Liquidity Provision and Market Making by HFTs∗

Report prepared for the Investment Industry Regulatory Organization of Canada

Katya Malinova† Andreas Park‡

September 8, 2015

Executive Summary

1. We classify high-frequency traders based on reaction speeds, buy-side institutionsbased on inventory and use of (off-exchange arranged) dealer-crosses, and retailtraders based on the usage of seek-dark-liquidity orders. Based on similarities intrading characteristics, we group HFT IDs with a cluster analysis. We identify(voluntary) market-makers based on the extent to which the buy and sell volume oftheir passive order submissions is balanced.

2. In our sample, HFTs account for 26% of active trades and 53% of passive trades,buy-side institutions account for 48% of active trades and 39% of passive trades.

3. HFTs account for around 80% of all orders, around 65% of all orders that improvethe best price and 70-80% of all orders that match the prevailing best prices.

4. The order cancellation rate of existing orders by (HFT) market makers is higher inthe first 10-50 milliseconds after a trade compared to half or a full second after thetrade, which documents the quote-fade phenomenon. Similarly, in the first 10msafter a trade, there is an increase in aggressive order submissions that are in thesame direction as the trade. This relation is positively related to the volume of theorder and the directional volume that the trader has already traded on the day.

5. We find (weak) evidence that there is transmission of activity between fundamentallylinked securities (e.g., stocks to preferred shares, or between stocks with differentvoting rights). We observe that trades in the frequently traded security have priceimpact and affect the order cancellation behavior by HFT market makers in theless-frequently traded security.

6. For TSXV securities, HFT participation is lower, and HFTs trade in only about halfof all TSXV securities. Retail trading participation, on the other hand, is higher inTSXV than in TSX securities, and it is higher than HFT participation.

∗We thank the Investment Industry Regulatory Organization of Canada (IIROC) and in particularVictoria Pinnington and Helen Hogarth.

†University of Toronto, katya.malinova@utoronto.ca.‡University of Toronto, andreas.park@utoronto.ca (corresponding author).

I. Introduction and Summary of Findings

In this report we describe and analyze the market-making behaviour of high frequency

traders. We describe how high-frequency market makers submit quotes relative to posted

prices, and we analyze how market makers react to trades by canceling their existing

quotes and by eliminating others’ stale quotes with aggressive, marketable orders. We are

particularly interested in understanding whether and how the cancellation and aggressive

order submission behaviour relates to the directional volume of the trader who submitted

the trade. Finally, we analyze whether there is transmission of activities among related

securities, such as between stocks with different voting rights.

We classify traders into several groups, using trading in a comprehensive sample

of 307 highly liquid securities from January to May 2013. We are interested in retail,

buy-side, and high-frequency traders. Our classification approach builds on Comerton-

Forde, Malinova, and Park (2015): we classify a trader as retail based on the usage of

an order type that only retail traders are allowed to used, buy-side based on the signed

dollar-volume that the trader accumulates over a number of days, and high frequency

based on the traders’ ability to react to market events quickly. We additionally classify

any trader as a (voluntary) market maker if this trader regularly posts similar passive

volume on both sides of the market on many days and across many securities.

We first study the distributional features of submitted orders relative to the best

prices on the marketplace where the orders are posted. The Canadian marketplaces are

separately but anonymously identified in the data, and we label them alphabetically. We

observe that about 52% of all orders are submitted at the local best prices, 7% strictly

improve the best prices, 37% are worse than the local best prices, and 4% are marketable.

There are differences across markets: on market B, which is the largest by value traded

and which also has the lowest quoted spread, only 3-4% of all orders improve the local

best bid and offer prices; on this venue, the quoted spread is regularly constrained by

the 1 cent minimum tick size. For market A, almost 10%, and for market C, slightly

over 10% of orders improve the price. A notable fraction of orders are submitted as

immediate-or-cancel (IOC) orders. Many of these orders are not marketable, but since

their intent is to seek immediate execution, we classify such orders as aggressive in our

subsequent analysis.

We then study the order submission behaviour of high-frequency traders and market

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makers. HFTs submit the bulk of all passive orders (just under 80%), and they account

for about 65% of all price-improving orders. There are, however, differences between

the marketplaces. HFTs are most active on markets B and C, at the time the largest

and the third largest market by value traded. On market A, they account for only 50%

of price improving orders in early 2013, but after a major technological change to this

market in April 2013, HFTs account for around 70% of all price improving orders. We

further observed an offsetting drop in the activities of market-makers that we did not

classify as HFT. The details of the trader-level data suggest that some of the non-HFT

market makers on that venue were likely part of an HFT strategy that our classification

approach could not detect. In the subsequent by-trade analysis, we thus study all market

makers as a group.

We next focus on HFT behaviour subsequent to trades. Theoretical models of market

making predict1 that market makers adjust their quotes subsequent to trades, as (a) these

trades may reveal information about fundamentals and (b) taking an inventory exposes

the market maker to risk. One would thus expect that market makers cancel existing

quotes, and we study the cancellation behavior after trades. We also study whether

market making traders submit aggressive orders, e.g., to “take out” other traders’ stale

quotes. In our analysis, we further ask, whether the cancellation and aggressive order

submission rates depend on the size of the trade, on the type of trade (smart-order-

routed trades vs. “normal” trades), on the type of liquidity provider (market maker vs.

non market-maker), and on how much the entity that submitted the marketable order

has already traded during the day.

We perform this part of the analysis for a smaller subset of securities and focus on

highly liquid, non-interlisted2 securities that are in the TSX60 index, and we focus on

two measures: cancellations in the opposite direction of trades (e.g., cancellations of

sell-orders following a buy)3 and aggressive order submissions in the same direction of

1See, for instance, Kyle (1985), Glosten and Milgrom (1985), Glosten (1994).2In Canada, cross-listed securities are commonly referred to as “’interlisted” securities.3Opposite-side cancellations can be interpreted as being indicative of “stepping aside” of possible

future trades from the same trader. Theoretically, however, when moving a quote, a market makerwould cancel orders on both sides of the market resubmit orders on both sides at different prices.Indeed, we ran components of our analysis also for same-side cancellations and found that these ordersare cancelled, too. This part of the analysis is both computationally intensive and difficult to presentconcisely when discussing both same-side and opposite-side cancellations. To simplify the exposition,we focus only on opposite-side cancellations.

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the trade (e.g., marketable or IOC buy orders following a buy). The cancellation rate

beyond the first 10ms decays rapidly. To the naked eye, which can at best observe market

movements after 250ms, the quotes would appear to have been cancelled concurrently

with the trade.

A formal regression analysis confirms the observations from the aggregate data: In

this part of the analysis, we additionally address two questions. First, we ask whether

the cancellation and aggressive order submission rates of market makers differ between

“normal” trades and trades that were submitted via a smart-order router (SOR), where

we classify a trade as stemming from a SOR if the order is from the same trader and hits

multiple markets at around the same time. Second, we ask whether the cancellation and

aggressive order submission rates are affected if the marketable order executes against a

market maker’s passive order. We find that trades generally have a positive, significant

effect on cancellation and aggressive order submission rates. SOR trades generally have

a larger impact except in the very first milliseconds after the trade; similarly for trades

that have a market maker on the passive side.

As a next step, we analyze whether a trader who has already traded a lot in the

same direction can be detected and thus triggers a stronger reaction by market makers.

To address this question, we estimate the effect of the market order submitter’s net

inventory on the cancellation and order submission rates.4 We perform this part of

the analysis by aggregating observations by the both trade-volume and net-inventory

deciles for the security and type of trader. Here, too, we observe that the effect on

the cancellation rate is strongest in the first 10-50ms after the trade and that there

is an increasing relation between the traders’ net inventories and the market makers’

cancellation rates and submission rates of aggressive orders.5

Overall, our analysis indicates that after, say, trading with a buyer, market-makers

cancel their sell orders quickly and submit aggressive buy orders. This latter behavior

can be interpreted as market makers either trading in anticipation of future orders or

taking advantage of and eliminating mis-priced, stale quotes. The more buys the buying

trader had already submitted, the stronger this effect.

4We control for market-wide data for the security such as daily return, volume traded, and aggregatenet inventory to ensure that our results are not driven by general market developments.

5The only exception is the case when the incoming trade was submitted by a non-market-makingHFT. For these traders, there is a non-negative aggressive order submission rate, but this rate does notdepend on this type of traders’ net inventory.

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We further explore (HFT) market-making across different securities. Specifically, we

analyze how trading in a frequently traded security (e.g., heavily traded BBD.B shares)

affects trading and quoting behaviour in related, but less-frequently traded securities

(e.g., more lightly traded BBD.A shares). For this part of the analysis, we look at

three classes of non-interlisted securities: dual-class shares, preferred shares, and deben-

tures. For each of these we observe that trades in the more frequently-traded securities

commonly affect trading behaviour in the related security in the sense of positive price

impacts and positive effects on market makers’ order cancellation rates.

Finally, we apply some components of our analysis to TSX Venture-listed securities.

We use the trader classification from our main analysis for TSX Venture-listed securi-

ties to take the advantage of the information from behaviour in much more frequently

traded securities where speed may be more important and where we may thus have more

opportunities to observe behaviour that reveals the ability to react quickly.6 Overall,

we observe trading in about 2,500 TSXV listed securities, though only about 1,300 of

these exhibit HFT trading. Of all transactions, around 20% have HFTs on the passive

side; aggressive trades by HFTs are negligible. Yet, HFTs still account for a very large

fraction of the price improving and BBO-matching orders (45% and 50%, respectively).

TSXV-securities have a much higher fraction of retail trader activities than TSX-listed

securities (20+% of all active trades and 10% of passive trades), and the shares of retail

exceeds the HFT fractions.

The remainder of this report is organized as follows: Section II. describes the in-

stitutional background and the organization of the different marketplaces. Section III.

describes the data and the sample. Section IV. outlines our classification approach,

Section V. presents our findings on the behaviour of the classified traders. Section VI.

analyzes the reaction of market-making traders to trades, Section VII. discusses how

market-making HFT help transmit information from trades across related securities.

Statistics concerning HFT trading in TSXV securities are in Section VIII.

6The downside is that we may be missing behaviour by trader IDs that only trade in TSXV securities.

4

II. The Institutional Setting

A. Core rules governing trading in Canada

The Toronto Stock Exchange (TSX) is the primary listing venue for large compa-

nies in Canada, small and mid-cap companies are typically listed on the TSX Venture

exchange. As in other major markets around the world, trading in TSX-listed stocks

is fragmented across multiple exchanges and Alternative Trading Systems (ATS), and

many TSX-listed companies are also listed on U.S. exchanges. Securities trading and

the activities of market participants in Canada are regulated by the Investment Industry

Regulatory Organization of Canada (IIROC), the members of the Canadian Securities

Administrators, and are governed by the Universal Market Integrity Rules (UMIR).

Most of the core elements of the UMIR are similar to those governing trading in

the U.S. equities markets. Brokers and marketplaces are required to respect the order

protection rule, which mandates that orders must be routed to the marketplace with

the best-priced orders available on lit markets. Brokers are also subject to obligations

regarding best execution for client orders.

In the context of our study, there are three critical differences between trading rules in

the U.S and Canada. First, the order protection rule in Canada applies to the whole-of-

book rather than the top-of-book as is the case in the US. Second, Canada also imposes

a strict version of an order exposure rule, with few exceptions. This rule requires that

client orders below a certain size be immediately sent to a marketplace that publicly

displays prices. This rule severely limits the practice of broker internalization, which oc-

curs when a broker trades against their customer’s order instead of sending the order to

a public marketplace, and the practice of selling retail orders to market makers. Third,

unlike the US, several Canadian marketplaces are allowed to offer broker-preferencing

on the market’s order book. This practice allows incoming orders to a marketplace

to match with other orders from the same broker-dealer ahead of similarly priced or-

ders from other broker-dealers, without regard to time priority. To take advantage of

broker-preferencing, brokers must elect to publicly display broker IDs when submitting

their orders.

A significant volume of trades is pre-arranged off-exchange, before entering orders

on a public marketplace. These trades must still be executed on a public marketplace,

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respecting all the applicable rules. There are usually very few such deals each day, but

they are large and, on average, account for roughly 10-12% of trading value. We omit

such trades from most of our analysis.

B. Marketplaces and their trading rules

The data in our sample contains observations for ten marketplaces. These mar-

ketplaces are separately, but anonymously identified in our data, and we label them

alphabetically. During our sample period, marketplaces A, B, and C together account

for about 90% of the dollar volume traded, respectively; marketplace D, which is a dark

pool, accounts for about 5% of dollar volume. The remaining marketplaces account for

no more than 2% market share each.

Marketplace A operates a public limit order book and a dark pool facility. The lit

market of A allows lit and partially hidden (iceberg) limit orders. Broker-preferencing is

allowed provided the broker chooses to publicly display its broker ID when submitting

the order. In most of our analysis, we only consider the lit portion of this market.

Marketplace B is a lit market that operates as a public limit order book. Broker-

preferencing is allowed, provided the broker chooses to publicly display its broker ID

when submitting the order. Traders may post lit, partially hidden (iceberg), and fully

hidden orders, including “mid-point” orders, which are pegged to execute at the floating

midpoint of the NBBO. Marketplace B operates a so-called electronic liquidity provider

program (ELP) that offers favorable trading fees to traders who routinely provide liq-

uidity in a sufficiently large number of stocks.

Marketplace C is a lit market that operates as a public limit order book. Like

marketplace B, it allows lit, iceberg, and fully hidden orders, which may be pegged to

the midpoint. Marketplace C does not offer broker-preferencing.

Marketplace D is a dark pool that allows traders to interact using two types of

orders. First, traders may submit passive dark orders that remain in the dark pool until

they are executed or cancelled. Second, traders may submit aggressive, liquidity taking

orders that are either executed immediately against a passive dark order or cancelled.

All trades are priced at the midpoint of the NBBO.

Marketplaces E, F, and G operate as public limit order books. These markets are

very small and account for less than 2% of daily value each. Markets F and G operate

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inverted, taker-maker pricing.

Marketplaces H and I are dark pools. During our sample period, marketplace H is

an institutional-only venue, marketplace I offers periodic matching with 1-second random

NBBO prices. These venues account for negligible shares of volume and we omit them

from our analysis.

Finally, marketplace J operates as a public limit order book and trades only secu-

rities that are listed on this venue, and trading on this marketplace thus does not feature

in our main analysis.

Towards the end of our sample period (end-May 2013), a new marketplace started

operating. The special feature of this new venue was the so-called “taker-maker” or

“inverted” pricing schedule under which the liquidity taking side of a transaction would

be paid a fee rebate and the liquidity making side would pay a fee. Trading in May in

this market was sparse and to avoid any confounding effects, we omit this venue from

the analysis.

III. Data and Sample

Data. The data for this study is provided by the Investment Industry Regulatory

Organization of Canada (IIROC). The dataset contains detailed records on all trades,

orders, order cancellations, order amendments, and updates to marketplaces best bid and

offer quotes from IIROC’s real-time surveillance system, for all trading on all regulated

Canadian marketplaces. Each order-related record includes, in particular:

• The marketplace where the order was sent (masked).

• Size, price, and the direction (buy or sell) of an order.

• Broker ID (masked), user ID (masked), and account type (e.g., specialist, client,

options-trader, or inventory).

• Other characteristics, including the duration of an order (for instance, good-

till-cancel or immediate-or-cancel), whether an order was transparent or non-

transparent, whether the order was a seek-dark-liquidity order, and a unique iden-

tifier for each order.

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For trades, the data additionally specifies the aggressive and passive (liquidity-providing)

side of a trade. The data also identifies the aforementioned intentional broker-crosses,

which we omit from the analysis. The information for marketplaces, brokers and users is

masked in the sense that IIROC provides a scrambled identifier. The masking is applied

consistently so that the same marketplace, broker and user are always assigned the

same identifier. Marketplaces time-stamps are reported with millisecond precision for

our sample period. Brogaard, Hendershott, and Riordan (2014), Korajczyk and Murphy

(2014), Comerton-Forde, Malinova, and Park (2015) and Devani, Tayal, Anderson, Zhou,

Gomez, and Taylor (2014) contain further information of the data.

Large Sample. We base our analysis on the period from January 1 to May 31,

2013. We end the sample at the end of May for two reasons. First, subsequent to the

integration of Alpha into the TMX Quantum platform, a large number of high-activity

trader IDs disappeared. At the same time, several new high activity IDs appeared

(for the same brokers), and the time horizon of the data is too short to characterize

many of the new IDs. Second, IIROC’s public market share statistics illustrate that a

new marketplace rapidly gained market share. The entry of this marketplace has been

associated with changes in behavior that we might not be able to fully capture as our

data ends too early (end June 2013).

We base our analysis on the 307 securities that are classified as “highly-liquid” se-

curities by IIROC during the entire sample period. Loosely, a security qualifies as

highly-liquid for a given day if over a 60-day period it traded more than 100 times per

trading day and had an average trading value of at least $1M. IIROC compiles a list of

highly-liquid securities daily; we include a security in our sample if that security is on

the list of highly liquid securities at the end of each month in our sample period. We ap-

plied no further filters, in particular, there are no corrections for stock splits, corporate

actions, halts, etc.

We use the entire set of securities for the classification of traders and for the general

description of trading behavior. For our analysis of market-making behavior we restrict

attention to two subsamples (partly due to data processing constraints).

Sub-Sample 1: non-interlisted TSX60 Securities. We determine the inter-

listing status based on the June 2013 TSX e-review publication. Of the 307 securities

in our sample, 87 are interlisted, 222 are not interlisted. Of the latter 222 securities,

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17 are S&P/TSX60 constituents, and these comprise our SubSample 1. We restrict

attention to non-interlisted securities because for these securities we know all the trades.

For interlisted securities, on the other hand, observed cancellations could be driven by

trades on U.S. markets. For this sub-sample, we further restrict the sampling horizon

to March and May 2013. It is part of the public record, that in April 2013, the TMX

Group integrated Alpha Exchange in its Quantum platform. It is not clear to us when

exactly TMX performed the move and whether all securities where affected at the same

time. We thus omit April from the sample.

Sub-Sample 2: “Fundamentally Linked” Securities. For our analysis of mar-

ket making in fundamentally-linked securities, we consider non-interlisted, highly liquid

securities that also have TSX listings of dual-class shares, preferred shares, or deben-

tures. These pairs of securities are linked by common fundamentals. Specifically, we

have 8 non-interlisted securities from our list that have dual class listings, 102 stock-

preferred share pairs, and 79 stock-debenture pairs.7 As for SumSample 1, we restrict

the sampling horizon to March and May 2013.

Outliers. We eliminated two days from our sample: January 21 (Martin Luther

King Day) and May 27 (Memorial Day); these days are public holidays in the U.S., and

trading activity on Canadian markets on such days is very low.

IV. Trader Classification

All traders access the marketplaces via brokers. We base our classification on the

analysis of order submission and trading behavior by trader IDs, where we define a

trader ID as the combination of broker ID plus user ID, plus the account type (client,

specialist, inventory, option market maker, and non-client).

The user ID is the most granular identification that is available to regulators in

Canada; IIROC researchers describe the usage of user IDs in detail in their research

reports (IIROC (2012), Devani, Tayal, Anderson, Zhou, Gomez, and Taylor (2014), and

Devani, Anderson, and Zhang (2015)). According to these research reports, market-

places assign user IDs, and an ID may identify a single trader, a business stream (for

example, all orders that originate through a broker’s online discount brokerage system),

7The most obvious pair would, of course, be options and their underlying. However, we do not haveaccess to derivative market data.

9

or a client that accesses trading venues directly (through a direct market access (DMA)

relationship). It is our understanding that the brokers separate different types of order

flows (e.g., retail vs. institutional) by user ID. For DMA clients, IIROC requires dedi-

cated IDs. However, according to Devani, Tayal, Anderson, Zhou, Gomez, and Taylor

(2014), a DMA client may be assigned more than one user IDs, for instance, to trade

through multiple brokers or to trade on different marketplaces, and they may choose to

use multiple user IDs for business or administrative purposes.

We classify traders based on trading characteristics during our entire sample period

in all securities from the large sample.

We group traders into four general categories: HFT, retail, buy-side, and other. The

“other” category includes trader IDs that we were not able to classify as HFT, retail, or

buy-side. The group of HFT and “other” are then each segmented into market-making

and non-market-making traders. In this report, we do not present information about

the behavior of non-market-making “other” traders.

Our general approach is to provide a classification for each trader based on the

trader’s behaviour in a large number of securities. Thus, for instance, to classify as

a market maker, a trader needs to exhibit market-making behaviour for a range of

securities. In our opinion, algorithmic strategies are scalable in these sense that they

can be applied to many securities and it is our intention to capture core characteristics

of an algorithmic strategy. We acknowledge that this approach will likely exclude firms

that employ security-specific, heterogenous strategies.

Table I provides summary statistics on these trader ID groups. We have a total of

4,892 trader IDs in our classification sample. Figure 1 shows the distribution of trader

categories and we discuss the details of our categorization in what follows.

Retail. On marketplace A, seek dark liquidity (SDL) orders are exclusively available

to retail investors. The use of SDL orders is the choice of the broker, not the customer.

We extract all trader IDs that use SDL orders from the complete database (which spans

January 1, 2012 to June 30, 2013 and all securities that trade on Canadian equity

markets), and we classify these traders IDs as retail. In our sample, we observe 134 of

these IDs. We know with certainty that these trader IDs are used to trade order flow

from retail investors, but there may be other trader IDs that are assigned for order flow

from retail investors that are not captured by our classification.

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Buy-Side Institutional: We conjecture that buy-side institutions will be involved

in large pre-arranged trades and accumulate large inventory positions. We therefore use

two criteria to identify buy-side institutions.

First, we extract all trader IDs that involve a client account and that are involved

in a so-called ”intentional cross”. An intentional cross is a trade, usually a large one,

that is pre-arranged off-exchange by a brokerage, for instance to match two client orders

or take an inventory from a client via a liability desk. These trades typically involve

human intervention.

Second, we search for trader IDs that accumulate very large inventory positions in

non-interlisted securities. We determine each trader’s maximum cumulative position for

the sample period, assigning a zero inventory at the beginning of the period. We focus

on non-interlisted securities to reduce the possibility that a seemingly large inventory

position of an entity is offset by an equally large position elsewhere. Since a trader

may buy in one jurisdiction and sell in another, for instance, to exploit an arbitrage

opportunity, it is imaginable that a Canada-only position is off-set by a U.S.-based

position. We acknowledge that this classification is imperfect, for instance, because

a trader ID may trade on behalf of multiple retail clients who jointly accumulate a

large position or because a DMA client may use different trader IDs for buying and

selling securities. To mitigate these imperfections, we set a high bar for the required

cumulative position. We classify the trader ID as a buy-side institution if its maximum

cumulative position during the classification period exceeds $100,000,000 in absolute

value for one security during our entire sample period. We classify 778 trader IDs as

buy-side institutions.

High Frequency: The critical component of high frequency trading is that trading

is automated and that traders have the ability to react quickly to market conditions.

Definitions used by various regulators or policy institutions (e.g., BAFin in Germany,

the European Commission, or the S.E.C.) often include a further requirement that HFTs

use many orders, in particular in relation to their trades. In our opinion, using orders or

order-to-trade ratios biases the classification against traders or strategies that use only

marketable orders.

We focus on reaction speeds as the main metric to identify HFTs, and we use reaction

times that are faster than human reaction times (the average duration of a single blink

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of a human eye is 100-400 milliseconds, according to the Harvard Database of Useful

Biological Numbers). We further require that trader IDs exhibit fast reaction times

across many orders and trades, and in many securities. We use three criteria to quantify

a trader ID’s reaction speed.

Our first criterion is the trader ID’s median order-to-cancel time. The order-to-cancel

time is the time from the submission to cancellation of the same order; for the purpose

of this classification, we exclude immediate-or-cancel (IOC) orders, because their order-

to-cancel time is determined by the processing speed of the marketplace.

Our second criterion is the number of trade and order messages that a trader ID

submits during a short interval after a daily scheduled public information release. We

focus on the first 500 milliseconds after 3:40 p.m., which is when the TSX first publishes

the imbalance between the buy and sell orders in its market-on-close facility.

The closing price for TSX-listed securities is determined in a multi-stage process.

Before 3:40 p.m., traders may submit market buy and sell orders tagged as market-

on-close orders. These orders will trade at the 4:00 p.m. closing price. At 3:40 p.m.,

the TSX publishes the imbalances of buy and sell orders, and traders then have the

opportunity to submit priced limit orders to trade at the market-on-close to off-set the

market order imbalance. The market-on-close imbalance is indicative of the closing price

and may help predict behavior over the last 20 minutes of trading.8

In aggregate, there is a significant spike in trades immediately after the publication

of the market-on-close imbalance, though this spike may not be visible or pronounced on

a stock-by-stock basis. Comerton-Forde, Malinova, and Park (2015) includes a plot of

the by-minute number of trades (Figure 1 in their paper), aggregated over all securities

in their sample (which is similar to ours, albeit for a different time horizon). The dataset

that is provided to us by IIROC does not contain information on the market-on-close

announcement. Thus, we are not able to determine the time between the publication

of the market-on-close imbalance and a trader’s action at the millisecond level. For this

reason, we classify trader IDs as HFTs based on their actions during a relatively long

interval of 500 milliseconds after the announcement.

Our third criterion is the fraction of orders and (non-IOC) cancellations that a trader

submits very quickly after a change in the order book that was not triggered by the trader

8The publication at 3:40 p.m. is merely the first publication. Between 3:40 and 4:00 p.m., TMXregularly publishes updates of the prevailing imbalance.

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him-/herself but by another trader.

For each trader ID, stock and day we compute the median order-to-cancel speed, and

we compute the total number of orders and aggressive trades during the 500 milliseconds

after 3:40 p.m. Furthermore, for each trader ID and security, we computed the number

of orders and cancellations that this trader submits and that this trader submits within

1 millisecond following another visible order submission by a trader other than him-

/herself in that security. A trader ID is classified as HFT

1. if the median of the trader ID’s median stock-day order-to-cancel speeds is below

250 milliseconds, or

2. if the trader ID submits more than 1,000 orders or is involved in more than 500

aggressive transactions in the first 500 milliseconds after the market-on-close pub-

lication across all securities in our classification sample during our classification

period, or

3. if the trader ID submits more than 85% of its orders and cancellations within 1

millisecond of some other trader’s order submission.

We classify a total of 101 trader IDs as HFT, though in each month, there are only

around 80 active HFT IDs.

In Devani, Tayal, Anderson, Zhou, Gomez, and Taylor (2014), IIROC researchers

discuss their classification of HFTs. In their data, they had direct information about

a subset of the existing HFT IDs in the Canadian market (49 IDs) and they used the

knowledge of these IDs to apply machine learning techniques to identify further IDs as

HFT. Their report does not list the details of the criteria, but Figure 1 in their report

shows that “speed” in various forms is a decisive criterion. For their sample period from

March to June 2013, which overlaps with ours, they identify 98 IDs as HFT, which is

close in number to our 101 HFT IDs.

Cluster Analysis of HFT Groups. The by-trader data displays some pronounced

similarities among subsets of traders in the sense that traders have very similar charac-

teristics for instance, in terms of numbers of trades and orders, or number of securities

traded. As IIROC researchers Devani, Tayal, Anderson, Zhou, Gomez, and Taylor (2014)

highlight, HFT firms may use several trader IDs for their strategies. For instance, it is

13

possible that an HFT firm uses one trader ID to submit buy orders and another to sub-

mit sell orders. Taking together, these two IDs may have a perfectly balanced end-of-day

inventory, whereas individually their inventory is imbalanced.

The usage of multiple IDs is particularly important and presents a challenge for an

analysis of market making behavior, in particular with respect to inventory positions and

order submission behavior. We thus group together trader IDs using a cluster analysis

approach to detect similarities in behaviour. Specifically, we use the following criteria:

the average per day number of securities traded, the average per day per stock number

of trades and orders, the average daily order imbalance and trade imbalances per stock,

the median order-to-cancel time, the total number of orders and trades submitted in the

500ms after 3:40 p.m., and the average percentage of orders and cancels submitted within

1ms of another trader ID’s order submission. For these nine criteria, critk, k = 1, . . . , 9,

we then compute the pair-wise absolute-value distance for traders i and j as follows9

Distij =

9∑

k=1

|critki − critkj |

critki + critkj. (1)

We use visual analysis of the pair-wise distances in an Excel table to identify the clusters.

Figure 2 displays the pairwise pair-wise distances based on these criteria, using color-

coding to highlight the pairwise distances, where darker colors indicate smaller pair-wise

distances. The color-coding in the figure shows that there are groups of securities that

have small pair-wise distances. Using a maximum pairwise distance of threshold of .25,

we identify four clusters of IDs. Notably, members within a group all have the same

underlying broker (but cluster groups have different brokers).

Market-Making Index. A defining feature of a market maker is that the trader

posts on both sides of the market and stands ready to trade. We thus expect that a

market-making trader would submit passive buy and sell orders on both sides of the

market so as to earn the bid-ask spread (and maker-taker fees) on as many trades as

possible. To account for strategies that are linked across multiple IDs, we treat each

HFT trader ID-cluster as a single entity. We then compute for each trader-cluster, day,

9As a convention, when both criteria are 0 for some k for i and j, then we set the distance to 0.

14

and security, the market maker index defined as

market maker index =

∣

∣

∣

∣

passive buy order volume− passive sell order volume

passive buy order volume+ passive sell order volume

∣

∣

∣

∣

. (2)

By construction, this index is between 0 and 1, where an index close to 0 indicates that

the trader’s order submission behaviour is well-balanced. A trader’s (or trader group’s)

market making index is the median index over all days and securities.10

Upon visually examining the data, it is apparent that for HFT IDs (including HFT

groups), there is a structural break for an imbalance score of 0.2 for our sample. We

thus classify a trader ID (cluster) as market-making if the trader ID (cluster) has an

imbalance score below 0.2. We identify 50 HFTs as market makers. In addition, we

identify 88 non-HFT IDs as (non-HFT) market makers.11

Inventories of Individual HFT Trader IDs. A common perception is that high-

frequency trading firms aim to hold no or only very small overnight inventories. We

observe that most trader IDs that we classify as HFT hold substantial median end-of-

day inventories, even in non-interlisted securities. Furthermore, several of the fastest

trader IDs that we classify as HFT trade more than 85% passive, have order-to-trade

ratios in the 99th percentile, and yet hold median inventories of 70% or more of their

daily trading volume.

This observation highlights the importance of understanding the usage of trader and

user IDs in different jurisdictions and in different datasets. In Canadian markets, a

single DMA client may use multiple trader IDs (IIROC (2012) and IIROC (2014)), and

it is thus possible that an HFT firm is assigned multiple user IDs. Furthermore, a single

user ID may be used for trading activity of multiple entities, for instance, for all the

brokerage’s retail order flow (which is balanced, on average). As a consequence, low end-

10For traders with low median scores, the averages are similar to the medians. Many traders frequentlypost perfectly unbalanced scores. By using the median, we can ensure that this high frequency ofunbalanced submissions is properly reflected in the score.

11As discussed in the introduction, it is possible that some of these latter market makers are, in HFTs,and that we were just not able to identify them based on our speed criteria. Indeed, at the beginningof May 2015, a number of IDs with similar trading characteristics retired from posting at market Awhile at the same time, some IDs in market A showed a significant increase in activity to the pointthat the number of orders from the disappeared IDs almost coincides with the increase in the numberof orders for the HFT IDs. It is thus imaginable that these non-HFT IDs were part of a market makingstrategy that used different IDs on different markets and that were consolidated when markets A’s andB’s system effectively merged.

15

of-day inventories are neither a necessary nor a sufficient attribute of an HFT trader ID

in our dataset.

HFT vs. designated market making. One question that often arises in debates

in industry and that may be relevant when interpreting our results is whether designated

market makers, such as stock specialists (sometimes referred to as odd-lot traders, iden-

tifiable through the usage of a specialist (ST) account), options market makers (OT

account), or ETF market makers are classified as HFT. These traders interact with the

market in a high-speed environment and may thus exhibit behavior that looks similar

to that of an HFT (in terms of reaction speed, or, using the S.E.C. or E.C. definitions,

uses many orders and has a high order-to-trade ratio). In contrast to an HFT, however,

they have an obligation to make a market under all circumstances.

In our classification approach, we included no special provision to exclude such des-

ignated market makers. None of the 101 traders that we classify as HFT are ST or

OT accounts. Of the classified HFT, four are non-client (NC) accounts, twenty are

broker-inventory (IN) accounts, and the remainder are client (CL) accounts. NC traders

account for .6% of HFT trades and .8% of HFT orders and their activities are thus

unlikely to affect our results. It is not fully clear to us under which circumstances a

trader uses the IN vs. the ST account. One reasonable possibility is that some of the

IN accounts are linked to, for instance, ETF or options market makers in the sense that

such market makers use the ST/OT account in the assigned security and hedge using

the IN account. Three of the twenty HFT IN accounts are “linked” to ST accounts in

the sense that for the same broker and userid, there are activities under an ST and an IN

account. These three linked ST accounts trade in ETFs. Two of these three combined,

however, account for less than 0.04% of HFT trades and less than 0.003% of orders. Even

if these two are ETF market makers, their activities are unlikely to affect our results

significantly. The remaining account is additionally linked to an OT account and trades

in a large number of securities using the ST account identifier, including infrequently

traded ones.12 This behavior suggests that this account may bundle a large number of

electronic-trading activities (options, ETF and regular market making). We further note

that the ST account of this userid is not classified as HFT or market-making, and thus

the activities of this trader in its direct market making role would not affect our results.

12We believe that Korajczyk and Murphy (2014) study the impact of this trader becoming a DMMin November 2012.

16

V. Characteristics of Traders

In this section, we describe characteristics of the trader groups for our classification

sample of 307 securities.

A. Trades and Orders.

Our HFT group displays the characteristics that are typically associated with high

frequency traders. Figure 3 plots the time series of the types’ shares of orders. As

a group, HFTs account for over 80% of all passive orders. Figure 3 plots the overall

share of active and passive value traded (Panel A) and transactions (Panel B); this

figure is based upon the sum of all trading in the 307 sample securities over the sample

horizon from January to May 2013. HFTs account for 25% of all aggressive and 55%

of all passive transactions. For value traded, HFTs account for a similar percentage of

aggressive trades, but for a lower percentage of passive volume (41%). Buy-side traders

account for 45-50% of all aggressive trades, and 35% of passive trades. Retail traders

represent around 12% of aggressive volume.

Non-HFT market makers account for around 4% and 8% of active and passive volume

respectively. On an average day, the average HFT trades in 111 securities.

Panel A in Figure 4 indicates that there is an uptick in HFT order submissions

starting at the end of April 2013, coinciding with a drop in non-HFT market maker

submissions. We are able to identify that this change is driven by changes in order

submission behaviour on marketplace A. At the time, this marketplace’s technology was

integrated with that of marketplace B. Examining the data in detail we observed that

several non-HFT market makers disappeared from market A. At the same time, some

of the existing market-making HFTs increased their activity to the point where the

April order volume of the disappearing IDs coincided with the increase in volume for

the existing HFTs. It thus appears the the group of the market-making non-HFT IDs

may, in fact, be part of a cluster of market-making HFTs. We thus have to admit the

possibility that we were unable to classify some HFT IDs as HFT. As such, in our formal

regression analysis we will combine HFT and non-HFT market-making activities.

17

B. Order Competitiveness.

We conjecture that a market maker would post quotes competitively in the sense that

they match or improve upon the best available prices. To assess the competitiveness of

quoting behaviour we analyze, for each trader ID cluster, where in the limit order book

traders place passive orders relative to the prevailing prices. We determine the best

prevailing local bid and ask prices for each order and we differentiate between marketable

orders (the buy-price matches or exceeds the ask or the sell-price matches or is below

the bid-price), immediate-or-cancel, and passive orders. Immediate-or-cancel orders can

be non-marketable, but they are not passive because these orders do not enter the book

and they are submitted with the aim of an immediate execution. These orders thus do

not provide liquidity to subsequent traders, and we consider them to be aggressive in

nature. For the best prices we use the local price for the venue where the order is posted.

We then compute, for each trader ID cluster, how many orders and how much order

volume the trader submits at the best price, one tick higher/lower, 2 ticks higher/lower,. . . ,

and 5 or more ticks higher/lower. In the data, a fraction of orders is unpriced; one ex-

ample are dark midpoint orders which are pegged to the prevailing midpoint. We omit

these orders from the data.

Panel B in Figure 4 shows the distribution of orders, where we group them into four

categories to simply the exposition: better-than-best, at-the-quote, worse-than-best,

and marketable. As the figure highlights, fewer than 10% of all orders are submitted

at prices that improve the best prices available at that venue. One explanation for this

small fraction is that bid-ask spreads in frequently traded securities are narrow, often

at one cent.

Panel C in Figure 4 plots the time series of fractions of price-improving orders by HFT

for the main markets A, B, and C. We observe that for markets B and C, HFTs comprise

of around 65% of all price-improving orders, whereas for market A this fraction is much

lower until May 2013, when the HFT fraction increased to around 70%, for reasons that

we discuss above. Panel D of Figure 4 shows the time series for the fraction of “at-best”

orders by HFT. The pattern is similar to Panel A, except that on market C, the fraction

of “at-best” submissions by HFTs is between 75-80%.

Finally, considering the composition of a trader type’s order submissions, we observe

that HFTs that are also market makers submit around 11.5% of their orders improving

18

the best price and 58% at the best price. Notably, buy-side institutions, submit a larger

fraction of their orders improving the price, around 21%, and they submit a further 48%

of their orders at the best price; this behavior suggests that buy-side traders want to get

trades done and thus use relatively more aggressively priced orders.

VI. Reactions to Trades

A. Aggregate Observations

Practitioners often describe the phenomenon of the so-called quote-fade, a situation

when following a trade, available liquidity at the best prices disappears market-wide.

Models of asymmetric information, such as Glosten and Milgrom (1985) and Glosten

(1994), will predict that a market maker would adjust quotes after observing trades,

usually by adjusting posted prices upward after buys and downward after sells. The

reason for the adjustment is that trades, on average, convey some information about

the fundamental value. For instance, a sell (at least on average) reveals that the seller

believes the stock to be overvalued and thus, upon observing a sell, the market maker

adjusts the price downward. And alternative view is that as a market maker takes an

inventory, e.g., when buying from a seller, then he accepts a liability. If the stock were

to fall in price, he would lose. Assuming that the market maker is risk averse, he would

accept further inventories only at lower prices. Both information and risk-aversion would

thus imply that market makers adjust quotes on the opposite side of the market relative

to the trade, i.e., they should adjust the bid following a sell and the ask following a

buy.13 If market makers quote on multiple markets, then they will adjust these quotes

on multiple venues. As a first step, we thus ask if this immediate adjustment is visible

in the data.

Using SubSample 1, we compute, for every trade, the volume cancelled by market

makers during the 2, 5, 10, 50, 100, 500, and 1,000 milliseconds subsequent to a trade and

in the opposite direction of the trade (e.g., cancellations of passive buy-orders following

a marketable sell order), where we distinguish between trades that were initiated by

13One can further make a case that the market maker should also adjust the quote on the same sideof the market, where the latter argument usually relies on a competition-based argument. We focus onthe opposite side here to simplify the exposition.

19

buy-side, retail and non-market making HF traders. We then compute the cancellation

rate x milliseconds after the trade as follows: for buyer-initiated trades, we compute

the total volume of cancelled sell-orders within x milliseconds of the trade by market

makers. We scale this number by (a) the number of milliseconds since the trade and

(b) the sum of all order-volume by market makers for the day for the security. Scaling

by market-maker order volume allows us to better compare results across the different

securities. It is computationally impractical to compute cancellations on a linear scale

(i.e., for every millisecond), and by dividing by passage-time, we can provide a better

assessment of the cancellation rate per millisecond.

Panel A in Figure 5 plots the aggregate distribution of opposite-side cancellations for

Subsample 1. It illustrates that the cancellation rate is largest in the first 10 milliseconds

after a trade, and the rate is 6 to 7 times smaller after 100 milliseconds. To the naked

eye, which cannot process information in intervals smaller than 250 milliseconds, the

quotes would thus indeed appear to disappear instantly.

By canceling quotes, a market maker aims to ensure that he is not “picked off” in

the future. However, it is possible that there are other traders’ orders in the book at

now “wrong” prices, e.g., buy orders that are at bid prices that became “too high” after

a sell. These stale quotes can present a profit opportunity if the fundamental value has

moved sufficiently. Thus assuming that non-HFTs are slow to react to the information

contained in prices and that such traders’ orders are present in the order book, we should

observe that fast traders, including HFT market makers, take advantage of stale quotes

and trade against them. An alternative view is that market makers have predictive power

over future order flow and thus trade in anticipation of such flow. Namely, large buy-side

orders (“parent” orders) are usually not traded in one large chunk, but they commonly

get split into smaller (“child”) orders that are traded over time. If, by observing the

order flow, market makers can detect the presence of a large parent order (for instance,

because the buy-side child orders are traded with a poorly designed algorithm), then

market makers may try to trade ahead of the large order and, as a consequence, would

trade against existing orders in the book. Both views presented here would result in a

situation where, subsequent to the trade, HFT market makers submit aggressive trades

in the direction of the trade.

We compute the submission rate of aggressive orders that are in the direction of the

20

trade analogously to the cancellation rate. We specifically consider not only marketable

orders (which trade) but also immediate-or-cancel orders (which were presumably sub-

mitted with the intention to trade but which may not find an execution). As with

cancelled volume, we compute the aggressive volume submitted 2, 5, 10, 50, 100, 500,

and 1,000 milliseconds subsequent to a trade, and we scale it by the market maker

aggressive volume for the day for the security and the passage time since the trade.

Panel B in Figure 5 plots the aggregate distribution of same-side aggressive order

submissions. As can be seen, the rate is also largest in the first 2,5, and 10 milliseconds

after a trade, and the rate is much smaller at longer horizons.

B. Trade-by-Trade Regression Analysis

Having analyzed the aggregate cancellations and order submission rates, we seek to

confirm these casual observations with a formal regression analysis. We approach the

problem from different angles, using different types of independent variable specifications

for our dependent variables, the cancellation and order submission rates.

We additionally analyze whether it matters if the trade was part of a smart-order-

routed trade and whether it matters if the liquidity provider of the trade was a market-

maker. We perform the regressions analysis in this subsection based on trade-by-trade

observations. As the trading day progresses, it may be possible for traders, in particular

market makers who are active in many trades, to detect whether a particular trader

accumulated a position. It is thus imaginable that over the day (and thus over larger

cumulative volume) cancellation rates increase. In the next subsection, we aggregate by

cumulative volume deciles to further study this issue.

Smart-Order Routed Trades. We classify a trade as stemming from a smart order

router (SOR) if all of the following three conditions are met: (1) trade originated from

the same trader, (2) the trade involves transactions on at least two different marketplaces

within 5 milliseconds and (3) if the time from the first to the last transaction does not

exceed 9 milliseconds. We aggregate the total value for such trades, and we consider the

cancellation and new order submission volume based on the time of the first transaction

21

that is part of the trade. We then estimate the following regression

DVt+m = α× SORt|volt|+ κ× (1− SORt)|volt|+3

∑

i=1

βjcontroljt + ǫt, (3)

where DVt+m is the dependent variable that measures the volume of cancelled orders in

the opposite direction of the time t trade in the m milliseconds following the trade at

time t; volt is the time t dollar-volume (aggregated by market order); the three control

variables controljt and are the log of the daily cumulative volume in the security up until

the trade, the signed trade imbalance up to but not including that trade (in percent),

and the security’s return since the open (in percent). Variable SORt is a dummy that is

1 if the trade at time t is a SOR trade and 0 otherwise. For this regression, we will test

whether αj = κj.

Which type of liquidity provider? Similarly to smart order routed trades, we

assess whether the cancellation rate depends on the type of trader who supplied liquidity.

For this test, we interact the value with dummies for market maker and non-market

maker passive traders

DVt+m = α×mmt|volt|+ κ× (1−mmt)|volt|+

3∑

i=1

βjcontroljt + δi + ǫt, (4)

where mmt is a dummy that is 1 if the trade at time t had a market maker on the passive

side (for any of the transactions) and 0 otherwise.

Results. Table II presents the results for the case where we do not distinguish between

the types of trader who initiated the order (except that we only consider marketable

orders from buy-side, retail and non-market-making HFT). To simplify the exposition,

we multiplied the dependent variable with 1,000,000.

We observe a positive impact of a trade’s dollar-volume on the cancellation and

aggressive order submission rates, and we observe that the effects on the rates are largest

in the first 5-10 milliseconds after the trade. We also observe that having a market maker

on the passive side or the trade being classified as a SOR trade increases the cancellation

rate, except in the first 5ms. For aggressive order submission rates, there is a similar

pattern for trades with HFT on the passive side in the sense that in the first 5-10

milliseconds after the trade, trades without an market maker on the passive side have

22

higher cancellation rates and that after the first 10 milliseconds, the order reverses. For

SOR trades, the estimated coefficient is always smaller, though the order of magnitude

is similar. Notably, SOR trades are three-times larger than non-SOR trades, and thus

when a SOR trade occurs, the observed impact will be larger. For most specifications,

the estimated coefficients are statistically significantly different. Since we aggregate the

data based on the first transaction of a trade, it is possible that the difference in the first

five milliseconds stems from trading system latency in the sense that we start counting

cancellations too early.

C. Which type of trader demands liquidity?

We determine the type of trader for the aggressive order and the trader’s daily ab-

solute net position up until and including this trade. We consider incoming trades only

from buy-side traders, retail traders, and non-market-making HFT; we omit market-

making HFTs because their trading and cancellation activities may be jointly deter-

mined. We perform the analysis by aggregating the data across dollar-volume and

inventory-deciles. Namely, for each security and for each type of volume (dollar value,

absolute value of directional volume across all traders and by group of traders (buy-

side, retail and non-market-making HFT) we determine the deciles. We then compute

for each day, stock and decile the averages for the cancellation rates, same-side aggres-

sive order submission rates, and the control variables (market-wide trade imbalance,

return, and volume traded). We aim to establish whether or not the cancellation rate

of market-makers depends on the volume that the trader had accumulated (expressed

by the trader’s cumulative volume) before he initiated the trade. We then estimate the

following regression

DVi

d,m = α + β × decile+3

∑

i=1

γjcontroljt + δ ×VIXt + ǫt, (5)

where DV d,m is the dependent variable that measures the average daily volume of can-

celled orders in the opposite direction of the trade for security i on day d in the m

milliseconds following the relevant trade; decile is the decile (1 to 10) for the cumula-

tive volume for the type of trader who submitted the market order; VIXt is the daily

realization of the U.S. volatility index VIX; the three control variables controljt are the

23

log of the daily cumulative volume in the security up until the trade, the signed trade

imbalance up to but not including that trade (in percent), and the security’s return since

the open (in percent). We estimate this regression separately for all traders and for the

three types of incoming trader (buy-side, retail, non-market making HFT). Transactions

by the same trader in the same direction within a time span of 9 milliseconds are con-

sidered to be a single trade. Standard errors in this regression are double-clustered by

date and firm to control for cross-sectional and serial correlations.

Results. Table III displays the summary statistics for the deciles of directional volume

for all traders, buy-side and non-market-making HFT. Figures 6 and 7 plot the average

cancelled and aggressively submitted volume for all traders, buy-side and non-market-

making HFT trades relative to the deciles for the cancellation and order submission

volume 2, 5 and 10 milliseconds after the trade. Buy-side traders generally have (much)

larger cumulative inventory than other types of traders, and the decile values for buy-

side mimic those of all traders combined. If the trader’s cumulative position matters,

then there should be a positive relationship between deciles and cancellation rates. As

can be seen, for all traders and for buy-side traders separately the rate is indeed increas-

ing,14 which suggests that as a buy-side trader accumulates an inventory, market makers

withdraw more volume from the market subsequent to trades. For non-market-making

HFT, however, the pattern is less clear: Panel C in Figure 7 indicates that there may

be only a weak relationship of accumulated inventory and cancellations, and Panel D

indicates that there may be no relationship of accumulated inventory and aggressive

order submissions.

Table IV presents the results for the case where we aggregate across all traders (either

by trading value or by directional volume). For all subsequent regression outcome tables,

we multiplied the dependent variable by 100,000 to ease the exposition. We observe a

positive impact of (directional) volume, and we also observe a positive slope, implying

that higher (directional) volume has a (proportionally) larger impact on the cancellation

and new order submission rates. Furthermore, we observe that the estimated effects for

cancellations are largest for the first 50 milliseconds (i.e., for the 2ms, 5 ms, 10ms and

50ms regressions) and for aggressive, same-side submission for the first 10ms. Indeed,

14In a robustness check, we also estimated a specification with an estimate for each decile. Then wechecked whether the coefficient for the 10th decile differed from the one for the first decile. The resultsare consistent.

24

the estimated coefficients are larger by an order of magnitude compared to those for

“later” (100ms+) cancellations.

Tables V displays the estimation results for the regressions by trader type. To sim-

plify the exposition, the table only shows the estimates for α, the intercept, and β, the

slope coefficient for the deciles. Thus each combination of α and β in the table represents

the result from a single regression.

For trades that stem from non-market making HFT, the slope coefficient is positive

and significant, except for long delays (500ms+), and the intercept for cancellations after

the trade is insignificant. For aggressive order submissions after the trade the slope and

most intercepts are insignificant, but positive. These results suggest that even those the

cancellation rate after HFT trades is positive, the net inventory of the HFT does not

affect the reaction of market makers. It is important to note that the decile values for

HFT and buy-side are different in the sense that buy-side traders generally accumulate

much more directional volume.

For trades from buy-side traders, the estimated slope for cancellations with regards

to the decile is positive and significant. Since the slopes are largest for the first four

estimations (2, 5, 10 and 50 ms), the cancellation effect of the volume is strongest

shortly after the trade. Since the intercept is non-negative (and the lowest decile value

is 1), the regression additionally confirms the trade-by-trade regression w.r.t. the overall

positive effect of a buy-side trade on the market-maker cancellation rate. For same-side

aggressive trades, the effect is strongly positive for buy-side traders, in particular for the

first three estimations (2, 5 and 10 ms). Since the intercept is positive and significant,

we conclude that there is a positive effect of a trade on same-side order submissions and

that this effect is positively related to the size of the inventory of the buy-side trader.

For trades from retail traders, the results are similar to those of buy-side traders.

Taken together, our decile analysis suggests that (a) market makers quickly move

the quote in response to trades, in particular from the buy-side, and (b) market makers

submit aggressive orders in the direction of the buy-side trade; furthermore, both effects

are amplified by the size of the inventory that the trader has already accumulated and

by the dollar-size of the incoming order.

25

VII. Market Making and Arbitrage

In this section we examine trading behaviour in securities that are linked by the same

underlying fundamentals. We consider three types of possible security pairs: stocks

with unequal voting rights, stocks with preferred shares, and stocks with debentures

(unsecured, exchange-traded debt).

We will explain our approach using the example of dual-class shares. When a firm has

dual-class shares —typically with different voting rights— one share class usually trades

more frequently than the other. An example in the Canadian context is Bombadier

Inc.: its BBD.B shares are among the most frequently traded securities, its BBD.A

shares trade less often. Even though they may represent the same claim on future cash

flows, stocks with unequal voting rights may trade at different prices, but over intra-

day horizons, it is unlikely that this value difference fluctuates strongly; see Shive and

Schultz (2010) and references therein. Intra-day price movements in both securities

should thus be highly correlated, except for extraordinary circumstances (e.g., when

corporate actions trigger a change in the difference between the two classes of shares).

At the high frequency level, when prices for one security move, the other should follow

suit, putting pressure on those traders that make the market in that security. Consider

a hypothetical firm for which its Class A securities trade frequently and its Class B

securities trade less frequently. We will study how trades in the Class A securities affect

trading and order submissions in the Class B securities. Consequently, in our regressions,

the dependent variables relate to the less-frequently traded securities (Class B in our

example here) whereas the explanatory variables relate to trading in the more-frequently

traded security (Class A).

We first observe that, as expected, there are fewer trades in the higher-voting rights

share class, preferred shares, and debentures compared to the other voting rights share

class, common shares, and equities respectively. For preferred shares, debentures, and

dual-class shares, there are, on average 125, 78 and 208 times as many trades in the

frequently-traded securities; see Table VI.

Next, we establish the price impact of trading in the more frequently traded securities

(Class A) on the less-frequently traded (Class B) securities. We compute price impacts

based on constructing the national best bid and offer price for the class B securities. We

define the price impact of a trade in the frequently traded security f on the infrequently

26

traded security i at time t as

price impactit = qft (mit+x −mi

t)/mit, (6)

where qft is 1 if the trade in f was a buy and −1 if it was a sell; mit is the midpoint

of the bid-ask spread in security i at time t; and mit+x is the midpoint of the bid-ask

spread in the security x units of time after time t, where we compute the price impact

for 1, 5 10, and 100 milliseconds, 1, 5, 10, and 30 seconds and 1,5, and 10 minutes. In

our regression analysis, we compute the volume-weighted averages per stock per day.

Finally, analogously to Section VI. we compute, for each trade in Class A securities,

how many trades and order cancellations follow in Class B securities by market makers

in the 2, 5, 10, 50, 100, 500 and 1,000 milliseconds after the Class A trade. For all

measures, we further differentiate between trades by the different types of traders.

We perform the analysis at the daily level, where, as in the last section, we scale

the daily observations by the daily market maker order volume and the time. We then

perform t-tests for the coefficients of interest. A statistically significant observation

indicates that the measure for buy-side, non-market-making HFT and retail respectively

is positive; the standard errors that we employ in these t-tests are clustered by firm and

date. In the last section, where we analyzed market making behavior following a trade

for the same security, we considered cancellations in the opposite direction of the trade.

Here, we study different securities and we include orders, cancellations and trades in both

directions because the direction of a strategy likely depends on the specific arbitrage

relation; for this reason, we also did not perform an analysis of same-side aggressive

order submissions.

Results. Our results for the daily price impact estimation are in table Table VII;

standard errors for this regression are clustered by security-pair and date. We first

observe that, in dual class shares, trades in the more frequently traded shares have a

positive and significant price impact for the less-often traded shares. For preferred shares

and debentures, we observe no clear pattern in terms of sign, size, or significance of the

estimated coefficients.

Our results for the daily estimations for canceled orders for debentures, preferred

shares and dual-class shares are in Table VIII. For debentures, we observe positive, but

insignificant effects of the trades on cancellation rates in the frequently-traded securities.

27

For preferred shares and dual class shares, we observe positive and significant effects for

cancellation rates. For all three classes of securities, consistent with the observations for

“isolated” securities, we observe that the cancellation effects are strongest in the first

10ms after the trade.

VIII. HFT in TSX Venture-Listed Securities

We discuss the extent of high-frequency trading in securities that are listed on the

Toronto Stock Exchange Venture, TSXV. The TSXV is the junior market to the TSX,

and its purpose is to bring young, smaller companies to the public market. Securities in

the TSXV tend to have small market capitalization and they often trade at sub-penny

prices. Nevertheless, even for low-priced stocks, the tick size is at least $0.005, making

it potentially beneficial to earn marking making profits with a low capital commitment.

Like TSX-listed securities, TSXV-listed securities can trade on any of Canada’s other

marketplaces. In this appendix, we present numbers for trading on all marketplaces

combined.

For this part of the analysis, we determined all TSXV-listed securities that traded

at any point between January and May 2013. We did not separately classify trader IDs

based on their trading in TSXV securities. Instead, we retained the trader groups from

the main analysis in the sense that trader IDs that trade in TSXV securities are classified

based on their trading in Large Sample securities. There are a number of reasons for why

we did not apply our classification method using trading in TSXV securities. Most of

the TSXV-listed securities trade infrequently, and it would thus be difficult to generate

enough data to assess reaction times. Furthermore, most TSXV securities commonly do

not qualify for the market-on-close facility, and we thus cannot classify traders based

on their reaction speed to the information about market-on-close imbalances. Since our

classification is based on broad, absolute measures, traders that act as HFTs in TSX

securities are also reasonably HFTs in TSXV securities. It is, however, possible that

some HFT IDs may specialize in TSXV-listed securities, and using the traders classified

for TSX-listed securities could thus lead to an underestimation of the extent of high

frequency involvement.

On average only around 8% of all passive trades in TSXV-listed securities were

by HFTs, and only 2% of aggressive trades. However, there is some significant cross-

28

sectional variation. Of the 2,478 TSXV securities, 1,266 have no HFT trading, and 1,676

have no aggressive HFT trades. Of those that do have some form of HFT trading, the

fraction of HFT trading is positively related to the trading volume in these securities

(this observation does not imply a causal relationship). Figure 8 plots the percentage

of total value traded by HFT (aggressive/passive in Panels A/B) in TSXV securities

against the total value (in logs).

Figure 9 shows the HFT participation as a fraction of all transactions and value.

Compared to the main market, HFT activity in TSXV stocks is lower, with only 20% of

transactions and less than 10% of value involving an HFT on the passive side (aggressive

volume is negligible). As Panel C indicates, however, they submit about 55% of all

orders, and they are thus noticeable in these securities. Panel D highlights the share

of HFT and other traders’ orders relative to best prices. HFTs generally submit more

than half of the orders that are submitted at the best price or that are improving the

best price.

Overall, there are many securities that see no HFT activity at all, but for the venture

market as a whole, HFT activity will be noticeable, in particular with regard to the

posting of aggressive, competitive quotes.

29

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and high frequency intermediation, Discussion paper, IIROC Working Paper.

Comerton-Forde, Carole, Katya Malinova, and Andreas Park, 2015, Regulating dark

trading: Order flow segmentation and market quality, Discussion paper, IIROCWork-

ing Paper.

Devani, Baiju, Lisa Anderson, and Yifan Zhang, 2015, Impact of the dark rule amend-

ments, Discussion paper, IIROC Working Paper.

Devani, Baiju, Ad Tayal, Lisa Anderson, Dawei Zhou, Juan Gomez, and Graham W.

Taylor, 2014, Identifying trading groups – methodology and results, Discussion paper,

IIROC Working Paper.

Glosten, Lawrence R., 1994, Is the electronic open limit order book inevitable?, The

Journal of Finance 49, 1127–1161.

, and Paul R. Milgrom, 1985, Bid, ask and transaction prices in a specialist

market with heterogenously informed traders, Journal of Financial Economics 14,

71–100.

IIROC, 2012, The HOT study, Discussion paper, Investment Industry Regulatory Or-

ganization of Canada.

Korajczyk, Robert, and Dermot Murphy, 2014, High frequency market making to large

institutional trades, Discussion paper, IIROC Working Paper.

Kyle, Albert S., 1985, Continuous auctions and insider trading, Econometrica 53, 1315–

1336.

Shive, Sophie, and Paul Schultz, 2010, Mispricing of dual-class shares: Profit opportu-

nities, arbitrage, and trading, Journal of Financial Economics 98, 524–549.

9988

778

3796

131

HFT MM buy−side other retail

Distribution of Trader Types

Figure 1

Trader Types

Figure 2

Visualization of Two-way clusters for HFT Groups

The figure represents the table of pairwise distances computed in equation (1) for the 101 trader IDs that are classified as HFT. Smallernumbers are represented by darker cell-shadings.

020

4060

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active passive

Distribution of Transactions by Types

HFT MM buy−side retail others

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4060

8010

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active passive

Distribution of Value by Types

HFT MM buy−side retail others

Panel A: Transactions Panel B: Value

Figure 3

Distribution of Trades by Trader-Types

The figure presents the distribution of aggregate trades (Panel A) and value traded (Panel B) for our large sample for the time fromJanuary to May 2013, split by classified trader-types.

020

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80%

orde

rs

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HFT Buyside non−HFT MM retail

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atbest better mktable worse

Distribution of Aggressive Orders by Types

HFT MM buy−side retail

Panel A: Times Series all Order Volume Panel B: Overall Distribution

4050

6070

80%

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ovin

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Market A Market B Market C

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Market A Market B Market C

Panel C: HFT as a percentage of improving Panel D: HFT as a percentage of at-best submissions

Figure 4

Distribution of Order Volume by Trader Type and Aggressiveness

Panel A plots the time series of the distribution of aggregated order volume. As of early May 2013, there was an upward shift in HFTorder volume and a simultaneous downward shift in non-HFT market maker volume. This shift was largely caused by changes to theorder submission behavior on market A: there, a number of market-making, non-HFT IDs stopped posting while at the same timenumber of previously classified HFT-market-making IDs increased their quoting behavior. The same shift is visible in Panels C and D,which plot the distribution of price-improving and at-best orders by trading venue. Taken together we thus hypothesize that severalnon-HFT and HFT market makers are, in fact, linked which is why we combine all market makers when we assess the reactions totrades. Panel B plots the distribution of orders by aggressiveness and type. Stacked up, the bars would add to 100%. Aggressivenessis defined relative to the prevailing best price posted on the respective trading venue.

0.5

11.

52

ms0002 ms0005 ms0010 ms0050 ms0100 ms0500 ms1000

Distribution of Opposite−Size Cancelations per unit of time

buyside retail non−MM HFT

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Distribution of Same−Side Aggressive Orders per unit of time

buyside retail non−MM HFT

Panel A Panel B

Figure 5

Cancellation and order-submission rates in response to trades.

The figures plot the opposite-side cancellation (Panel A) and same-side aggressive order submission (Panel B) rates by market-makingtraders. The rates are split by whether the trade that preceded the cancellations was by a retail, a buy-side or non-market-makingHFT.

050

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Market−makers’ cancellation vs. trader inventory at order submission

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Market−makers’ cancellation vs. volume at order submission

Panel A Panel B

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Market−makers’ aggressive orders vs. volume at order submission

Panel C Panel D

Figure 6

Cancellations and Order Submissions by Deciles of the Order Volume

and Incoming Trader’s Cumulative Inventory – all traders.

The figures plot the average opposite-side cancellation (Panels A and B) and same-side aggressive order submission (Panels C andD) volume by market-making traders against the dollar-volume of the incoming order and the deciles of the absolute inventory of thesubmitting trader. Deciles are computed across all trades per security. We do not scale volume here (thus for more passage-time, thevolume will be higher). We note that the dollar-volume deciles are very similar for the first 4 deciles.

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Panel A Panel B

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Market−makers’ aggressive orders vs. HFT inventory at order submission

Panel C Panel D

Figure 7

Cancellations and Order Submissions by Deciles of the Incoming Trader’s

Cumulative Inventory — by trader type.

The figures plot the average opposite-side cancellation (Panel A and C) and same-side aggressive order submission (Panel B and D)volume by market-making traders against the deciles of the absolute inventory of the submitting trader. Deciles are computed withregard to the trader-types. The rates are split by whether the trade that preceded the cancellations was by a buy-side or non-market-making HFT. In contrast to Figure 5, we do not scale volume here (thus for more passage-time, the volume will be higher).

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Panel A: Aggressive HFT vs. Log-Value Panel B: Passive HFT vs. Log-Value

Figure 8

Participation of HFT in TSXV-listed securities

The figure plots the log of value traded against the share of value traded actively (Panel A) and passively (Panel B) by HFT for oursample of 2,478 TSXV securities for the time from February 2013 to end-May 2013. The trader classification is based upon the mainsample of highly-liquid TSX-listed securities.

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Distribution of Transactions by Types

HFT MM buy−side retail others

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HFT MM buy−side retail others

Panel A: Transactions Panel B: Value

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Distribution of Aggressive Orders by Types

HFT MM buy−side retail

Panel C: Order Volume Panel D: Order Aggressiveness

Figure 9

TSX Venture Stocks: Distribution of Trades and Orders by Trader-Types

The figure plots the log of value traded against the share of value traded actively (Panel A) and passively (Panel B) by HFT for thoseTSXV securities that display any form of HFT-trading during the time from February 2013 to end-May 2013. The trader classificationis based upon the main sample of highly-liquid TSX-listed securities.

Table I

Summary Statistics for Trader Type Activities

The table presents summary statistics for trading activities by the different trader types; all numbers are averages per trader in therespective group. Total orders and trades are summed over the entire horizon from January to May 2013 for the Large Sample. Averagedaily orders are summed across all securities per day.

All traders HFT Buy-side Retailnon-HFTmarket makers

HFT marketmakers

Others

securities traded 14 67 19 42 59 157 9average daily trades 569 2,246 943 1,549 2,328 15,222 194total trades 47,434 173,677 84,674 159,970 150,012 1,500,000 11,343average daily orders 5,130 25,916 2,282 1,396 38,307 318,902 613total orders 466,299 2,032,000 215,933 144,629 2,509,000 31,160,000 46,415%orders within 1ms of market event 35 61 37 35 33 82 33median order to cancel time 274,124 38,494 193,351 550,132 825,670 11,116 274,494trades at 15:40 71 2,311 38 9 64 3,897 2orders at 15:40 317 3,353 125 3 690 23,130 14average daily trade imbalance 91 79 99 92 26 31 92average daily order imbalance 93 74 99 92 10 11 95

Table II

Cancellations after Trades: Smart-Order Routers and Passive MM-HFT

The table presents results from our OLS estimation of equations (3) and (4) which assesses whether the impact of a trade differsdepending on whether or not the aggressive order stemmed from a smart order router (Panel A and C) and whether or not thepassive-side trader was a market maker or not (Panel B and D). The regression is based on SubSample1 and it is estimated for eachmarketable order (1,534,305 observations). For most estimates in Panels A and C, we cannot reject a test of equality of the coefficientsfor the different trader groups, for most estimates in Panels B and D we can reject the equality hypotheses. All regressions includethree control variables: the log of the daily cumulative volume in the security up until the trade, the signed trade imbalance up tobut not including that trade (in percent), and the security’s return since the open (in percent). Standard errors are in parentheses. *indicates significance at the 10% level, ** at the 5% level, and *** at the 1% level.

2ms 5ms 10ms 50ms 100ms 500ms 1000ms

Panel A: SOR trades and opposite side cancellations

SOR trade 0.000799*** 0.00382*** 0.00473*** 0.00308*** 0.00168*** 0.000399*** 0.000208***(0.00009) (0.00022) (0.00027) (0.00016) (0.00009) (0.00002) (0.00001)

non-SOR trade 0.00374*** 0.00450*** 0.00378*** 0.00224*** 0.00125*** 0.000344*** 0.000188***(0.00014) (0.00020) (0.00017) (0.00009) (0.00005) (0.00001) (0.00001)

Panel B: HFT MM passive and opposite side cancellations

passive MM 0.00315*** 0.00591*** 0.00628*** 0.00365*** 0.00201*** 0.000492*** 0.000261***(0.00014) (0.00020) (0.00021) (0.00011) (0.00006) (0.00001) (0.00001)

passive other 0.00015 0.000734*** 0.000558*** 0.000924*** 0.000500*** 0.000152*** 0.0000831***(0.00008) (0.00009) (0.00007) (0.00007) (0.00004) (0.00001) (0.00001)

Panel C: SOR trades and same-side aggressive orders

SOR trade 0.0763*** 0.152*** 0.139*** 0.0416*** 0.0215*** 0.00454*** 0.00233***(0.01150) (0.01060) (0.00829) (0.00238) (0.00123) (0.00026) (0.00013)

non-SOR trade 0.441*** 0.304*** 0.188*** 0.0490*** 0.0258*** 0.00574*** 0.00304***(0.03030) (0.01530) (0.00980) (0.00247) (0.00123) (0.00028) (0.00014)

Panel D: HFT MM trades and same-side aggressive orders

passive MM 0.125*** 0.185*** 0.158*** 0.0476*** 0.0250*** 0.00543*** 0.00282***(0.01280) (0.00370) (0.00610) (0.00169) (0.00089) (0.00019) (0.00010)

passive other 0.453*** 0.285*** 0.166*** 0.0399*** 0.0206*** 0.00441*** 0.00231***(0.04420) (0.02470) (0.01470) (0.00356) (0.00183) (0.00039) (0.00020)

Table III

Summary Statistics: Cancellations and Aggressive Orders after Trades by Deciles

Opposite-side cancelled order volume Same-side aggressive volumeDecile |

∑volume| 2ms 5ms 10ms 50ms 100ms 500ms 1000ms 2ms 5ms 10ms 50ms 100ms 500ms 1000ms

Panel A: All traders

1 292 145 381 628 1,893 2,215 3,186 3,696 84 176 244 352 390 466 5172 959 170 454 744 2,142 2,467 3,470 3,977 95 203 281 398 434 507 5593 1,933 177 475 788 2,242 2,577 3,578 4,097 100 219 306 430 462 535 5944 3,358 189 521 869 2,437 2,768 3,737 4,266 103 233 335 475 506 571 6275 5,429 211 573 976 2,651 2,995 3,985 4,514 107 248 350 503 533 593 6446 8,427 215 580 996 2,675 3,027 3,992 4,498 110 255 367 536 566 624 6727 12,987 219 602 1,049 2,876 3,243 4,195 4,691 120 277 413 616 651 710 7558 20,600 230 642 1,140 3,093 3,435 4,363 4,888 130 298 478 737 773 840 8899 36,902 259 787 1,474 3,942 4,337 5,391 5,921 144 359 578 905 972 1,064 1,11610 84,009 244 814 1,722 4,244 4,653 5,720 6,247 138 423 692 1,057 1,102 1,200 1,274

Panel B: non-market-making HFT

1 139 103 220 334 703 816 1,258 1,498 168 334 487 754 830 1,063 1,2292 366 114 232 359 776 917 1,430 1,722 211 408 591 924 1,054 1,278 1,4313 727 161 319 486 1,004 1,186 1,778 2,092 258 478 682 1,143 1,275 1,574 1,7574 1,052 124 255 404 881 1,041 1,612 1,920 211 438 658 1,119 1,242 1,531 1,7185 1,802 121 252 413 890 1,198 1,709 2,108 253 496 756 1,248 1,419 1,686 1,9296 2,711 98 231 382 887 1,024 1,474 1,838 205 405 619 1,057 1,179 1,446 1,6697 4,455 104 225 397 900 1,050 1,484 1,745 212 417 667 1,050 1,197 1,443 1,7748 6,829 105 278 467 928 1,086 1,528 1,732 201 419 717 1,139 1,273 1,511 1,7049 12,697 152 331 498 929 1,040 1,432 1,623 301 558 880 1,381 1,488 1,665 1,85910 26,505 102 254 442 887 998 1,390 1,600 137 417 784 1,830 1,894 2,042 2,281

Panel C: buy-side

1 330 58 135 194 438 506 757 886 71 150 206 292 322 380 4212 1,086 69 160 228 489 562 823 950 85 184 252 349 379 434 4753 2,149 73 167 242 512 584 848 975 92 203 285 395 422 476 5244 3,670 79 187 273 561 631 893 1,028 98 223 318 446 472 528 5795 5,844 88 205 306 617 693 956 1,089 103 241 337 487 514 573 6206 8,941 88 209 315 618 698 956 1,079 110 256 368 530 559 613 6577 13,599 90 219 329 646 726 989 1,110 119 275 406 601 637 699 7458 21,388 98 234 360 698 770 1,031 1,166 132 303 483 732 766 832 8829 38,074 108 277 454 896 985 1,302 1,438 164 376 574 883 951 1,047 1,09910 86,522 103 299 552 1,028 1,114 1,428 1,562 132 412 684 1,053 1,096 1,185 1,251

Table IV

Regressions: Cancellations and Aggressive Orders after Trades by Deciles.

The table presents results from our OLS estimation of equation (5). It assesses whether the impact of a trade differs depending on thedecile of the order-submitter’s cumulative volume (Panel A) and directional volume (Panel B) at the time of the trade. The regressionis based on SubSample1 and it is estimated for the stock-day-deciles for all traders. All regressions include four control variables (allaveraged by decile): the log of the average daily cumulative volume in the security up until the trade, the signed trade imbalance upto but not including that trade (in percent), the security’s return since the open (in percent), and the daily realization of the U.S.volatility index VIX. Standard errors are in parentheses and they are double-clustered by firm and date. * indicates significance at the10% level, ** at the 5% level, and *** at the 1% level.

2ms 5ms 10ms 50ms 100ms 500ms 1000ms

Panel A: Directional volume and opposite side cancellations

Slope 1.70*** 1.98*** 2.00** 1.58*** 0.83*** 0.18*** 0.09***(0.35) (0.60) (0.90) (0.41) (0.21) (0.05) (0.02)

Intercept -82.84 -137.96 -150.78 50.21 30.89 12.06** 7.41**(109.08) (127.26) (124.30) (57.71) (29.95) (6.09) (3.31)

Panel B: Directional volume and same side aggressive volume

Slope 227.39*** 179.86*** 122.52*** 29.93*** 15.08*** 3.18*** 1.60***(72.81) (28.38) (21.08) (5.89) (2.99) (0.63) (0.31)

Intercept 17,691.69*** 9,654.24*** 4,763.13*** 1,000.57* 524.81* 121.07** 64.39**(3,096.71) (1,802.00) (1,521.84) (513.16) (273.12) (56.90) (30.49)

Panel C: Dollar volume and opposite side cancellations

Slope 2.62** 4.04*** 3.52*** 2.90*** 1.58*** 0.42*** 0.23***(1.19) (1.19) (0.95) (0.25) (0.13) (0.03) (0.02)

Intercept -25.74 -30.53 -21.10 62.36*** 35.99*** 11.68*** 7.06***(62.21) (58.63) (46.07) (19.59) (10.31) (2.21) (1.32)

Panel D: Dollar volume and same side aggressive volume

Slope 398.18*** 311.35*** 200.44*** 50.62*** 26.57*** 5.82*** 3.06***(47.52) (29.18) (17.51) (4.27) (2.30) (0.51) (0.27)

Intercept 8,103.25*** 4,315.75*** 2,296.57*** 576.27** 304.07** 70.69*** 39.38***(1,744.60) (1,172.79) (799.58) (228.08) (119.86) (26.27) (13.82)

Table V

Regressions: Cancellations and Aggressive Orders after Trades by Deciles.

The table presents results from our OLS estimation of equation (5). It assesses whether the impact of a trade differs depending onthe quintile of the order-submitter’s cumulative inventory at the time of the trade. The regression is based on SubSample1 and itis estimated for the stock-day-quintile (6,737 observations for buy-side, 5,418 for non-market-making HFT, and 6,291 for retail). Allregressions include four control variables (all averaged by quintile): the log of the average daily cumulative volume in the security upuntil the trade, the signed trade imbalance up to but not including that trade (in percent), the security’s return since the open (inpercent), and the daily realization of the U.S. volatility index VIX. Standard errors are in parentheses and they are double-clusteredby firm and date. * indicates significance at the 10% level, ** at the 5% level, and *** at the 1% level.

2ms 5ms 10ms 50ms 100ms 500ms 1000ms

Panel A: Opposite-side cancelled order volume

buy-side slope 1.878311*** 2.089765*** 2.129935** 1.679728*** 0.889664*** 0.210862*** 0.113055***(0.378322) (0.619629) (0.905711) (0.411327) (0.214700) (0.045083) (0.022218)

intercept -84.740302 -140.480081 -152.870120 46.217414 28.767977 11.466415* 7.026424**(108.310335) (126.154238) (123.677602) (57.278019) (29.502529) (5.933288) (3.189934)

non-MM HFT slope 1.409190* 1.873467*** 1.549070*** 0.911765*** 0.465798*** 0.084447 0.044462(0.816054) (0.709918) (0.573410) (0.288212) (0.170468) (0.057924) (0.033926)

intercept -501.438150 -408.846948 -315.444831 -42.357761 -23.404032 -0.714002 0.883114(349.255846) (281.482068) (222.976829) (89.330541) (49.824929) (10.480873) (6.078769)

retail slope 3.033805*** 3.339257*** 3.137842*** 2.240723*** 1.326900*** 0.344408*** 0.187405***(0.640917) (0.846633) (0.855842) (0.360650) (0.201783) (0.047876) (0.023550)

intercept -49.722733 -133.171311 -113.890587 111.328841* 65.179915** 19.089377*** 11.060655***(145.394688) (173.708333) (144.618198) (57.946775) (31.164041) (6.073277) (3.186634)

Panel B: Same-side aggressive volume

buy-side slope 353.867509** 235.803974*** 147.658130*** 36.767947*** 18.738474*** 4.005234*** 2.052980***(156.638508) (58.467007) (29.782993) (6.630350) (3.358143) (0.700256) (0.356427)

intercept 19262.840585*** 10166.689667*** 4,636.174092*** 950.908143* 495.681849* 116.196233** 61.414496**(4,517.726679) (2,068.787520) (1,491.000983) (501.075870) (264.236320) (54.748115) (29.667493)

non-MM HFT slope -25.455048 1.136734 35.005358 8.596510 5.456145 1.065000 0.751001(42.255192) (26.256268) (31.684198) (8.726318) (5.345547) (1.196771) (0.798077)

intercept 7,989.033811** 6,795.741798** 5,814.865456** 1,243.876197 693.614307 168.727052 97.825422(3,587.990560) (2,959.147648) (2,966.679349) (853.137856) (512.512151) (115.169678) (73.553756)

retail slope 160.835796*** 139.860817*** 100.599065*** 33.481836*** 19.298198*** 4.237356*** 2.167784***(24.368633) (18.602006) (20.152911) (6.114839) (3.528363) (0.701904) (0.336995)

intercept 13360.216706*** 7,662.132855*** 3,889.792290*** 1,233.983624*** 685.600488*** 166.089020*** 87.265567***(1,810.690969) (551.222590) (1,036.142418) (459.442243) (257.526106) (55.444537) (29.823494)

Table VI

Summary Statistics Related Securities

The table presents summary statistics for trading activities in debenture, preferred shares, the higher voting rights share class for dualclass shares and the more frequently traded security (last column). The table is based on SubSample2.

frequentlyMean Stdev max traded

Preferred trades 21 22 545 2,624volume 7,407 22,771 1,139,600 741,347value 187,547 570,439 28,600,000 13,800,000

Debentures trades 31 65 413 2,422volume 19,488 44,728 310,100 1,827,376value 80,962 158,995 1,381,529 12,700,000

Dual trades 9 15 203 1,869volume 74,113 120,740 1,891,000 775,860value 77,818 124,410 1,919,425 8,203,107

Table VII

Price Impact for Fundamentally Linked Securities

1ms 5ms 10ms 100ms 1s 5s 10s 30s 1min 5min 10min

Panel A: Dual Class SharesBuy-Side 0.0000 0.0000 0.0000 0.0020*** 0.0033*** 0.0045*** 0.0054*** 0.0073*** 0.0073*** 0.0112*** 0.0118***

[0.8064] [-0.8160] [-0.4745] [3.0274] [2.6539] [3.1843] [3.1869] [3.5267] [3.6548] [3.1281] [2.9697]

non-MM HFT 0.0000 0.0000 0.0000 0.0019* 0.0060** 0.0054*** 0.0073*** 0.0094*** 0.0135*** 0.0293** 0.0319**[0.5118] [0.3021] [-0.3739] [1.7273] [2.3903] [3.0148] [2.7094] [3.1750] [3.8955] [2.5343] [2.5062]

retail 0.0000 0.0000 0.0002** 0.0073 0.0002 0.0076*** 0.0059** 0.0084*** 0.0113*** 0.0142*** 0.0157**[1.0714] [1.2723] [2.4663] [1.5694] [0.0715] [3.1030] [2.3573] [3.5398] [3.7271] [2.8729] [2.2111]

Panel B: Preferred SharesBuy-Side 0.0000 0.0000 0.0000 0.0000** 0.0000 -0.0000** -0.0001** -0.0001* -0.0002* -0.0002 0.0000

[1.3964] [1.0008] [0.9689] [2.1890] [-0.5436] [-1.9891] [-2.4798] [-1.8232] [-1.9392] [-0.9644] [0.0773]

non-MM HFT 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 -0.0001 -0.0002* -0.0004 -0.0001[0.3410] [-0.5396] [0.0905] [0.1340] [0.8849] [1.1555] [-0.0819] [-1.2779] [-1.7901] [-1.4841] [-0.2758]

retail 0.0000 0.0000 0.0000 0.0000 0.0000 -0.0001 -0.0001 0.0001 -0.0001 0.0002 0.0002[0.2214] [0.0919] [0.9296] [1.5156] [0.5258] [-1.2956] [-1.5953] [0.4624] [-0.9515] [0.4251] [0.4883]

Panel C: DebenturesBuy-Side 0.0000 0.0001 0.0001 0.0000 -0.0013 -0.0035* -0.0023 -0.0004 0.0008 0.0036** 0.0042*

[-0.8097] [1.5864] [0.8445] [0.0099] [-1.0102] [-1.8927] [-1.5459] [-0.4042] [0.7784] [1.9764] [1.6621]

non-MM HFT 0.0000 0.0003* 0.0001*** -0.0005 -0.0014 -0.0035 -0.0022 -0.0006 0.0003 0.0038 0.007[0.7663] [1.9551] [3.0732] [-0.2822] [-0.4198] [-1.0016] [-0.7521] [-0.2195] [0.1171] [1.0988] [1.1256]

retail 0.0000 0.0001* 0.0002 0.0002 -0.0019 -0.0047** -0.0031* -0.0012 -0.0001 0.0019 0.002[0.0888] [1.7147] [1.3363] [0.1093] [-1.0613] [-2.0037] [-1.6451] [-0.9667] [-0.1189] [0.7863] [0.7332]

Table VIII

Cancellation Rates Across Fundamentally Linked Securities

Cancels 2ms 5ms 10ms 50ms 100ms 500ms 1000ms

Panel A: Debentures

Buy-side 25,337.70 10,135.08 5,067.54 1,013.51 506.7562 101.3566 50.6805[1.1525] [1.1525] [1.1525] [1.1525] [1.1525] [1.1526] [1.1526]

HFT 4,590.28 1,836.11 918.0574 183.6115 91.806 18.362 9.1816[1.1453] [1.1453] [1.1453] [1.1453] [1.1453] [1.1453] [1.1454]

retail 3,489.25 1,395.70 697.8506 139.5706 69.7855 13.9611 6.9816[1.5685] [1.5635] [1.5635] [1.5685] [1.5685] [1.5690] [1.5692]

Panel B: Preferred Shares

Buy-side 3,926.7934*** 1,570.7184*** 785.3613*** 157.0682*** 78.5345*** 15.7062*** 7.8538***[6.4050] [6.4050] [6.4050] [6.4052] [6.4052] [6.4056] [6.4064]

HFT 1,446.2056*** 578.4805*** 289.2405*** 57.8487*** 28.9231*** 5.7850*** 2.8927***[5.4669] [5.4668] [5.4663] [5.4669] [5.4666] [5.4671] [5.4678]

retail 1,339.9715*** 535.9893*** 267.9951*** 53.5995*** 26.7983*** 5.3585*** 2.6796***[6.1955] [6.1955] [6.1955] [6.1956] [6.1955] [6.1952] [6.1962]

Panel C: Dual-Class Listing

Buy-side 959.2655*** 383.7091*** 191.3604*** 38.3763*** 19.1834*** 3.8322*** 1.9213***[2.8018] [2.8019] [2.8020] [2.8023] [2.3020] [2.7979] [2.8108]

HFT 392.6936*** 157.0847*** 78.5517*** 15.7277*** 7.8680*** 1.5742*** 0.7940***[2.9130] [2.9132] [2.9139] [2.9203] [2.9233] [2.9317] [2.9700]

retail 57.1960*** 22.3788*** 11.4412*** 2.2906*** 1.1462*** 0.2279*** 0.1160***[4.1663] [4.1665] [4.1636] [4.1805] [4.1842] [4.3050] [4.3232]

Table IX

List of Securities used in SubSamples 1 &2

Non-CrossListed Preferred Debentures Dual Class

TSX60

ARX AIM AIM.PR.A PWF PWF.PR.A AFN AFN.DB AC.B AC.A

BBD.B ALA ALA.PR.A PWF PWF.PR.E ARE ARE.DB ACM.A ACM.B

COS ALA ALA.PR.U PWF PWF.PR.F ARE ARE.DB.A ATD.B ATD.A

CPG AQN AQN.PR.A PWF PWF.PR.G AX.UN AX.DB.F BBD.B BBD.A

CTC.A AX.UN AX.PR.A PWF PWF.PR.H AX.UN AX.DB.U CCL.B CCL.A

ERF AX.UN AX.PR.E PWF PWF.PR.I AYA AYA.DB DII.B DII.A

FM AX.UN AX.PR.U PWF PWF.PR.K CHE.UN CHE.DB QBR.B QBR.A

FTS BBD.B BBD.PR.B PWF PWF.PR.L CHE.UN CHE.DB.A TCL.A TCL.B

HSE BBD.B BBD.PR.C PWF PWF.PR.M CRR.UN CRR.DB.B

L BBD.B BBD.PR.D PWF PWF.PR.O CRR.UN CRR.DB.C

MRU BIR BIR.PR.A PWF PWF.PR.P CRR.UN CRR.DB.D

NA CF CF.PR.A PWF PWF.PR.R CSH.UN CSH.DB.B

POW CF CF.PR.C PWF PWF.PR.S CUF.UN CUF.DB.C

SAP CPX CPX.PR.A REI.UN REI.PR.A CUF.UN CUF.DB.D

SC CPX CPX.PR.C REI.UN REI.PR.C CUF.UN CUF.DB.E

SNC CPX CPX.PR.E RON RON.PR.A CUS CUS.DB

WN CU CU.PR.C TCL.A TCL.PR.D CUS CUS.DB.A

CU CU.PR.D VSN VSN.PR.A CUS CUS.DB.B

CU CU.PR.E WN WN.PR.A CWT.UN CWT.DB.B

CU CU.PR.F WN WN.PR.C D.UN D.DB.H

CU CU.PR.G WN WN.PR.D DC.A DC.DB

CWB CWB.PR.A WN WN.PR.E DIR.UN DIR.DB

DC.A DC.PR.A EIF EIF.DB.A

DC.A DC.PR.B EIF EIF.DB.B

DC.A DC.PR.C EIF EIF.DB.C

EMA EMA.PR.A EIF EIF.DB.D

EMA EMA.PR.C EIF EIF.DB.E

FFH FFH.PR.C EIF EIF.DB.F

FFH FFH.PR.E EXE EXE.DB

FFH FFH.PR.G EXE EXE.DB.B

FFH FFH.PR.I FCR FCR.DB.D

FFH FFH.PR.K FCR FCR.DB.E

FTS FTS.PR.C FCR FCR.DB.F

FTS FTS.PR.E FCR FCR.DB.G

FTS FTS.PR.F FCR FCR.DB.H

FTS FTS.PR.G FCR FCR.DB.I

FTS FTS.PR.H FCR FCR.DB.J

FTS FTS.PR.J HR.UN HR.DB.C

GWO GWO.PR.F HR.UN HR.DB.D

GWO GWO.PR.G HR.UN HR.DB.E

GWO GWO.PR.H HR.UN HR.DB.F

GWO GWO.PR.I HR.UN HR.DB.G

GWO GWO.PR.J HR.UN HR.DB.H

GWO GWO.PR.L INE INE.DB

GWO GWO.PR.M INN.UN INN.DB.B

GWO GWO.PR.N INN.UN INN.DB.C

GWO GWO.PR.P INN.UN INN.DB.D

GWO GWO.PR.Q INN.UN INN.DB.E

GWO GWO.PR.R INN.UN INN.DB.F

HSE HSE.PR.A INN.UN INN.DB.G

IAG IAG.PR.A KEY KEY.DB.A

IAG IAG.PR.C KMP KMP.DB.A

IAG IAG.PR.E KMP KMP.DB.B

IAG IAG.PR.F LW LW.DB

IAG IAG.PR.G MRT.UN MRT.DB.A

IFC IFC.PR.A MSI MSI.DB

IFC IFC.PR.C NKO NKO.NT

IGM IGM.PR.B NPI NPI.DB.A

INE INE.PR.A ORT ORT.DB

INE INE.PR.C PGF PGF.DB.A

L L.PR.A PGF PGF.DB.B

LB LB.PR.D PKI PKI.DB

LB LB.PR.E PKI PKI.DB.A

LB LB.PR.F PRE PRE.DB

NA NA.PR.K PXT PXT.DB

NA NA.PR.L RMM.UN RMM.DB.A

NA NA.PR.M RMM.UN RMM.DB.B

NA NA.PR.N RMM.UN RMM.DB.C

NA NA.PR.O RUS RUS.DB

NA NA.PR.P SPB SPB.DB.C

NA NA.PR.Q SPB SPB.DB.D

NPI NPI.PR.A SPB SPB.DB.E

NPI NPI.PR.C SPB SPB.DB.F

POW POW.PR.A SPB SPB.DB.G

POW POW.PR.B STP STP.DB

POW POW.PR.C TCN TCN.DB

POW POW.PR.D TCN TCN.DB.A

POW POW.PR.E TFI TFI.DB

POW POW.PR.F TFI TFI.DB.A

POW POW.PR.G VSN VSN.DB.C