Price Discovery without Trading:
Evidence from Limit Orders*
Jonathan Brogaard
Terrence Hendershott
Ryan Riordan
First Draft: November 2014
Current Draft: September 2015
Abstract: Adverse selection in financial markets is traditionally measured by the correlation
between the direction of market order trading and price movements. We show this relationship
has weakened dramatically with limit orders playing a larger role in price discovery and with
high-frequency traders’ (HFTs) limit orders playing the largest role. HFTs are responsible for
60–80% of price discovery, primarily through their limit orders. HFTs’ limit orders have 50%
larger price impact than non-HFTs’ limit orders, and HFTs submit limit orders 50% more
frequently. HFTs react more to activity by non-HFTs than the reverse. HFTs react more to
orders both within and across stock exchanges.
We thank Helen Hogarth, Victoria Pinnington, and IIROC for providing data and comments. All errors
are our own. We thank participants at the 2015 Cambridge Microstructure Theory and Application
Workshop, Baruch College, Stockholm Business School, Hong Kong University, Chinese University of
Hong Kong, University of Mannheim, Goethe University, Australia National University, and UC Santa
Cruz HFT Workshop for helpful comments
*
Contact: Jonathan Brogaard, Foster School of Business, University of Washington, (Email)
brogaard@uw.edu , (Tel) 206-685-7822; Terrence Hendershott, University of California – Berkeley,
Haas School of Business, (Email) hender@haas.berkeley.edu (Tel) 510-643-0619; and Ryan Riordan,
Queen’s School of Business, Queen’s University (Email) ryan.riordan@queensu.ca (Tel) 705.761.8800.
1
I.
Introduction
This paper examines the nature of price discovery for stocks in modern fragmented markets.
The fraction of information incorporated into prices through liquidity-demanding marketable
orders has fallen dramatically. Using the standard Hasbrouck (1991b) approach Figure 1 shows
this for a well-known stock, Royal Bank of Canada.1 Between 2007 and 2011 trading in RBC
fragments and the fraction of price discovery correlated with trading falls from close to 40
percent to roughly 10 percent.2
INSERT FIGURE 1 ABOUT HERE
Around the world traditional stock exchanges now face a range of competitors for order flow.
In the U.S. exchanges compete with each other, electronic communications networks (ECNs),
dark markets, and other execution venues. In Europe MiFID has led to a dramatic
fragmentation in order flow. As shown in Figure 1 in Canada the previously dominant Toronto
Stock Exchange lost market share to Chi-X, Alpha, and other smaller trading venues.
Using Canadian regulatory data we study the contribution of high-frequency traders’ (HFTs)
and non-HFTs’ trades and limit orders to price discovery overall and in each of the three largest
stock exchanges in Canada.3 While individual trades contribute more to price discovery than
individual limit orders, trades represent roughly five percent of orders. Limit order placements
and cancellations at the best prices represent almost 50 percent of orders. HFTs’ limit orders are
1 This analysis uses the Thomson Reuters DataScope Tick History archive data provided by SIRCA.
See Hendershott, Jones, and Menkveld (2011) for related evidence on the changing nature of price discovery for
New York Stock Exchange stocks and Riordan and Storkenmaier (2012) for Deutsche Borse stocks. Malinova, Park,
and Riordan (2013) show algorithmic trading increasing on the primary market, the Toronto Stock Exchange, from
2006 through 2009, with a sharp increase in the second half of 2008. The sharp increase occurred as the new
competitors, Chi-X and Alpha, entered with fast trading technology and lower fees (see Section III for details).
3 We use stock exchange and market interchangeably as Chi-X is technically an alternative trading system in Canada.
Our sample period follows the Toronto Stock Exchange’s (TSX) significant loss of market share to new entrants. In
2008 Chi-X and Alpha commenced trading and competed with the TSX by offering lower fees and new trading
technology. The TSX improved its technology and reduced its fees in response. HFTs are the algorithmic traders most
sensitive to exchange technology and lower trading fees are thought to have increased their activities dramatically
during this period. While the regulator data does not include the dates surrounding Chi-X’s entry, we examine price
discovery in the post-entry period where trade-related price discovery is greatly diminished and HFTs are very active.
2
2
individually more informative and are roughly twice as prevalent as non-HFTs’ limit orders.
Therefore, HFTs’ limit orders are the primary channel through which price discovery occurs.
We examine price discovery using three approaches: i) a standard vector autoregression
(VAR; Hasbrouck, 1991a) that incorporates limit order activity, ii) the frequency of order types
that move prices (Biais, Hillion, and Spatt, 1995) by HFTs and non-HFTs; and iii) information
shares (Hasbrouck, 1995) based on best limit orders by HFTs and non-HFTs. The VAR shows
that HFTs’ predominant role in price discovery stems from their new orders being more
informative and from their greater activity at the best prices. The frequency of order type
analysis provides an intuitive non-parametric confirmation of these results. For example, only
eight percent of price changes occur following trades. The VAR and frequency results also show
that HFTs react more to trading by non-HFTs than the reverse. The information shares show
that HFTs’ limit orders contribute more to price discovery than non-HFTs’ limit orders. Because
the information shares are estimated at a 1 second frequency, they also show that HFTs role in
price discovery is not primarily due to tiny differences in speed.
Finally, we examine HFTs’ activity and price discovery on each exchange and across
exchanges. As in the market-wide results, HFTs are the predominant channel of price discovery
on each exchange through their limit orders. HFTs react to information across exchanges more
than non-HFTs and faster than non-HFTs. Significant price discovery occurs within the same
second across exchanges with HFTs’ limit orders being primarily responsible.
II.
Literature Review
This paper contributes directly to the literature on high frequency trading. HFTs are
generally defined as technologically sophisticated short-horizon trades who hold low inventory,
use many orders, and make frequent small trades throughout the day. Jones (2013), Biais and
Woolley (2011), and Biais and Foucault (2014) provide an overview of this literature. Brogaard,
Hendershott, and Riordan (2014) and others use 2008-2009 data from NASDAQ that identifies
3
HFTs’ trades and show these trades impound information into prices.4 Our data allows us to
identify the HFTs ourselves without needing the exchanges to do so. We also show HFTs’ trades
are informative, but we find that HFTs’ limit orders play an even greater role in price discovery.
A number of theoretical papers examine how fast traders like HFTs can adversely select
slower traders. For example, Foucault, Hombert, and Rosu (2014), Biais, Foucault, and Moinas
(2014), and Budish, Cramton, and Shim (2014) examine how some traders trading faster on
public signals increases information asymmetry. Our results lend support to these concerns, but
suggest they play a relatively small role in overall price discovery. Jovanovic and Menkveld
(2015) show an equilibrium response to HFTs’ ability to react faster and better process
information is for other investors to not use limit orders. This leads to HFTs incorporating most
information through their limits order, which reduces measured information asymmetry
associated with trading. However, non-HFTs placing fewer limit orders can lead to “excess”
intermediation by HFTs.
Empirically, technological changes have been used to examine how speed and fast trading
impact markets. Hendershott, Jones, and Menkveld (2011) and Boehmer, Fong, and Wu (2012)
show how algorithmic trading improves liquidity on the New York Stock Exchange and
internationally.5 These technological changes have enabled new trading venues to compete with
existing exchanges. A growing body of literature analyzes the effects of market fragmentation on
liquidity and price discovery.6
Using the same NASDAQ Carrion (2013) also show that HFTs’ trades are more informative than non-HFTs’ trades.
Hirschey (2012) uses more detailed data from NASDAQ that identifies trading by individual HFTs and finds that
HFTs’ aggressive trades predicts subsequent non-HFTs’ liquidity demand.
5 Gai, Yao, and Ye (2014) find that technological improvements at the NASDAQ are associated with decreasing depth.
Menkveld and Zoican (2014) show that a new trading system introduced at NASDAQ OMX in 2010 increases spreads
due to faster HFTs picking off slower HFTs. Brogaard, Hagströmer, Norden, and Riordan (2014) use a colocation
upgrade at NASDAQ OMX Stockholm to find that HFTs’ supplying liquidity are able to utilize the upgrade to improve
liquidity. Malinova, Park, and Riordan (2013) use the introduction of a message fee on the Toronto Stock Exchange
to show that HFTs’ liquidity supplying orders are positively related to liquidity. Menkveld (2013) shows how the entry
of one liquidity-supplying HFT improves liquidity in Dutch stocks.
6 Papers examine competition in the U.S. from ECNs (see, for example, Barclay, Christie, Harris, Kandel, and van
Ness (1999), Weston (2000), Huang (2002), and Barclay, Hendershott, and McCormick (2003)). In Europe
fragmentation and competition followed the introduction of MiFID (see Hengelbrock and Theissen (2009), Degryse,
de Jong, and van Kervel (2011), and others).
4
4
The question of how to ensure market integration when trading fragments remains an
important research question. Battalio, Hatch, and Jennings (2004) analyze quote and execution
quality of multiple listed U.S. equity options and conclude that competition between trading
venues, improved technology, and the threat of increased regulation can integrate platforms
without a formal linkage.7 Stoll (2001) hypothesizes an informal linking of fragmented markets
without formal regulated linkages. He envisions integration through the routing decisions of
brokers and dealers. While the basic thrust of Stoll’s analysis is prescient, the role of new types
of market participants such as HFTs was not explicitly anticipated.
III.
Data and Institutional Details
Data is provided by the Investment Industry Regulatory Organization of Canada (IIROC).
The data include every order submitted on recognized equity markets in Canada. The data
include masked market IDs, masked participant IDs, security IDs, date and timestamp to the
millisecond, order type, order volume, and a buy/sell indicator.8 Importantly the data identifies
activities across exchanges as the anonymous IDs remain constant across days, securities, and
markets.
a. Trading Landscape
Canada has a number of equity markets upon which trading is organized. We identify 9 in
total and present summary statistics on the 3 largest exchanges.9 Trading on these 3 exchanges
makes up more than 98% of the total trading volume.
7
In contrast, Foucault and Menkveld (2008) find that the lack of formal market linkages discourages liquidity supply.
The data are structured similar to the NASDAQ ITCH. They contain every message sent by each participant to the
exchange. The messages include the initial order, cancels, and amendments to the order. As in the U.S. there are a
number of different order types, such as hidden orders and immediate or cancel (IOC) orders, which are flagged in
the data. We exclude hidden limit orders from the order book construction. IOC orders are included as an order and
cancel if they are not executed, and a trade if they are filled. IIROC receive data with homogenized fields from each
exchange in a format that allows for cross-platform integration. Specifically, exchange data must follow the Financial
Information Exchange (FIX) protocol (http://www.fixtradingcommunity.org/). Any deviation from the FIX
implementation must be approved by IIROC with a regulatory feed compliant solution. The data are timestamped by
each exchange. The exchanges are required to synchronize their clocks with IIROC, which follows the National
Research Council Cesium Clock.
9 See http://www.iiroc.ca/industry/marketmonitoringanalysis/Documents/SumCompEquityMarkets_en.pdf for an
overview of marketplaces as of June 1st, 2015.
8
5
Markets in Canada are organized similarly to United States markets with electronic limit
order books observing price-time-display priority. Orders in Canada are protected via order
protections rules (OPR).10 OPR apply to marketplaces that provide “automated functionality”.
Automated functionality includes the ability to immediately and automatically accept incoming
orders, execute those orders and cancel any unexecuted portion of those orders marked as
immediate-or-cancel as well as automatically display and update the status of each participants’
orders. OPR only apply to visible orders and the visible parts of orders. The OPR requires
marketplaces to implement rules to prevent trade-throughs “or executing before, immediately
accessible, visible, better-priced limit orders.”
In contrast to Regulation NMS in the United States Canadian Markets implement a full
depth-of-book protection. This means that before an order is executed at marketplaces must
ensure that all protected orders that are visible at better price levels have been executed.
Canadian regulations also impose best execution obligations on brokers. These regulations
require dealers and advisors “to execute a trade on the most advantageous terms reasonably
available under the circumstances when acting for a client.” See Korajczyk and Murphy (2014)
for additional institutional details.
The Canadian market has seen a dramatic increase in competition for investor order-flow
since 2008. In May of 2007 a consortium of Canada’s largest banks announced a trading
platform designed to compete with the TSX, called Alpha Trading Systems. Shortly thereafter in
December of 2007 Chi-X announced their intention to commence trading in selected Canadian
stocks on February 20th, 2008. Both Alpha and Chi-X planned to offer new trading technology
and lower trading fees than the incumbent TSX. In response TSX rolled out new trading
technology to all TSX-listed stocks in a staggered fashion (TSX Quantum) in the first half of
10
http://www.osc.gov.on.ca/en/Marketplaces_order-protection_index.htm
6
2008.11 Chi-X commenced trading in Canada as planned and Alpha commenced trading in
December of 2008.
Both Chi-X and Alpha introduced new trading technologies, innovative order types and new
fee models. The increased competition lead to a dramatic decrease in the TSX market share
falling from close to 100% in early 2008 to less than 65% in 2009. During 2006-2010 the TSX
transaction fees fell by 80% and they implemented an electronic liquidity supplier fee rebate
program designed to attract US-Based HFTs.12 In 2012 TSX’s parent company, the Maple
Group, purchased Alpha and now operates Alpha as a separate exchange within the TMX group
of exchanges.
b. Sample
We restrict our sample to the 15 securities that are part of the TSX 60, the primary
Canadian equity index, at the end of 2014 that are not cross-listed in the United States. The
other 45 stocks in the index are cross-listed. We exclude cross listed stocks as we are unable to
observe as precisely measure trading occurring off Canadian exchanges. In addition, crosslisted stocks may have different market making properties (Bacidore and Sofianos, 2002). Table
1 reports descriptive statistics for the stocks in our sample: market capitalization, share price,
trade size, number of trades, number of shares traded, dollar volume traded, national best bid
and offer (NBBO) quoted half-spread, %HFT, %HFT demand, %HFT supply and the standard
deviation of prices. Market capitalization is the January 31, 2012 market capitalization collected
from Datastream, all other variables are reported as stock day averages for the sample period,
from 10/15/2012 to 06/28/2013, using the IIROC data. Table 1 includes activities from all
exchanges, whereas the remaining tables only include observations from the three largest
exchanges.
11
See page 17 of the TSX Annual Report http://www.tmx.com/resource/en/77
See http://www.banqueducanada.ca/wp-content/uploads/2013/11/boc-review-autumn13-garriott.pdf
for more details on fragmentation in Canada equity markets.
12
7
INSERT TABLE 1 ABOUT HERE
The firms in our sample are relatively large. Market capitalization ranges from $1.95 Billion
CAD to more than $28 Billion CAD. Share prices are relatively similar, between $20 and $72,
with the exception of Bombardier with a price of $4.00. The stocks in our sample are actively
traded with between $11.84 (million) and $70.97 (million) traded per stock day. The stocks in
our sample are relatively liquid with quoted half-spreads between 1.38 and 12.64 basis points.
c. HFT Identification
We identify HFT using the following criteria, using a similar methodology to Kirilenko et al.
(2011) using CFTC data:
(a) Make up more than .25% of trading volume;
(b) Have an end of day inventory of less than 20% of their trading volume; and
(c) Never hold more than 30% of their trading volume at one time within the trading day.
In total we identify 61 HFT IDs from a total 1706 IDs in the Canadian market. The average HFT
is more active in terms of quotes, trades, shares and volume traded, and has a higher order to
trade ratio. Overall HFTs hold less inventory throughout and at the end of the trading day. HFTs
hold considerably less inventory than their trading would imply. Their end-of-day inventory is
roughly 10% of their traded volume versus 66% for non-HFTs.
Table 1 shows HFT participation varies across the sample of stocks ranging from 12.1% to
30.1%. HFT liquidity demand and supply participation are also not evenly distributed ranging
from 11.4% and 23.0% for demand and 9.5% and 40.6% for supply. HFTs generally supply more
liquidity than they demand in our sample.
Table 2 reports statistics on HFT and non-HFT participants. HFTs on average submit 15
times as many orders (4,450 versus 290) and trade six times more often (239 versus 41) than do
non-HFTs. This leads to HFTs having an order to trade ratio more than twice that of the non8
HFTs (64 versus 27). HFTs’ average trade size is less than one sixth the size of non-HFTs’ trades
($5,664 versus $37,532).
INSERT TABLE 2 ABOUT HERE
We also compile inventory statistics to better understand how HFT and non-HFT manage
their inventory.13 We report the absolute value of the end-of-day inventory / dollar volume
traded for that stock on that day, the absolute value of the maximum inventory observed / dollar
volume traded for that stock on that day, and the number of days where the absolute value of the
end-of-day inventory / dollar volume traded is below 3%. For all inventory statistics HFTs hold
less inventory, relative to their trading volume at the end-of-day 10.68% versus 69.82% and at
their intraday maximum 17.99% versus 79.63%. HFTs’ inventories are consistent with short-run
speculators closely managing risk.
To begin the examination of overall activities by HFTs and non-HFTs Table 3 reports the
frequency of orders broken down by participant type and order type/aggressiveness. Limit
orders’ aggressiveness is determined relative to the NBBO: marketable limit order (trade), limit
order/cancel at the NBBO, limit order/cancel 1 tick behind the NBBO, and limit order/cancel > 1
tick behind the NBBO. On the average stock day 84,518 orders, including trades and
cancelations, are placed.14 Table 2 shows individual HFTs being much more active, but the
larger number of non-HFTs results in HFTs comprising about 53% of aggregate order activity.
INSERT TABLE 3 ABOUT HERE
The inventory measure assumes each ID begins each day with a zero position.
Order amendments that increase quantity or improve the price, e.g., lower the price on a buy order, are considered
new orders. Other order amendments, i.e., lower quantity or worse price, are counted as cancellations. There are 904
order amendments per stock day.
13
14
9
HFTs’ trades are roughly 0.9% of all orders whereas non-HFTs’ trades make up 3%. HFTs’
new limit orders at the NBBO are the most numerous events making up 15.6% of all orders.
HFTs’ cancellations at the best prices are the next most numerous orders at 11.9%. non-HFTs’
order submissions and cancellations are less numerous but exhibit a similar ratio of 10.0% and
6.2%. Non-HFTs are more likely to submit and cancel less aggressive orders (> 1 tick behind the
NBBO) than they are to engage in any other activity.
IV.
Market-wide Price Discovery
Figure 1 demonstrates how price discovery and adverse selection change due to trading
change over time on Canadian stock exchanges. The IIROC sample period follows the dramatic
decline in trade-related adverse selection. To investigate how the different orders impact the
evolution of price discovery shown in Figure 1 we use Fleming, Mizrach, and Nguyen’s (2015)
extension of Hasbrouck (1991a). The approaches incorporate trades and limit order activity,
both submissions and cancelations, at various price levels into the standard price discovery
VAR. We extend it further by separating HFTs’ and non-HFTs’ activity. The VAR model is:
5
5
∑ 𝛼𝑖1 𝑟𝑡−𝑖
𝑖=1
𝑟𝑡 =
+
5
𝑋𝑡1
=
5
+
1
∑ 𝛽𝑖2,1 𝑋𝑡−𝑖
𝑖=1
+
1
∑ 𝛽𝑖3,1 𝑋𝑡−𝑖
𝑖=1
+
2
∑ 𝛽𝑖2,2 𝑋𝑡−𝑖
𝑖=1
5
14
+ ⋯ + ∑ 𝛽𝑖2,14 𝑋𝑡−𝑖
+ 𝜇𝑡2
𝑖=1
+
2
∑ 𝛽𝑖3,2 𝑋𝑡−𝑖
𝑖=1
5
14
+ ⋯ + ∑ 𝛽𝑖3,14 𝑋𝑡−𝑖
+ 𝜇𝑡3
𝑖=1
⋮
5
=
𝑖=0
5
⋮ =
𝑋𝑡14
14
+ ⋯ + ∑ 𝛽𝑖1,14 𝑋𝑡−𝑖
+ 𝜇1𝑡
5
5
∑ 𝛼𝑖3 𝑟𝑡−𝑖
𝑖=1
5
2
+ ∑ 𝛽𝑖1,2 𝑋𝑡−𝑖
𝑖=0
5
∑ 𝛼𝑖2 𝑟𝑡−𝑖
𝑖=1
5
𝑋𝑡2 =
1
∑ 𝛽𝑖1,1 𝑋𝑡−𝑖
𝑖=0
∑ 𝛼𝑖15 𝑟𝑡−𝑖
𝑖=1
5
+
1
∑ 𝛽𝑖15,1 𝑋𝑡−𝑖
𝑖=1
5
+
2
∑ 𝛽𝑖15,2 𝑋𝑡−𝑖
𝑖=1
10
5
14
+ ⋯ + ∑ 𝛽𝑖15,14 𝑋𝑡−𝑖
+ 𝜇15
𝑡
𝑖=1
where 𝛼 captures the coefficient on the midpoint return series, r, lagged 1 – 5 periods; 𝛽
captures the coefficient on the 14 limit order and trade variables, 𝑋1 − 𝑋14 . Note the return
equation includes the contemporaneous and five lag values of the limit order and trade
variables, whereas the remaining VAR regressions only include the five lagged values.
The VAR is in event time, t, with each order being an observation. X contains 14
variables: HFT Trade, HFT Order, HFT Cancel, HFT Order 1 tick from NBBO, HFT Cancel 1
tick from NBBO, HFT Order > 1 tick from NBBO, HFT Cancel > 1 tick from NBBO, non-HFT
Trade, non-HFT Order, non-HFT Cancel, non-HFT Order 1 tick from NBBO, non-HFT Cancel 1
tick from NBBO, non-HFT Order > 1 tick from NBBO, and non-HFT Cancel > 1 tick from
NBBO. “HFT” named variables captures activity by HFT firms, and “non-HFT” named variables
capture activity by non-HFT firms. Trade takes the value +1 for buy initiated trades, -1 for sell
initiated trades, and 0 otherwise. Order takes +1 for bids placed at the NBB, -1 for offers placed
at the NBO, and 0 otherwise. Order 1 tick from NBBO take +1 for bids placed at one cent from
the NBB, -1 for offers placed at one cent from the NBO, and 0 otherwise. Order > 1 tick from
NBBO take +1 for bids placed greater than one cent from the NBB, -1 for offers placed at greater
than one cent from the NBO, and 0 otherwise. For cancels the analogous definition applies with
the sign such that cancels at the bid take the value +1 and cancels at the offer take the value -1.
We assume the trading process restarts each day, resetting all lagged values to zero.
The observations include all displayed orders between 9:45 a.m. EST and 3:45 p.m. EST.
To be included a stock-day must have at least 20 orders in each variable on each exchange. This
eliminates 1,302 stock-days. The IRF is orthogonalized and order independent and reports the
forecasted midpoint return, in basis points, after a +1 (buy event for orders and trades, sell event
for cancels). The innovation is cumulative over 20 events. The model is calculated for each stock
day and the average IRF reported. For HFT and non-HFT. a *, ** next to the coefficient
represents that the coefficient differs from zero and is statistically significant at the 5 and 1%
11
level, respectively using standard errors clustered by stock and by day. In the Difference column
*, ** next to the coefficient represents that the HFT and non-HFT coefficients differs from each
other with statistical significance at the 5 and 1% level, respectively using standard errors
clustered by stock and by day.
To obtain the impulse response function we invert the VAR into its vector moving average
representation. We calculate the impulse response functions (IRFs) for an unexpected buy order
and measure its impact on returns. The IRFs measure all types of orders’ price impact, often
referred to as the contribution to price discovery or information content. The VAR is estimated
for each stock each day. The averages of these stock-day IRF estimates are reported in basis
points. Throughout the paper statistical significance is clustered by stock and day to control for
contemporaneous correlation across stocks and autocorrelation within stocks as in Thompson
(2011).
INSERT TABLE 4 ABOUT HERE
Table 4 shows that an HFT trade moves the efficient price 0.855 basis points. Despite Table
2 showing that HFTs’ trades are less than one sixth the size of non-HFTs’ trades, non-HFT
trades move price by less than half as much, 0.387 basis points. HFTs’ new limit orders at the
NBBO move price 0.316 basis points and non-HFT’s move price 0.220 basis points. The price
impact of non-marketable limit orders is smaller than that of trades, but Table 3 shows there are
five times as many non-marketable limit orders as trades. In addition, HFTs’ limit orders are
almost twice as numerous as non-HFTs’ orders. Thus, limit order submissions primarily by
HFTs are the predominant source of innovations in the efficient price.
Cancelations of limit orders at the NBBO are also information with HFTs’ and non-HFTs’
cancels both moving price by about 0.17 basis points. This price impact is smaller than that of
new limit orders at the NBBO. Limit order submissions and cancels at one or more price levels
12
away from the NBBO have much smaller price impacts that are often not statistically
significantly different from zero. For ease of exposition and because orders outside the NBBO
have little price impact the remainder of the paper focuses only on trades and orders/cancels at
the NBBO.
The VAR estimates used in Table 4 also generate IRFs for how innovations in buy and sell
orders affect the direction of subsequent buy and sell orders within and across order type and
participant type. These IRFs provide evidence on how HFTs and non-HFTs react to different
market events with different order types. As in Table 4, Table 5 reports the average of stock-day
IRF estimates.
INSERT TABLE 5 ABOUT HERE
The rows in Table 5 correspond to the order variable being shocked by one unit. The
columns denote the responses of the subsequent order variables. Therefore, the HFT trade row
provides IRF estimates for how all the HFT and non-HFT order types response to an HFT buy
trade. The 0.114 IRF for HFT trade following an HFT trade shows that 0.114 more HFT buy
trades than sell trades follow an HFT buy trade. Such positive autocorrelation can arise from
HFTs splitting their orders, from HFTs copying other HFTs, or from HFTs reacting to common
information. Similarly, the 0.245 IRF for HFT NBBO order following an HFT trade shows that
0.245 more HFT buy limit orders than sell limit orders follow an HFT buy trade. The 0.091 IRF
for HFT NBBO cancel following an HFT trade shows that 0.091 more HFT sell limit orders are
cancelled than buy limit orders are cancelled following an HFT buy trade. These two limit order
results are consistent with models where trades have a price impact for either informational or
inventory reasons. The price impact occurs through new orders in the same direction improving
the NBBO and orders being cancelled in the opposite direction.
13
All the coefficients in Table 5 indicate positive auto and cross correlations in order direction.
Both HFTs and non-HFTs respond more to activity by the same participant type than the other
participant type, i.e., HFTs respond to more HFTs than to non-HFTs and non-HFTs respond
more to non-HFTs than to HFTs. Summing the IRFs in each column provides a measure of how
responsive that order type is to prior market activity. By this measure HFTs respond more to
activity than non-HFTs, primarily through HFTs’ new limit orders. Furthermore, HFTs respond
more to non-HFTs than non-HFTs respond to HFTs. Overall, Table 5 shows HFTs monitoring
market activities and reacting to them. This is consistent with HFTs deriving information from
market data.
The VAR/IRF results reported in Tables 4-5 model market dynamics in a straightforward
linear way. O’Hara (2015) argues that traders’ algorithms make the linear VAR structure
inadequate in the modern market environment. However, absent non-linear theoretical models
it is difficult to formulate a better specification. Therefore, we follow Biais, Hillion, and Spatt’s
(1995) straightforward non-parametric approach of simply examining the frequencies of
different sequences of orders. Panel A of Table 6 presents stock-day averages of frequencies for
trades, new orders, and cancelled orders. Similar to Hendershott and Riordan (2013) we
separately analyze HFTs and non-HFTs. The frequencies represent the conditional probability
of each order type (the column) conditional on the prior order type (the row). Thus, the
frequencies within each row sum to 100 percent. Below the column frequencies are the
unconditional probabilities of each order. Frequencies for buy and sell orders are symmetric in
that buys following buys are similar to sells following sells and sells following buys is similar to
buys following sells. Therefore, to reduce dimensionality the rows in Table 6 aggregate buy and
sell orders. The columns in Table 6 are labeled same-side and opposite-side representing
whether or not the second order is in the same or opposite direction as the preceding order.
INSERT TABLE 6 ABOUT HERE
14
Consistent with Table 5, Table 6 shows a diagonal effect in that participants’ orders are likely
to be followed by the same type of participant order. Table 5 focuses on the imbalance between
buy and sell order occurrences after new orders. Table 6 provides the absolute magnitude of
activity for each order type. After HFTs’ trades 87% of the next orders are also by HFTs with
78% being in the same direction as the trade. After an HFT new limit order or cancel 74% of the
next orders are by HFTs. For non-HFTs’ trades and orders about 60% of the next orders are by
non-HFTs. Consistent with the autocorrelation in the direction of orders in Table 5, new limit
orders in the same direction by the same participant type are more likely than orders in the
opposite direction, and cancels in the opposite direction are more likely. This is consistent with
lagged price discovery as trades and orders lead to subsequent activity moving prices in the
same direction.
Panel B of Table 6 examines the subset of order sequences where the second order results in
a NBBO change. About 12 percent of the order sequences in Panel A lead to NBBO changes.
Panel B shows how order activity and sequences more directly related to price discovery differ
from other activity. The unconditional probabilities show how often different orders cause
NBBO changes. Consistent with price discovery correlated with trading being small as in Figure
1, only 8.1% of NBBO changes occur due to trades, corresponding to roughly 400 trades per
stock-day. Consistent with the HFTs’ trades and orders having a higher price impact in Table 4,
comparing the unconditional frequencies between Panels A and B shows that a higher
proportion of HFTs’ trades and new orders lead to price changes than the proportion for nonHFTs. The two most frequent conditional series of orders are HFT and nHFT trades followed by
an HFT order in the same direction, 45.1% and 38.6%, respectively.
Tables 4-6 show that HFTs’ new limit orders are the primary channel for price discovery.
The analyses are in event time which does not account for possibly very small time differences in
between when HFTs and non-HFTs incorporate new information. For example, if a public
15
information event, e.g., the S&P 500 futures contract price going, up leads to both HFTs’ and
non-HFTs’ buy limit orders with HFTs being slightly faster, event time analysis will attribute all
price discovery to HFTs. A standard approach to price discovery in calendar time is Hasbrouck’s
(1995) information shares. Mostly commonly this is done by different examining quotes in
different markets for the same security, e.g., Huang (2000). This can be directly extended to the
best quotes by different market participants. The information shares approach decomposes
variation in the common efficient price into individual components attributable to specific
markets or participants.
The information share methodology focuses on innovation in different groups’ prices (quote
midpoints). The information share of a group is measured as that group’s contribution to the
total variance of the common (random-walk) component. We calculate the price path for each
group (HFT/nHFT or Exchange); denote the price vector pt representing the prevailing prices
for each group i as 𝑝𝑡𝑖 = 𝑚𝑡 + 𝜖𝑡𝑖 . The prices are assumed covariance stationary. The common
efficient price path is the random walk process, mt = mt 1  u t where 𝐸(𝑢𝑡 ) = 0, 𝐸(𝑢2 𝑡) = 𝜎𝑢2 ,
and 𝐸(𝑢𝑡 𝑢𝑠 ) = 0. For 𝑡 ≠ 𝑠. The price process vector can be modeled as a VMA:
p t =  t   1 t 1   2  t  2  ,
where 𝜖 is a vector of innovations with a zero mean and a variance matrix of Ω. Ψ represents the
polynomial in the lag operator. The information share is:
𝐼𝑛𝑓𝑜𝑠ℎ𝑎𝑟𝑒𝑗 =
Ψ𝑗2 Ω𝑗
ΨΩΨ′
InfoSharej is interpreted as the fraction of price discovery attributable to participant j; the
numerator is the variance of the efficient price attributable to participant j; and the denominator
is total variance of the efficient price. As discussed in Hasbrouck (1995) when multiple series
move at the same time the information share cannot be uniquely attributed to either series. In
16
our setting this occurs if both the HFT and non-HFT prices move at the same time. The
information shares are typically estimated at a fixed sampling frequency. Higher sampling
frequencies allow for price discovery to be more uniquely attributed to HFTs and non-HFTs, but
also attribute price discovery occurring close together to the faster participant group,
presumably HFTs. To balance this tradeoff we estimate information shares at a one second
frequency.
Table 7 reports the information shares for HFTs and non-HFTs. As with the VARs in Tables
4-5, information shares are estimated for each stock each day. Table 7 provides the average
maximum and minimum information shares. Table 7 reports whether the average minimum
HFT information share is statistically significantly greater than the average maximum non-HFT
information share. Testing the minimum HFT against the maximum non-HFT shows whether
the HFT limit order price discovery results in Tables 4-6 are due to HFTs updating the quotes
slightly faster than non-HFTs.
INSERT TABLE 7 ABOUT HERE
Table 7 shows that the average 60 percent minimum information share for HFTs is greater
than the 40 percent maximum value for non-HFT. This demonstrates that even with
conservative timing assumptions HFT limit order activity contributes more to price discovery
than non-HFT activity. The HFT maximum information share attributes all the common
innovations in price discovery within the same second to HFTs and shows HFTs providing 82
percent of price discovery. Thus, 22 percent of the price discovery occurs within the same
second for HFTs and non-HFTs.
17
V.
Activity and Price Discovery within and across Markets
The market-wide price discovery analysis in Tables 4-7 shows that HFTs’ limit orders are the
primary channel through which price discovery occurs. Figure 1 shows that limit order activity
becomes much more important after trading fragments away from the traditional primary
exchange. This section studies whether HFTs’ role in price discovery is concentrated on the new
exchanges or is similar across the three largest exchanges. We extend Tables 4-7 to examine how
HFTs and non-HFT respond to trading and orders within and across markets.
Table 8 reports overall and by exchange statistics for each of the three exchanges: shares
traded, dollar volume traded, % of dollar volume traded, %HFT Demand, %HFT supply, and
%HFT, the quoted half-spread, % of time at both NBBO, % of time at either NBB or NBO, % of
time at neither NBBO, and % of time with no bid or offer.15 Exchange 2 is the dominant
exchange in terms of trading volume making up more than 63.0% in our sample stocks.
Exchange 2 also quotes the lowest spreads, 4.06 basis points versus 8.29 and 7.83, and quotes at
the NBBO more, 86.8% versus 38.5% and 40.3%. The fraction of trading by HFTs varies across
exchanges. HFTs make up roughly 18.6% of the trading volume on exchange 2 and 28.8% and
29.9% on exchanges 1 and 3. HFTs supply (demand) 45.3% (14.4%) of liquidity on exchange 3
and only 34.6% (23.1%) and 17.6% (19.6%) on exchanges 1 and 2.
INSERT TABLE 8 ABOUT HERE
Table 9 decomposes the order activity by participant type and order type relative to the
NBBO in Table 4 for each exchange. Most activity is concentrated at the best bid and offer (BBO)
across all three exchanges. Relative HFT activity varies some across exchanges. HFT are most
active on exchange 3 and least active on the highest volume exchange, exchange 2. Non-HFTs
submit and cancel orders more behind the NBBO than they submit and cancel at the NBBO on
The overall numbers in Table 8 are slightly less than Table 1 because Table 1 includes all exchanges while Table 8
only includes the three largest exchanges.
15
18
all three exchanges. This is striking on exchange 2 where non-HFTs are almost three times as
likely to submit an order > 1 tick behind the NBBO than are HFTs. Non-HFT are more likely to
submit an order more than 1 tick behind the best available prices than they are at the best and 1
tick behind together. Overall, while HFT and non-HFT activity differs across exchanges, the
basic qualitative patterns of where activity occurs in Table 4 hold on each of the individual
exchanges.
INSERT TABLE 9 ABOUT HERE
Table 10 extends the VAR in Tables 4-5 to allow order activity by HFTs and non-HFTs on the
different exchanges to have different impacts. This is done by indexing all trade and order
variables by exchange. The return variable continues to be the NBBO return. Thus, there are 7
order variables on each of the three exchanges for both HFTs and non-HFTs, making the system
have 43 equations and variables. As in Table 4, Table 10 reports the IRFs of returns on shocks to
the different order variables. As in Table 5 we only report the subset of coefficients capturing
activity at the top of the limit order book: trades, orders submissions at the NBBO, and cancels
at the NBBO. As before we estimate the VAR for each stock each day and report stock-day
averages.
INSERT TABLE 10 ABOUT HERE
The return IRFs in Table 10 show that the basic patterns in Table 4 hold across all three
exchanges. HFTs’ trades and new orders have larger price impact than non-HFTs on all three
exchanges. The price impacts of cancels are similar on exchanges 1 and 2, but on exchange 3
HFTs’ cancels have a larger price impact. The price impact of trades is noticeably lower on
exchange 1. Among the largest marketplaces in Canada some cater to specific clientele, such as
19
retail traders. The lower price impacts on exchange 1 could be due to a more retail-focused
clientele and the associated weaker trade-based price discovery of this group (Jones and Lipson
2005). The return IRFs in Table 10 suggest that the overall pattern of price discovery shown in
Figure 1 is not directly driven by the new exchanges, as it appears consistent across exchanges.
Table 11 provides the trade and order IRFs from the VAR used in Table 10. Thus, Table 11
relates to Table 10 in a similar way that Table 5 relates to Table 4. To avoid presenting all the
possible cross exchange IRFs we group together IRFs for same and other exchanges. The same
exchange IRFs are the across exchange average response of each variable to the variables on that
exchange. For example, the same exchange HFT trade response to an HFT trade is the average
of the IRFs for an HFT trade on exchange 1 response to an HFT trade on exchange 1, an HFT
trade on exchange 2 response to an HFT trade on exchange 2, and an HFT trade on exchange 3
response to an HFT trade on exchange 3. The other exchange IRFs is the across exchange
average response of each variable to the variables on other exchanges. For example, the other
exchange HFT trade response to an HFT trade is the average of the IRFs for an HFT trade on
exchange 1 response to an HFT trade on exchanges 2 and 3, an HFT trade on exchange 2
response to an HFT trade on exchanges 1 and 3, and an HFT trade on exchange 3 response to an
HFT trade on exchanges 1 and 2.
INSERT TABLE 11 ABOUT HERE
The IRFs in Table 11 provide insight into whether the autocorrelations and cross-correlation
patterns in Table 5 are driven by HFTs and non-HFTs responding to trades and order within
each exchange or whether activity is integrated across exchanges. As in Table 5, all the
coefficients in Table 11 indicate positive auto and cross correlations in order direction. In
addition, Table 11 shows this is true both within and across exchanges. The other results from
Table 5 hold both within and across exchanges: both HFTs and non-HFTs respond more to
20
activity by the same participant type than the other participant type; HFTs respond more to
activity than non-HFTs, primarily through HFTs’ new limit orders; HFTs respond more to nonHFTs than non-HFTs respond to HFTs. Table 11 shows that these responses are larger within
exchange than on any other individual exchange. However, because the other exchange IRFs are
the averages of twice as many IRFs as the within exchange IRFs, the aggregate other exchange
responses are almost as large as the same exchange response. Overall, Table 11 suggests that
HFTs monitor and react to cross market activities more strongly than non-HFTs.16
Table 12 extends the aggregate information share price discovery analysis in Table 7 to
incorporate prices from the different exchanges. Panel A calculates information shares by
exchange. All exchanges contribute to price discovery. While exchange 1 has higher information
shares, its minimum information is only 0.29. The wide gap between the maximum and
minimum exchange information shares suggests that price discovery is well integrated across
markets as significant common price discovery occurs across exchanges within one second.
INSERT TABLE 12 ABOUT HERE
For each exchange separately Panel B of Table 12 calculates HFT/non-HFT information
shares as in Table 7. On all exchanges the minimum information share for HFT is greater the
maximum information share than for non-HFT and these differences are statistically significant.
HFT dominates price discovery more on the smaller exchanges where the HFT minimum is
more than three times the non-HFT maximum. Not surprisingly, Table 8 shows that HFTs
supply liquidity more often on these smaller exchanges. Overall, while the new exchanges attract
Similar to Table 11’s decomposition of Table 5’s results, we decompose the frequencies of different
sequences of orders from Panel A of Table 6 into sequences where both orders are on the same exchange, and
sequences where the two order are on different exchanges. We report the results in the Internet Appendix.
The results are consistent with the IRF by exchange. That is, more than 50 percent of orders sequences occur
within exchange.
16
21
more HFT trading and HFTs provide more price discovery, the primary role of HFTs limit
orders in price discovery is not limited to the new, smaller exchanges.
VI.
Information Transmission Across Markets
Table 12 shows that price discovery is integrated across markets and that HFTs play a
dominant role in price discovery on each market. Table 11 shows that HFTs have stronger crossexchange activity than non-HFTs. To link these results we next examine more directly if HFTs’
cross-exchange activity leads to integrating price discovery across exchanges. Table 6 examines
sequences where the NBBO changes. Table 13 extends this by examining order sequences where
exchanges 2 and 3 start with the same best bid or offer price and both exchanges revise their
bid/offer in the same direction. We focus on exchanges 2 and 3 in this analysis as these are the
two largest exchanges by volume.17 The initial order that causes the two exchanges to go from
the same price to different prices is referred to as the first order and the subsequent order on the
second exchange which causes its price to move is referred to as the second order. Table 13
provides insight into the sequence of orders that result in common price discovery across the
two exchanges. Unlike Table 6 the first order does not need to immediately precede the second
order.
INSERT TABLE 13 ABOUT HERE
Panel A of Table 13 reports the frequencies of order sequences where the price changes on
the two exchanges do not occur simultaneously (not in the same millisecond). Panel B reports
the subset of these sequences where a trader with the same ID is responsible for both the first
and second order. Panel C examines the order sequences where both exchanges’ prices change
in the same millisecond. Panel D provides the subset of these simultaneous price changes where
17
See the Internet Appendix for a similar analysis for exchanges 1 and 2.
22
the same trader ID is responsible for both the first and second order. Because Table 13 studies
when both exchanges’ prices move in the same direction, not all order sequences are possible.
For example, after a trade consumes all the liquidity available at the best price on one exchange
the price on the same side of the market can only change in the same direction on the other
exchange due to a trade or an order cancelation. Because there are fewer sequence possibilities
Table 13 reports joint frequencies/probabilities as opposed to the conditional frequencies in
Table 6.
Consistent with our prior results showing the importance of HFT limit orders in price
discovery, Panel A of Table 13 shows that HFTs’ trades and limit orders/cancels initiate the
sequence of price changes 68 percent of the time. Initiating the price change sequence is
naturally interpreted as the most significant component of price discovery across markets. The
most frequent sequence is an HFT order cancel followed by an HFT order with 27.1%, followed
by HFT order cancel and then an HFT order cancel with 17.7%. HFTs also provide the second
orders more often than non-HFTs suggesting that they are responsible for both within and
across market price discovery. Non-HFTs are more likely to submit the second order than they
are the first perhaps because they are slower to update their quotes than are HFTs when both
react to the common information. In this way order cancels may be related to slow adjustments
to new information. Panels B-D of Table 13, which examine sequences by the same trader and
simultaneous sequences, are consistent with Panel A. HFTs open more of the price change
sequences, primarily through their new limit order and order cancelations.
Table 14 examines the duration of the non-simultaneous price change sequences in Table 13.
Table 14 reports the mean number of seconds between the first and second orders. For the
sequences in Panel A of Table 13, Panel A of Table 14 reports the length of time of all price
sequences conditional on the trader type and order type that open and close. HFTs close faster
when the price sequence is opened by an HFT. This is true overall and for each sequence pair,
except cancel-cancel.
23
INSERT TABLE 14 ABOUT HERE
Panel B examines the price sequences where both the open and close orders are from the
same trader ID. Average durations for HFTs are shorter for non-HFTs. HFTs generally close
price sequences faster than non-HFTs. When the same market participant is responsible on both
markets the time between open and close is noticeably shorter. HFTs are faster for trades and
new orders. Somewhat surprisingly this is not the case for order cancellations, showing nonHFTs can quickly cancel orders on multiple exchanges.
The results in Tables 13 and 14 on price changes sequences across exchanges show HFTs
playing an important role in cross exchange price discovery. This is primarily through their new
limit orders and cancelations of existing limit orders. Non-HFTs’ cancelations are important in
completing the price change sequence on the second exchange. This is consistent with nonHFTs being slower than HFTs. However, non-HFTs access multiple exchanges at speeds within
tens or hundreds milliseconds of the time HFTs access multiple exchanges. Whether or not
these small differential durations between HFTs’ and non-HFTs’ orders are meaningful is an
important unanswered question. Given the much greater numbers of HFTs’ limit orders and
their larger importance in price discovery, the importance of speed differences appears less
economically significant for trades.
VII.
Conclusion
Adverse selection is traditionally measured by the correlation between trade direction and
returns. This relationship has weakened as stock exchanges have upgraded their technology and
trading has fragmented. Canadian regulatory data shows that HFTs are responsible for between
60% and 80% of price discovery, primarily through their limit orders. HFTs’ orders are both
more informed and more numerous than non-HFTs limit orders. HFTs also react more to
24
activity by non-HFTs than the reverse. HFTs react more to orders both within and across stock
exchanges [and ATSs].
Autocorrelated non-HFTs’ trading and HFTs reacting to market activity is consistent with
HFTs anticipating non-HFTs’ trading. Critics of HFTs and the modern market structure
characterize this as HFTs systematically front-running non-HFT large orders that are sliced into
smaller components. Because HFTs react similarly to both HFTs’ and non-HFTs’ orders, our
results provide little support for HFTs’ specifically targeting non-HFTs. However, HFTs reacting
to market activity in general can move prices against large non-HFTs’ orders before completion.
We find that HFTs primarily react to market activity through their limit orders so HFTs
anticipation of non-HFTs is better described as HFTs’ market making activity fully
incorporating public information than as HFTs behaving as predatory traders and quasi-frontrunning non-HFTs.
The significant contemporaneous price discovery across markets and HFTs reacting more to
orders across multiple exchanges is consistent with HFTs integrating markets. We find little
evidence that HFTs use superior technology to pick off slower non-HFTs’ limit orders, often
referred to as latency arbitrage. Our findings are most consistent with HFTs dominating limit
order book activity leading to more efficient prices and a virtually integrated limit order book.
However, it is possible that HFTs’ speed and information processing abilities discourage nonHFTs from submitting limit orders. This could lead to less direct investor-to-investor trading
and excess intermediation.
25
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27
Table 1: Descriptive Statistics. The table reports summary statistics for the 15 stocks used in this study. The 15 stocks are chosen
as they are part of the TSX 60 and not cross-listed in the United States. The statistics are calculated using data from 10/15/2012 –
06/28/2013. Name is the ticker. Mkt. Cap is the average market capitalization from Datastream, in billions of Canadian dollars.
Share Price is the average traded stock price. Trade Size is the average trade size. Number of Trades is the average number of trades,
in thousands. Number of Shares Traded is the average number of shares traded, in thousands. Dollar Volume Traded is the number
of shares traded multiplied by the stock price, in millions of dollars. NBBO Quoted Half-Spread is the calendar time weighted onehalf quoted difference between the national best bid and the national best ask price, in basis points. % HFT is the double-sided dollarvolume % of trades by a high frequency trader (HFT). % HFT Demand is the dollar-volume percent of trades in which an HFT is the
liquidity taker. % HFT Supply is the dollar-volume percent of trades in which an HFT is the liquidity provider. Std. of Daily prices is
the standard deviation of the end-of-day price for the stock. All statistics except Std. of Daily Returns is the standard deviation of the
daily return, in percent.
5.47
2.28
10.14
9.13
1.67
13.41
3.91
7.28
2.99
2.11
4.31
5.25
1.99
3.22
0.91
Number of
Shares
Traded
(thousand)
1,053.84
446.81
12,697.71
2,129.80
343.34
3,656.19
791.23
1,545.42
783.63
3.97
797.08
1,224.45
421.56
756.68
160.60
Dollar
Volume
Traded ($
million)
$26.91
$24.03
$50.42
$43.52
$25.12
$70.97
$26.52
$45.27
$33.09
$20.87
$60.71
$32.39
$20.79
$32.31
$11.84
NBBO
quoted
half-spread
(bps)
2.72
4.07
12.64
2.52
4.37
2.92
1.84
2.18
2.89
4.11
1.38
2.17
3.81
3.70
5.77
4.94
1,787.49
$34.98
3.81
Name
Mkt. Cap
($ billion)
Share
Price
Trade
Size
Number of
Trades
(thousand)
ARX
ATD.B
BBD.B
COS
CTC.A
FM
FTS
HSE
L
MRU
NA
POW
SAP
SNC
WN
$8.00
$10.03
$6.95
$9.90
$6.77
$10.95
$6.96
$28.74
$11.62
$1.95
$12.46
$12.10
$9.61
$6.45
$9.35
$25.59
$53.40
$4.00
$20.43
$72.35
$19.77
$33.63
$29.24
$41.10
$52.49
$76.46
$26.28
$48.92
$42.50
$72.98
189.70
196.94
1218.14
233.27
204.86
272.27
206.43
215.69
236.91
193.85
185.93
236.28
226.63
236.82
174.92
Average
$10.12
$41.28
281.91
28
% HFT
% HFT
Demand
% HFT
Supply
21.6%
17.4%
30.1%
24.9%
15.3%
18.4%
23.5%
24.4%
12.1%
16.1%
21.4%
23.0%
20.3%
14.4%
15.8%
15.0%
22.9%
19.5%
14.4%
19.1%
14.2%
13.9%
19.0%
11.4%
16.6%
18.7%
14.4%
23.0%
16.4%
22.2%
28.1%
12.0%
40.6%
35.4%
11.6%
22.7%
33.2%
29.8%
12.8%
15.6%
24.1%
31.6%
17.7%
12.3%
9.5%
Std. Dev.
of
Returns
(percent)
1.23
1.17
2.00
1.27
1.51
2.71
0.77
1.28
1.56
0.85
0.62
0.92
0.97
1.54
1.08
19.9%
17.4%
22.5%
1.30
Table 2: Trader Type Statistics. The table reports summary statistics for trading, orders,
and positions for individual HFT and non-HFTs. Column HFT reports stock-day-trader
averages for HFT traders, column non-HFT reports stock-day-trader for non-HFT traders.
Number of Orders is the average number of quotes, quote cancels, and quote amends a trader
conducts. Number of Trades is the average number of trades conducted by a trader. Number of
Shares Traded is the average number of shares traded by a trader. Dollar Volume (DV) Traded
is the average number of shares traded by a trader multiplied by the share price. Order to Trade
Ratio is the number of orders deployed for each trade by a trader. DV Traded / Total DV Traded
is the dollar volume traded by a trader scaled by the total dollar volume traded on that stockday. Abs(EoD Inv.) / DV Traded is the absolute value of a trader’s end of day dollar-volume
inventory scaled by that trader’s dollar-volume traded. Abs(Max Intra. Inv.)/DV Traded is the
trader’s absolute value of the maximum intraday dollar-volume inventory position scaled by that
trader’s dollar-volume traded. % of days with Abs(EoD Inv) / DV Traded < 3% is the percent of
stock-day-trader observations with the Abs(EoD Inv.) / DV Traded is less than 3%. Average DV
Trade Size is the average dollar volume size of a trade. Number of Participants is the number of
traders on the average stock-day.
Number of Orders (thousand)
Number of Trades
Number of Shares Traded (thousand)
Dollar Volume (DV) Traded ($million)
Order to Trade ratio
Number of Orders / Total Orders
DV Traded / Total DV Traded
Abs(EoD Inv) / DV Traded
Abs(Max Intra. Inv.) / DV Traded
% of days with Abs(EoD Inv)/DV Traded < 3%
Average DV Trade Size
Number of Participants
29
HFT
non-HFT
4.45
239.58
68.96
$1.03
64.74
2.81%
1.51%
10.68%
17.99%
50.21%
$5,663.56
13.06
0.29
41.05
17.44
$0.35
27.01
0.21%
0.46%
69.82%
79.63%
6.64%
$37,531.60
185.36
Table 3: Distribution of Activities. The table reports the distribution order aggressiveness
by HFTs and non-HFTs. Panel A considers all orders on the three exchanges. Total # of
Observations, Overall is the number of observations on all three exchanges on the average
stock-day. The point estimates report the percent of activity by HFT and non-HFT that are
Trades, Orders, or Order Cancels. Order captures the number of orders at that exchange’s NBB
or NBO. Order 1 tick from NBBO captures the number of orders one cent away from that
exchange’s NBB or NBO. Order > 1 tick from NBBO captures the number of orders more than
one cent away from that exchange’s NBB or NBO. For cancels the analogous definition applies.
Total # of Observations, is the number of observations on the average stock-day.
Trade
Order
Cancel
Order 1 tick from NBBO
Cancel 1 tick from NBBO
Order > 1 tick from NBBO
Cancel > 1 tick from NBBO
Total # of Observations
30
HFT
0.9%
15.3%
11.9%
5.1%
6.1%
6.5%
7.4%
84,518
nonHFT
3.0%
10.0%
6.2%
2.2%
3.4%
11.0%
11.1%
Table 4: Return Impulse Response Function. The table reports stock-day average
Impulse Response Functions (IRF) from a Vector-autoregression (VAR) with 15 equations and 5
lags. One for each of the variables listed in the table, for each HFT and non-HFT, and the
midpoint NBBO midpoint return. The VAR is in event time with each order being an
observation. Trade takes the value +1 for buy initiated trades, -1 for sell initiated trades, and 0
otherwise. Order take +1 for bids placed at the NBB, -1 for offers placed at the NBO, and 0
otherwise. Order 1 tick from NBBO take +1 for bids placed at one cent from the NBB, -1 for
offers placed at one cent from the NBO, and 0 otherwise. Order > 1 tick from NBBO take +1 for
bids placed greater than one cent from the NBB, -1 for offers placed at greater than one cent
from the NBO, and 0 otherwise. For cancels the analogous definition applies with the sign such
that cancels at the bid take the value +1 and cancels at the offer take the value -1. The
observations include all displayed orders between 9:45 a.m. EST and 3:45 p.m. EST. To be
included a stock-day must have at least 20 orders in each variable. The IRF is orthogonalized
and order independent and reports the forecasted midpoint return, in basis points, after a +1
(buy event for orders and trades, sell event for cancels). The innovation is cumulative over 20
events. For HFT and non-HFT a *, ** next to the coefficient represents that the coefficient
differs from zero and is statistical significance at the 5 and 1% level, respectively using standard
errors clustered by stock and by day. For the Difference column *, ** next to the coefficient
represents that the HFT and non-HFT coefficients differs from each other with statistical
significance at the 5 and 1% level, respectively using standard errors clustered by stock and by
day.
Trade
Order
Cancel
Order 1 tick from NBBO
Cancel 1 tick from NBBO
Order > 1 tick from NBBO
Cancel > 1 tick from NBBO
HFT
0.855**
0.316**
-0.163**
0.003*
0.001
-0.027**
-0.006**
31
non-HFT
0.387**
0.220**
-0.173**
0.016**
0.002*
-0.001
-0.003**
Difference
0.468**
0.096**
0.010
-0.013**
-0.001
-0.026**
-0.003**
Table 5: Order Impulse Response Function. The table reports stock-day average order
Impulse Response Functions (IRF) from the same Vector-autoregression (VAR) used in Table 5.
The rows represent the variable being shocked by one unit. The columns represent the variable
being affected. *, ** next to the coefficient represents that the coefficient differs from zero and is
statistical significance at the 5 and 1% level, respectively using standard errors clustered by stock
and by day.
Order HFT
Cancel HFT
Trade nonHFT
Order
non-HFT
Cancel
non-HFT
Trade HFT
Variable
Trade HFT
0.114**
0.245**
0.091**
0.005**
0.026**
0.001
Order HFT
0.010**
0.198**
0.079**
0.006**
0.051**
0.005**
Cancel HFT
0.003**
0.088**
0.1401**
0.003**
0.027**
0.023**
Trade non-HFT
0.026**
0.208**
0.022**
0.119**
0.039**
0.020**
Order non-HFT
0.004**
0.069**
0.016**
0.010**
0.135**
0.060**
Cancel nonHFT
0.001**
0.035**
0.032**
0.014**
0.096**
0.114**
32
Table 6: Order Type Conditional on Past Order Type. The table reports stock-day
average order sequence frequencies. The table reports the frequency in which the order type in
the identified in the Row is followed by the order type in the Column. Each Row sums to 100%.
Unconditional is the frequency in which the Column variable is observed in the data. The Same
Columns represent probabilities of order following each other in the same direction (e.g. buy
order followed by a buy order). Other Columns represent probabilities of orders following each
other in the opposite direction (e.g. buy order followed by a sell order). Panel A includes all
observations used in the IRFs in Tables 5 and 6. Panel B only includes observations where the
NBBO changes in time t.
Panel A: All
t
t-1
HFT Trade
HFT Order
HFT Cancel
non-HFT
Trade
non-HFT
Order
non-HFT
Cancel
Unconditional
HFT
Trade
Same
HFT
Order
Same
HFT
Cancel
Same
HFT
Trade
Other
HFT
HFT
Order Cancel
Other Other
nonHFT
Trade
Same
nonHFT
Order
Same
nonHFT
Cancel
Same
nonHFT
Trade
Other
nonHFT
Order
Other
nonHFT
Cancel
Other
31.1%
1.4%
0.9%
31.5%
32.5%
24.2%
15.2%
20.7%
24.0%
0.1%
0.2%
0.4%
3.1%
6.7%
16.7%
6.0%
12.7%
6.2%
2.1%
2.5%
1.5%
4.7%
10.9%
7.3%
1.8%
2.9%
7.4%
0.6%
1.0%
1.6%
2.3%
4.6%
6.8%
1.4%
3.9%
2.9%
2.2%
20.6%
4.6%
0.2%
3.8%
8.2%
35.9%
9.9%
7.2%
1.0%
4.0%
2.5%
0.6%
16.8%
7.9%
0.4%
5.3%
8.2%
3.6%
22.8%
18.4%
1.8%
8.0%
6.1%
0.3%
9.2%
11.5%
0.2%
9.5%
5.1%
5.2%
29.3%
14.4%
1.3%
9.8%
4.3%
1.6%
23.3%
16.5%
0.3%
9.0%
5.0%
14.8%
9.1%
1.4%
6.5%
4.0%
8.7%
Panel B: NBBO Changes in time t
t
t-1
HFT Trade
HFT Order
HFT Cancel
non-HFT
Trade
non-HFT
Order
non-HFT
Cancel
Unconditional
HFT
Trade
Same
HFT
Order
Same
HFT
Cancel
Same
HFT
Trade
Other
HFT
Order
Other
HFT
Cancel
Other
nonHFT
Trade
Same
nonHFT
Order
Same
nonHFT
Cancel
Same
nonHFT
Trade
Other
nonHFT
Order
Other
nonHFT
Cancel
Other
19.0%
3.7%
1.5%
45.1%
31.4%
31.0%
19.3%
18.2%
18.5%
0.2%
0.5%
0.6%
2.4%
7.2%
12.1%
4.6%
11.4%
4.8%
1.1%
3.8%
1.8%
2.4%
10.8%
9.7%
0.8%
2.4%
11.9%
0.8%
0.9%
1.1%
2.3%
4.3%
4.2%
1.9%
5.5%
2.9%
3.8%
38.6%
2.9%
0.4%
2.5%
4.6%
13.9%
9.7%
17.9%
1.1%
2.4%
2.2%
1.7%
21.7%
2.1%
1.3%
7.5%
7.8%
3.4%
21.6%
15.6%
1.4%
7.8%
8.2%
0.5%
17.3%
9.0%
0.5%
9.9%
4.3%
2.8%
28.0%
15.9%
1.0%
6.8%
3.9%
12.5%
0.6%
3.7%
15.0%
10.8%
1.1%
2.7% 28.2%
8.5%
7.1%
33
5.2%
4.7%
Table 7: Information Shares. The table reports the average stock-day Hasbrouck (1995)
minimum and maximum information shares for HFT and non-HFT orders/quotes. * and ** next
to the HFT-Min point estimate represents a statistically significant difference at the 5% and 1%,
respectively, between the HFT Min and the non-HFT Max point estimates, using standard errors
clustered by stock and by day.
HFT
non-HFT
Min
0.60**
0.18
34
Max
0.82
0.40
Table 8: Exchange Descriptive Statistics. The table reports summary statistics for the
exchanges. The column Overall reports the statistics summed across the three largest exchanges
in Canada. Columns Exchange 1, Exchange 2, and Exchange 3 report the statistics for each of
the three exchanges separately. Shares Traded is the number of shares traded. Dollar Volume
Traded is the number of shares traded multiplied by the share price. % of Dollar Volume
Traded is the percent of the dollar volume trading on each exchange. % HFT is the double-sided
dollar-volume % of trades by a high frequency trader (HFT). % HFT Demand is the dollarvolume percent of trades in which an HFT is the liquidity taker. % HFT Supply is the dollarvolume percent of trades in which an HFT is the liquidity provider. Quoted Half-Spread is the
calendar time weighted one-half quoted difference between the best bid and the best ask price
on each exchange. For Overall it is the calendar time weighted one-half quoted difference
between the national best bid and the national best ask price on each exchange. % of time at
both NBBO is the percent of the calendar time at which an exchange is quoting the nationally
best bid and offer. % of time at either NBB or NBO is the percent of the calendar time at which
an exchange is quoting either the national best bid or the national best offer, but not both. % of
time at neither NBBO (while quoting) is the calendar time at which an exchange is quoting but
neither its bid nor offer are at the national best. % of time with no B or O is the calendar time at
which an exchange has no quotes on at least one side of the order book.
Overall
Shares Traded (thousand)
Dollar Volume Traded ($million)
% of Dollar Volume Traded
% HFT Demand
% HFT Supply
% HFT
Quoted half-spread (bps)
% of time at both NBBO
% of time at either NBB or NBO
% of time at neither NBBO (while quoting)
% of time with no B or O
1,701.22
$32.70
18.1%
23.2%
20.7%
3.78
35
Exchange 1
271.69
$3.55
10.9%
23.1%
34.6%
28.8%
8.29
38.5%
40.9%
20.5%
0.1%
Exchange 2
1,016.64
$20.61
63.0%
19.6%
17.6%
18.6%
4.06
86.8%
12.1%
1.1%
0.0%
Exchange 3
412.90
$8.54
26.1%
14.4%
45.3%
29.9%
7.83
40.3%
38.3%
20.4%
1.1%
Table 9: Distribution of Activities by Exchange. The table reports the average stock-day
distribution of orders by HFT and non-HFT on all three exchanges. The point estimates report
the percent of activity by HFT and non-HFT that are Trades, Orders, or Order Cancels. Order
captures the number of orders at that exchange’s NBB or NBO. Order 1 tick from NBBO
captures the number of orders one cent away from that exchange’s NBB or NBO. Order > 1 tick
from NBBO captures the number of orders more than one cent away from that exchange’s NBB
or NBO. For cancels the analogous definition applies. Total # of Observations is the number of
observations on that exchange on the average stock-day.
Exchange 1
Trade
Order
Cancel
Order 1 tick from NBBO
Cancel 1 tick from NBBO
Order > 1 tick from NBBO
Cancel > 1 tick from NBBO
Total # of Observations
Exchange 2
Trade
Order
Cancel
Order 1 tick from NBBO
Cancel 1 tick from NBBO
Order > 1 tick from NBBO
Cancel > 1 tick from NBBO
Total # of Observations
Exchange 3
Trade
Order
Cancel
Order 1 tick from NBBO
Cancel 1 tick from NBBO
Order > 1 tick from NBBO
Cancel > 1 tick from NBBO
Total # of Observations
36
HFT
0.7%
13.7%
10.5%
5.1%
5.5%
4.8%
5.9%
17,670
non-HFT
2.1%
10.8%
6.8%
1.9%
3.2%
14.3%
14.7%
1.3%
13.7%
10.3%
2.8%
4.2%
3.9%
4.8%
39,316
4.2%
13.0%
7.7%
2.9%
4.3%
13.3%
13.5%
0.4%
18.5%
15.0%
8.4%
9.0%
11.4%
12.2%
27,532
1.8%
5.2%
3.7%
1.4%
2.1%
5.5%
5.5%
Table 10: Return Impulse Response Function by Exchange. The table reports stock-day average
Impulse Response Functions (IRF) from a 5-lag Vector-autoregression (VAR). The VAR is in event time
with each order being an observation. Trade takes the value +1 for buy initiated trades, -1 for sell initiated
trades, and 0 otherwise. Order +1 for bids placed at the NBB, -1 for offers placed at the NBO, and 0
otherwise. Order 1 tick from NBBO take +1 for bids placed at one cent from the NBB, -1 for offers placed
at one cent from the NBO, and 0 otherwise. Order > 1 tick from NBBO take +1 for bids placed greater than
one cent from the NBB, -1 for offers placed at greater than one cent from the NBO, and 0 otherwise. For
cancels the analogous definition applies with the sign such that cancels at the bid take the value +1 and
cancels at the offer take the value -1. Only the Trade, Order, and Cancel point estimates are reported. The
observations include all displayed orders between 9:45 a.m. EST and 3:45 p.m. EST. To be included a
stock-day must have at least 20 orders in each variable. The IRF is orthogonalized and order independent
and reports the forecasted midpoint return, in basis points, after a +1 (buy event for orders and trades,
sell event for cancels). The innovation is cumulative over 20 events. The first column reports the HFT
impulse response function (IRF), the second column the non-HFT IRF, and the third column the
difference between the HFT and non-HFT IRF. The observations are separated based on whether they
occur on Exchange 1, 2, or 3 (there are 42 order variables, 7 order types on 3 exchanges for each HFT and
non-HFT). For HFT and non-HFT a *, ** next to the coefficient represents that the coefficient differs
from zero and is statistical significance at the 5 and 1% level, respectively using standard errors clustered
by stock and by day. For the Difference column *, ** next to the coefficient represents that the HFT and
non-HFT coefficients differs from each other with statistical significance at the 5 and 1% level, respectively
using standard errors clustered by stock and by day.
Exchange 1
Trade
Order
Cancel
Exchange 2
Trade
Order
Cancel
Exchange 3
Trade
Order
Cancel
HFT
0.331**
0.255**
-0.219**
non-HFT
0.179**
0.172**
-0.237**
Difference
0.152**
0.084**
0.018
0.958**
0.372**
-0.156**
0.416**
0.239**
-0.147**
0.542**
0.134**
-0.009
0.928**
0.294**
-0.149**
0.427**
0.217**
-0.073
0.501**
0.077*
-0.076*
37
Table 11: Order Impulse Response Function by Exchange. The table reports stock-day
average Trade Impulse Response Functions (IRF) from the same vector-autoregression (VAR)
used in Table 5. The rows represent the variable being shocked by one unit. The columns
represent the variable being affected. Panel A reports the average IRFs for the same exchange
(e.g. the IRF of an Order HFT innovation on Exchange 3 on Cancel HFT on Exchange 3). Panel
B reports the average IRFs for the other exchanges (e.g. the IRF of an Order HFT innovation on
Exchange 3 on Cancel HFT on Exchanges 1 and 2). *, ** next to the coefficient represents that
the coefficient differs from zero and is statistical significance at the 5 and 1% level, respectively
using standard errors clustered by stock and by day.
Panel A: Same Exchange
Variable
Trade HFT
Order HFT
Cancel HFT
Trade non-HFT
Order non-HFT
Cancel non-HFT
Trade
HFT
Order
HFT
Cancel
HFT
Trade
non-HFT
Order
non-HFT
Cancel
non-HFT
0.056**
0.004**
0.001**
0.011**
0.001**
0.001
0.124**
0.095**
0.045**
0.094**
0.022**
0.011**
0.070**
0.057**
0.074**
0.013**
0.002**
0.009**
0.001
-0.001**
0.001**
0.054**
0.003**
0.004**
0.009**
0.012**
0.004**
0.012**
0.061**
0.056**
0.001
-0.002**
0.004**
0.015**
0.043**
0.057**
Trade
HFT
Order
HFT
Cancel
HFT
Trade
non-HFT
Order
non-HFT
Cancel
non-HFT
0.022**
0.04**
0.001**
0.006**
0.002**
0.001**
0.053**
0.048**
0.017**
0.043**
0.022**
0.011**
0.011**
0.012**
0.031**
-0.001
0.001
0.009**
0.004**
0.004**
0.001**
0.027**
0.005**
0.005**
0.010**
0.019**
0.012**
0.015**
0.046**
0.018**
0.001
0.004**
0.010**
0.002**
0.008**
0.033**
Panel B: Other Exchanges
Variable
Trade HFT
Order HFT
Cancel HFT
Trade non-HFT
Order non-HFT
Cancel non-HFT
38
Table 12: Information Shares by Exchange. The table reports the average stock-day
Hasbrouck (1995) minimum and maximum information shares for each exchange (Panel A) and
for HFT and non-HFT orders/quotes on each exchange (Panel B). * and ** next to the HFT-Min
point estimates in Panel B represent a statistically significant difference at the 5% and 1%,
respectively, between the HFT Min and the non-HFT Max point estimates, using standard errors
clustered by stock and by day.
Panel A: By Exchange
Exchange 1
Exchange 2
Exchange 3
Min
0.29
0.21
0.15
Max
0.58
0.46
0.38
Min
0.75**
0.13
Max
0.87
0.25
0.58**
0.23
0.77
0.42
0.83**
0.07
0.93
0.17
Panel B: By Exchange HFT
Exchange 1
HFT
non-HFT
Exchange 2
HFT
non-HFT
Exchange 3
HFT
non-HFT
39
Table 13: Cross Exchange Price Change Sequences. The table reports the frequencies of
price change sequences on Exchange 2 and Exchange 3. The sequences capture all events in
which Exchange 2 and Exchange 3 start with the same bid or ask price, and are followed by one
of the exchanges best bid or ask price changing, and subsequently the other exchange updating
its quote in the same direction. In Panel A and B the deviation and resolution must take at least
one millisecond. In Panel C and D the deviation and resolution occur simultaneous. The
statistics are calculated using data from 10/15/2012 – 06/28/2013. Panel A evaluates the joint
probability of a HFT/non-HFT and Trade/Order/Cancel opening a sequence and an HFT/nonHFT and Trade/Order/ Cancel subsequently updating the second exchange’s quotes. The
average stock-day has 1009 sequences that last at least 1 millisecond. Panel B repeats the joint
probability analysis for the average stock-day 164 sequences with both orders by the same
trader. Panel C repeats the joint probability analysis for the average stock-day 1106 sequences
that occur simultaneously. Panel D repeat the joint probability analysis for the average stock-day
170 sequences by the same trader that happen simultaneously.
Panel A: Conditional on Open/Close Order Type and HFT, > 1 Millisecond
Second
First
HFT
Trade
Order
Cancel
non-HFT
Trade
Order
Cancel
% Close by
TraderOrder
% Close by
Trader
Trade
HFT
Order
Trade
non-HFT
Order
Cancel
Cancel
0.7%
--2.0%
--27.1%
---
0.9%
--17.7%
0.4%
--3.8%
--9.1%
---
0.2%
--7.0%
2.2%
36.1%
30.6%
68.9%
1.0%
--0.5%
--6.9%
---
3.0%
--4.6%
2.6%
--1.5%
--5.0%
---
2.0%
--4.1%
8.6%
11.9%
10.6%
31.1%
4.2%
33.9%
26.2%
8.3%
14.1%
13.3%
64.3%
35.7%
40
Table 13 Continued
Panel B: Conditional on Open/Close Order Type and HFT by Same Trader, > 1
Millisecond
Second
HFT
First
HFT
Trade
Order
Cancel
non-HFT
Trade
Order
Cancel
% Close by
Trader-Order
% Close by
Trader
non-HFT
Trade
Order
Cancel
Trade
Order
Cancel
% Open by
TraderOrder
2.7%
--0.2%
--45.7%
---
1.0%
--14.8%
-------
-------
-------
3.8%
45.7%
15.0%
64.5%
-------
-------
-------
10.0%
--3.5%
--5.8%
---
5.2%
--10.0%
15.3%
5.8%
13.6%
34.6%
3.0%
45.7%
15.8%
13.6%
5.8%
15.3%
64.5%
% Open
by
Trader
34.6%
Panel C: Conditional on Open/Close Order Type and HFT, Simultaneous
Second
nonHFT
HFT
First
HFT
Trade
Order
Cancel
non-HFT
Trade
Order
Cancel
% by
Trader-Order
% by
Trader
Trade
Order
Cancel
Trade
Order
Cancel
% by
TraderOrder
0.7%
--2.4%
--26.1%
---
0.9%
--17.3%
0.4%
--4.5%
--8.9%
---
0.2%
--7.2%
2.1%
35.0%
31.4%
68.5%
1.0%
--0.6%
--6.9%
---
3.0%
--4.7%
2.7%
--1.7%
--5.0%
---
2.0%
--4.0%
8.6%
11.9%
10.9%
31.5%
4.6%
33.1%
25.8%
9.2%
13.8%
13.5%
63.5%
36.5%
41
% by
Trader
Table 13 Continued
Panel D: Conditional on Open/Close Order Type and HFT by Same Trader,
Simultaneous
Second
nonHFT
HFT
First
HFT
Trade
Order
Cancel
non-HFT
Trade
Order
Cancel
% by
Trader-Order
% by
Trader
Trade
Order
Cancel
Trade
Order
Cancel
% by
TraderOrder
2.7%
--1.1%
--46.2%
---
1.1%
--14.7%
-------
-------
-------
3.8%
46.2%
15.7%
65.7%
-------
-------
-------
9.9%
--5.1%
--5.8%
---
3.4%
--10.1%
13.3%
5.8%
15.2%
34.3%
3.7%
46.2%
15.8%
15.0%
5.8%
13.5%
65.7%
34.3%
42
% by
Trader
Table 14: Duration of Cross Exchange Price Change Sequences. The table reports the
average length of time, in seconds, of price change sequences on Exchange 2 and Exchange 3.
The sequences capture all events in which Exchange 2 and Exchange 3 start with the same bid or
ask price, followed by one of the exchanges best bid or ask price changing, and subsequently the
other exchange updating its quote in the same direction. The sequences must take at least one
millisecond. The average stock-day has 1009 sequences. The average durations are calculated
using data from 10/15/2012 – 06/28/2013. Panel A evaluates the joint probability of a
HFT/non-HFT and Trade/Order/ Cancel opening a sequence and an HFT/non-HFT and
Trade/Order/ Cancel subsequently updating the second exchange’s quotes. Panel B repeats the
joint probability analysis for the 164 sequences by the same trader.
Panel A: Conditional on Open/Close Order Type and HFT
Second
First
HFT
Trade
Order
Cancel
non-HFT
Trade
Order
Cancel
Trade
HFT
Order
Trade
non-HFT
Order
Cancel
Cancel
0.24
--3.49
--0.45
---
0.35
--0.84
1.02
--3.87
--1.02
---
1.23
--1.92
1.61
--3.66
--1.17
---
0.69
--1.33
1.48
--2.79
--1.19
---
1.33
--1.21
Panel B: Conditional on Open/Close Order Type and HFT by Same Trader
Second
First
HFT
Trade
Order
Cancel
non-HFT
Trade
Order
Cancel
Trade
HFT
Order
Trade
non-HFT
Order
Cancel
Cancel
0.10
--1.13
--0.26
---
0.14
--0.36
-------
-------
-------
-------
-------
-------
0.38
--0.10
--0.45
---
0.24
--0.29
43
Figure 1: The Evolution of Price Discovery. The figure reports the trade correlated price
discovery and the Herfindahl Index for trading in the Royal Bank of Canada (RBC) on the
Toronto Stock Exchange, Alpha Trading System, and Chi-X. Data is provided by SIRCA on
behalf of Thomson-Reuters from 2007 through 2014.
44
Price Discovery without Trading:
Evidence from Limit Orders*
INTERNET APPENDIX
Jonathan Brogaard
Terrence Hendershott
Ryan Riordan
First Draft: November 2014
Current Draft: August 2015
Contact: Jonathan Brogaard, Foster School of Business, University of Washington, (Email)
brogaard@uw.edu , (Tel) 206-685-7822; Terrence Hendershott, University of California – Berkeley,
Haas School of Business, (Email) hender@haas.berkeley.edu (Tel) 510-643-0619; and Ryan Riordan,
Queen’s School of Business, Queen’s University (Email) ryan.riordan@queensu.ca (Tel) 705.761.8800.
45
Table A1: Order Type Conditional on Past Order Type by Exchange. The table reports
stock-day average order frequencies. The table reports the frequency in which the order type in
the identified in the Row is followed by the order type in the Column. The Same Columns
represent probabilities of events following each other in the same direction (e.g. a buy order
followed by a buy order). Other Columns represent probabilities of orders following each other
in the opposite direction (e.g. buy order followed by a sell order). Unconditional is the frequency
in which the Column variable is observed in the data Panels A and B include all observations
used in the IRFs in Tables 11 and 12. Panel A represents probabilities of events following each
other on the same exchange. Panel B represents probabilities of event following each other on
different exchanges. Panels C and D only includes observations where the NBBO changes in
time t. Panel C represents probabilities of events following each other on the same exchange.
Panel D represents probabilities of event following each other on different exchanges. The Rows
spanning Panels A and B sums to 100%, as do Panels C and D.
Panel A: Same Exchange, All
t
HFT
HFT
Trade Order
Same Same
26.3% 17.5%
0.6% 16.0%
0.5% 17.4%
t-1
HFT Trade
HFT Order
HFT Cancel
non-HFT
Trade
non-HFT
Order
non-HFT
Cancel
Unconditional
HFT
Cancel
Same
10.1%
16.1%
10.2%
HFT
Trade
Other
0.0%
0.1%
0.2%
HFT
Order
Other
1.4%
3.3%
8.9%
HFT
Cancel
Other
2.4%
6.5%
3.2%
nonHFT
Trade
Same
0.8%
0.5%
0.4%
nonHFT
Order
Same
2.2%
3.8%
2.9%
nonHFT
Cancel
Same
0.9%
1.1%
2.6%
nonHFT
Trade
Other
0.3%
0.4%
0.5%
nonHFT
Order
Other
1.4%
1.9%
2.6%
nonHFT
Cancel
Other
0.7%
1.5%
1.3%
1.6%
11.6%
1.5%
0.1%
1.9%
3.5%
27.8%
6.2%
5.7%
0.6%
2.4%
1.3%
0.3%
7.8%
2.9%
0.3%
1.9%
3.3%
2.2%
11.1%
14.5%
1.1%
4.3%
3.2%
0.1%
2.9%
4.5%
0.1%
3.5%
1.9%
3.2%
21.0%
7.9%
0.6%
5.3%
2.4%
1.0%
12.7%
9.3%
0.2%
4.3%
4.1%
2.9%
7.5%
5.5%
0.6%
3.1%
1.9%
Panel B: Other Exchange, All
t-1
HFT Trade
HFT Order
HFT Cancel
non-HFT
Trade
non-HFT
Order
non-HFT
Cancel
Unconditional
HFT
Trade
Same
4.8%
0.8%
0.4%
HFT
Order
Same
14.0%
16.5%
6.8%
HFT
Cancel
Same
5.0%
4.6%
13.8%
HFT
Trade
Other
0.1%
0.1%
0.2%
HFT
Order
Other
1.7%
3.4%
7.8%
HFT
Cancel
Other
3.6%
6.2%
3.1%
nonHFT
Trade
Same
1.3%
2.0%
1.1%
nonHFT
Order
Same
2.5%
7.2%
4.4%
nonHFT
Cancel
Same
0.9%
1.8%
4.8%
nonHFT
Trade
Other
0.3%
0.6%
1.2%
nonHFT
Order
Other
0.9%
2.7%
4.2%
nonHFT
Cancel
Other
0.7%
2.4%
1.6%
0.7%
9.0%
3.0%
0.1%
1.9%
4.6%
8.0%
3.7%
1.5%
0.4%
1.5%
1.2%
0.3%
9.0%
5.0%
0.1%
3.4%
4.9%
1.5%
11.6%
3.9%
0.7%
3.7%
2.8%
0.2%
0.6%
6.3%
10.6%
7.0%
7.2%
0.1%
0.1%
6.0%
4.7%
3.2%
4.6%
2.0%
2.0%
8.3%
7.3%
6.5%
3.6%
0.7%
0.8%
4.5%
3.4%
1.9%
2.1%
46
Table 12 Continued
Panel C: Same Exchange, NBBO Changes in time t
T
t-1
HFT Trade
HFT Order
HFT Cancel
non-HFT
Trade
non-HFT
Order
non-HFT
Cancel
Unconditional
HFT
Trade
Same
15.7%
1.3%
0.5%
HFT
HFT
Order Cancel
Same Same
28.0% 16.3%
14.3% 15.2%
20.4% 8.1%
HFT
Trade
Other
0.1%
0.3%
0.2%
HFT
Order
Other
1.3%
3.3%
6.2%
HFT
Cancel
Other
1.9%
5.3%
2.2%
nonHFT
Trade
Same
0.4%
0.8%
0.4%
nonHFT
Order
Same
1.1%
3.0%
2.3%
nonHFT
Cancel
Same
0.4%
0.5%
1.9%
nonHFT
Trade
Other
0.6%
0.6%
0.5%
nonHFT
Order
Other
1.5%
1.6%
1.4%
nonHFT
Cancel
Other
1.0%
1.8%
1.0%
3.1%
25.3%
1.0%
0.3%
1.1%
2.3%
10.9%
6.5%
16.5%
0.7%
1.4%
1.5%
0.8%
7.1%
0.6%
1.2%
2.9%
2.6%
1.6%
11.6%
14.3%
1.2%
3.6%
4.1%
0.2%
1.4%
6.2%
14.5%
3.3%
7.5%
0.3%
0.4%
4.0%
3.9%
1.5%
3.0%
1.3%
1.7%
20.3%
7.5%
9.4%
6.2%
0.6%
0.7%
3.1%
2.2%
1.8%
2.0%
Panel D: Other Exchange, NBBO Changes in time t
T
t-1
HFT Trade
HFT Order
HFT Cancel
non-HFT
Trade
non-HFT
Order
non-HFT
Cancel
Unconditional
HFT
Trade
Same
3.3%
2.4%
1.0%
HFT
Order
Same
17.1%
17.1%
10.6%
HFT
Cancel
Same
3.0%
3.0%
10.4%
HFT
Trade
Other
0.1%
0.2%
0.4%
HFT
Order
Other
1.2%
3.9%
5.9%
HFT
Cancel
Other
2.7%
6.1%
2.6%
nonHFT
Trade
Same
0.7%
3.0%
1.3%
nonHFT
Order
Same
1.3%
7.8%
7.4%
nonHFT
Cancel
Same
0.4%
2.0%
10.0%
nonHFT
Trade
Other
0.3%
0.3%
0.6%
nonHFT
Order
Other
0.8%
2.6%
2.8%
nonHFT
Cancel
Other
0.8%
3.7%
1.8%
0.7%
13.3%
1.9%
0.2%
1.3%
2.3%
3.0%
3.2%
1.4%
0.4%
0.9%
0.8%
0.8%
14.6%
1.5%
0.1%
4.6%
5.1%
1.7%
10.0%
1.3%
0.2%
4.2%
4.1%
0.3%
1.3%
11.1%
13.6%
5.8%
5.0%
0.2%
0.2%
6.0%
4.6%
2.7%
4.1%
1.4%
2.0%
7.8%
7.6%
6.5%
4.6%
0.4%
0.4%
3.7%
3.0%
2.2%
2.7%
47
Table A2: Cross Exchange Price Change Sequences. The table reports the frequencies of
price change sequences on Exchange 1 and Exchange 2. The sequences capture all events in
which Exchange 1 and Exchange 2 start with the same bid or ask price, and are followed by one
of the exchanges best bid or ask price changing, and subsequently the other exchange updating
its quote in the same direction. In Panel A and B the deviation and resolution must take at least
one millisecond. In Panel C and D the deviation and resolution occur simultaneous. The
statistics are calculated using data from 10/15/2012 – 06/28/2013. Panel A evaluates the joint
probability of a HFT/non-HFT and Trade/Order/Cancel opening a sequence and an HFT/nonHFT and Trade/Order/ Cancel subsequently updating the second exchange’s quotes. The
average stock-day has 960 sequences that last at least 1 millisecond. Panel B repeats the joint
probability analysis for the average stock-day 166 sequences with both orders by the same
trader. Panel C repeats the joint probability analysis for the average stock-day 890 sequences
that occur simultaneously. Panel D repeat the joint probability analysis for the average stock-day
196 sequences by the same trader that happen simultaneously.
Panel A: Conditional on Open/Close Order Type and HFT, > 1 Millisecond
Close
nonHFT
HFT
Open
HFT
Trade
Order
Cancel
non-HFT
Trade
Order
Cancel
% Close by
Trader-Order
% Close by
Trader
Trade
Order
Cancel
Trade
Order
Cancel
% Open by
TraderOrder
0.1%
--1.1%
--16.2%
---
0.7%
--15.4%
0.0%
--1.6%
--10.7%
---
0.2%
--24.8%
1.1%
26.9%
42.9%
70.8%
0.2%
--0.4%
--4.5%
---
2.0%
--3.0%
0.5%
--1.1%
--7.0%
---
1.8%
--8.8%
4.4%
11.4%
13.3%
29.2%
1.8%
20.6%
21.1%
3.3%
17.7%
35.5%
43.5%
56.5%
48
% Open
by
Trader
Table A2 Continued
Panel B: Conditional on Open/Close Order Type and HFT by Same Trader, > 1
Millisecond
Close
nonHFT
HFT
Open
HFT
Trade
Order
Cancel
non-HFT
Trade
Order
Cancel
% Close by
Trader-Order
% Close by
Trader
Trade
Order
Cancel
Trade
Order
Cancel
% Open by
TraderOrder
0.2%
--0.2%
--40.5%
---
1.3%
--34.7%
-------
-------
-------
1.5%
40.5%
34.9%
76.9%
-------
-------
-------
2.1%
--1.2%
--8.0%
---
5.2%
--6.6%
7.4%
8.0%
7.8%
23.2%
0.5%
40.5%
35.9%
3.3%
8.0%
11.8%
76.9%
% Open
by
Trader
23.2%
Panel C: Conditional on Open/Close Order Type and HFT, Simultaneous
Exchange 2
nonHFT
HFT
Exchange 1
HFT
Trade
Order
Cancel
non-HFT
Trade
Order
Cancel
% by
Trader-Order
% by
Trader
Trade
Order
Cancel
Trade
Order
Cancel
% by
TraderOrder
0.2%
--1.6%
--16.4%
---
1.4%
--12.5%
0.1%
--2.5%
--9.6%
---
0.4%
--14.9%
2.1%
26.0%
31.5%
59.7%
0.2%
--0.8%
--6.5%
---
2.4%
--4.4%
0.5%
--1.8%
--10.1%
---
4.5%
--9.0%
7.7%
16.6%
16.0%
40.3%
2.8%
22.9%
20.9%
4.9%
19.7%
28.8%
46.6%
53.4%
49
% by
Trader
Table A2 Continued
Panel D: Conditional on Open/Close Order Type and HFT by Same Trader,
Simultaneous
Exchange 2
nonHFT
HFT
Exchange 1
HFT
Trade
Order
Cancel
non-HFT
Trade
Order
Cancel
% by
Trader-Order
% by
Trader
Trade
Order
Cancel
Trade
Order
Cancel
% by
TraderOrder
0.4%
--0.2%
--34.3%
---
3.1%
--24.5%
-------
-------
-------
3.6%
34.3%
24.7%
-------
-------
-------
1.5%
--1.0%
--10.5%
---
13.8%
--10.6%
15.3%
10.5%
11.6%
0.6%
34.3%
27.6%
2.5%
10.5%
24.4%
37.4%
62.6%
50
% by
Trader
62.6%
37.4%
Table A3: Duration of Cross Exchange Price Change Sequences. The table reports the
average length of time, in seconds, of price change sequences on Exchange 1 and Exchange 2.
The sequences capture all events in which Exchange 1 and Exchange 2 start with the same bid or
ask price, followed by one of the exchanges best bid or ask price changing, and subsequently the
other exchange updating its quote in the same direction. The sequences must take at least one
millisecond. The average stock-day has 960 sequences. The average durations are calculated
using data from 10/15/2012 – 06/28/2013. Panel A evaluates the joint probability of a
HFT/non-HFT and Trade/Order/ Cancel opening a sequence and an HFT/non-HFT and
Trade/Order/ Cancel subsequently updating the second exchange’s quotes. Panel B repeats the
joint probability analysis for the 166 sequences by the same trader.
Panel A: Conditional on Open/Close Order Type and HFT
Close
Open
HFT
Trade
Order
Cancel
non-HFT
Trade
Order
Cancel
Trade
HFT
Order
Trade
non-HFT
Order
Cancel
Cancel
0.90
--3.86
--0.50
---
0.48
--0.60
3.75
--5.00
--0.66
---
2.00
--0.48
1.83
--5.00
--1.66
---
0.69
--1.61
1.23
--4.76
--1.71
---
1.00
--1.49
Panel B: Conditional on Open/Close Order Type and HFT by Same Trader
Close
Open
HFT
Trade
Order
Cancel
non-HFT
Trade
Order
Cancel
Trade
HFT
Order
Trade
non-HFT
Order
Cancel
Cancel
0.23
--1.70
--0.35
---
0.15
--0.65
-------
-------
-------
-------
-------
-------
0.34
--0.19
--0.46
---
0.18
--0.44
``
51