Electronic copy available at: http://ssrn.com/abstract=1686004

The Flash Crash: The Impact of High Frequency

Trading on an Electronic Market∗

Andrei Kirilenko—MIT Sloan School of Management

Albert S. Kyle—University of Maryland

Mehrdad Samadi—University of North Carolina

Tugkan Tuzun—Board of Governors of the Federal Reserve System

Original Version: October 1, 2010

This version: May 5, 2014

ABSTRACT

This study offers an empirical analysis of the events of May 6, 2010, that

became known as the Flash Crash. We show that High Frequency Traders (HFTs)

did not cause the Flash Crash, but contributed to it by demanding immediacy

ahead of other market participants. Immediacy absorption activity of HFTs results

in price adjustments that are costly to all slower traders, including the traditional

market makers. Even a small cost of maintaining continuous market presence

makes market makers adjust their inventory holdings to levels that can be too

low to offset temporary liquidity imbalances. A large enough sell order can lead

to a liquidity-based crash accompanied by high trading volume and large price

volatility – which is what occurred in the E-mini S&P 500 stock index futures

contract on May 6, 2010, and then quickly spread to other markets. Based on our

results, appropriate regulatory actions should aim to encourage HFTs to provide

immediacy, while discouraging them from demanding it, especially at times of

significant, but temporary liquidity imbalances. In fast automated markets, this

can be accomplished by a more diligent use of short-lived trading pauses that

temporarily halt the demand for immediacy, especially if significant order flow

imbalances are detected. These short pauses followed by coordinated re-opening

procedures would force market participants to coordinate their liquidity supply

responses in a pre-determined manner instead of seeking to demand immediacy

ahead of others.

∗We thank participants at numerous seminars and conferences for very helpful comments and suggestions. The views presented in this paper are our own and do not represent a position of any official

agency, its management or staff.
Electronic copy available at: http://ssrn.com/abstract=1686004

On February 21, 2014, the U.S. Commodity Futures Trading Commission (CFTC)

authorized this paper for public distribution. A draft of this paper was previously

authorized for public distribution prior to the release of the joint report of the staffs of

the CFTC and Securities and Exchange Commission (SEC) entitled “Findings Regarding

the Market Events of May 6, 2010”. The CFTC-SEC report was issued to the public

on September 30, 2010. Prior to the release, all matters related to the aggregation of

data, presentation of results, and sharing the results with the public were reviewed by

the CFTC Senior Staff, reviewers in the Office of the Chairman, the Division of Market

Oversight, the Office of the General Counsel, the Division of Enforcement, as well as staff

from other divisions of the CFTC. CFTC Chairman and Commissioners were briefed

on the analysis and results of the paper prior to the public release of the report. In the

latest communication about the release of the paper for public distribution, the CFTC

stated that the following disclaimer must be used:

The research presented in this paper was co-authored by Andrei Kirilenko, a former full-time CFTC employee, Albert Kyle, a former CFTC contractor who performed

work under CFTC OCE contract (CFCE-09-CO-0147), Mehrdad Samadi, a former fulltime CFTC employee and former CFTC contractor who performed work under CFTC

OCE contracts (CFCE-11-CO-0122 and CFOCE-13-CO-0061), and Tugkan Tuzun, a

former CFTC contractor who performed work under CFTC OCE contract (CFCE-10-

CO-0175). The Office of the Chief Economist and CFTC economists produce original

research on a broad range of topics relevant to the CFTCs mandate to regulate commodity futures 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 the Chief Economist, other Commission staff, or the

Commission itself.

2
On May 6, 2010, in the course of about 36 minutes starting at 2:32pm ET, U.S.

financial markets experienced one of the most turbulent periods in their history. Broad

stock market indices the S&P 500, the Nasdaq 100, and the Russell 2000 collapsed

and rebounded with extraordinary velocity. The Dow Jones Industrial Average (DJIA)

experienced the biggest intraday point decline in its entire history. Stock index futures,

options, and exchange-traded funds, as well as individual stocks experienced extraordinary price volatility often accompanied by spikes in trading volume. Because these

dramatic events happened so quickly, the events of May 6, 2010, have become known as

the “Flash Crash.” This paper uses audit trail data during May 3-6, 2010 to examine

the eco-system of the S&P 500 E-mini futures during these four days and the role of

high frequency traders and other market participants in the Flash Crash. The audit

trail data set time stamps trades to the second, sequences trades within each second,

identifies the account numbers associated with trades, and distinguishes the executable

from the non-executable side of each transaction.

On September 30, 2010, the staffs of the Commodity Futures Trading Commission

(CFTC) and Securities and Exchange Commission (SEC) issued a report on the events

of May 6, 2010. The 104-page report described how an automated execution program

to sell 75,000 contracts of the E-Mini S&P 500 futures, algorithmic trading activity, and

obscure order submission practices all conspired to create the Flash Crash.1

In the aftermath of the Flash Crash, the media became particularly fascinated with

the secretive blend of high-powered technology and hyperactive market activity known

as high frequency trading (HFT).2 To many investors and market commentators, high

frequency trading has become the root cause of the unfairness and fragility of automated

markets.3In response to public pressure, government regulators and self-regulatory

organizations (e.g., securities and derivatives exchanges) around the world have come

up with a variety of anti-HFT measures. These measures range from a tax on financial

transactions designed to make HFT prohibitively expensive and contribute to public

revenue to “throttles” on the number of messages a trader is allowed to send to an

1The CFTC-SEC report’s narrative of the triggering event of the Flash Crash was based in part on

the preliminary analysis contained in the original version of this paper (see footnote 22 of the CFTCSEC report). The narrative (the report) and the analysis (the paper) were presented separately in

part because the CFTC-SEC report was written for a very broad audience, while the methodology

and preliminary results in the original paper were intended for peer review by research scientists and

market experts. Both the report and the paper serve the same purpose of describing to the market

participants, the research community, and the general public how unrelated trading algorithms activated

across different parts of the financial marketplace can cascade into a systemic event for the entire U.S

financial market. The original version of this paper has been cited by numerous academic, governmentsponsored and industry-sponsored studies.

2See, “Disagreement on safe speed for HFT”, Financial Times, June 3, 2010. See also, “A Second Is

a Long Time in Finance”, The Wall Street Journal, March 3, 2011.

3“Testimony on Computerized Trading: What Should the Rules of the Road Be?” The Committee on

Banking, Housing, and Urban Affairs Subcommittee on Securities, Insurance and Investment, September

20, 2012.

1
exchange.4

This study offers an empirical analysis of trading at the time of market stress as

evidenced by the events of May 6, 2010. We show that HFT did not cause the Flash

Crash, but contributed to extraordinary market volatility experienced on May 6, 2010.

We also show how high frequency trading contributes to flash-crash-type events by exploiting short-lived imbalances in market conditions. We argue that in the ordinary

course of business, high frequency traders (HFTs) use their technological advantage to

aggressively remove the last few contracts at the best bid or ask levels and then establish

new best bids and asks at adjacent price levels. This type of trading activity accelerates,

albeit for only a few milliseconds, the price move imposing an “immediacy absorption”

cost on all other traders who are not fast enough to react to an imminent price move.

Under calm market conditions, this trading activity somewhat accelerates price

changes and adds to trading volume but does not result in a directional price move.

However, at times of market stress and elevated volatility, when prices are moving directionally due to an order flow imbalance, this trading activity can exacerbate a directional

price move and contribute to volatility. Higher volatility further increases the speed at

which the best bid and offer queues get depleted, which makes HFTs act faster, leading

to a spike in trading volume and setting the stage for a flash-crash-type event. On May

6, HFTs exacerbated the Flash Crash by aggressively removing the last few contracts

at best bids and demanding additional depth while liquidating inventories during key

moments of dwindling market liquidity.

Flash-crash-type events temporarily shake the confidence of some market participants

but probably have little impact on the ability of financial markets to allocate resources

and risks. These events though raise a broader set of questions about the optimal market

structure of automated markets. Grossman and Miller (1988) show that, in equilibrium,

the market structure is determined by a tradeoff between (i) the costs borne by the

intermediaries for supplying liquidity and maintaining a continuous market presence

and (ii) the benefits accrued to liquidity-demanding customers for being able to execute

trades as “immediately” as possible when they come to the market. The costs to the

intermediaries are primarily fixed costs - the opportunity cost of being open for business

– while the benefits to the customers are primarily marginal - lowering of the risk that

prices would move against them if they have to wait to execute a particular transaction.

In equilibrium, the intermediaries are compensated just enough to recover their fixed

costs of maintaining continuous market presence, as well as adverse selection costs of

trading with customers who come to the market at different times. There is also improved

risk sharing among customers with different attitudes toward market risk those who

are comfortable to wait longer get a better deal, while those who dislike waiting pay for

having their trades done sooner.

While the overall framework is still useful, advances in technology and infrastructure have altered the cost-benefit balance in favor of the most technologically-advanced

financial intermediaries with the smallest overhead per market the very definition of

4“High-Speed Traders Race to Fend off Regulators”, The Wall Street Journal, December 27, 2012.

2
high frequency traders. Because advanced trading technology can be deployed with little

alteration across many automated markets, the cost of providing intermediation services

per market has fallen drastically. As a result, the supply of immediacy provided by

the HFTs has skyrocketed. At the same time, the benefits of immediacy accrue disproportionally to those who possess the technology to take advantage of it. As a result,

HFTs have also become the main beneficiaries of immediacy, using it not only to lower

their adverse selection costs, but also to take advantage of the customers who dislike

adverse selection, but do not have the technology to be able to trade as quickly as they

would like to. These market participants express their demands for immediacy in their

trading orders, but are too slow to execute these orders compared to the HFTs. Consequently, HFTs can both increase their demand for immediacy and decrease their supply

of immediacy just ahead of any slower immediacy-seeking customer. This immediacyabsorption activity makes prices move against all slower customers who seek immediacy,

including more traditional intermediaries. This is different from the stylized GrossmanMiller framework in which intermediaries only provide immediacy, while customers only

demand it. In the modified framework, a handful of technologically-advanced HFTs

are not only able to provide immediacy and reduce their own cost of adverse selection,

but also to demand immediacy and impose an immediacy-absorption “cost” on all nonHFT market participants, including the market makers. Thus, high frequency trading

can make it both costlier and riskier for market makers to maintain continuous market

presence.

Building on the Grossman-Miller framework, Huang and Wang (2008) develop an

equilibrium model in which they link the cost of maintaining continuous market presence

with market crashes even in the absence of fundamental shocks and perfectly offsetting

idiosyncratic shocks. In their model, market crashes emerge endogenously when a sudden

excess of sell orders overwhelms insufficient risk-bearing capacity of liquidity providers.

The critical feature of the model is that the provision of continuous market presence is

costly. As a result, market makers choose to maintain equilibrium risk exposures that

are too low to offset temporary liquidity imbalances. In the event of a large enough sell

order, the liquidity on the buy side can only be obtained after a price drop that is large

enough to compensate increasingly reluctant market makers to take on additional risky

inventory. These equilibrium crashes are accompanied by high trading volume and large

price volatility as documented in the E-mini S&P 500 stock index futures contract on

May 6, 2010.

If the immediacy absorption activity of HFTs makes it costlier for the market makers

to maintain continuous market presence, then high frequency trading could be linked to

greater market fragility. Unfortunately, we are unable to conduct a direct estimation of

the cost that the immediacy absorption activity of HFTs imposes on the market makers,

because after the publication of our initial results, academic access to relevant data was

shut off by the CFTC. 5 Thus, we resort to documenting a number of empirical regularities, which we believe stem from the immediacy absorption activity of high frequency

5“CME Group Sparked Shutdown of CFTC‘s Academic Research Program, Reuters, April 24, 2013.

3
traders.

We show that HFTs are much more likely than market makers to aggressively execute

the last 100 contracts before a price move in the direction of a trade. As they get wind of

an imminent increase in net demand for immediacy on either the long or the short side

of the market, HFTs quickly demand it ahead of slower investors and move the price to

take advantage of it. We also show that HFTs trade aggressively in the direction of the

price move while market makers get “run over” by a price move. Furthermore, we find

that HFTs “scratch” - quickly buy and sell at the same price - more of their trades than

market makers.

Based on our results, appropriate regulatory actions should aim to encourage HFTs

to provide immediacy, while discouraging them from demanding it, especially at times

of market stress. We believe that this should be accomplished through changes in market design rather than transaction taxes, limits or fees as the higher opportunity costs

imposed on the HFTs would, at best, be passed on to other market participants, with

the least technologically-savvy investors bearing the brunt of the cost.

For example, automated matching engines should include a number of functionalities

to slow down or pause order matching and thus temporarily halt the demand for immediacy, especially if significant order flow imbalances are detected. These short pauses

followed by auction-based re-opening procedures would, in the spirit of Huang and Wang

(2010), force market participants to coordinate their liquidity supply responses in a predetermined manner instead of seeking to execute ahead of others.6 The five-second

trading pause triggered at the bottom of the Flash Crash is one example of such a

functionality. More diligent use of trading pauses of modest duration and coordinated

re-opening protocols can be an effective pre-trade safeguard in today’s fast automated

markets.

The paper is organized as follows. A brief description of the events of May 6, 2010 are

in Section I. Section II describes the activity of all traders (appropriately aggregated so

it does not reveal individual transactions or business practices) in a stock index futures

contract were the Flash Crash was triggered. Section III presents the analysis of the

Flash Crash and concludes that HFTs did not cause it. Section IV presents the analysis

of absorbing the large order flow imbalance that triggered the Flash Crash. An empirical

analysis of the activity of High Frequency Traders on the day of the Flash Crash, as

well as during three days prior to it are in Section V. In Section VI we summarize our

findings and offer our views on the lessons we could learn from the traumatic events of

May 6, 2010.

6Huang and Wang (2010) develop an equilibrium model in which both liquidity demand and supply

are determined endogenously and argue that forcing market participants to coordinate their liquidity

responses in a pre-determined manner could increase welfare.

4
I. The Events of May 6, 2010.

The CFTC-SEC report describes the events of May 6, 2010 as follows:

“At 2:32 p.m., against [a] backdrop of unusually high volatility and thinning liquidity, a large fundamental trader (a mutual fund complex) initiated a

sell program to sell a total of 75,000 E-Mini [S&P 500 futures] contracts (valued at approximately $4.1 billion) as a hedge to an existing equity position.

[. . . ] This large fundamental trader chose to execute this sell program via

an automated execution algorithm (“Sell Algorithm”) that was programmed

to feed orders into the June 2010 E-Mini market to target an execution rate

set to 9% of the trading volume calculated over the previous minute, but

without regard to price or time. The execution of this sell program resulted

in the largest net change in daily position of any trader in the E-Mini since

the beginning of the year (from January 1, 2010 through May 6, 2010). [. . . ]

This sell pressure was initially absorbed by: high frequency traders (“HFTs”)

and other intermediaries in the futures market; fundamental buyers in the

futures market; and cross-market arbitrageurs who transferred this sell pressure to the equities markets by opportunistically buying E-Mini contracts

and simultaneously selling products like SPY [(S&P 500 exchange-traded

fund (“ETF”))], or selling individual equities in the S&P 500 Index. [. . . ]

Between 2:32 p.m. and 2:45 p.m., as prices of the E-Mini rapidly declined,

the Sell Algorithm sold about 35,000 E-Mini contracts (valued at approximately $1.9 billion) of the 75,000 intended. [. . . ] By 2:45:28 there were less

than 1,050 contracts of buy-side resting orders in the E-Mini, representing

less than 1% of buy-side market depth observed at the beginning of the day.

[. . . ] At 2:45:28 p.m., trading on the E-Mini was paused for five seconds

when the Chicago Mercantile Exchange (“CME”) Stop Logic Functionality

was triggered in order to prevent a cascade of further price declines. [. . . ]

When trading resumed at 2:45:33 p.m., prices stabilized and shortly thereafter, the E-Mini began to recover, followed by the SPY. [. . . ] Even though

after 2:45 p.m. prices in the E-Mini and SPY were recovering from their

severe declines, sell orders placed for some individual securities and ETFs

(including many retail stop-loss orders, triggered by declines in prices of

those securities) found reduced buying interest, which led to further price

declines in those securities. [. . . ] [B]etween 2:40 p.m. and 3:00 p.m., over

20,000 trades (many based on retail-customer orders) across more than 300

separate securities, including many ETFs, were executed at prices 60% or

more away from their 2:40 p.m. prices. [. . . ] By 3:08 p.m., [. . . ] the E-Mini

prices [were] back to nearly their pre-drop level [. . . and] most securities had

reverted back to trading at prices reflecting true consensus values.”

Figure 1 below shows just how extreme the intraday volatility in stock index and

futures prices was on May 6, 2010. In the course of 13 minutes, between 2:32:00 ET

5
and 2:45:28 ET, the front-month E-mini S&P 500 futures fell 5.1%; during the next 23

minutes, it rose 6.4 percent.

<Insert Figure 1>

The extreme volatility in the E-mini was accompanied by a rapid spike in trading

volume, as illustrated in Figure 2. During the 36-minute period of the Flash Crash,

trading volume per minute was nearly 8 times greater than trading volume per minute

earlier in the day. A massive spike in trading volume is the critical distinguishing

characteristic of the events of May 6, 2010.

<Insert Figure 2>

As the event spread through the entire U.S. financial market system with extraordinary velocity, it left a broad universe of market participants – from professional traders

with decades of experience to small retail investors – with a realization that something

was terribly wrong inside the shining new automated markets.

A survey conducted by Market Strategies International during June 23-29, 2010

reported that over 80 percent of U.S. retail advisors believed that “overreliance on

computer systems and high-frequency trading” were the primary contributors to the

volatility observed on May 6, 2010. Calls for stricter regulation or even an outright ban

of high frequency trading quickly followed.

II. The Ecosystem of An Automated Market

In this section we describe the activity of all traders in the stock index futures contract

that serves as the price discovery vehicle for the entire U.S. stock market.

A. The E-Mini S&P 500

The E-mini S&P 500 E-mini futures contract (E-mini) owes its geeky name to the fact

that it is traded only electronically and in denominations 10 times smaller than the

original, floor-traded S&P 500 index futures contract. The Chicago Mercantile Exchange

(CME) introduced the E-mini contract in 1997. Since then it has become a popular

instrument to hedge exposures to baskets of U.S. stocks or to speculate on the direction

of the entire stock market. The E-mini contract attracts the highest dollar volume

among U.S. equity index products futures, options, stocks or exchange-traded funds.

The E-mini contract features a simple and robust design. The contracts are cashsettled against the value of the underlying S&P 500 equity index at expiration dates in

6
March, June, September, and December of each year. The contract with the nearest

expiration date, which attracts the majority of trading activity, is called the “frontmonth” contract. In May 2010, the front-month contract was the contract expiring in

June 2010. The notional value of one E-mini contract is $50 times the S&P 500 stock

index. During May 3-6, 2010, the S&P 500 index fluctuated slightly above 1,000 points,

making each E-mini contract be worth about $50,000. The minimum price increment,

or “tick” size, of the E-mini is 0.25 index points, or $12.50; a price move of one tick

represents a fluctuation of about 2.5 basis points.

The E-mini trades exclusively on the CME Globex trading platform, a fully electronic

limit order market. Trading takes place 24 hours a day with the exception of one 15-

minute technical maintenance break each day. The CME Globex matching algorithm

for the E-mini follows a “price priority-time priority” rule in that orders offering more

favorable prices are executed ahead of orders with less favorable prices, and orders with

the same prices are executed in the order they were received and time-stampted by

Globex.

The market for the E-mini features both pre-trade and post-trade transparency. Pretrade transparency is provided by transmitting to the public the quantities and prices

for buy and sell orders resting in the central limit order book up or down 10 tick levels

from the last transaction price. Post-trade transparency is provided by transmitting to

the public the prices and quantities of executed transactions. The identities of individual

traders submitting, canceling or modifying bids and offers, as well those whose bids and

offers have been executed, are not made available to the public.

Hasbrouck (2003) shows that the E-mini has become “the” market were the value of

the S&P 500 stock index is first “discovered” because a great number of different types

of traders all channel their demands into a single central limit order book for a single,

front-month contract trading on a single CME Globex platform.

B. The Data

For the day of the Flash Crash and three days prior to that, May 3-6, 2010, we examine transaction-level, “audit-trail” data for all regular transactions in the front-month

June 2010 E-mini S&P 500 futures contract. These data come from the Trade Capture

Report (TCR) dataset, which the CME provides to the Commodity Futures Trading

Commission (CFTC) - the U.S. federal regulator of futures, options, and swaps markets.

For each of the four days, we examine all transactions occurring during the 405

minute period starting at the opening of the market for the underlying stocks at 8:30

am CT (CME Globex is in the Central Time zone) or 9:30 am ET and ending at the

time of the technical maintenance break at 3:15 pm CT, 15 minutes after the close of

trading in the underlying stocks.

For each transaction, we utilize fields with the account numbers for the buyer and

the seller, the price and quantity transacted, the date and time (to the nearest second), a

sequence ID number which sorts trades into chronological order even within one second,

7
order type (market order or limit order), and an “aggressiveness” indicator stamped by

the CME Globex matching engine - “N” for the resting order and “Y” for the order that

executed against a resting order.

The source data is confidential. This means that the results we present often provide

a deliberately obscured illustration of what we have actually rigorously established and

validated. Moreover, even though we have checked and re-checked our results, they are

unlikely to be ever independently validated by other researchers. Even with these limitations though, we still believe that we owe to the public to provide the most informative

analysis of the extraordinary stressful events that unfolded in the E-mini on May 6, 2010

and the lessons for market design that we can learn from these events.

Table I provides aggregate summary statistics for the June 2010 E-Mini S&P 500

futures contract during May 3-6, 2010. The first column reports average statistics for

the three days prior to the Flash Crash, May 3-5, 2010, and the second column reports

statistics for the day of the Flash Crash itself, May 6, 2010.

<Insert Table I>

Table I illustrates what an extraordinary day May, 6, 2010 was. On May 6, the logdifference between the high and low prices of the day - an estimate of intraday volatility

- clocks at 9.82% or nearly 6.4 times higher than the 1.54% average during the previous

three days. On May 6, 5,094,703 June E-mini contracts with a total value of more

than $250 billion were traded – approximately twice the average volume of 2,397,639

contracts on the previous three days. On May 6, 15,422 accounts executed 1,030,204

trades. During the previous three days, 11,875 trading accounts executed on average

446,340 trades.

C. The Traders

The 15,422 trading accounts that traded during May 6, 2010 have drastically different

holding horizons and levels of trading activity. Some traders hold positions overnight,

while others take intra-day positions that may last hours, minutes, or seconds. Some

traders trade thousands of contracts every day, while other traders trade just a handful

of contracts once. To describe interactions among traders with different holding periods

and different levels of trading activity, we group the the trading accounts that traded on

May 6, 2010, into six distinct categories: High Frequency Traders (16 accounts), Market

Makers (179 accounts), Fundamental Buyers (1263 accounts), Fundamental Sellers (1276

accounts), Opportunistic Traders (5808 accounts), and Small Traders (6880 accounts).

Our definition of both High Frequency Traders and Market Makers is designed to

capture traders who consistently follow a strategy of buying and selling a large number of

contracts while maintaining low levels of inventory. Specifically, an account is classified

as a High Frequency Trader or Market Maker if and only if it satisfies the following three

requirements:

8
• Volume: The account must have traded 10 contracts or more on at least one of

the three days prior to the Flash Crash (May 3,4,5, 2010).

• End-of-day inventory balance: During the three days in which the account traded

10 contracts or more, the average of the absolute value of the end-of-day net

position cannot exceed 5% of its total trading volume for that day. For example,

if an account traded 100 contracts during the day, then by the end of the day, it

cannot hold more than 5 contracts either net long or net short. An account that

bought 52 contracts and sold 48 would satisfy this requirement, while an account

that bought 55 contracts and sold 45 would not.

• Intraday inventory balance: During the three days in which the account traded

10 contracts or more, the square root of the sum of squared deviations of the net

contract holdings for each of the 405 minutes from the net contract holdings at the

end of the day cannot exceed 1.5% of its total trading volume for that day. For

example, an account that either bought or sold one contract per minute throughout

the entire trading day (405 minutes) and ended up with 5 contracts net long at

the end of the day, would satisfy the requirement.

These three requirements separate trading accounts that hold small net intraday

and end-of-day positions relative to their trading volume. Of the 195 accounts satisfying

these three conditions, we further classify as High Frequency Traders 16 accounts with

the highest average number of trades during May 3-5. The other 179 accounts, we

classify as Market Makers. The 16 most active accounts are classified differently from

the other 179 accounts due to a large gap in the number of trades between the 16th and

17th accounts. Thus, a High Frequency Trader is classified similarly to a Market Maker

in all respects, except that the HFT participates in a significantly greater number of

transactions.

If an account is classified as a High Frequency Trader or a Market Maker on any of

the three days during May 3-5, 2010, we keep it within the same category during all

four days, May 3-6, 2010. Importantly, this restriction does not require that a High

Frequency Trader or a Marker Maker sticks with the low inventory relative to volume

requirement on the day of the Flash Crash. On May 6, 2010, the trading behavior

of an account classified as a High Frequency Trader or a Marker Maker based on its

trading activity on the previous three days could have changed. We examine whether

such a change did take place on May 6, 2010 and, if it did, whether it precipitated or

contributed to the extraordinary price volatility, and a spike in trading volume observed

on that day.

Unlike High Frequency Traders and Market Makers, the other four categories of

traders (Small Traders, Fundamental Buyers, Fundamental Sellers, and Opportunistic

Traders) are classified separately for each day based on their end-of-day inventory and

trading activity on that specific day. We set the following volume/inventory thresholds

for the four categories of traders. On each day, an account is classified as a Small

9
Trader if it trades fewer than 10 contracts. On each day, an account is classified as a

Fundamental Buyer if it trades 10 contracts or more and accumulates a net long end-ofday position equal to at least 15% of its total trading volume for the day. Similarly, an

account is classified as a Fundamental Seller if it trades 10 contracts or more and its net

short position at the end of the day is at least 15% of its total trading volume for the day.

All remaining accounts are classified as Opportunistic Traders. Opportunistic Traders

at times act like Market Makers (buying a selling around a given inventory target) and

at other times act like Fundamental Traders (accumulating a directional position).

Traders categorized as Fundamental Buyers and Fundamental Sellers accumulate

directional net positions. Each on of them gets to its end-of-day inventory in a different

way. Some acquire large net positions by executing many small-size orders throughout

the day, while others choose to reach their inventory target by executing just a few

large-size orders in the beginning and at the end of the day.

Traders categorized as Opportunistic Traders may follow a variety of arbitrage trading strategies, including cross-market arbitrage (e.g., long futures–short securities), statistical arbitrage (e.g., buy on statistically significant downside price movements–sell on

statistically significant upside price movements), news arbitrage (buy if the news indicators are positive–sell if the news indicators are negative) and many other strategies.

Unlike accounts that are classified as High Frequency Traders and Market Makers,

Fundamental, Opportunistic or Small accounts are determined based on their trading

activity on each of the four days that we investigate.

D. The Market Ecosystem

Figure 3 provides a visual representation of the trading activity and end-of-day positions

for all but the Small Traders, whose activity is negligible. Four panels correspond to

each of the four trading days. The shaded areas are stylistically drawn to cover the areas

populated by the individual trading accounts that fall into each of the categories based

on their trading volume (vertical axis) and end-of-day position scaled by trading volume

(horizontal axis).

<Insert Figure 3>

According to Figure 3, the ecosystem of the E-mini market consists of three fairly

distinct clusters of traders Fundamental Buyers, Fundamental Sellers, High Frequency

Traders, and Market Makers. In terms of their trading volume, High Frequency Traders

stand out from all the other trading categories and are clearly separated from the Market

Makers. By accumulating a significant negative inventory, the cloud of Fundamental

Sellers spreads out to the left of the origin, while the cloud of Fundamental Buyers

spreads out to the right. Opportunistic traders overlap to some extent with all the other

categories of traders.

10
Average indicators of trading activity for all categories of traders are presented in

Table II. Panel A presents averages for the the three days prior to the Flash Crash, May

3-5, 2010, while panel B presents indicators for the day of the Flash Crash itself, May

6, 2010.

<Insert Table II>

According to Table II, during the three days prior to the Flash Crash, High Frequency

Traders accounted for 34.22% of the total trading volume and Market Makers accounted

for an additional 10.49% of the total trading volume. On the day of the Flash Crash,

their respective shares of the total trading volume dropped to 28.57% and 9.00%.

Table II also presents trade-weighted and value-weighted “Aggressiveness Ratios,”

defined as the percentage of trades or contracts in which a trade results from an executable (i.e., Aggressive) order as opposed to a non-executable (i.e., Passive) order.

During May 3-6, 2010, the volume-weighted proportion of Aggressive order executions

by High Frequency Traders and Market Makers were 45.68% and 41.62%, respectively;

on May 6, 2010, the proportions are only slightly different, 45.53% and 43.55%, respectively. Overall, however, the averages are not granular enough to be informative about

how High Frequency Traders acted during the Flash Crash. The next section presents

a more detailed look at their trading activity.

III. Did High Frequency Traders Trigger the Flash

Crash?

In this section we examine whether High Frequency Traders changed their trading behavior on May 6, 2010 in a way that could have triggered the Flash Crash. We also

conduct the same analysis for the Market Makers. Specifically, we analyze inventory

dynamics of High Frequency Traders and Market Makers on the day of the Flash Crash

and compare it to their inventory dynamics during the previous three days. Figure

4 presents end-of-minute E-mini prices and minute-by-minute total inventory of High

Frequency Traders during each of the four days.

<Insert Figure 4>

The intra-day position of High Frequency Traders fluctuates around zero and rarely

exceeds 4,000 contracts (about $200 million). If the prices and dates on the four panels

were to be removed, a reader would not be able to tell by looking at the inventory of

High Frequency Traders which of the four days is May 6, 2010. The largest net intraday

inventory level of Market Makers is even smaller - roughly half that of High Frequency

11
Traders. During the early moments of the Flash Crash, HFTs accumulated inventories

and proceeded to sell aggressively at key moments in order to liquidate their inventories

We regress second-by-second changes in inventory levels of High Frequency Traders

on the level of their inventories the previous second, the change in their inventory levels

the previous second, the change in prices during the current second, and lagged price

changes for each of the previous 20 previous seconds. The regression equation is:

∆yt = α + φ · ∆yt−1 + δ · yt−1 +

X

20

i=0

[βi· ∆pt−i/0.25] + t, (1)

where yt and ∆yt denote inventories and change in inventories of High Frequency Traders

for each second of a trading day; t = 0 corresponds to the opening of stock trading on the

NYSE at 8:30:00 a.m. CT (9:30:00 ET) and t = 24, 300 denotes the close of Globex at

15:15:00 CT (4:15 p.m. ET); ∆pt denotes the price change in index point units between

the high-low midpoint of second t − 1 and the high-low midpoint of second t.

Table III presents coefficient estimates for this regression. Panel A reports the results

for May 3-5 (where the data is pooled) and Panel B for May 6. The t-statistics are

calculated using the White (1980) estimator.

<Insert Table III >

The first and second columns of Panel A present regression coefficients and t-statistics

for High Frequency Traders and Market Makers during May 3-5.7

The coefficient estimate for the long-term mean reversion parameter for High Frequency Traders is δ = −0.005 (t = 11.77), and the coefficient estimate for Market Makers

is δ = −0.004 (t = 8.93). These coefficients have the interpretation that High Frequency

Traders liquidate 0.5% of their aggregate inventories on average each second and Market

Makers liquidate 0.4% of their inventories each second, implying AR-1 half-lives for inventories of about 140 seconds for High Frequency Traders and 175 seconds for Market

Makers.

For High Frequency Traders, the coefficient estimate for contemporaneous price

changes β0 = 32.09 (t = 18.44) has the interpretation that High Frequency Traders buy

32 more contracts in seconds when prices rise one tick than in seconds when prices do

not change. The coefficient estimates for the first three lags in price changes β1 = 17.18,

β2 = 8.36, β3 = 5.09, and β4 = 3.62 are all positive and statistically significant as well.

These results are consistent with the interpretation that High Frequency Traders trade

in the direction of the price movement up to four seconds prior to a change in inventory

and as it happens.

7Dickey-Fuller tests verify that inventories of High Frequency Traders and Market Makers are stationary. Multicollinearity does not affect the reported results. Newey-West standard errors are very

close to White standard errors.

12
For Market Makers, the regression results are quite different. The coefficient for

contemporary price changes β0 = −13.54 (t = −23.83) is negative and statistically

significant, and the coefficient for a one-second lag β1 = −1.22 (t = −2.71) is negative

and statistically significant also; for lags of 3 to 8 seconds, the coefficients become

positive and statistically significant. These results are consistent with the interpretation

that Market Makers engage in traditional passive market making by buying during the

seconds when prices are falling. The positive coefficients at lags 3-8 suggest that market

makers liquidate these inventories after holding them for 3-8 seconds. These regression

results suggest that, possibly due to their slower speed or inability to anticipate possible

changes in prices, Market Makers buy when the prices are already falling and sell when

the prices are already rising.

At lags i = 10, . . . , 20 seconds, the coefficients βi turn negative and statistically

significant for High Frequency Traders but are not statistically different from zero for

Market Makers. These results are consistent with the interpretation that High Frequency

Traders liquidate inventories acquired through trading for 5 seconds in the direction of

the price movement by liquidating the positions 10-20 seconds later. Thus, the actual half

life of positions of High Frequency Traders is probably less than the 140 seconds implied

by interpreting δ as an AR-1 coefficient, without regard to the coefficients associated

with price dynamics.

Panel B presents coefficient estimates for equation 1 on May 6. The first column

of Panel B shows the results for High Frequency Traders and the second column the

results for Market Makers. For High Frequency Traders, the coefficient for the level of

inventories is δ = −0.005 (t = −6.76), the same coefficient as for May 3-5, implying

a half-life of about 140 seconds. For Market Makers, the coefficient is δ = −0.008

(t = −7.79), implying a decrease in the half-life of inventories from about 175 seconds

during May 3-5 to about 90 seconds on May 6. This decrease is consistent with the high

velocity of prices during May 6.

For High Frequency Traders and Market Makers, the estimated coefficient for contemporaneous price changes are β0 = 10.81 (t = 6.05) and β0 = −8.16 (t = −12.09),

respectively. Similar to May 3-5, the coefficient for High Frequency Traders is positive

and the coefficient for Market Makers is negative. The absolute values of the coefficients

are, however, smaller. The smaller absolute values are consistent with the interpretation

that the high volatility on May 6 implied many tick changes occurring at more closely

spaced periods of time, reduced market liquidity, and therefore reduced trading volume

at each tick.

To test whether or not HFTs and Market Makers changed their behavior on the day

of the Flash Crash, we interact dummy variables for the Up phase and the Down phase

of the Flash Crash with the regression coefficients in equation 2. Letting DD

t denote a

dummy variable for the Down phase (13:32:00 to 13:45:28 CT) and DU

t

a dummy variable

for the Up phase (13:45:33 to 14:08:00 CT), the regression specification becomes:

13
∆yt = α + φ∆yt−1 + δyt−1 + Σ20

i=0[βi × pt−i/0.25]

+ D

D

t {α

D + φD∆yt−1 + δDyt−1 + Σ20

i=0[β

D

i × pt−i/0.25]}

+ D

U

t {α

U + φU∆yt−1 + δU

yt−1 + Σ20

i=0[β

U

i × pt−i/0.25]} + t

,

By creating two sets of dummy variables for the Down and Up phases of the Flash

Crash, we are able to statistically test whether High Frequency Traders or Market Makers

changed their trading during the Flash Crash.

<Insert Table IV >

For HFTs, during the Down Phase, all coefficients except for one are statistically

insignificant. We interpret this as evidence that HFTs did not (either economically or

statistically) significantly alter their inventory during the Down phase, i.e. the time

when the prices were rapidly falling. We also find that during the Up phase which

commenced after a 5 second pause in trading, the coefficients for the contemporaneous

price change as well as two seconds prior to it are negative and significant for HFTs.

This suggests that during the Up phase, HFTs reduced their inventory 2 seconds prior to

and contemporaneously with price increases. In summary, during the critical 36 minutes

of the Flash Crash, HFTs are not doing much to their inventory when the prices are

falling and reducing their inventory when the prices are rising.

In contrast, Market Makers, increase their inventory during the 15th and 4th seconds

in the Down phase and then reduce their inventory 1 second prior to and contemporaneously with price decreases. Furthermore, Market Makers reduce their inventory between

the 10th and the 3rd second in the Up phase and then turn around and increase their

inventory 1 second prior to and contemporaneously with price increases. This empirical

patterns suggests that Market Makers get run over by the directional price move both

on the way Down and on the way Up and then manage their inventory by selling into

the falling market or buying into the rising market. The aggregate changes in their

inventory, however, are economically insignificant. They are simply being overwhelmed

by a very large liquidity imbalance that we examine in the next section.

IV. Absorbing a Large Order Flow Imbalance

There are strong theoretical reasons to believe that a large order flow imbalance can

trigger a market crash even in the absence of any fundamental shock by overwhelming

the limited risk-bearing capacity of the intermediaries.8 The important aspect of the

Flash Crash is how quickly the prices in the E-mini have recovered to the pre-crash levels

8See, for example, Huang and Wang (2008).

14
as liquidity rushed into the market attracted by lower prices. Which traders supplied

the liquidity in response to an order flow imbalance merely an hour before the stock

market closes, when and how did it happen, and why did the trading volume spike up?

To empirically investigate these questions, we divide the 36-minute Flash Crash

into two phases – 13 minutes of rapidly declining prices (from 1:32 p.m. to 1:45 p.m.

CT) followed by 23 minutes of rapidly increasing prices (from 1:45 p.m. to 2:08 p.m.

CT). Figure 5 plots minute-by-minute net purchases and sales by Fundamental Buyers,

Fundamental Sellers, and Opportunistic Traders from the period starting 15 minutes

before the down phase of the Flash Crash until the end of the up phase.

<Insert Figure 5 >

During the down phase of the Flash Crash, Fundamental Sellers were frequently selling more than 5,000 contracts per minute ($250 million). In the minutes surrounding

the bottom of the Flash Crash, sales by Fundamental Sellers reached 10,000 to 20,000

contracts per minute ($500 million to $1 billion). At the same time, purchases by Fundamental Buyers were significantly smaller than sales by Fundamental Sellers with the

balance being acquired by the Opportunistic Traders. At the beginning of the up phase,

Fundamental Sellers continued to sell heavily. Fundamental Buyers absorbed some of

the selling pressure with remainder going again to Opportunistic Traders. Towards the

end of the up phase, Opportunistic Traders both bought and sold in different minutes,

on average liquidating some of the purchases they had made earlier.

Table V presents total purchases and sales by the six trader categories during the

down- and up-phases of the Flash Crash on May 6 (panel A) with average quantities for

the three previous days May 3-5 (panel B).

<Insert Table V >

During the down phase, Fundamental Sellers made gross sales of 94,101 contracts

(net sales of 83,599 contracts), while Fundamental Buyers made gross purchases of 78,359

contracts (net purchases of 49,665 contracts). These quantities are 10 to 15 time larger

than the gross sales of 8,428 and gross purchases of 7,958 made by Fundamental Sellers

and Fundamental Buyers during the same period of May 3-5. During the down phase,

gross purchases and sales by Opportunistic Traders increased from 20,552 and 20,049

contracts during May 3-5 to 221,236 and 189,790 contracts on May 6.

During the up phase, Fundamental Sellers made gross sales of 145,396 contracts (net

sales of 110,177), while Fundamental Buyers made gross purchases of 165,612 contracts

(net purchases of 110,369 contracts). These quantities also exceed the average gross

sales of 15,585 contracts and gross purchases of 14,910 contracts by similar multiples

during the same time interval of May 3-5. During the up phase, gross purchases and

15
sales by Opportunistic Traders increased from 39,535 and 37,317 contracts during May

3-5 to 306,326 and 302,417 contracts

As the table shows, the process by which the market is able to absorb order flow

imbalances of such magnitude is a confluence of different responses from all six groups

of traders. Together, these responses resulted in a 14-fold increase in trading volume

compared to the size of the 75,000 contract sell program. This massive increase in

trading volume indicates how markets typically digest order flow imbalances. A small

order flow imbalance might generate a tiny increase in intermediation trades, perhaps a

few trades by a High Frequency trader or a Market Maker. In contrast, a large buy or sell

program generates many intermediation trades leading to significant price adjustments

and an increase in trading volume many times the size of the order that triggered the

imbalance. This occurs because different types of traders have different strategies: some

follow trends while others trade on mean reversion; some hold inventory for mere seconds,

while others hold it for minutes, hours, or days. As a result, contracts are passed around

from trader to trader before the the order flow imbalance plays itself out and the price

adjustment is completed.

During the down phase of the Flash Crash, High Frequency Traders traded faster than

all other traders, and by doing so have amplified downward price momentum as prices

approached intraday lows. After buying 3,000 contracts in a falling market in the first

ten minutes of the Flash Crash, some High Frequency Traders began to aggressively hit

the bids in the limit order book. Especially in the last minute of the down phase, many of

the contracts sold by High Frequency Traders looking to aggressively reduce inventories

were executed against other High Frequency Traders, generating a “hot potato” effect

and a rapid spike in trading volume. This is consistent with the fact that High Frequency

Traders as a group did not significantly change their total inventory even as the prices

were rapidly falling.

Figure 6 shows the magnitude of the hot potato effect. The figure presents the 5

second moving average of the ratio of the absolute value of the net position change of

High Frequency Traders to their trading volume.

<Insert Figure 6>

We find that compared to the three days prior to May 6, the level of HFT “hot potato”

trading volume was extremely high. The hot potato effect was especially pronounced

between 13:45:13 and 13:45:27 CT, when prices were plunging with a tremendous velocity. During this time, the HFTs traded over 27,000 contracts or about 49% of the total

trading volume, but their net position changed by a mere 200 contracts.

The downward spiral in prices and the spike in trading volume were interrupted by a

five-second trading pause triggered by the “stop-logic” functionality built into the CME’s

Globex trading system. A few seconds after the 5-second pause, transaction prices first

stabilized and then rebounded rapidly, as Fundamental Buyers and Opportunistic Trader

16
lifted offers. By 2:08 p.m. CT, 36 minutes after the Flash Crash began, prices of E-mini

futures had recovered to their pre-Flash-Crash levels.

V. What Do High Frequency Traders Do?

So far, we have established that High Frequency Traders did not trigger the Flash Crash,

but have exacerbated the price movement and fueled a spike in the total trading volume

during the time when the E-mini prices were falling rapidly in response to large order

flow imbalance. What kind of trading activity would make the HFTs contribute this

way to a flash-crash-type event?

We believe that in the ordinary course of business, HFTs use their technological

advantage to profit from aggressively removing the last few contracts at the best bid

and ask levels and then establishing new best bids and asks at adjacent price levels

ahead of an immediacy-demanding customer. As an illustration of this “immediacy

absorption” activity, consider the following stylized example, presented in Figure 7 and

described below.

<Insert Figure 7>

Suppose that we observe the central limit order book for a stock index futures contract. The notional value of one stock index futures contract is $50. The market is very

liquid – on average there are hundreds of resting limit orders to buy or sell multiple

contracts at either the best bid or the best offer. At some point during the day, due

to temporary selling pressure, there is a total of just 100 contracts left at the best bid

price of 1000.00. Recognizing that the queue at the best bid is about to be depleted,

HFTs submit executable limit orders to aggressively sell a total of 100 contracts, thus

completely depleting the queue at the best bid, and very quickly submit sequences of

new limit orders to buy a total of 100 contracts at the new best bid price of 999.75,

as well as to sell 100 contracts at the new best offer of 1000.00. If the selling pressure

continues, then HFTs are able to buy 100 contracts at 999.75 and make a profit of $1,250

dollars among them. If, however, the selling pressure stops and the new best offer price

of 1000.00 attracts buyers, then HFTs would very quickly sell 100 contracts (which are

at the very front of the new best offer queue), “scratching” the trade at the same price

as they bought, and getting rid of the risky inventory in a few milliseconds.

This type of trading activity reduces, albeit for only a few milliseconds, the latency

of a price move. Under normal market conditions, this trading activity somewhat accelerates price changes and adds to the trading volume, but does not result in a significant

directional price move. In effect, this activity imparts a small “immediacy absorption”

cost on all traders, including the market makers, who are not fast enough to cancel the

last remaining orders before an imminent price move.

17
This activity, however, makes it both costlier and riskier for the slower market makers to maintain continuous market presence. In response to the additional cost and risk,

market makers lower their acceptable inventory bounds to levels that are too small to offset temporary liquidity imbalances of any significant size. When the diminished liquidity

buffer of the market makers is pierced by a sudden order flow imbalance, they begin to

demand a progressively greater compensation for maintaining continuous market presence, and prices start to move directionally. Just as the prices are moving directionally

and volatility is elevated, immediacy absorption activity of HFTs can exacerbate a directional price move and amplify volatility. Higher volatility further increases the speed

at which the best bid and offer queues are being depleted, inducing HFT algorithms to

demand immediacy even more, fueling a spike in trading volume, and making it more

costly for the market makers to maintain continuous market presence. This forces more

risk averse market makers to withdraw from the market, which results in a full-blown

market crash.

Empirically, immediacy absorption activity of the HFTs should manifest itself in the

data very differently from the liquidity provision activity of the Market Makers. To

establish the presence of these differences in the data, we test the following hypotheses:

Hypothesis H1: HFTs are more likely than Market Makers to aggressively execute

the last 100 contracts before a price move in the direction of the trade. Market Makers

are more likely than HFTs to have the last 100 resting contracts against which aggressive

orders are executed.

Hypothesis H2: HFTs trade aggressively in the direction of the price move. Market

Makers get run over by a price move.

Hypothesis H3: Both HFTs and Market Makers scratch trades, but HFTs scratch

more.

To statistically test our “immediacy absorption” hypotheses against the “liquidity

provision” hypotheses, we divide all of the trades during the 405 minute trading day

into two subsets: Aggressive Buy trades and Aggressive Sell trades. Within each subset,

we further aggregate multiple aggressive buy or sell transactions resulting from the

execution of the same order into Aggressive Buy or Aggressive Sell sequences. The

intuition is as follows. Often a specific trade is not a stand alone event, but a part of a

sequence of transactions associated with the execution of the same order. For example,

an order to aggressively sell 10 contracts may result in four Aggressive Sell transactions:

for 2 contracts, 1 contract, 4 contracts, and 3 contracts, respectively, due to the specific

sequence of resting bids against which this aggressive sell order was be executed. Using

the order ID number, we are able to aggregate these four transactions into one Aggressive

Sell sequence for 10 contracts.

Testing Hypothesis H1. Aggressive removal of the last 100 contracts by

HFTs; passive provision of the last 100 resting contracts by the Market

Makers. Using the Aggressive Buy sequences, we label as a “price increase event” all

occurrences of trading sequences in which at least 100 contracts consecutively executed

18
at the same price are followed by some number of contracts at a higher price. To examine

indications of low latency, we focus on the the last 100 contracts traded before the price

increase and the first 100 contracts at the next higher price (or fewer if the price changes

again before 100 contracts are executed). Although we do not look directly at the limit

order book data, price increase events are defined to capture occasions where traders

use executable buy orders to lift the last remaining offers in the limit order book. Using

Aggressive sell trades, we define “price decrease events” symmetrically as occurrences

of sequences of trades in which 100 contracts executed at the same price are followed

by executions at lower prices. These events are intended to capture occasions where

traders use executable sell orders to hit the last few best bids in the limit order book.

The results are presented in Table VI.

<Insert Table VI>

For price increase and price decrease events, we calculate each of the six trader

categories’ shares of Aggressive and Passive trading volume for the last 100 contracts

traded at the “old” price level before the price increase or decrease and the first 100

contracts traded at the “new” price level (or fewer if the number of contracts is less than

100) after the price increase or decrease event.

Table VI presents, for the six trader categories, volume shares for the last 100 contracts at the old price and the first 100 contracts at the new price. For comparison, the

unconditional shares of aggressive and passive trading volume of each trader category

are also reported.9

Table VI has four panels covering (A) price increase events on May 3-5, (B) price

decrease events on May 3-5, (C) price increase events on May 6, and (D) price decrease

events on May 6. In each panel there are six rows of data, one row for each trader

category. Relative to panels A and C, the rows for Fundamental Buyers (BUYER)

and Fundamental Sellers (SELLER) are reversed in panels B and D to emphasize the

symmetry between buying during price increase events and selling during price decrease

events. The first two columns report the shares of Aggressive and Passive contract

volume for the last 100 contracts before the price change; the next two columns report

the shares of Aggressive and Passive volume for up to the next 100 contracts after the

price change; and the last two columns report the “unconditional” market shares of

Aggressive and Passive sides of all Aggressive buy volume or sell volume. For May 3-5,

the data are based on volume pooled across the three days.

Consider panel A of Table VI, which describes price increase events associated with

Aggressive buy trades on May 3-5, 2010. High Frequency Traders participated on the

Aggressive side of 34.04% of all aggressive buy volume. Strongly consistent with our

immediacy absorption hypothesis, the participation rate rises to 57.70% of the Aggressive

9We have also conducted the same analysis for 20 and 50 contracts as well as 10, 25 and 50 trades.

Results are qualitatively similar to those discussed here.

19
side of trades on the last 100 contracts of Aggressive buy volume before price increase

events and falls to 14.84% of the Aggressive side of trades on the first 100 contracts of

Aggressive buy volume after price increase events.

High Frequency Traders participated on the Passive side of 34.33% of all aggressive

buy volume. Consistent with our hypothesis, the participation rate on the Passive side

of Aggressive buy volume falls to 28.72% of the last 100 contracts before a price increase

event. It rises to 37.93% of the first 100 contracts after a price increase event.

These results are inconsistent with the idea that high frequency traders behave like

textbook market makers, suffering adverse selection losses associated with being picked

off by informed traders. Instead, when the price is about to move to a new level, high

frequency traders tend to avoid being run over and take the price to the new level with

Aggressive trades of their own.

Market Makers follow a noticeably more passive trading strategy than High Frequency Traders. According to panel A or Table VI, Market Makers are 13.48% of the

Passive side of all Aggressive trades, but they are only 7.27% of the Aggressive side

of all Aggressive trades. On the last 100 contracts at the old price, Market Makers’

share of volume increases only modestly, from 7.27% to 8.78% of trades. Their share

of Passive volume at the old price increases, from 13.48% to 15.80%. These facts are

consistent with the interpretation that Market Makers, unlike High Frequency Traders,

do engage in a strategy similar to traditional passive market making, buying at the bid

price, selling at the offer price, and suffering losses when the price moves against them.

These facts are also consistent with our hypothesis that High Frequency Traders have

lower latency than Market Makers.

Intuition might suggest that Fundamental Buyers would tend to place the Aggressive

trades which move prices up from one tick level to the next. This intuition does not

seem to be corroborated by the data. According to panel A of Table VI, Fundamental

Buyers are 21.53% of all Aggressive trades but only 11.61% of the last 100 Aggressive

contracts traded at the old price. Instead, Fundamental Buyers increase their share of

Aggressive buy volume to 26.17% of the first 100 contracts at the new price.

Taking into account symmetry between buying and selling, panel B of Table VI shows

the results for Aggressive sell trades during May 3-5, 2010, are almost the same as the

results for Aggressive buy trades. High Frequency Traders are 34.17% of all Aggressive

sell volume, increase their share to 55.20% of the last 100 Aggressive sell contracts at the

old price, and decrease their share to 15.04% of the last 100 Aggressive sell contracts at

the new price. Market Makers are 7.45% of all Aggressive sell contracts, increase their

share to only 8.57% of the last 100 Aggressive sell trades at the old price, and decrease

their share to 6.58% of the last 100 Aggressive sell contracts at the new price. Fundamental Sellers’ shares of Aggressive sell trades behave similarly to Fundamental Buyers’

shares of Aggressive Buy trades. Fundamental Sellers are 20.91% of all Aggressive sell

contracts, decrease their share to 11.96% of the last 100 Aggressive sell contracts at the

old price, and increase their share to 24.87% of the first 100 Aggressive sell contracts at

the new price.

20
Panels C and D of Table VI report results for Aggressive Buy trades and Aggressive

Sell trades for May 6, 2010. Taking into account symmetry between buying and selling,

the results for Aggressive buy trades in panel C are very similar to the results for

Aggressive sell trades in panel D. For example, Aggressive sell trades by Fundamental

Sellers were 17.55% of Aggressive sell volume on May 6, while Aggressive buy trades by

Fundamental Buyers were 20.12% of Aggressive buy volume on May 6. In comparison

with the share of Fundamental Buyers and in comparison with May 3-5, the Flash Crash

of May 6 is associated with a slightly lower—not higher—share of Aggressive sell trades

by Fundamental Sellers.

The number of price increase and price decrease events increased dramatically on

May 6, consistent with the increased volatility of the market on that day. On May

3-5, there were 4100 price increase events and 4062 price decrease events. On May 6

alone, there were 4101 price increase events and 4377 price decrease events. There were

therefore approximately three times as many price increase events per day on May 6 as

on the three preceding days.

A comparison of May 6 with May 3-5 reveals significant changes in the trading

patterns of High Frequency Traders. Compared with May 3-5 in panels A and B, the

share of Aggressive trades by High Frequency Traders drops from 34.04% of Aggressive

buys and 34.17% of Aggressive sells on May 3-5 to 26.98% of Aggressive buy trades and

26.29% of Aggressive sell trades on May 6. The share of Aggressive trades for the last 100

contracts at the old price declines by even more. High Frequency Traders’ participation

rate on the Aggressive side of Aggressive buy trades drops from 57.70% on May 3-5

to only 38.86% on May 6. Similarly, the participation rate on the Aggressive side of

Aggressive sell trades drops from and 55.20% to 38.67%. These declines are largely

offset by increases in the participation rate by Opportunistic Traders on the Aggressive

side of trades. For example, Opportunistic Traders’ share of the Aggressive side of the

last 100 contracts traded at the old price rises from 19.21% to 34.26% for Aggressive

buys and from 20.99% to 33.86% for Aggressive sells. These results suggest that some

Opportunistic Traders follow trading strategies for which low latency is important, such

as index arbitrage, cross-market arbitrage, or opportunistic strategies mimicking market

making.

Testing Hypothesis H2. HFTs trade aggressively in the direction of the

price move; Market Makers get run over by a price move. To examine this

hypothesis, we analyze whether High Frequency Traders use Aggressive trades to trade

in the direction of contemporaneous price changes, while Market Makers use Passive

trades to trade in the opposite direction from price changes. To this end, we estimate

the regression Equation 1 for Passive and Aggressive inventory changes separately.

<Insert Table VII >

21
Table VII presents the regression results of the two components of change in holdings on lagged inventory, lagged change in holdings and lagged price changes over one

second intervals. Panel A and Panel B report the results for May 3-5 and May 6,

respectively. Each panel has four columns, reporting estimated coefficients where the

dependent variables are net Aggressive volume (Aggressive buys minus Aggressive sells)

by High Frequency Traders (∆A HF T), net Passive volume by High Frequency Traders

(∆P HF T), net Aggressive volume by Market Makers (∆A MM), and net Passive volume by Market Makers (∆P MM).

We observe that for lagged inventories (NP HF Tt−1), the estimated coefficients for

Aggressive and Passive trades by High Frequency Traders are δA HF T = −0.005 (t =

−9.55) and δP HF T = −0.001 (t = −3.13), respectively. These coefficient estimates

have the interpretation that High Frequency Traders use Aggressive trades to liquidate

inventories more intensively than passive trades. In contrast, the results for Market

Makers are very different. For lagged inventories (NPMMt−1), the estimated coefficients

for Aggressive and Passive volume by Market Makers are δA MM = −0.002 (t = −6.73)

and δP MM = −0.002 (t = −5.26), respectively. The similarity of these coefficients

estimates has the interpretation that Market Makers favor neither Aggressive trades nor

Passive trades when liquidating inventories.

For contemporaneous price changes (in the current second) (∆Pt−1), the estimated

coefficient Aggressive and Passive volume by High Frequency Traders are β0 = 57.78

(t = 31.94) and β0 = −25.69 (t = −28.61), respectively. For Market Makers, the

estimated coefficients for Aggressive and Passive trades are β0 = 6.38 (t = 18.51) and

β0 = −19.92 (t = −37.68). These estimated coefficients have the interpretation that in

seconds in which prices move up one tick, High Frequency traders are net buyers of about

58 contracts with Aggressive trades and net sellers of about 26 contracts with Passive

trades in that same second, while Market Makers are net buyers of about 6 contracts

with Aggressive trades and net sellers of about 20 contracts with Passive trades. High

Frequency Traders and Market Makers are similar in that they both use Aggressive

trades to trade in the direction of price changes, and both use Passive trades to trade

against the direction of price changes. High Frequency Traders and Market Makers are

different in that Aggressive net purchases by High Frequency Traders are greater in

magnitude than the Passive net purchases, while the reverse is true for Market Makers.

For lagged price changes, coefficient estimates for Aggressive trades by High Frequency Traders and Market Makers are positive and statistically significant at lags 1-4

and lags 1-10, respectively. These results have the interpretation that both High Frequency Traders’ and Market Makers’ trade on recent price momentum, but the trading

is compressed into a shorter time frame for High Frequency Traders than for Market

Makers.

For lagged price changes, coefficient estimates for Passive volume by High Frequency

Traders and Market Makers are negative and statistically significant at lags 1 and lags

22
1-3, respectively.10

Panel B of Table VII presents results for May 6. Similar to May 3-5, High Frequency

Traders tend to use Aggressive trades more intensely than Passive trades to liquidate

inventories, while Market Makers do not show this pattern. Also similar to May 3-5,

High Frequency Trades and Market makers use Aggressive trades to trade in the contemporaneous direction of price changes and use Passive trades to trade in the direction

opposite price changes, with Aggressive trading greater than Passive trading for High

Frequency Traders and the reverse for Market Makers. In comparison with May 3-5,

the coefficients are smaller in magnitude on May 6, indicating reduced liquidity at each

tick. For lagged price changes, the coefficients associated with Aggressive trading by

High Frequency Traders change from positive to negative at lags 1-4, and the positive

coefficients associated with Aggressive trading by Market Makers change from being

positive and statistically significant at lags lags 1-10 to being positive and statistically

significant only at lags 1-3. These results illustrate accelerated trading velocity in the

volatile market conditions of May 6.

We further examine how high frequency trading activity is related to market prices.

Figure 8 illustrates how prices change after HFT trading activity in a given second.

The upper-left panel presents results for buy trades for May 3-5, the upper right panel

presents results for buy trades on May 6, and the lower-left and lower-right present

corresponding results for sell trades. For an “event” second in which High Frequency

Traders are net buyers, net Aggressive Buyers, and net Passive Buyers value-weighted

average prices paid by the High Frequency Traders in that second are subtracted from

the value-weighted average prices for all trades in the same second and each of the

following 20 seconds. The results are averaged across event seconds, weighted by the

magnitude of High Frequency Traders’ net position change in the event second. The

upper-left panel presents results for May 3-5, the upper-right panel presents results for

May 6, and the lower two panels present results for sell trades calculated analogously.

Price differences on the vertical axis are scaled so that one unit equals one tick ($12.50

per contract).

<Insert Figure 8>

When High Frequency Traders are net buyers on May 3-5, prices rise by 17% of a

tick in the next second. When HFTs execute Aggressively or Passively, prices rise by

20% and 2% of a tick in the next second, respectively. In subsequent seconds, prices in

all cases trend downward by about 5% of a tick over the subsequent 19 seconds. For

May 3-5, the results are almost symmetric for selling.

10We also introduce lead price changes up to 10 seconds into this regression framework. Price change

coefficients are positive and significant for the net aggressive volume of High Frequency Traders before

May 6. Coefficients are very similar when we include longer lags of prices and holdings changes. NeweyWest standard errors are very close to White standard errors. Results are available upon request.

23
When High Frequency Traders are buying on May 6, prices increase by 7% of a tick

in the next second. When they are aggressive buyers or passive buyers, prices increase

by increase 25% of a tick or decrease by 5% of a tick in the next second, respectively.

In subsequent seconds, prices generally tend to drift downwards. The downward drift

is especially pronounced after Passive buying, consistent with the interpretation that

High Frequency Traders were “run over” when their resting limit buy orders were “run

over” in the down phase of the Flash Crash. When High Frequency Traders are net

sellers, the results after one second are analogous to buying. After aggressive selling,

prices continue to drift down for 20 seconds, consistent with the interpretation that

High Frequency Traders made profits from Aggressive sales during the down phase of

the Flash Crash.

Testing Hypothesis H3. Both HFTs and Market Makers scratch trades;

HFTs scratch more. A textbook market maker will try to buy at the bid price, sell

at the offer price, and capture the bid-ask spread as a profit. Sometimes, after buying

at the bid price, market prices begin to fall before the market maker can make a one

tick profit by selling his inventory at the best offer price. To avoid taking losses in this

situation, one component of a traditional market making strategy is to “scratch trades in

the presence of changing market conditions by quickly liquidating a position at the same

price at which it was acquired. These scratched trades represent inventory management

trades designed to lower the cost of adverse selection. Since many competing market

makers may try to scratch trades at the same time, traders with the lowest latency will

tend to be more successful in their attempts to scratch trades and thus more successful

in their ability to avoid losses when market conditions change.

To examine whether and to what extent traders engage in trade scratching, we sequence each trader’s trades for the day using audit trail sequence numbers which not

only sort trades by second but also sort trades chronologically within each second. We

define an “immediately scratched trade” as a trade with the properties that the next

trade in the sorted sequence (1) occurred in the same second, (2) was executed at the

same price, (3) was in the opposite direction, i.e., buy followed by sell or sell followed

by buy. For each of the trading accounts in our sample, we calculate the number of

immediately scratched trades, then compare the number of scratched trades across the

six trader categories.

The results of this analysis are presented in the table below. Panel A provides results

for May 3-5 and panel B for May 6. In each panel, there are five rows of data, one for

each trader category. The first three columns report the total number of trades, the

total number of immediately scratched trades, and the percentage of trades that are

immediately scratched by traders in five categories. Small trader category results are

not reported for confidentiality reasons. For May 3-6, the reported numbers are from

the pooled data.

<Insert Table VIII>

24
This table shows that High Frequency Traders scratched 2.84 % of trades on May 3-

5 and 4.26 % on May 6; Market Makers scratched 2.49 % of trades on May 3-5 and

5.53 % of trades on May 6. While the percentages of immediately scratched trades by

Market Makers is slightly higher than that for High Frequency Traders on May 6, the

percentages for both groups are very similar.

The fourth, fifth, and sixth columns of Table VIII report the mean, standard deviation, and median of the number of scratched trades for the traders in each category.

Although the percentages of scratched trades are similar, the mean number of immediately scratched trades by High Frequency Traders is much greater than for Market

Makers: 540.56 per day on May 3-5 and 1610.75 on May 6 for High Frequency Traders

versus 13.35 and 72.92 for Market Makers. The differences between High Frequency

Traders and Market Makers reflect differences in volume traded. Table VIII shows that

High Frequency Traders and Market Makers scratch a significantly larger percentage of

their trades than other trader categories.

VI. Concluding Remarks

More than 40 years ago, stock exchanges began to think about switching from face-toface human trading to fully automated trading platforms. Fischer Black (1971) surmised

that, regardless of whether markets were human or automated, liquid markets would

exhibit price continuity only if trading is characterized by a large volume of small individual trades. As electronic central limit order books have replaced human trading,

Black’s insights have proven to be correct. Black (1995) also predicted that, to reduce

impact costs, electronic markets would induce institutions to shift from executing large

trades as blocks with “upstairs” human dealers to using “order shredding” strategies in

which computer algorithms submit many small trades over time into electronic trading

platforms. This insight has also proven to be correct.

Black did not foresee, however, how dramatically advances in the computing and

telecommunication technology would favor the most technologically-advanced financial

intermediaries known as high frequency traders or HFTs. We find that these traders

engage in immediacy absorption activity just ahead of any slower immediacy-seeking

market participant. This immediacy absorption activity makes prices move against all

slower customers who seek immediacy and, thus, imposes an immediacy absorption cost

on all slower traders, including the traditional market makers.

As suggested by Huang and Wang (2008), even a small cost of maintaining continuous

market presence makes market makers choose to maintain risk exposures that are too

low to offset temporary liquidity imbalances. In the event of large enough sell order, the

liquidity on the buy side could only be obtained after a price drop that is large enough to

compensate increasingly reluctant market makers to take on additional risky inventory.

These liquidity-based crashes are accompanied by high trading volume and large price

volatility as documented during a series of events that took place on May 6, 2010 that

collectively became known as the Flash Crash.

25
The events of May 6, 2010 were extremely traumatic to many market participants.

Was the Flash Crash caused by the high frequency traders? What have we learned from

this event? How do we make sure that events like that are less likely to happen in the

future?

In this paper, we show that HFTs did not cause the Flash Crash, but accelerated

a price movement due to a large order imbalance caused by an automated execution

program to sell E-mini S&P 500 futures contracts. We also show that HFTs contributed

to the Flash Crash by engaging in their typical immediacy-absorption practice of aggressively removing the last few contracts at the best bid or ask levels and then establishing

new best bids and asks at adjacent price levels.

Under calm market conditions, this trading activity accelerates, albeit for only a few

milliseconds, the price movement and adds to trading volume, but does not result in a

directional price move. At times of market stress, when prices are moving directionally,

due to an order flow imbalance and the volatility is already elevated, this trading activity

can amplify a directional price move and significantly add to volatility. Higher volatility

further increases the speed at which the best bid and offer queues get depleted, inducing

HFTs to act faster, leading to a spike in trading volume, and setting the stage for a

flash-crash-type event.

The Flash Crash has forced regulators and self-regulatory organizations to re-visit

the intricacies of market design and to contemplate policies that prevent these events

from happening in the future. The proposed responses vary from a tax on all financial

transactions to imposing delays on the cancellation or modification of resting orders or

restricting directional changes in prices on a security-by-security basis.

Based on our results, appropriate regulatory actions should aim to encourage HFTs

to provide immediacy, while discouraging them from demanding it. We believe that

this can be accomplished through changes in market design rather than taxes, limits

or restrictions as higher opportunity costs imposed on the technologically-advanced intermediaries would, at best, be passed on to other market participants. For example,

a more diligent use of market-wide trading pauses of short duration, which give slower

algorithms a few much needed seconds to decide on what terms they are willing to

replenish liquidity in the central limit order book, can be a highly effective pre-trade

safeguard in today’s fast and interlinked markets.

We acknowledge that in markets for individual securities, fragmentation of order flow

across competing trading venues makes the coordination of brief trading pauses difficult.

We also acknowledge that the task of coordinating responses across competing markets

overseen by different regulators with contradictory objectives is even more difficult. This

paper is our call to rise to these challenges.

26
References

Black, Fischer, 1971, Towards a Fully Automated Exchange, Part I, Financial Analysts

Journal 27, 29-34.

Black, Fischer, 1995, Equilibrium Exchanges, Financial Analysts Journal 51, 23-29.

CFTC-SEC Staff Report, Preliminary Findings Regarding the Market Events of May 6,

2010.

CFTC-SEC Staff Report, Findings Regarding the Market Events of May 6, 2010.

Grossman, Sanford J., and Miller, Merton H., 1988, Liquidity and Market Structure,

Journal of Finance 43,3,617–633.

Hasbrouck, Joel, 2003, Intraday Price Formation in U.S. Equity Index Markets, Journal

of Finance 58, 2375–2400.

Huang, Jennifer. and Jiang Wang, 2008, Liquidity and market crashes, Review of

Financial Studies, 2607-2643.

Huang, Jennifer and Jiang Wang, 2010, Market Liquidity, Asset Prices, and Welfare,

Journal of Financial Economics, 95, 107-127.

White, Halbert, 1980, A Heteroskedasticity-Consistent Covariance Matrix Estimator

and a Direct Test for Heteroskedasticity, Econometrica 48, 817–838.

27
Table I: Market Descriptive Statistics

May 3-5 May 6th

Daily Trading Volume 2,397,639 5,094,703

# of Trades 446,340 1,030,204

# of Traders 11,875 15,422

Trade Size 5.41 4.99

Order Size 10.83 9.76

Limit Orders % Volume 95.45% 92.44%

Limit Orders % Trades 94.36% 91.75%

Log High-Low Range 1.54% 9.82%

Return -0.02% -3.05%

This table presents summary statistics for the June 2010 E-Mini S&P 500 futures contract. The first column presents averages calculated for May 3-5, 2010 between 8:30 and

15:15 CT. The second column presents statistics for May 6, 2010 between 8:30 to 15:15 CT.

Volume is the number of contracts traded. The number of traders is the number of trading

accounts that traded at least once during a trading day. Order size and trade sizes are

measured in the number of contracts. The use of limit orders is presented both in percent

of the number of transactions and trading volume. Volatility is calculated as range, the

natural logarithm of maximum price over minimum price within a trading day.

28
Table II: Summary Statistics of Trader Categories

Panel A: May 3-5 3 Day Average

Trader Type % Volume % of Trades # Traders Trade Size Order Size Limit Orders Limit Orders Agg Ratio Agg Ratio

(Avg.) (Avg.) % Volume % Trades Trade-Weighted Vol-Weighted

High Frequency Traders 34.22% 32.56% 15 5.69 14.75 100.000% 100.000% 49.91% 45.68%

Market Makers 10.49% 11.63% 189 4.88 7.92 99.614% 98.939% 43.10% 41.62%

Fundamental Buyers 11.89% 10.15% 1,013 6.34 14.09 91.258% 91.273% 66.04% 64.09%

Fundamental Sellers 12.11% 10.10% 1,088 6.50 14.20 92.176% 91.360% 62.87% 61.13%

Opportunistic Traders 30.79% 33.34% 3,504 4.98 8.80 92.137% 90.549% 55.98% 54.71%

Small Traders 0.50% 2.22% 6,065 1.22 1.25 70.092% 71.205% 59.04% 59.06%

Volume # of Trades # Traders Trade Size Order Size Limit Orders Limit Orders Volatility Return

(Avg.) (Avg.) % Volume % Trades

All 2,397,639 446,340 11,875 5.41 10.83 95.45% 94.36% 1.54% -0.02%

Panel B: May 6th

Trader Type % Volume % of Trades # Traders Trade Size Order Size Limit Orders Limit Orders Agg Ratio Agg Ratio

(Avg.) (Avg.) % Volume % Trades Trade-Weighted Vol-Weighted

High Frequency Traders 28.57% 29.35% 16 4.85 9.86 99.997% 99.997% 50.38% 45.53%

Market Makers 9.00% 11.48% 179 3.89 5.88 99.639% 99.237% 45.18% 43.55%

Fundamental Buyers 12.01% 11.54% 1,263 5.15 10.43 88.841% 89.589% 64.39% 61.08%

Fundamental Sellers 10.04% 6.95% 1,276 7.19 21.29 89.985% 88.966% 68.42% 65.68%

Opportunistic Traders 40.13% 39.64% 5,808 5.05 10.06 87.385% 85.352% 61.92% 60.28%

Small Traders 0.25% 1.04% 6,880 1.20 1.24 63.609% 64.879% 63.49% 63.53%

Volume # of Trades # Traders Trade Size Order Size Limit Orders Limit Orders Volatility Return

(Avg.) (Avg.) % Volume % Trades

All 5,094,703 1,030,204 15,422 4.99 9.76 92.443% 91.750% 9.82% -3.05%

This table presents summary statistics for trader categories and the overall market. The first column presentsstatistics prior to May 6 as the average over three trading days, May 3-5, 2010 from 8:30 to 15:15 CT. The secondcolumn presents statistics for May 6 from 8:30 to 15:15 CT.

29
Table III: HFTs and Market Makers: Net Holdings and Prices

Panel A: May 3-5 Panel B: May 6

∆ NP HFT ∆ NP MM ∆ NP HFT ∆ NP MM

Intercept -1.64 -0.53 Intercept -3.22 0.04

(-3.54) (-3.33) (-3.38) (0.13)

∆NPHF Tt−1 -0.006 ∆NPHF Tt−1 0.011

(-0.69) (1.19)

NPHF Tt−1 -0.005 NPHF Tt−1 -0.005

(-11.77) (-6.76)

∆NPMMt−1 -0.006 ∆NPMMt−1 -0.035

(-0.79) (-2.69)

NPMMt−1 -0.004 NPMMt−1 -0.008

(-8.93) (-7.79)

∆Pt 32.09 -13.54 ∆Pt 10.81 -8.16

(18.44) (-23.83) (6.05) (-12.09)

∆Pt−1 17.18 -1.22 ∆Pt−1 4.63 6.64

(12.58) (-2.71) (3.39) (13.88)

∆Pt−2 8.36 2.16 ∆Pt−2 -1.52 2.73

(7.15) (4.99) (-1.25) (4.44)

∆Pt−3 5.09 2.53 ∆Pt−3 -1.36 1.14

(4.93) (5.97) (-1.06) (2.84)

∆Pt−4 3.91 2.65 ∆Pt−4 -1.82 0.49

(3.62) (6.54) (-1.48) (1.11)

∆Pt−5 1.81 2.50 ∆Pt−5 -0.23 -0.77

(1.56) (5.91) (-1.17) (-1.68)

∆Pt−6 -0.08 2.16 ∆Pt−6 -0.31 -0.31

(-0.07) (5.42) (-0.23) (-0.78)

∆Pt−7 -1.00 1.84 ∆Pt−7 -5.04 -0.62

(-0.97) (4.96) (-3.62) (-1.33)

∆Pt−8 -1.76 1.47 ∆Pt−8 -1.78 -0.36

(-1.56) (3.83) (-1.41) (-0.93)

∆Pt−9 -1.81 0.45 ∆Pt−9 -1.68 -1.11

(-1.70) (1.19) (-1.35) (-2.45)

∆Pt−10 -3.90 0.52 ∆Pt−10 -1.65 -0.39

(-3.78) (1.37) (-1.13) (-0.84)

∆Pt−11 -4.73 -0.03 ∆Pt−11 -1.08 -0.63

(-4.70) (-0.07) (-0.74) (-1.28)

∆Pt−12 -3.46 0.15 ∆Pt−12 0.71 -1.17

(-3.33) (0.41) (0.43) (-2.58)

∆Pt−13 -3.80 0.27 ∆Pt−13 2.26 -0.62

(-3.74) (0.72) (1.43) (-1.49)

∆Pt−14 -4.77 0.32 ∆Pt−14 -2.66 -0.27

(-4.70) (0.86) (-1.85) (-0.71)

∆Pt−15 -2.74 -0.19 ∆Pt−15 0.43 -0.83

(-2.63) (-0.53) (0.34) (-2.19)

∆Pt−16 -2.21 -0.64 ∆Pt−16 -0.68 0.23

(-2.09) (-1.72) (-0.41) (0.61)

∆Pt−17 -2.52 -0.10 ∆Pt−17 -0.66 0.29

(-2.45) (-0.26) (-0.45) (0.73)

∆Pt−18 -4.36 0.04 ∆Pt−18 0.45 -0.77

(-3.96 (0.12) (0.29) (-2.04)

∆Pt−19 -4.21 0.57 ∆Pt−19 -2.63 -0.30

(-4.16) (1.51) (-1.87) (-0.76)

∆Pt−20 -5.86 -0.12 ∆Pt−20 -1.07 -0.71

(-5.86) (-0.33) (-0.79) (-1.65)

#obs 72837 72837 #obs 24275 24275

Adj − R2 0.019 0.026 Adj − R2 0.010 0.039

This table displays estimated coefficients of the following regression: ∆yt = α + φ∆yt−1 + δyt−1 +

P20

i=0[βi × ∆pt−i/0.25] + t. The dependent variable is changes in holdings of High Frequency

Traders and Market Makers, respectively. Both changes in holdings, ∆yt, and lagged holdings,

yt−1, are in the number of contracts. Price changes, ∆pt−i, are in ticks. Estimates are computed for

second-by-second observations. The t-statistics are calculated using the White (1980) estimator.

t values reported in parentheses are in bold if the coefficients are statistically significant at the 5%

level. Observations are stacked for May 3-5.

30
Table IV: HFTs and Market Makers: The Flash Crash

Variable ∆ NP HFT ∆ NP MM Variable (cont) ∆ NP HFT ∆ NP MM Variable (cont) ∆ NP HFT ∆ NP MM

Intercept -2.04 -0.48 InterceptD 9.22 9.15 InterceptU 2.27 0.49

(-4.78) (-3.34) (1.19) (2.41) (0.55) (0.33)

∆NPt−1 -0.005 -0.024 ∆NP D

t−1

-0.031 -0.024 ∆NP U

t−1

0.004 0.085

(-0.69) (-3.31) (-0.80) (-0.63) (0.10) (2.74)

NPt−1 -0.005 -0.005 NP D

t−1

-0.002 -0.007 NP U

t−1

-0.001 0.000

(-12.95) (-10.78) (-0.38) (-1.62) (-0.21) (-0.17)

∆Pt 31.47 -15.48 ∆P D

t

1.29 14.13 ∆P

U

t

-40.83 14.29

(16.89) (-21.96) (0.18) (6.73) (-12.18) (13.68)

∆Pt−1 14.96 -0.54 ∆P D

t−1

-3.02 11.44 ∆P

U

t−1

-9.60 5.63

(12.17) (-1.23) (-0.57) (5.11) (-3.44) (7.12)

∆Pt−2 6.24 2.69 ∆P D

t−2

-6.84 1.87 ∆P

U

t−2

-9.72 -1.83

(5.36) (5.99) (-1.26) (0.81) (-3.57) (-2.20)

∆Pt−3 3.02 2.65 ∆P D

t−3

-4.16 -2.03 ∆P

U

t−3

-3.97 -2.47

(3.31) (7.14) (-0.69) (-1.22) (-1.61) (-3.75)

∆Pt−4 1.92 2.74 ∆P D

t−4

-9.74 -4.91 ∆P

U

t−4

-1.12 -2.51

(2.04) (7.78) (-1.98) (-3.11) (-0.49) (-3.70)

∆Pt−5 0.63 2.21 ∆P D

t−5

-10.94 -3.45 ∆P

U

t−5

1.86 -2.86

(0.64) (5.99) (-1.57) (-2.25) (0.75) (-4.36)

∆Pt−6 -1.89 1.99 ∆P D

t−6

0.59 -2.91 ∆P

U

t−6

4.27 -2.45

(-2.03) (5.72) (0.11) (-1.86) (1.78) (-3.71)

∆Pt−7 -2.85 1.92 ∆P D

t−7

-1.66 -2.71 ∆P

U

t−7

-4.54 -3.38

(-2.89) (5.18) (-0.31) (-1.59) (-1.73) (-5.05)

∆Pt−8 -2.52 1.43 ∆P D

t−8

2.45 -2.97 ∆P

U

t−8

1.79 -1.65

(-2.68) (4.33) (0.44) (-1.92) (0.76) (-2.76)

∆Pt−9 -2.59 0.48 ∆P D

t−9

-4.32 -2.98 ∆P

U

t−9

2.69 -1.64

(-2.76) (1.44) (-0.61) (-1.70) (1.12) (-2.54)

∆Pt−10 -5.18 0.91 ∆P D

t−10 3.93 -3.40 ∆P

U

t−10 4.41 -1.52

(-4.66) (2.12) (0.50) (-1.78) (1.76) (-2.22)

∆Pt−11 -5.07 -0.05 ∆P D

t−11 9.84 -6.35 ∆P

U

t−11 6.01 -0.36

(-5.76) (-0.16) (1.30) (-2.96) (2.27) (-0.51)

∆Pt−12 -4.05 -0.10 ∆P D

t−12 8.38 -0.73 ∆P

U

t−12 4.37 -0.79

(-4.46) (-0.31) (1.07) (-0.37) (1.34) (-1.26)

∆Pt−13 -3.86 -0.07 ∆P D

t−13 11.92 -4.69 ∆P

U

t−13 10.02 0.28

(-4.27) (-0.20) (1.64) (-2.10) (3.34) (0.43)

∆Pt−14 -4.36 0.28 ∆P D

t−14 -8.56 0.79 ∆P

U

t−14 1.64 -0.59

(-5.01) (0.84) (-1.29) (0.41) (0.62) (-0.98)

∆Pt−15 -2.05 -0.17 ∆P D

t−15 8.46 -5.41 ∆P

U

t−15 1.47 -0.09

(-2.27) (-0.50) (1.17) (-2.55) (0.64) (-0.15)

∆Pt−16 -2.01 -0.39 ∆P D

t−16 -3.25 3.92 ∆P

U

t−16 1.07 0.99

(-2.10) (-1.11) (-0.41) (1.80) (0.37) (1.56)

∆Pt−17 -2.67 0.01 ∆P D

t−17 6.24 -1.57 ∆P

U

t−17 5.19 0.48

(-3.05) (0.02) (0.81) (-0.69) (2.13) (0.75)

∆Pt−18 -3.89 0.19 ∆P D

t−18 -8.62 0.86 ∆P

U

t−18 7.37 -0.69

(-4.10) (0.58) (-1.05) (0.42) (2.58) (-1.12)

∆Pt−19 -3.50 0.70 ∆P D

t−19 -1.05 -3.07 ∆P

U

t−19 -0.75 -0.88

(-3.88) (2.08) (-0.12) (-1.39) (-0.30) (-1.44)

∆Pt−20 -5.30 -0.33 ∆P D

t−20 -2.32 3.13 ∆P

U

t−20 4.88 -0.06

(-5.82) (-1.00) (-0.30) (1.36) (2.14) (-0.09)

# of Obs 93092 93092

Adjusted R2 0.021 0.036

This table displays estimated coefficients of the following regression: ∆yt = α+φ∆yt−1 +∆yt−1 +

Σ

20

i=0[βi×pt−i/0.25]+DD

t {α

D +φD∆yt−1+δDyt−1+Σ20

i=0[β

D

i ×pt−i/0.25]}+DU

t {α

U +φU∆yt−1+

δ

U yt−1 + Σ20

i=0[β

U

i × pt−i/0.25]} + t during May 3-6 with dummy variables DD

t and DUt

included

to interact with observations during the Down (from 13:32:00 CT to 13:45:28 CT) and Up (from

13:45:33 CT to 14:08:00 CT) phases of the Flash Crash, respectively. The period between 13:45:28

CT and 13:45:33 CT corresponds to the 5 second pause in trading; there are no changes in prices or

inventory during the 5 second pause. The cutoff for observations on May 6, 2010 is 14:08:00 CT.

The dependent variable is changes in holdings of High Frequency Traders and Market Makers,

respectively. Both changes in holdings, ∆yt, and lagged holdings, yt−1, are in the number of

contracts. Price changes, ∆pt−i, are in ticks. Estimates are computed for second-by-second

observations. The t-statistics are calculated using the White (1980) estimator. The t-statistics

reported in parentheses are in bold if the coefficients are statistically significant at the 5% level.

31
Table V: Trading Volume During the Flash Crash

Panel A: May 3-5

DOWN UP

Sell Buy Net Sell Buy Net

High Frequency Traders 23,746 23,791 45 40,524 40,021 -503

Market Makers 6,484 6,328 -156 11,469 11,468 -1

Fundamental Buyers 3,064 7,958 4,894 6,127 14,910 8,783

Fundamental Sellers 8,428 3,118 -5,310 15,855 5,282 -10,573

Opportunistic Traders 20,049 20,552 503 37,317 39,535 2,218

Small Traders 232 256 24 428 504 76

Total 62,003 62,003 0 111,720 111,720 0

Panel B: May 6th

DOWN UP

Sell Buy Net Sell Buy Net

High Frequency Traders 152,436 153,804 1,368 191,490 189,013 -2,477

Market Makers 32,489 33,694 1,205 47,348 45,782 -1,566

Fundamental Buyers 28,694 78,359 49,665 55,243 165,612 110,369

Fundamental Sellers 94,101 10,502 -83,599 145,396 35,219 -110,177

Opportunistic Traders 189,790 221,236 31,446 302,417 306,326 3,909

Small Traders 1,032 947 -85 1,531 1,473 -58

Total 498,542 498,542 0 743,425 743,425 0

This table presents the number of contracts sold and bought by trader categories during

DOWN and UP periods. DOWN period is defined as the interval between 13:32:00 and

13:45:28 CT. UP period is defined as the interval between 13:45:33 and 14:08:00 CT.

Panel A reports the average number of contracts bought and sold between May 3 and

May 5, 2010 during the DOWN and UP periods in the day. Panel B reports the number

of contracts bought and sold on May 6, 2010 during the DOWN and UP periods.

32
Table VI: Shares of Passive and Aggressive Trading Volume Around Price Increase and

Price Decrease Events

Panel A: Aggressive Buy Trades, Price Increase Events, May 3-5, 2010

Last 100 Contracts First 100 Contracts All Aggressive Buy Trades

Passive Aggressive Passive Aggressive Passive Aggressive

HFT 28.72% 57.70% 37.93% 14.84% 34.33% 34.04%

MM 15.80% 8.78% 19.58% 7.04% 13.48% 7.27%

BUYER 6.70% 11.61% 4.38% 26.17% 4.57% 21.53%

SELLER 16.00% 2.65% 11.82% 7.09% 16.29% 5.50%

OPP 32.27% 19.21% 25.95% 43.39% 30.90% 31.08%

SMALL 0.51% 0.04% 0.34% 1.46% 0.44% 0.58%

Panel B: Aggressive Sell Trades, Price Decrease Events, May 3-5, 2010

Last 100 Contracts First 100 Contracts All Aggressive Sell Trades

Passive Aggressive Passive Aggressive Passive Aggressive

HFT 27.41% 55.20% 38.31% 15.04% 34.45% 34.17%

MM 15.49% 8.57% 20.64% 6.58% 13.79% 7.45%

SELLER 5.88% 11.96% 3.83% 24.87% 5.67% 20.91%

BUYER 17.98% 3.22% 12.71% 8.78% 15.40% 6.00%

OPP 32.77% 20.99% 24.18% 43.41% 30.30% 30.89%

SMALL 0.47% 0.06% 0.34% 1.32% 0.39% 0.58%

Panel C: Aggressive Buy Trades, Price Increase Events, May 6, 2010

Last 100 Contracts First 100 Contracts All Aggressive Buy Trades

Passive Aggressive Passive Aggressive Passive Aggressive

HFT 28.46% 38.86% 30.55% 14.84% 30.94% 26.98%

MM 12.95% 5.50% 13.88% 5.45% 12.26% 5.82%

BUYER 6.31% 17.49% 5.19% 21.76% 5.45% 20.12%

SELLER 13.84% 3.84% 14.30% 5.71% 14.34% 4.40%

OPP 38.26% 34.26% 35.94% 51.87% 36.86% 42.37%

SMALL 0.19% 0.06% 0.16% 0.37% 0.16% 0.31%

Panel D: Aggressive Sell Trades, Price Decrease Events, May 6, 2010

Last 100 Contracts First 100 Contracts All Aggressive Sell Trades

Passive Aggressive Passive Aggressive Passive Aggressive

HFT 28.38% 38.67% 30.13% 14.59% 30.09% 26.29%

MM 12.27% 5.04% 14.85% 5.64% 12.05% 5.88%

SELLER 4.19% 16.46% 3.77% 21.21% 3.82% 17.55%

BUYER 15.83% 5.90% 13.89% 6.97% 15.27% 7.26%

OPP 39.12% 33.86% 37.15% 51.10% 38.56% 42.68%

SMALL 0.21% 0.08% 0.21% 0.48% 0.21% 0.34%

This table presents each trader category’s share of aggressive and passive trading volume for the last 100 contracts

traded before a price increase event or price decrease event and the first 100 contracts traded at the new higher

price after a price increase event or the new lower price after a price decrease event. For comparison purposes,

this Table also presents the unconditional share of aggressive and passive trading volume of each trader category.

Trading categories are High Frequency Traders (HFT), Market Makers (MM), Fundamental Buyers (BUYER),

Fundamental Sellers (SELLER), Opportunistic Traders (OPP), and Small Traders (SMALL). To emphasize the

symmetry between buying and selling, the rows for BUYER and SELLER in panels B and D have been reversed

relative to panels A and C.

33
Table VII: HFTs and Market Makers: Liquidity Provision/Removal

Panel A: May 3-5 Panel B: May 6

∆ A HFT ∆ P HFT ∆ A MM ∆ P MM ∆ A HFT ∆ P HFT ∆ A MM ∆ P MM

Intercept -1.29 -0.35 -0.34 -0.19 -2.86 -0.36 -0.25 0.28

(-2.64) (-1.24) (-3.15) (-1.36) (-3.22) (-0.65) (-1.40) (1.15)

∆NPHF Tt−1 -0.042 0.036 -0.003 0.014

(-4.67) (6.95) (-0.29) (1.76)

NPHF Tt−1 -0.005 -0.001 -0.004 -0.001

(-9.55) (-3.13) (-5.24) (-2.73)

∆NPMMt−1 0.007 -0.013 -0.003 -0.032

(1.71) (-1.91) (-0.56) (-2.60)

NPMMt−1 -0.002 -0.002 -0.003 -0.004

(-6.73) (-5.26) (-5.60) (-4.80)

∆Pt 57.78 -25.69 6.38 -19.92 23.70 -12.89 4.94 -13.10

(31.94) (-28.61) (18.51) (-37.68) (12.72) (-8.26) (11.20) (-15.73)

∆Pt−1 22.55 -5.37 5.79 -7.01 -1.12 5.74 3.91 2.73

(15.88) (-7.33) (18.79) (-17.44) (-0.91) (4.71) (11.09) (6.33)

∆Pt−2 9.61 -1.26 4.75 -2.59 -2.66 1.14 1.66 1.08

(7.80) (-1.82) (15.87) (-7.04) (-2.26) (1.05) (5.65) (1.86)

∆Pt−3 5.44 -0.36 3.64 -1.12 -1.15 -0.21 0.54 0.60

(4.91) (-0.56) (12.86) (-3.16) (-0.89) (-0.16) (1.98) (1.41)

∆Pt−4 3.29 0.62 3.11 -0.46 -2.81 1.00 0.23 0.26

(2.84) (0.92) (11.11) (-1.36) (-2.54) (0.94) (0.90) (0.65)

∆Pt−5 1.93 -0.12 2.59 -0.09 -0.69 0.46 0.16 -0.93

(1.63) (-0.17) (8.90) (-0.26) (-0.55) (0.42) (0.61) (-1.86)

∆Pt−6 -0.99 0.91 2.04 0.13 -1.82 1.51 0.05 -0.37

(-0.85) (1.37) (7.21) (0.38) (-1.58) (1.44) (0.21) (-1.02)

∆Pt−7 -0.29 -0.71 2.10 -0.26 -2.69 -2.35 -0.52 -0.10

(-0.26) (-1.07) (8.46) (-0.81) (-2.22) (-1.85) (-1.90) (-0.21)

∆Pt−8 -0.98 -0.79 1.74 -0.27 -2.22 0.44 -0.63 0.27

(-0.80) (-1.16) (6.61) (-0.82) (-1.90) (0.48) (-2.35) (0.69)

∆Pt−9 -0.73 -1.08 1.16 -0.71 -0.80 -0.88 -0.10 -1.01

(-0.64) (-1.68) (4.59) (-2.15) (-0.71) (-0.83) (-0.35) (-2.20)

∆Pt−10 -2.54 -1.36 1.01 -0.48 -2.96 1.30 -0.51 0.13

(-2.33) (-2.20) (3.89) (-1.48) (-2.03) (1.19) (-1.70) (0.24)

∆Pt−11 -3.54 -1.19 0.43 -0.45 -1.10 0.02 -0.87 0.24

(-3.32) (-1.91) (1.67) (-1.44) (-0.91) (0.02) (-3.16) (0.51)

∆Pt−12 -2.52 -0.93 0.21 -0.05 0.97 -0.27 -0.40 -0.78

(-2.31) (-1.44) (0.81) (-0.17) (0.82) (-0.19) (-1.48) (-1.85)

∆Pt−13 -2.13 -1.67 0.50 -0.24 1.17 1.09 -0.29 -0.32

(-1.98) (-2.71) (1.91) (-0.77) (0.92) (0.83) (-1.13) (-0.85)

∆Pt−14 -4.39 -0.38 0.11 0.21 -1.25 -1.42 -0.45 0.18

(-4.08) (-0.61) (0.40) (0.65) (-1.16) (-1.27) (-1.84) (0.53)

∆Pt−15 -1.97 -0.77 0.10 -0.29 1.01 -0.58 -0.54 -0.30

(-1.83) (-1.21) (0.38) (-0.93) (0.77) (-0.63) (-2.03) (-0.77)

∆Pt−16 -2.43 0.23 -0.18 -0.46 -1.30 0.62 0.22 0.01

(-2.19) (0.37) (-0.67) (-1.44) (-1.06) (0.54) (0.82) (0.04)

∆Pt−17 -2.19 -0.33 0.24 -0.34 -1.71 1.05 -0.24 0.53

(-2.01) (-0.52) (0.89) (-1.04) (-1.35) (1.03) (-0.87) (1.29)

∆Pt−18 -3.26 -1.10 0.31 -0.27 0.48 -0.04 0.05 -0.82

(-2.87) (-1.75) (1.25) (-0.84) (0.44) (-0.03) (0.19) (-2.32)

∆Pt−19 -3.59 -0.63 0.54 0.02 -0.75 -1.88 -0.27 -0.031

(-3.31) (-1.03) (2.09) (0.08) (-0.61) (-1.78) (-0.97) (-0.08)

∆Pt−20 -4.62 -1.24 0.21 -0.33 -0.54 -0.54 -0.50 -0.21

(-4.42) (-2.11) (0.86) (-1.09) (-0.46) (-0.66) (-1.95) (-0.53)

#obs 72837 72837 72837 72837 24275 24275 24275 24275

Adj − R2 0.043 0.026 0.020 0.063 0.025 0.027 0.046 0.070

This table presents estimated coefficients of the following regression: ∆yt = α+φ∆yt−1 +∆yt−1 +

P20

i=0[βi ×∆pt−i/0.25]+t. Dependent variables are changes in Aggressive and Passive holdings of

High Frequency Traders and Market Makers. Changes in holdings, ∆yt, and lagged holdings, yt−1,

are in the number of contracts. Price changes, ∆pt−i, are in ticks. Estimates are computed for

second-by-second observations. The t-statistics are calculated using the White (1980) estimator.

t-statistics reported in parentheses are in bold if the coefficients are statistically significant at the

5% level. Observations are stacked for May 3-5.

34
Table VIII: Immediately Scratched Trades

Panel A: May 3-5

All Trades Scratched Trades % of All Trades Mean Std Median

HFT 871,177 24,781 2.84 540.56 768.32 218.50

Market Maker 314,780 7,847 2.49 13.35 54.44 0.00

Buyer 268,808 977 0.38 0.30 6.22 0.00

Seller 257,637 816 3.2 0.25 4.92 0.00

Opportunistic 893,262 15,980 1.79 1.45 39.97 0.00

Panel B: May 6

All Trades Scratched Trades % of All Trades Mean Std Median

HFT 604,659 25,772 4.26 1610.75 2218.86 553.00

Market Maker 236,434 13,064 5.53 72.98 422.19 0.00

Buyer 236,501 2,715 1.15 2.15 30.86 0.00

Seller 141,853 295 0.21 0.23 7.18 0.00

Opportunistic 810,901 11,571 1.43 1.99 71.94 0.00

This table presents statistics for immediate trade scratching which measures how many times a trader changeshis/her direction of trading in a second aggregated over a day. We define a trade direction change as a buytrade right after a sell trade or vice versa at the same price level in the same second. These statistics aretaken across the 3 day sample period for May 3-5.

35
Figure 1: U. S. Equity Indices on May 6, 2010

Source: “Preliminary Findings Regarding the Market Events of May 6, 2010”. This figure

presents end-of-minute transaction prices of the Dow Jones Industrial Average (DJIA),

S&P 500 Index, and the June 2010 E-Mini S&P 500 futures contract on May 6, 2010

between 8:30 and 15:15 CT.

36
Figure 2: Prices and Trading Volume of the E-Mini S&P 500 Stock Index Futures

Contract

Source: “Preliminary Findings Regarding the Market Events of May 6, 2010”. This

figure presents minute-by-minute transaction prices and trading volume of the June 2010

E-Mini S&P futures contract on May 6, 2010 between 8:30 and 15:15 CT. Trading volume

is calculated as the number of contracts traded during each minute. Transaction price is

the last transaction price of each minute.

37
Figure 3: Trading Accounts Trading Volume and Net Position Scaled by Market Trading

Volume

100

200

300

400

500

600

700

Trader Volume

1000

2000

3000

4000

5000

6000

7000

Trader Volume

0

0000

0000

0000

0000

0000

0000

0000

-0.00736 -0.00536

N

Fundamen

0

000

000

000

000

000

000

000

-0.00736 -0.00536

N

Fundamenta

6 -0.00336 -0.00136

Net Position Scaled b

May

ntal Sellers

-0.00336 -0.00136

Net Position Scaled b

May 

al Sellers

6 0.00064 0.00264

by Market Trading Vo

y 3

High Frequency 

Opportunistic Tr

Market Makers

Fundame

0.00064 0.00264

by Market Trading Vo

5

High Frequency Tr

Opportunistic Tra

Market Makers

Fund

0.00464 0.00664

olume

Traders

raders and 

ental Buyers

0.00464 0.00664

olume

raders

aders and 

damental Buyers

10000

20000

30000

40000

50000

60000

70000

Trader Volume

0

100000

200000

300000

400000

500000

600000

700000

-0.00

Trader Volume

0

00

00

00

00

00

00

00

-0.00736 -0.00536 -

Net 

Fundam

0736 -0.00536 -0.0

Net Po

Fundamental Se

-0.00336 -0.00136 0

Position Scaled by M

May 4

H

M

mental Sellers

00336 -0.00136 0.00

osition Scaled by Ma

May 6

H

Op

Ma

ellers

0.00064 0.00264 0.0

Market Trading Volu

High Frequency Trad

Opportunistic Trader

Market Makers

Fundamental B

0064 0.00264 0.0

arket Trading Volume

High Frequency Trade

pportunistic Traders a

arket Makers

Fundamental B

00464 0.00664

ume

ders

rs and 

Buyers

0464 0.00664

e

ers

and 

Buyers

This figure presents trader categories superimposed (as shaded areas) over all individual

trading accounts ranked by their trading volume and net position scaled by market trading

volume. The figures reflect trading activity in the June 2010 E-Mini S&P 500 futures

contract for May 3-6, 2010.

38
Figure 4: Net Position of High Frequency Traders

This figure presents the net position of High Frequency Traders (left vertical axis) and

transaction prices (right vertical axis) in the June 2010 E-Mini S&P 500 futures contract

over one minute intervals during May 3, 4, 5, and 6 between 8:30 to 15:15 CT. Net position

is calculated as the difference between total open long and total open short positions of

High Frequency Traders at the end of each minute. Transaction price is the last transaction

price of each minute.

39
Figure 5: Change in Net Position of Fundamental and Opportunistic Traders

1020

1040

1060

1080

1100

1120

1140

-25000

-20000

-15000

-10000

-5000

0

5000

10000

15000

20000

25000

13:19 13:29 13:39 13:49 13:59 14:09

Price

Net Position Change

Time

Opportunistic Fundamental Sellers Fundamental Buyers Price

DOWN UP

This figure presents the change in net position of Fundamental and Opportunistic Traders

(left vertical axis) and transaction prices (right vertical axis) in the June 2010 E-Mini S&P

500 futures contract over one minute intervals on 6 between 13:19 to 14:09 CT. Net position

is calculated as the difference between total open long and total open short positions of

Opportunistic Traders at the end of each minute. Transaction price is the last transaction

price of each minute.

40
Figure 6: Hot Potato Volume

This figure shows the price and the scaled trading volume by HFTs and Market Makers

over one second intervals. Scaled trading volume is calculated as the 5 second moving

average of contracts traded over absolute value net holdings. Price reflects the last transaction price during an interval. Prices and scaled trading volumes are reported from 13:44

to 13:46 CT.

41
Figure 7: An Illustration of Immediacy Absorption Activity of High Frequency Traders

This figure presents an illustration of the “immediacy absorption” activity of HFTs. The

top left panel illustrates a starting liquidity event – temporary selling pressure that results

in an erosion of depth at best bid to a total of just 100 contracts (in deep blue) at the best

bid price of 1000.00. The top right panel illustrates the response of HFTs: (i) absorbing

immediacy by aggressively selling a total of 100 contracts at the best bid, thus completely

depleting the queue at the best bid, and (ii) very quickly submitting sequences of new

limit orders to buy a total of 100 contracts at the new best bid price of 999.75, as well

as (iii) submitting orders to to sell 100 contracts at the new best offer of 1000.00. The

two bottom panels illustrate alternative scenarios. The bottom left panel illustrates a

scenario of continuing selling pressure. Under this scenario, the market comes to the

HFTs, enabling them to buy 100 contracts at 999.75 and pocket 1,250 dollars among

them (the notional value of one contract is set at $50). The bottom right panel illustrates

a scenario when the selling pressure stops. Under this scenario, HFTs quickly buy 100

contracts which are offered at the new best ask price of 1000.00, “scratching” their initial

aggressive sell trade by buying at the same price, and getting rid of risky inventory.

42
Figure 8: HFT Trading and Prices

‐0.3

‐0.25

‐0.2

‐0.15

‐0.1

‐0.05

0

0.05

0.1

0.15

0.2

Price in Ticks

HFT Sell: May 3‐5

HFT Net Sell HFT Net Agg. Sell HFT Net Pass. Sell

‐0.6

‐0.5

‐0.4

‐0.3

‐0.2

‐0.1

0

0.1

0.2

0.3

0.4

HFT Buy: May 6

HFT Net Buy HFT Net Agg Buy HFT Net Pass Buy

‐0.7

‐0.6

‐0.5

‐0.4

‐0.3

‐0.2

‐0.1

0

0.1

0.2

0.3

0.4

HFT Sell: May 6

HFT Net Sell HFT Net Agg. Sell HFT Net Pass. Sell ‐0.1

‐0.05

0

0.05

0.1

0.15

0.2

0.25

0.3

HFT Buy: May 3‐5

HFT Net Buy HFT Net Agg. Buy HFT Net Pass. Buy

This figure illustrates how prices change after HFT trading activity in a given second. The

upper-left panel presents results for buy trades for May 3-5, the upper right panel presents

results for buy trades on May 6, and the lower-left and lower-right present corresponding

results for sell trades. For an “event” second in which High Frequency Traders are net

buyers, net Aggressive Buyers, and net Passive Buyers value-weighted average prices paid

by the High Frequency Traders in that second are subtracted from the value-weighted

average prices for all trades in the same second and each of the following 20 seconds. The

results are averaged across event seconds, weighted by the magnitude of High Frequency

Traders’ net position change in the event second. The upper-left panel presents results

for May 3-5, the upper-right panel presents results for May 6, and the lower two panels

present results for sell trades calculated analogously. Price differences on the vertical axis

are scaled so that one unit equals one tick ($12.50 per contract).

43