conditional mean, the quantile regression deter-mines coefficients based on a conditional observation level, such as the median.I am interested in understanding the relationship between HFT and volatility asvolatility levels change. Therefore, I perform the regression:

V olai,t = α+HFTi,t ∗ β1 + ϵi,t,

where V olai,t is the 15 minute realized return volatility for firm i on day t,and HFTi,t is the percent of shares for firm i on day t involving HFT, in PanelA it includes trades with HFT in any capacity, in Panel B it is the percent whereHFT demand liquidity, and in Panel C it is the percent where HFT supply liquid-ity. This regression is done at the 5% (low volatility), 20%, 40%, 60%, 80% and95% (high volatility). Firm fixed effects are used to control for HFT variabilitydue to firm characteristics. The results are in table 10. Panel A - HFT - ALLshows that as volatility increases from the 5% group to the 80% group, HFT per-cent of trades increases, but for the most extreme groups, those firm-days in the95th percentile, HFT activity is not statistically significant. Note though that theconstant, or baseline HFT participation increases with volatility. Next, Panel Band C break down HFT activity by liquidity. Panel B looks at HFT demandingliquidity activity. As volatility increases the coefficients on HFT Demand Percentincrease, except in the 95th percentile, which is positive but less than the 80 %regression. Again though the constant is increasing in volatility. The results ofPanel C, HFT supplying liquidity activity , is the opposite: as volatility increasesthe HFT Supply Percent coefficient tends to decrease. The coefficient doubles be-tween the 80% and 95%, but the constant also rises substantially. [Note: statisticalanalysis available soon.]

Table 10 looks at day level volatility. But higher frequencies are also of interestgiven that prices can fluctuate dramatically throughout the day but end relativelyunchanged, and this would not be picked up at a day level analysis. Therefore, Ilook at the data in 15 minute intervals. In addition, instead of looking at volatilityI examine returns in the 15 minute period. Given this, I can separate the analysisinto positive and negative return episodes. Instead of using the quintile regressionapproach as I did above, I implement an OLS regression with dummy variablesand interaction terms to capture the variation in the HFT - volatility relationshipacross different market conditions. The regression I run is:

31

Table 10: HFT - Volatility Relationship. This table reports the results from running thequantile regression, V olai,t = α + HFTi,t ∗ β1 + ϵi,t where V olai,t is the 15 minuterealized return volatility for firm i on day t, and HFTi,t is the percent of shares for firm ion day t involving HFT, which in Panel A includes trades having HFT in any capacity, inPanel B it is the percent where HFT is demanding liquidity, and in Panel C it is the percentwhere HFT is supplying liquidity. The regression is performed at the 5% (low volatility)in column (1), 20% in column (2), 40% in column (3), 60% in column (4), 80% in column(5) and 95% (high volatility) in column (6) levels. Firm fixed effects are used.

(1) (2) (3) (4) (5) (6)5 % 20 % 40 % 60 % 80 % 95 %

Panel A - HFT - ALLHFT Percent 0.0111∗∗∗ 0.0106∗∗∗ 0.0163∗∗∗ 0.0258∗∗∗ 0.0313∗∗∗ -0.00804

(0.00167) (0.00118) (0.00158) (0.00216) (0.00297) (0.00802)Constant 0.0178∗∗∗ 0.0488∗∗∗ 0.0685∗∗∗ 0.0940∗∗∗ 0.128∗∗∗ 0.227∗∗∗

(0.00174) (0.00135) (0.00185) (0.00258) (0.00367) (0.0103)Observations 61014 61014 61014 61014 61014 61014

Panel B - HFT - Demand LiquidityHFT Demand Percent 0.0226∗∗∗ 0.0291∗∗∗ 0.0411∗∗∗ 0.0569∗∗∗ 0.0689∗∗∗ 0.0587∗∗∗

(0.00164) (0.00136) (0.00170) (0.00220) (0.00355) (0.00780)Constant 0.0174∗∗∗ 0.0489∗∗∗ 0.0677∗∗∗ 0.0943∗∗∗ 0.129∗∗∗ 0.227∗∗∗

(0.00169) (0.00150) (0.00188) (0.00248) (0.00420) (0.00964)Observations 61014 61014 61014 61014 61014 61014

Panel C - HFT - Supply LiquidityHFT Supply Percent -0.0136∗∗∗ -0.0292∗∗∗ -0.0452∗∗∗ -0.0560∗∗∗ -0.0741∗∗∗ -0.144∗∗∗

(0.00236) (0.00176) (0.00224) (0.00265) (0.00429) (0.00947)Constant 0.0193∗∗∗ 0.0509∗∗∗ 0.0725∗∗∗ 0.101∗∗∗ 0.140∗∗∗ 0.235∗∗∗

(0.00176) (0.00146) (0.00191) (0.00234) (0.00395) (0.00876)Observations 61014 61014 61014 61014 61014 61014Standard Errors in parentheses∗ p < 0.05, ∗∗ p < 0.01, ∗∗∗ p < 0.001

32

HFTi,t = α+ 5%Di,t ∗ β1 + 20%Di,t ∗ β2 + 40%Di,t ∗ β3 + 60%Di,t ∗ β4 + 80%Di,t ∗ β5+95%Di,t ∗ β6 +Reti,t ∗ β7 + 5%Di,t ∗Reti,t ∗ β8+20%Di,t ∗Reti,t ∗ β9 + 40%Di,t ∗Reti,t ∗ β10 + 60%Di,t ∗Reti,t ∗ β11+80%Di,t ∗Reti,t ∗ β12 + 95%Di,t ∗Reti,t ∗ β13 + ϵi,t.

HFT takes on one of four definitions: Buy-Demand, Buy-Supply, Sell-Demand,or Sell-Supply where each defines HFT as the percent of all trades that occur inthe market that satisfy the criteria implied in the name, where the Buy/Sell refersto HFTs activity, and Supply/Demand refers to HFTs role in the transaction. Thebaseline dummy excluded from the regression is for return periods that are in thelowest 5%. 5%Di,t is a dummy variable equal to one if the price decline (incline)for firm i in time t was in the smallest 5% - 20% of all observations and zero oth-erwise. 20%D is a dummy variable equal to one if the price decline (incline) forfirm i in time t was in the smallest 20% - 40% of all observations and zero other-wise.Similarly defined are the 40%Di,t, 60%Di,t, 80%Di,t, and 95%Di,t dummyvariables. Reti,t is the percent change in price for stock i during time t. Theremaining explanatory variables are interactions between the different dummyranges and the Reti,t variable.

The table 11 shows the results. Focusing on the dummy variables, and thenegative returns first, column (1) Buy-Demand and column (2) Buy-Supply tendto increase with larger sized declines, but this increase is non-monotonic. Column(3) Sell-Demand and column (4) Sell-Supply do not show a noticeable pattern.As for the interactive terms,they appear noisy, but across the four columns as theprice drop increases the coefficient tends to cancel out the Ret coefficient value.

The positive return dummy results are also noisy. There is no clear patternin any of the columns. Column (5) Buy-Demand tends to decrease as the priceincline increases. Column (6) Buy-Supply is high in the low and high returnperiods, and near zero in the middle events. Column (7) Sell-Demand is large untilthe 95% Dummy. Column (8) Sell-Supply is high in the low and high return periodand near zero in the middle events, similar to column (6). The interactive termsalso lack a clear pattern. Like the price decline results though during large priceinclines, the interactive slope coefficient tends simply to cancel out the baselineslope coefficient in each column.

These results suggest that during large price declines HFTs do not make un-usually large sell demands, and they do not stop providing liquidity to those who

33

are selling. Similarly with price inclines HFTs do not make unusually large buydemands, and they do not stop providing liquidity to those who are buying. [Note:statistical analysis available soon.]

The above results still don’t overcome the likely endogeneity between HFTand volatility. To overcome this one must find situations in which there are exoge-nous shocks to volatility. Exogenous shocks to volatility typically come from newinformation entering the public domain. Thus, a natural time to expect exoge-nous shocks to volatility is during quarterly firm earnings announcements. In theHFT sample dataset, days on which firms announce their quarterly earnings havehigher volatility than the average non-announcement day for that stock. Thus, notonly is it that the volatility is likely exogenous, coming from news and not traders’churning, it is at elevated levels. The difference is small, but statistically signif-icant. Using OLS regression, I regress the percent of shares in which HFT wereinvolved on a dummy variable, QuarterlyEADummy, which is one for firm iif the observation is on the day of or the day after firm i reported its quarterlyearnings, and zero otherwise. The dependent variable in column (1) is the percentof shares in stock i in which HFT was involved, in column (2) it is the percentof shares in stock i in which HFT was involved and was demanding liquidity, incolumn (3) it is the percent of shares in stock i in which HFT was involved andwas supplying liquidity. The results in table 12 Panel A show that HFT activityincreases with a shock to volatility. For the quarterly earnings announcements, theincrease arises from HFT supplying liquidity in a larger fraction of shares.

Another time in which there was an identifiable exogenous shock to volatilitywas the week of September 15 - September 19., 2008. This was the week inwhich Lehman Brothers collapsed, volatility spiked, and there was a high levelof information uncertainty. Like the quarterly earnings announcements, the weekin September when Lehman failed and a randomly chosen week in Novemberalso shows that firms in the September week have statistically significantly highervolatility. I therefore test whether there is a difference in HFT activity duringthe week of September 15, 2008 and the week of November 3, 2008 (this weekis chosen as it is sufficiently far away to reduce the autocorrelation impact ofvolatility, but not too far away as for there to have been a significant change inHFTs strategies. Using OLS regression, I regress the percent of shares in whichHFT were involved on a dummy variable, LehmanWeekDummy, which is onefor all firms for observations on the dates September 15, 2008 - September 19,2008 and zero otherwise. The dependent variable in column (1) is the percentof shares in stock i in which HFT was involved, in column (2) it is the percentof shares in stock i in which HFT was involved and was demanding liquidity, in

34

Tabl

e11

:H

FTB

ehav

ior

Aro

und

Diff

eren

tSiz

ePr

ice

Cha

nges

Thi

stab

lesh

owst

here

sults

toth

ere

gres

sion

:HFTi,t=

α+5%

Di,t∗

β1+20%D

i,t∗β2+40

%D

i,t∗β3+60

%D

i,t∗β4+80

%D

i,t∗β5+95

%D

i,t∗β6+Ret

i,t∗β7+5%

Di,t∗Ret

i,t∗β8+20

%D

i,t∗

Ret

i,t∗β9+40

%D

i,t∗Ret

i,t∗β10+60

%D

i,t∗Ret

i,t∗β11+80

%D

i,t∗Ret

i,t∗β12+95

%D

i,t∗Ret

i,t∗β13+ϵ i,t

.HFT

take

son

one

offo

urde

finiti

ons:

Buy

-Dem

and,

Buy

-Sup

ply,

Sell-

Dem

and,

orSe

ll-Su

pply

whe

reea

chde

fines

HFT

asth

epe

rcen

tofa

lltr

ades

that

occu

rin

the

mar

kett

hats

atis

fyth

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iteri

aim

plie

din

the

nam

e,w

here

the

Buy

/Sel

lref

ers

toH

FTs

activ

ity,a

ndSu

pply

/Dem

and

refe

rsto

HFT

sro

lein

the

tran

sact

ion.

The

base

line

dum

my

excl

uded

from

the

regr

essi

onis

for

retu

rnpe

riod

sth

atar

ein

the

low

est5

%.5%

Di,t

isa

dum

my

vari

able

equa

lto

one

ifth

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ice

decl

ine

(inc

line)

for

firm

iin

timet

was

inth

esm

alle

st20

%-

40%

ofal

lobs

erva

tions

and

zero

othe

rwis

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Dis

adu

mm

yva

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ualt

oon

eif

the

pric

ede

clin

e(i

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rfir

mi

intim

et

was

inth

esm

alle

st5%

-20

%of

allo

bser

vatio

nsan

dze

root

herw

ise.

Sim

ilarl

yde

fined

are

the40

%D

i,t,6

0%D

i,t,8

0%D

i,t,a

nd95

%D

i,t

dum

my

vari

able

s.Ret

i,t

isth

epe

rcen

tcha

nge

inpr

ice

for

stoc

ki

duri

ngtim

et.

The

rem

aini

ngex

plan

ator

yva

riab

les

are

inte

ract

ions

betw

een

the

diff

eren

tdum

my

rang

esan

dth

eRet

i,t

vari

able

.The

first

lette

r,B

orS,

stan

dfo

rBuy

orSe

ll,th

ese

cond

lette

r,D

orS,

stan

dfo

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and

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pply

liqui

dity

.C

olum

ns(1

)to

(4)a

refo

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ativ

ere

turn

s,a

ndco

lum

ns(5

)to

(8)a

refo

rpos

itive

retu

rns.

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fixed

effe

cts

are

used

.

Neg

ativ

eR

etur

nsPo

sitiv

eR

etur

ns(1

)(2

)(3

)(4

)(5

)(6

)(7

)(8

)B

-DB

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DS-

SB

-DB

-SS-

DS-

S5

%D

umm

y0.

166∗

∗∗0.

131∗

∗∗0.

0805

∗∗∗

0.13

6∗∗∗

0.13

9∗∗∗

0.21

7∗∗∗

0.24

2∗∗∗

0.22

4∗∗∗

(0.0

0901

)(0

.005

94)

(0.0

0797

)(0

.007

45)

(0.0

0862

)(0

.006

31)

(0.0

0831

)(0

.006

48)

20%

Dum

my

0.19

7∗∗∗

0.00

812

-0.1

12∗∗

∗0.

0047

00.

0096

80.

170∗

∗∗0.

210∗

∗∗0.

0646

∗∗∗

(0.0

0870

)(0

.005

74)

(0.0

0770

)(0

.007

20)

(0.0

0895

)(0

.006

55)

(0.0

0862

)(0

.006

73)

40%

Dum

my

0.10

7∗∗∗

0.08

17∗∗

∗0.

190∗

∗∗0.

129∗

∗∗0.

337∗

∗∗-0

.007

500.

0885

∗∗∗

-0.0

734∗

∗∗

(0.0

0888

)(0

.005

85)

(0.0

0785

)(0

.007

34)

(0.0

0853

)(0

.006

24)

(0.0

0822

)(0

.006

42)

60%

Dum

my

0.21

8∗∗∗

0.22

8∗∗∗

0.17

1∗∗∗

0.23

8∗∗∗

0.09

56∗∗

∗-0

.048

0∗∗∗

0.38

8∗∗∗

0.21

6∗∗∗

(0.0

0858

)(0

.005

66)

(0.0

0759

)(0

.007

10)

(0.0

0847

)(0

.006

20)

(0.0

0816

)(0

.006

37)

80%

Dum

my

0.11

4∗∗∗

0.13

6∗∗∗

0.05

73∗∗

∗0.

152∗

∗∗0.

0079

10.

0946

∗∗∗

0.19

4∗∗∗

0.19

1∗∗∗

(0.0

0855

)(0

.005

64)

(0.0

0756

)(0

.007

07)

(0.0

0870

)(0

.006

37)

(0.0

0839

)(0

.006

55)

95%

Dum

my

0.20

2∗∗∗

0.21

0∗∗∗

0.14

9∗∗∗

0.13

9∗∗∗

0.02

35∗∗

0.07

48∗∗

∗0.

0146

0.13

7∗∗∗

(0.0

0834

)(0

.005

50)

(0.0

0738

)(0

.006

90)

(0.0

0823

)(0

.006

02)

(0.0

0793

)(0

.006

19)

Ret

-446

.8∗∗

∗-2

28.4

∗∗∗

-403

.5∗∗

∗-1

25.6

∗∗∗

9.79

740

7.7∗

∗∗50

9.1∗

∗∗49

1.4∗

∗∗

(44.

51)

(29.

36)

(39.

38)

(36.

82)

(46.

32)

(33.

90)

(44.

65)

(34.

84)

5%D

umm

y*R

et51

9.1∗

∗∗36

7.2∗

∗∗33

6.2∗

∗∗35

4.4∗

∗∗-3

57.7

∗∗∗

-702

.9∗∗

∗-8

08.2

∗∗∗

-766

.4∗∗

∗

(45.

88)

(30.

26)

(40.

59)

(37.

95)

(47.

11)

(34.

48)

(45.

41)

(35.

44)

20%

Dum

my*

Ret

557.

5∗∗∗

95.7

4∗∗

54.5

0-8

.780

-14.

70-4

90.7

∗∗∗

-581

.9∗∗

∗-3

62.1

∗∗∗

(44.

92)

(29.

63)

(39.

74)

(37.

16)

(46.

86)

(34.

30)

(45.

17)

(35.

25)

40%

Dum

my*

Ret

458.

4∗∗∗

237.

8∗∗∗

507.

4∗∗∗

196.

6∗∗∗

-228

.5∗∗

∗-2

97.5

∗∗∗

-482

.7∗∗

∗-3

01.7

∗∗∗

(44.

68)

(29.

47)

(39.

53)

(36.

96)

(46.

39)

(33.

95)

(44.

71)

(34.

89)

60%

Dum

my*

Ret

437.

4∗∗∗

287.

4∗∗∗

434.

8∗∗∗

181.

6∗∗∗

-36.

92-3

19.4

∗∗∗

-609

.7∗∗

∗-5

14.2

∗∗∗

(44.

54)

(29.

38)

(39.

40)

(36.

85)

(46.

34)

(33.

92)

(44.

67)

(34.

86)

80%

Dum

my*

Ret

450.

8∗∗∗

239.

9∗∗∗

391.

0∗∗∗

156.

7∗∗∗

-1.1

06-4

03.6

∗∗∗

-538

.3∗∗

∗-5

18.1

∗∗∗

(44.

52)

(29.

36)

(39.

38)

(36.

83)

(46.

33)

(33.

91)

(44.

66)

(34.

85)

95%

Dum

my*

Ret

451.

0∗∗∗

232.

5∗∗∗

400.

8∗∗∗

118.

6∗∗

-8.9

42-4

06.4

∗∗∗

-506

.6∗∗

∗-4

90.1

∗∗∗

(44.

51)

(29.

36)

(39.

38)

(36.

82)

(46.

32)

(33.

90)

(44.

65)

(34.

84)

Con

stan

t0.

136∗

∗∗0.

0576

∗∗∗

0.15

2∗∗∗

0.08

38∗∗

∗0.

202∗

∗∗0.

0395

∗∗∗

0.11

0∗∗∗

0.01

50∗

(0.0

0801

)(0

.005

28)

(0.0

0709

)(0

.006

63)

(0.0

0799

)(0

.005

85)

(0.0

0771

)(0

.006

01)

Obs

erva

tions

4647

2746

4727

4647

2746

4727

3674

6836

7468

3674

6836

7468

Adj

uste

dR

20.

084

0.04

90.

024

0.08

40.

055

0.04

40.

087

0.08

2St

anda

rder

rors

inpa

rent

hese

s∗p<

0.05

,∗∗p<

0.01

,∗∗∗

p<

0.00

1

35

column (3) it is the percent of shares in stock i in which HFT was involved andwas supplying liquidity. The results show that HFT activity increases with a shockto volatility. For the Lehman Week increase in HFT, the increase arises from HFTsupplying liquidity and demanding liquidity in a larger fraction of shares.

5.2 Profitability

HFTs engage in a price reversal strategy and they make up a large portion of themarket. Given their trading amount a question of interest is how profitable is theirbehavior. HFTs have been portrayed as making tens of billions of dollars fromother investors. Due to the limitations of the data, I can only provide an estimateof the profitability of HFTs. The HFT labeled trades come from many firms,but I cannot distinguish which HFT firm is buying and selling at a given time.Also, recall that the dataset only contains Nasdaq trades. Therefore, there willbe many other trades that occur that the dataset does not include. Nasdaq makesup 20% - 30% of all trades and so two out of every three trades are unobserved.I circumvent these limitations by making estimates using the market behaviorresults from above to arrive at an overall annual profitability of HFT.

I consider all HFT actions to come from one trader. I take all HFT buys andsells at their respective prices and calculate how much money was spent on pur-chases and received from sales. HFTs regularly switch between being net longand net short throughout the day, but at the end of the day they tend to hold veryfew shares. With these considerations in mind, I can estimate the total profitabil-ity of these 26 firms. As many HFTs do not end the day with an exact net zeroposition in each stock I take any excess shares and assume they were traded at themean price of that stock for that day. Thus, the daily profitability for each stock iscalculated as:

Profit =T∑t=1

[1Sell ∗ Pricet ∗ Sharest − 1Buy ∗ Pricet ∗ Sharest] +

1∑Tt=1 Sharest

T∑t=1

[Pricet ∗ Sharest] ,

where 1Sell is a dummy indicator that equals one if HFTs sold a stock in trans-action t and zero otherwise, 1Buy is similarly defined for HFTs buying, Pricetis the price at which transaction t occurred, Sharest is the number of shares ex-changed in transaction t. Summing up the Profit for each stock on a given day

36

Table 12: HFT - Exogenous Volatility Relationship. This table shows the results fromtwo different approaches of trying to understand the impact volatility has on HFT activity.The dependent variable in column (1) is the percent of shares in stock i in which HFT wasinvolved, in column (2) it is the percent of shares in stock i in which HFT was involvedand was demanding liquidity, in column (3) it is the percent of shares in stock i in whichHFT was involved and was supplying liquidity. In Panel A the explanatory variable,QuarterlyEADummy which is one for firm i if the observation is on the day and nextday on which firm i reported its quarterly earnings, and zero otherwise. In Panel B theexplanatory variable, LehmanWeekDummy is one for all firms for observations on thedates September 15, 2008 - September 19, 2008 and zero otherwise. Firm fixed effectsare used.

Panel A - HFT - Exogenous Volatility, Quarterly Earnings(1) (2) (3)

HFT - ALL HFT - Demand HFT - SupplyQuarterly EA Dummy 0.00684∗ -0.00116 0.0124∗∗∗

(0.00311) (0.00288) (0.00231)Constant 0.756∗∗∗ 0.402∗∗∗ 0.545∗∗∗

(0.0167) (0.0155) (0.0125)Observations 4806 4806 4806Adjusted R2 0.743 0.606 0.783Standard errors in parentheses∗ p < 0.05, ∗∗ p < 0.01, ∗∗∗ p < 0.001

Panel B - HFT - Exogenous Volatility, Lehman Failure

(1) (2) (3)HFT - ALL HFT - Demand HFT - Supply

Lehman Week Dummy 0.0130∗∗ 0.0103∗ 0.0142∗∗∗

(0.00464) (0.00435) (0.00322)Constant 0.753∗∗∗ 0.390∗∗∗ 0.542∗∗∗

(0.0257) (0.0242) (0.0179)Observations 1200 1200 1200Adjusted R2 0.840 0.730 0.883Standard errors in parentheses∗ p < 0.05, ∗∗ p < 0.01, ∗∗∗ p < 0.001

37

results in the total HFT profitability for that day.The result of this exercise is that on average, per day, HFTs make $298,113.1

from the 120 stocks in my sample on trades that occur on Nasdaq.The above number substantially underestimates the actual profitability of HFTs.

First, the 120 stocks have a combined market capitalization of $2,110,589.3 (mil-lion), a fraction of Compustat firms’ combined market capitalization is $17,156,917.3(million). Second, Nasdaq is one of several venues where trades occur and onaverage makes up between 20 - 30% of trading activity. To account for these lim-itations in the data I carry out the following exercise: I use the non-endogenousregression coefficient estimates in the HFT percent determinant estimation foundin table 9 to estimate the percent of trades involving HFT and multiply it by thefraction of shares where HFTs are not trading with each other, as a HFTr ex-change with a HFTr will have a net zero profit when considering HFTs profit inthe aggregate.

ˆHFT = .6835[.0308866+MarketCap∗.0725419−Market/Book∗.0119239.],

where MarketCap is the log of the daily shares outstanding of company imultiplied by the closing price of company i, andMarket/Book is the ratio of theMarketCap divided by the Compustat book value based on the the most recentpreceding quarterly report, winsorized at the 99th percentile. ˆHFT is calculatedfor each stock. I multiply ˆHFT by the dollar volume traded for each stock on eachday in 2008 and 2009, and I multiply this value by the profit per dollar traded byHFTs found above. Thus, I arrive at the annual estimated profits of HFTs by:

ˆHFTAnnualProfit =1

2

N∑i=1

T∑t=1

[ˆHFT i,t ∗DV olumei,t ∗ .000106

](4)

The .000106 value represents the profit per dollar volume HFT traded with anon-HFT. It is determined by taking the total profit of HFTs from the 120 samplefirms over the sample time period and divide it by the HFT - non-HFT dollarvolume traded ($151,739,574/$2,089,346,000,000). The result of this calculationis that HFTs gross profit is approximately $ 2.995 billion annually.

There is no adjustment made for transaction costs yet. However, such costswill be relatively small, the reason being that when HFT provide liquidity they re-

38

ceive a rebate from the exchange, for example Nasdaq offers $.20 per 100 sharesfor which traders provided liquidity, but this is only for large volume traders likeHFTs. On the other hand, Nasdaq charges $.25 per 100 shares for which tradestake liquidity. As the amount of liquidity demanded is slightly less than the liquid-ity supplied by HFT, these two values practically cancel themselves out. A roughestimate of the cost of trading is calculated by assuming that there is an equalnumber of shares demanded and supplied, thus I can estimate each trade of 100shares costs .025 (.05 per trade, but only half of trades are demanding liquidity.)If I assume the average stock price is $30, then using the total number of impliedshares traded (including HFTr-to-HFTr transactions), the annual transaction costfor HFTs is $344,469,548.

What is important isn’t the level of profitability of HFT, but what it is relativeto the alternative, a market consisting of non-HFT market makers. Thus, I com-pare how profitable HFTs trades are per dollar traded as compared to other marketmakers, specifically specialists of NYSE stocks in 2000. Hasbrouck and Sofianos(1993) and Coughenour and Harris study the trading activity and profitability ofthe NYSE specialists. From the above results, HFT make on average 1/100th ofa penny ($.000106) per dollar traded. Using the data from Coughenour and Har-ris, specialists before HFT and before decimalization (and after decimalizationmade $.000894 ($.00052) per dollar traded in small stocks, $.00292 ($.00036)per dollar traded in medium stocks, and $.0025 ($.00059) per dollar traded inlarge stocks. From this perspective, HFTs are less than an eighth as expensiveas pre-decimalization market makers, and still less than a fourth as expensive astraditional market makers post-decimalization.

Figure 3 displays the time series of HFT profitability per day. The graph is afive day-moving average of profitability of HFT per day for the 120 firms in thedataset. Profitability varies substantially from day to day, even after smoothingout the day to day fluctuations.

To try to understand what drives the changes in profitability per day I lookat the determinants for what stocks on different days are the most profitable. Iregress the profitability on several potentially important variables, the same onesused in the regression to determine HFT percent of the market. I run the followingstandardized regression:

Profiti,t = α+Hi,t ∗ β1 +MCi ∗ β2 +MBi ∗ β3 +NTi,t ∗ β4 +NVi,t ∗ β5 +Depi,t ∗ β6 + V oli,t ∗ β7 + ACi,t ∗ β8,

39

Figure 3: Time Series of HFT Profitability Per Day. The figure shows the 5-day movingaverage profitability for all trading days in 2008 and 2009 for trades in the HFT data set.Profitability is calculated by aggregating all HFT for a given stock on a given day andcomparing the cost of shares bought and the revenue from shares sold. For any end-of-day imbalance the required number of shares are assumed traded at the average share pricefor the day in order to end the day with a net zero position in each stock.

−100

0000

010

0000

020

0000

030

0000

0$

Prof

it Pe

r Day


40

where all variables are defined as before, and the dependent variable Profittakes on three different definitions. The results are displayed in table 13 and arestandardized coefficients. In the first column Profit is defined as the profit perHFT share traded averaged over stock i on day t; in the second column it is theamount of money HFT made for stock i on day t; in the third column it is the num-ber of HFT shares traded for stock i on day t. The second and third regressiondecompose the parts of the first regression’s dependent variable. Again, the re-ported coefficients have been standardized so that the coefficient value representsa one standard deviation movement in a particular variable’s impact on Profit.

The Profit per HFT Share Traded regression has no statistically or economi-cally significant variables and has a negative r-squared. The second regression,with the dependent variable as profits, has two coefficients that are statisticallysignificant. Autocorrelation and V olatility. Autocorrelation has a smaller co-efficient and is negative, implying the less predictable price movements in a stockthe more profitable is that stock for HFT. The V olatility measure has a largepositive economic impact and is highly statistically significant.

The third regression, HFT shares traded, has three statistically significant andeconomically significant variables. MarketCap. is positive with a coefficient of0.21, the AverageDepth coefficient is positive and has a coefficient of 0.098,and the V olatility coefficient, which also has a positive relationship with thedependent variable, shows the largest coefficient magnitude of 0.622.

This section has shown that HFTs engage in a price reversal trading strategy,that HFT tends to occur more in large stocks with relatively low volume withnarrow spreads and depth. In addition, there is little change in HFT activity duringextreme market conditions and HFT slightly increases with exogenous shocks tovolatility. Also, HFTs are profitable, making approximately $3 billion a year,but on a dollar traded basis they are significantly less expensive than traditionalmarket makers, and that the profitability is related to volatility. Next, I investigatethe role HFT plays in the demand and supply of liquidity.

6 Market QualityThe following section analyzes HFT impact on market quality. Market qualityrefers to liquidity, price discovery, and volatility. Each analysis uses differenttechniques to study the relationship between HFT and each type of market quality.

41

Table 13: Determinants of HFT Profits Per Stock Per Day The dependent variable forthe first column is defined as the profit per HFT share traded averaged over each stock ion day t; in the second column it is the amount of money HFT made for each stock oneach day; in the third column it is the number of HFT shares traded.

Profit per HFT Share Traded Profits HFT Shares TradedHFT Percent -0.087 -0.024 0.062

(-1.04) (-0.40) (1.42)Market Cap. -0.015 -0.059 0.210∗∗∗

(-0.16) (-0.86) (4.20)Market / Book 0.014 -0.003 0.013

(0.23) (-0.07) (0.43)$ of Non HFT Volume -0.058 0.019 -0.073

(-0.76) (0.36) (-1.90)Average Spread -0.004 -0.015 0.000

(-0.06) (-0.35) (0.01)Average Depth -0.009 -0.008 0.098∗∗∗

(-0.16) (-0.19) (3.33)Volatility 0.038 0.359∗∗∗ 0.622∗∗∗

(0.67) (8.67) (20.70)Autocorrelation -0.033 -0.078∗ -0.036

(-0.62) (-1.97) (-1.24)# of Non HFT Trades 0.027 -0.025 0.031

(0.29) (-0.41) (0.69)Constant ∗∗∗

(0.96) (1.45) (-3.66)Observations 360 590 590Adjusted R2 -0.014 0.111 0.532Standardized beta coefficients; t statistics in parentheses∗ p < 0.05, ∗∗ p < 0.01, ∗∗∗ p < 0.001

42

6.1 HFT Liquidity

Liquidity supply and demand in the microstructure literature refers to which sideof a trade had a limit order in place that was executed and which side of the trans-action entered the marketable order. The side with the limit order is the liquiditysupplier, and the marketable order side is the liquidity taker. In this section I lookat the descriptive statistics of HFT demanding liquidity, then I examine the roleof HFT in supplying liquidity, finally I analyze how much liquidity is provided inthe quotes and the order book by HFT.

6.1.1 HFT Liquidity Demand

The results in table 4 show that liquidity is demanded by HFTs in 50.4% of alltrades. This section will examine how HFT initiated trades tend to behave com-pared to non-HFT trades. HFTs tend to demand liquidity in similar dollar sizetrades as do non HFTs. There appears to be clustering in trades, whereby if aprevious trade is a buy, it is much more likely the next trade will also be a buy,and the same is true for sales, and this clustering is stronger for HFTs than fornon-HFTs. Trades that either proceed a HFTr trade or follow a HFTr trade tend tooccur more quickly than those proceeding or following a non-HFTr. As trade sizeincreases, the time between trade decreases, and this is true regardless of the sizeof the firm. Finally, HFTs liquidity demand is quite consistent across the day, butthey make up a significantly smaller portion of trades at the opening and close ofthe trading day.

Table 14 looks at the percent of all transactions for different size trades, indollar terms, and with different HFTs and non-HFTs liquidity providers and de-manders. The first column of Table 14 reports the fraction of trading volume fordifferent combinations of HFTs and non-HFTs as liquidity providers and takers.For small trades, those worth less than $1,000, HFTs are not as involved as non-HFTs, this is consistent with the previous results that show HFTs tend to trademore in stocks with large market caps, which typically have stock prices in thedouble digits. Most trades occur in the value range of $1,000 to $4,999. HFT intwo of the three categories are the most engaged in these transactions. HFTs shareof trades engaged in falls in the $5,000 to $14,999 category, except for when theyare demanding liquidity. It is this size trade that Chakravarty (2001) and Barclayand Warner (1993) find to have the largest impact on stock prices and thus arethe size of trades informed investors tend to use. In the $30,000 plus category oftrades, HFTs provide the least amount of liquidity, but tend to demand the most.This suggest that HFT are liquidity takers in large trades and liquidity providers

43

Table 14: HFT Volume by Trade-size Category. This table reports dollar-volume par-ticipation by HFTs and non-HFTs in five dollar-trade size categories. The first letter inthe column labels represents the liquidity seeking side of a trade. The second letter in thecolumn labels represents the passive party of a trade. H represents a HFTr, N represents anon-HFTr.

Type of Liquidity Taker and Liquidity SupplierDollar Size Categories HH HN NH NN Total N

0-1,000 21.5% 25.7% 25.3% 27.5% 100.0% 245,4011,000-4,999 25.8% 24.5% 28.3% 21.5% 100.0% 1,473,0475,000-14,999 23.7% 27.0% 26.3% 23.0% 100.0% 940,63415,000-29,999 25.1% 25.9% 26.2% 22.8% 100.0% 308,10230,000 + 17.4% 32.2% 19.6% 30.7% 100.0% 141,609Total 24.4% 25.8% 26.8% 23.0% 100.0% 3,108,793

N 757,864 803,177 833,883 713,869 3,108,793

in small shares, which is consistent with the theory that HFTs are concerned withinformed traders in big trades.

A concern among many is that if HFTs use similar trading strategies, theywill exacerbate market movements. To determine whether HFTs strategies aremore correlated than those of non-HFTs I examine the frequency at which HFTstrade with each other and compare it to a benchmark model used in Chaboudet al. (2009) that produces theoretical probabilities of different types of trades(demander - supplier) under the assumption that traders’ activities are randomand independent. Then I can compare the actual occurrence of different trades tothe predicted amount. As above, there are four types of trades, HH, HN, NH, NN,where the first letter represents the liquidity demander and the second the liquiditysupplier.

Let Hs be the number of HFT liquidity suppliers, Hd be the number of HFTliquidity demanders, Ns be the number of non-HFT liquidity suppliers, Nd be thenumber of non-HFT liquidity demanders. The probability that a HFTr will provideliquidity is then αs = Prob(HFT − supply) = Hs

Ns+Hs, and the probability the

44

liquidity is supplied by a non-HFTr is 1 − αs. The probability that a HFTr willdemand liquidity is αd = Prob(HFT − demand) = Hd

Nd+Hd, and the probability

the liquidity is demanded by a non-HFTr is 1−αd. The probabilities of a specificdemander and supplier can be calculated: Prob(HH) = (αd)(αs), Prob(HN) =(αd)(1− αs), Prob(NH) = (1− αd)(αs), Prob(NN) = (1− αd)(1− αs).

As a result, the follow fraction holds: Prob(NN)Prob(NH)

≡ Prob(HN)Prob(HH)

. Let RN ≡Prob(NN)Prob(NH)

be the non-HFTr demanding liquidity ratio and RH ≡ Prob(HN)Prob(HH)

be theHFTr demanding liquidity ratio. When non-HFTs are greater than HFTs thenProb(NN) > Prob(NH) and Prob(HN) > Prob(HH). However, regardlessof the number of non-HFTs or HFTs, the ratio of ratios, R ≡ RH

RNwill equal one as

non-HFT will take liquidity from other non-HFT in the same proportion as HFTstake liquidity from other HFTs. Therefore, if R = 1, it must be that HFTs andnon-HFTs trade with each other as much as expected when there trading strategiesare equally correlated. if R > 1 then it is the case that HFTs trade with each otherless than expected, or that HFT trade with non-HFT more than expected.

The proxy used for R in the data is R̂N = V ol(NN)V ol(NH)

and R̂H = V ol(HN)V ol(HH)

.Table 15 shows the results. The column R shows the results for each stock ofthe average RH

RNper day. The column Std.Dev. is the standard deviation of the R

ratio for that stock over time. The column %DaysR < 1 is the fraction of daysin which R < 1. Starting with %DaysR < 1, all but two stocks have the ratioR < 1 over 50% of the time. 20 are in the 50%’s, 26 are in the 60%’s, 12 are inthe 70%’s, 17 are in the 80%’s, 37 are in the 90%’s, and 6 always have R < 1.Overall 79% of days haveR < 1. Of the 120 firms, 88 have an averageR less than1. This suggests that HFTs trade with each other more than expected or that HFTstrade with non-HFTs less than expected. The interpretation of this result is thatHFTs engage in a more diverse variety of strategies than non-HFTs, whereby thediverse strategies result in one HFTr deciding to buy and another HFTr decidingto sell simultaneously. [Note: statistical analysis available soon.]

Table 14 analyzed the frequency of different types of trades, the next tableexamines the conditional frequency and occurrence of different types of trades.Table 16, similar to that in Biais, Hillion, and Spatt (1995) and Hendershott andRiordan (2009), provides evidence on the clustering of HFT in trade sequences.In the table, H stands for HFTr and N stands for non-HFTr. The first letter in therows for Panel A and B is who is demanding liquidity at Time t-1. The secondletter in these two panels is who is demanding liquidity at time t. Panel A reportsthe unconditional frequency of observing HFTr and non-HFTr trades. Seeing aHFTr demand liquidity in time t − 1 followed by a HFTr demanding liquidity

45

Tabl

e15

:D

iver

sity

ofH

FTs

Stra

tegi

es.

Thi

sta

ble

repo

rts

the

mea

npe

rst

ock

ofth

eda

ilyra

tioR

=RH/RN

whe

reR̂N

=Vol(NN)

Vol(NH)

andR̂H

=Vol(HN)

Vol(HH).

The

resu

ltsar

efo

rth

efu

llsa

mpl

epe

riod

.Std.D

ev.

isth

est

anda

rdde

viat

ion

ofth

eda

ilyra

tioR

for

that

part

icul

arst

ock

over

time.

The

colu

mn%DaysR

<1

isth

efr

actio

nof

days

inw

hich

R<

1fo

rth

atst

ock. Sy

mbo

lR

Std.

Dev

.%

Day

sR<

1Sy

mbo

lR

Std.

Dev

.%

Day

sR<

1Sy

mbo

lR

Std.

Dev

.%

Day

sR<

1A

A0.

600.

141.

00C

PWR

0.64

0.17

0.58

JKH

Y0.

720.

260.

95A

APL

0.79

0.08

0.65

CR

1.12

1.72

0.81

KM

B0.

720.

170.

57A

BD

1.03

0.98

0.98

CR

I0.

780.

320.

74K

NO

L1.

362.

220.

99A

DB

E0.

660.

130.

91C

RVL

0.88

0.96

0.99

KR

0.62

0.15

0.58

AG

N0.

730.

210.

88C

SCO

0.63

0.11

0.93

KT

II5.

7240

.77

0.83

AIN

V0.

710.

270.

99C

SE0.

650.

260.

65L

AN

C0.

740.

360.

85A

MA

T0.

670.

130.

92C

SL0.

950.

600.

68L

EC

O0.

710.

410.

73A

ME

D0.

660.

240.

97C

TR

N0.

880.

470.

99L

PNT

0.85

0.29

0.86

AM

GN

0.77

0.13

0.94

CT

SH0.

640.

130.

69L

STR

0.76

0.23

0.26

AM

ZN

0.81

0.13

0.60

DC

OM

0.87

0.48

0.99

MA

KO

5.59

10.0

10.

85A

NG

O1.

060.

850.

74D

EL

L0.

660.

131.

00M

AN

T0.

690.

370.

67A

POG

0.80

0.35

0.72

DIS

0.52

0.12

0.53

MD

CO

0.94

0.44

0.82

AR

CC

0.90

0.66

1.00

DK

2.92

30.2

30.

99M

EL

I0.

760.

350.

54A

XP

0.63

0.13

0.60

DO

W0.

560.

120.

99M

FB1.

554.

240.

53A

YI

0.94

0.47

0.63

EB

AY

0.60

0.12

0.57

MIG

1.54

3.06

0.98

AZ

Z1.

131.

480.

71E

BF

1.29

2.05

0.60

MM

M0.

680.

140.

62B

AR

E0.

910.

540.

68E

RIE

1.01

0.66

0.83

MO

D1.

121.

460.

99B

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46

in time t is as common as seeing any other time t − 1, t sequence. If all HFTswere market makers and non-HFTs were not, then it appears that about a quarterof trades are ”hot potato” rebalancing as discussed by Lyons (1997), wherebymarket makers trade with each other to eliminate inventory imbalances. Panel Breports the conditional frequency of observing HFTr and non-HFTr initiated tradesafter observing trades of other participants. In Panel B, the columns are whetherthe liquidity taker is buying (B) or selling (S). The first letter represents what theliquidity taker is doing in the time t−1 trade. The second letter represents what theliquidity taker is doing in the time t trade. In column and row headings t indexestrades, not time. The results suggest that one tends to see liquidity demanderspurchase shares follow a previous trade of a liquidity demander purchasing shares,and the same with sales, regardless of what type of trader was demanding theliquidity. The clustering affect is stronger, in both buying and selling, for HFTdemanders than it is for non-HFT demanders.

Panel C provides conditional probabilities based on the previous trade’s sizeand type of trader. The rows represent the type of trader taking liquidity at timet − 1, either H for HFTr or N for non-HFTr. In addition, the rows are furtherpartitioned based on the size of the trade, measured by the dollar size of sharesexchanged in the t-1 trade. 1 represents a trade of size $0 -$999; 2 representsa trade of size $1,000 - $4,999; 3 represents a trade of size $5,000 - $14,999;4 represents a trade of size $15,000 - $29,999; and 5 represents a trade of sizegreater than $30,000. The columns identify who was the liquidity demander attime t (H or N) and is further partitioned along the size categories discussed above.The results show that trades of size and type of liquidity demander are highlydependent on the previous trade type. HFTs tend to trade with HFTs, and thelarger the dollar size of a trade the higher the likelihood the next trade will belarge.

The next set of results regarding type of trader initiated trading looks at thetime between trades. Table 17 reports the average time between trades depen-dent on different trade characteristics. All times reported are in seconds. PanelA reports the average amount of time between two trades, two HFTr liquiditydemanding trades, and two non-HFTr liquidity demanding trades, and between atrade where the t − 1 trade was initiated by a trader who was a HFTr, or a non-HFTr. Both trades when the liquidity demander is a HFTr at both t − 1 and t,and when a HFTr is the liquidity demander at t − 1, regardless of who demandsliquidity at time t, are more rapidly executed.

Panel B provides the average amount of time between two different trade or-derings and total dollar-volume and per trade dollar-volume categories. The first

47

Table 16: Trade Frequency Conditional on Previous Trade. Panel A reports the unconditionalfrequency of observing HFTr and non-HFTr initiated trades. Panel B reports the conditional fre-quency of observing HFTr and non-HFTr trades after observing trades of other participants. Incolumn and row headings t index trades. Panel C provides conditional probabilities based on theprevious trade’s size and participant. The first letter in the rows for Panel A and B represents whois demanding liquidity at Time t − 1. The second letter in these two panels is who is demandingliquidity at time t.

Panel AT-1 Type and T Type %

HH 24.4%HN 25.8%NH 26.8%NN 23.0%Total 100.0%

Panel BT-1 Buy or Sell and T Buy or Sell

T-1 Type and T Type BB BS SB SS Total% % % % %

HH 44.3% 5.9% 5.9% 43.9% 100.0%HN 44.1% 6.5% 6.3% 43.1% 100.0%NH 41.9% 7.5% 7.7% 42.9% 100.0%NN 41.5% 7.7% 7.8% 42.9% 100.0%Total 43.0% 6.9% 6.9% 43.2% 100.0%

Panel CLD Size

lag LD Size H1 H2 H3 H4 H5 N1 N2 N3 N4 N5 Total% % % % % % % % % % %

H1 25.9% 32.2% 13.3% 2.5% 1.0% 7.5% 10.8% 5.4% 0.8% 0.4% 100.0%H2 5.1% 58.2% 14.8% 3.8% 1.6% 1.3% 11.4% 3.0% 0.7% 0.3% 100.0%H3 3.2% 23.1% 46.2% 6.1% 2.3% 0.9% 4.3% 12.0% 1.3% 0.5% 100.0%H4 1.9% 18.2% 18.7% 35.0% 7.6% 0.5% 2.9% 4.5% 8.6% 2.1% 100.0%H5 1.7% 17.0% 16.2% 17.3% 27.8% 0.5% 2.7% 3.9% 5.2% 7.6% 100.0%N1 6.8% 7.4% 3.5% 0.7% 0.3% 39.6% 29.5% 9.6% 1.7% 0.8% 100.0%N2 1.7% 11.5% 2.8% 0.7% 0.3% 5.3% 57.9% 14.5% 3.6% 1.8% 100.0%N3 1.3% 4.6% 12.4% 1.6% 0.6% 2.7% 23.1% 44.8% 6.0% 2.7% 100.0%N4 0.6% 3.4% 3.9% 9.0% 2.5% 1.5% 17.8% 18.6% 34.5% 8.1% 100.0%N5 0.7% 3.7% 4.0% 4.8% 7.9% 1.5% 18.3% 18.0% 17.3% 23.9% 100.0%Total 3.7% 23.9% 15.4% 5.1% 2.3% 4.2% 23.6% 14.9% 4.8% 2.2% 100.0%48

two columns in Panel B are for some trade type at time t − 1, and at time t thereis a liquidity taker of H or N, where the columns are separated based on the timet liquidity taker. The last two columns are similar except that the columns aredistinguished based on the time it takes when the time t − 1 liquidity taker is acertain type (H or N). Rows S1 through L5 represent different types of stocks. Thefirst character, S,M, or L, represents the dollar volume traded in a given stock ona given day, with S being for trades in small stocks with total dollar volume under$800 Million, M for medium stocks with dollar volume between $800 Million and$1.2 Billion, and L for large stocks with dollar volume greater than $1.2 Billion.The second character, the number 1 through 5 represents the size of the partic-ular trade. If the trade was less than $1000 then it is a 1, if its between $1,000and $4,999 its a 2, if between $5,000 and $14,999 its a 3, if between $15,000and $29,999 its a 4, and if its greater than $30,000 it is a 5. The results suggestthat as greater dollar volume is traded ,the time between trades decreases. Also,within each dollar volume category, the larger the trade, usually the shorter thetime before another trade occurs. This is the opposite of what Hendershott andRiordan (2009) find; they see that small orders for AT tend to execute faster thanlarge orders. This result is evidence that HFTs actively monitor the market forliquidity, but that they focus their trading strategy around order imbalances fromlarge trades. Finally, for most of the different categories, HFTs tend to trade morerapidly, whether looking at time t− 1 or time t.

Finally, I examine the intraday pattern of HFT supply and demand of liquid-ity. If HFTs do try and end the day with a near net zero position in stocks thenthey should wind down their trading before the end of the trading day in order toprevent getting stuck with assets they do not want to hold overnight. Similarly,at the beginning of the trading day HFTs will have few positions in which theyare trying to maintain a near net zero position in and so trading should be lessprevalent. To analyze this I create a time series of the type of traders throughoutthe day. I take all trades that occur on February 22, 2010 - February 26, 2010 andput them in to ten second bins based on the time of day they occurred, regardlessof the day. Then, I split them into the types of trades based on who was supply-ing liquidity and who was demanding liquidity and calculate the percent of eachtype of transaction per time period bin. Figure 4 shows the make up of differenttypes of trades throughout the day. The four different patterns, HH, HN, NH, NNrefer to the type of liquidity demander (first letter) and liquidity supplier (secondletter). The figure is stacked so that each time period sums to one. During theday the trading ratios are quite stable, except at the beginning and end of the day.During these periods HFTs tend to trade with each other much less frequently and

49

Table 17: Average Time Between Trades. All values are in seconds. Panel A reportsthe average amount of time between two trades, two HFTr liquidity demanding trades,and two non-HFTr liquidity demanding trades, and between a trade where the initial tradehad a HFTr, or a non-HFTr liquidity demander. Panel B provides the average amount oftime between two different trade orderings and trade-size categories (refer to the previoustable for the different trade-size categories) The first two columns in Panel B is for sometrade type at t − 1 and at time t there is a liquidity taker of H or N, where the columnsare separated based on the time t liquidity taker. The last two columns are similar exceptthat the columns are distinguished based on the time it takes when the time t− 1 liquiditytaker is a certain type (H or N).

Panel AHFT Non-HFT

Unconditional Time Between Trades 3.351 5.667Time Between Trades of Same Type of Trader 8.696 9.081

Panel BTime t Liquidity Taker Time t-1 Liquidity TakerHFT Non-HFT HFT Non-HFT

S1 30.746 25.449 18.384 35.843S2 9.620 10.578 7.582 12.657S3 5.069 5.513 4.485 6.134S4 3.426 3.354 2.742 4.067S5 4.576 4.065 3.572 5.056M1 0.988 1.538 1.183 1.378M2 1.219 1.399 1.064 1.572M3 1.095 1.435 1.112 1.434M4 1.098 1.166 0.998 1.273M5 1.136 0.989 0.851 1.290L1 0.746 1.266 0.899 1.118L2 1.135 1.119 0.841 1.447L3 0.746 1.149 0.842 1.065L4 0.780 0.724 0.668 0.833L5 0.729 0.639 0.602 0.760

50

HFTs tend to initiate fewer trades and to provide liquidity in fewer trades. This isconsistent with the scenario of HFTs trying to end the day near net-zero in theirequity positions.

Figure 5 also looks at trades throughout the day, but only charts the percent ofdollar volume in which HFTs are demanding liquidity (top graph) and supplyingliquidity (bottom graph). Again this shows that HFTs significantly reduce boththeir supply and their demand for liquidity at the start and end of trading hours.

Figure 4: Type of Liquidity Providers / Takers throughout the day. The figure showsthe make up of traders throughout the day. It shows that HFTs tend to reduce their tradingactivity at the opening and closing of the trading day. the first letter is the liquidity taker,the second letter is the liquidity provider.

.2.4

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9:43 11:6 12:30 1:53 3:16 4:40Time of Day

HH Transaction HN TransactionNH Transaction NN Transaction

6.1.2 HFT Liquidity Supply

This section analyzes HFT and the supply of liquidity. I focus on the amountof liquidity HFTs supply. I show that, beyond supplying liquidity in 51.4% ofall trades, HFTs also often supply the inside quotes throughout the day. I thenconsider the determinants that influence which stocks, and on what days, HFTsprovide the inside quotes. Finally, I examine what the additional price impactwould be on stocks if HFTs were not part of the order book. There is a sizeableimpact, which shows the importance of HFT in creating liquid markets.

51

Figure 5: HFT Liquidity Demander or Supplier throughout the day. The graph showsthe make up of HFT throughout the day. The first graphs shows the HFT demand for liq-uidity throughout the day. The second graph shows the HFT supply of liquidity through-out the day.

.3.4

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9:43 11:6 12:30 1:53 3:16 4:40Time of Day

52

6.1.2.1 HFT Time at Inside Quotes To begin analyzing HFT role in provid-ing liquidity in the stock market I look at the amount of time HFTs supply theinside bid or ask compared to non-HFTs. For each stock, on each day, I takethe number of minutes HFTs are providing the inside bid or ask and, either: (a)subtract the number of minutes non-HFTs are providing the best inside bid or ask(ties are dropped), these are the “Minutes” results, or (b), divide this value by thetotal number of minutes were HFTs and non-HFTs did not have the same insidequotes, these are the “Percent” results. The results are shown in table 18.

Table 18 looks at, for the 120 sample stocks, whether HFTs provide moreliquidity than non-HFTs by considering how often they are providing the insidequote (bid or ask). The manner in which the metric is constructed results in therebeing a total of 780 minutes ( 2*60*6.5) that a HFT could potentially be providingthe inside quote. This is twice as many minutes then what actually occur duringthe trading day. The table is separated into two categories - the category “HFT -”displays statistics for when HFTs provides fewer inside quotes than the non-HFTfor a stock on a given day; category “HFT +” displays statistics for when HFTsprovide more frequently the inside quote for a particular stock on a given day. Thereason to separate out the two types is that it may be that in some stocks HFTsdo not actively try and provide inside quotes, thus just taking the average acrossall stocks would underweight the liquidity they do provide in the stocks they areactively place competitive quotes. Table 18 has three panels, and within eachpanel either a category called “Minutes” or “Percent.” Panel A considers quotesfor all stocks; Panel B considers quotes for stocks on days they are below theiraverage spread; and Panel C considers quotes for stocks on days they are abovetheir average spread. The Minutes results display the number of minutes HFTsprovide the inside quotes more than non-HFTs through the following calculation:sum the number of minutes HFTs provide the best bid or ask, subtract the numberof minutes non-HFTs are providing the best inside bid or ask, and drop ties. Aproblem with this is that since the ties will vary across days and stocks, the Min-utes approach does not necessarily capture the frequency that HFTs provide betterinside quotes than non-HFTs. The Percent results avoids this issue by dividing thenumber of minutes HFTs provide the best quotes by the total number of minuteswhere HFTs and non-HFTs did not have the same inside quotes.

There does not appear to be a significant difference between the stocks inwhich HFTs decide to place aggressive bid/ask orders and those in which it doesnot. The very low value for the mean of Net - by itself may imply that the HFTsdo not attempt to match or out-price the quotes of non-HFTs for some stocks.

53

But looking at the “Percent” data, shows that the Net - and Net + results areabout equally distant from .5. Thus, the “Minutes” Net - results must be biaseddownwards as a result of a large number of periods where HFTs and non-HFTsprovide the same prices. Looking at the Panel A - Percent results, on averageHFTs provide the best inside quotes 45% of the time, a significant portion of thetrading day. This suggests that HFTs act as market makers and are competitivequote suppliers.

Panel B and C divide the stocks into those that are offering higher spreadsthan average and those offering lower spreads than average. Panel B reports thelow spread stock days, Panel C the high spread stock days. The results betweenthe two subsets do not differ much from one another. The average time HFTsoffer the best quotes is slightly higher when spreads are high at 71.7% comparedto 70.1% when it is low. Also, HFTs provide the best quotes more often thannon-HFTs slightly more often when spreads are high, doing so 46% of the time asopposed to 45.1% when spreads are low. This is consistent with HFTs attemptingto capture liquidity supply profits as found in Foucault and Menkveld (2008) andHendershott and Riordan (2009) make/take liquidity cycle, but as the differenceis small it does not provide much support for it.

6.1.2.2 HFT Time at Inside Quotes Determinants Table 18 shows that HFTsproduce the inside quotes frequently, but not as often as non-HFT. I perform anOLS regression similar to that found in table 9 to understand what determinantsare related to which stocks and days HFT prduces the best quotes. Table 19 showsthe results. It is very similar to table 9, with all variables being defined exactly thesame as before except the dependent variable. The regression is:

Li,t = α+MCi ∗ β1 +MBi ∗ β2 +NTi,t ∗ β3 +NVi,t ∗ β4 +Depi,t ∗ β5 + V oli,t ∗ β6 + ACi,t ∗ β7,

where the variables and subscripts are defined as above, and the dependentvariable, Li,t is the percent of the time for which HFTs provide the best insidequotes compared to all times when HFTs and non-HFTs quotes differ.

The coefficients reported, like those in table 9, are standardized beta coeffi-cients which allows for an easy way to decide which determinants are more impor-tant. The results suggest there are several explanatory variables that matter, all ex-cept Autocorrelation are statistically significant, and all except AverageDepthhave coefficient magnitudes greater than .16. MarketCap. and #ofNonHFTTrades

54

Table 18: HFT Time at Best Quotes. This table reports the number of minutes HFTsare at the best bid or ask compared to non-HFTs. The remainder of time both HFTs andnon-HFTs are both at the best quotes is not considered. Panel A is for all stocks at alltimes, Panel B is for days when the spread is below average for that stock, Panel C is fordays when the spread is above average.

Panel A All -MinutesHFT mean min p25 p50 p75 max NNet - -255.6 -779.7 -368.5 -190.3 -75.8 -0.4 353.0Net + 65.8 0.1 14.3 55.1 94.0 343.0 242.0Average -124.9 -779.7 -223.5 -41.2 33.1 343.0 595.0

-PercentNet - 0.281 0.000 0.162 0.307 0.410 0.499 353.000Net + 0.709 0.502 0.587 0.708 0.802 0.964 242.000Average 0.455 0.000 0.272 0.446 0.668 0.964 595.000

Panel B Low Spread -MinutesNet - -243.1 -779.7 -367.0 -183.0 -70.9 -0.4 187.0Net + 67.7 0.1 17.5 58.6 94.0 319.8 125.0Average -118.5 -779.7 -205.9 -40.4 39.8 319.8 312.0


Panel C High Spread -MinutesNet - -269.8 -779.1 -401.2 -204.0 -84.9 -1.1 166.0Net + 63.6 1.1 13.3 50.4 91.5 343.0 117.0Average -131.9 -779.1 -227.1 -41.2 28.9 343.0 283.0


55

have positive coefficients, with MarketCap. being the most important determi-nant of HFTs providing the best quotes. The other coefficients are negative, sug-gesting that HFTs prefer to provide the inside quotes for value firms, less volatilityfirms, firms with narrower spreads, and firms with a lower book depth.

Table 19: Determinants of HFT Percent of Liquidity Supplying The dependent vari-able is the ratio of number of minutes HFTs provides the inside bid or ask divided bythe total number of minutes of when the inside bid and ask differ between HFTs andnon-HFTs.

(1)Economic Impact

Market Cap. 0.654∗∗∗

(15.05)Market / Book -0.163∗∗∗

(-4.72)$ of Non HFT Volume -0.162∗∗∗

(-3.82)Average Spread -0.165∗∗∗

(-4.90)Average Depth -0.086∗∗

(-2.65)Volatility -0.241∗∗∗

(-7.14)Autocorrelation -0.006

(-0.18)# of Non HFT Trades 0.217∗∗∗

(4.28)Constant ∗

(-2.55)Observations 590Adjusted R2 0.410Standardized beta coefficients; t statistics in parentheses∗ p < 0.05, ∗∗ p < 0.01, ∗∗∗ p < 0.001

6.1.2.3 Price Impact Reduction from HFT Liquidity Thus far, the analysison liquidity has been by looking at the best inside bid and ask. Another way oflooking at HFT impact on liquidity is by looking at the depth of the book supplied

56

by HFT. I analyze what difference having HFTs provide liquidity in the book pro-vides in decreasing the price impact of a trade. That is, one can observe the bookwith all of the limit orders in it and then remove the liquidity provided by HFTsand see what the impact would be on the cost of executing a trade for differentsize trades. The results of this exercise are presented in table 20. I consider avariety of different impacts based on the number of shares hypothetically bought.The number of shares varies from 100 to 1000. Table 20 shows the price impactbased on market capitalization and also for the overall sample (column All). Themarket capitalizations are divided so that Very Small includes firms under $ 400million, Small are those between $400 million and $1.5 billion, Medium are thosebetween $1.5 billion and $3 billion, and large are for firms valued at more than $3billion. I present both the dollar impact, where a 1 represents one dollar increasein the price impact if HFT were not in the book, and a Basis impact, where a 1represents a 1 basis percent increase if HFT were not in the book.

As the trade size increases, the price impact increases across firms of all sizesand for all ten trade size increases. Interestingly the Small category tends to bemore impacted by the withdrawal of HFT liquidity than is the Very Small category.One might expect the very small to impacted the most and their be a downwardtrend in impact as one moves to the large firms, but this need not be the case ifHFTs did not have many orders in the book to begin with. The price impact issubstantial. For an average 1000 share trade, if HFT were not part of the book theprice impact would be .19 percent higher than it actual is because of the liquidityHFTs provide.

A concern with this analysis is the endogeneity of limit orders (Rosu, 2009)and the information they may contain (Harris and Panchapagesan, 2005; Cao et al.,2009). That is, a market participant who sees a limit order at a given price or ina certain quantity (or absence thereof) may alter his behavior as a result. Firstthough, it is not clear whether once the market participant observed a given limitorder he would be influenced to place his own limit order entry, place a marketableorder, or to withhold from entering the market. Thus, the dynamics are not clearwhether this increases or reduces the impact of the previous analysis. In addition,this concern should be even further dampened as market participants can alwayshide their limit orders.

6.2 HFT Price Discovery

HFT makes up a significant portion of market activity, both on the demand sideand the supply side, but that does not imply its activities increase price efficiency.In this section I utilize three of Hasbrouck’s methodologies to see whether HFTs

57

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84.

619

0.01

613

.233

0.04

022

.283

0.03

78.

784

0.02

250

01.

592

0.01

15.

161

0.01

916

.307

0.05

125

.041

0.04

210

.147

0.02

760

01.

663

0.01

36.

042

0.02

319

.934

0.06

528

.749

0.04

811

.866

0.03

370

01.

770

0.01

67.

162

0.02

822

.472

0.07

531

.133

0.05

213

.176

0.03

880

01.

855

0.01

79.

394

0.03

726

.358

0.08

834

.587

0.05

815

.250

0.04

590

01.

955

0.01

811

.539

0.04

529

.677

0.09

838

.725

0.06

417

.330

0.05

010

002.

036

0.01

913

.204

0.05

233

.324

0.10

842

.900

0.07

219

.352

0.05

6

58

provide new information to the market. First, I utilize the impulse response func-tion whose results can be interpreted as the amount of private information differenttraders bring to prices by measuring the amount of the price adjustment from thetrade that is permanent. HFTs provide more private information to the market thando non-HFTs. Second, I use a variance decomposition technique that takes the re-sults of the impulse response function and relates the different type of traders’trades to the price discovery process. The results show that HFTs are more im-portant in the price discovery process than non-HFTs. Finally, I implement theinformation shares approach which takes the innovations in HFTs and non-HFTsquotes and decomposes the variance of the common component of the price toattribute contribution to the efficient price path between the two types of traders.HFTs provide substantially more information to the price process than do non-HFTs. The Hasbrouck methodologies utilized in this paper are similar to thosefound in Hendershott and Riordan (2009) and other papers.

6.2.1 Permanent Price Impact

To measure the information content of HFT and non-HFT I calculate the perma-nent price impact of HFTs and non-HFTs trades. Hendershott and Riordan (2009)performed a similar calculation for trader types looking at algorithmic trading,while Barclay, Hendershott, and McCormick (2003) used the technique to com-pare information from different markets. The HFT dataset is especially well suitedfor this as it is in milliseconds and thus avoids problems of multiple trades occur-ring in one time period, as occurs with data denoted in seconds. I estimate themodel on a trade-by-trade basis using 10 lags for HFT and non-HFT trades. Iestimate the model for each stock for each day. As in Barclay, Hendershott, andMcCormick (2003) and Hendershott and Riordan (2009), I estimate three equa-tions, a midpoint quote return equation, a HFT equation, and a non-HFT tradeequation. The time index, t, is based on event time, not clock time, and so eacht is an event that is a trade or quote change. qH is defined as the signed (+1 for abuy, -1 for a sell) HFTs trades and qN is the similarly denoted signed non-HFTstrades. rt is defined as the quote midpoint to quote midpoint return between tradechanges. The 10-lag vector auto regression (VAR) is:

59

rt =10∑i=1

αirt−i +10∑i=0

βiqHt−i +

10∑i=0

γiqNt−i + ϵ1,t,

qHt =10∑i=1

δirt−i +10∑i=0

ρiqHt−i +

10∑i=0

ζiqNt−i + ϵ2,t,

qNt =10∑i=1

πirt−i +10∑i=0

νiqHt−i +

10∑i=0

ψiqNt−i + ϵ3,t.

After estimating the VAR model, I invert the VAR to get the vector movingaverage (VMA) model to obtain: rtqHt

qNt

=

a(L) b(L) c(L)d(L) e(L) f(L)g(L) h(L) i(L)

ϵ1,tϵ2,tϵ3,t

, (5)

where the vectors a(L) - i(L) are lag operators. Hasbrouck (1991a) interpretsthe impulse response function for HFT,

∑10t=0 b(L), as the private information

content of an innovation in HFT. The non-HFT impulse response function is∑10t=0 c(L) and is the private information content of an innovation in non-HFT.

The impulse response function is a technology first used in the macro-economicliterature to determine the impact of an exogenous shock to the economy as itworked its way through the economy. Hasbrouck (1991a) and Hasbrouck (1991b)took this methodology and applied it to the microstructure literature. The expectedportion of a trade should not impact prices and so should not show up in the im-pulse response function; however, the unexpected portion, the innovation, of atrade should influence the price of future trades. The impulse response functionestimates this impact on future trades.

Table 21 shows the results of the HFT and non-HFT impulse response func-tion for 10 events into the future. There are 105 firms presented as fifteen stocksdo not contain enough data to calculate the VAR. Each stock is reported indi-vidually. For each stock I estimate the statistical significance of the differenceof the impulse response function for the HFT and non-HFT 5 trading days usinga t-test. The t-test is adjusted using Newey-West standard errors to account forthe time-series correlation in observations. Also, I calculate the overall averageHFT and non-HFT impulse response function, this calculation incorporates the

60

Newey-West correction for time series and also a correction for the cross-sectioncorrelation standard errors.

Of the 105 companies represented 90 of them have the HFT impulse responsefunction being larger than the non-HFT impulse response. None of the 15 firmswhere the non-HFT impulse response function is larger than HFT’s are statisti-cally significant. Of the 90 in the other direction, 26 of the differences are sta-tistically significant. On average, HFT’s impulse response function is 1.017 andNon HFT’s impulse response is 0.759. The overall difference is statistically sig-nificant. This suggests that HFTs trades provide more private information thando non-HFTs trades. This is similar to the findings in Hendershott and Riordan(2009) with algorithmic trades. Thus, an innovation in HFT tends to lead to a 34%greater permanent price change than does a trade by a non-HFTr.

6.2.1.1 LR - SR Price Impact The results in table 21 show that HFT has alarger price impact than does non-HFT over the ten period interval. An item ofinterest is whether the price impact is immediate or gradual over the ten futuretime periods. Similar to the methodology used in Chaboud, Hjalmarsson, Vega,and Chiquoine (2009) and Hendershott and Riordan (2009), I test whether theprice process may cause an immediate overreaction to one type of trade and thatover the next nine periods in the future the impact decreases. If it is the casethat there is an immediate overreaction to a HFTs trade this would support thetheory that HFTs increase the volatility of markets. To analyze this I report thedifference between the long-run (LR; 10 event forecast horizon) and short-run(SR; immediate) impulse response functions in table 22.

Of the 105 The LR-SR impulse response is less for HFTs than for non-HFTsin 25 of the 105 firms. Of those 25 firms none are statistically significant. Ofthe 80 firms where the LR-SR impulse response function is greater for HFTs thannon-HFTs 15 are statistically significant. Also, for each market participant col-umn, a positive number implies that the LR impact of a trade is greater than theSR impact, and a negative number implies there is a short run overreaction andthat over the next nine periods the permanent price impact falls. The results oftable 22 suggest that HFTs individual innovations have more private informationthan non-HFTs trades and that the difference is persistent and increases beyondthe immediate impact of the trade.

6.2.2 Aggregate Amount of Information in HFT - Variance Decomposition

The permanent price impact section above shows that HFTr demanded trades addimportant information to the market, but the methodology does not directly esti-

61

Tabl

e21

:H

FTan

dno

n-H

FTL

ong-

Run

Impu

lse

Res

pons

eFu

nctio

ns.T

his

tabl

ere

port

sth

eav

erag

elo

ng-r

un(1

0ev

ents

inth

efu

ture

)im

puls

ere

spon

sefu

nctio

nfo

rHFT

and

non-

HFT

.The

last

colu

mn

repo

rts

the

T-st

atis

tics

fort

heH

FT-n

on-H

FTdi

ffer

ence

fore

ach

secu

rity

.

Stoc

kH

FTN

onH

FTT

Test

Stoc

kH

FTN

onH

FTT

Test

Stoc

kH

FTN

onH

FTT

Test

AA

1.60

71.

596

0.06

1C

SCO

2.26

11.

483

1.19

3L

EC

O0.

857

-0.1

301.

482

AA

PL0.

150

0.44

9-1

.066

CSE

1.01

10.

596

5.73

1L

PNT

1.89

71.

212

1.10

7A

BD

9.98

54.

546

1.04

3C

SL3.

189

7.42

8-3

.511

LST

R2.

202

1.13

61.

808

AD

BE

1.04

90.

753

2.40

5C

TR

N1.

631

-0.0

031.

491

MA

KO

1.48

80.

899

2.08

0A

GN

1.15

70.

089

2.98

2C

TSH

13.2

10-1

0.87

71.

717

MA

NT

-8.0

91-0

.540

-0.8

14A

INV

3.84

52.

204

2.87

5D

CO

M0.

707

0.54

92.

407

MD

CO

1.87

21.

872

-0.0

00A

MA

T1.

536

1.05

02.

501

DE

LL

4.95

54.

255

0.23

7M

EL

I5.

887

3.15

92.

195

AM

ED

2.84

31.

877

1.54

3D

IS1.

518

0.84

02.

553

MFB

3.39

90.

788

3.28

4A

MG

N0.

647

0.41

82.

744

DO

W1.

042

0.96

00.

593

MIG

-29.

172

-2.5

89-0

.726

AM

ZN

0.69

90.

535

1.65

9E

BA

Y1.

565

0.90

42.

480

MM

M5.

719

3.78

30.

356

APO

G0.

323

1.65

8-0

.688

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IE1.

219

1.21

40.

034

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D0.

846

0.48

54.

458

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CC

4.21

50.

358

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8E

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C-0

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811

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608

3.08

51.

320

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P2.

604

1.71

91.

110

FCN

2.80

01.

984

1.43

1M

RT

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687

1.08

72.

154

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I1.

054

0.74

62.

691

FFIC

1.85

40.

900

2.67

5M

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521.

680

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003

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440.

145

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589

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701.

435

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3.04

52.

259

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10.9

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239

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2.97

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671

0.42

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1.37

50.

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0.65

90.

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781

0.88

92.

979

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1.97

31.

155

0.95

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457

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066

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0.66

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1.46

30.

525

3.01

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3.46

52.

360

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91.

217

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34B

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4.94

52.

890

0.39

3G

E1.

328

0.84

01.

159

PNC

0.67

60.

553

2.08

3B

Z1.

627

0.86

40.

647

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NZ

1.20

60.

980

1.35

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Y0.

820

0.68

11.

342

CB

3.88

24.

642

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87G

ILD

0.78

20.

585

1.40

1PT

P1.

905

1.39

80.

517

CB

EY

0.81

30.

581

3.38

4G

LW0.

644

0.67

0-0

.476

RIG

L2.

105

1.64

30.

656

CB

T3.

313

1.77

01.

041

GO

OG

1.53

91.

700

-0.6

37R

OC

2.76

83.

592

-0.3

93C

CO

2.23

91.

239

1.79

0G

PS0.

819

0.46

83.

575

RO

CK

2.51

61.

762

0.54

8C

DR

10.9

742.

623

1.04

1H

ON

1.45

01.

513

-0.4

95SF

2.70

42.

025

0.38

4C

EL

G5.

719

2.64

90.

551

HPQ

1.23

70.

604

4.78

6SF

G2.

356

2.09

20.

286

CE

TV

0.95

60.

579

3.21

5IM

GN

0.73

00.

633

1.84

0SW

N1.

680

0.43

92.

349

CK

H3.

798

1.99

33.

061

INT

C3.

440

3.23

50.

140

CM

CSA

0.84

10.

644

0.19

IPA

R1.

021

0.76

96.

930

CN

QR

1.35

10.

931

3.63

8IS

IL3.

365

2.17

70.

262

CO

O2.

941

0.58

34.

398

ISR

G2.

364

1.40

94.

782

CO

ST1.

813

1.09

51.

301

JKH

Y1.

849

0.94

03.

497

CPS

I0.

676

0.57

51.

867

KM

B2.

094

0.71

22.

191

CPW

R2.

911

1.78

20.

519

KN

OL

1.22

50.

394

4.98

6C

R3.

431

0.80

84.

790

KR

0.35

72.

713

-0.2

25C

RI

2.29

6-0

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2.31

4L

AN

C1.

448

1.53

9-0

.431

Ove

rall

1.01

70.

759

3.47

6

62

Tabl

e22

:L

ong-

Run

-Sho

rtR

unIm

puls

eR

espo

nse

Func

tions

.Thi

sta

ble

repo

rts

the

aver

age

long

-run

-sho

rtru

nH

FTan

dno

n-H

FTim

puls

ere

spon

sefu

nctio

n(I

RF)

,whe

reth

elo

ngru

nis

the

10ev

ents

inth

efu

ture

IRF

min

usth

eon

epe

riod

IRF.

The

last

colu

mn

repo

rts

the

T-st

atis

ticfo

rthe

HFT

-non

-HFT

diff

eren

cefo

reac

hse

curi

ty.

Stoc

kH

FTN

onH

FTT

Test

Stoc

kH

FTN

onH

FTT

Test

Stoc

kH

FTN

onH

FTT

Test

AA

0.81

50.

848

-0.2

25C

SCO

0.75

60.

777

-0.0

44L

EC

O0.

158

-0.4

691.

027

AA

PL-0

.050

0.17

4-0

.886

CSE

0.63

30.

405

3.43

3L

PNT

0.35

40.

755

-0.5

99A

BD

4.77

20.

514

1.19

8C

SL2.

343

2.96

3-0

.607

LST

R0.

849

0.50

50.

527

AD

BE

0.61

10.

382

2.38

3C

TR

N0.

110

-0.2

950.

418

MA

KO

0.49

40.

199

1.20

2A

GN

0.14

6-0

.247

1.11

8C

TSH

5.02

3-7

.641

1.38

4M

AN

T-8

.150

-3.7

40-0

.483

AIN

V2.

239

1.08

12.

615

DC

OM

0.26

00.

117

2.46

7M

DC

O0.

709

1.23

3-0

.339

AM

AT

1.14

50.

726

3.18

6D

EL

L0.

751

11.4

27-1

.098

ME

LI

1.94

01.

303

0.50

4A

ME

D1.

535

1.31

50.

436

DIS

1.06

80.

655

2.25

7M

FB2.

008

0.45

92.

375

AM

GN

0.30

00.

099

2.76

7D

OW

0.49

30.

417

0.75

7M

IG1.

961

-2.4

270.

625

AM

ZN

0.16

60.

114

1.02

6E

BA

Y0.

515

0.04

02.

195

MM

M3.

294

0.73

20.

510

APO

G-2

.298

2.48

9-1

.480

ER

IE0.

707

0.72

8-0

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MO

D0.

330

0.15

43.

837

AR

CC

0.59

1-1

.159

0.92

2E

WB

C-4

.875

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51-0

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MO

S1.

646

-0.7

951.

134

AX

P1.

294

0.66

51.

706

FCN

1.16

80.

803

1.14

5M

RT

N0.

739

0.41

81.

863

AY

I0.

475

0.23

13.

598

FFIC

0.37

20.

247

0.36

4M

XW

L1.

457

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061.

794

BA

S-2

.271

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67-0

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FL0.

698

-6.9

411.

333

NSR

1.66

00.

030

2.21

6B

HI

7.15

80.

875

3.21

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ER

2.15

71.

165

1.87

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0.54

2-0

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1.24

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IIB

0.09

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1.08

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847

0.19

43.

179

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TM

0.07

90.

328

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57B

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758

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917

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D3.

590

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955

0.96

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H7.

416

5.84

60.

169

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E0.

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0.48

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303

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180.

276

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244

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0.39

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170

0.67

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2.08

21.

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1.30

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0.77

80.

801

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XS

0.22

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0.29

2G

E0.

080

0.36

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0.37

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3.13

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0.64

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0.18

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123

0.89

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433

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710

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0.34

52.

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0.68

91.

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0.15

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0.49

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035

1.27

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0.25

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0.26

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546

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471.

868

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H2.

284

1.07

32.

266

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C2.

013

0.17

11.

588

CM

CSA

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850.

343

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5IP

AR

0.67

70.

611

1.36

8C

NQ

R0.

994

0.67

73.

392

ISIL

3.15

41.

229

0.48

6C

OO

1.25

50.

031

2.28

2IS

RG

1.58

10.

640

5.74

0C

OST

0.31

80.

392

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09JK

HY

1.20

00.

662

2.47

1C

PSI

0.31

80.

203

1.78

1K

MB

0.98

80.

014

1.98

0C

PWR

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620.

528

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86K

NO

L0.

539

0.13

33.

710

CR

2.68

40.

499

5.84

4K

R-8

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71-0

.119

CR

I0.

623

-1.2

521.

768

LA

NC

0.94

60.

925

0.11

7O

vera

ll0.

515

0.34

13.

563

63

mate the importance of HFT and non-HFT in the overall price formation process.To examine this I follow Hasbrouck (1991b) to decompose the variance of the effi-cient price into the portion of total price discovery that is correlated with HFT andnon-HFT. The results indicate which trades contribute more to price discovery.The methodology decomposes the variance of the efficient price into the portionof total price discovery that is correlated with HFT and non-HFT trades.

This analysis was also in Hendershott and Riordan (2009) to determine whetheralgorithmic or human traders contribute more to price discovery and I follow asimilar methodology. To perform the variance decomposition the return seriesrt(using midpoint returns to avoid the bid-ask bounce) is separated into its ran-dom walk component mt and stationary component st: rt = mt + st.

mt represents the efficient price where mt = mt−1 + wt and wt is a randomwalk with Ewt = 0; st is the non-persistent price component. Let σ2

ϵ1= Eϵ21, σ2

ϵ2

= Eϵ22, and σ2ϵ3

= Eϵ23, I decompose the variance of the efficient price mt intotrade-correlated and trade-uncorrelated changes:

σ2w = (

10∑i=0

ai)2σ2

ϵ1+ (

10∑i=0

bi)2σ2

ϵ2+ (

10∑i=0

ci)2σ2

ϵ3, (6)

where the a, b, c are as defined in the previous section as the lag coefficientsfound in the VMA matrix. The (

∑10i=0 bi)

2σ2ϵ2

term represents the proportion of theefficient price variance attributable to HFT and the (

∑10i=0 ci)

2σ2ϵ3

term representsthe non-HFT proportion of the efficient price variance. The (

∑10i=0 ai)

2σ2ϵ1

term isthe already public information portion of price discovery.

The results from this exercise are found in table 23. I report the average con-tribution by HFT and by non-HFT for each company over the five days. The finalcolumn is the t-statistic for the difference between the HFT and non-HFT contri-bution and is adjusted for its time-series correlation with Newey-West standarderrors. I also report the average overall contribution, whose t-statistic is correctedfor time-series correlation and for cross-sectional correlation. The HFT columnis the contribution to price discovery from HFTs, and the same interpretation istrue with the non-HFT column. The contribution to the Returns component (thepublic information) is the public information related to price discovery, it is unre-ported here for lack of space, but can be easily calculated by taking the differencebetween 1 and the sum of the HFT and non-HFT components.

Of the 118 firms 68 of them show HFT as having a greater contribution toprice discovery, and 28 of those stocks’ HFT - non-HFT contribution differenceis statistically significant. In the 50 stocks where the non-HFT contribution is

64

greater than that of the HFT, the difference is statistically significant for 7 firms.On average HFT contributes 86% more to price discovery than do non-HFT.

6.2.3 Information Share

This section examines the role HFTs and non-HFTs quotes play in the pricediscovery process, whereas the previous two sections had been analyzing therole of trades. I use the Information Shares (IS) approach introduced by Has-brouck (1995) and that is used in, among others, Chaboud, Hjalmarsson, Vega,and Chiquoine (2009) and Hendershott and Riordan (2009). This approach hasbeen used to determine which of several markets contributes more to price dis-covery, and, as will be done here, to determine which type of market participantcontributes more to the price discovery process.

The approach is as follows. I calculate the HFT and non-HFT price path. Next,if prices follow a random walk then I can represent the change in price as a vectormoving average (VMA). I can decompose the VMA variance into the lag opera-tor coefficients and the variance of the different market participants’ price paths.The market participants’ variance is considered the contribution of that partici-pant to the information in the price discovery process. From the VMA I gather thevariance of the random walk and the coefficients of the VMA innovations.

The price process is calculated from the HFT and non-HFT midpoint,MPHFTt

= InsideBidHFTt +InsideAskHFT

t )/2 for HFT, and done similarly for non-HFT.Then the price process for HFT and non-HFT is pHFT

t = mt + ϵHFTt and pnHFT

t =mt + ϵnHFT

t respectively, and the common efficient price path is the random walkprocess, mt = mt−1 + ut.

The price vector of the HFT and non-HFT price process can be put into aVMA model:

∆pt = ϵt + ψ1ϵt−1 + ψ2ϵt−2 . . . , (7)

where ϵt = [ϵHFTt , ϵnHFT

t ] and is the information coming from HFT and non-HFT. The variance σ2

u can be decomposed as:

σ2u =

[ΨHFT ΨnHFT

] [ σ2HFT σ2

HFT,nHFT

σ2HFT,nHFT σ2

nHFT

] [ΨHFT

ΨnHFT

], (8)

where Ψ represent the lag operator vector from above and the sigmas representthe V ar(ϵt) from above.

65

Tabl

e23

:H

FT-n

on-H

FTVa

rian

ceD

ecom

posi

tion.

Thi

sta

ble

repo

rts

the

perc

enta

geof

the

vari

ance

ofth

eef

ficie

ntpr

ice

corr

elat

edw

ithH

FTan

dno

n-H

FTtr

ades

.T

here

mai

nder

isin

the

Ret

urn

colu

mn

(unr

epor

ted)

and

isin

terp

rete

das

the

pric

edi

scov

ery

from

publ

icly

avai

labl

ein

form

atio

n.

Stoc

kH

FT%

Non

HFT

%T

Test

Stoc

kH

FT%

Non

HFT

%T

Test

Stoc

kH

FT%

Non

HFT

%T

Test

AA

0.36

60.

113

3.79

0C

PWR

0.02

50.

030

-1.7

29JK

HY

0.10

70.

067

3.92

9A

APL

0.00

20.

002

-1.4

63C

R0.

027

0.02

01.

907

KM

B0.

002

0.00

3-1

.428

AB

D0.

117

0.10

21.

115

CR

I0.

000

0.00

0-1

.652

KN

OL

0.11

90.

048

2.24

7A

DB

E0.

053

0.02

94.

171

CRV

L0.

278

0.17

85.

319

KR

0.00

20.

004

-3.1

06A

GN

0.01

50.

013

0.50

2C

SCO

0.00

30.

003

-0.7

81K

TII

0.07

90.

070

0.53

5A

INV

0.12

00.

096

1.20

7C

SE0.

032

0.03

00.

254

LA

NC

0.04

70.

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2.93

3A

MA

T0.

016

0.01

41.

511

CSL

0.00

20.

002

0.73

8L

EC

O0.

021

0.02

00.

189

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ED

0.14

70.

111

1.26

1C

TR

N0.

141

0.07

05.

130

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039

0.01

62.

923

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GN

0.24

30.

041

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0.00

20.

018

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59L

STR

0.00

20.

008

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005

0.01

0-0

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OM

0.14

70.

268

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64M

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021

0.05

5-2

.115

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0.00

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098

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490

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105

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205

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0.03

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0.11

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059

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002

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0.08

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045

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010

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71B

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91.

851

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08B

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0.00

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043

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000

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003

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484

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017

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NZ

0.13

90.

109

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001

0.00

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D0.

039

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0.00

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203

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0.02

70.

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0.07

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178

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0.03

72.

671

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0.00

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0.08

50.

027

2.32

6R

IGL

0.02

00.

008

3.75

9C

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V0.

044

0.10

0-5

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HO

N0.

082

0.03

72.

897

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C0.

003

0.00

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005

CH

TT

0.06

80.

018

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PQ0.

002

0.00

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RO

CK

0.00

00.

000

1.94

7C

KH

0.21

00.

182

0.81

7IM

GN

0.30

00.

168

5.20

7R

OG

0.00

30.

003

-1.3

50C

MC

SA0.

025

0.02

40.

150

INT

C0.

001

0.00

2-2

.164

RVI

0.03

20.

034

-0.5

02C

NQ

R0.

026

0.02

02.

054

IPA

R0.

043

0.02

91.

534

SF0.

030

0.02

41.

352

CO

O0.

139

0.09

71.

838

ISIL

0.11

20.

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2.43

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G0.

001

0.00

03.

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ST0.

007

0.00

7-0

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ISR

G0.

024

0.02

30.

381

SJW

0.07

30.

017

3.70

1C

PSI

0.05

90.

250

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99O

vera

ll.1

95.1

052.

654

66

As the quote data I have is updated every time a new inside bid or ask isposted by a HFT or a non-HFT the diagonal values of the covariance matrix shouldbe nearly perfectly identified. That is, as the book limit order book is updatedevery millisecond for which an order arrives, there should be no contemporaneouscorrelation between HFT and non HFT quote changes.

The results are found in table 24. The information share attributable to HFTsand non-HFTs from their quote time-series process. The table shows the averageinformation share (which sums to 1 for each stock) for each stock. The average isover the five days in the dataset. The t-statistics are based on the difference in theinformation share between HFT and the non-HFT and incorporates Newey Weststandard errors to account for time series correlation.

The results in Table 24 show which quotes contribute more to price discovery,HFT or non-HFT. The information share of a participant is measured as that par-ticipant’s contribution to the total variance of the common component of the price.103 stocks have the HFT information share being larger than the non-HFT infor-mation share. Of those 63 of the stock have HFT being statistically significantlyproviding more information in their quotes than non-HFT. Of the 17 companieswhere the non-HFT have a larger information share than HFT, only two of thedifferences are statistically significant. This suggest that in quotes, like in trades,HFT are important in the price discovery process.

6.3 Volatility

The final market quality measure I analyze is the relationship between HFT andvolatility. I first do an OLS regression to observe whether there is any relationshipbetween HFT and volatility. The results suggest that HFT and volatility are nothighly related, especially contemporaneously. Next, using the period surroundingthe short sale ban in September, 2008 I evaluate the impact on volatility of anexogenous decrease in HFT. Finally I compare the price path of stocks with andwithout HFT being part of the data generation process. The results suggest thatHFT reduces volatility to a degree.

I begin this analysis by performing two simple regressions. The first is a re-gression with the dependent variable being volatility, calculated in terms of 10second realized volatility for each stock over the five trading days February 22 -26, 2010, and the explanatory variables are the total shares traded during that 10second period and the percent of trades involving a HFT during that ten secondperiod, as well as leads and lags for these two variables, as well as the volatility,for the previous ten periods.

Similarly, I switch the regression so that the dependent variable is the HFT

67

Tabl

e24

:H

FTan

dno

n-H

FTIn

form

atio

nSh

ares

:T

his

tabl

ere

port

sth

eH

asbr

ouck

(199

5)in

form

atio

nsh

ares

for

HFT

and

non-

HFT

.

Firm

HFT

nHFT

Tst

atFi

rmH

FTnH

FTT

stat

Firm

HFT

nHFT

Tst

atA

A0.

911

0.08

95.

879

CD

R0.

994

0.00

613

1.67

3FL

0.69

80.

302

3.19

9A

APL

0.70

60.

294

1.27

5C

EL

G0.

864

0.13

64.

053

FME

R0.

875

0.12

53.

175

AB

D0.

541

0.45

90.

242

CE

TV

0.82

70.

173

1.88

9FP

O0.

646

0.35

41.

236

AD

BE

0.99

90.

001

835.

842

CH

TT

0.95

80.

042

11.0

02FR

ED

0.46

80.

532

-0.5

64A

GN

0.41

10.

589

-1.3

65C

KH

0.49

90.

501

-0.0

13FU

LT0.

962

0.03

812

.070

AIN

V0.

529

0.47

10.

933

CM

CSA

0.91

30.

087

8.33

5G

AS

0.52

00.

480

0.98

8A

MA

T0.

999

0.00

115

88.1

93C

NQ

R0.

961

0.03

914

.953

GE

0.98

40.

016

36.8

18A

ME

D0.

881

0.11

95.

472

CO

O0.

575

0.42

50.

400

GE

NZ

0.61

60.

384

0.60

1A

MG

N0.

772

0.22

82.

581

CO

ST0.

836

0.16

42.

047

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D0.

476

0.52

4-0

.111

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ZN

0.64

90.

351

0.82

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PSI

0.38

70.

613

-1.3

56G

LW0.

999

0.00

116

03.1

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O0.

574

0.42

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0.28

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0.35

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0.00

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608

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0.16

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0.72

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0.55

00.

450

0.27

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0.99

60.

004

122.

520

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L0.

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10.

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0.34

70.

653

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0.86

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0.52

70.

473

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0.54

80.

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1.00

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4.59

e+10

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I0.

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0.52

60.

474

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183

7.48

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9.91

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0.29

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AY

0.58

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74.

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0.48

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0.95

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0.04

820

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0.98

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35.6

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0.91

90.

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9.94

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PNT

0.73

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0.97

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87.

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0.68

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0.46

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0.68

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0.49

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48M

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0.29

10.

709

-1.1

78M

IG1.

000

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015

57.6

24M

MM

0.98

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28.2

53M

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0.98

30.

017

29.1

00M

OS

0.85

80.

142

3.87

4M

RT

N0.

856

0.14

42.

656

MX

WL

0.98

40.

016

30.3

46N

C0.

346

0.65

4-0

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NSR

0.87

90.

121

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1N

US

1.00

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2.40

e+10

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0.54

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H0.

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0.48

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0.66

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0.98

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0.36

90.

734

PNY

0.84

80.

152

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D0.

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0.45

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0.98

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000

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0.78

00.

220

1.60

3RV

I0.

715

0.28

51.

097

SF0.

987

0.01

337

.185

SFG

1.00

00.

000

8.55

e+10

Ove

rall

0.75

70.

258

19.9

23

68

percent of trades in that ten second window, and the volatility is one of the ex-planatory variables, along with the others previous included in the regression. Thetwo regressions are as follows:

V oli,t = α+ β1−11 × rvlagi,0−10 +β12−22 × totshareslagi,0−10 +β23−33 ×Hperclagi,0−10 +

HPerci,t = α+ β1−11 × rvlagi,0−10 +β12−22 × totshareslagi,0−10 +β23−33 ×Hperclagi,0−10

Each explanatory variable has a subscript 0-10, this represents the numberof ten-second time periods prior to the dependent variable time t event that thevariable represents. Subscript 0 represents the contemporaneous value for thatvariable. Volatility is defined as, for example using the fourth lag, rvlag4 =(log(pricei,t−5/pricei,t4))

2. The betas represent row vectors of 1x11 and the ex-planatory variables column vectors of 11x1. rv is the squared price change forcompany i for the respective time period. totshares is the number of shares thatwere traded for a company i in that ten second time period. Hperc is the percentof trades for stock i in that time period for which HFT was involved.

Table 26 shows the results of the two regressions and only reports the variablesof interest, “HFT%” for the first regression and “RV ” for the second regression.In the first two columns are the results of the first regression with volatility asthe dependent variable. The last two columns display the result for the secondregression with HFT percent of market activity as the dependent variable. Forboth, only the results of the variables of interest are shown. The results suggestthat there is some statistically significant relationship between the two variables.when volatility is the dependent variable, the Percent of HFT trading coefficientis statistically significant and negative in the two period lag period.

In the second regression, with HFTPercent as the dependent variable, manyof the prior volatility coefficients are statistically significant. The periods lag 1, 2,5, 9, and 10 statistically significant. All of the statistically significant lag coeffi-cients are positive except for period 9. This suggests that after volatility has beenelevated HFT tend to make up more of the market trades. Of course, because ofthe endogeneity problem not much weight should be put on these results. I includethem only to show a possible link between HFT and volatility. The next sectionattempts to avoid the econometric issues and to reduce the endogeneity problem.

69

Table 25: HFT - RV Relationship. This table tries to capture whether there is a relation-ship between HFT and short-term market volatility.

Dep = RV Dep = HFTPercentVariable Coefficient Std. Err. Variable Coefficient Std. Err.

HFT % lag0 -0.00025 0.00022 RV lag0 -0.00917 0.00822HFT % lag1 -0.00048∗ 0.00027 RV lag1 0.12203∗∗∗ 0.04379HFT % lag2 -0.00031 0.00026 RV lag2 0.09531∗∗∗ 0.03580HFT % lag3 0.00004 0.00025 RV lag3 -0.03216 0.02459HFT % lag4 -0.00001 0.00025 RV lag4 0.00072 0.02362HFT % lag5 -0.00005 0.00025 RV lag5 0.03959∗ 0.02196HFT % lag6 0.00003 0.00025 RV lag6 -0.00092 0.01904HFT % lag7 0.00010 0.00025 RV lag7 -0.02628 0.01746HFT % lag8 0.00006 0.00025 RV lag8 0.02731 0.01675HFT % lag9 0.00017 0.00025 RV lag9 -0.04089∗∗ 0.01608HFT % lag10 -0.00018 0.00025 RV lag10 0.05887∗∗∗ 0.01552

N 552845 N 552845R2 0.12254 R2 0.89658F (187,552657) 1135.02718 F (187,552657) 70461.35190Significance levels : ∗ : 10% ∗∗ : 5% ∗ ∗ ∗ : 1%

70

6.3.0.1 HFT Impact on Volatility I next try to disentangle the HFT - Volatil-ity relationship and minimize the endogeneity problem. I do so using two meth-ods, first I look at a time when HFT activity was exogenously reduced and exam-ine what happened to volatility, and second I consider what volatility would looklike if HFT activity had not participated in the market.

As seen in Section 5.1.5, HFT is influenced by volatility. Now I study whetherHFT influence volatility. Before I used exogenous shocks to volatility to study itsinfluence on HFTs. Here I use an exogenous shock on HFTs to study the reverse.The exogenous shock I utilize is the September 19, 2008 ban on short sale tradingfor 799 financial firms, which was in place until October 9, 2008. Of the 120firms in the HFT sample dataset, 13 were on the ban list. The ban did not directlystop HFTs from trading in those shares. However, after talking with HFT firms, itis clear they avoided these stocks as their strategies require them to switch freelybetween being long or short a stock, and observing in the data that HFT activitydropped precipitously during this period (for the 13 affected stocks), it was infact a defacto ban on a portion of HFTs. In a quick-to-follow clarification, theSEC made clear that officially designated market makers were not subject to theban and could freely short sell the 799 stocks. One reason HFT during this perioddoes not drop further is that a portion of firms identified as HFT are official marketmakers and so they did not experience the same trading limitations as their non-designated counterparts.

With the 13 effected firms I use the variation in the decline in HFT activity asdifferent levels of treatment and study the subsequent change in volatility. As all13 firms are in the short sale ban, their is no concern that my results are actuallyan implication of the ban itself. I run the following OLS regression:

∆V ola = HFT%Changei,t ∗ β1 + ϵi,t,

where ∆V ola is the change in volatility for firm i between the pre- and post-ban period, HFT%Changei,t is the change in HFT activity pre- and post- ban,HFTpre−HFTpost

HFTpre. Firm fixed effects are used. The results are in table 27. Column

(1) show the results when looking at the one-day level activity. That is, the preban data are for September 18, 2008, and the post ban data are for September19, 2008. The results in column (1) shows no relationship between an exogenousshock in HFT and volatility. Column (3) performs the same analysis but usesthe week average, using the average per stock data of the five trading days prior toSeptember 19, 2008, for the pre ban data, and the average per stock data of the fivetrading days after the ban for the post ban data. This approach produces a negative

71

coefficient on HFT%Change which is interpreted as the more HFT decreased,the greater the rise in volatility. However, the coefficient is not statistically sig-nificant above the 20th percentile. Given the sparse number of observations, Iimplement a non-parametric bootstrap looping through the data 50 times (usingreplacement). This has no impact on the statistical significance of the Day levelanalysis as seen in column (2). However, using the bootstrap techniques for theWeek level analysis results in HFT % Change showing statistical significance atthe 5% level.

Table 26: Exogenous HFT - Volatility Relationship. This table shows the results of anexogenous removal of HFT and its impact on volatility. It uses the short sale ban as thesource of exogenous shock. 13 firms are impacted. I run the following OLS regression:∆V ola = HFT%Changei,t ∗ β1 + ϵi,t, where ∆V ola is the change in volatility forfirm i between the pre- and post- ban period, HFT%Changei,t is the change in HFTactivity pre- and post- ban, HFTpre−HFTpost

HFTpre. Firm fixed effects are used. Column (1)

shows the results using the day before and day after data; column (3) shows the resultsusing the average values from the week before and week after for pre and post data points.Columns (2) and (4) utilize a non-parametric bootstrap looping through the data 50 times(and using replacement).

(1) (2) (3) ( 4)1 Day 1 Day - Bootstrap 1 Week 1 Week - Bootstrap

HFT % Change 0.368 0.368 -1.723 -1.723∗

(0.28) (0.41) (-1.48) (-2.42)Constant 0.523 0.523 0.568 0.568

(0.92) (0.98) (1.26) (1.84)Observations 13 13 13 13Adjusted R2 -0.083 0.091∗ p < 0.05, ∗∗ p < 0.01, ∗∗∗ p < 0.001

I also take an alternative approach to studying the impact of HFT on volatil-ity. To reduce the impact of endogeneity, I take advantage of the book data Ihave available in one minute increments. With this data I can estimate what theprice impact would have been had there been no HFTs demanding liquidity orsupplying liquidity. That is, I have the actual price series for each stock, but Ican supplement that with the hypothetical price series of each stock assuming thatthere were no HFT in the market. Table 28, 29, and 30 shows the results. For eachstock I calculate the realized volatility, the sum over one minute increments ofthe absolute value of the returns over the day. I perform this calculation for eachstock on each day and do it for the actual price path, and also for an alternativeprice path based on the role of HFT. In table 28 I remove HFTr initiated trades

72

and also HFTr liquidity providing trades. Thus, were the realized volatility calcu-lation would have used a trade by a HFTr initiated trade, it instead has to grab theprice from the next trade that is initiated by a non-HFTr. Also, when the realizedvolatility would have had a trade where a HFTr was providing the liquidity, I ad-just the price based on the size of the trade and the price impact it would have onthe book after removing the HFT book entries. Table 29 does the same calculationbut only removes the HFT liquidity providing trades. Finally, table 30 removesonly the HFT initiated trades from the alternative price path.

In table 28 of the 120 stocks, only one exhibits that volatility would not bereduced if HFT had not been in the market. Of those stocks were HFT reducedvolatility, 85 of them have volatility that is statistically significantly less than whatit would be if HFT had not been part of the market. The t statistics for the indi-vidual firms use Newey-West standard errors to account for the time series cor-relation. the overall t-statistic also corrects for cross-sectional correlation. Theseresults suggest that HFT helps to reduce the volatility in the market.

Table 29 looks at what happens when HFT is only removed from providingliquidity. Only one firm shows that volatility is increased by removing HFT fromproviding liquidity. Of the 119 that show HFT is reduced, 82 show a statisti-cally significant difference in volatility. The t statistics for the individual firms useNewey-West standard errors to account for the time series correlation. the overallt-statistic also corrects for cross-sectional correlation. This is the mechanical por-tion of the HFT price reduction: when liquidity is removed, the only way pricescan move is further away from their previous path, thus increasing volatility.

Table 30 again compares the realized volatility of the 120 firms, but it com-pares the volatility of the actual price path with the volatility of the price path ifonly HFTr initiated trades are removed. Table 30, unlike the previous table, mayshow a positive, negative, or no direction in its impact on volatility. Of the 120firms, 72 of them have a higher volatility when HFTr initiated trades are present.Thus, a small majority of firms experience slightly higher volatility with HFTrinitiated trades. However of these 72 stocks, only one is statistically significant.Of the 48 stocks where the presence of HFTr initiated trades reduces volatilitynone show a statistically significant difference in volatility. The t statistics forthe individual firms use Newey-West standard errors to account for the time se-ries correlation. the overall t-statistic also corrects for cross-sectional correlation.These results suggest that HFT initiated trades do not result in increased volatility.

73

Tabl

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74

Tabl

e28

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look

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76

7 ConclusionThis paper examines high frequency trading and its role in financial markets. HFTmake up a large majority of all trades. HFTs supply liquidity in about half of alltrades and demand liquidity in about half as well. Their activities in the market,both in initiating trades and in providing liquidity, are stable over time. They tendto engage in a price reversal strategy, and this is stronger when they are demandingliquidity. There is no evidence of abusive front running occurring. HFT firms areprofitable, making around $3 billion annually. HFT prefer to trade in large stockswith lower volume, lower spreads and depth, and companies that are consideredvalue firms. They tend to make more money in volatile times. HFTs prefer todemand liquidity in small amounts, usually in value between $1,000 and $4,999,and they tend to have lower time between trades than non-HFTs. They providethe best quotes about 45% of the time. They provide more inside quotes for largervalue firms, with lower volume, lower volatility, lower spreads and depth, and withgreater number of trades. From the different Hasbrouck measures, the evidencesuggest HFT plays a very important role in price efficiency and the price discoveryprocess. In fact, it provide more useful information to the price generation processthan do non-HFT. Finally, HFT activity either has no impact on volatility or tendsto decrease it.

77

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Examination of High Frequency Trading

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