1

Liquidity provision, Commonality and High-Frequency trading

(WORKING PAPER – 31/03/2017)

Panagiotis Anagnostidis (1) Patrice Fontaine (2)

(1) Institut Europlace de Finance (IEF) and European Financial Data Institute (EUROFIDAI)

(2) European Financial Data Institute (EUROFIDAI), CNRS and Léonard de Vinci Pôle Universitaire,

Research Center

Abstract

We investigate empirically the role of high frequency (HF) quoting i) in the liquidity provision process

and ii) in the formation of market-wide systematic (il)liquidity movements — (il)liquidity commonality

— in the Euronext Paris CAC 40 stock market. The related literature has, so far, focused on the effect

of HF algorithms on firm specific liquidity, whereas there is little evidence on the role of HF quoting in

liquidity risk. Thus, our results contribute to the current understanding of how low latency activity

influences market quality. We find that up to the best 10 limits of the order book a large part of

liquidity provision is attributed to non-marketable HF quotes (more than 90% of available shares)

which are submitted, mainly, by designated liquidity providers and large Institutions. On the other

hand, non HF quotes are less aggressive, lying deeper into the order book. To this extent, our empirical

findings indicate that HF quotes improve liquidity, narrowing the spreads, whereas they are more

susceptible to adverse selection compared to non HF quotes. Trading activity is driven mainly by

individual brokers (almost 70% of marketable orders), although a significant proportion of executed

messages are associated with the submission of marketable orders by active market makers (almost

30% of marketable orders). Based on the estimation of an extended version of the single liquidity

factor model of Chordia et al. (2000) and a subsequent, corroborating, principal component analysis

applied on the liquidity series, our liquidity commonality results indicate that both HF and non HF

quotes contribute to the formation of systemic liquidity risk. HF quotes, however, have a greater

impact on systematic liquidity movements, while they contribute significantly to the formation of

asynchronous liquidity commonality. Overall, the common liquidity factor is prominent at the top of

the book as well as beyond the best quotes and, thus, traders should consider il(liquidity) risk in their

investment decisions. Also, regulators of low latency markets should consider rules that enhance the

market in times of higher liquidity uncertainty.

Key words: High-Frequency Trading, Liquidity, Liquidity commonality, Euronext Paris

(1) Panagiotis Anagnostidis. Email: panos@eurofidai.org

(2) Patrice Fontaine. Email: patrice.fontaine@eurofidai.org

2

1. Introduction

Modern electronic markets are characterized by a high speed of information transition that is partly,

though significantly, attributed to the extensive use of High Frequency Trading algorithms (hereafter

referred to, also, as HFTs). Indeed, HFTs are heavily used by investors and fund managers to acquire

information within milliseconds and, in turn, to re-allocate their portfolios, reducing the risk of being

adversely selected while improving their benefits from trade. Nonetheless, the vast increase of HF

trading in the last decade has raised several concerns and questions regarding the effect of automated

algorithms on the quality of financial markets. Are traditional aspects of market quality, like liquidity

and price discovery, affected by HFTs? And if yes, is the contribution of HFTs to market quality positive

or negative? The present study aims to investigate the relation between HF quotes and one particular

aspect of market quality, namely liquidity. More specifically, using intraday data from the Euronext

Paris CAC 40 market, we examine empirically: i) the contribution of HF quotes to liquidity and ii) the

potential role of HFTs in the formation of systematic (market-wide) liquidity movements, a feature

that is widely known as “liquidity commonality”.

Liquidity is a multidimensional concept in market microstructure and, so far, it has been

difficult to provide a single definition that encapsulates all of its aspects. Kyle (1985) and Hasbrouck

(2007), for instance, point out several characteristics of market liquidity; the authors describe,

collectively, as liquid, a market where investors are able to acquire the desired amount of shares

(“depth”) at the minimum cost (“tightness”) and as fast as possible (“immediacy”), without affecting

severely the continuity of prices (“resiliency”). The abovementioned description implies several

dimensions of market liquidity and, consequently, different ways of quantifying it.

One dimension of liquidity, important in our study, is market depth; that is, the number of

available shares on the order book. It is well documented in the microstructure literature that one of

the basic characteristics of HF trading algorithms is their ability to submit and cancel orders at ultra-

high speeds and across multiple trading venues, faster than any other human (slow) trader. Naturally,

however, the implementation of frequent “submit-cancel” strategies by HFTs (e.g., spoofing strategies

overloading the market) raises the question of whether the net effect of HF quoting activity on market

depth is economically important; is liquidity provided by HFTs reliable? O’ Hara (2015, p. 258), for

instance, argues that “the ability of high frequency traders to enter and cancel orders faster than

everyone else also makes it hard to discern where liquidity exists across the fragmented markets”.

Similarly, Jain et al. (2016, p. 9) mention that “the speed with which the quotes are posted and canceled

has been criticized by market participants because it creates a false sense of deep liquidity supply for

a stock”. In other words, an elevated number of order submissions and cancellations at the highest

frequencies is not necessarily translated into an overall persistent effect on liquidity supply.

3

In the present study we, also, emphasize on a second dimension of liquidity, the cost of

transaction; that is, market tightness. Markets with narrow spreads involve lower transaction costs

for investors and are, typically, considered as liquid and vice versa. The impact of HFTs on the limit

order book state and, consequently, on the cost of trade (i.e., liquidity) is twofold, in the sense that

HFTs are active market agents who continuously a) demand liquidity through their marketable orders

and b) supply liquidity through their non-marketable orders (Brogaard et al., 2014). The trading

activity of HF algorithms imposes, often, additional adverse selection costs on slow traders, mainly

through their ability to aggregate disperse information about fundamentals and, consequently, to

form superior signals compared to the information available to the rest of the trading public. Biais et

al. (2015), in a theoretical paper, show how HFTs generate adverse selection by gathering information

before slow investors. On the other hand, although trading at slow investors’ expense, HFTs seem to

lead the price discovery process through their informationally superior marketable orders, thus

enhancing price efficiency (Biais and Woolley, 2011; Brogaard, 2010). Regarding the liquidity supplying

activity of HFTs, there is ample empirical evidence that their non-marketable orders are often

adversely selected. In an empirical study, for example, Brogaard et al. (2014) find that HFT orders

providing liquidity in the NASDAQ market are adversely selected. Similarly, Carrion (2013) finds that

HFTs provide liquidity in the NASDAQ market when the spreads are wider; i.e., when liquidity is low.

These findings are consistent with the implementation of market making strategies by HFTs.

To the extent that HFTs have a significant positive or negative effect on liquidity, an important

empirical question, central to the present study, emerges: are (il)liquidity movements related to the

activity of HF quotes systematic? The existing literature on market liquidity has focused more on the

impact of HFTs on liquidity and less on the potential presence of systemic liquidity risk due to HF

trading. From this point of view, our analysis contributes significantly to the current understanding of

liquidity commonality in low latency trading environments. In a recent study, Jain et al. (2016) have

examined the presence of systemic risk due to HFT in the TOKYO stock exchange. They conduct an

event analysis that focuses on the eras before and after the introduction of Arrowhead, a low-latency

trading platform. The authors find that Arrowhead has led to a vast increase of HFT activity as well as

quote cross-correlation and systemic return risk. Our analysis complements the aforementioned

study, as well as the existing literature on the U.S. markets, providing further insights from a major

European Exchange.

To study the contribution of HFTs to market liquidity and liquidity commonality, we utilize a

unique set of intraday data retrieved from the AMF (Autorité des marchés financiers) EUROFIDAI-

4

BEDOFIH Euronext Paris CAC 401 database that enables us to distinguish between HFT and non HFT

activity.2 In particular, the data set includes details from orders and trades for the CAC 40 stocks,

together with a unique flag of HFT activity for each order and trade message. The HFT flag is

constructed on the basis of the average lifetime of orders canceled or modified for each trader,

compared to the average lifetime of total orders canceled or modified in the market. Therefore, by

using the aforementioned flag, we are able to disentangle HFT from NON HFT activity.

In the first step of our analysis we focus on the examination of the order flow as well as the

standing shares (liquidity) on the central Limit Order Book (hereafter referred to, also, as LOB). We

find evidence that HFTs are responsible for a significant percentage of liquidity provision (in number

of shares) on the LOB (more than 90% up to the best ten limits). To this extent, our empirical findings

suggest that a large percentage of non-marketable HF limit orders are submitted (or canceled) by

market makers and broker accounts representing large Institutions. We, also, find that almost 70% of

marketable orders in our sample stem from individual brokers, who use either HF or NON HF

algorithms. A significant amount of trading, however, is associated with active market making (almost

30%). We postulate that market makers are engaged in active trading (i.e., they submit aggressive

marketable quotes) either to eliminate other traders’ stale quotes or because they are able to predict

(and profit from) future order flows (e.g., Malinova and Park, 2015).

In the second stage of our analysis, we conduct a unique experiment to investigate the

contribution of HF quotes to stock liquidity. In particular, we re-build the central limit order book

exclusively in terms of a) HFT related queuing shares and b) NON HFT related queuing shares. This

construct allows us to evaluate directly the influence of HF quotes on liquidity. Our liquidity analysis

focuses on the two basic dimensions of the constructed LOB, the depth and the spread, while it is

forward looking. More specifically, we employ an intuitive ex-ante (i.e., before trade) liquidity

measure, proposed in Domowitz et al. (2005, p. 354), that captures the cost of any potential trade

size, spanning over the entire LOB depth. The particular liquidity measure is a function of the current

supply-demand state of the LOB and, thus, it provides investors with valuable information regarding

the cost of their future transactions. Also, the specific liquidity measure improves over the bid-ask

spread and the effective spread, which are frequently utilized in microstructure studies of market

liquidity, incorporating both market tightness and market depth. We find evidence that investors

would have to pay significantly larger amounts to execute their orders in a market of NON HF traders,

1 The CAC 40 database includes messages from the 40 most traded stocks in the Euronext Paris Exchange. These stocks comprise the CAC 40 Index. 2 The AMF (Autorité des marchés financiers) is responsible for the regulation of market participants and products in French financial markets. More information regarding the AMF can be found at the following link: http://www.amf-france.org/en_US/L-AMF/Missions-et-competences/Presentation.html

5

compared to a pure HFT market. Thus, we infer that HF quotes reduce trading costs substantially and

that market makers as well as large Institutions (whose quotes constitute a significant percentage of

total HF order placement activity) enhance the liquidity provision process.

Although not among the main results of our liquidity analysis, we find evidence of a distinct

intraday periodic feature that is related to the quoting activity of NON HF traders. More specifically,

our results on liquidity suggest that NON HF quotes are associated with the 15 minute delay in the

dissemination of the actual (real-time) prices of securities, imposed by the Euronext Paris authorities.3

Indeed, we find that the intraday pattern of liquidity calculated on the basis of NON HF quotes as well

as the corresponding autocorrelation function exhibit 15 minute seasonality, whereas liquidity

calculated on the set of HF quotes is not affected by the specific delay. We attribute this finding to the

fact that HFTs are able to gather information fast and accurately from multiple (costly) data sources,

whereas NON HF traders are more exposed to out-of-date information, including the delay in the

dissemination of real-time quotes. We also find that the delay effect on liquidity for NON HF quotes is

more prominent at the top of the book, whereas it fades away deeper into the book.

In the last part of our study, we examine the presence of liquidity commonality in the Paris

CAC 40 market, first by estimating an extended version of the single liquidity factor model of Chordia

et al. (2000) and second by applying standard principal component analysis on the liquidity series to

extract the common market-wide liquidity factor. We find strong evidence of liquidity commonality

over several depths of the central LOB. More important, our empirical findings suggest that both NON

HF and HF quotes contribute to the emergence of liquidity commonality. HFTs, however, have a

greater contribution to systemic liquidity risk than NON HFTs. Our results indicate, further, that apart

from (overall) market liquidity, individual stock volatility is, also, a significant factor in explaining stock

liquidity movements. This is in line with the argument that stock volatility may influence investors’

inventory handling strategies (i.e., the flow of orders) and, in turn, liquidity provision, leading to

systematic liquidity movements.

The remaining of the paper is organized as follows: Section 2 offers a brief review of the

literature on liquidity, liquidity commonality and HFT. Section 3 describes the NYSE Euronext Paris

trading platform and the CAC 40 data sample employed in the empirical analysis. Section 4 provides a

detailed description of the order placement activity within the sample period. Section 5 introduces

the liquidity measure employed in the present analysis and evaluates the contribution of HF quotes

on stock liquidity. Section 6 assesses liquidity commonality. Finally, Section 7 concludes the paper.

3 For traders who wish to have access to real-time prices there are certain fees charged by the Exchange. More information regarding this issue can be found at: https://www.boursedeparis.fr/centre-d-apprentissage/les-bases-de-l-investissement-en-bourse/questions-frequentes-sur-l-investissement

6

2. Review of the literature

2.1 High frequency trading and liquidity

Several empirical studies have addressed the issue of market liquidity and high frequency trading so

far, whereas most of them are devoted to the U.S. markets. Hendershott et al. (2011) study the NYSE

market and find that algorithmic trading improves liquidity and price efficiency (mainly for large

stocks). Brogaard et al. (2014) and Carrion (2013) examine the NASDAQ market and find evidence that

HFTs participate actively both in the liquidity supply and the liquidity demand process. Moreover,

these studies indicate, collectively, that HFTs often impose adverse selection costs to investors

through their trades (by exploiting their informational advantage), whereas their liquidity supply

orders are often adversely selected. Hasbrouck and Saar (2013) study the NASDAQ market and find

that low latency trading decreases the spreads while increasing market depth. Brogaard (2010) finds

that HFTs improve liquidity and price discovery in the NASDAQ OMX market. Conrad et al. (2015) study

the full cross-section of U.S. securities as well as the Tokyo Stock Exchange (TSE) market and find that

low-latency trading has decreased the cost of trade. The majority of studies related to HFTs and

liquidity focus on the U.S. markets, like the NASDAQ and the NYSE, and, to this extent, our study

complements the literature by examining a major European market.

2.2 Liquidity commonality

A significant body of the microstructure literature has examined the presence of systematic liquidity

risk in financial markets. One group of studies focuses on the U.S. equity markets (e.g., NYSE, NADAQ

and AMEX), providing empirical evidence of market-wide liquidity variations; see, for example,

Amihud and Mendelson (1986), Chordia et al. (2000, 2001), Hasbrouck and Seppi (2001), Huberman

and Halka (2001), Amihud (2002), Pastor and Stambaugh (2003), Coughenour and Saad (2004),

Acharya and Pedersen (2005), Hasbrouck (2009) and Comerton-Forde et al. (2010). An important

feature, common across these studies, is that most of them utilize liquidity measures based on the

prevailing quotes of the order book (e.g., quoted spread and/or effective spread). Our analysis

contributes to this body of the literature as it extends deeper into the LOB, providing insight on the

cost of trade for both small and large trades. Further, our study involves a major European market

and, therefore, it offers a comparison with the existing empirical results on the U.S. markets.

Regarding the literature on the European markets, Foran et al. (2015), Kempf and Mayston

(2008) and Anagnostidis et al. (2016) investigate the London Stock Exchange, the Frankfurt Stock

Exchange and the Athens Stock Exchange, respectively. These studies provide evidence of liquidity

commonality which increases by moving deeper into the order book. That is, large traders are exposed

to greater non-diversifiable transaction costs. Moreover, the aforementioned studies are devoted to

7

pure order driven systems where liquidity is provided mainly by the trading public, in contrast to U.S.

markets where liquidity provision is handled by dealers and/or specialists (e.g., the NASDAQ dealers’

market and the NYSE specialists’ market). Similarly, Brockman and Chung (2002) and Domowitz et al.

(2005) and Fabre and Frino (2004) analyze the Hong Kong Stock Exchange and the Australian Stock

Exchange, respectively, which are order-driven markets. These studies also find evidence of liquidity

commonality. Our analysis is closer to this stream of the literature as it focuses on an order driven

system.

The literature on liquidity commonality has indicated several factors that drive individual

security liquidity variations. For example, liquidity commonality may emerge from common inventory

adjustments by market makers who handle common pools of shares (Coughenour and Saad, 2004,

Comerton-Forde et al., 2010). Liquidity commonality may also emerge from price variations (volatility)

that, in turn, lead to common inventory adjustments by investors (Chordia et al., 2001). Although

much of emphasize has been placed on the explanation of liquidity commonality and the factors that

affect liquidity movements, there is very limited evidence regarding the role of HFTs on this particular

issue. Jain et al. (2016) have recently examined the TSE and found that the increase of HFT has caused

significant liquidity commonality and return co-movement after the introduction of a low-latency

electronic trading platform in the market. Further, Jain et al. (2016) utilize traditional liquidity

measures (like spread and depth) as well as measures that span beyond the top of the book, like the

slope of the LOB, in their liquidity analysis. From this point of view, our study is closely related to their

analysis and offers a direct comparison between the Japanese market and the Paris stock market.

3. Institutional details and data

3.1 The NYSE Euronext Paris stock market

There are two main markets for securities traded on the Paris platform: a) the order-driven market

and b) the LP quote driven market. The order driven market model, examined herein, is an automated

system where liquidity is supplied by brokers and designated market makers (“Liquidity Providers” or

“LPs”). Market makers are obliged to post pairs of bid-ask quotes that comply with certain parameters

fixed by market authorities (e.g., size of the quoted spread and frequency of quote submission). By

contrast, the quote driven market is exclusively operated by the quotations of designated liquidity

providers.4

The order driven market model includes two types of trading, continuous and periodic; the latter

is for less liquid securities which are traded via frequent periodic call auctions during the day. The

4 More information on the Euronext Paris trading platforms and rules can be found at the following link: https://www.euronext.com/en/regulation/organization-of-trading

8

continuous method, which is the focus of the present study, follows the time schedule delineated

below:

1) 07:15 to 09:00: Preopening phase - Order accumulation period

2) 09:00 : Opening call auction (random time)

3) 09:00 to 17:30: Main trading session: Continuous session

4) 17:30 to 17:35: Pre-closing phase - Order accumulation period

5) 07:15 to 17:35: Closing auction

6) 17:35 to 17:40: Trading at the last phase (at the close)

7) 17:40 to 07:15: After hours trading

The trading day starts with an extended pre-opening order batching period followed by an opening

call auction for the determination of the opening price. The procedure is conducted for each listed

security until all securities are open and the main continuous session follows. The trading day closes

with a call auction that determines the closing price for each security. There is also trading after hours

but this period is out of the scope of the current study; rather, we focus on the organized trading. It is

worth mentioning that the continuous mechanism, examined herein, concerns the trading of more

liquid securities, in contrast to the periodic trading mechanism which is designed for less liquid

securities.

During the continuous double auction session traders are allowed to submit, modify or cancel

their orders. The main types of orders allowed in the system are: a) market orders, which have no

price preference and are matched with the queuing orders on the prevailing quotes at the spot, b)

limit orders, which have price preference and are stored into the central order book with price-time

priority, c) stop market and stop limit orders, which are transformed into market and limit orders,

respectively, when the trade price of the security reaches a certain threshold, defined by the broker

who submits the order, d) pegged orders which follow the best quotes and e) market to limit orders;

these are market orders which if partially executed, the remaining part is stored into the LOB as a new

limit order at the price of the partial execution.

It is important to note that limit orders can be marketable, depending on the limit price and

the best quotes at the time of submission. For example, a sell (buy) limit order with a limit price smaller

(greater) than the prevailing bid (ask) is an aggressive order which is executed instantly. Thus, not only

market orders are marketable but aggressive limit orders as well.

9

3.2 The data sample

For the purposes of the present study we utilize a unique intraday data-set for stocks comprising the

CAC 40 Index, retrieved from the AMF (Autorité des marchés financiers) - EUROFIDAI/BEDOFIH

European high frequency database.5 The sample includes details for all order and trade messages for

a three month period, from 02/01/2013 to 28/03/2013. We have excluded four stocks from our

sample, either because they are not traded directly on the Euronext platform (hence there are not

available order data) or because they are related to extended periods (i.e., several days) of no trade.

Thus, our final sample consists of 36 stocks for which orders and transactions are available for a period

of 62 trading days. Some basic descriptive statistics regarding the stock sample are presented in

Appendix Table A1. In particular, we report the average daily number of company shares, trading

volume in number of shares and value of transactions.6

One feature of the data set, critical for the purposes of our study, is that each message (order

or trade) encompasses a unique HFT flag. In particular, traders are classified into three categories:

“HFT”, “NON HFT” and “MIXED” (hereafter, we, also, use the term “strategy” to refer to these flags:

e.g., HFT strategy). The first category is for pure HF investors, the second is for non HF investors and

the third one is for investment banks that apply HF algorithms. The aforementioned classification is

provided by the AMF and is based on the comparison of the average lifetime of orders submitted and,

subsequently, canceled or modified by each trader, relative to the average lifetime of total orders

modified or canceled in the Paris market. For example, brokers who cancel or modify their orders too

frequently are classified as HFTs. Using the HFT flag in the orders record file, we are able to decompose

the order book in terms of HFT and NON HFT shares. Therefore, we are able to study directly the effect

of HFTs on market liquidity.

A second unique variable, important in our analysis, is a special flag included in the file of

transactions that indicates if a trade was buyer or seller initiated. In other words, this variable indicates

if a trade was triggered by a buy or a sell order. Using this flag, together with the HFT classification,

we are able to distinguish directly when a trade was initiated by a HFT, NON HFT or MIXED trader.

4. The Paris market order flow and trading activity

Here we present a detailed analysis of the Paris stock market order flow and trading activity, to

motivate further the empirical analysis on liquidity and liquidity commonality. Using the CAC 40 data

set, we re-construct and utilize 1-min order book snapshots for the sample period (02/01/2013 to

5 More information on the BEDOFIH European High-Frequency financial database can be found at the following link: https://www.eurofidai.org/en/bedofih-database 6 The daily descriptive statistics for the CAC 40 stock sample are retrieved from the EUROFIDAI daily database via the following link: https://www.eurofidai.org/en/database/stocks-europe

10

28/03/2013).7 Table 1 reports the distribution of the aggregated order book depth, up to the best ten

limits.

[Table 1 here]

The top of the book is relatively thin as the medium depth is only 1,071 shares on the buy side and

1,072 shares on the sell side. Therefore, we infer that relatively large transactions (e.g., over 1,000

shares) can consume liquidity deeper in the order book, resulting in higher transaction costs for

investors. Notice also that the two sides of the book are almost symmetrical (in depth) up to the 10th

best limit, hinting the absence of significant supply/demand imbalances.

[Table 2 here]

Table 2 reports statistics regarding the available liquidity on the LOB due to NON HFT, HFT and

MIXED quotes. In specific, it presents the, across days and stocks, average percentage of total

outstanding shares for each trader category (NON HFT, HFT and MIXED), relative to the total number

of outstanding shares on the LOB. Statistics are reported both for the buy and the sell market side and

up to the 10 best limits of the constructed LOB. Because MIXED traders are large investment banks

that apply HF algorithms, and for the purposes of the present analysis (that is, to isolate HF from NON

HF quotes), we consider MIXED and HF quotes as one group (the HFT group) when interpreting the

order flow results. Evidently, the vast majority of queuing shares, up to the best ten limits, is

associated with the order flow of HFT and MIXED algorithms. For example, at the top of the book, the

percentages of available shares associated with HFT and MIXED orders are 41.8% and 44.3%,

respectively, on the buy side. The corresponding percentages for the sell side are 41.9% and 45.1%.

We find that, on average, approximately 94.4% and 93.6% of available shares up to the best ten limits

are attributed to HFT and MIXED flagged orders, for the buy and the sell side respectively. Therefore,

we can readily infer that the vast majority of liquidity provision stems from the implementation of HF

algorithms.8 Notice, also, that by moving deeper into the order book, the percentage of HFT flagged

shares decreases, whereas for MIXED shares it increases.

[Table 3 here]

7 The opening and closing sessions are excluded from the order flow analysis. 8 Note that this result concerns the best 10 limits of the LOB which is the focus of our study (we later show that the vast majority of transactions are associated, mostly, with the best limits of the LOB). Our computations, however, show that by moving deeper into the LOB, the percentage of NON HF quotes is significantly increased.

11

Table 3 summarizes the distribution of newly submitted, modified and canceled limit orders

which are non-marketable (that is, not executed at the spot), thus providing liquidity to the market.

The term “Investors” represents accounts of individual brokers or parent company accounts, while

the term “Market Makers” refers to designated Liquidity Providers (LPs).9 Newly submitted limit

orders have a medium size of only 200, 208 and 214 shares for HFT, MIXED and NON HFT investors,

respectively (Panel A). These figures could mean that traders apply “slice and dice” techniques to avoid

revealing their information and trading intentions, or to handle better their execution costs. In line

with the market depth statistics presented in Table 2, the vast majority of newly submitted non-

marketable limit orders are attributed to HFT and MIXED strategies. For broker accounts (“Investors”

in Panel A), almost 12.96% and 82.15% of limit order submissions are related to HFT and MIXED

algorithms, respectively. The corresponding statistics for market makers are 70.59% and 29.40%. On

the other hand, NON HFTs have by far the smallest participation in liquidity provision (almost 4.88 and

0 % for investors and market makers, respectively). Thus, we infer that liquidity provision in the CAC

40 market is, mostly, associated with the use of HF algorithms applied by brokers (representing mainly

large Institutions) and market makers. Further, according to Panel A, the vast majority of HFT

messages for new limit order submissions are related to market making purposes (almost 91.10%),

whereas MIXED strategies are applied both by investors and market makers; the corresponding

percentages are 59.75% and 40.24%. Lastly, NON HFT new limit order submissions are mostly related

to broker accounts (99.99%).

Panel B in Table 3 presents statistics on modified limit order messages. Similar to Panel A, the

medium size of limit order modifications is rather small; 50, 328 and 756 shares for HFT, MIXED and

NON HFT strategies, respectively. Further, for investors, limit order modifications are distributed as

follows: 20.16%, 56.79% and 23.03% for HFT, MIXED and NON HFT strategies, respectively. The

corresponding figures for market makers are 23.31%, 75.89% and 0.79%. Hence, market makers’

modifications are strongly related to the application of HFT and MIXED strategies. Interestingly,

however, the vast majority of modifications are attributed to investors; 88.89%, 87.37% and 99.62%

for HFT, MIXED and NON HFT strategies, respectively. These results suggest that market makers rarely

modify their quotes, whereas individual brokers modify their orders rather frequently.

Panel C in Table 3 reports statistics regarding the flow of limit order cancelations. Evidently,

most cancelations stem from HFT and MIXED strategies, both for investors and market makers.

However, it is important to notice that for HFT strategies market makers are responsible for most limit

9 Because individual investors can also be liquidity providers, to avoid confusion, we use the term “market maker” instead of the term “liquidity provider”.

12

order cancelations (91%). For MIXED strategies, both investors and market makers cancel their orders,

whereas investors are related to almost 99% of total NON HFT limit order cancelations. Again, these

results suggest that both investors and market makers use HFT and MIXED strategies to implement

their order placement activities.

[Table 4 here]

Table 4 reports summary statistics on the flow of marketable orders, that is orders that trigger

instant transactions. As mentioned earlier, marketable orders can be aggressive limit orders (buy/sell

limit orders with price equal or higher/lower than the prevailing ask/bid) as well as market orders;

denoted by “LO” and “MO”, respectively, in Table 4. Panel A focuses on the trading activity of Investors

(broker accounts). The medium aggressive limit (market) order size for HFT, MIXED and NON HFT

strategies is 300 (390), 270 (255) and 301 (357) shares, respectively. Investors’ trades are on average

rather small, suggesting that they follow “slice and dice” techniques to reduce price impact (i.e., the

cost of executing) (e.g., Barclay and Warner, 1993). To this extent, the average market depth

presented in Table 1 indicates that most trades should be associated with the top of the order book.

Nonetheless, there exist trades in our sample that go beyond the prevailing quotes. Interestingly,

investors prefer, by far, to trade with aggressive limit orders, rather than using market orders. Almost

99.95%, 98.63% and 72.18% of HFT, MIXED and NON HFT marketable orders, respectively, are

aggressive limit orders (Panel A). Also, from the total of aggressive limit orders, only 6.49% concern

HFTs, whereas 73.57% and 19.94% stem from MIXED and NON HFT traders. As for market orders, only

MIXED and NON HFT investors prefer them for realizing their liquidity demand needs (11.69% and

88.27%, accordingly).

Regarding the trading activity of Market Makers (Panel B), the medium aggressive limit order

size is 246, 281 and 1,300 shares, for HFTs, MIXED and NON HFT strategies, respectively (market orders

are not allowed for market making purposes). Again, marketable orders stemming from market

makers are rather small, compared to the average number of shares available on the LOB (see Table

1). Also, trades from market makers are triggered exclusively from HFT and MIXED strategies; 84.62%

and 15.38% of these trades correspond to HFT and MIXED, strategies, respectively.

Overall, HFT, MIXED and NON HFT strategies are associated with 13.69%, 90.93% and 100% of

total trades, respectively, for investors (Panel C). On the other hand, the vast majority of trades related

to market making activity are attributed to HFTs (86.31%), whereas only 9.07% stems from MIXED

strategies (Panel C). Further, according to Panel C, we infer that 69.2% of total marketable orders

(trades) are related to the activity of individual brokers (mainly large Institutions), while the significant

13

amount of 30.8% of total marketable orders are associated with the activity of market makers.

Regarding the latter, we postulate that market makers post aggressive quotes to eliminate market

imbalances or to profit from their ability to predict the future order flow. Malinova and Park (2015),

for instance, in a report prepared for the Investment Industry Regulatory Organization of Canada,

document that HF market makers in the Toronto Stock Exchange (TSE) tend to cancel their sell (buy

quotes) and to submit aggressive buy (sell) orders after a trade with a buyer (seller), either to eliminate

stale sell (buy) queuing quotes or because they are able to predict future quotes and trades.10

The main findings of the order flow for the Euronext Paris CAC 40 stocks in our sample can be

summarized as follows:

The liquidity supply process is driven by HFT and MIXED algorithms (more than 90% of non-

marketable shares queuing on the LOB). Moreover, a significant part of non-marketable

orders in our sample are associated with the quoting activity of market makers, who enhance

liquidity supply. This feature explains, partially, the fact that up to the best 10 limits of the

central LOB, supply-demand imbalances are practically absent.

An increased percentage of limit order cancelations comes from market makers (Table 3,

Panel C). This feature is not surprising, though, as market makers frequently cancel their

quotes to avoid being picked-off by other traders (Malinova and Park, 2015).

Individual broker accounts (mainly from large Institutions) are responsible for a significant

part of limit order submissions and cancelations as well as for the vast majority of limit order

modifications. Further, most of these messages are attributed to the implementation of HFT

and MIXED strategies (Table 3, Panel B). We associate these figures with “stuffing” or

“spoofing” strategies implemented by machines, filling the market with “fake” orders that are

never meant to be executed (e.g., Gai et al. 2012; Jain et al., 2016).

Concerning the trading process, this is driven mainly by individual investors (almost 70% of

total trading); a significant amount of trading, however, is attributed to active market making

strategies (30%). We postulate that market makers are engaged in active trading either to

eliminate other traders’ stale quotes (i.e., mispriced quotes) or because they are able to

predict (and profit from) future order flows (Malinova and Park, 2015).

10 Since the focus of the paper is on liquidity provision and liquidity commonality, we avoid to examine the determinants of “active” market making in the present study. We aim, however, to investigate this particular issue in a future work.

14

5. Liquidity provision and HF quotes

In this Section we examine the effect of HF quotes on liquidity. For the purposes of our analysis, we

employ the following liquidity measure, introduced in Domowitz et al. (2005):

𝑙𝑡(𝑞) = ∫[𝑆𝑡(𝑄) − 𝐷𝑡(𝑄)]𝑑𝑄

𝑞

0

, (1)

where St(𝑄) is the supply schedule and 𝐷𝑡(𝑄) is the demand schedule on the central LOB at time 𝑡.

Equation (1) represents the area between the supply and demand schedules, as illustrated in Figure

1. Quantity 𝑙𝑡(𝑞) is a function of St(𝑄) and 𝐷𝑡(𝑄) and corresponds to the total round-trip cost for a

hypothetical trade size of 𝑞 shares (i.e., the inverse of liquidity) at time 𝑡. In other words, 𝑙𝑡(𝑞)

represents the cost that an impatient trader would have to pay for his/her order to be executed at the

spot. Moreover, the greater (smaller) is the distance between the supply and demand lines, the

greater (smaller) is the trading cost (i.e., the lower (higher) is liquidity for the stock) and vice versa.

The aforementioned liquidity measure improves over several traditional market-

microstructure related measures of liquidity. First, it is an ex-ante variable, meaning that it measures

the transaction cost of a hypothetical order. Therefore, it contains valuable information regarding the

cost of investors’ future trades. From this point of view, it improves over the effective spread, which

is an ex-post measure based on the prices of realized transactions. Furthermore, 𝑙𝑡(𝑞) expands over

the entire depth of the order book, thus improving over the bid-ask spread and the quoted spread

which are associated only with the top of the order book.

[Figure 1 here]

To investigate the contribution of HFTs on market liquidity, we conduct a unique experiment

using the HFT flag that is available in the dataset. In particular, we decompose directly the observable

state of the LOB in terms of HFT and NON HFT share volume. To do so, we build three separate LOBs:

the first LOB includes the entire set of quotes (HFT, NON HFT and MIXED), the second LOB is

constructed on the basis of queuing NON HFT orders, and the third one is built using only the active

HFT and MIXED orders that are related to HF algorithms. Accordingly, we apply equation (1) to

calculate three separate liquidities. With the construction of three different equilibrium states, we are

able to study and compare directly the effect of each type of trader (HF or non HFT) on the LOB state

and, in turn, on market liquidity. To better illustrate the aforementioned arguments, consider Figure

2 which plots the order book state for stock Accor - Act. (Appendix Table A1) on 03/01/2013 at 10:35,

for the following two cases: a) only for HFT and MIXED orders (dashed supply-demand lines) and b)

only for NON HFT orders (solid supply-demand lines). Evidently, NON HFT related quotes impose a

15

much wider spread compared to that of HFT quotes. Therefore, an order executed over the NON HFT

order book would involve a rather increased transaction cost compared to the cost of trade in a pure

HFT/MIXED market.

[Figure 2 here]

Table 5 reports summary statistics on the distribution of liquidity, calculated according to

equation (1), for the following hypothetical order sizes: 1, 1,000, 5,000, 10,000 and 15,000 shares, and

for the three cases: a) the full order book, b) the order book attributed to NON HFT orders and c) the

order book constructed on the basis of HFT and MIXED orders. We choose not to move deeper into

the LOB, as the average size of marketable orders is relatively limited (see, Table 4). For purposes of

comparison, liquidity is divided by the corresponding order size and, therefore, it is normalized as Euro

per share price impact for all order sizes (Domowitz et al., 2005).

[Table 5 here]

The first thing to notice is that the cost of transaction increases monotonically with the order size in

all cases. Thus, executed large orders are associated with increased transaction costs compared to

smaller trades. This result is consistent with the empirical findings in other order driven systems; see,

for example, Domowitz et al. (2005) for the Australian market and Kempf and Mayston (2008) for the

Frankfurt Stock Exchange. Even more important, observe that after removing the queuing orders due

to HFT and MIXED strategies transaction costs increase drastically, in line with what is illustrated in

Figure 2. For example, the median spread for the NON HFT market is 0.096 Euros, whereas for the

actual order book it is only 0.018 Euros (almost 81% less). For the HFT market the median spread is

0.018 euros, as in the actual market.

Our interpretation for the aforementioned findings is based on two facts: i) the vast majority

of non-marketable limit orders are attributed to HFT and MIXED traders who often place their quotes

near the top of the book, taking advantage of their ability to enter and exit the market at ultra-high

speeds (see Table 2), and ii) a significant percentage of the queuing HFT and MIXED shares are related

to market making strategies (see the analysis in Section 4). According to the Euronext Paris trading

rules, designated liquidity providers are obliged to provide liquidity in a systematic manner and in

favorable prices that are close to the market. Thus, their quotes should decrease transaction costs

(i.e., tighten the spreads) and enhance market depth and price continuity.11 In this respect, the

11 More information on the obligations of Liquidity Providing can be found at the following link:

16

liquidity results presented in Table 5 indicate strongly this type of quoting. Further, our findings imply

that the non-marketable quotes of HFT and MIXED traders should be more susceptible to adverse

selection (either by HFTs or by NON HFT investors). On the other hand, NON HF investors’ quotes lie

rather far from the market (i.e., deeper in the book) and, therefore, are less likely to be adversely

selected. Overall, we infer that NON HFTs place their non-marketable quotes less aggressively

compared to HFTs and MIXED traders, to avoid increased adverse selection costs (e.g., Glosten and

Milgrom, 1985).

Our overall findings on the order flow and the liquidity process in the Paris market suggest

that HF algorithms enhance liquidity, adding to market depth and reducing the cost of trade; this is

partly achieved by the quoting activity of designated liquidity providers. Similar, Brogaard (2010) for

the NASDAQ OMX, Hendershott et al. (2011) for the NYSE, Hasbrouck and Saar (2013), Brogaard et al.

(2014) and Carrion (2013) for the NASDAQ market and Conrad et al. (2015) for the full cross-section

of U.S. securities as well as the Tokyo Stock Exchange (TSE), all provide empirical evidence that HFTs

participate actively in the liquidity process, enhancing liquidity by reducing the spreads and by

increasing market depth.

6. Liquidity commonality and HFT

6.1 Preparation of variables: liquidity and volatility time series

In this Section we examine the presence of liquidity commonality in the Paris CAC 40 market as well

as the potential contribution of HFTs in systematic liquidity movements. As in Hasbrouck and Seppi

(2001) and Kempf and Mayston (2008), we wish to focus on the potential unexpected (il)liquidity

shocks which investors face during the trading day; that is, the unexpected liquidity risk. To this end,

our first task is to remove any periodic components from the liquidity series. To illustrate the presence

of such periodicities, the top graph in Figure 3 plots the average, across days and stocks, intraday

liquidity for a hypothetical order size of 𝑞 = 5,000 shares and for the three cases: a) full order book,

b) HFT and MIXED order book and c) NON HFT order book. Liquidity exhibits an inverse J-shaped

pattern that is typically observed in organized market trading (e.g., Andersen and Bollerslev, 1997;

Domowitz et al., 2005; Anagnostidis et al., 2016). Trading costs are significantly elevated at the start

and at the end of the trading session due the increased market stress at that times of the day.12

Observe, also, that trading on the NON HFT order book involves considerably higher transaction costs,

https://www.euronext.com/en/regulation/organization-of-trading 12 Such periodicity patterns are commonly associated with the order flow, which is more pronounced at the start and the end of the main session (e.g., Domowitz et al., 2005). Herein, however, we do not focus on the examination of the correlation between the order flow and liquidity; rather, we wish to explain unexpected liquidity commonality. Therefore, we choose to remove periodicity from the time series.

17

compared to the actual order book and the HFT-MIXED order book (see, also, the discussion in Section

5). The intraday periodicity pattern in liquidity is further illustrated in the the bottom graph of Figure

3 which plots the autocorrelation function of the liquidity series calculated on the full order book and

for a hypothetical order size of 𝑞 = 5,000 shares for the stock Accor - Act. (see, also, Appendix Table

A1), together with the plot of the corresponding 95% confidence interval.

It is interesting to notice in Figure 3 the two peaks in the average cost of trade at 14:30 (CET

time) and 16:00 (CET time) that are present for the cases of the full (actual) LOB and the HFT LOB. The

first peak (14:30) corresponds to the announcement of the monetary policy decisions by the European

Central Bank (ECB) as well the U.S. macroeconomic news announcements at 08:30 (EST time), while

the second peak (16:00) corresponds to the U.S. macroeconomic news announcements at 10:00 (EST

time) (e.g., Kurov et al., 2016).13 In a published report on the behavior of HFTs on Euronext Paris, the

AMF, also, documents the specific peaks for the CAC 40 market stocks, while it relates the increase in

the cost of trade with the fact that HF algorithms are designed to withdraw from the market a few

minutes before the, expected, important economic new announcements. Similarly, our results

indicate that HF quotes reduce substantially the cost of trade, whereas in the absence of HFTs spreads

widen significantly. Thus, we naturally link these two peaks with the withdrawal of HFTs from the

market at stressful times, such as the announcement of important economic news. Moreover,

according to Figure 3, the two peaks are not present in the NON HFT LOB case, suggesting further the

difference between the quoting strategies of HF and NON HFT traders.

[Figures 3 and 4 here]

To illustrate further the feature of intraday periodicity, the top graph in Figure 4 plots the

average, across days and stocks, intraday volatility pattern, calculated on the basis of the full order

book. Volatility is calculated by squaring the 1 min intraday logarithmic returns, constructed using the

bid-ask midpoint as the current price of the stock (e.g., Hasbrouck, 1991). Notice that intraday

volatility exhibits, also, an inverse J-shaped deterministic pattern, associated with the increased

market stress at the opening and at the closing of the session (e.g., Andersen and Bollerslev, 1997).14

Further, the bottom graph in Figure 4 plots the autocorrelation function for the volatility series

13 More information on the ECB news announcements can be found at the following link: https://www.ecb.europa.eu/press/tvservices/webcast/html/index.en.html 14 The autocorrelation graphs of the liquidity and the volatility series support, also, the presence of intraday periodicity. To preserve space, however, we avoid including them herein. These plots are available for the interested reader upon request.

18

calculated on the full order book up to 2,000 lags for stock Carrefour - Act. (see, also, Appendix Table

A1), together with the plot of the corresponding 95% confidence interval.

An interesting characteristic revealed by our LOB experiment is related to the response of

NON HF traders to lagged intraday price adjustments. The Euronext Paris disseminates information on

the actual (i.e., real-time) security prices with a delay of 15 minutes, whereas for investors who wish

to have less lag on their monitors there are certain fees charged by the Exchange.15 To illustrate the

effect of lagged quotes on liquidity, Figure 5 plots the intraday evolution of the, across days and stocks,

average cost of trade for the case of a hypothetical order size of 𝑞 = 1 share (that is, an order that

will consume liquidity at the spread). Similar to Figure 3, the intraday liquidity pattern exhibits an

inverse J-shaped pattern for all three cases: a) full LOB, b) HFT and MIXED LOB and c) NON HFT LOB.

Notice, however, that in the NON HFT case there is an additional, distinct, seasonality pattern in

liquidity that is prevalent during the trading day. To understand better this periodicity, Figure 6 plots

the autocorrelation function of the, across days and stocks, average NON HFT liquidity and for the

case of an order of 𝑞 = 1 share (at the spread). The apparent periodicity is of 15 minute frequency

that matches with the 15 minute lag of price dissemination. It is well documented in the

microstructure literature that HFTs acquire information from various electronic networks and at ultra-

high speeds at the expense of elevated resource costs. Therefore, it is natural to expect that HFTs form

more accurate and up-to-date signals compared to the rest of the trading public, whereas NON HFTs

are more exposed to out-of-date information, including the delay in the dissemination of real-time

quotes.16 It is worth noting that the particular delay effect on liquidity is apparent only for the case of

smaller orders that consume liquidity near the top of the book, whereas for larger order sizes it fades

away. For example, the liquidity pattern for the NON HFT book illustrated in Figure 3 (𝑞 = 5,000

shares) does not support the presence of such a periodic effect.

[Figures 5 and 6 here]

15 More information on the feature of delayed quotation can be found at: https://www.boursedeparis.fr/centre-d-apprentissage/les-bases-de-l-investissement-en-bourse/questions-frequentes-sur-l-investissement 16 We postulate that NON HFTs do not hold private information; rather, they submit orders simply by observing the available public information. A more detailed example of the effect of Euronext delay in the dissemination of prices on investors’ order placement strategies can be found in AMF Ombudsman (May 2015).

19

To filter out the abovementioned seasonality effects, for the liquidity series we use first

differences, 𝐿𝑡𝑖 = log (𝑙𝑡

𝑖 /𝑙𝑡−1𝑖 ), as in Chordia et al. (2000) and Brockman and Chung (2002).17 For the

volatility series, we apply the method of standardization (Hasbrouck and Seppi, 2001; Kempf and

Mayston, 2008):

𝑉𝑡𝑖 ≡ 𝑣𝑖,𝑑,𝑛 =

𝑣𝑖,𝑑,𝑛 − 𝑚𝑒𝑎𝑛(𝑣𝑖,𝑛)

𝑠𝑡𝑑(𝑣𝑖,𝑛) (2)

where 𝑣𝑖,𝑑,𝑛 = 𝑅𝑖,𝑑,𝑛2 = [𝑙𝑜𝑔 (

𝑃𝑖,𝑑,𝑛

𝑃𝑖,𝑑,𝑛−1)]

2

is intraday volatility for security 𝑖, 𝑑 is the trading day, 𝑛 is the

intraday interval, 𝑃𝑖,𝑑,𝑛 is the corresponding mid-price and 𝑚𝑒𝑎𝑛(𝑣𝑖,𝑛) and 𝑠𝑡𝑑(𝑣𝑖,𝑛) are the, across-

days mean and standard deviation, respectively, for volatility for the 𝑖-th security and the intraday

interval 𝑛. The time index 𝑡 is defined such that: 𝑡 ≡ 𝑁(𝑑 − 1) + 𝑛 where 𝑁 is the number of total

intraday intervals with 𝑛 = 1, … , 𝑁. Thus, the 1 min time series consist of 𝑁 × 𝐷 consecutive 1 min

observations, where 𝐷 is the number of total trading days in the sample with 𝑑 = 1, … , 𝐷. Herein, the

volatility series consist of 𝑁 × 𝐷 = 509 × 62 = 31,558 observations.18

6.2 The liquidity factor model

To start our analysis on liquidity commonality, we first evaluate the following, extended, liquidity

factor model of Chordia et al. (2000):

𝐿𝑡𝑖 = 𝑎 + 𝑏1𝐿𝑡

𝑀 + 𝑏2𝐿𝑡−1𝑀 + 𝑏3𝐿𝑡+1

𝑀 + 𝑑1𝑉𝑡𝑖 + 𝑑2𝑉𝑡−1

𝑖 + 𝑑3𝑉𝑡+1𝑖

+𝑓𝑅𝑡𝑀 + 𝑓2𝑅𝑡−1

𝑀 + 𝑓3𝑅𝑡+1𝑀 + 𝑒𝑡 . (3)

17 Chordia et al. (2000) use percentage changes, whereas we use logarithmic first differences. An alternative method to remove periodicity from the liquidity series is the method of standardization (Hasbrouck and Seppi, 2001; Kempf and Mayston, 2008; Anagnostidis et al. 2016). For robustness purposes, we have additionally replicated the liquidity commonality analysis using the method of standardization and results are similar to those reported herein. Nonetheless, we choose to follow the method of first differencing due to specific econometric reasons. First, for several standardized liquidity series we have applied the Augmented-Dickey-Fuller (ADF) test and the test Kwiatkowski–Phillips–Schmidt–Shin (KPSS) test for non-stationarity. The ADF test results reject the null hypothesis of non-stationarity up to several lags, whereas the KPSS test results reject the null hypothesis for stationarity. On the other hand, for the logarithmic first differences, both tests indicate stationarity. Second, when using the standardized series, the matrix of independent variables exhibits strong multi-collinearity; we have estimated Variance Inflation Factors (VIF) as well as the Belsley test for multi-collinearity (Belsley, 1982), whereas with the first differences multi-collinearity is practically absent (see appendix Table B1). Third, the t-statistics for the estimated coefficients are rather large (e.g., in some cases at the magnitude of 40) when using the standardized liquidity variables, suggesting spurious standard errors, whereas with the first differences they are reduced drastically. To preserve space, we do not report herein our results on most of the aforementioned robustness tests. These results, however, are available upon request for the interested reader. 18 In our analysis we exclude the opening and the closing sessions as in Andersen and Bollerslev (1997). Also, the number of total 1-min intraday time-stamps is 510, whereas the intervals are 𝑛 = 509.

20

The variables included in the model are as follows:

𝐿𝑡𝑖 is liquidity for security 𝑖 at time 𝑡, calculated using the full order book set according to

equation (1). This is individual security liquidity and we aim to examine its sensitivity to market

liquidity movements as well as various other market factors, described below. Note that for

the estimation of model (3) we use the de-trended liquidity series, according to equation (2).

𝐿𝑡𝑀 is market liquidity calculated, using the full order book set, as the average liquidity across

stocks, weighted by firm capitalization.19 If liquidity commonality exists, then market-wide

liquidity movements should explain individual stock liquidity; that is, 𝐿𝑡𝑖 . 𝐿𝑡−1

𝑀 and 𝐿𝑡+1𝑀 are lag

and lead terms for market liquidity, to capture potentially asynchronous trading effects; see,

for example, Chordia et al. (2000).

𝑉𝑡𝑖 is individual stock volatility and 𝑉𝑡−1

𝑖 and 𝑉𝑡+1𝑖 are lag and lead volatility terms, respectively,

to capture nonsynchronous trading effects. It is well documented in microstructure literature

that higher price uncertainty (i.e., increased price volatility) may influence inventory risk and,

in turn, the liquidity supply process (Kempf and Mayston, 2008). Thus, volatility is a good

candidate as a control variable in equation (3). Similar to the liquidity series, we remove

volatility periodicity using the method of standardization, represented by equation (2).

𝑅𝑡𝑀 is market performance, calculated as the market capitalization weighted average return

across stocks. We include the average market return to control for liquidity movements that

are related to inventory adjustments pertaining to the overall market performance (e.g.,

Kempf and Mayston, 2008). Accordingly, 𝑅𝑡−1𝑀 and 𝑅𝑡+1

𝑀 terms are included to take the

asynchronous trading effect into account.

[Table 6 here]

Table 6 reports the results from the OLS estimation for model (3). In particular, we present the, across

stocks, average estimated coefficients, the percentage of significant coefficients and the percentage

of positive and significant coefficients (95% level of statistical significance), for each of the following

19 Market capitalization for each security is selected for 01/02/2013, the start of our sample period. The data for market capitalization are retrieved from the EUROFIDAI daily database. See the following link for more information: https://www.eurofidai.org/en/database/stocks-europe

21

hypothetical order sizes: 1, 1,000, 5,000, 10,000 and 15,000 shares. The first thing to notice is that

there exists strong liquidity commonality in all cases. 100% of the estimated 𝑏1 coefficients are positive

and statistically significant at the 5% probability level, for all order sizes. This finding strongly suggests

that an increase (decrease) in market liquidity causes an increase (decrease) in individual liquidity.

Further, notice that the estimated 𝑏1 coefficient increases from 0.319 to 0.693 by moving deeper into

the LOB, while, similarly, the across stocks average 𝑅2 (%) increases from 1.142 to 12.212. These

figures indicate that liquidity commonality increases by moving deeper into the order book. Therefore,

investors submitting larger executable orders face increased systemic liquidity risk, compared to

smaller traders.

We also find significant evidence of asynchronous liquidity commonality. 61.1%, 91.7%,

52.8%, 38.9% and 38.9% of the total 𝑏2 coefficient estimates (i.e., lag liquidity commonality) are

positive and statistically significant at the 5% probability level for the case of 1, 1,000, 5,000, 10,000

and 15,000 shares, respectively. The corresponding percentages for the 𝑏3 coefficient (lead liquidity

commonality) are 83.3%, 86.1%, 69.4%, 61.1% and 61.1%. Overall, there is significant evidence that

stock liquidity is sensitive to contemporaneous as well as asynchronous market liquidity movements.

Further, it is worth noticing that asynchronous liquidity commonality decreases by moving deeper into

the book. This finding, however, is reasonable because the majority of transactions occur near the top

of the LOB, having a greater effect on liquidity adjustments. 20

For the remaining variables, results reported in Table 6 hint that firm specific volatility is, also,

an important factor for the explanation of individual liquidity movements. Contemporaneous volatility

is systematically positively correlated with firm specific liquidity; for the case of 1, 1,000, 5,000, 10,000

and 15,000 shares, respectively, 94.4%, 94.4%, 100%, 100% and 100% of 𝑑1 coefficient estimates are

positive and significant at the 5% level. Thus, when volatility is increased (decreased), the cost of trade

is also increased (decreased). This feature can be explained by the argument that increased volatility

may lead HFTs to withdraw from the market (e.g., Aït-Sahalia and Saglam, 2013). Indeed, our results

in Section 5 imply that when HFTs withdraw from the market, spreads widen significantly. Lag volatility

has a systemic effect on firm liquidity, as approximately 66.7%, 91.7%, 97.2%, 97.2% and 97.2% of

estimated coefficients are statistically significant (5% level), for the case of 1, 1,000, 5,000, 10,000 and

15,000 shares, respectively. Moreover, notice that for all the examined LOB depths lag volatility

coefficient estimates are systematically negative. Thus, increased (decreased) volatility changes at a

certain point in time are associated with a transitory decrease (increase) in the cost of trade for both

20 As in Chordia et al. (2000) and Brockman and Chung (2002), we have additionally conducted sign tests with the null hypothesis that the sum (𝑏1 + 𝑏2 + 𝑏3) has a median value equal to zero. Results reject the null hypothesis in all cases, suggesting the presence of liquidity commonality. These results are available upon request for the interested reader.

22

small and large investors (i.e., potential trades near the top of the book and deeper in the book) within

the next minute. We attribute this feature to the activity of HF algorithms that are able to assess and

to predict the current and the future order flows, respectively, and (in turn) to enter or exit the market

accordingly. For example, Brogaard et al. (2014) report evidence that HFTs tend to trade in the

opposite direction of transitory price errors, enhancing price efficiency and decreasing the cost of

trade for future investors. Lastly, lead volatility is less significant in explaining liquidity movements;

only 52.8%, 22.2%, 30.6%, 33% and 38.9% of estimated coefficients are statistically significant for the

case of 1, 1,000, 5,000, 10,000 and 15,000 shares, respectively.21

Regarding market performance, the percentage of statistically significant 𝑓1, 𝑓2 and 𝑓3

coefficient estimates is very low and, therefore, we infer that market performance is a poor

explanatory factor for individual security liquidity adjustments. Overall, the aforementioned results

indicate that liquidity commonality is prevalent in the Paris CAC 40 market.

To investigate whether liquidity commonality is associated with NON HFT and/or HFT

activities, we re-evaluate equation (3) but instead of the average market liquidity term, we include

the following terms:

𝐿𝑡𝑀,𝐻𝐹𝑇 is HFT market liquidity calculated, using the HFT and MIXED set of orders, as the across

stocks average liquidity weighted by firm capitalization. We utilize this variable as a proxy of

overall market liquidity movements due to HFTs and MIXED traders. Thus, if liquidity

commonality exists in the market and it is related with the implementation of common HF

algorithms, we expect that this variable should have significant explanatory power on

individual liquidity movements. 𝐿𝑡−1𝑀,𝐻𝐹𝑇 and 𝐿𝑡+1

𝑀,𝐻𝐹𝑇 are lag and lead terms for HFT market

liquidity, respectively, to capture asynchronous liquidity commonality.22

𝐿𝑡𝑀,𝑁𝑂𝑁 𝐻𝐹𝑇 is market liquidity calculated, using the NON HFT order book set, as the average

liquidity across stocks, weighted by firm capitalization. Similar to the construction of the

𝐿𝑡𝑀,𝐻𝐹𝑇 variable, we expect that if liquidity commonality due to NON HFTs exists, then

𝐿𝑡𝑀,𝑁𝑂𝑁 𝐻𝐹𝑇 will have significant explanatory power on individual liquidity movements.

21 We have also tested the null hypothesis that the sum (𝑑1 + 𝑑2 + 𝑑3) has a median value equal to zero. Results reject the null hypothesis in all cases. Thus, volatility has a significant influence on firm specific liquidity. These results are available upon request for the interested reader. 22 Missing values from the liquidity series are omitted from the regression estimations. For example, for order books at specific time-stamps and dates when calculation of liquidity is not meaningful, as in intraday trading halts where spreads are negative due to the auction.

23

𝐿𝑡−1𝑀,𝑁𝑂𝑁 𝐻𝐹𝑇 and 𝐿𝑡+1

𝑀,𝑁𝑂𝑁 𝐻𝐹𝑇 are lag and lead terms for NON HFT market liquidity, respectively,

to control for asynchronous liquidity commonality.

Taking the aforementioned variables into account, equation (3) now becomes:

𝐿𝑡𝑖 = 𝑎 + 𝑏1𝐿𝑡

𝑀,𝑁𝑂𝑁 𝐻𝐹𝑇 + 𝑏2𝐿𝑡−1𝑀,𝑁𝑂𝑁 𝐻𝐹𝑇 + 𝑏3𝐿𝑡+1

𝑀,𝑁𝑂𝑁 𝐻𝐹𝑇 + 𝑑1𝐿𝑡𝑀,𝐻𝐹𝑇 + 𝑑2𝐿𝑡−1

𝑀,𝐻𝐹𝑇 + 𝑑3𝐿𝑡+1𝑀,𝐻𝐹𝑇 +

𝑓1𝑉𝑡𝑖 + 𝑓2𝑉𝑡−1

𝑖 + 𝑓3𝑉𝑡+1𝑖 + 𝑤1𝑅𝑡

𝑀 + 𝑤2𝑅𝑡−1𝑀 + 𝑤3𝑅𝑡+1

𝑀 + 𝑒𝑡 . (4)

[Table 7 here]

Table 7 presents the results from the OLS estimations for equation (4). In line with the results

presented in Table 6, we find strong evidence of liquidity commonality. For example, 97.2% and 100%

of 𝑏1 (market NON HFT liquidity) and 𝑑1 (market HFT liquidity) coefficient estimates, respectively, are

positive and statistically significant (at the 5% level) at the top of the LOB (1 share). Similar results are

obtained for the other order sizes, suggesting that liquidity commonality spans over the best limits of

the LOB. Moreover, the across stocks average estimated 𝑅2 (%) suggests that liquidity commonality

becomes more prevalent by moving deeper into the order book, as it increases from 1.239 to 13.232

from the case of a 1 share order up to the case of a 15,000 shares order. Notice, also, that compared

to the results from the estimation of equation (3) reported in Table 6, the estimated 𝑅2 (%) statistic

in Table 7 is slightly but systematically elevated, hinting that equation (4) captures better liquidity

commonality.

Results in Table 7 suggest that both NON HFT and HFT market liquidity movements explain,

significantly, individual stock liquidity movements. Notice, though, that the percentage of statistically

significant 𝑏1 coefficients decreases by moving deeper into the book, from 97.2% to 58.3%. Moreover,

the contribution of HFTs to liquidity commonality is systematically greater than that of NON HFTs. For

the case of the spread, for instance, the average 𝑏1 coefficient estimate is 0.061, whereas the average

𝑑1 coefficient estimate is 0.298. Similarly, the average 𝑏1 coefficient estimate is consistently lower

than the average 𝑑1 estimate, across all market depths examined herein. Thus, our results suggest

that HFTs have a greater impact on systematic liquidity risk, compared to NON HFTs.

Interestingly, we find that asynchronous liquidity commonality due to HFTs is rather

significant compared to that caused by NON HFTs. For the spread (order size of 1 share),

approximately 5.6% and 2.8% of 𝑏2 and 𝑏3 coefficient estimates (that is, for NON HFT liquidity),

respectively, are statistically significant at the 5% level. On the other hand, the corresponding

percentages for 𝑑2 and 𝑑3 coefficient estimates (HFT liquidity) are 63.9% and 72.2%. Accordingly,

24

19.4% (8.3%), 11.1% (0%), 25% (0%) and 38.9% (5.6%) of 𝑏2 (𝑏3) coefficient estimates are statistically

significant at the 5% level, for the cases of 1,000, 5,000, 10,000 and 15,000 shares, respectively. By

contrast, the corresponding percentages for 𝑑2 (𝑑3) coefficients, that pertain to HFT-MIXED

asynchronous liquidity, are 83.3% (83.3%), 38.9% (41.7%), 50% (50%) and 52.8% (55.6%). This feature

could be attributed to the fact that machines are faster in assessing information, compared to slow

traders, and, therefore, their systematic lag and lead (temporary) quotes have a greater effect on

liquidity movements, compared to that of NON HFT investors.23

For the rest of the variables, as in the case of equation (3), we find that volatility has a

significant impact on liquidity movements. For instance, at the top of the LOB, 94.4% of 𝑓1 coefficient

estimates are positive and statistically significant at the 5% level, while similar results hold for the rest

of the order sizes. Further, the 𝑓2 coefficient for lag volatility is found systematically negative, as in the

case of the estimated equation (3) (see, Table 6). Lastly, market performance (𝑤 coefficient estimates)

performs poorly in explaining individual liquidity, in line with the results presented in Table 6. Thus,

we conclude that liquidity movements of individual stocks are not strongly associated with the overall

market return.

6.3 Principal component analysis

To corroborate our findings on liquidity commonality, we apply a second methodology that is based

on the application of standard principal component analysis (hereafter PCA) on the matrix of liquidity

series (e.g., Hasbrouck and Seppi, 2001). The PCA method uses the singular value decomposition

algorithm (SVD) to extract the common liquidity factor from the covariance matrix of the constructed

liquidity series. We use the standardized liquidity series matrix for this purpose (𝐿𝑖,𝑡), while we conduct

the analysis for the three cases: a) the full order book, b) the NON HFT order book and c) the HFT (HFT

and MIXED flags in our data) order book.

Table 8 reports the results from the PCA analysis for the hypothetical order sizes considered

previously; that is, for 1, 1,000, 5,000, 10,000 and 15,000 shares. In particular, it presents the first

three principal component variances (i.e., the first three eigenvalues of the covariance matrix of

liquidities) and the percentage of total explained variance that corresponds to each of the first three

principal components. For the full LOB case, the first eigenvalue for standardized liquidities is 4.70,

5.98, 7.35, 7.28 and 7.18 for the case of a hypothetical order of 1, 1,000, 5,000, 10,000 and 15,000

shares, respectively. The corresponding percentages of total explained variance are 13.27%, 16.88%,

20.75%, 20.56% and 20.27%. By contrast, for the second and third components the explained variance

23 As in the estimation of equation (3), in equation (4) we have also tested for the null hypotheses that (𝑏1 +𝑏2 + 𝑏3) and (𝑑1 + 𝑑2 + 𝑑3) variables are distributed with a median equal to zero. Again, results have rejected the null hypotheses in all cases hinting liquidity commonality.

25

is drastically reduced, while the eigenvalues are closer to unity, especially for the smaller order sizes

(1, 1,000 and 5,000 shares). For instance, for the spread case (1 share), the second principal

component is equal to 1.35 while the corresponding explained variance is just 3.82%, These results

hint that a dominant market-wide liquidity factor exists in the CAC 40 market. Similar results hold for

the liquidity series calculated on the HFT and the NON HFT order books, although liquidity

commonality is more prevalent in the HFT market. For example, the first principal component at the

spread of the HFT LOB is equal to 4.73 and explains almost 13.35% of total liquidity variation, whereas

the corresponding eigenvalue for the NON HFT LOB is 3.92 and explains 11.07% of total variance of

the data. The same finding holds for the other order sizes.

It is worth to observe that the PCA analysis results indicate that liquidity commonality

increases by moving deeper into the order book. For instance, for the full LOB case the explained

variance attributed to the first component increases from 13.27% (1 share order size) to 20.27%

(15,000 shares order size) by moving deeper into the book. Similarly, the estimated 𝑅2 (%) statistics

from the estimation of the liquidity factor model presented in Table 6 and 7 suggest that liquidity

commonality exists and that it increases by moving deeper into the book. Nonetheless, the market-

wide component range suggested by the PCA analysis (e.g., 13.27% to 20.27% for the full LOB case) is

systematically larger compared to that suggested by the 𝑅2 (%) statistic from the estimation of the

liquidity factor model (1.142% to 12.212% in Table 6 and 1.239% to 13.232% in Table 7). This finding,

however, is natural as the common factor in the PCA analysis is not restricted to be the across stocks

average liquidity factor, as with the 𝑅2 (%) statistics presented in Tables 6 and 7 (Kempf and Mayston,

2008).

6.4 Discussion

Our findings on liquidity commonality and HFTs are similar to those reported by Jain et al. (2016) for

the Tokyo Stock Exchange. The authors report that HF algorithms have a significant effect on market

liquidity, while they contribute to the emergence of systemic risk, mainly due to the implementation

of common trading and spoofing strategies. Although we do not examine separately the effect of

broker and market maker HF activity on liquidity commonality, our evidence on the order flow

suggests that liquidity commonality due to HFTs should be associated with the implementation of

common market making strategies as well as with common quoting strategies applied by brokers.

Our results are, also, similar to other studies on liquidity commonality. For instance, there is

ample empirical evidence of liquidity commonality at the top of the book in the US markets (e.g.,

Chordia et al., 2000), while studies on other, non U.S., markets have indicated a common liquidity

factor that increases by moving deeper into the order book; e.g., Kempf and Mayston (2008) for the

26

Frankfurt market. We provide empirical evidence that supports the presence of significant systematic

liquidity at the top as well as deeper into the order book; commonality, though, seems to increase

deeper in the book. Overall, we infer that the feature of liquidity commonality is associated with the

fact that liquidity provision is mainly related to HF quotes which stem from common algorithms (e.g.,

market making strategies).

7. Conclusions

The present study investigates empirically the effect of High Frequency quotes on liquidity provision

and the potential contribution of High Frequency Traders (HFTs) in systematic liquidity movements, in

the Euronext Paris CAC 40 stock market. Microstructure literature has focused more on the impact of

HFTs on liquidity and less on the issue of liquidity commonality and HFTs. Further, most empirical

studies on liquidity commonality concern the U.S. markets (e.g., NYSE and NASDAQ), whereas

European markets have been less explored thus far.

We find significant evidence that the vast majority of quotes lying on the best ten limits of the

central LOB are related to HF quotes (more than 90%), whereas NON HFT quotes lie deeper into the

book. Consequently, HFTs play an important role in liquidity provision. We link this finding with the

fact that a significant percentage of non-marketable HF quotes are related to market making strategies

that enhance the liquidity supply process. On the other hand, individual investors drive the trading

process, as they are responsible for approximately 70% of total trades in the market. A certain amount

of active trading, however, is attributed to market making strategies (30%). We postulate that market

makers are engaged in active trading, by submitting marketable quotes, either to eliminate mispriced

stale quotes or because they are able to profit from predicting the incoming order flow (Malinova and

Park, 2015).

To study liquidity and liquidity commonality, we employ an ex-ante (i.e., prior to trade)

liquidity measure that spans over the entire market depth, allowing us to examine the price impact of

various hypothetical order sizes. Further, we calculate liquidities over two uniquely constructed LOB

states: a) the first is based on the set of NON HFT orders and b) the second is based on the set of

orders that are related to HF algorithms. We find that the price impact associated with the first state

(a) is systematically larger compared to the price impact related to the second state (b). Therefore,

investors would have to pay larger transaction costs in a NON HFT market, compare to a market where

only HF traders are present. Our results on liquidity suggest, also, that NON HFT quotes are associated

with the 15 minute delay in the dissemination of actual (current) quotes by the Euronext Paris

authorities. Indeed, we find that the autocorrelation function of liquidity series calculated exclusively

on the basis of NON HFT quotes exhibits a 15 minute intraday periodicity. By contrast, the liquidity

27

series calculated on the set of HF quotes are free from this feature. We attribute this finding to the

fact that HFTs gather information from multiple data sources, whereas NON HFTs place their quotes

mainly on the basis of the lagged prices disseminated (free of charge) by the Euronext Paris Exchange.

By estimating an extended version of the standard single factor liquidity model of Chordia et

al. (2000) and, subsequently, by applying corroborating principal component analysis on the liquidity

series, we find that the CAC 40 market involves strong liquidity commonality that increases the risk of

additional non-diversifiable liquidity costs for traders. Further, we find that both HF and NON HF

market liquidity movements play a significant role in explaining individual stock liquidity adjustments.

Therefore, both HFTs and NON HFTs contribute to the emergence of liquidity commonality. HFTs,

however, have a greater impact on systematic liquidity movements than NON HFTs. Our empirical

results are similar with those of Jain et al. (2016) who investigate the Japanese stock market and find

that HFTs constitute a significant source of systemic risk.

The empirical findings of the present study have several implications, both for investors and

policy makers. First, investors face increased costs of trade when willing to execute orders that

consume liquidity deeper in the book. Therefore, “slice and dice” techniques are more suitable for

handling large orders. Second, liquidity commonality should be considered in risk assessment,

especially in times of higher liquidity uncertainty. Third, because HFTs contribute to the emergence of

asynchronous liquidity commonality, investors should consider timing more promptly when assessing

their risk. Fourth, market authorities should consider new regulations that will enhance the trading

process when the market is stressed and liquidity is uncertain (see, for example, Kirilenko et al. (2016)

for the E-mini S&P 500 stock index futures market flash crash, attributed to HFTs).

Acknowledgement

We acknowledge support from the French State through the National Agency for Research under the

program “Investments for the Future” (reference ANR-11-EQPX-0006).

28

References

Acharya, V., Pedersen, L.H., 2005. Asset pricing with liquidity risk. Journal of Financial Economics 77,

375–410.

Aït-Sahalia, Y., Saglam, M., 2013. High frequency traders: Taking advantage of speed (No. w19531).

National Bureau of Economic Research.

AMF Ombudsman, May 2015. Beware! One market order can hide another: what are the rules on the priority of execution of orders? Retrieved from http://www.amf-france.org/en_US/Le-mediateur-de-l-AMF/Actions-du-mediateur/Niveau-international.html? AMF, 2017. Study of the behavior of High-Frequency Traders on Euronext Paris. Retrieved from: http://www.amf-france.org/en_US/Publications/Lettres-et-cahiers/Risques-et-tendances/Archives.html?docId=workspace%3A%2F%2FSpacesStore%2F619a82db-11ea-4544-a03e-991b7af2864d Amihud, Y. 2002. Illiquidity and Stock Returns: Cross-Section and Time-Series Effects. Journal of Financial Markets 5, 31–56. Anagnostidis, P., Papachristou, G., Thomaidis, N. S., 2016. Liquidity commonality in order-driven

trading: evidence from the Athens Stock Exchange. Applied Economics 48, 2007–2021.

Andersen, T. G., Bollerslev, T., 1997. Intraday periodicity and volatility persistence in financial

markets. Journal of Empirical Finance 4, 115–158.

Barclay, M. J., Warner, J. B., 1993. Stealth trading and volatility: Which trades move prices? Journal

of Financial Economics 34, 281–305.

Belsley, D. A., Kuh E., Welsch, R. E., 1980. Regression Diagnostics. Hoboken, NJ: John Wiley & Sons.

Belsley, D. A., 1982. Assessing the presence of harmful collinearity and other forms of weak data

through a test for signal-to-noise. Journal of Econometrics 20, 211–253.

Biais, B., Hillion, P., Spatt, C., 1999. Price discovery and learning during the preopening period in the

Paris Bourse. Journal of Political Economy 107, 1218–1248.

Biais, B., Woolley, P., 2011. High frequency trading. Manuscript, Toulouse University, IDEI.

Biais, B., Foucault, T., Moinas, S., 2015. Equilibrium fast trading. Journal of Financial Economics 116, 292–313. Brogaard, J., 2010. High frequency trading and its impact on market quality. Northwestern University

Kellogg School of Management, Working Paper 66.

Brogaard,J., Hendershott,T., Riordan,R., 2014. High frequency trading and price discovery. Review of

Financial Studies 27, 2267–2306.

Brockman, P., Chung, D., 2002. Commonality in Liquidity: Evidence from an Order-Driven Market Structure. Journal of Financial Research 25, 521–539. Carrion, A., 2013. Very fast money: High-frequency trading on the NASDAQ. Journal of Financial

Markets 16, 680–711.

29

Chordia, T., Roll, R., Subrahmanyam, A., 2000. Commonality in liquidity. Journal of Financial Economics 56, 3–28. Chordia, T., Roll, R., Subrahmanyam, A., 2001. Market Liquidity and Trading Activity. Journal of Finance 56, 501–530. Comerton-Forde, C., Hendershott, T., Jones, C., Moulton, P., Seasholes, M., 2010. Time variation in liquidity: The role of market maker inventories and revenues. Journal of Finance 65: 295–331. Conrad, J., Wahal, S., Xiang, J., 2015. High-frequency quoting, trading, and the efficiency of prices. Journal of Financial Economics 116, 271–291. Coughenour, J., Saad, M., 2004. Common Market Makers and Commonality in Liquidity. Journal of Financial Economics 73, 37–69. Domowitz, I., Hansch, O., Wang, X., 2005. Liquidity, Commonality and Return Co‒movement. Journal of Financial Markets 8, 351–376. Fabre, J., Frino. A., 2004. Commonality in Liquidity: Evidence from the Australian Stock Exchange. Accounting & Finance 44, 357–368. Foran, J., Hutchinson, M. C., O’Sullivan, N., 2015. Liquidity Commonality and Pricing in UK Equities. Research in International Business and Finance 34, 281–293. Gai, Jiading, Yao, Chen, Ye, Mao, 2012. The externalities of high-frequency trading Working paper. University of Illinois at Urbana-Champaign. Glosten, L. R., Milgrom, P. R., 1985. Bid, ask and transaction prices in a specialist market with heterogeneously informed traders. Journal of Financial Economics 14, 71–100. Hasbrouck, J., 1991. Measuring the Information Content of Stock Trades. Journal of Finance 46, 179–207. Hasbrouck, J., Seppi, D., 2001. Common Factors in Prices. Order Flows and Liquidity, Journal of Financial Economics 59, 383–411. Hasbrouck, J., 2007. Empirical market microstructure: The institutions, economics, and econometrics of securities trading. Oxford University Press. Hasbrouck, J., 2009. Trading Costs and Returns for US Equities: Estimating Effective Costs from Daily Data. Journal of Finance 64, 1445–1477. Hendershott, T., Jones, C. M., Menkveld, A. J., 2011. Does algorithmic trading improve liquidity? Journal of Finance 66, 1–33. Huberman, G., Halka, D., 2001. Systematic Liquidity. Journal of Financial Research 24, 161–178. Jain, P. K., Jain, P., McInish, T. H., 2016. Does high-frequency trading increase systemic risk? Journal of Financial Markets 31, 1–24.

30

Kempf, A., Mayston, D., 2008. Liquidity commonality beyond best prices. Journal of Financial Research 31, 25–40. Kirilenko, A. A., Kyle, A. S., Samadi, M., Tuzun, T., 2016. The flash crash: High frequency trading in an electronic market. Kurov, A., Sancetta, A., Strasser, G., Wolfe, M. H, 2016. Price drift before US macroeconomic news: private information about public announcements? European Central Bank, Working Paper 1901. Kyle, A.S., 1985. Continuous auctions and insider trading. Econometrica: Journal of the Econometric Society, 1315–1335. Malinova, K., Park, A., 2015. Liquidity Provision and Market Making by HFTs. Report prepared for the Investment Industry Regulatory Organization of Canada. Pastor, L., Stambaugh, R. F., 2003. Liquidity Risk and Expected Stock Returns. Journal of Political Economy 111, 642–685.

31

FIGURES

Figure 1: Calculation of (il)liquidity for a hypothetical order size of 𝑞 shares and for a hypothetical

order book state: 𝐴1, 𝐴2 and 𝐴3 are the best three ask limits and 𝑆1, 𝑆2 and 𝑆3 are the corresponding

quantities. Similarly, on the buy side, 𝐵1 and 𝐵2 are the two best bids while 𝐷1 and 𝐷2 are the

corresponding quantities. The shaded area between the supply-demand schedule represents the total

round trip cost for an order of 𝑞 shares at time 𝑡, 𝑙𝑡(𝑞), which is represented by equation 𝑙𝑡(𝑞) =

∫ [𝑆𝑡(𝑄) − 𝐷𝑡(𝑄)]𝑑𝑄𝑞

0 in integral form.

Figure 2: The order book state for stock Accor - Act. (see Appendix Table A1) on 03/01/2013 at 10:35,

for the following two cases: a) only for HFT and MIXED orders (dashed supply-demand lines) and b)

only for NON HFT orders (solid supply-demand lines).

32

Figure 3: Top graph: Average, across days and stocks, intraday liquidity pattern for a hypothetical

order size of 5,000 shares for: a) the full order book, b) the NON HFT market and c) the HFT and MIXED

market, per 1 min interval. Liquidity is calculated according to equation (1) and then normalized as

Euro per share price impact, dividing by the order size. Notice the two peaks in the cost of trade at

14:30 (CET time) and 16:00 (CET time) for the full order book case (a) and the HFT and MIXED order

book case (c). The first peak (14:30) corresponds to the announcement of the monetary policy

decisions by the European Central Bank (ECB) as well the U.S. macroeconomic news announcements

at 08:30 (EST time), while the second peak (16:00) corresponds to the U.S. macroeconomic news

announcements at 10:00 (EST time). Bottom graph: Autocorrelation function for the liquidity series

(𝐿𝑡) for the full order book (case a) up to 5,000 lags for stock Accor - Act. (see Appendix Table A1),

together with the plot of the 95% confidence interval.

33

Figure 4: Top graph: Intraday volatility pattern in 1 min intervals, from 09:01 to 17:30. Volatility is

calculated as the average, across days and stocks, squared intraday 1 min logarithmic return. We use

the bid-ask midpoint as the current stock price for the calculation of the returns. Bottom graph:

Autocorrelation function for the volatility series (𝑣𝑡) for the full order book (case a) up to 2,000 lags

for stock Carrefour - Act. (see, also, Appendix Table A1), together with the plot of the 95% confidence

interval.

34

Figure 5: Average, across days and stocks, intraday liquidity pattern for a hypothetical order size of 1

share (that is, at the spread) for: a) the full order book, b) the NON HFT market and c) the HFT and

MIXED market, per 1 min interval. Liquidity is calculated according to equation (1) and then normalized

as Euro per share price impact, dividing by the order size (in this case 𝑞 = 1). As in Figure 3 (𝑞 = 5,000

shares), notice the two peaks in the cost of trade at 14:30 (CET time) and 16:00 (CET time) for the full

order book case (a) and the HFT and MIXED market case (c). The first peak (14:30) corresponds to the

announcement of the monetary policy decisions by the European Central Bank (ECB) as well the U.S.

macroeconomic news announcements at 08:30 (EST time), while the second peak (16:00) corresponds

to the U.S. macroeconomic news announcements at 10:00 (EST time).

35

Figure 6: The autocorrelation function for the average, across days and stocks, intraday liquidity

pattern for a hypothetical order size of 1 share for the NON HFT order book, per 1 min interval. Firm

specific liquidity is calculated according to equation (1) and then normalized as Euro per share price

impact, dividing by the order size (in this case 𝑞 = 1). Top graph: up to 509 lags. Bottom graph: up to

50 lags.

36

TABLES

Percentile

Depth buy 5% 25% 50% 75% 95%

Level 1 100 437 1,071 2,493 11,276

Level 2 364 1,133 2,353 5,105 22,369

Level 3 712 1,875 3,826 7,990 34,714

Level 4 1,188 2,792 5,651 11,387 47,849

Level 5 1,688 3,788 7,593 14,882 63,457

Level 6 2,156 4,783 9,454 18,310 78,793

Level 7 2,641 5,816 11,190 21,639 91,731

Level 8 3,152 6,842 12,732 24,648 102,540

Level 9 3,698 7,804 14,249 27,695 110,095

Level 10 4,258 8,734 15,772 30,748 116,783

Percentile

Depth sell 5% 25% 50% 75% 95%

Level 1 99 436 1,072 2,488 11,365

Level 2 361 1,145 2,374 5,135 22,327

Level 3 715 1,898 3,871 8,075 34,619

Level 4 1,200 2,817 5,712 11,498 47,777

Level 5 1,703 3,817 7,677 15,008 63,686

Level 6 2,176 4,813 9,545 18,443 78,776

Level 7 2,671 5,859 11,305 21,702 91,764

Level 8 3,189 6,900 12,857 24,729 102,843

Level 9 3,747 7,889 14,405 27,864 110,589

Level 10 4,337 8,870 16,017 30,910 117,384

Table 1: This Table reports the distribution (5%, 25%, 50%, 75% and 95% percentiles) for the aggregated shares depth, up to the best 10 limit levels of the LOB, both on the buy and the sell side.

37

Buy side Sell side

LOB depth NON HFT (%) HFT (%) MIXED (%) NON HFT (%) HFT (%) MIXED (%)

Level 1 13,0 41.8 44.3 13,9 41.9 45.1 Level 2 5,6 42.7 51.4 6,0 42.7 51.8 Level 3 4,7 37.8 57.3 5,0 37.3 57.9 Level 4 4,2 33.9 61.8 4,3 33.6 62.2 Level 5 4,5 33.6 61.9 4,6 33.4 62.1 Level 6 4,8 31.6 63.5 4,9 31.5 63.7 Level 7 5,3 27.3 67.2 5,4 27.2 67.6 Level 8 5,8 22.4 71.7 5,9 22.2 72.0 Level 9 7,2 18.1 74.5 7,4 17.2 75.6 Level 10 8,1 17.8 73.9 8,3 16.9 75.0

Table 2: This Table reports the available liquidity on the LOB due to NON HFT, HFT and MIXED quotes, as the, across days and stocks, average percentage of total outstanding shares for each trader category, relative to the total number of outstanding shares on the LOB. Statistics are reported both for the buy and the sell market side and up to the 10 best limits of the constructed LOB.

38

Panel A: Submitted limit orders Order size distribution percentiles

Strategy 5% 25% 50% 75% 95%

HFT 10 100 200 459 1,300

MIXED 27 110 208 436 1,864

NON HFT 11 86 214 584 3,500

Percentage (%) relative to total limit order submissions

Strategy Investors

Market Makers Investors

Market Makers Total sum

HFT 12.9631 70.5942 8.8910 91.1090 100.0000

MIXED 82.1554 29.4057 59.7545 40.2455 100.0000

NON HFT 4.8815 0.0001 99.9942 0.0058 100.0000

Total sum 100.0000 100.0000

Panel B: Modified limit orders Order size distribution percentiles

Trader 5% 25% 50% 75% 95%

HFT 5 10 50 214 1,500

MIXED 48 145 328 1,300 13,509

NON HFT 51 500 756 3,000 7,500

Percentage (%) relative to total limit order modifications

Strategy Investors

Market Makers Investors

Market Makers Total sum

HFT 20.1679 23.3170 88.8908 11.1092 100.0000

MIXED 56.7960 75.8909 87.3790 12.6210 100.0000

NON HFT 23.0361 0.7921 99.6297 0.3703 100.0000

Total sum 100.0000 100.0000

Panel C: Canceled limit orders Order size distribution percentile

Trader 5% 25% 50% 75% 95%

HFT 10 100 200 400 1,000

MIXED 26 111 210 439 1,883

NON HFT 13 100 235 622 3,504

Percentage (%) relative to total limit order cancelations

Strategy Investors

Market Maker Investors

Market Makers

Total sum

HFT 13.5594 70.2534 8.9968 91.0032 100.0000

MIXED 83.1427 29.7465 58.8763 41.1237 100.0000

NON HFT 3.2979 0.0001 99.9918 0.0082 100.0000

Total sum 100.0000 100.0000

Table 3: This Table reports summary statistics on the distribution of newly submitted, modified and canceled limit orders which are not executed at the spot (that is, non-marketable limit orders), relative to the type of trader (stop limit orders are included). The 5%, 25%, 50%, 75% and 95% percentiles of the limit order size for HFT, MIXED and NON HFT strategies are reported. The percentage of limit order submissions, modifications and cancellations for each of the three strategy types are also reported. The term “investors” represents accounts of individual brokers or parent company accounts. “Market Makers” are designated Liquidity Providers.

39

Panel A: Investors Size in shares of marketable orders (percentiles) 5% 25% 50% 75% 95%

HFT LO (HFT MO) 18 (45) 100 (132) 300 (390) 971 (1,005) 5,886 (3,976)

MIXED LO (MIXED MO) 20 (18) 101 (100) 270 (255) 782 (762) 3,819 (4,192)

NON HFT LO (NON HFT MO) 20 (24) 107 (127) 301 (357) 900 (1,055) 5,022 (7,257)

Percentage (%) of marketable orders Limit (LO) Market (MO) Limit (LO) Market (MO) Total sum

HFT 6.49 0.04 99.95 0.05 100.00 MIXED 73.57 11.69 98.63 1.37 100.00 NON HFT 19.94 88.27 72.18 27.82 100.00

Total sum 100.00 100.00

Panel B: Market Makers Size in shares of marketable orders (percentiles) 5% 25% 50% 75% 95%

HFT LO (HFT MO) 20 (0) 100 (0) 246 (0) 585 (0) 2,400 (0) MIXED LO (MIXED MO) 21 (0) 116 (0) 281 (0) 665 (0) 2,224 (0) NON HFT LO (NON HFT MO) 550 (0) 1,300 (0) 1,300 (0) 1,300 (0) 1,300 (0)

Percentage (%) of marketable orders Limit (LO) Market (MO) Limit (LO) Market (MO) Total sum

HFT 84.62 0.00 100.00 0.00 100.00 MIXED 15.38 0.00 100.00 0.00 100.00 NON HFT 0.00 0.00 0.00 0.00 -

Total sum 100.00 -

Panel C: In total Percentage (%) of marketable orders for each trader type Investors Market Makers Total sum

HFT 13.69 86.31 100.00 MIXED 90.93 9.07 100.00 NON HFT 100.00 0.00 100.00

Percentage (%) of marketable orders in total

Investors 69.20 Market makers 30.80

Table 4: This Table reports summary statistics for marketable orders; that is orders that trigger instant trades. Such orders can be aggressive Limit Orders (LO) and Market Orders (MO). Panel A presents statistics for individual broker (Investors) accounts: the distribution of the order size and the percentage of HFT, MIXED and NON HFT limit and market orders. Panel B presents statistics for Market Making (Liquidity Providers) accounts: the distribution of the order size and the percentage of HFT, MIXED and NON HFT limit and market orders. Finally, Panel C summarizes the total percentage of marketable orders (market and limit) for brokers and market makers.

40

Full order book Percentile

Order size (shares) 5% 25% 50% 75% 95% 1 0.003 0.011 0.018 0.027 0.081

1,000 0.003 0.013 0.021 0.041 0.116 5,000 0.004 0.020 0.039 0.087 0.240

10,000 0.005 0.028 0.058 0.146 0.375 15,000 0.006 0.035 0.076 0.236 0.618

NON HFT orders Percentile

Order size (shares) 5% 25% 50% 75% 95% 1 0.016 0.054 0.096 0.173 0.289

1,000 0.023 0.093 0.194 0.377 0.698 5,000 0.040 0.176 0.365 0.832 1.606

10,000 0.051 0.251 0.551 1.467 2.627 15,000 0.059 0.304 0.699 2.140 3.895

HFT and MIXED orders Percentile

Order size (shares) 5% 25% 50% 75% 95% 1 0.003 0.012 0.018 0.028 0.082

1,000 0.003 0.014 0.022 0.044 0.125 5,000 0.004 0.021 0.041 0.097 0.262

10,000 0.005 0.030 0.062 0.191 0.482 15,000 0.006 0.037 0.084 0.365 0.943

Table 5: This Table reports summary statistics on the distribution of liquidity series, for the following hypothetical order sizes: 1, 1,000, 5,000, 10,000 and 15,000 shares, and for three cases: a) the order book calculated on the basis of the full set of orders, b) the order book resulting only from NON HFT orders and c) the order book attributed to HFT and MIXED orders. Liquidity is calculated according to equation (1) and then normalized as Euro per share price impact, dividing by the order size.

41

Order size 1 share 1,000 shares 5,000 shares

Coefficient Average % % (+) Average % % (+) Average % % (+)

�̂� -0.001 8.3 0.0 -0.001 27.8 0.0 -0.001 27.8 0.0

�̂�1 0.319 100.0 100.0 0.426 100.0 100.0 0.613 100.0 100.0

�̂�2 0.057 61.1 61.1 0.073 91.7 91.7 0.040 58.3 52.8

�̂�3 0.067 83.3 83.3 0.072 86.1 86.1 0.049 69.4 69.4

�̂�1 0.025 94.4 94.4 0.024 94.4 94.4 0.020 100.0 100.0

�̂�2 -0.009 66.7 2.8 -0.012 91.7 2.8 -0.013 97.2 0.0

�̂�3 -0.006 52.8 0.0 -0.002 22.2 0.0 0.000 30.6 22.2

𝑓1 -0.003 16.7 8.3 -0.014 25.0 8.3 -0.003 11.1 5.6

𝑓2 0.001 2.8 2.8 0.002 5.6 5.6 -0.006 5.6 0.0

𝑓3 -0.014 2.8 2.8 0.002 2.8 2.8 0.004 2.8 2.8 𝑅2 (%) 1.142 2.681 8.472 Order size 10,000 shares 15,000 shares

Coefficient Average % % (+) Average % % (+) �̂� 0.000 25.0 0.0 0.000 22.2 0.0 �̂�1 0.683 100.0 100.0 0.693 100.0 100.0 �̂�2 0.031 50.0 38.9 0.032 50.0 38.9 �̂�3 0.054 61.1 61.1 0.057 61.1 61.1 �̂�1 0.017 100.0 100.0 0.016 100.0 100.0 �̂�2 -0.012 97.2 0.0 -0.011 97.2 0.0 �̂�3 0.001 33.3 30.6 0.002 38.9 38.9 𝑓1 -0.008 27.8 13.9 -0.010 30.6 13.9 𝑓2 0.002 19.4 13.9 0.006 33.3 22.2 𝑓3 0.003 0.0 0.0 0.002 0.0 0.0 𝑅2 (%) 11.841 12.212

Table 6: This Table reports the results from the estimation of equation (3) for each CAC 40 stock in our sample (𝑖 = 1, … ,36):

𝐿𝑡𝑖 = 𝑎 + 𝑏1𝐿𝑡

𝑀 + 𝑏2𝐿𝑡−1𝑀 + 𝑏3𝐿𝑡+1

𝑀 +

𝑑1𝑉𝑡𝑖 + 𝑑2𝑉𝑡−1

𝑖 + 𝑑3𝑉𝑡+1𝑖 + 𝑓1𝑅𝑡

𝑀 + 𝑓2𝑅𝑡−1𝑀 + 𝑓3𝑅𝑡+1

𝑀 + 𝑒𝑡.

𝐿𝑡𝑖 is individual stock liquidity at time 𝑡, 𝐿𝑡

𝑀, 𝐿𝑡−1𝑀 and 𝐿𝑡+1

𝑀 are concurrent, lag and lead market liquidity, respectively, calculated over the full set

of active orders on the LOB, 𝑉𝑡𝑖, 𝑉𝑡−1

𝑖 and 𝑉𝑡+1𝑖 are concurrent, lag and lead individual security volatility, respectively, calculated as squared

logarithmic returns, using the mid-point price of the LOB, and 𝑅𝑡𝑀, 𝑅𝑡−1

𝑀 and 𝑅𝑡+1𝑀 are concurrent, lag and lead market return. All market

measures are calculated as weighted capitalization averages. For each regression, security 𝑖 is excluded from the calculation of market

measures, to remove additional biases. We report the, across stocks, average coefficient estimates, the, across stocks, percentage of statistically

significant coefficient estimates (95% confidence level) as well as the, across stocks, percentage of statistically significant and positive coefficient

estimates (95% confidence level). We also report the average coefficient of determination 𝑅2 (%). Standard errors in all regressions are Newey-

West corrected for serial correlation and heteroscedasticity.

42

Order size 1 share 1,000 shares 5,000 shares

Coefficient Average % % (+) Average % % (+) Average % % (+)

�̂� -0.001 2.8 0.0 -0.001 16.7 0.0 0.000 16.7 0.0

�̂�1 0.061 97.2 97.2 0.069 88.9 88.9 0.076 61.1 61.1

�̂�2 -0.001 5.6 5.6 -0.007 19.4 5.6 0.017 11.1 11.1

�̂�3 0.000 2.8 2.8 -0.003 8.3 0.0 -0.004 0.0 0.0

�̂�1 0.298 100.0 100.0 0.449 100.0 100.0 0.595 100.0 100.0

�̂�2 0.058 63.9 63.9 0.071 83.3 83.3 0.023 38.9 30.6

�̂�3 0.064 72.2 72.2 0.067 83.3 83.3 0.028 41.7 41.7

𝑓1 0.024 94.4 94.4 0.023 94.4 94.4 0.020 100.0 100.0

𝑓2 -0.008 63.9 2.8 -0.012 91.7 2.8 -0.013 97.2 0.0

𝑓3 -0.006 55.6 0.0 -0.002 22.2 0.0 0.000 27.8 19.4

�̂�1 0.002 16.7 8.3 -0.009 22.2 8.3 -0.007 11.1 5.6

�̂�2 0.003 2.8 2.8 0.001 5.6 5.6 -0.009 8.3 0.0

�̂�3 -0.013 2.8 2.8 0.004 5.6 5.6 0.008 8.3 8.3

𝑅2 (%) 1.239 2.978 10.329

Order size 10,000 shares 15,000 shares Coefficient Average % % (+) Average % % (+)

�̂� 0.000 8.3 0.0 0.000 13.9 0.0

�̂�1 0.083 63.9 58.3 0.096 66.7 58.3

�̂�2 0.039 25.0 25.0 0.055 38.9 38.9

�̂�3 -0.008 0.0 0.0 -0.009 5.6 0.0

�̂�1 0.612 100.0 100.0 0.605 100.0 100.0

�̂�2 0.007 50.0 27.8 0.012 52.8 33.3

�̂�3 0.026 50.0 41.7 0.034 55.6 50.0

𝑓1 0.017 100.0 100.0 0.016 100.0 100.0

𝑓2 -0.012 97.2 0.0 -0.011 97.2 0.0

𝑓3 0.001 33.3 30.6 0.002 38.9 38.9

�̂�1 -0.009 25.0 13.9 -0.009 30.6 13.9

�̂�2 -0.009 19.4 11.1 -0.008 36.1 19.4

�̂�3 0.010 2.8 2.8 0.012 0.0 0.0 𝑅2 (%) 13.536 13.232

Table 7: This Table reports the results from the estimation of equation (4) for each CAC 40 stock in our sample (𝑖 = 1, … ,36):

𝐿𝑡𝑖 = 𝑎 + 𝑏1𝐿𝑡

𝑀,𝑁𝑂𝑁 𝐻𝐹𝑇 + 𝑏2𝐿𝑡−1𝑀,𝑁𝑂𝑁 𝐻𝐹𝑇 + 𝑏3𝐿𝑡+1

𝑀,𝑁𝑂𝑁 𝐻𝐹𝑇 + 𝑑1𝐿𝑡𝑀,𝐻𝐹𝑇 + 𝑑2𝐿𝑡−1

𝑀,𝐻𝐹𝑇 + 𝑑3𝐿𝑡+1𝑀,𝐻𝐹𝑇 +

𝑓1𝑉𝑡𝑖 + 𝑓2𝑉𝑡−1

𝑖 + 𝑓3𝑉𝑡+1𝑖 + 𝑤1𝑅𝑡

𝑀 + 𝑤2𝑅𝑡−1𝑀 + 𝑤3𝑅𝑡+1

𝑀 + 𝑒𝑡.

𝐿𝑡𝑖 is individual stock liquidity at time 𝑡, 𝐿𝑡

𝑀,𝑁𝑂𝑁 𝐻𝐹𝑇, 𝐿𝑡−1𝑀,𝑁𝑂𝑁 𝐻𝐹𝑇 and 𝐿𝑡+1

𝑀,𝑁𝑂𝑁 𝐻𝐹𝑇 are concurrent, lag and lead market liquidity, respectively,

calculated over the NON HFT LOB, 𝐿𝑡𝑀,𝐻𝐹𝑇, 𝐿𝑡−1

𝑀,𝐻𝐹𝑇 and 𝐿𝑡+1𝑀,𝐻𝐹𝑇 are concurrent, lag and lead market liquidity, respectively, calculated over the

HFT and MIXED LOB, 𝑉𝑡𝑖, 𝑉𝑡−1

𝑖 and 𝑉𝑡+1𝑖 are concurrent, lag and lead individual security volatility, respectively, calculated as squared logarithmic

returns, using the mid-point price of the actual LOB, and 𝑅𝑡𝑀, 𝑅𝑡−1

𝑀 and 𝑅𝑡+1𝑀 are concurrent, lag and lead market return. All market measures

are calculated as weighted capitalization averages. For each regression, security 𝑖 is excluded from the calculation of market measures, to

remove additional biases. We report the, across stocks, average coefficient estimates, the, across stocks, percentage of statistically significant

coefficient estimates (95% confidence level) as well as the, across stocks, percentage of statistically significant and positive coefficient estimates

(95% confidence level). We also report the average coefficient of determination 𝑅2 (%). Standard errors in all regressions are Newey-West

corrected for serial correlation and heteroscedasticity.

43

PCA results

Full LOB NON HFT LOB HFT LOB (HFT and MIXED)

1 share Eigenvalue Explained (%) Eigenvalue Explained (%) Eigenvalue Explained (%)

1st component 4.70 13.27 3.92 11.07 4.73 13.35

2nd component 1.35 3.82 1.35 3.81 1.36 3.85

3rd component 1.09 3.09 1.19 3.35 1.10 3.09

1,000 shares 1st component 5.98 16.88 4.20 11.87 6.14 17.34

2nd component 1.48 4.19 1.52 4.31 1.52 4.29

3rd component 1.14 3.21 1.40 3.95 1.16 3.28

5,000 shares 1st component 7.35 20.75 5.07 14.36 7.41 20.92

2nd component 1.74 4.91 1.88 5.31 1.92 5.43

3rd component 1.23 3.46 1.56 4.42 1.28 3.61

10,000 shares 1st component 7.28 20.56 5.56 15.89 6.93 19.72

2nd component 2.14 6.05 2.00 5.72 2.55 7.26

3rd component 1.44 4.07 1.77 5.05 1.85 5.26

15,000 shares 1st component 7.18 20.27 4.69 14.08 7.10 20.22

2nd component 2.52 7.13 2.98 8.95 3.01 8.56 3rd component 1.68 4.75 2.36 7.08 2.18 6.20

Table 8: This Table reports the results from the PCA analysis on the covariance matrix of the standardized liquidity series calculated according to equation (1) for the three cases: i) the full order book, ii) the order book constructed on the basis of NON HFT quotes and iii) the order book based on the set of HFT and MIXED quotes, for the hypothetical order sizes of 1, 1,000, 5,000, 10,000 and 15,000 shares. The Table presents the first three principal component variances (i.e., the first three eigenvalues of the covariance matrix of liquidities) and the percentage of total explained variance that corresponds to each of the first three principal components, for each of the aforementioned cases. Explained variance is calculated as the eigenvalue divided by the sum of all eigenvalues.

44

Appendix A Table A1: The 36 stock sample from the CAC 40: The daily average number of company shares, trading volume (in shares) and value of transactions for the sample period: 02/01/2013 to 28/03/2013.

Company name ISIN code Shares Trading Volume Capitalization

Accor - Act. FR0000045072 2,552,838,411.0 7,322,527.9 26,437,962,450.9

Air Liquide - Act. FR0000073272 417,029,585.0 921,055.9 21,578,667,747.8

Airbus Group - Shs FR0000120073 329,357,869.3 805,845.0 34,063,207,255.4

Alcatel-Lucent - Act. FR0000120172 728,358,105.5 2,835,535.0 19,174,643,842.6

Alstom - Act. FR0000120271 2,386,465,722.5 5,769,478.7 105,785,462,532.5

Axa - Act. FR0000120321 582,245,707.9 672,620.8 79,708,226,120.3

BNP Paribas-A- - Act. - Cat.A FR0000120404 229,943,813.9 948,638.5 8,444,621,082.5

Bouygues - Act. FR0000120503 328,685,176.2 1,230,372.7 9,590,640,328.4

Cap Gemini - Act. FR0000120578 1,321,657,757.0 2,933,698.7 106,845,351,051.9

Carrefour - Act. FR0000120628 2,419,883,246.3 7,158,324.9 46,475,052,815.6

Credit Agricole - Act. FR0000120644 641,624,276.3 1,722,765.2 36,109,372,890.5

Danone - Act. FR0000120693 265,396,103.1 544,864.4 24,966,496,824.8

Engie - Act. FR0000121014 507,901,146.4 869,490.7 72,552,384,896.3

Essilor Intl - Act. FR0000121261 185,634,464.1 685,950.1 15,145,483,1505

Kering - Act. FR0000121485 126,206,954.2 274,241.2 20,513,217,981.0

Klepierre - Act. FR0000121501 598,793,794.0 4,907,772.5 7,482,453,636.0

LOreal - Act. FR0000121667 215,258,762.8 565,274.7 19,355,788,420.3

Legrand - Act. FR0000121964 235,817,949.5 350,747.4 8,697,442,418.5

Lvmh - Act. FR0000121972 574,501,896.8 1,713,066.5 35,526,067,059.5

Michelin Nom. - Act. FR0000124141 552,385,012.3 2,607,262.6 8,022,594,392.9

Orange - Act. FR0000125007 556,508,843.5 1,997,989.8 21,010,249,151.6

Pernod Ricard - Act. FR0000125338 162,579,630.2 717,571.6 9,417,991,614.3

Peugeot - Act. FR0000125486 597,198,429.6 1,637,691.9 21,034,464,280.1

Publicis Groupe - Act. FR0000127771 1,345,786,798.2 5,009,997.5 25,998,119,454.3

Renault - Act. FR0000130007 2,660,332,314.3 26,773,175.6 7,203,710,127.8

SAFRAN - Act. FR0000130338 79,456,775.3 381,688.9 7,464,398,099.4

Saint Gobain - Act. FR0000130577 216,506,875.5 757,276.1 13,221,462,991.9

Sanofi - act. FR0000130809 799,052,709.8 4,723,645.4 31,058,948,532.2

Schneider Electric - Act. FR0000131104 1,244,995,556.6 4,268,441.7 63,915,587,948.5

Societe Generale - Act. FR0000131708 114,161,979.7 669,083.1 7,714,530,007.3

Technip - Act. FR0000131906 295,722,284.0 1,200,235.1 20,112,641,082.3

Total - Act. FR0000133308 2,648,885,383.2 9,376,542.0 30,625,807,936.8

Valeo - Act. FR0010208488 2,420,635,302.0 5,530,482.2 42,522,939,860.4

Veolia Environn. - Act. FR0010220475 309,089,499.9 1,604,573.9 8,486,879,537.7

Vinci - Act. FR0010307819 265,033,979.1 647,289.0 11,571,996,542.1

Vivendi - Act. NL0000235190 794,523,517.9 2,712,980.1 39,723,859,695.2

45

Appendix B This Appendix reports the results from the Variance Inflation Factor calculations for the correlation

matrix of the independent variables in equations (3) and (4) in Section 6. VI factors are calculated as

the diagonal elements of the inverse of the correlation matrix of the independent variables (e.g.,

Belsley et al., 1980). In other words, VIFs explain the amount of correlation between the predictors.

According to Table B1 all VIFs are close to unity both for models (3) and (4), indicating that there is

very little correlation among the predictors. Hence, we infer that there is no multi-collinearity in the

models.

Order size (shares) 1 1,000 5,000 10,000 15,000

𝐿𝑡𝑀 1.526 1.331 1.174 1.095 1.063

𝐿𝑡−1𝑀 1.275 1.166 1.086 1.048 1.034

𝐿𝑡+1𝑀 1.275 1.166 1.086 1.049 1.035

𝑉𝑡𝑖 1.093 1.093 1.093 1.093 1.093

𝑉𝑡−1𝑖 1.074 1.074 1.074 1.074 1.074

𝑉𝑡+1𝑖 1.074 1.074 1.074 1.074 1.074

𝑅𝑡𝑀 1.000 1.000 1.000 1.000 1.001

𝑅𝑡−1𝑀 1.000 1.000 1.000 1.000 1.001

𝑅𝑡+1𝑀 1.000 1.000 1.000 1.001 1.001

Order size (shares) 1 1,000 5,000 10,000 15,000

𝐿𝑡𝑀,𝑁𝑂𝑁 𝐻𝐹𝑇 1.506 1.242 1.151 1.087 1.066

𝐿𝑡−1𝑀,𝑁𝑂𝑁 𝐻𝐹𝑇 1.307 1.144 1.095 1.061 1.048

𝐿𝑡+1𝑀,𝑁𝑂𝑁 𝐻𝐹𝑇 1.306 1.145 1.095 1.061 1.047

𝐿𝑡𝑀,𝐻𝐹𝑇 1.659 1.313 1.173 1.074 1.051

𝐿𝑡−1𝑀,𝐻𝐹𝑇 1.380 1.169 1.098 1.047 1.036

𝐿𝑡+1𝑀,𝐻𝐹𝑇 1.380 1.170 1.098 1.048 1.037

𝑉𝑡𝑖 1.094 1.094 1.093 1.093 1.094

𝑉𝑡−1𝑖 1.075 1.074 1.074 1.074 1.075

𝑉𝑡+1𝑖 1.075 1.075 1.074 1.074 1.074

𝑅𝑡𝑀 1.001 1.001 1.001 1.001 1.002

𝑅𝑡−1𝑀 1.001 1.001 1.001 1.001 1.002

𝑅𝑡+1𝑀 1.000 1.000 1.001 1.001 1.002

Table B1: This Table reports the calculated Variance Inflation Factor (VIF) for the matrix of independent variables in equation (3):

𝐿𝑡𝑖 = 𝑎 + 𝑏1𝐿𝑡

𝑀 + 𝑏2𝐿𝑡−1𝑀 + 𝑏3𝐿𝑡+1

𝑀 + 𝑑1𝑉𝑡𝑖 + 𝑑2𝑉𝑡−1

𝑖 + 𝑑3𝑉𝑡+1𝑖 + 𝑓1𝑅𝑡

𝑀 + 𝑓2𝑅𝑡−1𝑀 + 𝑓3𝑅𝑡+1

𝑀 + 𝑒𝑡

and equation (4):

𝐿𝑡𝑖 = 𝑎 + 𝑏1𝐿𝑡

𝑀,𝑁𝑂𝑁 𝐻𝐹𝑇 + 𝑏2𝐿𝑡−1𝑀,𝑁𝑂𝑁 𝐻𝐹𝑇 + 𝑏3𝐿𝑡+1

𝑀,𝑁𝑂𝑁 𝐻𝐹𝑇 + 𝑑1𝐿𝑡𝑀,𝐻𝐹𝑇 + 𝑑2𝐿𝑡−1

𝑀,𝐻𝐹𝑇 + 𝑑3𝐿𝑡+1𝑀,𝐻𝐹𝑇 +

𝑓1𝑉𝑡𝑖 + 𝑓2𝑉𝑡−1

𝑖 + 𝑓3𝑉𝑡+1𝑖 + 𝑤1𝑅𝑡

𝑀 + 𝑤2𝑅𝑡−1𝑀 + 𝑤3𝑅𝑡+1

𝑀 + 𝑒𝑡 .

Liquidities are in logarithmic first differences (more information on the variables can be found in Tables 6 and 7). VI factors are calculated as the diagonal elements of the inverse of the correlation matrix of the independent variables (Belsley et al., 1980).