Electronic copy available at: http://ssrn.com/abstract=2433118

Risk and Return in High Frequency Trading*

Matthew Baron, Jonathan Brogaard, and Andrei Kirilenko

First Draft: October 2011

Current Draft: April 2014

Abstract

This paper studies high frequency trading (HFT) in the E-mini S&P 500 futures contract over a 

two-year period and finds that revenue is concentrated among a small number of HFT firms who 

achieve greater investment performance through liquidity-taking activity and higher speed. 

While the median HFT firm realizes an annualized Sharpe ratio of 4.3 and a four-factor 

annualized alpha of 22.02%, revenues persistently and disproportionally accumulate to top 

performing HFTs, consistent with winner-takes-all industry structure. New entrants are less 

profitable and more likely to exit. Our results imply that HFT firms have strong incentives to 

take liquidity and compete over small increases in speed.

 

*

Contact: Matthew Baron, Princeton University, e-mail: mdbaron@princeton.edu; Jonathan Brogaard, Foster 

School of Business, University of Washington, e-mail: brogaard@uw.edu; Andrei Kirilenko, MIT Sloan School of 

Management, e-mail: ak67@mit.edu. Please see the CFTC disclaimer on the following page. We thank Hank 

Bessembinder, Tarun Chordia, Richard Haynes, Harrison Hong, Charles Jones, Terry Hendershott, Robert 

Korajczyk, Norris Larrymore, Ananth Madhavan, Ryan Riordan, Ronnie Sadka and Wei Xiong for their valuable 

feedback. We also thank the participants at the Advances of Financial Mathematics conference, the Banff 

International Research Station for Mathematical Innovation and Discovery workshop, the Bank of Canada Market 

Microstructure conference, the NBER Market Microstructure conference, the Recent Advances in Quantitative 

Finance conference, the Western Finance Association meeting, and the World Federation of Exchanges conference, 

as well as seminar participants at Blackrock, Boston College, Boston University, the CFTC, the Federal Reserve 

Board of Governors, Fields Institute of Mathematics, Imperial College, London Business School, London School of 

Economics, MIT, the University of Massachusetts at Amherst, Northwestern University, Princeton University, 

Rutgers University, and the University of Washington, for helpful comments.
Electronic copy available at: http://ssrn.com/abstract=2433118

2

On February 19, 2014, the U.S. Commodity Futures Trading Commission (CFTC)

authorized this paper for public disseminating. This paper was previously authorized for public 

disseminating by the CFTC's Office of General Counsel (OGC) on September 27, 2012 and has 

previously circulated under the titled "The Trading Profits of High Frequency Traders." The 

CFTC requests the following disclaimer:

Disclaimer

The research presented in this paper was co-authored by Matthew Baron, a former CFTC 

contractor who performed work under contracts CFCE-11-CO-0126 and CFOCE-12-CO-0154, 

and Jonathan Brogaard, a former CFTC contractor who performed work under contracts CFCE

11-CO-0236 and CFOCE-12-CO-0210. Andrei Kirilenko, former CFTC Chief Economist, was 

also a co-author who wrote this paper in his official capacity with the CFTC. The Office of the 

Chief Economist and CFTC economists produce original research on a broad range of topics 

relevant to the CFTC’s mandate to regulate commodity future markets, commodity options 

markets, and the expanded mandate to regulate the swaps markets pursuant to the Dodd-Frank 

Wall Street Reform and Consumer Protection Act. These papers are often presented at 

conferences and many of these papers are later published by peer-review and other scholarly 

outlets. The analyses and conclusions expressed in this paper are those of the authors and do not 

reflect the views of other members of the Office of Chief Economist, other Commission staff, or 

the Commission itself.
Driven in part by their seeming ability to profit in all circumstances, high-frequency 

trading (HFT) firms have recently attracted a great deal of attention. Still, many basic questions 

about their strategies and profitability remain unanswered. For example, how do HFT firms

make money? How do they compete with one another? And how useful is speed in driving 

revenue?

This paper seeks to address these questions, motivated by concerns raised in the academic 

literature and popular press concerning the incentives of individual HFTs to take liquidity and to 

compete over small increases in speed. We use a proprietary transaction-level data set from the 

Commodity Futures Trading Commission (CFTC) to study the these concerns through the lens of 

risk and return of individual HFT firms in the E-mini S&P 500 futures contract.1

Consistent with these concerns, we show that HFT firms who specialize in liquiditytaking (aggressive) strategies generate substantially more revenue than those who specialize in 

liquidity-providing (passive) strategies. Moreover, revenue persistently and disproportionally 

accumulates to the top performing HFTs, suggesting winner-takes-all market structure. We 

further show that speed is an important determinant of revenue generation, and the relation is 

strongest for HFTs with liquidity-taking (aggressive) strategies. Our results imply that, consistent 

with many of the concerns highlighted in the theoretical literature, HFT firms have strong 

incentives to take liquidity and to compete over small increases in speed.

We start by establishing some basic empirical facts regarding the risk and return 

characteristics of individual HFT firms. The median HFT firm demonstrates unusually high and 

persistent risk-adjusted performance with an annualized Sharpe ratio of 4.3 and a four-factor 

 

1 We identify "HFT" firms by using activity-based selection criteria introduced in Kirilenko, Kyle, Samadi, and 

Tuzun (2014). For brevity, we use the term "firm" to be synonymous with a specific trading account, even though 

several HFT firms in our data set have more than one trading desk, as it is our understanding that, due to regulatory 

and clearing requirements, most (but not all) trading desks operate as semi-independent trading entities.
4

(Fama-French plus momentum) annualized alpha of 22.02%.2 Unlike for many non-HFT 

investment strategies, firm-level performance is strongly persistent over both days and months. 

Risks are kept low by strict inventory management and rapid turnover of contracts. Despite the 

strong outperformance on the firm level, effective HFT trading costs paid by non-HFT investors 

are only 0.22 basis points.

Our focus on distinguishing liquidity-demanding versus liquidity-providing trading 

strategies of HFTs is motivated by the idea that speed can be helpful in different ways. The 

theoretical literature puts forth several ideas about the ways that HFTs use speed to generate 

profits. Some theories (e.g., Martinez and Rosu, 2013; Foucault, Hombert and Rosu, 2013; and 

Biais, Foucault, and Moinas, 2014) view HFTs as aggressive (liquidity-demanding) traders who 

use speed and aggressive orders to trade an instant before others -- whether in reaction to news, 

order flow, or latency arbitrage -- and pick off stale limit orders or trade ahead of others' 

information. In this view, HFTs increase adverse selection and trading costs on other investors.

Other theories, in contrast, (e.g., Jovanovic and Menkveld, 2012; Ait-Sahalia and Seglam, 2013; 

and various viewpoints presented in the mainstream media3), view HFTs as passive market 

makers who use speed to cancel or modify limit orders in response to informed trading, thus 

mitigating adverse selection and providing tighter bids and asks.

In distinguishing these two different views of HFTs, we find firm-level specialization: a 

majority of HFTs consistently specialize either in liquidity taking (whom we label Aggressive 

HFTs) or liquidity-provision (Passive HFT). More importantly, Aggressive HFTs earn 

 

2 As explained further in Section III, these returns assume fully-capitalized positions in the futures contract and 

should thus be interpreted as a highly conservative lower bound on returns. Given that margin requirements in the Emini are about 10% of the notional value of the contract, actual HFT returns on capital are most likely several times 

higher than reported here.

3

See, for example, http://www.bloombergview.com/articles/2014-03-20/why-do-high-frequency-traders-never-losemoney
5

substantially higher returns than Passive HFTs -- the average Aggressive HFTs earns an 

annualized alpha of 90.67%, while the average Passive firm earns 23.22% -- suggesting that 

there is a strong profit motive for liquidity taking rather than liquidity providing. 

We further distinguish Aggressive and Passive HFTs in terms of their risk and return 

characteristics and trading behavior. Spectral analysis (following Hasbrouck and Sofianos, 1993) 

shows that Aggressive HFTs as a whole lose money on shorter time scales (presumably from the 

bid-ask spread and price impact) but gain money by predicting price movements on longer (but 

still intraday) time scales. In contrast, Passive HFTs show the opposite, making money at short 

horizons and losing money over longer intervals. We also decompose from whom (i.e. from 

which other trader types) HFT firms earn their trading revenue, and show that Passive and 

Aggressive HFTs win and lose from different trader types. In particular, Aggressive HFTs make 

about 45% of their revenue from adversely selecting the other HFT subtypes.

A second motivation for studying trading revenue and competition among firms is that 

the competitive trading structure of HFT firms can lead to a winner-takes-all environment, 

whereby the trader who is first able to identify and respond to a profitable opportunity will 

capture all the gains (see, for example, Budish, Cramton and Shim, 2013; Jones, 2013; Weller, 

2013).

4 Other firms who are even milliseconds late will miss out: the magnitude of the profit 

may be sharply reduced or the trading opportunity may have disappeared completely. A winnertakes-all environment leads to socially inefficient investment in faster technology (Budish, 

Cramton and Shim, 2013; Biais, Foucault, and Moinas, 2014), as small increases in trading speed 

lead to large payouts, driving an arms race for seemingly small reductions in latency. This type 

 

4

Short-lived profit opportunities may derive from trading on news (for example, using direct data feeds) or on order 

flow (using information obtained from "pinging", flash quotes, or exploiting delays in public order book updates), 

taking advantage of mispriced orders or others' trading mistakes, or using other predictive, momentum or signal 

trading strategies.
6

of environment may further lead to incentives to exploit speed advantages via liquidity-taking 

trading strategies: picking off limit orders of slower traders and liquidity-providers, which may 

reduce liquidity or force effective trading costs upon other investors.

According to the winner-takes-all hypothesis, we expect to see a highly right-skewed 

cross-sectional distribution of revenue and a high concentration of revenue (measured by the 

Herfindahl index) that persists over time. Several other consequences may follow from a winnertakes-all environment. For example, Budish, Cramton and Shim (2013) theorize that that if speed 

advantages are relative, then increased competition won't drive profit opportunities to zero, since 

HFTs can always one-up the competition with an ever-smaller increase in speed. Thus, aggregate 

trading revenue and the concentration of revenue would not decrease over time. Additionally, we 

expect entrants to earn substantially lower returns than established HFT firms and be more likely 

to exit, as presumably incumbents have advantages due to their experience allowing them to 

capture most of the profits. Finally, we also expect speed to be a strong determinant of 

profitability, and the relation is strongest for HFTs with liquidity-taking (aggressive) strategies.

In looking at the data, we find evidence consistent the above predictions: the crosssectional distribution of returns is highly right-skewed, with revenue disproportionally and 

persistently accumulating to top-performing firms. Revenue is concentrated among the top 

performers, as measured by the Herfindahl index. Both results are consistent with a winnertakes-all environment. Additionally, we find that aggregate revenue and concentration of revenue 

among top-performers does not decrease over our two-year sample, after adjusting for volatility 

and non-HFT trading volume. New entrants earn substantially fewer profits and are more likely 

to exit. Finally, we study a measure of relative (rank-order) speed developed in Weller (2013), 

which measures latency in terms of reaction time to incoming order flow. While Weller (2013) 
7

previously demonstrated that relative speed is correlated with returns, we show that the relation 

is strongest Aggressive HFTs. Each of the above findings is consistent with a winner-takes-all 

environment with speed and aggressiveness being key components of success. Overall, our 

analysis thus reveals an industry dominated by a small number of increasingly-fast, liquiditytaking incumbents with high and persistent returns.

The rest of the paper is as follows. Section II discusses the related literature, Section III

describes the data and methods, Section IV examines the risk and return performance of HFTs, 

Section V analyzes competition, market concentration, and entry/exit of firms within the HFT 

sector, Section VI studies speed, and Section VII concludes.

II. Related Literature

This paper contributes mainly to two literatures: the growing body of work on HFT and 

the study of investment performance of different groups of traders. Given that there is no 

publicly available data set on HFT firms, several papers study HFT activity despite being unable

to directly observe individual high frequency traders (e.g., Hasbrouck and Saar, 2013). Other 

papers make use of limited or aggregated proprietary data sets. For example, Jovanovic and 

Menkveld (2012) and Menkveld (2013) study the July 2007 entry into Dutch stocks of a single 

high-frequency market maker, and Brogaard, Hendershott, and Riordan (2013) study aggregated 

HFT activity on NASDAQ. In contrast to these papers, this paper uses a data set that allows us to 

identify the trades of individual HFT firms. In this way, our paper is similar to Kirilenko, Kyle, 

Samadi, and Tuzun (2014), which studies whether HFTs caused the Flash Crash of May 6, 2010.

Most empirical papers on HFT and algorithmic trading assess the potential costs and 

benefits of HFT using natural experiments, such as analyzing technological upgrades to trading 
8

venues (e.g., Hendershott, Jones, and Menkveld, 2011; Boehmer, Fong, and Wu, 2014; Riordan 

and Storkenmaier, 2012; and Gai, Yao, and Ye, 2013) or changes in fee structures only affecting 

HFT firms (e.g., Malinova, Park, and Riordan, 2013). These papers generally show that HFT 

activity improves liquidity (in terms of bid-ask spreads, depth, and price impact), lowers adverse 

selection (for example, more price discovery taking place via quotes rather than trades), and 

lowers transaction costs for institutional and retail traders. In contrast to these papers, this study 

looks at HFT from a risk and returns perspective and analyzes the incentives and competitive 

forces that shape HFT activity.

Finally, a number of previous studies have evaluated the investment performance of 

different types of traders. For example, Harris and Schultz (1998) study the profitability of SOES 

bandits, a group of individual traders in the 1990s who would quickly enter and exit trades and 

who were thought by some to have unfair advantages. Hasbrouck and Sofianos (1993) study the 

profitability of NYSE specialists. Like Ackermann, McEnally, and Ravenscraft (1999), who 

study the profitability of different hedge fund strategies, this paper studies different trading 

strategies of HFTs. Similar to studies look into factors that induce different traders to trade (e.g.,

Grinblatt and Keloharju, 2001), this paper studies incentives for entry and exit, speed, and 

aggressiveness.

III. Data and Methods

We use transaction-level data with trader identifiers for the E-mini S&P 500 stock index 

futures contract (E-mini). Our data set spans over two years, from the start of August 2010 to the 

end of August 2012.

The E-mini is a favorable setting for studying HFT for the following reasons. 
9

First, it is an important and highly liquid market with several different types of market 

participants regularly trading, including a high number of HFT firms. The E-mini is the secondmost traded futures contract in the world with a notional trading volume of approximately $200 

billion per day in August 2010. Hasbrouck (2003) shows that the E-mini futures contract is the 

largest contributor to the price discovery process of the S&P 500 index. 

Second, the contract is in zero net supply and buying and selling are symmetrical, so 

there are no short-selling constraints. Trading in the E-mini is a zero-sum game: one trader’s 

profits come directly at the expense of the opposite trader. 

Third, because the contract trades only electronically and only on the Chicago Mercantile 

Exchange (CME), there is no concern about unobserved trades occurring on other exchanges or 

on the floor. 

Lastly, the E-mini has no designated market makers, no maker-taker fees or liquidity 

rebates for the front-month contract, and no obligations for certain market participants (such as 

quoting two sides or making prices continuous). There is no institutionalized class of 

intermediaries in this market. HFT trading activity is presumably in explicit pursuit of profits,

undistorted by other requirements or competing incentives.

Our data set is trade-by-trade and contains common fields such as price, number of 

contracts traded, and time of the trade in units of seconds (and in milliseconds for a few months). 

The CME's Globex matching engine stamps a unique matching ID on each regular transaction, 

which enables us to construct the exact ordering of transactions. Cancelled and other irregular 

transactions are filtered out. In addition, the data set contains unique identifiers for the ultimate 

buyer and the ultimate seller (not just their brokers), an identifier for which side initiated the 

trade (passive for the side with the resting order, aggressive, otherwise), and an identifier for 
10

each executed order that allows us to group multiple transactions into a single underlying order 

(since large executable orders may be executed against several different resting limit orders). 

Each E-mini contract is $50 times the value of the underlying S&P 500 index; as a result, 

the notional contract is valued at approximately $50,000. The tick size is $12.50. The contract is 

cash-settled against the value of the underlying S&P 500 index. Initial margins for speculators 

and hedgers (members) are $5,625 and $4,500, respectively, in August 2010; maintenance 

margins for all traders are $4,500. We exclude months in which the leading contract expires 

(March, June, September, December) in order to exclude rollover effects and multiple 

expirations trading simultaneously. Outside of the rollover months, the front-month contract 

usually has well over 99% of the trading volume, although we do analyze trades of all 

expirations. While the E-mini futures contract trades nearly around-the-clock, we only use data 

during normal trading hours: 8:30 a.m. - 3:15 p.m. Central Standard Time (CST).

One limitation of the paper is that our profit calculations do not account for all the costs 

of an HFT firm. While we know such direct costs of trading as trading fees ($0.15 per contract), 

the cost of direct data feeds, and the cost of co-location, we cannot adequately calculate other 

costs such as computer systems, labor, and risk management systems. We report gross trading 

revenues throughout to limit speculative assumptions from influencing our findings and because 

our focus is on trading performance.

Categorizing Traders

Following Kirilenko, Kyle, Samadi, and Tuzun (2014), we define different trader types

based on two selection criteria: inventory and trading volume. HFTs are identified as those firms 

with extremely high volume, low intraday inventory and low overnight inventory. As shown in 
11

Kirilenko, Kyle, Samadi, and Tuzun (2014) and confirmed by us, by analyzing all market 

participants along the dimensions of volume and inventories, HFT firms stand out as a distinct 

cluster, with daily trading volume orders of magnitude higher than other traders. In addition, we 

use the aggressiveness indicator (assigned by the matching engine) to group HFT firms into three 

different categories based on their liquidity impact.

The precise selection criteria for HFTs are as follows. For all individual market 

participants, we calculate four metrics: median trading volume (median trading volume across 

days which the firm is active, where active is defined as an HFT trading more than 1000 

contracts per day), end-of-day inventory ratio (daily end-of-day inventory position divided by 

total volume, median across days which the firm is active), intraday inventory ratio (maximum 

daily position minus minimum daily scaled by daily total volume, median across days which the 

firm is active), and aggressiveness ratio (ratio of aggressive trading volume to total trading 

volume). For each month, there are three categories a potential trader must satisfy to be 

considered a HFT: (1) median trading volume greater than 5,000 contracts per day (about $250 

million in notional daily trading volume)

5

, (2) end-of-day inventory ratio less than 5%, and (3) 

intraday inventory ratio less than 10%. As a final step, we drop from our sample firms that are 

active fewer than 10 trading days per month. We find 85 firms satisfy these HFT criteria, though 

because of entry and exit, not all these firms necessarily trade in the same months.

We find that a majority of HFT firms (or HFTs) consistently specialize either in liquidity 

taking (Aggressive HFTs) or liquidity-provision (Passive HFTs) over the two-year sample we 

study. Thus, we categorize HFTs as follows: Aggressive HFTs have an aggressiveness ratio 

greater than 60%, while Passive HFTs have an aggressiveness ratio less than 20%. The 

 

5

This is a small (overly-inclusive) minimum requirement for trading volume compared to what most HFTs in our 

sample actually trade. The average daily trading volume per firm in our sample is 36,000 contracts (about $1.8 

billion).
12

Aggressive HFT designation is meant to capture HFTs who are liquidity takers and generate 

trading profits by predicting future market movements, while the Passive HFT designation is 

meant to capture algorithmic market makers and liquidity providers whose revenue is partly 

generated by the bid-ask spread. We later show that these two classes of HFTs have markedly 

different characteristics in terms of trading behavior and profitability. We call firms that are not 

in either category Mixed HFTs and later show that they have characteristics that resemble a mix 

the two main categories. There are 18 Aggressive, 39 Mixed, and 28 Passive HFTs in our 

sample, though again not all these firms necessarily trade in the same months.

For each month we classify the rest of the universe of non-HFT firms into four different 

subcategories: Non-HFT Market Maker, Fundamental, Small, and Opportunistic traders. The 

non-HFT market maker category captures traditional market makers and liquidity providers, such 

as those examined by Hasbrouck and Sofianos (1993) and Coughenour and Saad (2004). 

Specifically, Non-HFT market makers are non-HFT market participants who have a (1) 

aggressiveness ratio less than 20%, (2) end-of-day inventory ratio less than 15%, and (3) median 

trading volume of at least 20 contracts (about $1 million) per day. The fundamental trader 

category is meant to capture large institutional traders who adopt buy-and-hold strategies, such 

as those studied by Anand, Irvine, Puckett, and Venkataraman (2012) and Puckett and Yan

(2011). Specifically, Fundamental traders have a (1) median trading volume of 1000 contracts 

per day (about $50 million) and (2) end-of-day inventory ratio greater than 30%. The Small 

trader category most likely captures retail traders (e.g. Kaniel, Saar, and Titman, 2008; Seasholes 

and Zhu, 2010). Small traders have a median daily trading volume of less than 20 contracts (or 

about $1 million). Note that HFTs and the above three categories are all mutually exclusive by 

definition. The remaining firms are designated Opportunistic. The Opportunistic category 
13

captures either medium-sized buy-and-hold investors (firms not big enough to be considered 

Fundamental traders) or large traders who unlike Fundamental traders move in and out of 

positions throughout the day but with significantly larger fluctuations and lower frequency than 

HFTs. This group likely captures arbitrageurs, small asset managers, hedge funds, and other 

hard-to-classify traders. In August 2010, we identify 737 Non-HFT Market Maker, 346 

fundamental traders, 21,761 small traders and 8,494 opportunistic traders.

Table 1 presents a summary of trading behavior for these different trader types for 

August 2010.

INSERT TABLE 1 ABOUT HERE

For each trader type, we report two statistics: the daily percent of market volume traded

and the daily aggressiveness ratios (aggressive contracts by trader category divided by total 

contracts by trader category). Table 1 Row 8 shows that, on average, 3.2 million contracts are 

traded in the E-mini market per day. The E-mini is an extremely liquid market with an average of 

about 70 contracts traded every second. HFTs as a whole trade 54.4% of the double-counted 

trading volume











 

MktVolume

Buys Sells HFT HFT

2*

, or 1.73 million contracts daily (Row 1+2+3). The next 

largest category is Opportunistic, with 31.93% of contract volume by its 8,494 participants (Row 

7). 

The variation within the HFT categories over different days is considerable. For example, 

Aggressive HFTs range from 9.5% to 17.6% of market volume across days; they have the largest 

variation of the three HFT categories (Row 1). Passive HFTs make up a significantly smaller 

portion of HFT volume (8.87%, Row 3) than Aggressive HFTs (15.22%, Row 1). Looking at 

liquidity taking, Aggressive HFTs take liquidity in 84.22% (Row 9) of the contracts they trade, 

while Passive HFTs only take liquidity in 12.35% (Row 11). Fundamental traders make up 
14

8.42% (Row 4) of trade quantity, while taking liquidity about half of the time (57.68%, Row 10). 

Small traders and non-HFT market makers are both a small share of the market, with 1.04% 

(Row 5) and 4.24% (Row 6) of the trade quantity, respectively, while taking liquidity 57.82% 

(Row 11) and 12.98% (Row 12) of the time, respectively. Opportunistic traders make up the 

largest share of trading volume at 31.93% (Row 7), while taking liquidity 59.08% (Row 13) of 

the time.

Figure 1 examines trading volume of the different trader types across the two-year span.

INSERT FIGURE 1 ABOUT HERE

Panel A shows the average daily HFT volume of the HFT subgroups for each month over the

two year span. The total HFT market volume decreases over the two-year span from a peak of 

3,187,011 contracts in August 2010 to 2,322,787 in August 2012. About half of that decline was 

from a reduction in Mixed HFT trading from 960,643 contracts in August 2010 to 564,200 

contracts in August 2012, while Aggressive and Passive HFT volume was relatively constant. 

Panel B looks at the percent of market volume traded by each trader type over the two 

year span. Although average daily market volume fluctuates considerably over the two-year 

span, the percent traded by each type is relatively stable. For example, HFT percentage volume 

starts in August 2010 at 54.37% and ends in August 2012 at 55.53%; However, Aggressive HFT 

volume increases over the two years from 15.22% to 22.63%, while Mixed HFT volume 

decreases from 30.28% to 24.59%. Overall, Figure 1 highlights the strong stability in HFT 

trading volume over a two year span in the E-mini S&P 500 futures contract.
15

Returns and Profitability

Throughout the paper, daily profits for each firm, i, are calculated for each trading day, t,

according to marked-to-market accounting, assuming that each trader starts each day with a zero 

inventory position. More precisely, for each trader, we calculate the end-of-day profits as the 

cumulative cash received from selling short positions minus the cash paid from buying long 

positions, plus the value of any outstanding positions at the end-of-day, marked to the market 

price at close: 



 

Ni t

n

i t n i n N i N p y p y

,

1

 , , , where pn is the price of the nth trade (out of N total 

trades on day t) and yi,n is the signed quantity of the nth trade by trader i. As Table 5 shows, 

HFTs usually end the day flat, so marking-to-market at the end of the trading day is relatively 

innocuous.

Daily returns are calculated by dividing the daily profits of each firm by the assumed 

capitalization of each firm. Capitalization is calculated for each firm on a monthly basis by 

looking at the maximum position taken in the month and multiplying by the notional value of the 

contract. Since HFTs inventory generally exhibit sharp, well-defined maximum and minimum 

positions they’re willing to take (for example, bounds of 100 or 200 contracts exactly), this 

number represents the maximum amount of capital that an HFT would need to execute its 

specific strategy.6

Finally, we evaluate the Sharpe ratios of HFTs (Sharpe, 1966). Four-factor (Fama-French 

plus momentum) alphas are computed for each HFT using the standard Fama-French model 

 

6

In practice, HFTs may use much less capital than the amount we calculate, since firms only have to satisfy margin 

requirements, which are generally about one-tenth the notional value of the contract. We decided to use the notional 

value of the contract rather than the margin requirement per contract to calculate the firm’s capitalization because a 

firm that loses money on any given day will have to post new margins. The maximum possible capital that a firm 

would need is the full notional value of the contract. In practice, HFT returns on capital are presumably several 

times higher than we report, and thus these numbers should be interpreted as conservative lower bounds.
16

(Fama and French, 1993) plus the Carhart (1997) momentum factor, using daily portfolio returns 

data from Kenneth French's website. The Sharpe ratio for each trader is calculated as

* 252

i

i f

i

r r

SR







, where ri is the average daily return, rf is the risk-free rate, which is zero 

throughout our sample, and σi is the standard deviation of trader i's returns over the calculated 

sample period (usually one month).

IV. Risk and Return Performance of HFTs

In this section we present empirical facts about the investment performance of HFTs. 

First, HFTs consistently outperform the market, with the median HFT firm achieving an 

annualized Sharpe ratio of 4.3 and a four-factor annualized alpha of 22.02%. Aggressive HFTs 

earn substantially higher returns than Passive HFTs -- the average Aggressive HFTs achieves an 

annualized alpha of 90.67%, while the average Passive firm earns 23.22% -- suggesting that 

there is a strong profit motive for liquidity taking rather than liquidity providing. Second, the 

cross-sectional distribution of returns is highly skewed towards top earners whose Sharpe ratios 

and alphas are many times those of the median, and firm-level performance is strongly persistent 

over both days and months. We interpret this as showing profits persistently and 

disproportionally accumulate to the top performing HFTs, suggesting winner-takes-all 

competition. The winner-takes-all nature of returns is further confirmed in Section V when we 

look at industry concentration of returns and report high Herfindahl concentration indices. 

Looking further into how HFTs minimize their risk, we show that high Sharpe ratios are 

achieved by minimizing positional risk through strict inventory control and rapid turnover of 

contracts. Finally, to help differentiate Aggressive versus Passive HFTs' strategies, we analyze 

returns to different types of HFTs by performing spectral analysis (following Hasbrouck and 
17

Sofianos, 1993) and by decomposing from whom (i.e. from which other trader types) HFTs earn 

their profits. We show that Aggressive HFTs as a whole lose money on shorter time scales 

(presumably from the bid-ask spread and price impact) but gain money by predicting price 

movements on longer (but still intraday) time scales; in contrast, Passive HFTs show the 

opposite, making money at short horizons and losing money over longer intervals. In particular, 

Aggressive HFTs make a large part of their profits from adversely selecting Passive HFTs. 

Finally, the decomposition of profits also shows that despite strong outperformance on 

the individual firm level, effective HFT trading costs imposed on non-HFT investors are only 

0.22 basis points.

Distribution of Returns

To get a general sense of HFT returns, we first present the distribution of daily returns 

pooled across all firms within each subtype. We highlight the higher profitability of Aggressive 

HFTs, suggesting a stronger profit motive for liquidity taking than liquidity providing. In the 

next subsection, we look more specifically at the cross-sectional distribution across firms.

Table 2 presents the distribution of HFT returns and profits per contract. Panel A reports 

annualized returns, determined from the daily returns of each HFT firm and aggregated into 

groups. Panel B reports profit per contract. Mean, median, skew, and kurtosis are reported for 

both returns and profits per contract.

INSERT TABLE 2 ABOUT HERE

Table 2 shows that Aggressive HFTs earn substantially higher returns than Passive HFTs 

suggesting that there is a strong profit motive for liquidity taking rather than liquidity providing. 

For example, Aggressive HFTs earn a mean annualized return of 122.10% (Column 2), while 
18

Mixed and Passive HFTs earn significantly less: only 32.29% and 25.69%, respectively.7The pvalues on the statistical significance of profits (Column 7) show that these values differ 

significantly from zero. While the averages are all positive, there is a sizeable distribution of 

profitability across observations: the standard deviation of returns (Column 4) has Aggressive

HFTs realizing the highest variation in profits (28.39%) and Passive HFTs the lowest (8.89%). 

The daily skewness and kurtosis (Columns 5 and 6) statistics show that the distribution of profits 

is non-normal: there is excess weight in the tails, in the upper tail especially (positive skew), for 

all three types of HFTs.

Panel B reports profits per contract and similarly confirms that Aggressive HFTs are 

considerably more profitable than Mixed and Passive HFTs. We also find, in untabulated results, 

that in dollar terms the average Aggressive HFT firm earns a daily profit of $74,000 in gross 

trading revenues, while average Mixed and Passive firms earn $27,910 and $12,600, 

respectively. Annualized, these numbers corresponds to trading revenues of over $18.6, $7.0, and 

$3.2 million for Aggressive, Mixed, and Passive HFTs, respectively, in the E-mini alone. 

Overall, Table 2 highlights the higher profitability of Aggressive HFTs, suggesting a stronger

profit motive for liquidity taking than liquidity providing.

HFT Risk and Return in the Cross-Section

Next, we look at the cross-section of HFTs to study the winner-takes-all nature of 

competition and find wide variation in returns across HFT firms in the cross-section. In 

particular, we analyze returns, abnormal returns (alphas), profits per contract, and Sharpe ratios.

Other than profits per contract, the reported statistics are annualized. The cross-sectional 

 

7 We also calculate the returns for 24-hour continuous trading (as opposed to looking only at regular trading 

hours) and find qualitatively similar results for the three subtypes of HFTs.
19

distribution of returns is highly skewed towards top earners whose Sharpe ratios and alphas are 

many times those of the median.

Table 3 reports the mean and standard deviation across firms, in addition to the 10th, 25th, 

50th, 75th and 90th percentiles. The results are broken down for Aggressive, Mixed, and Passive 

HFTs. The cross-sectional distribution of annualized returns (Rows 1-4) shows that there is a 

wide distribution of returns across firms.

INSERT TABLE 3 ABOUT HERE

We focus on alphas (abnormal returns), which provide a better sense of risk-adjusted 

performance than absolute returns. Alphas are reported for various specifications, though we 

emphasize the four-factor (Fama-French + Carhart momentum) alphas. The average HFT firm

earns abnormal annualized returns of 39.92%. Comparing this number to absolute returns of 

39.49% shows that the returns of HFTs are unrelated to market returns. The breakdown among

the subcategories is striking. Aggressive HFTs earn alphas of 90.67% while Mixed and Passive 

earn 28.18% and 23.22%, again suggesting a stronger profit motive for liquidity taking than 

liquidity providing.

The fact about the distribution we wish to emphasize is the winner-takes-all aspect: that 

firms in the top decile strongly outperform those at the median. Firms in the bottom ten percent 

earn small negative returns, while firms above the median earn large positive profits. The 

distribution is right skewed, reflecting a few high earners at the top. For example, 25% of HFTs 

have annualized four-factor alphas greater than 50.92%, and 10% of HFTs have alphas greater 

than 70.51%. Similarly, the fact that the median firm's alpha (22.02%) is lower than mean firm's 

alpha (39.78%), especially for Aggressive HFTs (median = 37.06%, mean = 90.67%), suggests 
20

that the mean is driven by top performing firms who earn particularly high returns, providing 

further evidence for positive skewness in the cross-section of firms.

Table 3 also reports the distribution across firms of average daily profit per contract

(rows 11-14). Similar to the raw returns and alphas, profit per contract is widely dispersed

around the median with a pronounced positive skew: profit per contract in the top decile of firms 

is $2.01, compared with 0.46% for the median.

Lastly, we examine annualized Sharpe ratios, which show that while HFTs bear some 

risk, their risk-adjusted returns are unusually high. Menkveld (2013) has previously calculated

the annualized Sharpe ratio of an HFT firm trading in equities markets to be 9.35. Passive HFTs 

generate the highest Sharpe ratio of 5.85, implying that they keep risk low, as their annualized 

returns are the lowest at 23.13%. Mixed and Aggressive HFTs earn the Sharpe ratios of 5.26 and 

4.29, respectively. To get a sense of the magnitude of these numbers, the performance of the 

median HFT firm Sharpe ratio (4.30) is over 13 times higher than the Sharpe ratio of the S&P 

500 (0.31) (Fama and French, 2002) and 18 times higher than the mean Passive HFT firm. Thus, 

while HFTs bear some risk, their risk-adjusted returns are high.

Yet even within these different types of HFTs, the Sharpe ratio for firms varies widely, 

especially with the top earners, consistent with the winner-takes-all idea. For example, 25% of 

HFTs have a Sharpe ratio greater than 9.10, and 10% of HFTs have a Sharpe ratio greater than

12.68. Again, firms in the top decile strongly outperform those at the median, suggesting winnertakes-all.
21

Persistence of Returns

Next we test for persistence of returns, both in terms of absolute returns and also relative 

to other HFT firms. Persistent profits over time suggest that something other than luck is driving 

a firm’s performance. There is an extant literature showing that performance for activelymanaged mutual funds in period t generally does not predict performance in period t+1 (e.g. 

Carhart, 1997). However, there is evidence of persistence by some investors (e.g. Jagannathan, 

Malakhov, and Novikov (2010) for hedge funds and Kaplan and Schoar (2004) for private 

equity). Nonetheless, the expectation for most types of investors and funds is that ability has 

little influence in investing returns. The null hypothesis here is thus that HFT firms do not 

exhibit persistence in returns.

To formally analyze persistence of returns, we look at the role that lagged returns (or rank 

ordering versus other firms) have in predicting today’s returns (or rank order), both using daily 

and monthly firm-level returns. We estimate the following ordinary least squares (OLS)

regression:

  (1)

where ri,t is daily or monthly returns. While there may be higher idiosyncratic risk in daily 

returns, resulting in moderate persistence at the daily level, we find that returns are more strongly 

persistent on the monthly level. The regression is estimated for each group, Aggressive, Mixed,

and Passive, separately. We also estimate Equation (1) with other dependent variables and their 

lags, including normalized returns, normalized profits, normalized profits per contract, Sharpe 

ratios, and the rank order of these metrics.

8

 

8

By normalized, we mean subtracting out the mean and dividing by the standard deviation across firms for that day. 

We normalize to control for the time-varying mean and volatility of HFT returns
22

The results are reported in Table 4. Results based on daily observations are reported in 

Panel A, those from monthly observations are reported in Panel B, and those based on rank 

ordering in Panel C. Regressions considering normalized dependent variables are performed 

without time fixed effects as the normalization removes any average time variation. With 

normalization, the estimate of the constant, which is always zero, is not reported.

INSERT TABLE 4 ABOUT HERE

Estimates for each type of HFT show that one-day lagged performance is a strong 

predictor of current performance. HFTs exhibit persistence. For daily returns, Aggressive HFTs 

have coefficients of 0.421 (for daily returns) and 0.723 (for monthly returns). Mixed and Passive 

HFTs have mild or no persistence on the daily level (0.109 and -0.73, respectively), at least 

before normalizing returns, but strong persistence on the monthly level (0.407 and 0.725, 

respectively). Normalized daily returns are qualitatively similar, though we see slightly weaker 

persistence for Aggressive HFTs on the daily level than before (0.276) and stronger persistence 

for Mixed and Passive HFTs on the daily level than before (0.169 and 0.205, respectively). The 

coefficients reported above are all statistically significant with p<0.001. 

The adjusted R

2

estimates imply strong explanatory power of past returns: 25.5%, 7.9%

and 12.4% for daily returns and 52.2%, 22.4% and 33.5% for monthly returns for Aggressive, 

Mixed and Passive HFTs, respectively. Persistence estimates using normalized profits and profits 

per contract are qualitatively similar, though slightly weaker, than those using returns. However, 

persistence estimates using monthly normalized Sharpe ratios, however, are particularly strong 

with coefficients of 0.639, 0.659 and 0.452 for Aggressive, Mixed and Passive HFTs, 

respectively, with also high adjusted R2estimates.
23

The above findings show that the level of performance in the past is predictive of the 

level of performance in the future. We perform a similar analysis in Panel C but instead consider 

whether relative rank among HFTs within their subcategories in the past is predictive of current 

rank. Rank is calculated using daily returns, monthly returns, monthly profits, monthly profits 

per contract, and Sharpe ratios. For each measure separately, we rank the relative performance 

of the HFT firms in each day or month, with 1 representing the best performing firm, 2 the 

second-best performing firm, etc. We then repeat the analysis in Equation (8). A positive 

coefficient means that if a firm performed well in the past, it is likely to perform well in the 

future. All measures and all subcategories suggest persistence in relative performance.9 

In thinking about the drivers of persistence, it may be that human skill and experience 

allow firms to distinguish themselves. Alternatively, it could be purely technological advantages. 

A combination of the both is also probable. Regardless of the precise mechanism driving the 

persistence, persistent performance may lead to industry concentration as strong performing 

firms will continue to perform well. Less successful firms may exit the industry. In Section IV 

we observe both and analyze the implications of competition among HFT given strong 

persistence among firms.

Risk and Inventory Management

We’ve shown that HFTs earn unusually high risk-adjusted returns with a distribution that 

is strongly positively skewed: top earners achieve alphas and Sharpe ratios many times the 

median. In addition, firm-level performance is highly persistent over the sample. The next three 

 

9 As the dependent variables are both discrete and restricted to non-negative values there are additional econometric 

techniques that apply other than OLS. Two techniques include Poisson and negative binomial models. See Long 

(1997) for a thorough description these models and how to analyze count data. In untabulated results, we repeat the 

Table 4, Panel C analysis using both the Poisson and negative binomial models. The results are qualitatively the 

same.
24

subsections on inventory management, spectral analysis, and HFTs profits by counterparties 

provide further evidence of how HFTs consistently produce high risk-adjusted returns.

First, we show that high risk-adjusted returns (alphas and Sharpe ratios) are partly 

achieved by minimizing positional risk through strict inventory control and rapid turnover of 

contracts. As shown earlier, HFT risk is low, both in terms of systematic risk (as evidenced by 

the high alphas) and total risk (as evidenced by Sharpe ratios). Minimizing intraday positional 

risk not only minimizes HFT exposure to market risk but also puts a bound on maximum 

possible losses.

INSERT TABLE 5 ABOUT HERE

Table 5 provides evidence on the inventories of HFTs in the cross-section. The first row 

reports the Average Daily Volume, which captures the average number of contracts an HFT firm 

trades each day. The remainder of the table focuses on inventory. The average end-of-day 

inventory is the average number of contracts (across days) held at the end of the regular trading 

day, 3:15 CST, by the median firm. The end of day inventory is not always zero, but is generally 

very low. End-of-day inventory of the median Aggressive HFT is 49.3 contracts, while end-ofday inventory of the median Passive HFT is only 10.5 contracts. The small standard deviations 

(across firms) show almost all firms keep their average end-of-day inventories very low. To get a 

sense of how large a position this is for a given firm, we normalize the average end-of-day 

inventory for each firm by that firm’s average daily trading volume. For Aggressive HFTs, this 

reveals that only 0.4% of trading volume is held at the end of the day by the median firm, while 

for Passive HFTs, it is only 0.1%. 

The second measure of inventory is the average intraday inventory range, which 

represents the average (across days) of the maximum intraday inventory variation (daily 
25

maximum position minus minimum position). This is an estimate of how much exposure a firm 

is willing to bear. Aggressive HFT take a maximum variation in intraday positions as large as 

525.9 contracts on average, while Passive HFTs take a maximum variation of 204.2 contracts. 

But a fractions of each firm’s average daily trading volume though, these numbers are only 7.3% 

and 2.2%, respectively.

While we select HFTs based on low intraday and end-of-day inventories, Table 5 shows 

that intraday and end-of-day inventories for the majority of firms are substantially lower than the 

bounds in our selection criteria, implying that tight inventory management is not just an artifact 

of our selection criteria but an active goal of HFTs. The results show that minimizing positional 

risk, and elimination the potential large loss associated with a sizeable direction position, is an 

important component of HFTs maximizing risk-adjusted returns.

Spectral Analysis

To further understand the investment horizon of HFTs, we follow Hasbrouck and 

Sofianos (1993) and decompose HFT profits over different time horizons using spectral analysis. 

The time horizon over which HFTs make their profits provides insight into their trading 

strategies and allows us to further examine the differences between the types of HFTs. We find 

that Aggressive HFTs as a whole lose money on shorter time scales (presumably from the bidask spread and price impact) but gain money by predicting price movements on longer (but still 

intraday) time scales (after 1,000 market transactions). In contrast, both Mixed and Passive HFTs 

show the opposite, tending to make money at short horizons (1,000 transactions or fewer) and 

lose money over longer intervals.
26

Spectral analysis decomposes profits for each firm into different time horizons. Profits 

are calculated from two time series, prices and inventories, which are analyzed as sums of 

Fourier modes of varying frequencies. Intuitively, for any given frequency, if prices and 

inventories are waves that move in phase (traders buy before the price is going up), profits are 

generated, while if they are out of phase (traders buy before the price goes down), traders incur 

losses.

Mathematically, we start with marked-to-market profit for any individual trader at 

transaction time10τ: 

 

 

 

 

 

 

(2)

where xt is the inventory holdings of that trader and pt is the price at time t.

11 By defining the 

following functions:

 

 

 

(3)

 

 

 

(4)

where ω is interpreted as a wavelength having units of transaction time and and are 

the spectral densities of the xt and pt, we can re-express marked-to-markets profits using the 

following formula (see Hasbrouck and Sofianos, 1993, for mathematical details)12: 

 

 

 

 

 

 

 

 

 

 

 

 

 

 (5)

The 

 

 term captures the component of the marked-to-market profits 

generated at trading wavelength ω. Thus, if the summation in Equation (5) is broken up into 

 

10 For computational reasons, spectral analysis must be conducted in transaction time, as opposed to clock time. For 

reference, there are approximately 10 transactions per second.

11 Spectral analysis requires us to assume that xt and Δpt are stationary processes, which is a valid assumption to 

make given that xt, HFT firms’ inventories, is a mean-reverting process and Δp, is the first difference of the price 

process.

12 Real is the function that takes the real part of a complex number. The last equality follows because the imaginary 

part of 

 

sums to 0. 
27

wavelength blocks, then it is possible to decompose profits into the following time horizons bins 

(expressed in units of market transactions): ω = 1-10, 11-100, 101-1,000, 1,001-10,000, 10,000-

100,000, and 100,000+. We thus decompose profits into these time horizon bins each HFT firm.

Then for each time horizon, we take the median profits across days and then across firms (along 

with the 25th and 75th percentiles across firms). Spectral analysis results are reported in Table 

6.13

INSERT TABLE 6 ABOUT HERE

Table 6 shows that in Aggressive HFTs tend to make positive profits at medium time 

scales, in the 1,001-10,000 and 10,001-100,000 transaction range, with negative profits at short 

ranges (11-100 and 101-1,000 transaction intervals) and the longest time scale of 100,000+ 

transactions. In order for an aggressive trade to be profitable, an HFT must not only predict the 

direction of the price process but also overcome the bid-ask spread. We suspect that this is the 

reason Aggressive HFTs fail to make money at the shortest time intervals. The spectral analysis 

results are consistent with the notion that Aggressive HFTs make money by anticipating price 

movements in the 1,000 – 100,000 transactions range, while losing money at both very short and 

long time scales. In contrast, both Mixed and Passive HFTs tend to gain money at short time 

scales (1-10, 11-100, and 101-1,000 transactions) while losing money on longer time scales 

(1,001-10,000, 10,001-100,000, and 100,000+ transactions). These results are consistent with the 

idea that Mixed and Passive HFTs earn the bid-ask spread in the short-run but are adversely 

selected on a longer time scale.

 

13 We only analyze one month (August 2010) rather than two years of HFT profits due to the computational 

challenges involved in doing spectral analysis. However, results from several other months were qualitatively 

similar.
28

HFT Profits by Counterparty

We would like to know from whom HFTs earn their profits. We decompose HFT profits 

by counterparty, analyzing both dollar profits and profits-per-contract. Analyzing dollar profits 

tells us where the money is (which groups HFTs have strong incentives to target), and analyzing 

profits-per-contract tells us about adverse selection costs and which traders are informed traders 

or best able to evade HFT activity. Interestingly, Aggressive HFTs make about 45% of their 

profits from adversely selecting the other HFT subtypes.

To calculate from whom HFTs earn their profits, we divide the remaining universe of 

traders in the E-mini into four categories of traders, as discussed in Data and Methods: 

Fundamental traders (likely large institutional traders), Non-HFT market makers, Small traders 

(likely retail traders), and Opportunistic traders (likely arbitrageurs, small asset managers, hedge 

funds, and other hard-to-classify traders). We find that: 1) HFTs in aggregate make most of their 

largest dollar profits from Opportunistic traders, 2) on a per-contract basis, Fundamental traders 

incur the least cost to HFTs, while Small traders incur the most, 3) interestingly, Aggressive 

HFTs make a large fraction of their profits from Mixed and Passive HFTs, and 4) the effective 

HFT transaction cost on non-HFT trades is approximately 0.22 basis points.

Whether HFTs make more or fewer profits from different types of other traders is hard to 

predict using theory. For example, Fundamental traders may trade in a way that makes their 

order flow noticeable and leaves a detectable pattern in their trading activity (as in Hirschey, 

2013; Heston, Korajczyk and Sadka, 2010), in which case HFTs would make more profits 

against them. On the other hand, due to their size and sophistication (as in Badrinath, Kale, and 

Noe, 1995; Boehmer and Wu, 2008; Boulatov, Hendershott, and Livdan, 2013; Hendershott, 
29

Livdan, and Schurhoff, 2012), Fundamental traders may be more skilled at evading HFTs and 

minimizing price impact, in which case HFT would profits less against them. 

Similarly, Small traders (retail investors) might be relatively less informed (e.g.,

Hvidkjaer, 2008; Kaniel, Saar, and Titman, 2008; Barber, Odean, and Zhu, 2009) and thus incur 

significant losses to HFTs. However, because retail traders are small and trade noisily, they may 

not leave patterns in the data and consequently HFTs may have a more difficult time detecting 

them and thus earn less from them. As noted earlier, the result that we find is, on a per-contract 

basis, Fundamental traders incur the least cost to HFTs while Small traders incur the most, 

demonstrating that size and sophistication (even at the expense of leaving detectable order-flow 

patterns) are likely important for minimizing HFT-related trading costs.

Table 7 breaks down the trading profits by trading pairs in August 2010: the rows 

identify who receives the profits, whereas the different columns represent from whom the profits 

are derived. Table 7 is constructed by considering only the trades (in August 2010) between two 

groups and calculating the profit flows that result from those trades. To illustrate, we calculate 

the Aggressive HFT-Fundamental profit flows by removing all trades except those for which one 

party was an Aggressive HFT and the other party was a Fundamental trader. Since gains/losses 

from large, long-term positions can make profits look extremely volatile, we calculate short-term 

profits: defined here as gains/losses resulting 1 minute after each trade. Since the futures market 

is a zero-sum game, the resulting profits matrix is symmetrical and zero along the diagonals.14

INSERT TABLE 7 ABOUT HERE

 

14 Note that our focus is on returns during a short horizon. A loss during this interval does not imply that the trader 

(or trader category) loses money overall. In addition, we only observe a market participant’s activities in the E-mini, 

which may be one of multiple markets in which a trader participates. For instance, Fundamental traders may be 

using the E-mini contract as a hedge against real-world risks and Opportunistic traders may be doing cross-market 

arbitrage. Thus, a loss in the E-mini market does not imply the trading firm loses money overall.
30

Panel A shows that Aggressive and Mixed HFTs make positive profits from all other 

types of traders, while Passive HFTs make positive profits from all other types of traders except 

from fundamental traders. In particular, Aggressive HFTs make about 45% of their profits (= 

(7,190,140 + 2,557,038) / 21,952,215 = 44.4%) from adversely selecting the other HFT subtypes. 

Panel A shows that all types of HFTs make the majority of their dollar profits from opportunistic 

traders. Panel B describes the profits and losses on a per contract basis. These results provide an 

estimate of the effective transaction costs involved in trading with certain groups. Since we 

compute profits on a 1 minute basis while resetting each trader’s inventory to zero, their profits 

can be interpreted as short-term transaction costs extracted from the rest of the market, not gains 

from long-term directional positions. For example, Fundamental traders incur a loss of -$1.92 

(Column 2, Row 5) when trading with Aggressive HFTs, while Small traders experience a much 

larger loss of -$3.49 (Column 2, Row 7). Interestingly, Small traders lose similar amounts per 

contract to non-HFT traders. 

Finally, the "Total" column in Panel A allows us to calculate the effective HFT 

transaction cost imposed on all other traders. Since HFTs make $35.23 million from all nonHFTs in August 2010 (= $21.95 million + $12.77 million + $0.50 million), while everyone else 

trades 31.96 million contracts (see Table 1), the effective HFT cost per trade on all other traders 

is $1.10 per contract. Scaling this per-contract transaction cost by $50,000 the approximate price 

of a contract yields an estimated HFT-imposed transaction cost of 0.0022% or 0.22 basis points.

V. Competition

We analyze competition in the HFT industry to show and understand why profits are 

concentrated among a small number of incumbents who realize high and persistent returns. 
31

According to the winner-takes-all idea, we expect to see a high concentration of profits 

(measured by the Herfindahl index) that persist over time. Combined with the evidence from the 

previous section showing high firm-level persistence and strong outperformance of top-earning 

firms, this section provide evidence of an industry with profits concentrated among a small 

number of established firms.

In trying to understand the strong performance and persistence of returns to HFT firms, 

we also examine new entry. New entrants can potentially introduce competition and drive down 

both firm-level and industry profits. Given HFTs’ high profitability, one might expect there to be 

strong incentives for entry, especially for firms that already have the technological capabilities 

and financial expertise to trade (market makers, hedge funds, broker-dealers, etc.), leading to 

increased competition and downward pressure on both firm-level and industry profits. However, 

in contrast to this expectation, we find that new entrants are substantially less profitable than 

incumbents and more likely to exit. Likely as a result, we further observe that industry 

concentration (as measured by the Herfindahl index) remains high and relatively constant over 

the two year sample. Also, aggregate profitability does not decrease, after adjusting for volatility 

and non-HFT trading volume. Combined with the evidence from the previous section showing 

high firm-level persistence and strong outperformance of top-earning firms, this section provides

evidence of an industry dominated by a handful of established firms that are somehow able to 

keep the challengers at bay.

Our results are consistent with theoretical predictions regarding winner-takes-all 

competition based on speed. As mentioned previously, Budish, Cramton and Shim (2013) 

theorize that that if speed advantages are relative, then increased competition won't drive profit 

opportunities to zero, since HFTs can always one-up the competition with an ever-smaller 
32

increase in speed. Thus, aggregate profits and the concentration of profits would not decrease 

over time. Additionally, we expect entrants to earn substantially lower returns than established 

HFT firms and be more likely to exit, as presumably incumbents have advantages due to their 

experience allowing them to capture most of the profits.

HFT Market Concentration over Time

Here we show that the HFT industry concentration (as measured by the Herfindahl index 

of profits or trading volume) remains high and relatively constant over the two-year sample and 

also that aggregate profitability does not decrease, after adjusting for volatility and non-HFT 

trading volume. Our results indicate that the HFT industry exhibits concentration, in line with 

competition and new entry not decreasing the profitability of the most successful HFT firms. 

Combined with high firm-level persistence of returns, a high and steady Herfindahl index 

suggests that top performing incumbents maintain their position in the market.

We calculate Herfindahl indices, a commonly used measure of concentration of market 

share or earnings within an industry, for both profits and trading volume. The profit Herfindahl

index is calculated as 

 

 

 

 

 

 

 

 (6)

where N is the number of firms in the HFT subgroup (Aggressive, Mixed, or Passive) in month t 

that earn non-negative profits, Profiti,t is firm i’s total trading profits in month t, and HFT Profitt

is the total trading profits of all HFT firms in the HFT subgroup. The volume Herfindahl index is 

calculated using the same formula but considering the number of contracts traded instead of 

trading profits. The Herfindahl index has a range of (0,1].
33

Table 8 reports the Herfindahl index for each subgroup of HFTs, first by calculating the 

index for each trading day and then averaging over days for every half-year block in the data set. 

Standard deviations are reported in parentheses, and stars indicate the significance from a t-test 

comparing the daily Herfindahl index in 2010 to the current half-year period.

INSERT TABLE 8 ABOUT HERE

A larger number implies a more concentrated industry, which is a proxy for the level of 

competition in the industry. As a reference, Van Ness, Van Ness, and Warr (2005) find that 

market makers have an average Herfindahl index (created with trading volume, instead of profit) 

on NASDAQ of .14, with a range of .037 to .439. The results in Table 8 for both the Profit-based 

and Volume-based number are in line with this range. Perhaps more interesting, however, than 

the level is the direction. By performing a regression with time-based dummy variables, we show 

that Profit-based and Volume-based Herfindahl indices between 2010 and each subsequent halfyear block are not decreasing, and in fact are somewhat increasing for Mixed and Passive HFTs.

For example, for Aggressive HFTs, the profit and volume Herfindahl indices are 0.362 

and 0.2, respectively; these Herfindahl indices increase to 0.381 and decrease to 0.183 in the 

second half of 2011 and is not significant for other half-year blocks. In other words, there is no 

apparent directional trend. However, contrast those results with those of Passive HFTs, whose 

Profit Herfindahl index increases from 0.287 in 2010, trending steadily upward, to 0.545 in the 

second half of 2012; similarly the volume Herfindahl index of Passive HFTs increases from 

0.129 in 2010, trending steadily upward, to 0.331 in the second half of 2012. We conclude that 

for Mixed and Passive HFTs, concentration of volume and profits actually increases between 

2010 and 2012.
34

HFT is a rather new industry, and so one might expect concentration to decrease as new 

entrants join the market. We observe the opposite.

HFT Profitability over Time

In line with HFT industry concentration not decreasing over time, we find that HFT daily 

returns, profits and profits-per-contract have not fallen, and in some cases have actually 

increased over time, after taking into account market volatility and non-HFT trading volume.

INSERT FIGURE 2 ABOUT HERE

Figure 2, Panel A shows that the aggregate monthly profits of HFTs vary substantially, 

though there is no clear directional trend. Aggressive HFTs consistently earn positive daily profit 

over the two-year span, with a mean of $395,875 per day over the two-year span, a high of 

$2,745,724 per day in August 2011 and a low of -$86,296 in January 2012. Mixed HFTs earn an 

even higher positive average daily profit over the two-year span (because there are more firms, 

even though each firm individually makes less), with a mean of $525,064 per day over the twoyear span, a high of $890,828 per day in October 2010 and a low of $63,027 in January 2011. 

Passive HFTs earn the lowest average daily profit over the two-year span, with a mean of 

$107,239 per day over the two-year span, a high of $403,259 per day in January 2012 and a low 

of -$22,499 in February 2011. 

The same is roughly true of profits per contract: Panel B shows the time-series of total 

monthly profits divided by total monthly contracts traded. Aggressive HFTs earn the highest 

average daily profits per contract over the two-year span, with a mean of $0.85 over the two-year 

span, a high of $2.01 in May 2011 and a low of $0.09 in January 2012. Mixed HFTs earn less 

with a mean of $0.52 per day over the two-year span, a high of $0.93 in May 2011 and a low of -
35

$0.23 in January 2011. Passive HFTs earn the lowest with a mean of $0.46 over the two-year 

span, a high of $1.18 in January 2012 and a low of -$0.47 in February 2011.

More formally we examine the daily returns per firm, after controlling for daily volatility 

and non-HFT trading volume, which may affect returns on a daily or longer-term basis. To do 

this analysis, we estimated the following regression, where we use indicator variables to evaluate 

the average profits over half-year blocks:

 1 baseline 1st half 11 nd half 1 (7)

 log volatility log non HFT volume 

where the indicator variables take the value of 1 during the corresponding half-year period, and 

controlling for daily log volatility (calculated in transaction time) and daily non-HFT trading 

volume 15

INSERT TABLE 9 ABOUT HERE

The coefficients are reported in Table 9 for average daily returns, daily profits and daily 

profit per contract for Aggressive, Mixed and Passive HFTs. The constant α is interpreted as the 

average HFT returns or profitability for 2010 (after controlling for volatility and non-HFT 

volume), and the coefficients β1 through β4 capture the cumulative increase or decrease in 

average returns or profits (after controlling for volatility and non-HFT volume) since 2010. 

According to, the baseline HFT returns for 1 (α) are . 19%, .1 5% and . 841% for 

Aggressive, Mixed and Passive HFTs, respectively; the baseline HFT average daily profits for 

 1 (α) are $68,100, $58,800 and $2,140 for Aggressive, Mixed and Passive HFTs, 

 

15 Both controls (log volatility and log non-HFT volume) are reported as deviation from the average so that the 

constant in the regression can be interpreted as the average profitability in 2010 when volatility and volume are 

average. 
36

respectively; and the baseline HFT average daily profits per contract for 1 (α) are $1.74, 

$0.872 and $0.254 for Aggressive, Mixed and Passive HFTs, respectively. 

Interestingly, the coefficients on log volatility are positive and statistically significant for 

Aggressive HFTs and negative or not significantly different from zero for Mixed and Passive 

HFTs, suggesting that Aggressive HFTs benefit from increased volatility (perhaps more 

opportunities to adversely select other traders), whereas Mixed and Passive HFTs are harmed by 

increased volatility (more opportunities to be adversely selected themselves). The coefficients on 

log non-HFT volume are positive but only sometimes statistically significant, suggesting that 

increasing that increased trading by non-HFT market participants increases returns and profits, 

especially for Aggressive HFTs, though may have no effect on returns and profits for Mixed and 

Passive HFTs.

The indicator coefficients, β1 through β4, test whether average daily returns and 

profitability decreases over the two year sample. In most cases, they are not statistically 

significantly different from zero. When the coefficients are significant, they are positive for all 

but one coefficient, suggesting that profits per firm were constant or increasing from 2010 to 

2012. The non-statistically significant coefficients are evenly divided between being positive and 

negative, suggesting that the issue isn’t simply a lack of statistical power but that there is no

downward trend on returns and profits over time. Taken together the evidence fails to support the 

hypothesis that HFT profits and returns have decreased over time. They appear to be highly 

variable day-to-day and month-to-month, but there is no trend either up or down in the aggregate 

or on the firm level.
37

Entry and Exit

We analyze entry and exit of HFTs into the E-mini market. Focusing on new entrants, we 

find that new entrants (especially Aggressive HFT entrants) underperform established HFTs and 

have a higher probability of exiting. We regress returns and profitability measures on indicator 

variables for length of time in the market, designating less than 1 month, 2 months or 3 months

as indicators of new entry16. We exclude the observations in 2010 as this is when we first 

observe any firm. Formally, we estimate the following OLS regression equation:

  (8) 

If new entrants are less competitive and profitable than established firms, the coefficient on the 

one-month dummy should be negative; the two- and three-month dummy coefficients should 

also be negative but increasing, showing that experience in the market matters. Based on the 

regression specification, the constant is interpreted as average returns for established firms. In 

addition to daily returns, we also look at normalized returns, normalized profits and normalized

profits per contract: coefficients in the normalized regressions are interpreted as how many 

standard deviations new entrants performance are above or below the mean. 

INSERT TABLE 10 ABOUT HERE

The results are reported in Table 10, Panel A. Looking at daily returns (Columns 1-3), 

Aggressive HFTs have statistically significant negative coefficients corresponding to the new 

entry dummies, with the largest negative value for the 1-month dummy (-0.749%) and 

decreasing over time (-0.625% and -0.254%). By comparing these coefficients to the constant 

 

16 Specifically, the 1 month old indicator variable takes the value 1 (otherwise 0) for firm i during days t to t + 30 if 

firm i began trading on day t-1. The 2 and 3 month old indicators likewise use t + 60 and t + 90 windows, 

respectively. In accounting for entry and exit, we look at the entire lifetime of each firm, not just the months for 

which the firm is classified as an HFT or as a specific type of HFT. Finally, we ignore gaps and just count the 

overall first and last trading days of a firm as entry and exit dates.
38

(0.665%), we can see that new entrants have negative returns for the first month and only slowly 

increase their profitability over the subsequent two months. Thus, new Aggressive HFTs show a 

large discrepancy in average daily returns between new entrants and established firms. 

For Mixed HFTs, the coefficients are less negative and only significant for the 1-month 

dummy; comparing the 1-month coefficient (-0.065%) to the constant (0.144%), we see that new

entrants who are Mixed HFTs still have positive returns, though less so than established firms. 

For Passive HFTs, the results are even weaker, suggesting that there is no disadvantage for new 

entrants who are Passive HFTs. Similar results hold when looking at normalized daily returns 

(Column 4-6), normalized daily profits (Columns 7-9) and normalized profits per contract 

(Columns 10-12): for Aggressive HFTs (and less so for Mixed HFTs) entrants are considerably 

less profitable than established firms, while for Passive HFTs entrants are associated with no 

such disadvantage.

For further evidence on the lack of competition, we examine whether new entrants are 

more likely to exit. We find that new Aggressive and Mixed HFTs have an approximately 1% 

per day increase in the probability of exit than more established HFTs. To address the probability 

of exit, we perform a probit regression on each month separately to determine whether new 

entrants are more likely to exit:

  (9)

where Exiti,t takes the value 1 on day t for firm i if that is the last day firm i trades. The 

coefficients of interest are again those on the dummy variable for new entrants, x-month, which 

takes the value one, two, or three for either one-, two- or three-months after first appearing as an 

HFT, depending on the regression specification. We do not count exits in August 2012, due to it

being the last month of the data set.
39

The marginal effects corresponding to the coefficients of the probit regression are 

reported in Table 10, Panel B. The Pseudo R2is reported below the coefficients. Column 1

shows that Aggressive HFTs who are new entrants (1 month) are much more likely to stop 

trading than their more experienced competitors, with a coefficient of 0.0186: a new entrant has 

an increased daily probability of exit of 1.86%, which is reasonably high considering that this is 

the increased probability of exit for each day (not the cumulative probability of exit at any future 

point). Aggressive probability of exit for new entry is statistically significant and positive for the 

first three months. Mixed HFT new entrants have heightened exit probabilities in months two 

and three. However, for Passive HFTs the marginal effects are not statistically significant.

In conclusion, new entrants are less profitable and more likely to exit than established 

HFTs. This finding helps explain the continued concentration of profits among a small subset of 

established firms: if new entrants are less profitable and tend to exit, then concentration of profits 

will continue or even increase among established firms. Furthermore, we speculate that new 

entrants’ propensity to exit will limit the degree to which competitive forces reduce the profits of 

existing HFTs.

VI. Speed

Why might HFT be dominated by a small number of incumbents whose past experience 

allows them to stay ahead of the competition and maintain their market share? In Section IV, we 

show that Aggressive HFTs outperform their Mixed and Passive counterparts. Here we focus on

another important factor, relative (rank-order) speed, which we show to be an important 

determinant of profitability, especially for Aggressive HFTs.
40

We look at the relationship between speed and profits and show a positive association. 

Our measure of latency comes from Weller (2013): we measure latency of a firm as the 5th 

percentile of the duration between switching from a passive trade to an aggressive trade, 

measured in milliseconds. While this measure may not be ideal for every HFT, such as HFTs that 

trade all passively or all aggressively, it is a way to capture an active decision that is likely a 

response to market events. In contrast to other measures such as the duration between switching 

from an aggressive buy to an aggressive sell, which may suggest more about the timing of a 

firm’s inventory management strategies, our latency measure aims to capture a firm’s reaction 

speed to market events given its technological constraint.

We sort Aggressive, Mixed and Passive HFTs’ firm-day observations into decile bins 

corresponding to latency. Speed is the reciprocal of the average latency (plus 1 millisecond, to 

ensure we do not divide by zero). Figure 3 plots the average of Speed versus average profits 

overall all firm-day observations within each decile bin.

INSERT FIGURE 3 ABOUT HERE

Panel A shows Speed vs. average profits for Aggressive and Mixed HFTs (grouped 

together), and Panel B shows the same for Passive HFTs. The three lines trace the relationship 

between speed and profits at approximately one-year intervals (October 2010, July 2011, August 

2012).17 Figure 3 suggests a positive relationship between profits and Speed. In the months 

examined, there is a roughly increasing relationship between profits and Speed.

The graphs, which trace the relationship between Speed and profits at approximately oneyear intervals (October 2010, July 2011, August 2012), show that Speed is increasing over the 

two-year span. Between October 2010, July 2011 and August 2012, the average Speed of the top 

 

17 Because millisecond time stamps were needed for this analysis, we are limited to which months we can analyze.
41

decile increases from approximately 0.4 to 0.75 to 1. To interpret, a value of 0.5 implies that an 

HFT switches from aggressive to passive, or vice versa, in one millisecond. A value of 1 implies 

that an HFT switches within the same millisecond. The speed of the second-to-top decile 

increases from approximately 0.27 to 0.32 to 1. There are similar increases in Speed for Passive 

HFTs. Although Speed increases over the two-year span, average profit fluctuates month-tomonth with no clear trend over time. 

For a formal analysis, we estimate the following regression from firm-day observations 

of HFT profitability:

  (10)

where log(Profits,i,t) is a modified version of log profits, actually sign(profits)*log(1+|profits|), to 

allow for negative values, RelativeSpeedi,t is the firm's ranking that day in terms of speed among 

all firms of that subtype scaled by the total number of firms that day of that subtype. The results 

are reported in Table 11.

INSERT TABLE 11 ABOUT HERE

Table 11 shows that for all three subtypes of HFTs relative speed is important, with 

statistically significant coefficients of -6.72, -4.44 and -2.62 for Aggressive, Mixed, and Passive 

HFTs, respectively. The signs of the coefficients are as one would expect: profits are decreasing 

in relative speed (higher relative rank means higher profits). The coefficient is highest for 

Aggressive HFTs. Given that the left-hand side of the regression is in logs, this translates to a 

four order-of-magnitude higher change in profits for Aggressive HFTs than Passive HFTs, 

conditional in a one-rank improvement in speed. By showing that speed is an important 

determinant of profitability, our analysis suggests that HFTs have strong incentives to compete 
42

over small increases in speed in an industry dominated by a small number of incumbents earning 

high and persistent returns.

VII. Conclusion

We study the risk and return performance of HFT firms. We document several important 

descriptive statistics, many of which suggest superior investment performance of HFTs. HFTs 

earn Sharpe ratios that are several times higher than those for other asset classes or trader types. 

HFT returns are highly persistent, while risks are kept very low through tight inventory control

and rapid turnover of contracts. HFT profits accumulate to the fastest and most aggressive 

liquidity-taking incumbents, while new entrants are less profitable and more likely to exit.

These facts highlight the importance of understanding the industrial organization of 

HFTs. Economists generally think that competition from new entrants will improve markets: 

there will be more liquidity, greater price efficiency, lower transaction costs for investors, and 

less potential for any one firm to influence markets. However, the cutthroat competitive 

environment in which HFTs interact may influence their impact on market quality. With limited 

competition from new entrants to engage incumbent HFTs, market quality may not improve as 

much as it would otherwise. Recent theoretical papers have highlighted concerns of faster traders

adversely selecting slower traders and competition on speed leading to socially inefficient arms 

races for speed.

Our results suggest that HFTs have strong incentives to take liquidity and compete over 

small increases in speed in an industry dominated by a small number of incumbents earning high 

and persistent returns. Understanding the industrial organization of HFTs allows researchers to 

think more comprehensively about the role and implications of HFTs in financial markets.
43

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46

Figure 1: Aggregate HFT trading activity

Panel A shows the average daily HFT volume of all HFT accounts combined (with standard 

error bars). Panel B shows the percent of market volume by trader type.

Panel A: HFT average daily trading volume

Panel B: Percent market volume by trader types

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

Aug 

2010

Oct Nov Jan 

2011

Feb Apr May July Aug Oct Nov Jan 

2012

Feb Apr May July Aug

Contracts in Millions

Average daily HFT trading volume

HFTa

HFTm

HFTp

0%

20%

40%

60%

80%

100%

Aug 

2010

Oct Nov Jan 

2011

Feb Apr May July Aug Oct Nov Jan 

2012

Feb Apr May Jul Aug

Percent market volume

Month

Percent market volume by trader type (cumulative)

opp

fund

small

MM

HFTp

HFTm

HFTa
47

Figure 2: Aggregate HFT returns and profitability

Panel A shows the average daily HFT returns of all HFT accounts combined. Panel B shows

average daily profits per contract, where the contract price is approximately $50,000. Standard 

error bars are calculated based on daily observations.

Panel A: Aggregate HFT profits

Panel B: Aggregate HFT profits per contract

-1

0

1

2

3

Aug 

2010

Oct Nov Jan 

2011

Feb Apr May July Aug Oct Nov Jan 

2012

Feb Apr May July Aug

$ in Millions

Average Daily HFT profits

HFTa

HFTm

HFTp

-3

-2

-1

0

1

2

3

4

Aug 

2010

Oct Nov Jan 

2011

Feb Apr May July Aug Oct Nov Jan 

2012

Feb Apr May July Aug

$ per contract

Average daily HFT profits per contract

HFTa

HFTm

HFTp
48

Figure 3: Speed and profitability

The figures shows the relationship between speed and profits. Speedi,t = (1+Latencyi,t)

-1

, where

Latencyi,t is calculated as the 5th percentile (within each firm-day) of the time in milliseconds 

between successive trades that switch from a passive trade to an aggressive trade. Speed 

observations are grouped into decile bins, which are plotted against median profits within each 

bin. Panel A analyzes Aggressive and Mixed HFTs, and Panel B analyzes Passive HFTs. Within 

each panel, the relationship between speed and profits is plotted separately for three months for 

which we have millisecond data , October 2010, July 2011, and August 2012.

Panel A: Aggressive and Mixed HFT 

Panel B: Passive HFT

-$15,000

-$10,000

-$5,000

$0

$5,000

$10,000

$15,000

$20,000

$25,000

$30,000

0 0.2 0.4 0.6 0.8 1

Median profits

Speed

Profits vs. Speed

Oct 2010

July 2011

Aug 2012

-$10,000

$0

$10,000

$20,000

$30,000

$40,000

$50,000

0 0.2 0.4 0.6 0.8 1

Median profits

Speed

Profits vs. Speed

Oct 2010

July 2011

Aug 2012
49

Table 1: Summary statistics of S&P 500 E-mini market, August 2010

The mean, standard deviation, minimum, median, and maximum of the daily trading activity of 

seven different trader types' trading activity are reported: Aggressive HFTs (HFTA), Mixed HFTs 

(HFTM), Passive HFTs (HFTP), fundamental, small trader, non-HFT market maker, and 

opportunistic. Two different statistics are reported: Daily % Market Volume is the daily percent 

of market volume traded and Daily Aggressive Ratio is the daily fraction of contracts that are

liquidity taking.

Daily % Market Volume Mean Std. Dev. Min. Median Max

HFTA (n=14) 15.22% 1.89% 9.50% 15.74% 17.57%

HFTM (n=3 ) 30.28% 1.65% 27.46% 30.11% 33.94%

HFTP(n= 1) 8.87% 0.96% 6.36% 8.96% 10.93%

Fundamental (n=346) 8.42% 1.17% 6.97% 8.26% 12.69%

Small Trader (n=21761) 1.04% 0.11% 0.82% 1.02% 1.24%

Non-HFT Market Maker (n=737) 4.24% 0.37% 3.60% 4.31% 4.83%

Opportunistic (n=8494) 31.93% 1.40% 29.78% 31.77% 34.44%

Total (n=31403) 3,187,011 819,419 1,652,052 3,081,016 4,465,574

Daily Aggressive Ratio

HFTA 84.22% 1.90% 80.05% 84.26% 87.79%

HFTM 37.08% 1.56% 34.66% 37.29% 40.08%

HFTP 12.35% 1.45% 10.73% 11.83% 15.54%

Fundamental 57.68% 3.83% 48.68% 57.58% 64.90%

Small Trader 57.82% 1.25% 55.64% 57.53% 59.94%

Non-HFT Market Maker 12.98% 0.99% 11.45% 12.88% 15.12%

Opportunistic 59.08% 1.21% 56.80% 58.91% 61.89%
50

Table 2: HFT returns

The table reports statistics on the daily returns and profitability of HFT firms from August 2010

to August 2012. Each observation is a firm-day. Panel A reports returns and Panel B reports 

profits per contract (nominal contract value of approximately $50,000). The labels HFTA, HFTM, 

and HFTPcorrespond to Aggressive, Mixed, and Passive HFTs, respectively. Means, medians, 

and standard deviations are reported annualized, while skewness and kurtosis are based on daily 

observations. The p-value tests whether daily means are statistically significantly different from 

zero (tested over N=530 trading days).

Panel A: Annualized Returns (in %)

N Mean Median Std. Dev. Skew. Kurt. P-Value

HFT (all) 13713 51.67 18.56 16.78 6.816 147.154 < 0.001

HFTA 3274 122.10 25.15 28.39 5.679 65.525 < 0.001

HFTM 6147 32.29 18.84 11.40 0.547 58.503 < 0.001

HFTP 4292 25.69 15.35 8.89 6.402 249.666 < 0.001

Panel B: Profit Per Contract

N Mean Median Std. Dev. Skew. Kurt. P-Value

HFT (all) 13713 $0.641 $0.519 $0.486 $0.125 $79.320 < .05

HFTA 3274 $1.296 $0.792 $0.536 $5.556 $96.318 < .001

HFTM 6147 $0.404 $0.466 $0.568 $-2.044 $46.798 0.15

HFTP

4292 $0.481 $0.470 $0.268 $-3.986 $183.799 < 0.01
51

Table 3: Cross-sectional distribution of returns across firms

The table reports statistics on the cross-section of HFT firms who are active for at least three 

months. Returns, alphas, profits per contract (on a notional value of approximately $50,000), and 

Sharpe ratios (based on daily observations and reported in annualized terms) are first calculated 

for each firm; statistics on the cross-section of firms are reported below. The labels HFTA, 

HFTM, and HFTPcorrespond to Aggressive, Mixed, and Passive HFTs, respectively. Data-use 

restrictions prevent certain top and bottom percentiles from being reported.

N Mean S.D. 10% 25% 50% 75% 90%

Returns (% annualized)

HFT (all) 85 39.49 87.83 -0.35 8.07 20.40 51.14 74.13

HFTA

18 91.08 170.55 46.64

HFTM 39 27.42 45.61 22.51

HFTP

28 23.13 22.24 15.02

Alphas (% annualized)

HFT (all), CAPM 85 39.92 88.81 -0.26 8.95 19.20 51.15 73.33

 3-factor 85 39.74 89.43 -1.49 8.09 19.10 50.82 72.93

 4-factor 85 39.78 89.21 -1.80 8.13 22.02 50.92 70.51

HFTA 4-factor 18 90.67 174.74 37.06

HFTM 4-factor 39 28.18 44.90 23.15

HFTP 4-factor 28 23.22 22.24 14.88

Profit per contract ($)

HFT (all) 85 0.54 1.43 -0.16 0.28 0.46 0.82 2.01

HFTA

18 0.65 1.56 0.65

HFTM 39 0.40 1.68 0.46

HFTP

28 0.66 0.91 0.41

Sharpe Ratios (annualized)

HFT (all) 85 5.25 5.01 -0.18 2.16 4.30 9.10 12.68

HFTA

18 4.29 4.57 3.86

HFTM 39 5.26 5.75 4.38

HFTP

28 5.85 4.18 4.52
52

Table 4: Persistence of returns

The table analyzes persistence in firms' returns and profits on both a daily and monthly level. The following regression is estimated: 

 . Regressions are also estimated in which the dependent variable (and lag) is 

normalized across firms for each day (or month) to account for the time-varying mean and variance of returns. With normalization, the 

regression is performed without time fixed effects as the normalization removes any average time trend, and the estimate of the constant, 

which is always zero, is not reported. Similar regressions are estimated with profits, profits-per-contract, and Sharpe ratios. Panel A 

analyzes persistence using daily observations, Panel B uses monthly observations, and Panel C considers persistence of rank ordering of 

firms on each day or month. *, ** and *** correspond to p-values < 5%, 1%, 0.1%, respectively. Standard errors are in parentheses.

Panel A: Daily persistence

Returns(i,t) Normalized returns(i,t) Normalized profits(i,t) Normalized profits-percontract(i,t)

HFTA HFTM HFTP HFTA HFTM HFTP HFTA HFTM HFTP HFTA HFTM HFTP

Dependent .421*** .109*** -.073*** .276*** .169*** .205*** .16*** .141*** .227*** .111*** .093*** .074***

 var (i,t-1) (.0193) (.0147) (.0167) (.0195) (.0147) (.0174) (.0199) (.0148) (.0173) (.0202) (.015) (.0176)

Constant .271*** .111*** .11***

(.0322) (.0103) (.0086)

Adj-R

2

0.255 0.079 0.124 0.077 0.029 0.044 0.035 0.021 0.054 0.018 0.010 0.010

N 2703 4728 3458 2702 4724 3454 2702 4724 3454 2702 4724 3454
53

Panel B: Monthly persistence

Returns(i,t) Normalized returns(i,t) Normalized profits(i,t) Normalized profits-percontract(i,t)Normalized

Sharpe ratio(i,t)

HFTA HFTM HFTP HFTA HFTM HFTP HFTA HFTM HFTP HFTA HFTM HFTP HFTA HFTM HFTP

Dependent .723*** .407*** .725*** .809*** .449*** .699*** .416*** .33*** .616*** .418*** .296*** .52*** .639*** .659*** .452***

 var (i,t-1) (.0654) (.0569) (.0978) (.0495) (.0541) (.0623) (.0839) (.0585) (.0523) (.0812) (.0598) (0.080) (.0634) (.0441) (.0686)

Constant .149* .0779*** .0234

(.061) (.0165) (.0158)

Adj-R

2

0.522 0.224 0.335 0.656 0.216 0.428 0.176 0.114 0.452 0.208 0.099 0.246 0.439 0.470 0.212

N 161 270 197 161 270 197 161 270 197 161 270 197 161 270 197

Panel C: Persistence of rank ordering

Daily returns(i,t) Monthly returns(i,t) Monthly profits(i,t) Monthly profits-percontract(i,t)Sharpe ratio(i,t)

HFTA HFTM HFTP HFTA HFTM HFTP HFTA HFTM HFTP HFTA HFTM HFTP HFTA HFTM HFTP

Dependent 0.376*** 0.238*** 0.278*** 0.695*** 0.474*** 0.444*** 0.679*** 0.490*** 0.402*** 0.479*** 0.328*** 0.289*** 0.629*** 0.555*** 0.479***

 var (i,t-1) (0.0152) (0.0121) (0.014) (0.0504) (0.0478) (0.0551) (0.0515) (0.0474) (0.0562) (0.0616) (0.0513) (0.0588) (0.0545) (0.0452) (0.0539)

Constant 3.868*** 7.802*** 5.678*** 2.150*** 5.775*** 4.978*** 2.265*** 5.607*** 5.347*** 3.677*** 7.384*** 6.362*** 2.614*** 4.892*** 4.666***

(0.111) (0.144) (0.128) (0.422) (0.61) (0.575) (0.431) (0.604) (0.588) (0.515) (0.654) (0.615) (0.456) (0.576) (0.564)

Adj-R

2

0.141 0.056 0.077 0.481 0.223 0.194 0.458 0.238 0.159 R-sq 0.225 0.105 0.393 0.306 0.226

N 2703 4728 3458 161 270 197 161 270 197 161 270 197 161 270 197
54

Table 5: HFT inventories

Inventory statistics are reported for Aggressive HFTs (HFTA), Mixed HFTs (HFTM), and 

Passive HFTs (HFTP). Median and standard deviations across firms are reported for three

statistics: Average Daily Volume (in thousands), Average end-of-day inventory (both in number

of contracts and as a percentage of the firm's average daily trading volume), and Average

intraday inventory range. Medians (and s.d.) across firms are calculated by taking the average 

across days for each firm and then the median (and s.d.) across firms.

Median (and s.d.) across firms

HFTA HFTM HFTP

Average Daily Volume (thous.) 7,838 9,134 8,693

(28,087) (36,826) (17,895)

Average end-of-day inventory 49.3 16.7 10.5

 (154.6) (266.2) (203.8)

- Normalized by firm's average 0.4% 0.2% 0.1%

 daily trading volume (4.6%) (1.3%) (1.3%)

Average intraday inventory range 525.9 313.6 204.2

(861.1) (1030.0) (659.3)

- Normalized by firm's average 7.3% 4.0% 2.2%

 daily trading volume (5.8%) (3.7%) (3.4%)
55

Table 6: Spectral Analysis

The table analyzes trading profits in August 2010 over different time horizons using spectral analysis, following the methods of 

Hasbrouck and Sofianos (1993). We first compute the spectral decomposition of profits for each individual HFT firm and each trading 

day, decomposing profits over the following intervals: 1-10, 11-100, 101-1,000, 1,001-10,000, 10,000-100,000 and 100,000+ market 

transactions. For each HFT firm we calculate the median profit across days for each interval, and then report the median and the 25th

and 75th percentiles (in brackets) across firms.

Transaction interval

1-10 11-100 101-1,000 1,001-10,000 10,001- 100,000 100,000+

HFTA

$870 -$678 -$5,348 $21,939 $22,108 -$8,637

[$-2825, $8252] [$-10887, $5997] [$-45231, $12597] [$-9633, $73428] [$6213, $44481] [$-19056, $4234]

HFTM $12,145 $23,171 $8,811 -$21,832 -$8,483 -$1,935

[$7825, $19111] [$12301, $35883] [$-5835, $27894] [$-36494, $-5288] [$-13018, $2360] [$-4179, $1452]

HFTP

$5,236 $12,991 $11,408 -$7,917 -$9,774 -$3,428

[$3840, $11170] [$10174, $20701] [$7920, $19186] [$-14282, $-1512] [$-20778, $-6990] [$-9596, $-2509]
56

Table 7: Profit Breakdown

The table analyzes the decomposition of average daily short-term profits among different trader types in August 2010. The table is 

constructed by considering the trades between each pair-wise group and calculating the profit flows that result from those trades. We 

calculate each type’s short-term profits (gains/losses realized on a trade one-minute after that trade). The rows identify who receives 

the profits, whereas the different columns represent from whom the profits are derived. Panel A analyzes average daily trading profits, 

and Panel B describes the profits on a per contract basis.

Counterparty

Profits to:

HFTA HFTM HFTP Non-HFT 

MM

Fundamental Opportunistic Small Total

Panel A: Profits

HFTA $0 $7,190,140 $2,557,038 $1,962,675 $1,691,738 $8,171,350 $379,275 $21,952,215

HFTM -$7,190,140 $0 $1,400,125 $1,607,400 $376,300 $15,358,325 $1,219,050 $12,771,060

HFTP -$2,557,038 -$1,400,125 $0 $84,300 -$373,438 $4,323,100 $425,538 $502,338

Non-HFT MM -$1,962,675 -$1,607,400 -$84,300 $0 -$382,688 $1,060,000 $120,525 -$2,856,538

Fundamental -$1,691,738 -$376,300 $373,438 $382,688 $0 $2,321,775 $119,550 $1,129,413

Opportunistic -$8,171,350 -$15,358,325 -$4,323,100 -$1,060,000 -$2,321,775 $0 $339,150 -$30,895,400

Small Trader -$379,275 -$1,219,050 -$425,538 -$120,525 -$119,550 -$339,150 $0 -$2,603,088

Total -$21,952,215 -$12,771,060 -$502,338 $2,856,538 -$1,129,413 $30,895,400 $2,603,088 $0

Panel B: Profit/Loss Per Trade

HFTA $0.00 $2.02 $1.93 $2.64 $1.92 $2.49 $3.49 $2.04

HFTM -$2.02 $0.00 $0.94 $1.95 $0.18 $1.92 $4.42 $0.60

HFTP -$1.93 -$0.94 $0.00 $0.75 -$0.62 $1.79 $5.05 $0.08

Non-HFT MM -$2.64 -$1.95 -$0.75 $0.00 -$1.59 $1.11 $4.25 -$0.97

Fundamental -$1.92 -$0.18 $0.62 $1.59 $0.00 $1.45 $2.87 $0.19

Opportunistic -$2.49 -$1.92 -$1.79 -$1.11 -$1.45 $0.00 $2.05 -$1.38

Small Trader -$3.49 -$4.42 -$5.05 -$4.25 -$2.87 -$2.05 $0.00 -$3.67

Total -$2.04 -$0.60 -$0.08 $0.97 -$0.19 $1.38 $3.67 $0.00
57

Table 8: HFT Herfindahl Concentration 

The table reports estimates on the Herfindahl index for each class of HFTs over successive sixmonth sample windows and analyzes whether market concentration is increasing or decreasing over 

time. We report a profit-based Herfindahl Index as well as a volume-based one. The profit 

Herfindahl index is calculated as 

 

 

 

 

 

 

 , and the volume 

Herfindahl is calculated similarly using trading volume instead of trading profits. A larger index

implies a more concentrated industry. To assess whether market concentration is increasing or 

decreasing over time, the first-half of 2010 is used a baseline, and subsequence six-month sample 

periods are tested against the baseline. *, ** and *** correspond to p-values < 5%, 1%, 0.1%, 

respectively. Standard errors are in parentheses.

 Profit Herfindahl Index Volume Herfindahl Index

HFTA HFTM HFTP HFTA HFTM HFTP

1st half 2010 0.362 0.287 0.287 0.2 0.239 0.129

(0.131) (0.135) (0.167) (0.059) (0.061) (0.056)

1st half 2011 0.377 0.316 0.495*** 0.195 0.26 0.329***

(0.202) (0.164) (0.236) (0.106) (0.142) (0.104)

2nd half 2011 0.318* 0.259 0.471*** 0.183* 0.174*** 0.289***

(0.155) (0.135) (0.229) (0.039) (0.136) (0.083)

1st half 2012 0.34 0.376*** 0.513*** 0.199 0.266 0.348***

(0.178) (0.156) (0.286) (0.054) (0.132) (0.182)

2nd half 2012 0.347 0.412*** 0.545*** 0.199 0.248 0.331***

(0.144) (0.141) (0.219) (0.062) (0.063) (0.129)
58

Table 9: Long-run profitability

The table analyzes long-run trends in HFT profitability by reporting estimates of the following OLS regression: 

 . The notation corresponds to a series of indicators capturing six-month 

windows in 2011 and 2012; a positive coefficient on one of these indicators would correspond to an increasing trend in HFT firms' profits 

in comparison to the benchmark year 2010 (the first year in which we have data). We control for daily volatility and non-HFT-volume. *, 

** and *** correspond to p-values < 5%, 1%, 0.1%, respectively. Standard errors are in parentheses.

Daily returns (%) Daily profits ($, thous.) Daily profit-per-contract

HFTA HFTM HFTP HFTA HFTM HFTP HFTA HFTM HFTP

Constant (2010 baseline) .219*** .105*** .0841*** 68.1*** 58.8*** 2.14 1.74*** .872* .254

 (.0567) (.0232) (.0227) (13.2) (11.5) (9.66) (.303) (.347) (.195)

1st half of 2011 indicator -.0233 .0258 -.032 .132 -17.8 -4.04 -.501 -.332 -.218

(.0762) (.0333) (.0369) (17.7) (16.4) (15.7) (.407) (.498) (.317)

2nd half 2011 indicator .0494 .0645* .128*** 7.36 -33.5* 35.4* -.762 -.391 .627*

(.0771) (.0328) (.0349) (17.9) (16.2) (14.8) (.412) (.49) (.299)

1st half 2012 indicator .321*** .132*** .0632 21.8 -13.1 25.1 -.38 .016 .575

(.0752) (.0331) (.0345) (17.5) (16.3) (14.7) (.402) (.495) (.296)

2nd half 2012 indicator .353*** .0584 -.0719 10.3 -31.1 8.83 -.897 -.177 -.691

(.0917) (.0426) (.0443) (21.3) (21) (18.9) (.49) (.637) (.38)

Log volatilityt

.209** -.0331 -.0326 43.4** -44.6** -23.3 .892* -.861 -.719*

(deviation from mean) (.0669) (.0334) (.0344) (15.6) (16.5) (14.6) (.358) (.5) (.295)

Log non-HFT volumet

.196* .18*** .047 68.7*** 39.7 3.49 .177 .813 .699

(deviation from mean) (.0777) (.0488) (.0429) (18.1) (24) (18.2) (.415) (.728) (.367)

Adj-R

2

0.026 0.009 0.013 0.027 0.004 0.004 0.006 0.001 0.008

N 3195 4525 2679 3195 4525 2679 3195 4525 2679
59

Table 10: HFT Entry and Exit

The table analyzes the performance of new HFT entrants. Panel A reports the results of the following OLS regression: 

  The notation takes the value 1 if firm i began 

trading in the last 30 days, otherwise 0; two and three month dummy variables are defined similarly. We exclude the observations in 2010 

as this is when we first observe any firm. Panel B reports the results of the probit regression 

  where Exiti,t takes the value 1 on day t for firm i if that is the last day firm i trades. The coefficient of interest is again the 

dummy variable, x-monthi,t, defined as above, but regressions are univariate (one indicator at a time, with x-month representing either one-

, two-, or three- months) in contrast to Panel A. In addition to the excluded observations described in Panel A, this regression excludes 

observations in August 2012, the last month of the analysis, due to this being the last month of the data set. *, ** and *** correspond to pvalues < 5%, 1%, 0.1%, respectively. Standard errors are in parentheses.

Panel A: Profitability of New Entrants

Daily returns(i,t) Normalized daily returns(i,t) Normalized daily profits(i,t) Normalized profits-percontract(i,t)

HFTA HFTM HFTP HFTA HFTM HFTP HFTA HFTM HFTP HFTA HFTM HFTP

< 1 month old indicator

-.749*** -.0653* -.0169 -.479*** -.144*** -.0283 -.396*** -.173*** -.0394 -.144** .0047 .003

(.0858) (.0276) (.0224) (.0511) (.039) (.0419) (.0513) (.039) (.0419) (.0517) (.0391) (.0419)

< 2 month old indicator

-.625*** -.0605 .0176 -.316*** -.132* .128* -.179 -.154* -.0237 -.0356 -.0388 .0254

(.16) (.044) (.0325) (.0953) (.0622) (.0607) (.0957) (.0622) (.0607) (.0964) (.0623) (.0607)

< 3 month old indicator

-.254* .006 -.0734* -.103 .0418 -.0032 -.0357 -.121* -.112* -.0034 .0082 -.0886

(.12) (.0338) (.029) (.0715) (.0478) (.0542) (.0718) (.0478) (.0542) (.0724) (.0479) (.0542)

Constant .665*** .144*** .113*** .138*** .0366* -0.0063 .103*** .066*** 0.0323 0.0345 0.001 0.0104

(0.04) (0.01) (0.01) (0.02) (0.02) (0.03) (0.02) (0.02) (0.03) (0.02) (0.02) (0.03)

Adj-R

2

0.134 0.074 0.113 0.026 0.003 0.001 0.018 0.004 0.001 0.002 0.000 0.001

N 3695 6433 4741 3694 6429 4737 3694 6429 4737 3694 6429 4737
60

Panel B: Probability of Exit, marginal effects

HFTA HFTM HFTP

< 1 month old indicator 0.0186** (0.009) 0.0046 (0.005) 0.0017 (0.005)

Pseudo R20.057 0.0076 0.0032

< 2 month old indicator 0.0204** (0.008) 0.0123* (0.007) 0.0003 (0.004)

Pseudo R20.076 0.053 0.0026

< 3 month old indicator

 

0.0184*** (0.007)

 

0.0082* (0.005) 0.0024 (0.003)

Pseudo R20.077 0.053 0.0055
Table 11: Speed and Profits

The table reports coefficients from the regression: 

 , where log(profits),i,t is a modified version of log profits, namely 

sign(profits)*log(1+|profits|) to allow for negative values. RelativeSpeedi,t is the firm's ranking that 

day in terms of speed among all firms of that sub-type scaled by the total number of firms that day of 

that sub-type. *, ** and *** correspond to p-values < 5%, 1%, 0.1%, respectively. Standard errors 

are in parentheses.

HFTA HFTM HFTP

Relative Speed -6.72*** -4.44*** -2.62***

(1.3) (0.73) (0.77)

N 730 1693 1334

Adj-R

2

0.035 0.020 0.009