High Frequency Traders and Hidden Liquidity in NASDAQ

John Ritter∗†

May 2016

Abstract

I examine how the speed of market participants affects the decision to conceal a limit order. In

terms of the order initiator, I find that traders with a speed advantage, high-frequency traders (HFTs),

are more likely to hide an order in the limit order book, but slower traders, non-high frequency traders

(NHFTs), are more likely to hide an order when supplying liquidity in a trade. This difference occurs

because NHFTs are more likely to conceal their aggressively priced limit orders, which reduces their

adverse selection costs. Hiding a limit order does not reduce the adverse selection faced by HFTs,

who are more likely to conceal their less aggressively priced limit orders. In terms of other market

participants, I find that the limit orders of both HFTs and NHFTs are less likely to be concealed as

the proportion of trading volume in which HFTs participate increases. Overall, these findings suggest

that the speed of both the order initiator and other market participants affect a trader’s decision to

conceal their limit order.

JEL Classification: G10, G12, G14

Keywords: Market Microstructure, Hidden Liquidity, Pre-trade Transparency, Limit order book,

Informed Trading, Market Impact, High Frequency Trading

∗I would like to thank Michael Dambra, Jacquelyn Gillette, Ron Goettler, Ron Kaniel, Jordan Moore, Robert Novy-Marx,Dmitry Orlov, Bryce Schonberger, Gideon Saar, Jerold Warner, Brian Wolfe, and seminar participants at the Simon BusinessSchool for their comments and suggestions. I would also like to thank NASDAQ OMX for supplying the data used in thisstudy and the Center for Integrated Research Computing (CIRC) at the University of Rochester for providing the computerresources used in this study. All remaining errors are my own.†William E. Simon Graduate School of Business Administration, University of Rochester, Rochester, NY 14627;

Email: john.ritter@simon.rochester.edu

1 Introduction

Two common features of today’s electronic limit order markets are the prevalence of high-frequency traders

(HFTs) and the ability to conceal an order from other traders.1 HFTs account for over 50% of trading

volume on US exchanges2 and the SEC estimates that an average of 13.8%3 of stock volume traded on

U.S. public exchanges executes against hidden liquidity.4. Despite the prevalence of hidden liquidity and

HFTs on today’s exchanges, we still do not have a good understanding of how trading speed influences

the decision to conceal a limit order.5 This paper investigates this topic by examining how differences in

the trading speed of both the order submitter and other market participants affects the decision to hide

a limit order.

Specifically, I utilize data sets provided by NASDAQ to examine how high frequency traders (HFTs)

differ from non-high frequency traders (NHFTs) in their tendency to conceal their limit orders and how

variation in the proportion of trading volume in which HFTs are active affects the decision to hide an

order.6 The data provided by NASDAQ contains snapshots at the beginning of each minute of the

aggregated depth at the ten best prices in the NASDAQ limit order book for a sample of 120 randomly

selected stocks. The aggregated depth at each price is broken down and classified based on whether it is

hidden or displayed and whether it is supplied by a high-frequency trader (HFT) or non-high frequency

trader (NHFT).7 NASDAQ also provided trade data that identifies if the liquidity demander and supplier

1. Limit order markets that allow the use of hidden orders fall into one of two types. The first type of market, whichis common outside the U.S., only allows traders to post ”iceberg” or reserve orders, which require the trader to display aminimum portion of their order size. The second type of market, which is studied in this paper and is common in the U.S.,allows the posting of iceberg orders as well as completely hidden orders, which do not contain any displayed shares. In amarket that allows completely hidden orders, there is uncertainty regarding the price at which a market order will execute,because prices that are available for execution will not be displayed in the limit order book if there is no displayed depth atthe price.

A third type of exchange that allows a trader to conceal their orders is a dark pool. Dark pools are private exchangesused by institutional investors that are usually not available to the public. Usually all orders in a dark pool are hidden untilafter the transactions are completed. The majority of dark pools in the United States are organized as midpoint crossingnetworks. See Zhu (2014) for an overview and discussion of dark pools.

2. Source: Securities Exchange Act Release N0. 34-61358, 75 FR 3594, 3606 (January 21, 2010)(”Concept Release”).3. An average of 21.4% of traded volume executed against hidden volume for stocks in the smallest marketcap decile, while

12.7% of traded volume executed against hidden volume for stocks in the largest market cap decile in the first quarter of2016.

4. Source: Market Structure Data Downloads on SEC website (https://www.sec.gov/marketstructure/data)5. In the context of this paper, the term trading speed is used to indicate differences in how quickly a trader can cancel or

modify their limit orders or respond to changes in the limit order book. Another possible definition, which is not the focusof this paper, could indicate differences in how quickly investors gather and trade on new information.

6. This paper does not specifically test, but instead makes the assumption that, on average, the traders classified asHFTs in this study have a speed advantage over the traders classified as NHFTs. However, this assumption appears tobe valid based on the criteria NASDAQ used to select the HFT identifier, the colocation services utilized by HFTs, andevidence documented in Brogaard, Hendershott, and Riordan (2013) and Hirschey (2013), which use the same HFT/NHFTclassification criteria.

7. The HFT indicator used in this study is an aggregate indicator identifying if a trade or limit order book depth belongsto one of the 26 firms that NASDAQ identifies as high-frequency traders in the data provided. NASDAQ classifies the 26

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are HFTs or NHFTs and whether the liquidity supplied in the trade was displayed on the limit order book

or hidden.8 For each stock on each day, I aggregate the volume of shares supplied by HFTs and NHFTs

in the limit order book and in transactions to determine the proportion that is hidden.

When I examine how differences in the trading speed of the order submitter affects the decision to

conceal the order, I find that orders in the limit order book are more likely to be hidden when they are

submitted by HFTs. On average, HFTs concealed 31.2% of their shares in the limit order book, while

NHFTs concealed 26.5%. This result supports one of the predictions from Ritter (2016), who models how

differences in trader speed and information affects the decision to conceal a limit order. One of the main

costs of hiding a limit order is that it has lower priority than displayed orders at the same price, even if

the displayed order was submitted at a later time. His model predicts that fast traders are more likely

to hide an order than slow traders, because their speed advantage lowers the cost of concealing an order

by allowing them to adjust their hidden order quicker if it loses priority to a displayed limit order at the

same price.

Surprisingly, when I examine liquidity supplied in transactions, I find that NHFTs are more likely

than HFTs to conceal their order when they are supplying liquidity in a trade. On average, 20.2% of the

volume NHFTs used to supply liquidity in trades was hidden, while only 15.6% of the trading volume

supplied by HFTs was concealed. The difference between the rates at which HFTs hide their liquidity

in the limit order book and in transactions occurs because HFTs are more likely to conceal their less

aggressively priced limit orders. In comparison, NHFTs are more likely to conceal their more aggressively

priced limit orders, which are more likely to execute in trades.

Harris (1997) and Bessembinder, Panayides, and Venkatamaran (2009) note that one reason traders

conceal their limit orders is to reduce the chance that they are adversely selected or picked off if they

become mispriced. One possible explanation for the differences in the way HFTs and NHFTS conceal

their orders could be that the hidden and displayed limit orders of NHFTs and HFTs face different adverse

selections costs. I test this hypothesis and find that the hidden orders of NHFTs face less adverse selection

and earn higher revenues than their displayed orders, both before and after liquidity rebates are factored

in. On the other hand, I do not find a significant difference between the adverse selection faced by

firms as HFTs based on an analysis of their trading activity, including how long their orders last, how long they hold theirinventory, and their order to trade ratio. Unfortunately, the data cannot classify all HFT activity. Firms that engage inbrokerage services and also run proprietary trading desks would not be identified as HFTs in the analysis, nor would HFTswho route their orders through large brokerage firms. The data set can be thought of as indicating a lower bound on theactivity of HFTs. The data also does not provide a firm level id, so it is not possible to identify the transactions or limitorders for individual HFT firms.

8. The transaction data is the same one used in Brogaard, Hendershott, and Riordan (2013) to study the role of HFTs inprice discovery. NASDAQ makes the HFT data freely available for research to academics who sign a nondisclosure agreement.

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HFT hidden and displayed orders. This could explain why NHFTs are more likely to conceal their more

aggressively priced limit orders, which face higher adverse selection costs than less aggressively priced

orders.

I investigate how the speed of other market participants affects the decision to conceal a limit order

and find that the limit orders supplied by both HFTs and NHFTs are less likely to be hidden when HFTs

account for a higher proportion of trading volume. This result is consistent with the theoretical model

in Ritter (2016), which predicts that the use of hidden liquidity will decrease when the proportion of

fast traders increases, because an increase in the proportion of fast traders increases the chance that a

standing hidden order is front-run by a displayed limit order.

One possible problem is that the observed relationship between hidden liquidity and HFT activity is

endogenous, since the proportion of transactions in which HFTs participate and their decision to hide an

order are joint outcomes of a simultaneous decision process.9 I address this issue using an instrument

variable approach based on the runs in process instrument variable developed in Hasbrouck and Saar

(2013). Specifically, I construct instrument variables that are aggregated market measures of the average

percentage of NASDAQ dollar trading volume each day in which HFTs demand and supply liquidity. In

order to ensure the instrument variables are uncorrelated with the decision to hide liquidity, I exclude

stocks that are in the same index and industry from the aggregations when I calculate the instruments

for each stock. After controlling for endogeneity, I confirm the negative relationship between the decision

to conceal an order and how actively HFTs trade.

When I separate the proportion of overall HFT trading activity into its liquidity demanding and

liquidity supplying components, I find that the decision of HFTs to conceal a limit order is negatively

related to the proportion of liquidity that HFTs demand, while the decision of NHFTs to conceal an

order is negatively related to the proportion of liquidity that HFTs supply. These results could indicate

that HFT hidden orders are more sensitive than NHFT hidden orders to the increase in adverse selection

that is associated with an increase in HFT liquidity demanding activity. Comparatively, NHFT hidden

orders are more sensitive to the increased chance of being front-run by a competing displayed order that

is associated with an increase in HFT liquidity supplying activity.

I examine how HFT liquidity demand affects the adverse selection costs of hidden orders. I find that

as the proportion of liquidity demanded by HFTs increases the adverse selection HFT hidden limit orders

face increases, but the adverse selection NHFT hidden orders face does not.

9. Both the model in Ritter (2016) and the model in Butti and Rindi (2013) emphasize that the choice of order price andorder exposure will be simultaneous decisions.

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I also examine the ability of HFT and NHFT liquidity demanders to detect the presence of hidden

liquidity. I find that HFT liquidity demanders trade with hidden liquidity at a greater frequency than if

the interactions occurred by chance, which is evidence that they are better at detecting the presence of

hidden liquidity in the limit order book than NHFTs. This is consistent with the intuition of Xu (2014),

who theorizes that HFTs can use their speed to aid in the detection of hidden liquidity in the limit order

book through the use of pinging, the rapid submission and cancellation of limit orders inside the bid-ask

spread.10

One disadvantage of supplying liquidity using a hidden order is that the rebate earned for supplying

liquidity is about half the value of the rebate earned for supplying liquidity using a displayed order.

However, before May 1, 2008, the highest liquidity rebates on NASDAQ for supplying liquidity using

displayed and non-displayed shares were the same.11 I use this difference to examine how a change in the

value of nondisplayed liquidity rebates affects the decision to conceal a limit order. I find that reducing

the rebate decreases the proportion of liquidity supplied in transactions that is hidden by 2.2%. This

result is significant for both HFT and NHFT liquidity suppliers. Surprisingly, I also find that reducing

the rebate increases the proportion of total limit order book depth that is hidden. However, this change

is mainly driven by an increase in the use of hidden liquidity above the best displayed quotes, which is

less likely to trade with a market order and earn the rebate.

This papers adds to the literature on concealed orders in limit order markets. In terms of the theoretical

literature, this paper is most closely related to the model presented in Ritter (2016), who models how

differences in trader speed and information affects the decision to conceal a limit order. As discussed

earlier, his model predicts that fast traders experience lower costs when their hidden orders lose priority

to displayed orders and are more likely to hide a limit order than slow traders. He also predicts that

traders are less likely to conceal their orders as the proportion of fast traders increases. In other theoretical

work, Harris (1997) proposes that traders can hide their limit orders to reduce the chance of them being

adversely selected or front-run by ”parasitic traders”. Butti and Rindi (2013) examine order exposure

costs in a model in which an uninformed trader competes to supply liquidity by simultaneously deciding

10. The SEC concept release on equity market structure from January 21, 2010 is concerned that the pinging strategiesemployed by HFTs to detect undisclosed orders may be manipulative and harm market quality.

11. On NASDAQ, hidden orders currently earn lower rebates than displayed orders for supplying liquidity in a transaction.During the sample period, the highest rebates for supplying liquidity in a transaction on NASDAQ using displayed ordersranges from 0.25 to 0.295 cents per share executed. The highest rebates for supplying liquidity using non-displayed ordersranges from 0.15 to 0.27 cents per share executed. From the beginning of sample period in January, 2008 until April 30,2008, the highest rebate for supplying liquidity using displayed and non-displayed shares were the same, 0.27 cents per shareexecuted. In the period beginning May 1, 2008, the highest rebate for supplying liquidity using non-displayed orders wasreduced to 0.15 cents per share executed. (Source: http://www.nasdaqtrader.com/trader.aspx?id=pricelisttrading2)

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on an order’s price, size, and the amount of the order that is visible. They show that large traders

use hidden orders to reduce exposure costs and avoid being undercut by competing liquidity suppliers.

Cebiroglu, Hautsch, and Horst (2013) also model an uninformed trader’s decision to expose their order

when competing to supply liquidity in the limit order book while also competing with an off-exchange

upstairs market for order flow. They find that requiring orders to be displayed in the limit order book

attracts order flow from the upstairs market and improves market quality by helping coordinate the supply

and demand of liquidity. Allowing hidden orders in the limit order book generates excess volatility and

higher trading costs due to a lack of coordination between liquidity demand and supply.

In terms of the empirical literature, Bessembinder, Panayides, and Venkatamaran (2009) examine the

use of iceberg orders on Euronext Paris and find that iceberg orders have lower execution probabilities

and take longer to fill, but also experience lower execution costs in the form of lower implementation

shortfall costs. De Winne and D’Hondt (2007) also examine hidden orders on Euronext and find that

uninformed traders use hidden orders to manage their picking off risk. Anand and Weaver (2004) look at

the removal and reintroduction of iceberg orders on the Toronto Stock Exchange and find that spreads,

volume, and quoted depth are unaffected but total depth increases when hidden orders are allowed. They

also find evidence that traders use hidden orders to manage their exposure risk and reduce their price

impact. Hautsch and Huang (2012) use order data from NASDAQ to examine executions against hidden

orders and find that traders use hidden liquidity to compete for the provision of liquidity and to avoid

being adversely selected or having their orders front-run. My paper contributes to this literature by being

the first to empirically show how differences in the trading speed of the order submitter and other market

participants affect the decision to conceal a limit order.

This paper also contributes to the growing empirical literature studying HFTs. Brogaard, Hendershott,

and Riordan (2013) use the HFT transaction data set used in this paper to analyze the role HFTs play in

price discovery. They find that HFTs who demand liquidity aid in price discovery by trading in the same

direction as the permanent price impact, while HFTs who supply liquidity trade in the opposite direction

of the permanent price impact and are adversely selected. They also examine the revenues earned by

HFTs and NHFTs and find that before liquidity fees and rebates are considered, HFT and NHFT liquidity

demanders earn positive revenue from trading, while HFT and NHFT liquidity suppliers earn negative

revenue. If liquidity fees and rebates are included, HFTs earn positive revenue from both supplying and

demanding liquidity, whereas NHFTs earn negative revenue. My findings complement their results by

showing that HFTs and NHFTs earn positive revenue when they supply liquidity using hidden orders,

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but negative revenue when they supply liquidity using displayed orders.

A number of papers focus on the role HFTs play in supplying liquidity. Hagstromer and Norden (2013)

look at different types of HFTs on the NASDAQ-OMX Stockholm exchange and find that HFT market

makers compromise the majority of HFT trading volume and help reduce intraday volatility. Menkveld

(2013) looks at the trading activity of an HFT firm on NYSE-Euronext and Chi-X and finds that the

HFT supplies liquidity on 80% of its trades and earns money on the bid-ask spread, but loses money

due to its inventory positions. Hagstromer, Norden, and Zhang (2013) examine the aggressiveness of

HFT order submissions and find that HFTs submit more aggressive orders when same side depth is large

and supply liquidity when the spread is wide. Brogaard et al. (2014) use data on changes in the speed

of trader colocation subscriptions on NASDAQ OMX Stockholm to examine how trading speed affects

trading activity and market quality. They find that traders with faster colocation connections face lower

adverse selection costs, improve their inventory management, and increase the share of liquidity they

supply to the market. My paper contributes to the literature on HFT liquidity supply by examining how

competition from HFTs affects the decisions of HFTs and NHFTS to conceal or display their limit order

when supplying liquidity.

The rest of the paper is organized as follows. Section 2 discusses the NASDAQ data used in this

study. Section 3 examines the use of hidden liquidity by HFTs and NHFTs in the limit order book and in

transactions. Section 4 examines how changes in HFT activity affect the use of hidden liquidity. Section

5 examines the adverse selection costs and revenue earned when supplying liquidity using hidden and

displayed orders. Section 6 examines the ability of HFT and NHFT liquidity demanders to detect the

presence of hidden orders. Section 7 concludes.

2 Data

2.1 Sample Description

This study utilizes a number of data sources made available by NASDAQ to investigate hidden liquidity

in the limit order book. The primary data sets used in this study are the same ones used in Brogaard,

Hendershott, and Riordan (2013) to analyze the impact high frequency traders (HFTs) have on price

discovery. The sample provided by NASDAQ consists of 120 stocks that were randomly chosen by selecting

40 firms from three different market cap categories. The stocks were selected so that 20 firms in each

category have a primary listing on NASDAQ and 20 firms have a primary listing on NYSE. The Large

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cap stocks were selected from the largest market capitalization, the medium cap stocks were selected

from stocks around the 1,000th largest stock in the Russell 3000, and the small cap stocks were selected

from stocks around the 2,000th largest stock in the Russell 3000. Two of the stocks in the dataset were

excluded from this study, because TAQ data was not available for these stocks during the entire sample

period.

The first dataset contains data on all transactions that occurred on NASDAQ during regular trading

hours in 2008, 2009, and the week of 02/22/2010-2/26/2010.12 The trades are timestamped to the

millisecond and include data on the price and size of the trade, whether the trade was buyer or seller

initiated, and whether the liquidity demander and supplier were high frequency traders (HFTs) or non-

high frequency trader (NHFTs).13 NASDAQ classifies 26 firms as HFTs based on an analysis of their

trading activity, including how long their orders last, how long they hold their inventory, and their order

to trade ratio. Unfortunately, the data cannot classify all HFT activity. Firms that engage in brokerage

services and also run proprietary trading desks would not be identified as HFTs in the analysis, nor would

HFTs who route their orders through large brokerage firms. The data set can be thought of as indicating

a lower bound on the activity of HFTs.

NASDAQ also provides a dataset that contains snapshots of the NASDAQ limit order book at the

beginning of each minute during regular trading hours. The dataset contains data for the first full week of

the first month of each quarter in 2008 and 2009, the week of 09/15/2008 - 09/19/2008 during the financial

crisis, and the week of 2/22/2010-2/26/2010. Each snapshot includes the ten best bid and offer prices

on Nasdaq’s order book along with the aggregate depth at each price, broken down based on whether

the depth is hidden or displayed and whether it is supplied by an HFT or an NHFT. Since the short-sale

ban imposed by the SEC during September and October 2008 might have altered liquidity provision and

trading behavior, I exclude data from these months from my sample. I also exclude observations that

occur less than five minutes after the open or less than five minutes before the close, leaving me with 380

snapshots for each of 40 trading days for each stock in the sample .

I also utilize data from NASDAQ TotalVieW ITCH, which contains information on displayed limit

orders that are canceled or added to the NASDAQ limit order book and market orders on NASDAQ

that execute against displayed and hidden liquidity. I merge the NASDAQ ITCH dataset with the HFT

transaction dataset to identify for each trade whether an HFT or NHFT supplied liquidity using a hidden

12. The trade data does not include trades that occur during the opening, closing, or intraday crossings sessions.13. The HFT indicator is an aggregate indicator identifying if a trade or limit order book depth belongs to one of the 26

firms that NASDAQ identifies as high-frequency traders in this study; it does not provide a firm level id, so it is not possibleto identify the transactions or limit orders for individual HFT firms.

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or displayed order. Due to the size of the NASDAQ ITCH datasets, I limit my study of the transaction

data to days in which I also have data for the limit order book snapshots. I also use the NASDAQ ITCH

data to identify displayed orders that were added to or canceled from the limit order book.

Quote data from TAQ was used to calculate NBBO spreads, depths, midpoint prices, and midpoint

volatilities. When using TAQ data, trades are signed using the Lee and Ready (1991) algorithm and the

interpolated time method of Holden and Jacobsen (2014) to match quotes and trades. CRSP is used to

calculate daily measures of total dollar trading volume, market capitalization, share price, daily returns,

and daily volatility14.

Table 1 provides descriptive statistics for the stock-days in the whole sample and each of the market

capitalization groups. The average market capitalization for the whole sample is $16.9 billion. The

different market cap groups vary greatly in size, with the large cap group having an average marketcap

of $48.0 billion, the medium cap group an average of $1.6 billion, and the small cap group an average of

$397 million. Prices tend to be higher and daily volatility tends to be lower in the large cap stocks. On

average, the stocks in the sample experienced negative daily returns of -9 bp, with a standard deviation

of 3.1%. The average daily trading volume is $205 million, and exhibits a wide range from an average of

$580 million in large cap stocks to an average of $3.6 million in small cap stocks. Trading on NASDAQ

accounts for an average of 30% of daily traded volume, but experiences a wide range from a minimum of

3.4% to a maximum of 94.8%. The wide range is caused by the sample being constructed from a mix of

firms whose primary listings are on NASDAQ and NYSE. The distribution of the percent of trading on

NASDAQ appears to be similar across the different market cap groups.

On average HFTs account for 28.9% of the NASDAQ daily trading volume within the sample. They

demand liquidity for 33.2% of NASDAQ traded volume and supply liquidity to 24.6% of traded volume.

HFT liquidity supply differs greatly across market cap groups, with HFTs supplying liquidity to 40.8%

of traded volume in large cap stocks and 13.1% of traded volume in small cap stocks. Similarly, HFTs

demand liquidity for 41.9% of traded volume in large caps and 21.6% of traded volume in small caps

stocks. These patterns support the findings in other studies, that HFTs tend to concentrate more of their

trading activity in large, liquid stocks.

Hidden orders constitute 18.1% of the dollar volume in supplied liquidity that market orders trade

against on NASDAQ, with the 25% and 75% percentile distributions accounting for 10.4% and 23.8% of

supplied liquidity. Hidden liquidity tends to be slightly greater in smaller stocks, representing on average

14. Daily volatility is computed as the difference between the daily high and low trading prices on CRSP divided by theCRSP closing price

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20.7%, 18.6%, and 16.1% of the liquidity supplied in trades in small, medium, and large cap stocks. Hidden

orders account for 15.5% of the liquidity that HFTs supply in transactions and 20.5% of the liquidity that

NHFTs supply. The percentage of hidden liquidity supplied in transactions varies more for HFTs than for

NHFTs, with the 25th and 75th percentile distributions for HFTs ranging from 1.7% to 20.6%, whereas

the NHFT distribution ranges from 10.5% to 26.1%. NHFT hidden liquidity does not vary much across

market cap groups, averaging around 20% in all market cap groups. HFT hidden liquidity is greater in

smaller stocks, increasing from an average of 11.4% in large cap stocks to 18.9% in small cap stocks.

2.2 Limit Order Book

In order to make the limit order book data easier to analyze, I aggregate the depth offered at different

price quotes together into groups based on where they are in relation to the best displayed prices in the

limit order book. The limit order book shares are aggregated together in each group based on whether

they are hidden or displayed and if they are supplied by an HFT/NHFT. Hidden shares at prices inside

the NASDAQ best visible quotes15 are grouped together (Inside). Shares at prices inside and at the

best visible price quotes are grouped together (At and Inside). Shares at prices above16 the best visible

quotes are grouped together (Above). Mean values for limit order book variables are then calculated by

averaging across all limit order book snapshots in each stock-day.

Table 2 provides a summary of the NBBO spread17 as well as both the displayed and true spreads on

NASDAQ for each market cap group.18 Data in the table is reported from the pooled sample of stock-days

in each market cap group. As expected, stocks in the large market cap group have the lowest spreads,

with median NBBO spreads of 1.14 cents and 4.0 bp. Spreads vary greatly over the different market cap

groups, with medium and small cap median NBBO spreads being 2.3 and 6.3 times greater, respectively,

when measured in basis points. Both the NASDAQ displayed and true spreads are larger than the NBBO

spreads across all market cap groups, with the median true and displayed spreads being 4.5 bp and 5.2

bp for large cap stocks, 13.9 bp and 16.4 bp for medium cap stocks, and 34.2 bp and 41.1 bp for small

cap stocks. The true spread is less than the displayed spread 12.2%, 30.9%, and 34.3% of the time for the

median large, medium, and small cap firm, indicating hidden orders inside the visible spread are more

15. The best visible quotes represent the highest displayed bid quote and the lowest displayed offer quote on NASDAQ.16. Offer prices higher than the lowest displayed offer quote and bid prices less than the highest displayed bid quote are

referred to as being above the best quotes17. NBBO stands for national best bid and offer, which is the best displayed bid and offer price across all public exchanges

in which the stock trades in the U.S. National Market System18. The true spread is the difference between the best bid and offer quotes among both hidden and displayed limit orders

on NASDAQ. The displayed spread is the difference between the best bid and offer quotes among only displayed limit orderson NASDAQ.

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common in small and medium cap stocks than in large cap stocks. This also is supported by the fact

that the NBBO spread is 1 tick (1 cent) 43.5% of the time for the median large cap firm, but only 12.8%

and 11.8% of the time for the median medium and small cap firms. The NASDAQ best displayed quote

is also more likely to be at either the national best bid or offer in large cap stocks. For the median large

cap firm, the best displayed quote on NASDAQ is either at the national best bid or national best offer

86% of the time, compared to 70% and 66.5% of the time for the median medium and small cap firms.

Table 2 also summarizes the aggregated depths from the limit order book. Total depth is greatest in

large cap stocks. With a dollar value of $1,544,000, the median total depth for the large cap sample is over

5 times larger than the median value of the medium cap sample ($297,000) and over 10 times larger than

the median value of the small cap sample ($149,000). The median depth inside and at the best displayed

quotes is $145,000 for large cap stocks, which represents 10.2% of the median total depth for the 10 best

price levels. HFT liquidity supply appears to vary across the market cap groups. HFTs in the large cap

group focus their liquidity supply at and inside the best displayed quotes, accounting for 36.8% of quoted

depth inside the best displayed quotes and 41.5% inside and at the best displayed quotes. However, HFTs

tend to be less active at quotes above the best displayed quotes, accounting for only 21.9% of quoted

depth. HFTs do not concentrate their supplied liquidity at and inside the best displayed quotes as much

in medium and small cap stocks. Instead, they tend to distribute it more evenly throughout the book in

medium cap stocks and concentrate more liquidity above the best displayed quotes in small cap stocks.

The use of hidden orders varies greatly across the different market cap groups and tends to be inversely

related to size, with hidden orders accounting for 15.8% of the quoted depth in large cap stocks and 37.4%

of the quoted depth in small cap stocks. The use of hidden liquidity also varies with the location of the

quoted price. Hidden liquidity inside the best displayed quotes accounts for 0.2% of the median total

depth in large cap stocks and 1.0% of total depth in small cap stocks. It accounts for 2.6% of the total

depth at and inside the displayed quotes in large cap stocks and 13.9% in small cap stocks. Hidden

depth at and inside the best displayed quotes accounts for 33.3% of the total depth at and inside the best

displayed quotes for large cap stocks and 45.16% for small cap stocks. The supply of hidden liquidity

deeper in the limit order book varies across different market cap groups, with hidden depth accounting

for 13.9% of the total depth above the best displayed quotes in large cap stocks and 35.5% of the depth

in small cap stocks. HFTs and NHFTs tend to use hidden liquidity differently, with HFTs showing a

larger variation across the market cap groups. NHFTs use a greater percentage of hidden depth in their

orders than HFTs in large cap stocks, but a smaller percentage then HFTs in small cap stocks. In large

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cap stocks, HFTs and NHFTs tend to use more hidden depth closer to the best displayed quotes, with

11.1% of HFT depth and 45.0% of NHFT depth at and inside the best visible quotes being hidden, while

only 5.8% of HFT depth and 15.9% of NHFT depth above the best displayed quotes is hidden. NHFTs

tend to use hidden liquidity similarly in small and large cap stocks, whereas HFTs use hidden liquidity

differently in smaller cap stocks, where they tend to use more hidden liquidity above the best displayed

quotes. In small cap stocks, 27% of HFT depth inside and at the best displayed quotes is hidden, while

52.0% of their depth above the best displayed quotes is hidden.

The use of hidden liquidity also varies throughout the trading day. Figure 1 shows the percentage of

shares hidden in the limit order book throughout the trading day. The percentage of book depth that

is hidden is greatest in the morning and tends to decrease throughout the trading day. The pattern is

similar for the hidden liquidity supplied by both HFTs and NHFTs. This could be evidence that traders

value the priority of displayed limit orders more closer to the end of the trading day.

3 Do HFTs or NHFTs use more hidden liquidity?

3.1 Comparison of HFT and NHFT hidden liquidity

One of the primary questions this paper seeks to answer is how differences in trading speed affect a trader’s

decision to conceal their order when supplying liquidity? As Harris (1997) and Ritter (2016) theorize,

one of the main benefits of concealing an order is to reduce the chance that it is adversely selected if

it becomes mispriced. HFTs are able to adjust their displayed limit orders quicker than NHFTs if they

become mispriced, which reduces the benefit of an HFT hiding their order relative to an NHFT. The

main cost to concealing an order is that it loses priority to any displayed orders that are later entered at

the same price. This cost should be lower for HFTs than NHFTs, because they are quicker at adjusting

their hidden orders if they lose priority to a displayed order. With these two competing effects, it is not

clear if HFTs are more likely to conceal an order than NHFTs.

Ritter (2016) examines this tradeoff in a theoretical setting and finds that the cost savings fast traders

face from concealing their orders is greater than the decreased benefit. He predicts that fast traders are

more likely to use hidden orders than slow traders, since their ability to adjust their hidden orders quicker

if they lose priority to displayed orders lowers the cost of concealing an order. This section examines this

hypothesis by comparing the amount of hidden liquidity that HFTs and NHFTs use in the limit order

book and in transactions in which they supply liquidity.

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When examining the behavior of HFTs, it is important to remember that the term HFT encompasses

a wide variety of trading strategies. The strategies can range from the arbitrage and order anticipation

(directional) trading described in Hirschey (2013) and SEC (2010), to the more traditional market making

activities described in Hagstromer and Norden (2013). Since the indicator that is used in this study to

identify HFT activity is an aggregate indicator, it is not possible to formally sub classify HFT activity

based on their strategies. However, the HFTs that conceal their limit orders and supply liquidity would

probably tend to fall under the category of market making activities described in Hagstromer and Norden

(2013), while the HFTs that demand liquidity would most likely fall into the short term opportunistic

and order anticipation activities described in Hirschey (2013) and Brogaard, Hendershott, and Riordan

(2013). Characteristics of market maker HFTs include lower inventories, higher quote to trade ratios, a

higher percentage of their orders and trades are made via limit orders, and limit orders that they submit

stay on the book longer compared to opportunistic HFTs.

In order to examine hidden liquidity in the limit order book, I construct stock-day measures for the

percentage of hidden liquidity for each trader type as detailed in Section 2. I sum the total dollar value

(shares times price) of hidden liquidity supplied by the trader type in the limit order book across all

limit order book snapshots and divide it by the total dollar value of liquidity (displayed plus hidden)

supplied by the trader type. I construct the percentage measure for the entire limit order book as well

as separately for: prices inside the best displayed quotes (Inside), prices inside and at the best displayed

quotes (At and Inside), and prices above the best displayed quotes (Above). The percentage of hidden

liquidity for inside the best displayed quotes (Inside) is calculated by dividing the total dollar value of

hidden liquidity inside the best displayed quotes by the total dollar value of liquidity supplied inside and

at the best displayed quotes. I calculate separate measures examining hidden liquidity inside and at the

NBBO and inside and at the best displayed quotes on NASDAQ. The percentage of liquidity supplied in

transactions (in Transactions) by each trader type is calculated for each stock-day by summing up the

total dollar value of all transactions on NASDAQ in which the trader type supplied liquidity using hidden

orders and dividing it by the total dollar value of all transactions on NASDAQ in which the trader type

supplied liquidity.

The left hand side of Table 3 presents the mean and median of the stock-day measures of All Traders,

HFTs, and NHFTs for the entire sample and for each market cap group. The right hand side of the table

presents the mean difference between HFT and NHFT hidden order usage (Mean Diff) and p-values for

a two-sided pairs t-test (p(t-test)) and Wilcoxon singed-rank test (p(W-test)) against the hypothesis

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of zero difference between HFT and NHFT hidden liquidity usage.

The limit order book results in Table 3 support the hypothesis that HFTs are more likely to hide a

limit order than NHFTs. When examining the percentage of shares that are hidden in the limit order

book for the entire sample, I find that on average 31.2% of HFT shares are hidden compared to 26.5% of

NHFT shares. The mean difference, 4.7%, is positive and statistically significant at the 1% level for both

the two-sided pairs t-test and the Wilcoxon signed-rank test.

When I examine hidden liquidity at different prices in the limit order book, I find that NHFTs are

more likely to hide their limit orders when they are at the best displayed quotes, either the NBBO or the

best displayed quotes on NASDAQ. On average, 46.2% of NHFT depth at and inside the best displayed

quotes is hidden, whereas only 29.5% of HFT depth at and inside the best displayed quotes is hidden.

Given the greater percentage of NHFT liquidity that is hidden at and inside the best displayed quotes,

it is surprising to find that, on average, HFTs have a greater percentage of hidden depth inside the best

displayed quotes, 17.8%, than NHFTs, 12.4%. This indicates that NHFTs have a greater percentage of

their depth at the best diplayed quotes hidden than HFTs. One reason for this could be that NHFTs

are more likely to use hidden orders that are pegged to either the NBBO or the best displayed quote on

NASDAQ. When I examine the use of hidden liquidity in the limit order book at prices above the best

displayed quotes, I find that a greater percentage of HFT shares are hidden, 30.2%, than NHFT shares,

23.7%.

Surprisingly, when I examine the data on liquidity supplied in transactions, I find a different result.

I find that NHFTs tend to conceal their limit orders more than HFTs when they supply liquidity in

transactions. 20.2% of the liquidity NHFTs supply in trades is hidden, compared to 15.6% of the liquidity

HFTs supply. The average difference is -4.6% and is statistically significant at the 1% level.

I find that the relationship between HFT and NHFT hidden liquidity varies when I compare it across

market cap groups. In large cap stocks, NHFTs are more likely to hide their limit orders than HFTs.

I find that in large cap stocks, 20.5% of NHFT shares in the limit order book are hidden compared to

14.5% of HFT shares. Comparatively, HFTs tend to hide their limit orders more in medium and small

cap stocks. I find that hidden depth accounts for 32.1% and 47.8% of HFT depth in medium and small

cap stocks, but only 26.3% and 33.1% of NHFT depth.

When I examine how the use of hidden liquidity at different prices in the limit order book varies across

market cap groups, I find that across all market cap groups, HFTs are more likely to hide orders inside

the best displayed quotes and NHFTs are more likely to hide orders at the best displayed quotes and

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when supplying liquidity in transactions. I also find that HFTs are more likely to hide orders at prices

above the best displayed quotes in medium and small cap stocks, but NHFTs are more likely to hide

orders above the best displayed quotes in large cap stocks. However, the results for differences in HFT

and NHFT hidden liquidity above the best displayed quotes needs to interpreted cautiously, especially

for large cap stocks. Since the data is limited to the 10 best prices on the bid and offer side of the order

book, the limit order book snapshots for the large cap stocks might represent a smaller fraction of the

entire limit order book than those of the medium and small cap stocks, since the large cap stocks tend to

be more actively traded. This could bias the results for large cap stocks if they have additional hidden

liquidity located further from the best displayed quotes, similar to that found in medium and small cap

stocks, that is not in the ten best price levels.

HFTs appear to vary their use of hidden liquidity more across the different market cap groups than

NHFTs. In large cap stocks, a greater percentage of HFT depth is hidden at prices inside and at the

best displayed quotes, 35.2%, than at prices above it, 13.0%. However, in small cap stocks, a greater

percentage of HFT depth is hidden at prices above the best displayed quotes, 47.8%, than at prices inside

and at the best displayed quotes, 35.2%.

3.2 Aggressiveness of HFT and NHFT hidden liquidity

One possible explanation for the observed difference between the rates at which HFTs and NHFTs hide

their orders in the limit order book and when supplying liquidity in transactions could be that the

strategies HFTs and NHFTs use to conceal their orders differ based on how aggressively the orders are

priced. While Ritter (2016) predicts that the marginal cost of hiding an order due to its loss in priority

is lower for a less aggressively priced limit order, Moinas (2010) and Butti and Rindi (2013) predict that

the costs of exposing an order are higher for more aggressively priced orders. How these marginal costs

vary with the aggressiveness of the order is likely affected by the speed with which a trader interacts with

the market. In this subsection I examine differences in the aggressiveness of HFT and NHFT hidden and

displayed liquidity in the limit order book.

Unfortunately, the data used in this study does not let me observe individual hidden or displayed

orders, making it difficult to determine their aggressiveness. Instead, I compute the aggressiveness of

hidden and displayed liquidity in the limit order book as a weighted average of the distance between the

price the shares are quoted at and the true midpoint of the best bid and ask prices in the limit order

book. The aggressiveness of an ask share is the difference between the price the share is quoted at and

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the true midpoint of the best bid and ask prices in the limit order book. The aggressiveness of a bid share

is the difference between the true midpoint of the best bid and ask prices in the limit order book and the

price the share is quoted at. The aggregated aggressiveness measure for each stock-day is calculated as a

weighted average of the aggressiveness of all shares in all limit order book snap shots for each stock-day,

with the weights corresponding to the number of shares at each price level. The aggressiveness measure is

normalized by dividing by one half the average true spread for each stock-day. Aggressiveness is calculated

separately based on whether the liquidity is supplied by a HFT or NHFT and whether the depth is hidden

or displayed. A higher value of the aggressiveness measure indicates the liquidity is farther from the quote

midpoint and less aggressively priced.

Table 4 presents results for tests of differences between the aggressiveness measures of hidden and

displayed liquidity of HFTs and NHFTs. The table reports the mean and median of the aggressiveness

measures being compared as well the mean difference (Variable 1 - Variable 2) and p-values for a two-

sided pairs t-test (p(t-test)) and Wilcoxon singed-rank test (p(W-test)) against the hypothesis of zero

difference between aggressiveness measures.

The results in Table 4 indicate that the hidden liquidity of the combined pool of traders is priced

more aggressively than their displayed liquidity in the limit order book. However, the results differ when

liquidity is broken down by trader type. The displayed liquidity of HFTs is more aggressively priced than

their hidden liquidity, but the hidden liquidity of NHFTs is more aggressively priced than their displayed

liquidity. Both tests of differences are statistically significant at the 1% level.

When I compare the overall aggressiveness of the limit orders of HFTs and NHFTs, I do not find a

significant difference. However, when comparison is broken down by different types of liquidity, I find

that NHFT hidden liquidity is more aggressively priced while HFT displayed liquidity is more aggressively

priced.

In terms of support for the predictions of Ritter (2016) and Moinas (2010) and Butti and Rindi (2013),

it appears that price aggressiveness plays different roles in the decision to expose an order for HFTs and

NHFTs. The results for HFTs tend to support the prediction of Ritter (2016) and indicate that for their

aggressive orders that compete to supply liquidity, HFTs tend to value the increased priority associated

with displaying an order over the benefits of concealing it. The results for NHFTs tend to support the

predictions of Moinas (2010) and Butti and Rindi (2013) and indicate that for aggressively priced orders,

NHFTs value the benefits of not exposing an order more than the increased priority that comes with

displaying it. The fact the hidden orders of NHFTs are more aggressively priced helps explain why a

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greater percentage of the liquidity NHFTs supply in transactions is concealed, while HFTs use more

hidden liquidity in the limit order book. I explore this explanation more in Section 5 by examining the

difference in adverse selection costs faced by HFT and NHFT hidden and displayed liquidity.

It should be noted that another possible explanation for the observed difference between the rates at

which HFTs and NHFTs hide their orders could be that HFTs are more likely to cancel a hidden limit

order that they submitted than NHFTs. One of the characteristics that defines HFTs in the dataset is

their excessive order to trade ratio. If HFTs are more likely to cancel a hidden order when it loses priority

and replace it with either a market order or a displayed limit order that is more likely to execute, then

this might partially explain the difference between the hidden percentages observed between HFTs and

NHFTs in the limit order book snapshots and in transactions.

4 Hidden Liquidity and HFT Activity

4.1 Daily Analysis

This section examines how the trading speed of other market participants affects the decision to conceal

a limit order. The model in Ritter (2016) predicts that the use of hidden liquidity will decrease when the

proportion of fast traders in the market place increases, since an increase in the proportion of fast traders

increases the chance that a standing hidden order is either front-run by a displayed order or picked off by

a market order if it becomes mispriced. Ritter (2016) also predicts that fast traders are more sensitive to

these changes and will decrease their use of hidden orders more than slow traders when the proportion of

fast traders increases.

Table 5 tests these predictions by regressing the daily percentage of HFT and NHFT liquidity that

is hidden in the limit order book and in transactions on the proportion of NASDAQ trading volume in

which HFTs trade. I also run separate regressions with the percentage of NASDAQ dollar trading volume

for which an HFT demanded liquidity and the percentage of NASDAQ dollar trading volume for which

an HFT supplied liquidity as explanatory variables to try and determine the separate affects that HFTs

demanding and supplying liquidity have on the decision to conceal an order. However, it is important to

note that in Ritter (2016) the decision to supply or demand liquidity is endogenous and so the model’s

prediction corresponds to overall HFT activity and does not take into account the separate effects of HFT

liquidity demanding and supplying activity.

In order to help isolate the affect of HFT activity, I include a number of variables in the regression

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to control for other factors that might influence the decision to conceal a limit order. I include the log of

total dollar trading volume reported by all exchanges to control for the variation in hidden liquidity across

different sized stocks. I also include the daily opening value of VIX and the average daily volatility of 5

minute NBBO midpoint returns, because Ritter (2016) predicts that the use of hidden orders increases

with volatility. I include the log of the daily closing price and the average NBBO percentage spread,

because studies have shown that hidden liquidity inside the displayed quotes is more common when the

spread is wider and the relative tick size is smaller. I also include the percentage of daily trading volume

that is traded on NASDAQ, because hidden orders at the best quotes are not eligible to be included in

the NBBO and cannot attract market orders from other exchanges.

Since Harris (1996) predicts that hiding an order reduces the chance of being adversely selected by

informed liquidity demanders and Moinas (2010) predicts that informed liquidity suppliers can use hidden

orders to conceal their information, I include the Probability of Informed Trading (PIN) as well as the

daily market return and the stock’s daily abnormal return to control for informed traders.19 The abnormal

return is the difference between the stock’s daily return and the expected return from a model that is

estimated by regressing the daily returns of each stock on a 5 factor model that includes the Carhart 4

factor model and the Pastor-Stambaugh liquidity factor. I separate out the abnormal and market returns

into positive and negative returns to account for possible asymmetric effects of positive and negative

information.

I include a number variables calculated from NASDAQ ITCH data to control for limit order book

activity. I include the average number of displayed shares added each minute at the best displayed

price on NASDAQ (At), at prices that improve the best displayed price on NASDAQ (Aggressive), and

at prices worse than the best displayed price (Above). I also include the average number of displayed

shares canceled each minute at the best displayed price on NASDAQ (At) and at prices worse than the

best displayed price (Above). All limit order book addition and cancellation variables are normalized by

dividing by the average number of shares traded in the stock on NASDAQ each minute. I also include

the average quoted depth at the NBBO.

Panel A in Table 5 analyzes the determinants of the use of hidden liquidity in the limit order book. The

unit of observation is each stock-day. Dependent variables are the daily percentage of the dollar volume

in the limit order book that is hidden for all traders supplying liquidity (All Hidden), the percentage

19. I use quarterly PIN data computed using the Venter and Jongh (2006) extension of the Easley et al. (1996) model.I downloaded the PIN data from Stephen Brown’s website at http://scholar.rhsmith.umd.edu/sbrown/pin-data. It issimilar to the PIN data used in Brown and Hillegeist (2007).

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that is hidden for HFTs supplying liquidity (HFT Hidden), the percentage that is hidden for NHFTs

supplying liquidity (NHFT Hidden), and the difference between the percentage of dollar volume that

is hidden for HFTs supplying liquidity and the percentage of dollar volume that is hidden for NHFTs

supplying liquidity (Diff Hidden). All explanatory variables are standardized so the coefficients can be

interpreted as the percentage increase in the use of hidden liquidity for a one standard deviation increase

in the explanatory variable. Parenthesis contain standard errors double clustered by stock and day, using

the methodology described in Thompson (2011).

The negative relationship between the percentage of hidden liquidity in the limit order book and HFT

activity supports the hypothesis from Ritter (2016), that hidden liquidity is negatively related to the

proportion of fast traders. The coefficient is negative and significant for the hidden liquidity supplied by

both HFTs and NHFTs. In column 2, I separately examine the relationship between hidden liquidity in

the limit order book and HFT liquidity demanding and supplying activity. I find that hidden liquidity is

negatively related to both the proportions of liquidity that HFTs demand and supply. Hidden liquidity

in the limit order book supplied by NHFTs is negatively related to both the rate at which HFTs demand

and supply liquidity, but hidden liquidity supplied by HFTs is only negatively related to the rate at which

HFTs supply liquidity. One possible problem is that the observed relationship between hidden liquidity

and HFT activity is endogenous, since the proportion of transactions in which HFTs participate and their

decision to hide an order are joint outcomes of a simultaneous decision process. Subsection 4.2 attempts

to control for the endogeneity of HFT activity using instrument variables in a 2SLS framework.

I examine other determinants of hidden liquidity in the limit order book and find that hidden liquidity

is negatively related to trading volume and positively related to the stock’s price, indicating hidden

liquidity is more common in smaller, higher priced stocks. The use of hidden liquidity in the limit order

book by HFTs is positively related to midpoint volatility and negatively related to the percentage spread,

how centralized the stock is traded on NASDAQ, and positive market returns.

The use of hidden liquidity in the limit order book by NHFTs is positively related to both the stock’s

positive and negative abnormal returns, which indicates NHFTs use more hidden liquidity when there is

stock specific information. This could either be because they want to reduce the chance of being adversely

selected by informed liquidity demanders, or because they are informed traders who want to conceal their

information. NHFT hidden liquidity use is positively related to the rate at which displayed shares are

added to the limit order book and negatively related to the rate at which displayed shares are canceled

from the limit order book.

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Panel B in Table 5 analyzes hidden liquidity supplied in transactions. The use of hidden orders when

supplying liquidity in transactions is also negatively related to HFT activity. The coefficients for HFT

activity are negative in regressions where hidden liquidity is supplied by HFTs and NHFTs, but only the

coeffiicent in the NHFT regression is significant. When I separately examine the activity of HFT liquidity

demanders and suppliers, I find that the use of hidden liquidity in transactions is negatively related to

both. The use of hidden liquidity in transactions by NHFTs is negatively related to both HFT liquidity

demand and supply, but the use of hidden liquidity by HFTs is not significantly related to either.

When I examine the other determinants of hidden liquidity supplied in transactions, I find that the

results vary based on whether the liquidity was supplied by an HFT or an NHFT. For HFTs, the use

of hidden liquidity in transactions is positively related to volatility, the stock’s price, and the displayed

depth at the NBBO and negatively related to trading volume. In contrast, the use of hidden liquidity

in transactions for NHFTs is positively related to trading volume and negatively related to the displayed

depth at the NBBO. These results could indicate that the hidden liquidity HFTs supply in transactions

is more likely to be hidden inside the displayed spread in the limit order book, while the hidden liquidity

supplied by NHFTs is hidden at the best displayed quotes.

I also find that both HFTs and NHFTs use more hidden liquidity in transactions when the spread is

wider, since hidden liquidity is more likely to be inside the displayed spread when it is wider. HFTs are

more likely to use hidden liquidity in a transaction when trading is centralized on NASDAQ, but NHFTs

are less likely to hide their orders. When trading is more centralized, posting the best displayed quotes

is less likely to draw liquidity demand from other exchanges under Reg NMS, which decreases one of

the costs of using hidden orders. The speed advantage HFTs enjoy from colocation services they often

employee could increase the value of algorithms that hide liquidity inside the displayed spread when there

is less concern with drawing traders demanding liquidity from other exchanges. NHFTs’ lack of a speed

advantage means they place greater value on the time priority associated with displayed liquidity when

trading is centralized.

One disadvantage of supplying liquidity using a hidden order is that the rebate earned for supplying

liquidity is about half the value of the rebate earned for supplying liquidity using a displayed order.

However, before May 1, 2008, the highest liquidity rebates on NASDAQ for supplying liquidity using

displayed and non-displayed shares were the same.20 In Table 6 I examine how the change in the liquidity

20. On NASDAQ, hidden orders currently earn lower rebates than displayed orders for supplying liquidity in a transaction.During the sample period, the highest rebates for supplying liquidity in a transaction on NASDAQ using displayed ordersranges from 0.25 to 0.295 cents per share executed. The highest rebates for supplying liquidity using non-displayed ordersranges from 0.15 to 0.27 cents per share executed. From the beginning of sample period in January, 2008 until April 30,

19

rebate for nondisplayed orders affects the decision to conceal an order. I create a binary variable entitled

Fee Indicator that equals one from the beginning of the sample period in January, 2008 until April 30,

2008, the dates when the highest rebates for supplying liquidity using displayed and non-displayed shares

were the same, 0.27 cents per share executed. Fee Indicator equals zero for the period beginning on

May 1, 2008, when the highest rebate for supplying liquidity using non-displayed orders was reduced to

0.15 cents per share executed. I regress the measures of hidden liquidity in the limit order book and in

transactions on the Fee Indicator and the other explanatory variables that were used in the regressions

in Table 5. However, for the sake of brevity, I only report results for the Fee Indicator. I also create 3

binary variables entitled Price Index 1, Price Index 2, and Price Index 3 that equal 1 if the stock’s closing

price: is less than $20, between $20 and $40, or greater than $40, respectively. Since liquidity rebates

do not vary with the price of a stock, I regress measures of hidden liquidity on the Price Index variables

interacted with the Fee Indicator to investigate how the affect of the liquidity rebate change varies across

different price groups.

Panel A in Table 6 presents results for hidden liquidity in the whole limit order book and for liquidity

supplied in transactions, while Panel B presents results for hidden liquidity in the different limit order

book price groups. I find that a reduction in the liquidity rebate for nondisplayed orders decreases the

proportion of liquidity supplied in transactions that is hidden by 2.2%. This result is significant for

both HFT and NHFT liquidity suppliers with HFTs experiencing the greatest decrease. Surprisingly, a

reduction in the rebate increases the proportion of total limit order book depth that is hidden. However,

this change is mainly driven by an increase in the use of hidden liquidity above and at the best displayed

quotes by NHFTs. A reduction in the liquidity rebate also decreases the use of hidden liquidity by HFTs

inside the best displayed quotes.

When I separate out the rebate change to see how it differentially affects low vs high priced stocks,

I find that the decrease in hidden liquidity supplied in transactions is greatest for high priced stocks,

which are most likely to have hidden depth inside the best displayed quotes. Comparatively, the increase

by NHFTs in the use of hidden liquidity above and at the best displayed quotes in the limit order book

is greatest in low priced stocks. I examine the changes for hidden liquidity inside the best displayed

quotes and find that when nondisplayed rebates are reduced NHFTs decrease their hidden liquidity inside

the quotes in low and high priced stocks, but increase it in medium priced stocks. HFTs decrease their

2008, the highest rebate for supplying liquidity using displayed and non-displayed shares were the same, 0.27 cents per shareexecuted. In the period beginning May 1, 2008, the highest rebate for supplying liquidity using non-displayed orders wasreduced to 0.15 cents per share executed. (Source: http://www.nasdaqtrader.com/trader.aspx?id=pricelisttrading2)

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hidden liquidity inside the spread in all price groups, but the greatest decreases are in low and high priced

stocks. For low priced stocks, a larger change probably occurs because liquidity rebates represent a larger

percentage of the revenue earned from supplying liquidity in a round lot trade. For high price stocks, a

larger change probably occurs because the spread is wider, so hidden liquidity is more likely to be inside

the best displayed quotes.

4.2 Endogeneity of HFT Activity

The results in Table 5 indicate that hidden liquidity in the limit order book is negatively related to

the trading activity of HFTs. However, this relationship is likely to be endogenous. Both the model in

Ritter (2016) and the model in Butti and Rindi (2013) emphasize that the choice of order price and order

exposure will be simultaneous decisions, which also means that the amount of transactions in which HFTs

participate and their hidden order activity are joint outcomes of a simultaneous decision process. This

likely results in biased coefficients when HFT and NHFT hidden liquidity are regressed on the percentage

of transactions in which HFTs take place.21 This subsection attempts to address this endogeneity by

instrumenting for HFT trading activity in a 2SLS regression.

The instrument variable used is based on the runs in process instrument variable utilized in Hasbrouck

and Saar (2013). The instrument variable is an aggregated market measure of the average percentage of

NASDAQ dollar trading volume in which HFTs trade each day. Since one of the requirements of the IV is

for it to be uncorrelated with the decision of HFTs and NHFTs to hide liquidity, the stock for which the

IV is being calculated, stocks in the same four digit SIC code, and stocks in the same index, if the stock

for which the IV is being calculated is in the S and P 500 or NASDAQ 100 indices, are excluded from the

averages. The purpose of these exclusions is to make sure that the instrument variable is not correlated

with the use of hidden liquidity by HFTs and NHFTs in the stock for which the IV is calculated. HFTs

or other firms pursuing trading strategies within an industry or index are more likely to coordinate their

strategies for how they supply liquidity. Once these sources of potential coordination are removed, it is

not clear why HFT activity in the remaining stocks would be correlated with the decision by an HFT

or NHFT to hide liquidity in the target stock.22 I also construct separate instrument variables for HFT

liquidity demand and HFT liquidity supply using the same method.

Table 7 presents the results of the first stage regressions. The results indicate that the IV for overall

21. NHFT hidden liquidity would be endogenously related to HFT activity by definition, because the percentage of NHFTactivity is equal to one minus the percentage of HFT activity.

22. Hasbrouck and Saar (2013) offers further discussion about why their instrument is unlikely to be correlated with marketquality, a similar argument is likely applicable for the decision of HFTs and NHFTs to hide liquidity.

21

market HFT activity is positively correlated with HFT activity in the individual stock. When I separate

HFT activity out into HFT liquidity demand and supply, I find that HFT liquidity demand and supply

are both positively correlated with the IVs for HFT liquidity demand and supply in the overall market,

with HFT demand having the greatest correlation with overall market HFT demand and HFT supply

having the greatest correlation with overall HFT supply. The F-stats for the exclusion tests are all over 10,

indicating there is not a problem with weak IVs. The R-squared values also indicate that the explanatory

variables provide a decent fit for the data.

Table 8 presents the results of the second stage of the 2SLS, which reproduces the regressions from

Table 5, after instrumenting for the endogeneity of HFT activity. After instrumenting, the coefficients

associated with HFT activity remain negative and significant for both HFT and NHFT hidden liquidity.

Separating out the effects of HFT liquidity demand and supply, I find that after instrumenting, the

coefficients controlling for HFT demand and supply in the regression for All Hidden activity remain

negative and significant. The coefficients associated with HFT demand are negative and significant in the

HFT Hidden regression, but are insignificant in the NHFT Hidden regression. The coefficients for HFT

supply are negative and significant in the NHFT Hidden regression and insignificant in the HFT Hidden

regression.

After controlling for endogeneity, the results from the regression confirm the negative relation between

hidden order usage and HFT activity predicted by Ritter (2016). It appears that HFT hidden liquidity is

more sensitive to HFT liquidity demand while NHFT hidden liquidity is more sensitive to HFT liquidity

supply. This could indicate that NHFT hidden liquidity is more sensitive to HFT liquidity suppliers front-

running their hidden orders with displayed orders, whereas HFT hidden liquidity is more sensitive to the

adverse selection caused by HFT liquidity demanders as documented in Hirschey (2013) and Brogaard,

Hendershott, and Riordan (2013). Section 5 studies this hypothesis by examining the adverse selection

that HFT and NHFT hidden liquidity face.

4.3 Intraday Analysis

Section 4.1 examined the determinants of Hidden liquidity at the stock-day level. This section examines

how changes in intraday variables affect the use of hidden liquidity in the limit order book. Table 9

presents analysis for OLS and 2SLS regressions examining the intraday determinants of changes in the

percentage of HFT and NHFT volume that is hidden in the NASDAQ limit order book. The percentage

of hidden liquidity is calculated for each one minute limit order book snap shot by summing up the

22

number of hidden shares on the bid and offer side of the limit order book supplied by the trader type and

dividing it by the total shares of liquidity (displayed plus hidden) supplied by the trader type. The 2SLS

is meant to control for endogeneity that may arise in the percentage of NASDAQ dollar trading volume

in which HFTs trade. The instrument variables are based on the runs in process instrument variable

utilized in Hasbrouck and Saar (2013). The instrument variables used in the first stage are the change

in the average NASDAQ dollar trading volume for which HFTs demanded liquidity for stocks that are

in the same market cap group and the change in the average NASDAQ dollar trading volume for which

HFTs supplied liquidity for stocks that are in the same market cap group. The stock for which the IV is

being calculated, stocks in the same four digit SIC code, and stocks in the same index, if the stock for

which the IV is being calculated is in the S and P 500 or NASDAQ 100 indices, are excluded from the

average. Dependent variables are the change in the percentage of hidden shares in the limit order book

for all traders supplying liquidity (Hidden), the change in the percentage of hidden shares for HFTs in

the order book (HFT Hidden), and the change in the percentage of hidden shares for NHFTs in the limit

order book (NHFT Hidden). Explanatory variables are the one minute change in the percentage of dollar

trading volume for which HFTs demanded and supplied liquidity and their fitted values for the 2SLS

regressions. Other explanatory variables are the change in the total trading volume of the stock across

all US markets, the change in the percent of total stock trading volume that is traded on NASDAQ, the

change in the total displayed depth at the best displayed quotes on NASDAQ, the change in the total

displayed depth above the best displayed quotes on NASDAQ, the change in displayed shares added to

the NASDAQ limit order book that improve the best displayed bid or offer, the change in shares added

at the best displayed bid or offer, the change in shares added at prices worse than the best displayed bid

or offer, the change in the shares canceled from the limit order book at the best displayed bid or offer,

the change in shares canceled at prices worse than the best displayed bid or offer, the change in the five

minute midpoint return volatility, positive and negative quote midpoint returns, the change in the NBBO

percentage spread, and the change in the NASDAQ displayed percentage spread. The positive (negative)

quote midpoint return equals the one minute percentage change in the NBBO midpoint (minus the one

minute percentage change in the NBBO midpoint) if the midpoint return is positive (negative) and zero

otherwise. All observations are at the minute interval and all variables are calculated as sums over the

one minute period between limit order book snapshots. The regressions are performed for changes in

variables to account for persistence in hidden liquidity in the limit order book that can occur during the

trading day. Before differencing, all variables are normalized so that each stock-day has a mean value of

23

0 and standard deviation of 1. Parenthesis report standard errors double clustered by stock and day.

Before accounting for the endogeneity of HFT liquidity supply and demand, the results indicate that

the use of hidden liquidity by NHFTs in the limit order book increases as HFTs account for a greater

share of intraday liquidity supply and decreases as HFTs account for a greater share of intraday liquidity

demand. The opposite relationship holds for HFTs, with HFTs increasing their use of hidden liquidity in

the limit order book as HFT liquidity demand increases and lowering their use of hidden liquidity as HFT

liquidity supply increases. After controlling for endogeneity in the 2SLS regressions, the use of hidden

liquidity for the overall sample and NHFTs is negatively related to the proportion of liquidity supplied

by HFTs and not significantly related to the proportion of liquidity that HFTs demand.

In terms of additions explanatory variables, the chance of an NHFT hiding liquidity in the limit order

book increases as the rate at which shares are canceled from the limit order book increases, volatility

increases, and NBBO and NASDAQ spreads increase. The chance of an NHFT hiding liquidity in the

limit order book decreases as the trading volume increases, the percentage of trading volume on NASDAQ

increases, the number of displayed shares on the NASDAQ limit order book increases, and the rate at

which shares are added to the limit order book increases. The chance of an HFT hiding liquidity in the

limit order book increases as the rate at which shares are added above the best displayed quote increases,

volatility increases, the NASDAQ displayed spread increases, or the stock experiences positive or negative

midpoint returns. The chance of an HFT hiding liquidity in the limit order book decreases as the number

of displayed shares on the NASDAQ limit order book increases, the rate at which shares are canceled

above the best displayed quote increases, and the NBBO displayed spread increases.

5 Does HFT or NHFT hidden liquidity face adverse selection?

Harris (1997) and Ritter (2016) predict that one of the benefits of concealing a limit order is that it

reduces the chance the order is adversely selected if it becomes mispriced. Bessembinder, Panayides, and

Venkatamaran (2009) confirms that iceberg orders on Euronext Paris experience lower implementation

shortfall costs than displayed orders. Section 4 showed that both HFTs and NHFTs decrease their use of

hidden liquidity when overall HFT activity increases. One possible explanation could be that the ability

of concealed orders to reduce the costs of adverse selection decreases as the activity of HFTs increases.

This section examines if the hidden limit orders of HFTs and NHFTs face less adverse selection

than their displayed orders by using a modified version of the VAR presented in Hasbrouck (1991a) and

24

Hasbrouck (1991b) to estimate the permanent price impact that HFTs and NHFTs face when supplying

liquidity using hidden and displayed orders. I then study how this adverse selection varies with the

activity of HFTs. Finally, I examine the trading revenues that HFTs and NHFTs generate supplying

liquidity using hidden and displayed orders to see which is more profitable.

5.1 Permanent Price Impact

This subsection examines whether hidden or displayed orders by HFTs and NHFTs are more likely to

face adverse selection by utilizing a modified version of the Hasbrouck (1991a) and Hasbrouck (1991b)

VAR methodology to estimate the permanent price impact that HFTs and NHFTs face when supplying

liquidity using hidden and displayed orders. This methodology is similar to the one used in Brogaard

(2010) to estimate whether HFT or NHFT liquidity suppliers faced greater adverse selection.

A five equation, 10 lag VAR is estimated for each stock-day. The VAR system is given by:

rt =10∑

i=1

α1,irt−i +10∑

i=0

γ1,iqHF T displayt−i +

10∑i=0

β1,iqHF T hiddent−i +

10∑i=0

λ1,iqNHF T displayt−i +

10∑i=0

θ1,iqNHF T hiddent−i + ε1,t

qHF T displayt =

10∑i=1

α2,irt−i +10∑

i=1

γ2,iqHF T displayt−i +

10∑i=1

β2,iqHF T hiddent−i +

10∑i=1

λ2,iqNHF T displayt−i +

10∑i=1

θ2,iqNHF T hiddent−i + ε2,t

qHF T hiddent =

10∑i=1

α3,irt−i +10∑

i=1

γ3,iqHF T displayt−i +

10∑i=1

β3,iqHF T hiddent−i +

10∑i=1

λ3,iqNHF T displayt−i +

10∑i=1

θ3,iqNHF T hiddent−i + ε3,t

qNHF T displayt =

10∑i=1

α4,irt−i +10∑

i=1

γ4,iqHF T displayt−i +

10∑i=1

β4,iqHF T hiddent−i +

10∑i=1

λ4,iqNHF T displayt−i +

10∑i=1

θ4,iqNHF T hiddent−i + ε4,t

qNHF T hiddent =

10∑i=1

α5,irt−i +10∑

i=1

γ5,iqHF T displayt−i +

10∑i=1

β5,iqHF T hiddent−i +

10∑i=1

λ5,iqNHF T displayt−i +

10∑i=1

θ5,iqNHF T hiddent−i + ε5,t

where t indicates an event interval, i indicates the number of lagged events, rt is the quote midpoint return

(measured in basis points) between events, and qHFT display, qHFT hidden, qNHFT display, and qNHFT hidden

are the net dollar volume, in $10,000’s of dollars, in HFT displayed liquidity, HFT hidden liquidity, NHFT

displayed liquidity, and NHFT hidden liquidity supplied in transactions on NASDAQ over an event in-

terval. For each type of liquidity, the net dollar volume is calculated as the dollars of liquidity supplied

using limit buy orders minus the liquidity supplied using limit sell orders. A positive (negative) value

indicates that more liquidity was supplied using buy (sell) limit orders during the event interval.

After the VAR is estimated, it is inverted to get the vector moving average (VMA) model:

25

rt

qHF T displayt

qHF T hiddent

qNHF T displayt

qNHF T hiddent

=

a(L) b(L) c(L) d(L) e(L)

f(L) g(L) h(L) i(L) j(L)

k(L) l(L) m(L) n(L) o(L)

p(L) q(L) r(L) s(L) t(L)

u(L) v(L) w(L) x(L) y(L)

ε1,t

ε2,t

ε3,t

ε4,t

ε5,t

where a(L) − y(L) are lagged polynomial operators. Following Hasbrouck (1991a), the impulse response

function for qHFT display is∑10t=0 b(L) and represents the private information content of an innovation

(the unexpected portion) in which HFTs supply liquidity using displayed orders. Similarly, the impulse

response functions∑10t=0 c(L),

∑10t=0 d(L), and

∑10t=0 e(L) estimate the permanent price impact of innova-

tions in HFT hidden, NHFT displayed, and NHFT hidden liquidity supply, respectively.

The VAR is estimated for two separate event intervals, one in calendar time, using one second time

intervals, and one in event time, where each transaction represents an event interval. The calendar time

VAR uses one second NBBO midpoint returns and the event time VAR uses displayed NASDAQ BBO

midpoint returns between events. The VAR is estimated separately each stock-day and the stock-day es-

timates are averaged together for statistical inference. Standard errors are calculated by double clustering

on stock and trading day, as described in Peterson (2009) and Thompson (2011).

Table 10 reports the average long-run (10 events in the future) impulse response functions from the

estimated VARs. The first row reports results for NBBO midpoint returns over one second intervals. The

second row reports results for trade by trade changes in the midpoint of the displayed NASDAQ BBO.

Coefficients are reported in units of basis points per $10, 000 in supplied liquidity. The left hand side of

the tables report the average impulse responses from transactions in which HFTs and NHFTs supplied

liquidity using hidden and displayed orders for all stock-day observations in the sample. The center of the

table reports the average differences between the impulse responses of transactions in which HFTs/NHFTs

supplied liquidity using hidden orders and transactions in which they used displayed orders (HFT and

NHFT Diff). It also reports the average differences between the impulse responses of transactions in

which displayed/hidden liquidity is supplied by HFTs and transactions in which displayed/hidden liquidity

is supplied by NHFTs (Display and Hidden Diff). The right hand side of the table reports the average

difference in adverse selection differences between HFT and NHFT hidden and displayed liquidity (HFT

Diff - NHFT Diff). Parenthesis report t-statistics double clustered by stock and day. Since liquidity

supplied using buy (sell) limit orders is positive (negative), a negative value means the trader is supplying

liquidity in the opposite direction of the permanent price impact and is being adversely selected.

26

With statistically significant negative values, the results in rows one and two indicate that HFTs and

NHFTs face adverse selection when supplying liquidity with both hidden and displayed orders. The results

agree with those found in Brogaard, Hendershott, and Riordan (2013), who estimate a state space model

for overall HFT and NHFT liquidity supply and find that both HFTs and NHFTs face adverse selection

when they supply liquidity.

The tests of differences between NHFT hidden and displayed liquidity (NHFT Diff) are positive

and statistically significant for both rows, which supports the hypothesis that NHFTs’ hidden orders

face less adverse selection than their displayed orders. The results for the tests of differences for HFTs

indicate that there is not a difference between the adverse selection faced by their hidden and displayed

liquidity. The tests of differences between hidden liquidity supplied by NHFTs and HFTs (Hidden Diff)

are negative and statistically significant, indicating NHFTs face less adverse selection than HFTs when

supplying liquidity using hidden orders. The results for the difference in displayed liquidity (Display

Diff) are also negative, which indicates NHFTs also face less adverse selection than HFTs when they

supply liquidity using displayed orders. The results from the difference in adverse selection differences

between HFT and NHFT hidden and displayed liquidity (HFT Diff - NHFT Diff) are negative and

statistically significant in both rows. This indicates that the benefit in reducing adverse selection that

NHFTs receive from concealing an order is greater than the benefit HFTs receive.

Table 11 examines how the adverse selection faced by HFT and NHFT hidden liquidity relates to the

level of HFT activity. It controls for endogeneity in HFT activity using the same instrument variables

that were used in Table 8 to study the relationship between the use of hidden liquidity and HFT activity.

It uses the same control variables used in Tables 5 and 8 to control for other factors that might influence

adverse selection costs. Panel A reports the results for HFT and NHFT hidden and displayed liquid-

ity. Panel B reports the results for differences between HFT and NHFT hidden and displayed liquidity

(HFT and NHFT Diff) and for differences between hidden liquidity supplied by HFTs and NHFTs and

for differences in displayed liquidity supplied by HFTs and NHFTs (Hidden Diff and Display Diff).

Parenthesis report standard errors which are calculated by double clustering on stock and trading day, as

described in Peterson (2009) and Thompson (2011). Since liquidity supplied using buy (sell) limit orders

is positive (negative), a negative coefficient means the liquidity supplier faces greater adverse selection.

In Panel A of Table 11, the coefficient on fitted HFT Volume is negative and statistically significant

for HFT hidden and displayed liquidity and for NHFT hidden liquidity. This shows that the adverse

selection cost faced by HFT hidden and displayed limit orders and NHFT hidden orders increases as

27

overall HFT activity increases. Looking at HFT liquidity demanding and supplying activity separately,

it appears that the adverse selection HFT and NHFT hidden liquidity faces responds differently. The

adverse selection faced by HFT hidden liquidity appears to be strongly affected by the activity of HFT

liquidity demanders, while the adverse selection faced by NHFT hidden liquidity is strongly affected by

the activity of HFT liquidity suppliers. This could indicate that NHFT hidden liquidity suppliers are

more likely to suffer from HFT liquidity suppliers use pinging strategies to engage in parasitic trading

strategies and front-running their existing orders, while HFT hidden liquidity suppliers are more likely to

suffer from adverse selection caused by HFT liquidity demanders as documented in Hirschey (2013) and

Brogaard, Hendershott, and Riordan (2013). The results in the table also show that the adverse selection

faced by displayed and hidden liquidity increases when quote midpoint volatility, the percentage spread,

and the rate that shares are added to the limit order book increase. Adverse selection decreases when

trading volume, prices, the proportion of volume traded on NASDAQ, depth at the NBBO, and the rate

that shares are canceled from the limit order book increase.

5.2 Trading Revenue from Liquidity Supply

The previous subsection found that both hidden and displayed liquidity supplied by HFTs and NHFTs

in transactions faced adverse selection. However, HFT and NHFT liquidity suppliers could still earn

a profit, both from the bid-ask spread and from rebates that NASDAQ awards for supplying liquidity.

This subsection examines the trading revenues that HFTs and NHFTs generate supplying liquidity using

hidden and displayed orders.

Brogaard, Hendershott, and Riordan (2013) reports that without liquidity supplying rebates, HFTs

and NHFTs earn negative revenue from supplying liquidity . After taking rebates into account, they

find HFTs earn positive revenue, but NHFTs still earn negative revenue. Using a similar methodology as

Brogaard, Hendershott, and Riordan (2013), I separately examine the trading revenues that HFTs and

NHFTs generate supplying liquidity using hidden and displayed orders. I assume that each stock-day

HFTs and NHFTs start and end the day with zero inventory for both their hidden and displayed shares.

The revenue HFTs earn supplying liquidity using displayed orders each stock-day is given by:

πHFT display =∑Nn (SSHFT display

n ∗ Pn − SBHFT displayn ∗ Pn) + INV HFT displayN ∗ PT

max[∑N

n SSHFT displayn ,

∑Nn SB

HFT displayn

]

28

where n subscripts each of the N transactions in a stock-day, SSHFT displayn is the shares sold in trans-

action n by an HFT supplying liquidity using displayed orders, SBHFT displayn is the shares bought in

transaction n by an HFT supplying liquidity using displayed orders, Pn is the price of transaction n,

INV HFT displayN is the end of day inventory (HFT displayed shares bought supplying liquidity - HFT

displayed shares sold supplying liquidity) for an HFT using displayed shares to supply liquidity, PT is

the closing quote midpoint.23 The numerator represents the net cash flow the HFT receives from sup-

plying liquidity using displayed shares and reducing his end of day inventory position to zero by buying

or selling any remaining shares at the end of day closing midpoint. The denominator is the greater of

the displayed shares the HFT bought or sold while supplying liquidity during the stock-day. Since the

number of hidden and displayed shares used by HFTs and NHFTs varies greatly, I calculate the revenue

on a per share basis in order to make the results more comparable. By dividing by the greater of the

shares being bought or sold, the calculated revenue can be thought of as the profit each share earns on a

round trip transaction. HFT revenues for hidden liquidity and NHFT revenues for hidden and displayed

liquidity are all calculated in a similar manner. Revenue is calculated separately for each stock-day.

In addition to earning the bid-ask spread, liquidity suppliers on NASDAQ can also earn rebates for

supplying liquidity. Liquidity rebates could be an important factor when discussing the revenues HFTs

and NHFTs earn for supplying liquidity using hidden and displayed shares, since the rebate for supplying

displayed liquidity on NASDAQ is larger than then rebate for supplying hidden liquidity. Over the sam-

ple period, the rebate for supplying displayed liquidity on NASDAQ ranged from $0.0025 to $0.0028 per

share, while the rebate for supplying liquidity using hidden orders was usually $0.0015 per share.24 I cal-

culate the revenue for HFT and NHFT liquidity supply both with and without rebates for displayed and

non-displayed orders. Like Brogaard, Hendershott, and Riordan (2013), I assume HFTs and NHFTs are in

the highest volume categories when determining rebates for supplying liquidity. On NasdaqTrader.com,

I identify 6 changes in the rebates for supplying displayed and non-displayed liquidity for the top volume

category during the sample period.

Before examining the results it is important to note a number of issues that make it difficult to accu-

rately calculate HFT revenue. First, since I only observe an aggregate indicator and not the transactions

of individual HFTs, the revenue earned by individual HFT firms could differ greatly from the revenue

23. Carrion (2013) shows that revenue decomposition for HFTs and NHFTs demanding and supplying liquidity can varybased on the method used to value the closing inventory. See the discussion in Chordia et al. (2013) for further discussionon how these methods affect HFT revenue calculations.

24. From January until April 2008, the NASDAQ rebate for supplying liquidity using non-displayed orders ranged from0.0026 to 0.0027 dollars per share for the highest volume level. Throughout the rest of the sample the NASDAQ rebate forsupplying liquidity using non-displayed orders was 0.0015 dollars per share for the highest volume level.

29

that I calculate based on treating all HFTs as being a single firm. Second, I do not observe HFT activity

on other exchanges, so and I cannot accurately calculate their inventory. If an HFT enters a position on

NASDAQ and exits the position on another exchange, my end of day inventory estimates will be wrong.

Third, I do not include HFT liquidity demanding trades in my calculations. Since HFTs likely demand

liquidity and also supply it using both hidden and displayed orders in the course of a trading day, this

could cause my estimates of HFT hidden and displayed end of day inventories to be invalid.

Table 12 reports the average revenue HFTs and NHFTs earn from supplying liquidity using hidden

and displayed orders in units of cents per share traded. The first row reports results for revenue without

any rebates earned from NASDAQ for supplying liquidity. The second row reports results for revenue

that includes rebates from NASDAQ. The left hand side of the tables report the average revenue HFTs

earn from supplying liquidity using displayed and hidden orders and from their combined liquidity supply

(All). The center reports revenues earned by NHFTs. The right hand side of the tables report the average

difference in the revenue for transactions in which HFTs/NHFTs supplied liquidity using hidden orders

and transactions in which they used displayed orders (HFT and NHFT Diff). It also reports the av-

erage difference in revenue for transactions in which displayed/hidden liquidity is supplied by HFTs and

transactions in which displayed/hidden liquidity is supplied by NHFTs (Display and Hidden Diff).

Parenthesis report t-statistics double clustered by stock and day.

The results in the first row provide evidence that the revenue NHFTs earn from supplying liquidity us-

ing displayed orders is negative without rebates, the value of -0.77 cents per share is statistically significant

at the 10% level. After rebates are included, the results in the second row for NHFT displayed revenue

become insignificant. The results do not indicate that HFTs earn positive revenue from their displayed

liquidity. Without fees, HFT earn revenue of -0.29 cents per share, with the result being statistically

insignificant. After rebates are included, the revenue HFTs earn from displayed liquidity is positive, but

still statistically insignificant.

Both HFTs and NHFTs earn more revenue supplying liquidity using hidden orders. Overall, HFTs

earn 1.14 cents per share and NHFTs earn 1.28 cents per share before rebates, with both results being

statistically significant. After liquidity rebates, HFTs earn 1.42 cents per share and NHFTs earn 1.56

cents per share supplying liquidity using hidden orders.

The test of differences between the revenues HFTs earn from supplying liquidity using hidden and

displayed orders is positive and insignificant for revenues earned with and without rebates, with average

differences of 1.12 and 1.32 cents per share with and without liquidity rebates, respectively. The average

30

difference between revenue NHFTs earn supplying liquidity using hidden and displayed orders is 1.82 and

2.03 cents per share for liquidity supplied with and without rebates, respectively. The results are positive

and statistically significant.

The results for overall HFT and NHFT revenues differ from those in Brogaard, Hendershott, and

Riordan (2013). Overall, the revenue HFTs earn from liquidity supply is positive but insignificant before

rebates, but becomes significant after rebates. Overall NHFT revenue is negative and insignificant before

including rebates and positive and insignificant after including rebates. One reason these results may

differ from those in Brogaard, Hendershott, and Riordan (2013) could be due to the difference in samples,

I only analyze revenues for the subset of their sample for which limit order book data is available.

6 Can HFTs or NHFTs detect hidden liquidity?

In section 4, it was shown that both HFTs and NHFTs decrease their use of hidden liquidity when overall

HFT activity increases. Although an increase in HFT activity likely increases the chance of a hidden

order losing priority, it might also reduce the benefits of hiding an order if HFTs have an advantage in

detecting the presence of hidden liquidity. If concealing an order does not prevent it from being picked

off by liquidity demanders or reduce the chance of it being front-run by competing liquidity suppliers,

then a hidden order is inferior to a displayed order, since it has lower execution priority. One method

traders might use to detect hidden liquidity is pinging, the rapid submission and cancellation of limit

orders between the bid-ask spread to see if they execute against hidden liquidity. Hasbrouck and Saar

(2009) first documented the presence of fleeting orders, aggressive limit orders that are submitted and then

rapidly canceled, on INET and hypothesized that one of their uses was to detect the presence of hidden

orders. Because of their speed advantage in being able to submit and cancel orders, HFTs might be better

at pinging for the presence of hidden liquidity in the limit order book than NHFTs. Xu (2014) presents

a model in which HFTs use their speed advantage as a pinging strategy to detect hidden liquidity.

This section tests this hypothesis by comparing the frequencies that HFTs and NHFTs trade with

hidden liquidity to those predicted from the model in Chabound et al. (2014), which produces predictions

for the probabilities of different types of liquidity demander-supplier pairings under the assumption that

the activities of liquidity demanders are independent of the activities of liquidity suppliers. Chabound

et al. (2014) used their model to examine algorithmic trading activity in the foreign exchange market.

Brogaard (2010) also used this model with data from NASDAQ to examine if HFTs’ strategies were more

31

correlated than NHFTs’.

The theoretical probabilities are constructed based on four types of trade pairings: HD, HH, ND, and

NH. The first letter identifies if the liquidity demander is an HFT (H) or an NHFT (N). The second

letter identifies if the liquidity supplied was displayed (D) or hidden (H). Let Hd be the number of HFT

liquidity demanders, Nd be the number of NHFT liquidity demanders, Hs the number of traders who

supply liquidity using hidden orders, and Ds be the number of traders who supply liquidity using displayed

orders. These give rise to the following probabilities:

Prob(HFT demand) = Hd

Hd +Nd= αd

Prob(NHFT demand) = Nd

Hd +Nd= 1 − αd

Prob(Hidden supply) = Hs

Hs +Ds= αs

Prob(Displayed supply) = Ds

Hs +Ds= 1 − αs

If the actions of liquidity demanders and suppliers are independent, then the probability of a trade pairing

is given by:

Prob(HD) = (αd)(1 − αs)

Prob(HH) = (αd)(αs)

Prob(ND) = (1 − αd)(1 − αs)

Prob(NH) = (1 − αd)(αs)

This results in the following relationship: Prob(HD)Prob(HH) = Prob(ND)

Prob(NH) . I define RH = Prob(HD)Prob(HH) as the HFT

demanding ratio and RN = Prob(ND)Prob(NH) as the NHFT demanding ratio. Regardless of the difference in

volumes between HFTs and NHFTs and hidden and displayed liquidity, the ratio of RHRN will equal 1 as long

as HFTs take liquidity from hidden orders in the same proportion as NHFTs. I define Rhidden = ln(RHRN).

If Rhidden = 0, then HFTs and NHFTs trade with hidden liquidity in equal proportion and neither

appears to have an advantage in detecting hidden liquidity. If Rhidden < 0 then HFTs trade with

hidden liquidity in greater proportions than NHFTs trade with hidden liquidity, which could indicate that

32

HFT liquidity demanders are better at detecting and trading against hidden liquidity than NHFTs.25 I

calculate the Rhidden ratio separately for each stock-day by counting the frequency of HD, HH, ND, NH

trade pairings. I also construct similar ratios, RhiddenHFT and RhiddenNHFT , which examine the

frequency that HFT and NHFT liquidity demand interact with hidden liquidity supplied by HFTs and

NHFTs, respectively.

Table 13 shows the average Rhidden, RhiddenHFT , and RhiddenNHFT ratios calculated from all

stock-days in the sample. The table also reports t-statistics which are double clustered by stock and day,

as well as the percentage of stock-days for which Rhidden was not missing and for which it was greater

than 0.

The results for Rhidden, RhiddenHFT , RhiddenNHFT are all negative and statistically significant,

with RhiddenNHFT being lower than RhiddenHFT . This indicates that HFTs trade with hidden

liquidity at a greater frequency than if the interactions occurred by chance. The results support the

hypothesis that HFTs are better at detecting and executing against hidden orders.

7 Conclusion

High-frequency traders (HFTs) and the ability to conceal orders are two of the most common features

in today’s electronic limit order markets. Using data from NASDAQ detailing the use of hidden and

displayed liquidity by high-frequency traders in the limit order book and when supplying liquidity in

trades, I explore how differences in the trading speed of HFTs and NHFTs affects their decision to conceal

an order.

I find that HFTs are more likely to use hidden liquidity in the limit order book, but non-high frequency

traders (NHFTs) are more likely to use hidden orders when supplying liquidity in a transaction. This

difference occurs because NHFTs are more likely to conceal their aggressively priced limit orders, while

HFTs are more likely to conceal their less aggressively priced limit orders.

I also examine how the speed of other market participants affects the decision to conceal a limit order.

I find that the use of hidden orders decreases as the proportion of overall trading volume in which HFTs

participate increases. After controlling for the endogenous relationship between HFT activity the decision

to conceal an order, I find that the decision of HFTs to conceal a limit order is negatively related to the

25. Other possible interpretations could be that NHFT liquidity demanders are better at detecting and avoiding hiddenliquidity or that hidden liquidity suppliers are better at anticipating and interacting with HFT order flow. Although thisis unlikely, since Hirschey (2013) and Brogaard, Hendershott, and Riordan (2013) report that liquidity supplied to HFTliquidity demanders is more likely to be adversely selected.

33

proportion of liquidity that HFTs demand, while the decision of NHFTs to conceal an order is negatively

related to the proportion of liquidity that HFTs supply.

I examine the role that adverse selection plays in the use of hidden orders and find that hidden orders

used by NHFTs to supply liquidity in transactions are less likely to be adversely selected and earn more

revenue than their displayed orders. There does not appear to be a significant difference between the

adverse selection that HFT hidden and HFT displayed orders face, which could explain why HFTs reduce

their hidden orders when they face more adverse selection from an increase in the activity of HFT liquidity

demanders. I also examine the ability of traders to detect hidden liquidity and find that HFT liquidity

demanders trade with hidden liquidity at a greater frequency than if the interactions occurred by chance,

which indicates that HFT liquidity demanders are better at detecting the presence of hidden liquidity in

the limit order book than NHFTs.

Overall, my findings suggest that the speed of both the order initiator and other market participants

affect a trader’s decision to conceal their limit order.

34

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36

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37

Table 2: Limit Order Book Descriptive StatisticsThis table summarizes the use of hidden liquidity in the NASDAQ limit order book snapshots for each market cap group. Quoteinformation from the 10 best price levels on the bid and ask side are aggregated together (Total Depth) and into the following pricegroups: at prices inside the best displayed quotes (Inside), prices at and inside the best displayed quotes (At and Inside), and pricesabove the best displayed quotes (Above). Mean values are calculated for each stock-day in the sample by averaging across limit orderbook snapshots. The table reports the median, 25th, and 75th percentile values from the pooled stock-days in each market cap group.The variables reported are the NASDAQ displayed and true spread (taking into account hidden quotes inside the displayed spread)measured in cents and as a percentage of the midpoint (displayed and true) of the best NASDAQ bid and offer quotes, the NBBOspread measured in cents and as a percentage of the NBBO midpoint, the dollar value (number of shares times quoted price in $1000sof dollars) of supplied liquidity (hidden plus displayed) in each price group, the percentage of depth in the price group relative to thetotal depth in the limit order book, the percentage of depth that is supplied by High-Frequency Traders (HFTs) in each price group,the percentage of depth that is hidden in each price group, the percentage of HFT depth that is hidden in each price group, andthe percentage of NHFT depth that is hidden in each price group. The percentage of hidden depth and HFT/NHFT hidden depthinside the best displayed quotes is calculated as the hidden depth inside the quotes divided by the total depth inside and at the bestdisplayed quotes. Large cap stocks are selected from the largest market capitalization. Medium cap stocks are selected from stocksaround the 1,000th largest stock in the Russell 3000. Small cap stocks are selected from stocks around the 2,000th largest stock in theRussell 3000.

Large Cap Medium Cap Small CapVariable 25% Median 75% 25% Median 75% 25% Median 75%Displayed Spread (cents) 1.09 1.51 3.31 2.17 4.43 7.31 3.20 4.78 8.90True Spread (cents) 1.04 1.36 2.51 1.86 3.61 5.98 2.61 3.99 7.23NBBO Spreads (cents) 1.00 1.14 1.97 1.61 2.66 4.65 2.06 3.02 4.95Displayed Spread Percent (bp) 3.91 5.15 7.21 11.77 16.39 24.30 27.63 41.10 66.51True Spread Percent (bp) 3.33 4.54 6.27 9.85 13.95 20.00 22.88 34.23 54.01NBBO Spread Percent (bp) 2.92 3.99 5.32 8.41 11.17 14.77 18.89 24.85 34.91True Spread <Displayed Spread (%) 4.62 12.18 38.80 16.11 30.95 47.18 22.76 34.32 48.02Time NBBO 1 tick (%) 23.21 43.53 60.95 4.35 12.82 31.20 2.81 11.79 28.90Time NASDAQ Displayed at NBB/NBO (%) 65.58 86.03 95.65 57.03 70.08 83.89 51.66 66.54 78.13Total Depth ($1000s) 879.92 1,544.16 3,001.37 226.53 296.90 426.18 105.78 148.65 243.65

Percent Depth HFT 16.77 23.58 33.37 12.12 18.51 28.36 9.82 23.52 38.01Percent Depth Hidden 10.93 15.78 24.03 16.27 25.91 39.26 24.31 37.47 53.32Percent HFT Depth Hidden 1.38 6.92 19.26 9.99 27.41 50.45 19.21 50.82 73.80Percent NHFT Depth Hidden 12.84 18.42 25.67 13.73 22.48 35.80 15.98 27.81 50.67

Inside Depth ($1000s) 1.21 3.48 10.34 0.98 2.85 6.38 0.73 1.53 3.67Percent Total Depth 0.05 0.20 1.28 0.33 1.01 2.10 0.50 1.04 1.96Percent Displayed Quote Depth 0.56 2.57 11.97 3.82 11.48 21.02 7.01 13.89 24.10Percent Depth HFT 16.76 36.77 64.89 6.16 17.22 39.21 3.84 10.70 24.90Percent HFT Depth Hidden 0.45 1.44 10.14 1.82 8.56 32.12 4.24 15.05 38.88Percent NHFT Depth Hidden 0.42 3.02 11.32 3.44 10.11 19.36 6.28 12.88 22.60

At and Inside Depth ($1000s) 90.58 145.23 300.83 20.09 30.72 47.39 8.19 12.65 20.67Percent Total Depth 7.40 10.16 13.36 7.48 10.33 13.91 5.82 8.43 12.33Percent Depth HFT 28.17 41.46 52.47 9.57 16.94 28.13 6.25 10.48 18.48Percent Depth Hidden 20.73 33.34 51.10 28.72 40.82 56.63 34.09 45.16 60.36Percent HFT Depth Hidden 3.10 11.15 34.17 7.83 23.94 53.53 12.60 27.00 53.44Percent NHFT Depth Hidden 31.67 44.99 58.55 30.18 42.99 58.67 33.82 46.99 61.86

Above Depth ($1000s) 766.15 1,368.31 2,709.28 198.80 259.90 379.27 94.80 133.75 216.80Percent Total Depth 86.64 89.84 92.60 86.09 89.67 92.52 87.67 91.57 94.18Percent Depth HFT 15.28 21.91 32.01 11.71 18.00 28.75 9.87 24.52 40.26Percent Depth Hidden 9.42 13.89 20.68 13.92 23.25 36.90 21.87 35.48 51.99Percent HFT Depth Hidden 0.80 5.83 16.74 8.25 23.78 49.61 16.69 52.00 74.90Percent NHFT Depth Hidden 10.52 15.91 22.32 10.86 19.80 32.04 13.20 23.94 47.86

38

Table 3: HFT and NHFT Hidden Liquidity ComparisonThis table presents analysis comparing the use of hidden liquidity by HFTs and NHFTs in the NASDAQ limit order book and inliquidity supplied in transactions on NASDAQ. Nasdaq Quote information from the 10 best price levels on the bid and ask sideof the limit order book are aggregated together and into the following price groups: prices inside the NBBO, prices at and insidethe NBBO, prices inside the best displayed quotes on NASDAQ, prices at and inside the best displayed quotes on NASDAQ, andprices above the best displayed quotes on NASDAQ (Above). The percentage of hidden liquidity for each trader type in each pricegroup is calculated for each stock-day by summing up across all NASDAQ limit order book snapshots the total dollar value (sharestimes price) of hidden liquidity supplied by the trader type in the limit order book price group and dividing it by the total dollarvalue of liquidity (displayed plus hidden) supplied by the trader type in the same price group. The percentage of hidden liquidityfor Inside the Best Displayed Quotes (inside the NBBO) is calculated by dividing the total dollar value of hidden liquidity insidethe best displayed quotes (NBBO) by the total dollar value of liquidity supplied Inside and At the Best Quotes (NBBO). Thepercentage of Liquidity Supplied in Transactions by each trader type is calculated for each stock-day by summing up the totaldollar value of all transactions in which the trader type supplied liquidity using hidden orders and dividing it by the total dollarvalue of all transactions in which the trader type supplied liquidity. The mean and median stock-day measures of percentages ofhidden liquidity are presented for all combined traders and for HFTs and NHFTs separately. Mean Diff is the mean differencebetween HFT and NHFT hidden order usage from the pooled stock-day sample.p(t-test) and p(W-test) provide p-values fortwo-sided pairs t-test and Wilcoxon singed-rank test against the hypothesis of zero difference between HFT and NHFT hiddenliquidity usage. The analysis is performed for the whole sample of pooled stock-day observations and is also repeated for theobservations in each market cap group. Large cap stocks are selected from the largest market capitalization. Medium cap stocksare selected from stocks around the 1,000th largest stock in the Russell 3000. Small cap stocks are selected from stocks aroundthe 2,000th largest stock in the Russell 3000.

ALL Hidden HFT Hidden NHFT Hidden HFT - NHFTHidden Type Mean Median Mean Median Mean Median Mean Diff p(t-test) p(W-test)All Stocks:All Limit Order Book 28.83 24.55 31.20 21.55 26.53 21.77 4.66 <.0001 <.0001Inside NBBO Quotes 9.83 5.65 11.24 3.04 9.29 5.28 1.95 <.0001 0.0196Inside and At NBBO quotes 44.73 43.60 24.83 15.57 49.58 49.39 -24.74 <.0001 <.0001Inside Best Displayed Quotes 13.37 9.44 17.81 6.60 12.36 8.69 5.46 <.0001 <.0001Inside and At Best Displayed Quotes 42.33 40.62 29.51 21.07 46.19 45.15 -16.69 <.0001 <.0001Above Best Displayed Quotes 26.65 21.89 30.25 18.90 23.70 18.80 6.55 <.0001 <.0001Liquidity Supplied in Transactions 18.25 15.81 15.57 7.57 20.18 18.68 -4.62 <.0001 <.0001Large Cap:All Limit Order Book 19.18 15.78 14.48 6.92 20.53 18.42 -6.05 <.0001 <.0001Inside NBBO Quotes 6.34 1.57 6.21 1.06 5.97 1.85 0.24 0.4242 <.0001Inside and At NBBO quotes 38.83 34.89 21.54 11.05 48.21 47.96 -26.68 <.0001 <.0001Inside Best Displayed Quotes 8.64 2.57 9.69 1.44 7.87 3.03 1.82 <.0001 0.2227Inside and At Best Displayed Quotes 36.81 33.34 21.93 11.15 45.53 44.99 -23.61 <.0001 <.0001Above Best Displayed Quotes 16.56 13.89 12.97 5.83 17.47 15.91 -4.50 <.0001 <.0001Liquidity Supplied in Transactions 16.11 13.67 11.64 4.27 20.75 19.95 -9.11 <.0001 <.0001Medium Cap:All Limit Order Book 28.81 25.91 32.09 27.41 26.29 22.48 5.81 <.0001 <.0001Inside NBBO Quotes 11.24 7.92 12.08 4.36 10.78 7.02 1.29 0.005 0.0298Inside and At NBBO quotes 45.51 44.55 26.78 16.71 48.42 47.75 -21.63 <.0001 <.0001Inside Best Displayed Quotes 14.28 11.48 18.92 8.56 13.34 10.11 5.58 <.0001 <.0001Inside and At Best Displayed Quotes 42.89 40.82 31.65 23.94 44.86 43.00 -13.21 <.0001 <.0001Above Best Displayed Quotes 26.47 23.25 30.80 23.78 23.38 19.80 7.43 <.0001 <.0001Liquidity Supplied in Transactions 18.42 16.43 16.15 9.35 19.46 17.86 -3.32 <.0001 <.0001Small Cap:All Limit Order Book 39.02 37.47 47.84 50.82 33.11 27.81 14.73 <.0001 <.0001Inside NBBO Quotes 12.10 7.93 15.80 7.17 11.27 7.14 4.53 <.0001 <.0001Inside and At NBBO quotes 50.31 49.10 26.31 17.90 52.32 51.96 -26.01 <.0001 <.0001Inside Best Displayed Quotes 17.39 13.89 25.19 15.05 16.04 12.88 9.15 <.0001 <.0001Inside and At Best Displayed Quotes 47.57 45.16 35.23 27.00 48.30 46.99 -13.08 <.0001 <.0001Above Best Displayed Quotes 37.45 35.48 47.84 52.01 30.59 23.94 17.26 <.0001 <.0001Liquidity Supplied in Transactions 20.30 17.86 19.13 10.37 20.33 17.66 -1.24 0.0631 <.0001

39

Table 4: HFT and NHFT Aggressiveness ComparisonThis table presents analysis comparing the aggressiveness of hidden and displayed liquidity supplied by HFTsand NHFTs in the NASDAQ limit order book. Aggressiveness is calculated from the 10 best price levels onthe bid and ask side of snapshots of the NASDAQ limit order book. The Aggressiveness of an ask share is thedifference between the price the share is quoted at and the true midpoint of the best bid and ask prices in thelimit order book. The Aggressiveness of a bid share is the difference between the true midpoint of the best bidand ask prices in the limit order book and the price the share is quoted at. The aggregated Aggressivenessmeasure for each stock-day is calculated as a weighted average of the aggressiveness of all shares in all limitorder book snap shots for each stock-day, with the weights corresponding to the number of shares at each pricelevel. The aggressiveness measure is normalized by dividing by one half the average true spread for each stock-day. Aggressiveness is calculated separately based on whether the liquidity is supplied by a HFT or NHFT andwhether the depth is hidden or displayed. For each comparison, the measures of aggressiveness that are beingcompared are reported in Variable 1 and Variable 2. The mean and median of the stock-day measures beingcompared are reported for Variable 1 and Variable 2. Mean Diff is the mean difference between Variable1 and Variable 2 from the pooled stock-day sample.p(t-test) and p(W-test) provide p-values for two-sidedpairs t-test and Wilcoxon singed-rank test against the hypothesis of zero difference between Variable 1 andVariable 2. The analysis is performed for the whole sample of pooled stock-day observations.

Variable 1 Variable 2 Variable 1 -Variable 2Variable 1 Variable 2 Mean Median Mean Median Mean Diff p(t-test) p(W-test)

Order Book Hidden Order Book Displayed 8.49 7.99 8.80 8.21 -0.31 <.0001 <.0001HFT Hidden HFT Displayed 8.18 5.71 6.74 5.71 1.45 <.0001 <.0001

NHFT Hidden NHFT Displayed 7.27 6.90 8.90 8.52 -1.63 <.0001 <.0001HFT All NHFT All 8.53 6.85 8.57 8.35 -0.04 0.5573 <.0001

HFT Hidden NHFT Hidden 8.18 5.71 7.27 6.90 0.92 <.0001 0.0002HFT Displayed NHFT Displayed 6.74 5.71 8.90 8.52 -2.16 <.0001 <.0001

40

Table 5: Daily Determinants of Hidden VolumeThis table presents analysis using linear regression models to examine the determinants of the percentage of HFTand NHFT volume that is hidden in the NASDAQ limit order book and in liquidity supplied in transactions onNASDAQ. Nasdaq Quote information from the 10 best price levels on the bid and ask side of the limit order bookare aggregated together. The percentage of hidden liquidity for each trader type is calculated for each stock-dayby summing up across all limit order book snapshots the total dollar value (shares times price) of hidden liquiditysupplied by the trader type in the limit order book and dividing it by the total dollar value of liquidity (displayedplus hidden) supplied by the trader type. The percentage of Liquidity Supplied in Transactions is calculated foreach stock-day by summing up the total dollar value of all transactions in which the trader type supplied liquidityusing hidden orders and dividing it by the total dollar value of all transactions in which the trader type suppliedliquidity.Hidden liquidity results are presented in 2 panels: Panel A examines hidden liquidity in the limit order book andPanel B examines hidden liquidity supplied in transactions. Dependent variables in each panel are the percentageof hidden dollar volume for all traders supplying liquidity (All Hidden), the percentage of hidden dollar volumefor HFTs supplying liquidity (HFT Hidden), the percentage of hidden dollar volume for NHFTs supplying liquidity(NHFT Hidden), and the difference between the percentage of hidden dollar volume for HFTs supplying liquidityand the percentage of hidden dollar volume for NHFTs supplying liquidity (Diff Hidden). Explanatory variables arethe percentage of NASDAQ dollar trading volume in which HFTs trade, the percentage of NASDAQ dollar tradingvolume for which HFTs demanded liquidity, and the percentage of NASDAQ dollar trading volume for which HFTssupplied liquidity, the log of total dollar trading volume reported by all exchanges, the log of the stock’s closing price,the percentage of total dollar trading volume that is traded on NASDAQ, the stock’s positive abnormal return,the stock’s negative abnormal return, the positive CRSP daily value weighted market return, the negative CRSPdaily value weighted market return, the daily opening value of VIX, the volatility of 5 minute NBBO midpointreturns, the average depth at the NBBO inside quotes, the average NBBO percentage spread, the average numberof displayed shares added to the NASDAQ limit order book each minute that improve the best displayed bid oroffer, the number of displayed shares added to the book at the best displayed bid or offer, the number of displayedshares added to the book at prices worse than the best displayed bid or offer, the average number of displayedshares canceled from the limit order book each minute at the best displayed bid or offer, the number of displayedshares canceled from the book at prices worse than the best displayed bid or offer, and the stock’s probability ofinformed trading (PIN). The stock’s abnormal return is the difference between the stock’s daily return and theexpected return from a model that is estimated by regressing the daily returns of each stock on a 5 factor modelthat includes the Carhart 4 factor model and the Pastor-Stambaugh liquidity factor. Abnormal returns and marketreturns are separated out into positive and negative returns to account for possible asymmetric effects of positiveand negative information. If the return is positive (negative) on the stock-day, then the positive (negative) returnvariable is equal to the return value (minus the return value) and the negative (positive) return is equal to zero.NASDAQ ITCH addition and cancellation variables are normalized by dividing by the average number of sharestraded on NASDAQ each minute. All explanatory variables are standardized so the coefficients can be interpretedas the percentage increase in the use of hidden liquidity for a one standard deviation increase in the explanatoryvariable. Parenthesis report standard errors double clustered by stock and day. ***, **, and * indicate significanceat the 1%, 5%, and 10% level, respectively.

41

Tabl

e5:

Det

erm

inan

tsof

Hid

den

Volu

me:

Pane

lALi

mit

Ord

erB

ook

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

Varia

ble

All

Hid

den

HFT

Hid

den

NH

FTH

idde

nD

iffH

idde

nH

FTVo

lum

e%

-4.8

4***

-2.5

2*-5

.42*

**2.

90*

(0.6

7)(1

.31)

(0.7

2)(1

.57)

HFT

Dem

and

Volu

me

%-1

.79*

**-0

.23

-2.1

5***

1.92

(0.6

5)(1

.04)

(0.6

8)(1

.26)

HFT

Supp

lyVo

lum

e%

-4.5

1***

-3.4

1**

-4.8

4***

1.43

(0.9

2)(1

.64)

(0.7

6)(1

.81)

Log

Dai

lyTr

adin

gVo

lum

e-7

.36*

**-5

.91*

**-2

0.71

***

-18.

90**

*-0

.78

0.64

-19.

92**

*-1

9.53

***

(1.2

6)(1

.50)

(2.2

2)(2

.79)

(1.2

7)(1

.42)

(2.4

5)(3

.17)

Log

Pric

e6.

67**

*5.

67**

*16

.88*

**15

.64*

**2.

89**

*1.

9213

.99*

**13

.72*

**(1

.30)

(1.5

2)(2

.42)

(2.6

9)(0

.96)

(1.1

7)(2

.23)

(2.5

8)N

asda

q%

Dol

lar

Volu

me

-0.6

9-0

.61

-4.1

6***

-4.0

6***

0.66

0.75

-4.8

3***

-4.8

1***

(0.7

3)(0

.73)

(1.0

9)(1

.11)

(0.6

2)(0

.63)

(1.1

6)(1

.18)

Pos

Adj

Ret

0.91

**0.

94**

-0.3

5-0

.32

1.63

***

1.66

***

-1.9

8*-1

.97*

(0.4

6)(0

.46)

(0.8

7)(0

.87)

(0.5

1)(0

.51)

(1.0

6)(1

.06)

Neg

Adj

Ret

1.55

**1.

56**

*0.

480.

481.

87**

*1.

87**

*-1

.39

-1.3

9(0

.60)

(0.6

0)(0

.92)

(0.9

1)(0

.64)

(0.6

3)(1

.04)

(1.0

4)Po

sM

arke

tR

et-0

.40

-0.3

8-4

.52*

**-4

.50*

**1.

531.

55-6

.05*

**-6

.05*

**(1

.09)

(1.0

3)(1

.61)

(1.5

6)(1

.30)

(1.2

5)(2

.11)

(2.1

1)N

egM

arke

tR

et0.

150.

16-0

.15

-0.1

40.

460.

47-0

.61

-0.6

1(0

.62)

(0.5

9)(0

.81)

(0.8

1)(0

.95)

(0.9

2)(1

.49)

(1.5

0)O

peni

ngV

IX0.

510.

31-0

.26

-0.5

01.

080.

90-1

.34

-1.4

0(0

.63)

(0.6

4)(1

.17)

(1.1

7)(0

.73)

(0.7

5)(1

.43)

(1.4

5)Ta

qM

PVo

latil

ity2.

61**

*2.

19**

*8.

22**

*7.

70**

*0.

23-0

.17

7.98

***

7.87

***

(0.7

3)(0

.75)

(1.3

4)(1

.37)

(0.8

2)(0

.79)

(1.6

6)(1

.61)

NB

BO

Dep

th0.

620.

562.

162.

100.

220.

161.

951.

93(0

.84)

(0.8

6)(1

.65)

(1.6

6)(0

.58)

(0.6

0)(1

.36)

(1.3

6)N

BB

OSp

read

%-2

.66*

**-2

.18*

*-5

.01*

**-4

.41*

*-0

.72

-0.2

5-4

.29*

*-4

.17*

*(0

.92)

(0.9

4)(1

.78)

(1.7

6)(0

.94)

(1.0

0)(1

.94)

(1.9

0)Sh

ares

Add

Agg

ress

ive

17.8

3***

17.1

0***

6.31

5.40

20.1

3***

19.4

2***

-13.

83-1

4.02

(4.0

0)(3

.98)

(7.4

5)(7

.40)

(3.9

9)(4

.01)

(8.5

3)(8

.58)

Shar

esA

ddA

tQ

uote

11.3

5***

10.8

2***

3.06

2.41

14.2

0***

13.6

9***

-11.

14*

-11.

28*

(3.0

2)(3

.01)

(5.6

9)(5

.63)

(3.0

2)(3

.04)

(6.5

5)(6

.57)

Shar

esA

ddA

bove

Quo

te38

.83*

**35

.42*

**14

.29

10.0

447

.74*

**44

.40*

**-3

3.45

-34.

36(1

0.01

)(9

.60)

(17.

33)

(17.

26)

(11.

47)

(11.

35)

(22.

45)

(23.

00)

Shar

esC

ance

lAt

Quo

te-1

8.33

***

-17.

42**

*-4

.12

-2.9

9-2

2.85

***

-21.

96**

*18

.73*

18.9

7*(4

.81)

(4.8

2)(9

.15)

(9.0

6)(4

.75)

(4.8

1)(1

0.50

)(1

0.53

)Sh

ares

Can

celA

bove

Quo

te-4

3.15

***

-39.

80**

*-2

0.48

-16.

32-4

9.59

***

-46.

32**

*29

.11

30.0

0(1

0.29

)(9

.89)

(17.

57)

(17.

53)

(11.

78)

(11.

66)

(22.

86)

(23.

39)

PIN

0.44

0.66

1.63

1.89

0.97

1.18

0.66

0.72

(1.0

7)(1

.06)

(1.4

6)(1

.52)

(1.0

0)(0

.99)

(1.4

8)(1

.56)

Con

stan

t28

.12*

**28

.10*

**32

.38*

**32

.36*

**24

.87*

**24

.85*

**7.

51**

*7.

51**

*(0

.87)

(0.8

7)(1

.82)

(1.8

3)(1

.07)

(1.0

6)(2

.40)

(2.4

0)O

bser

vatio

ns4,

275

4,27

54,

275

4,27

54,

275

4,27

54,

275

4,27

5R

-squ

are

0.33

30.

336

0.39

10.

393

0.18

90.

192

0.20

40.

204

42

Tabl

e5:

Det

erm

inan

tsof

Hid

den

Volu

me:

Pane

lBIn

Tran

sact

ions

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

Varia

ble

All

Hid

den

HFT

Hid

den

NH

FTH

idde

nD

iffH

idde

nH

FTVo

lum

e%

-3.7

5***

-0.8

4-3

.26*

**2.

43**

*(0

.38)

(0.6

7)(0

.45)

(0.8

1)H

FTD

eman

dVo

lum

e%

-1.5

9***

-0.7

8-1

.76*

**0.

98(0

.33)

(0.6

0)(0

.37)

(0.6

7)H

FTSu

pply

Volu

me

%-3

.20*

**-0

.07

-2.2

1***

2.14

**(0

.58)

(0.7

9)(0

.53)

(0.8

9)Lo

gD

aily

Trad

ing

Volu

me

2.02

***

2.86

***

-4.3

1***

-4.7

6***

5.62

***

5.78

***

-9.9

2***

-10.

54**

*(0

.66)

(0.9

7)(1

.30)

(1.5

7)(0

.61)

(0.8

7)(1

.42)

(1.7

3)Lo

gPr

ice

4.35

***

3.78

***

14.9

3***

15.2

4***

-0.3

3-0

.44

15.1

5***

15.5

7***

(0.7

7)(0

.92)

(1.6

0)(1

.81)

(0.3

8)(0

.48)

(1.4

5)(1

.64)

Nas

daq

%D

olla

rVo

lum

e0.

010.

063.

21**

*3.

18**

*-0

.62*

*-0

.61*

*3.

88**

*3.

85**

*(0

.28)

(0.2

8)(0

.57)

(0.5

7)(0

.28)

(0.2

8)(0

.63)

(0.6

3)Po

sA

djR

et0.

48*

0.50

*0.

78*

0.77

*0.

420.

420.

400.

39(0

.28)

(0.2

8)(0

.41)

(0.4

1)(0

.26)

(0.2

6)(0

.45)

(0.4

5)N

egA

djR

et0.

62*

0.62

*1.

08**

1.08

**0.

420.

420.

710.

71(0

.34)

(0.3

4)(0

.49)

(0.4

9)(0

.29)

(0.2

9)(0

.48)

(0.4

7)Po

sM

arke

tR

et-0

.05

-0.0

3-1

.84*

*-1

.84*

*0.

260.

26-2

.10*

**-2

.10*

**(0

.50)

(0.4

9)(0

.85)

(0.8

6)(0

.49)

(0.4

9)(0

.72)

(0.7

3)N

egM

arke

tR

et0.

230.

230.

160.

160.

290.

29-0

.13

-0.1

3(0

.41)

(0.4

3)(0

.63)

(0.6

2)(0

.40)

(0.4

1)(0

.40)

(0.3

9)O

peni

ngV

IX0.

420.

310.

870.

930.

470.

450.

390.

47(0

.29)

(0.2

9)(0

.56)

(0.5

7)(0

.30)

(0.3

0)(0

.56)

(0.5

8)Ta

qM

PVo

latil

ity1.

36**

*1.

12**

4.64

***

4.77

***

0.02

-0.0

34.

56**

*4.

74**

*(0

.46)

(0.4

9)(1

.01)

(1.0

6)(0

.36)

(0.3

8)(0

.92)

(0.9

6)N

BB

OD

epth

-1.1

3***

-1.1

6***

1.24

*1.

26*

-1.8

0***

-1.8

0***

3.05

***

3.07

***

(0.3

0)(0

.30)

(0.7

5)(0

.75)

(0.2

8)(0

.28)

(0.8

2)(0

.82)

NB

BO

Spre

ad%

2.51

***

2.79

***

5.90

***

5.75

***

1.48

***

1.53

***

4.58

***

4.37

***

(0.3

9)(0

.41)

(1.0

9)(1

.14)

(0.4

1)(0

.45)

(1.2

8)(1

.33)

Shar

esA

ddA

ggre

ssiv

e-2

.56

-2.9

9-3

.98

-3.7

50.

190.

11-4

.32

-4.0

0(2

.39)

(2.4

3)(3

.83)

(3.7

5)(2

.41)

(2.4

8)(3

.66)

(3.6

4)Sh

ares

Add

At

Quo

te-2

.38

-2.6

8-3

.63

-3.4

6-0

.29

-0.3

5-3

.45

-3.2

2(1

.71)

(1.7

3)(2

.71)

(2.6

5)(1

.76)

(1.7

9)(2

.72)

(2.7

1)Sh

ares

Add

Abo

veQ

uote

-1.6

5-3

.61

-8.9

5-7

.88

0.89

0.52

-10.

10-8

.65

(5.8

0)(5

.96)

(8.2

8)(8

.10)

(6.7

9)(7

.05)

(8.6

1)(8

.74)

Shar

esC

ance

lAt

Quo

te3.

874.

404.

814.

520.

590.

694.

424.

03(2

.87)

(2.9

1)(4

.44)

(4.3

4)(2

.89)

(2.9

6)(4

.35)

(4.3

2)Sh

ares

Can

celA

bove

Quo

te1.

163.

098.

147.

10-1

.22

-0.8

59.

668.

23(5

.91)

(6.0

9)(8

.48)

(8.3

2)(7

.01)

(7.2

6)(8

.86)

(9.0

0)PI

N0.

360.

492.

74**

*2.

67**

*0.

320.

352.

16**

*2.

08**

*(0

.61)

(0.6

5)(0

.78)

(0.7

8)(0

.49)

(0.5

1)(0

.74)

(0.7

4)C

onst

ant

17.7

1***

17.6

9***

15.5

0***

15.5

1***

19.5

8***

19.5

8***

-4.1

3***

-4.1

3***

(0.5

1)(0

.52)

(0.9

1)(0

.91)

(0.4

8)(0

.48)

(0.7

8)(0

.78)

Obs

erva

tions

4,27

54,

275

4,26

04,

260

4,27

54,

275

4,26

04,

260

R-s

quar

e0.

303

0.30

50.

536

0.53

60.

112

0.11

30.

432

0.43

2

43

Table 6: Liquidity Rebates and Hidden VolumeThis table presents analysis using linear regression models to examine how liquidity rebates for supplying liquidityin trades using displayed and nondisplayed shares affects the percentage of HFT and NHFT volume that is hiddenin the NASDAQ limit order book and in liquidity supplied in transactions on NASDAQ. Nasdaq Quote informationfrom the 10 best price levels on the bid and ask side of the limit order book are aggregated together and into thefollowing price groups: at prices inside the best displayed quotes, prices at and inside the best displayed quotes,and prices above the best displayed quotes (Above). The percentage of hidden liquidity for each trader type in eachprice group is calculated for each stock-day by summing up across all limit order book snapshots the total dollarvalue (shares times price) of hidden liquidity supplied by the trader type in the limit order book price group anddividing it by the total dollar value of liquidity (displayed plus hidden) supplied by the trader type in the same pricegroup. The percentage of hidden liquidity for Inside the Best Displayed Quotes is calculated by dividing the totaldollar value of hidden liquidity inside the best displayed quotes by the total dollar value of liquidity supplied Insideand At the Best Quotes. The percentage of Liquidity Supplied in Transactions is calculated for each stock-day bysumming up the total dollar value of all transactions in which the trader type supplied liquidity using hidden ordersand dividing it by the total dollar value of all transactions in which the trader type supplied liquidity.Results are presented in 2 panels: Panel A examines the whole limit order book and liquidity supplied in transactions,and Panel B examines prices inside the best displayed quotes, prices inside and at the best displayed quotes, andprices above the best displayed quotes. Dependent variables in each panel are the percentage of hidden dollarvolume for all traders supplying liquidity (All Hidden), the percentage of hidden dollar volume for HFTs supplyingliquidity (HFT Hidden), the percentage of hidden dollar volume for NHFTs supplying liquidity (NHFT Hidden),and the difference between the percentage of hidden dollar volume for HFTs supplying liquidity and the percentageof hidden dollar volume for NHFTs supplying liquidity (Diff Hidden).For each dependent variable, the table presents the parameter estimates from two regressions. The first regressioncontains Constant and Fee Indicator. The second regression contains Price Index 1, Price Index 2, Price Index3, and their interactions with the Fee Indicator. Fee Indicator is a binary variable that equals 1 if the stock-dayoccurred before May 1, 2008, when the displayed and nondisplayed rebates for supplying liquidity on NASDAQwere the same. Fee Indicator equals 0 if the stock-day occurred on May 1, 2008 or later, when the nondisplayedrebate for supplying liquidity on NASDAQ was reduced. Price Index 1, 2, and 3 are binary variables that equal 1if the stock’s closing price: is less than $20, between $20 and $40, or greater than $40, respectively.Both regressions also include the explanatory variables used in the regressions in Table 5. However, the regressionthat includes Price Index 1, 2, and 3 does not include the log of stock’s closing price. Results for these explanatoryvariables are not reported for brevity. All explanatory variables are standardized except for binary variables, so thecoefficients can be interpreted as the percentage increase in the use of hidden liquidity for a one standard deviationincrease in the explanatory variable. Parenthesis report standard errors double clustered by stock and day. ***,**, and * indicate significance at the 1%, 5%, and 10% level, respectively.

44

Tabl

e6:

Liqu

idity

Reb

ates

and

Hid

den

Volu

me:

Pane

lA

Tota

lBoo

kTr

ansa

ctio

nsVa

riabl

eA

llH

idde

nH

FTH

idde

nN

HFT

Hid

den

Diff

Hid

den

All

Hid

den

HFT

Hid

den

NH

FTH

idde

nD

iffH

idde

nC

onst

ant

29.2

1***

31.8

7***

26.5

6***

5.31

*17

.10*

**14

.14*

**18

.89*

**-4

.81*

**(0

.96)

(2.1

4)(1

.12)

(2.7

3)(0

.46)

(0.8

8)(0

.45)

(0.9

3)Fe

eIn

dica

tor

-3.9

6***

1.86

-6.0

8***

7.94

**2.

20**

*4.

92**

*2.

49**

*2.

43(1

.45)

(2.4

7)(1

.86)

(3.5

7)(0

.67)

(1.2

0)(0

.87)

(1.5

7)Pr

ice

Inde

x1

28.9

2***

28.8

3***

26.5

9***

2.25

16.0

2***

7.26

***

19.8

7***

-12.

58**

*(1

.61)

(3.2

0)(1

.55)

(3.6

0)(0

.81)

(1.5

7)(0

.58)

(1.5

0)Pr

ice

Inde

x2

28.0

2***

31.8

6***

25.3

1***

6.55

**16

.90*

**16

.18*

**18

.47*

**-2

.34

(1.1

3)(2

.62)

(1.3

1)(3

.14)

(0.6

4)(1

.42)

(0.6

2)(1

.54)

Pric

eIn

dex

332

.54*

**40

.32*

**28

.43*

**11

.89*

**19

.86*

**24

.94*

**17

.98*

**6.

79**

*(1

.42)

(2.8

7)(1

.48)

(3.2

5)(0

.98)

(2.1

7)(0

.77)

(2.1

0)Fe

e*

Pric

eIn

dex

1-8

.65*

**-3

.06

-9.5

0***

6.44

1.87

*5.

13**

*1.

923.

16(1

.87)

(4.3

4)(2

.38)

(5.7

0)(1

.00)

(1.7

3)(1

.19)

(2.0

2)Fe

e*

Pric

eIn

dex

2-0

.56

4.16

-4.1

4*8.

301.

87**

3.42

*2.

85**

*0.

55(2

.15)

(3.8

9)(2

.33)

(5.1

4)(0

.84)

(2.0

6)(0

.97)

(2.5

2)Fe

e*

Pric

eIn

dex

3-1

.93

5.38

*-3

.84*

9.21

**3.

17**

*7.

01**

*2.

64**

4.43

*(1

.57)

(2.9

3)(2

.12)

(4.0

6)(0

.90)

(1.9

9)(1

.18)

(2.4

9)

45

Tabl

e6:

Liqu

idity

Reb

ates

and

Hid

den

Volu

me:

Pane

lBTr

ansa

ctio

ns

Insid

eQ

uote

At

and

Insid

eQ

uote

Varia

ble

All

Hid

den

HFT

Hid

den

NH

FTH

idde

nD

iffH

idde

nA

llH

idde

nH

FTH

idde

nN

HFT

Hid

den

Diff

Hid

den

Con

stan

t12

.50*

**15

.92*

**11

.76*

**4.

16**

*43

.34*

**29

.40*

**47

.06*

**-1

7.66

***

(0.4

4)(1

.03)

(0.4

1)(1

.10)

(0.7

7)(1

.42)

(0.7

6)(1

.57)

Fee

Indi

cato

r1.

76**

*7.

35**

*0.

946.

41**

*-4

.64*

**3.

15*

-5.2

3***

8.39

***

(0.6

0)(1

.36)

(0.6

7)(1

.45)

(1.1

9)(1

.69)

(1.4

3)(2

.27)

Pric

eIn

dex

16.

84**

*6.

08**

*6.

96**

*-0

.88

39.4

7***

17.8

1***

46.0

2***

-28.

21**

*(1

.11)

(1.8

3)(0

.86)

(1.4

8)(1

.30)

(2.0

8)(1

.23)

(2.3

3)Pr

ice

Inde

x2

14.4

3***

19.2

6***

13.6

4***

5.63

***

42.8

8***

32.1

4***

46.4

4***

-14.

29**

*(0

.77)

(1.7

3)(0

.68)

(1.6

8)(1

.20)

(2.4

6)(1

.07)

(2.5

6)Pr

ice

Inde

x3

20.9

1***

30.3

3***

18.2

9***

12.0

5***

50.7

9***

47.1

8***

49.4

0***

-2.2

2(1

.14)

(2.3

7)(0

.91)

(2.1

8)(1

.52)

(3.0

2)(1

.30)

(3.1

8)Fe

e*

Pric

eIn

dex

13.

47**

*9.

69**

*2.

50**

7.19

***

-5.3

0***

5.87

**-6

.84*

**12

.70*

**(1

.12)

(2.1

6)(1

.00)

(1.9

4)(1

.84)

(2.5

3)(1

.92)

(2.9

3)Fe

e*

Pric

eIn

dex

2-0

.97

4.64

**-1

.93*

6.56

***

-3.6

6**

0.23

-3.5

7*3.

79(1

.12)

(2.3

3)(1

.08)

(2.4

9)(1

.67)

(2.8

6)(1

.91)

(3.8

4)Fe

e*

Pric

eIn

dex

33.

31**

*8.

58**

*2.

66**

*5.

92**

*-3

.85*

*4.

89*

-4.6

8**

9.57

***

(0.5

0)(2

.07)

(0.6

7)(2

.22)

(1.8

6)(2

.58)

(2.2

9)(3

.59)

Abo

veQ

uote

Varia

ble

All

Hid

den

HFT

Hid

den

NH

FTH

idde

nD

iffH

idde

nC

onst

ant

26.9

9***

31.0

5***

23.6

5***

7.40

***

(1.0

4)(2

.18)

(1.1

8)(2

.78)

Fee

Indi

cato

r-4

.03*

**0.

97-6

.29*

**7.

25**

(1.5

1)(2

.56)

(1.8

9)(3

.64)

Pric

eIn

dex

127

.16*

**29

.28*

**23

.78*

**5.

50(1

.63)

(3.2

2)(1

.59)

(3.7

1)Pr

ice

Inde

x2

25.8

1***

30.9

6***

22.5

0***

8.46

***

(1.2

2)(2

.66)

(1.3

7)(3

.20)

Pric

eIn

dex

329

.44*

**37

.58*

**25

.14*

**12

.43*

**(1

.51)

(2.8

4)(1

.61)

(3.3

2)Fe

e*

Pric

eIn

dex

1-9

.01*

**-4

.47

-9.4

6***

4.99

(2.0

1)(4

.42)

(2.4

9)(5

.80)

Fee

*Pr

ice

Inde

x2

-0.4

43.

29-4

.46*

7.76

(2.2

1)(3

.95)

(2.3

8)(5

.19)

Fee

*Pr

ice

Inde

x3

-1.9

74.

73-4

.25*

*8.

98**

(1.5

8)(3

.15)

(2.0

8)(4

.17)

46

Table 7: First Stage Regression for Endogenous HFT ActivityThis table presents first stage regression results for 2SLS regressions for hidden volumes. The 2SLS is meant tocontrol for endogeneity that may arise due to HFT activity. The instrument variable for each stock-day is basedon the runs in process instrument variable utilized in Hasbrouck and Saar (2013). The instrument variable is theaverage percentage of NASDAQ dollar trading volume each day in which HFTs trade for stocks that are in thesame market cap group. The stock for which the IV is being calculated, stocks in the same four digit SIC code,and stocks in the same index, if the stock for which the IV is being calculated is in the S and P 500 or NASDAQ100 indices, are excluded from the average. Instrument variables are also constructed for the average percentageof NASDAQ dollar trading volume each day in which HFTs demand liquidity and for the average percentage ofNASDAQ dollar trading volume each day in which HFTs supply liquidity for stocks that are in the same marketcap group Dependent variables in the first stage regressions are the percentage of NASDAQ dollar trading volumein which HFTs trade, the percentage of NASDAQ dollar trading volume for which HFTs demanded liquidity, andthe percentage of NASDAQ dollar trading volume for which HFTs supplied liquidity. Explanatory variables are theconstructed IVs for the average percentage of NASDAQ dollar trading volume each day in which HFTs trade forstocks that are in the same market cap group, the constructed IVs for the average percentage of NASDAQ dollartrading volume each day in which HFTs demand and supply liquidity, the log of total dollar trading volume reportedby all exchanges, the log of the stock’s closing price, the percentage of total dollar trading volume that is traded onNASDAQ, the stock’s positive abnormal return, the stock’s negative abnormal return, the positive CRSP daily valueweighted market return, the negative CRSP daily value weighted market return, the daily opening value of VIX, thevolatility of 5 minute NBBO midpoint returns, the average depth at the NBBO inside quotes, the average NBBOpercentage spread, the average number of displayed shares added to the NASDAQ limit order book each minutethat improve the best displayed bid or offer, the number of displayed shares added to the book at the best displayedbid or offer, the number of displayed shares added to the book at prices worse than the best displayed bid or offer,the average number of displayed shares canceled from the limit order book each minute at the best displayed bid oroffer, the number of displayed shares canceled from the book at prices worse than the best displayed bid or offer, andthe stock’s probability of informed trading (PIN). The stock’s abnormal return is the difference between the stock’sdaily return and the expected return from a model that is estimated by regressing the daily returns of each stockon a 5 factor model that includes the Carhart 4 factor model and the Pastor-Stambaugh liquidity factor. Abnormalreturns and market returns are separated out into positive and negative returns to account for possible asymmetriceffects of positive and negative information. If the return is positive (negative) on the stock-day, then the positive(negative) return variable is equal to the return value (minus the return value) and the negative (positive) returnis equal to zero. NASDAQ ITCH addition and cancellation variables are normalized by dividing by the averagenumber of shares traded on NASDAQ each minute. All explanatory variables are standardized so the coefficientscan be interpreted as the percentage increase in the use of hidden liquidity for a one standard deviation increasein the explanatory variable. Parenthesis report standard errors double clustered by stock and day. ***, **, and* indicate significance at the 1%, 5%, and 10% level, respectively. The F-statistic reported is for a test on theexcluded instrument in the first stage regression.

47

Table 7: First Stage Regression for Endogenous HFT Activity

(1) (2) (3)VARIABLES HFT Volume % HFT Demand Volume % HFT Supply Volume %IV Alt HFT Volume % 0.36***

(0.04)IV Alt HFT Demand Volume % 0.34*** 0.05*

(0.04) (0.02)IV Alt HFT Supply Volume % 0.07** 0.20***

(0.03) (0.03)Log Daily Trading Volume 0.43*** -0.23*** 0.88***

(0.07) (0.08) (0.07)Log Price -0.07 0.36*** -0.44***

(0.05) (0.04) (0.05)Nasdaq % Dollar Volume -0.01 -0.06* 0.04

(0.03) (0.03) (0.02)Pos Adj Ret -0.09*** -0.10*** -0.06***

(0.02) (0.02) (0.02)Neg Adj Ret -0.13*** -0.12*** -0.09***

(0.02) (0.03) (0.02)Pos Mkt Ret -0.05** -0.03 -0.05***

(0.02) (0.03) (0.02)Neg Mkt Ret -0.06*** -0.06*** -0.04***

(0.01) (0.01) (0.01)Opening VIX -0.01 0.07*** -0.08***

(0.02) (0.02) (0.02)Taq MP Volatility -0.00 0.17*** -0.16***

(0.02) (0.03) (0.02)NBBO Depth 0.05 0.07 0.01

(0.05) (0.05) (0.04)NBBO Spread % 0.05 -0.16*** 0.23***

(0.04) (0.04) (0.05)Shares Add Aggressive -1.06*** -0.85*** -0.92***

(0.19) (0.19) (0.20)Shares Add At Quote -0.64*** -0.49*** -0.58***

(0.13) (0.14) (0.14)Shares Add Above Quote -3.56*** -2.41*** -3.49***

(0.50) (0.55) (0.51)Shares Cancel At Quote 1.16*** 0.89*** 1.04***

(0.21) (0.22) (0.23)Shares Cancel Above Quote 3.79*** 2.67*** 3.61***

(0.51) (0.57) (0.53)PIN -0.08** -0.17*** 0.03

(0.03) (0.04) (0.03)Constant 0.12*** 0.11*** 0.08***

(0.03) (0.04) (0.03)Observations 4,275 4,275 4,275R-square 0.670 0.501 0.709F-stat 86.92 53.53 20.63

48

Table 8: Endogenous Determinants of Hidden VolumeThis table presents analysis for the 2nd stage of a 2SLS regression examining the determinants of the percentageof HFT and NHFT volume that is hidden in the NASDAQ limit order book. The percentage of hidden liquidityis calculated for each stock-day by summing up across all limit order book snapshots the total dollar value (sharestimes price) of hidden liquidity supplied by the trader type in the limit order book and dividing it by the totaldollar value of liquidity (displayed plus hidden) supplied by the trader type.The 2SLS is meant to control for endogeneity that may arise in the percentage of NASDAQ dollar trading volumein which HFTs trade. The instrument variables for each stock-day are based on the runs in process instrumentvariable utilized in Hasbrouck and Saar (2013). The instrument variables used in the first stage are the averagepercentage of NASDAQ dollar trading volume each day in which HFTs trade for stocks that are in the same marketcap group, the average percentage of NASDAQ dollar trading volume for which HFTs demanded liquidity for stocksthat are in the same market cap group, and the average percentage of NASDAQ dollar trading volume for whichHFTs supplied liquidity for stocks that are in the same market cap group. The stock for which the IV is beingcalculated, stocks in the same four digit SIC code, and stocks in the same index, if the stock for which the IVis being calculated is in the S and P 500 or NASDAQ 100 indices, are excluded from the average. Dependentvariables are the percentage of hidden dollar volume for all traders supplying liquidity (All Hidden), the percentageof hidden dollar volume for HFTs supplying liquidity (HFT Hidden), the percentage of hidden dollar volume forNHFTs supplying liquidity (NHFT Hidden), and the difference between the percentage of hidden dollar volume forHFTs supplying liquidity and the percentage of hidden dollar volume for NHFTs supplying liquidity (Diff Hidden).Explanatory variables are the fitted value for the percentage of NASDAQ dollar trading volume in which HFTtrades, the fitted values for the percentage of NASDAQ dollar trading volume in which HFTs demanded liquidity,the fitted values for the percentage of NASDAQ dollar trading volume in which HFTs supplied liquidity, the logof total dollar trading volume reported by all exchanges, the log of the stock’s closing price, the percentage oftotal dollar trading volume that is traded on NASDAQ, the stock’s positive abnormal return, the stock’s negativeabnormal return, the positive CRSP daily value weighted market return, the negative CRSP daily value weightedmarket return, the daily opening value of VIX, the volatility of 5 minute NBBO midpoint returns, the averagedepth at the NBBO inside quotes, the average NBBO percentage spread, the average number of displayed sharesadded to the NASDAQ limit order book each minute that improve the best displayed bid or offer, the number ofdisplayed shares added to the book at the best displayed bid or offer, the number of displayed shares added to thebook at prices worse than the best displayed bid or offer, the average number of displayed shares canceled from thelimit order book each minute at the best displayed bid or offer, the number of displayed shares canceled from thebook at prices worse than the best displayed bid or offer, and the stock’s probability of informed trading (PIN). Thestock’s abnormal return is the difference between the stock’s daily return and the expected return from a modelthat is estimated by regressing the daily returns of each stock on a 5 factor model that includes the Carhart 4factor model and the Pastor-Stambaugh liquidity factor. Abnormal returns and market returns are separated outinto positive and negative returns to account for possible asymmetric effects of positive and negative information.If the return is positive (negative) on the stock-day, then the positive (negative) return variable is equal to thereturn value (minus the return value) and the negative (positive) return is equal to zero. NASDAQ ITCH additionand cancellation variables are normalized by dividing by the average number of shares traded on NASDAQ eachminute. All explanatory variables are standardized so the coefficients can be interpreted as the percentage increasein the use of hidden liquidity for a one standard deviation increase in the explanatory variable. Parenthesis reportstandard errors double clustered by stock and day. ***, **, and * indicate significance at the 1%, 5%, and 10%level, respectively.

49

Tabl

e8:

Endo

geno

usD

eter

min

ants

ofH

idde

nVo

lum

e

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

VAR

IAB

LES

All

Hid

den

HFT

Hid

den

NH

FTH

idde

nD

iffH

idde

nFi

tted

HFT

Volu

me

%-1

2.94

***

-18.

27**

*-1

0.57

***

-7.7

0*(3

.12)

(4.6

5)(2

.78)

(4.2

3)Fi

tted

HFT

Dem

and

Volu

me

%-4

.52*

-15.

38**

*0.

97-1

6.35

***

(2.5

5)(4

.56)

(2.6

6)(5

.17)

Fitt

edH

FTSu

pply

Volu

me

%-1

2.97

***

-3.2

3-1

8.41

***

15.1

8*(4

.50)

(8.2

7)(4

.59)

(9.1

1)Lo

gD

aily

Trad

ing

Volu

me

-1.4

23.

42-9

.15*

*-1

7.38

*3.

0014

.75*

**-1

2.15

***

-32.

13**

*(2

.35)

(4.7

2)(4

.35)

(8.8

9)(1

.99)

(4.6

9)(4

.23)

(9.8

7)Lo

gPr

ice

6.01

***

2.84

15.6

0***

21.0

0***

2.48

***

-5.2

2*13

.13*

**26

.22*

**(1

.28)

(2.7

5)(2

.58)

(4.9

4)(0

.91)

(2.8

4)(2

.38)

(5.4

4)N

asda

q%

Dol

lar

Volu

me

-0.8

4-0

.59

-4.4

6***

-4.9

0***

0.57

1.19

*-5

.03*

**-6

.10*

**(0

.71)

(0.7

3)(1

.08)

(1.1

6)(0

.62)

(0.7

0)(1

.15)

(1.3

6)Po

sA

djR

et0.

040.

10-2

.04*

*-2

.14*

*1.

08**

1.21

**-3

.12*

**-3

.34*

**(0

.53)

(0.5

2)(0

.97)

(0.9

9)(0

.54)

(0.5

5)(1

.02)

(1.0

8)N

egA

djR

et0.

400.

36-1

.76

-1.7

01.

131.

04-2

.90*

*-2

.74*

*(0

.77)

(0.7

5)(1

.29)

(1.3

3)(0

.72)

(0.7

3)(1

.28)

(1.3

7)Po

sM

arke

tR

et-1

.19

-1.1

6-6

.07*

**-6

.13*

**1.

021.

11-7

.09*

**-7

.24*

**(1

.24)

(1.1

3)(1

.83)

(2.0

7)(1

.36)

(1.2

0)(2

.06)

(2.3

9)N

egM

arke

tR

et-0

.57

-0.5

9-1

.55

-1.5

20.

00-0

.03

-1.5

6-1

.49

(0.8

0)(0

.77)

(0.9

8)(0

.99)

(1.0

3)(0

.97)

(1.3

8)(1

.33)

Ope

ning

VIX

0.68

0.08

0.07

1.10

1.19

-0.2

7-1

.12

1.37

(0.7

7)(0

.93)

(1.3

3)(1

.29)

(0.7

9)(0

.96)

(1.4

4)(1

.36)

Taq

MP

Vola

tility

2.13

***

0.81

7.29

***

9.54

***

-0.0

7-3

.28*

**7.

36**

*12

.82*

**(0

.79)

(1.1

9)(1

.34)

(2.1

7)(0

.89)

(1.2

5)(1

.63)

(2.5

3)N

BB

OD

epth

0.97

0.82

2.86

3.11

0.44

0.08

2.42

3.03

**(1

.16)

(1.2

5)(2

.28)

(2.1

4)(0

.76)

(0.9

9)(1

.74)

(1.5

3)N

BB

OSp

read

%-2

.11*

*-0

.57

-3.9

5**

-6.5

8**

-0.3

73.

38**

-3.5

8*-9

.96*

**(0

.91)

(1.4

6)(1

.86)

(2.6

6)(0

.93)

(1.6

1)(2

.00)

(3.0

9)Sh

ares

Add

Agg

ress

ive

5.92

3.09

-16.

86-1

2.05

12.5

5***

5.69

-29.

41**

*-1

7.74

(5.7

2)(6

.37)

(10.

90)

(12.

45)

(4.8

0)(5

.96)

(10.

76)

(13.

32)

Shar

esA

ddA

tQ

uote

3.79

1.82

-11.

63-8

.27

9.39

***

4.59

-21.

02**

*-1

2.86

(4.0

1)(4

.37)

(7.7

9)(8

.89)

(3.3

7)(4

.13)

(7.8

5)(9

.71)

Shar

esA

ddA

bove

Quo

te-0

.12

-12.

55-6

1.45

**-4

0.27

22.9

6-7

.27

-84.

41**

*-3

3.00

(16.

54)

(19.

97)

(29.

57)

(37.

83)

(14.

39)

(19.

05)

(29.

11)

(40.

58)

Shar

esC

ance

lAt

Quo

te-5

.13

-1.6

921

.55*

15.6

9-1

4.45

***

-6.0

936

.00*

**21

.79

(6.6

7)(7

.45)

(12.

93)

(14.

79)

(5.5

8)(7

.00)

(12.

96)

(15.

96)

Shar

esC

ance

lAbo

veQ

uote

-2.0

710

.25

59.3

9*38

.41

-23.

466.

4882

.85*

**31

.94

(17.

09)

(20.

43)

(30.

40)

(38.

53)

(14.

95)

(19.

56)

(30.

04)

(41.

47)

PIN

-0.2

20.

420.

34-0

.76

0.55

2.11

*-0

.21

-2.8

7(0

.97)

(1.1

1)(1

.37)

(1.9

0)(0

.95)

(1.1

0)(1

.51)

(2.1

2)C

onst

ant

29.4

0***

29.3

9***

34.8

8***

34.9

0***

25.6

9***

25.6

6***

9.19

***

9.24

***

(1.0

9)(1

.08)

(2.0

1)(2

.09)

(1.2

1)(1

.23)

(2.4

0)(2

.58)

Obs

erva

tions

4,27

54,

275

4,27

54,

275

4,27

54,

275

4,27

54,

275

R-s

quar

e0.

260

0.24

30.

282

0.24

20.

158

0.01

770.

160

-0.0

0782

50

Table 9: Intraday Determinants of Changes in Hidden VolumeThis table presents analysis for OLS and 2SLS regressions examining the intraday determinants of changes in thepercentage of HFT and NHFT volume that is hidden in the NASDAQ limit order book. The percentage of hiddenliquidity is calculated for each one minute limit order book snap shot by summing up the number of hidden shareson the bid and offer side of the limit order book supplied by the trader type and dividing it by the total shares ofliquidity (displayed plus hidden) supplied by the trader type.The 2SLS is meant to control for endogeneity that may arise in the percentage of NASDAQ dollar trading volumein which HFTs trade. The instrument variables are based on the runs in process instrument variable utilized inHasbrouck and Saar (2013). The instrument variables used in the first stage are the change in the average NASDAQdollar trading volume for which HFTs demanded liquidity for stocks that are in the same market cap group and thechange in the average NASDAQ dollar trading volume for which HFTs supplied liquidity for stocks that are in thesame market cap group. The stock for which the IV is being calculated, stocks in the same four digit SIC code, andstocks in the same index, if the stock for which the IV is being calculated is in the S and P 500 or NASDAQ 100indices, are excluded from the average. Dependent variables are the change in the percentage of hidden shares inthe limit order book for all traders supplying liquidity (Hidden), the change in the percentage of hidden shares forHFTs in the order book (HFT Hidden), and the change in the percentage of hidden shares for NHFTs in the limitorder book (NHFT Hidden). Explanatory variables are the one minute change in the percentage of dollar tradingvolume for which HFTs demanded and supplied liquidity and their fitted values for the 2SLS regressions. Otherexplanatory variables are the change in the total trading volume of the stock across all US markets, the change inthe percent of total stock trading volume that is traded on NASDAQ, the change in the total displayed depth atthe best displayed quotes on NASDAQ, the change in the total displayed depth above the best displayed quotes onNASDAQ, the change in displayed shares added to the NASDAQ limit order book that improve the best displayedbid or offer, the change in shares added at the best displayed bid or offer, the change in shares added at pricesworse than the best displayed bid or offer, the change in the shares canceled from the limit order book at the bestdisplayed bid or offer, the change in shares canceled at prices worse than the best displayed bid or offer, the changein the five minute midpoint return volatility, the positive quote midpoint return, the negative quote midpoint return,the change in the NBBO percentage spread, and the change in the NASDAQ displayed percentage spread. Thepositive (negative) quote midpoint return equals the one minute percentage change in the NBBO midpoint (minusthe one minute percentage change in the NBBO midpoint) if the midpoint return is positive (negative) and zerootherwise. All observations are at the minute interval and all variables are calculated as sums over the one minuteperiod between limit order book snapshots. Before differencing, all variables are normalized so that each stock-dayhas a mean value of 0 and standard deviation of 1. Parenthesis report standard errors double clustered by stockand day. ***, **, and * indicate significance at the 1%, 5%, and 10% level, respectively.

51

Tabl

e9:

Intr

aday

Det

erm

inan

tsof

Cha

nges

inH

idde

nVo

lum

e

OLS

2St

age

LS(1

)(2

)(3

)(4

)(5

)(6

)VA

RIA

BLE

SH

idde

nH

FTH

idde

nN

HFT

Hid

den

Hid

den

HFT

Hid

den

NH

FTH

idde

nH

FTD

eman

dVo

lum

e%

-0.0

018*

*0.

0041

***

-0.0

030*

**(0

.000

7)(0

.000

9)(0

.000

6)H

FTSu

pply

Volu

me

%0.

0007

-0.0

023*

*0.

0015

*(0

.000

9)(0

.001

1)(0

.000

9)Fi

tted

HFT

Dem

and

Volu

me

%-0

.029

60.

0418

-0.0

596

(0.0

394)

(0.0

282)

(0.0

384)

Fitt

edH

FTSu

pply

Volu

me

%-0

.534

9***

-0.1

368

-0.5

396*

**(0

.199

1)(0

.172

9)(0

.198

9)M

arke

tTr

adin

gVo

lum

e-0

.002

3**

0.00

12-0

.003

1***

-0.0

289*

*-0

.003

0-0

.031

5**

(0.0

012)

(0.0

015)

(0.0

011)

(0.0

126)

(0.0

098)

(0.0

124)

NA

SDA

Q%

ofTr

adin

gVo

lum

e-0

.006

0***

-0.0

006

-0.0

069*

**-0

.064

4***

-0.0

141

-0.0

667*

**(0

.001

6)(0

.001

3)(0

.001

4)(0

.023

7)(0

.019

4)(0

.023

6)N

ASD

AQ

Disp

laye

dD

epth

At

Quo

te-0

.034

8***

-0.0

323*

**-0

.026

8***

-0.0

360*

**-0

.031

6***

-0.0

286*

**(0

.004

1)(0

.003

1)(0

.002

2)(0

.004

1)(0

.003

3)(0

.002

2)N

ASD

AQ

Disp

laye

dD

epth

Abo

veQ

uote

-0.2

343*

**-0

.139

2***

-0.1

678*

**-0

.230

8***

-0.1

381*

**-0

.164

4***

(0.0

172)

(0.0

108)

(0.0

087)

(0.0

171)

(0.0

105)

(0.0

088)

Shar

esA

ddA

ggre

ssiv

e-0

.018

3***

-0.0

012

-0.0

209*

**-0

.019

7***

-0.0

020

-0.0

221*

**(0

.002

1)(0

.002

1)(0

.001

9)(0

.002

8)(0

.002

3)(0

.002

5)Sh

ares

Add

At

Quo

te-0

.012

7***

0.00

08-0

.017

3***

0.00

780.

0043

0.00

45(0

.003

4)(0

.003

0)(0

.002

6)(0

.010

4)(0

.007

6)(0

.010

2)Sh

ares

Add

Abo

veQ

uote

-0.0

292*

**0.

0143

***

-0.0

432*

**-0

.027

8***

0.01

49**

*-0

.041

9***

(0.0

072)

(0.0

048)

(0.0

051)

(0.0

077)

(0.0

050)

(0.0

057)

Shar

esC

ance

lAt

Quo

te0.

0164

***

-0.0

008

0.02

19**

*0.

0158

***

-0.0

006

0.02

10**

*(0

.003

7)(0

.003

0)(0

.002

7)(0

.004

1)(0

.003

3)(0

.003

4)Sh

ares

Can

celA

bove

Quo

te0.

0210

***

-0.0

109*

**0.

0320

***

0.03

07**

*-0

.010

7*0.

0431

***

(0.0

059)

(0.0

041)

(0.0

045)

(0.0

081)

(0.0

055)

(0.0

073)

5m

inut

eM

Pvo

latil

ity0.

0039

**0.

0067

***

0.00

41**

0.01

51**

0.00

770.

0166

***

(0.0

015)

(0.0

023)

(0.0

018)

(0.0

062)

(0.0

048)

(0.0

063)

Pos

Mid

poin

tR

et0.

0097

***

0.01

75**

*0.

0053

**-0

.005

20.

0135

**-0

.009

7(0

.002

7)(0

.002

7)(0

.002

4)(0

.006

9)(0

.005

5)(0

.007

0)N

egM

idpo

int

Ret

0.00

63**

0.01

19**

*0.

0030

-0.0

106

0.00

75-0

.013

9*(0

.002

5)(0

.002

6)(0

.002

3)(0

.007

3)(0

.006

0)(0

.007

5)N

BB

OPe

rcen

tSp

read

0.01

28**

*-0

.027

1***

0.01

62**

*0.

0196

***

-0.0

259*

**0.

0233

***

(0.0

039)

(0.0

049)

(0.0

027)

(0.0

048)

(0.0

060)

(0.0

035)

NA

SDA

QD

ispla

yed

Perc

ent

Spre

ad0.

0442

***

0.15

70**

*0.

0191

***

0.03

99**

*0.

1550

***

0.01

54**

*(0

.005

9)(0

.008

9)(0

.003

9)(0

.006

4)(0

.008

9)(0

.004

6)C

onst

ant

-0.0

032*

-0.0

094*

**-0

.002

00.

0086

*-0

.006

00.

0096

*(0

.001

8)(0

.001

7)(0

.001

3)(0

.004

9)(0

.004

3)(0

.004

9)O

bser

vatio

ns1,

318,

419

1,30

0,89

01,

318,

390

1,31

8,41

91,

300,

890

1,31

8,39

0R

-squ

ared

0.05

640.

0358

0.03

07

52

Table 10: The Permanent Price Impact of Hidden and Displayed LiquidityThis table presents analysis comparing the permanent price impact of trades in which hidden or displayed liquidityis supplied by an HFT or NHFT. The table reports the average long-run (10 events in the future) impulse responsefunctions for trades in which HFTs and NHFTs supply liquidity using hidden and displayed limit orders. A highervalue indicates the trade faces less adverse selection. The qs are defined separately as the net dollar value, in$10, 000s, of hidden or displayed liquidity supplied in trades by HFTs or NHFTs. Liquidity supplied using buyorders is positive and liquidity supplied using sell orders in negative. Coefficients are reported in units of basispoints per $10, 000. The first row reports results for NBBO midpoint returns over one second intervals. Theqs are the net dollar values of all liquidity supplied in transactions during each second. The second row reportsresults for trade by trade changes in the midpoint of the NASDAQ displayed BBO. The qs are the dollar valuesof the liquidity supplied in each transaction. Impulse responses are calculated for each stock-day. The left handside of the table reports the average long-run Impulse responses across all stock-day observations separately forhidden and displayed liquidity supplied by HFTs and NHFTs. The right hand side of the table reports the averagedifferences between the long-run impulse responses of transactions in which HFTs/NHFTs supplied liquidity usinghidden orders and transactions in which they used displayed orders (HFT and NHFT Diff). It also reportsthe average differences between the long-run impulse responses of transactions in which displayed/hidden liquidityis supplied by HFTs and transactions in which displayed/hidden liquidity is supplied by NHFTs (Display andHidden Diff). The right most column reports the average difference between the differences in HFT hidden anddisplayed long-run Impulse responses and the differences in NHFT displayed long-run Impulse responses (HFTDiff - NHFT Diff). The t-statistics reported in parenthesis are calculated using standard errors double clusteredby stock and day, using the techniques of Thompson (2011).

HFT HFT NHFT NHFT HFT NHFT Display Hidden HFT Diff -Display Hidden Display Hidden Diff Diff Diff Diff NHFT Diff

NBBO Midpoint -7.52 -8.23 -3.99 -1.00 -0.71 2.99 -3.52 -7.23 -3.71(-7.45) (-6.24) (-7.98) (-5.31) (-1.05) (8.61) (-6.53) (-6.16) (-4.42)

NASDAQ Midpoint -16.43 -19.71 -9.89 -2.62 -3.28 7.26 -6.54 -17.09 -10.55(-6.22) (-3.58) (-7.44) (-3.28) (-0.83) (6.93) (-3.98) (-3.30) (-2.35)

53

Table 11: Endogenous Determinants of the Permanent Price Impact of Hidden and Displayed LiquidityThis table presents analysis for the 2nd stage of a 2SLS regression examining the permanent price impact of tradesin which hidden or displayed liquidity is supplied by an HFT or NHFT. The dependent variables are the averagelong-run (10 events in the future) impulse response functions for trades in which HFTs and NHFTs supply liquidityusing hidden and displayed limit orders, in units of basis points per $10, 000 trading volume. A higher value indicatesthe trade faces less adverse selection. The results are reported for NBBO midpoint returns over one second intervals.The 2SLS is meant to control for endogeneity that may arise in the percentage of NASDAQ dollar trading volumein which HFTs trade. The instrument variables for each stock-day are based on the runs in process instrumentvariable utilized in Hasbrouck and Saar (2013). The instrument variables used in the first stage are the averagepercentage of NASDAQ dollar trading volume each day in which HFTs trade for stocks that are in the same marketcap group, the average percentage of NASDAQ dollar trading volume for which HFTs demanded liquidity for stocksthat are in the same market cap group, and the average percentage of NASDAQ dollar trading volume for whichHFTs supplied liquidity for stocks that are in the same market cap group. The stock for which the IV is beingcalculated, stocks in the same four digit SIC code, and stocks in the same index, if the stock for which the IV is beingcalculated is in the S and P 500 or NASDAQ 100 indices, are excluded from the average. In Panel A the dependentvariables are the permanent price impact that HFTs and NHFTs face in trades where they supply liquidity usinghidden and displayed orders. In Panel B the dependent variables are the differences between the long-run impulseresponses of transactions in which HFTs/NHFTs supplied liquidity using hidden orders and transactions in whichthey used displayed orders (HFT and NHFT Diff) and the differences between the long-run impulse responses oftransactions in which displayed/hidden liquidity is supplied by HFTs and transactions in which displayed/hiddenliquidity is supplied by NHFTs (Display and Hidden Diff).Explanatory variables are the fitted value for the percentage of NASDAQ dollar trading volume in which HFTtrades, the fitted values for the percentage of NASDAQ dollar trading volume in which HFTs demanded liquidity,the fitted values for the percentage of NASDAQ dollar trading volume in which HFTs supplied liquidity, the logof total dollar trading volume reported by all exchanges, the log of the stock’s closing price, the percentage oftotal dollar trading volume that is traded on NASDAQ, the stock’s positive abnormal return, the stock’s negativeabnormal return, the positive CRSP daily value weighted market return, the negative CRSP daily value weightedmarket return, the daily opening value of VIX, the volatility of 5 minute NBBO midpoint returns, the averagedepth at the NBBO inside quotes, the average NBBO percentage spread, the average number of displayed sharesadded to the NASDAQ limit order book each minute that improve the best displayed bid or offer, the number ofdisplayed shares added to the book at the best displayed bid or offer, the number of displayed shares added to thebook at prices worse than the best displayed bid or offer, the average number of displayed shares canceled fromthe limit order book each minute at the best displayed bid or offer, the number of displayed shares canceled fromthe book at prices worse than the best displayed bid or offer, the stock’s probability of informed trading (PIN),and a binary indicator that equals 1 if the liquidity rebates for displayed and nondisplayed liquidity are equal. Thestock’s abnormal return is the difference between the stock’s daily return and the expected return from a modelthat is estimated by regressing the daily returns of each stock on a 5 factor model that includes the Carhart 4factor model and the Pastor-Stambaugh liquidity factor. Abnormal returns and market returns are separated outinto positive and negative returns to account for possible asymmetric effects of positive and negative information.If the return is positive (negative) on the stock-day, then the positive (negative) return variable is equal to thereturn value (minus the return value) and the negative (positive) return is equal to zero. NASDAQ ITCH additionand cancellation variables are normalized by dividing by the average number of shares traded on NASDAQ eachminute. All explanatory variables are standardized so the coefficients can be interpreted as the percentage increasein the use of hidden liquidity for a one standard deviation increase in the explanatory variable. Parenthesis reportstandard errors double clustered by stock and day. ***, **, and * indicate significance at the 1%, 5%, and 10%level, respectively.

54

Tabl

e11

:E

ndog

enou

sD

eter

min

ants

ofth

ePe

rman

ent

Pric

eIm

pact

ofH

idde

nan

dD

ispl

ayed

Liqu

idity

:Pa

nelA

HFT

and

NH

FTLi

quid

ity

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

VAR

IAB

LES

HFT

Disp

lay

HFT

Hid

den

NH

FTD

ispla

yN

HFT

Hid

den

Fitt

edH

FTVo

lum

e%

-4.4

5***

-8.1

2**

-1.0

5-1

.41*

(1.6

6)(3

.44)

(0.6

6)(0

.73)

Fitt

edH

FTD

eman

dVo

lum

e%

-4.1

3**

-9.0

0**

-1.0

6-0

.04

(1.7

8)(4

.26)

(0.7

4)(0

.66)

Fitt

edH

FTSu

pply

Volu

me

%-0

.62

0.88

-0.0

3-1

.94*

*(2

.87)

(4.1

9)(1

.10)

(0.8

8)Lo

gD

aily

Trad

ing

Volu

me

6.45

***

4.22

6.50

***

0.36

2.73

***

2.08

*1.

19**

2.27

**(1

.27)

(3.0

1)(2

.30)

(4.9

9)(0

.55)

(1.2

0)(0

.49)

(0.9

7)Lo

gPr

ice

2.58

***

4.19

**4.

43**

*8.

85**

1.26

***

1.73

***

0.21

-0.5

7(0

.46)

(1.6

6)(1

.24)

(3.6

5)(0

.18)

(0.6

4)(0

.17)

(0.6

0)N

asda

q%

Dol

lar

Volu

me

1.45

***

1.35

***

2.07

**1.

780.

98**

*0.

94**

*0.

54**

*0.

60**

*(0

.36)

(0.3

9)(1

.00)

(1.1

0)(0

.14)

(0.1

5)(0

.15)

(0.1

6)Po

sA

djR

et-1

.40*

-1.4

7**

-1.3

7-1

.56

-0.3

6-0

.38

-0.0

8-0

.05

(0.7

2)(0

.72)

(1.2

5)(1

.21)

(0.2

3)(0

.23)

(0.2

9)(0

.29)

Neg

Adj

Ret

-1.8

2**

-1.8

6**

-3.0

7-3

.16

-0.6

3*-0

.64*

-0.0

10.

00(0

.88)

(0.8

8)(1

.99)

(2.0

1)(0

.37)

(0.3

7)(0

.42)

(0.4

2)Po

sM

ktR

et-1

.84*

*-1

.90*

**1.

591.

44-0

.17

-0.1

9-0

.15

-0.1

3(0

.76)

(0.7

2)(1

.89)

(1.8

5)(0

.24)

(0.2

4)(0

.29)

(0.2

9)N

egM

ktR

et-1

.09*

**-1

.11*

**0.

330.

29-0

.23*

-0.2

4*-0

.08

-0.0

7(0

.37)

(0.3

7)(0

.98)

(0.9

8)(0

.14)

(0.1

4)(0

.20)

(0.2

0)O

peni

ngV

IX-0

.34

-0.1

2-2

.37*

**-1

.74*

*-0

.00

0.07

-0.0

0-0

.11

(0.3

5)(0

.35)

(0.8

2)(0

.86)

(0.1

2)(0

.14)

(0.1

4)(0

.13)

Taq

MP

Vola

tility

-2.3

3***

-1.6

7*-2

.02*

-0.2

2-1

.30*

**-1

.11*

**-0

.40

-0.7

1*(0

.49)

(1.0

1)(1

.16)

(1.9

1)(0

.21)

(0.3

8)(0

.27)

(0.4

0)N

BB

OD

epth

0.82

**0.

94**

*2.

23**

2.56

***

0.14

0.18

0.20

0.14

(0.3

9)(0

.33)

(0.8

8)(0

.96)

(0.1

3)(0

.13)

(0.1

6)(0

.18)

NB

BO

Spre

ad%

-6.0

8***

-6.8

7***

-9.3

6***

-11.

53**

*-3

.47*

**-3

.70*

**-1

.63*

**-1

.25*

*(1

.08)

(1.4

4)(2

.12)

(2.9

1)(0

.47)

(0.5

8)(0

.54)

(0.5

4)Sh

ares

Add

Agg

ress

ive

-3.2

2-2

.04

-1.7

81.

472.

34**

2.69

***

-2.1

4*-2

.71*

*(2

.68)

(2.9

5)(6

.73)

(7.1

3)(0

.93)

(1.0

4)(1

.09)

(1.2

0)Sh

ares

Add

At

Quo

te-1

.50

-0.6

02.

184.

642.

36**

*2.

62**

*-1

.14

-1.5

7**

(1.7

6)(1

.94)

(4.3

8)(4

.90)

(0.6

9)(0

.72)

(0.7

1)(0

.78)

Shar

esA

ddA

bove

Quo

te-3

5.90

***

-30.

44**

*-4

4.92

***

-29.

91-5

.19*

-3.6

1-7

.48*

*-1

0.11

**(8

.27)

(11.

71)

(15.

97)

(20.

02)

(3.0

9)(4

.22)

(3.7

4)(4

.62)

Shar

esC

ance

lAt

Quo

te2.

460.

96-1

.87

-6.0

2-3

.73*

**-4

.16*

**2.

112.

84**

(2.9

6)(3

.31)

(7.9

0)(8

.50)

(1.1

6)(1

.25)

(1.3

2)(1

.45)

Shar

esC

ance

lAbo

veQ

uote

38.8

2***

33.5

1***

49.4

6***

34.8

3*6.

14*

4.60

8.43

**11

.01*

*(8

.68)

(11.

92)

(16.

69)

(20.

46)

(3.2

4)(4

.31)

(3.9

1)(4

.75)

PIN

0.03

-0.3

3-0

.26

-1.2

60.

50**

*0.

39**

-0.1

20.

05(0

.65)

(0.6

5)(1

.11)

(1.4

2)(0

.16)

(0.1

9)(0

.29)

(0.3

3)H

idde

nFe

e-2

.59*

**-2

.94*

**-3

.83*

*-4

.78*

*-0

.27

-0.3

7-0

.52

-0.3

5(0

.83)

(0.8

4)(1

.70)

(2.0

1)(0

.31)

(0.3

4)(0

.39)

(0.4

2)C

onst

ant

-5.6

7***

-5.5

4***

-7.7

4***

-7.3

8***

-4.0

1***

-3.9

7***

-0.9

5**

-1.0

2***

(0.7

4)(0

.72)

(1.8

1)(1

.91)

(0.2

9)(0

.30)

(0.3

8)(0

.37)

Obs

erva

tions

3,87

93,

879

3,87

93,

879

3,87

93,

879

3,87

93,

879

R-s

quar

e0.

334

0.33

20.

102

0.09

490.

530

0.52

60.

0556

0.04

94

55

Tabl

e11

:E

ndog

enou

sD

eter

min

ants

ofth

ePe

rman

ent

Pric

eIm

pact

ofH

idde

nan

dD

ispl

ayed

Liqu

idity

:Pa

nelB

Diff

eren

ces

HFT

and

NH

FTLi

quid

ity

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

VAR

IAB

LES

HFT

Diff

NH

FTD

iffD

ispla

yD

iffH

idde

nD

iffFi

tted

HFT

Volu

me

%-3

.66

-0.3

6-3

.41*

*-6

.71*

*(3

.46)

(0.8

2)(1

.42)

(3.3

0)Fi

tted

HFT

Dem

and

Volu

me

%-4

.87

1.01

-3.0

7**

-8.9

5**

(4.1

3)(0

.74)

(1.2

6)(4

.17)

Fitt

edH

FTSu

pply

Volu

me

%1.

50-1

.91*

*-0

.60

2.82

(3.4

9)(0

.92)

(2.0

8)(3

.88)

Log

Dai

lyTr

adin

gVo

lum

e0.

06-3

.86

-1.5

4**

0.19

3.72

***

2.13

5.32

**-1

.91

(2.1

7)(4

.06)

(0.6

1)(1

.09)

(1.0

4)(2

.15)

(2.1

9)(4

.67)

Log

Pric

e1.

854.

66-1

.06*

**-2

.30*

**1.

32**

*2.

46**

4.23

***

9.42

***

(1.2

5)(3

.40)

(0.2

5)(0

.62)

(0.3

8)(1

.20)

(1.2

6)(3

.57)

Nas

daq

%D

olla

rVo

lum

e0.

610.

43-0

.43*

*-0

.35*

0.48

0.40

1.52

1.18

(0.8

8)(0

.94)

(0.1

9)(0

.20)

(0.2

9)(0

.32)

(0.9

8)(1

.07)

Pos

Adj

Ret

0.02

-0.1

00.

280.

33-1

.04

-1.0

9-1

.29

-1.5

2(0

.97)

(0.9

4)(0

.38)

(0.3

8)(0

.68)

(0.6

9)(1

.26)

(1.2

2)N

egA

djR

et-1

.24

-1.3

00.

61*

0.64

*-1

.20*

-1.2

2*-3

.05

-3.1

6(2

.06)

(2.0

7)(0

.36)

(0.3

7)(0

.71)

(0.7

0)(2

.01)

(2.0

3)Po

sM

ktR

et3.

43*

3.34

*0.

020.

06-1

.67*

*-1

.71*

**1.

751.

57(1

.86)

(1.8

8)(0

.25)

(0.2

6)(0

.65)

(0.6

2)(1

.77)

(1.7

0)N

egM

ktR

et1.

421.

390.

150.

16-0

.86*

**-0

.87*

**0.

410.

36(1

.01)

(1.0

1)(0

.21)

(0.2

3)(0

.32)

(0.3

1)(0

.97)

(0.9

6)O

peni

ngV

IX-2

.03*

**-1

.63*

*0.

00-0

.18

-0.3

4-0

.18

-2.3

7***

-1.6

3**

(0.6

7)(0

.71)

(0.1

5)(0

.15)

(0.2

7)(0

.26)

(0.7

9)(0

.82)

Taq

MP

Vola

tility

0.30

1.45

0.90

**0.

39-1

.03*

*-0

.56

-1.6

30.

50(1

.14)

(1.5

6)(0

.35)

(0.4

5)(0

.49)

(0.8

4)(1

.07)

(1.7

0)N

BB

OD

epth

1.41

*1.

62*

0.06

-0.0

30.

67**

0.76

***

2.02

**2.

42**

*(0

.80)

(0.9

1)(0

.19)

(0.2

1)(0

.33)

(0.2

9)(0

.83)

(0.9

2)N

BB

OSp

read

%-3

.28*

-4.6

6*1.

84**

*2.

45**

*-2

.61*

**-3

.17*

**-7

.72*

**-1

0.28

***

(1.9

7)(2

.48)

(0.4

7)(0

.54)

(0.8

1)(1

.00)

(2.0

5)(2

.80)

Shar

esA

ddA

ggre

ssiv

e1.

443.

51-4

.48*

**-5

.39*

**-5

.57*

*-4

.73*

0.35

4.18

(5.8

3)(6

.24)

(1.3

9)(1

.53)

(2.3

5)(2

.56)

(6.8

0)(7

.38)

Shar

esA

ddA

tQ

uote

3.67

5.24

-3.5

0***

-4.1

9***

-3.8

5**

-3.2

2*3.

326.

21(3

.89)

(4.4

1)(0

.96)

(1.0

7)(1

.52)

(1.7

0)(4

.37)

(5.0

7)Sh

ares

Add

Abo

veQ

uote

-9.0

20.

53-2

.28

-6.5

0-3

0.71

***

-26.

83**

*-3

7.45

**-1

9.80

(14.

55)

(17.

47)

(3.8

7)(4

.63)

(7.5

9)(9

.77)

(16.

07)

(20.

07)

Shar

esC

ance

lAt

Quo

te-4

.34

-6.9

75.

83**

*7.

00**

*6.

19**

5.12

*-3

.98

-8.8

5(6

.92)

(7.5

3)(1

.71)

(1.9

0)(2

.58)

(2.9

0)(7

.94)

(8.8

0)Sh

ares

Can

celA

bove

Quo

te10

.63

1.32

2.30

6.41

32.6

9***

28.9

1***

41.0

2**

23.8

2(1

5.22

)(1

7.87

)(4

.08)

(4.8

0)(7

.95)

(10.

00)

(16.

77)

(20.

51)

PIN

-0.2

9-0

.93

-0.6

2*-0

.34

-0.4

7-0

.73

-0.1

4-1

.31

(1.1

9)(1

.48)

(0.3

2)(0

.35)

(0.6

2)(0

.60)

(1.1

3)(1

.44)

Hid

den

Fee

-1.2

4-1

.85

-0.2

50.

02-2

.32*

**-2

.57*

**-3

.31*

*-4

.43*

*(1

.85)

(2.2

1)(0

.48)

(0.5

1)(0

.77)

(0.7

5)(1

.61)

(1.9

5)C

onst

ant

-2.0

7-1

.84

3.06

***

2.95

***

-1.6

6**

-1.5

7**

-6.7

9***

-6.3

6***

(1.9

7)(2

.08)

(0.3

8)(0

.37)

(0.7

3)(0

.73)

(1.7

9)(1

.86)

Obs

erva

tions

3,87

93,

879

3,87

93,

879

3,87

93,

879

3,87

93,

879

R-s

quar

e0.

0083

60.

0047

30.

175

0.15

90.

104

0.10

40.

0788

0.06

93

56

Table 12: Liquidity Supplying Revenues: cents per shareThis table presents analysis on HFTs’ and NHFTs’ trading revenue from supplying liquidity using hidden anddisplayed shares. Revenue is calculated for each stock-day by subtracting the total dollar value of all trades onNASDAQ in which a trader supplied liquidity using a buy order from the total dollar value of all trades in whichthey supplied liquidity using a sell order. Any remaining inventory the trader possesses at the end of the trading dayis assumed to be bought or sold at the closing midpoint price. Revenues are calculated separately for transactionsbased on trader type (HFT/NHFT) and whether the liquidity was supplied using hidden or displayed orders. Netrevenues are then divided by the maximum of the total shares bought or sold each day, so revenue is given in unitsof cents per share traded. The stock-day averages for HFT and NHFT, hidden and displayed orders are reported.The first row reports results for revenues without any rebates from NASDAQ for supplying liquidity. The secondrow reports results for revenues with rebates from NASDAQ for supplying liquidity. The right hand side of thetable reports the average differences between the revenues for transactions in which HFTs/NHFTs supplied liquidityusing hidden orders and transactions in which they used displayed orders (HFT and NHFT Diff). It also reportsthe average differences between revenues of transactions in which displayed/hidden liquidity is supplied by HFTsand transactions in which displayed/hidden liquidity is supplied by NHFTs (Display and Hidden Diff). Thet-statistics reported in parenthesis are calculated using standard errors double clustered by stock and day, using thetechniques of Thompson (2011).

HFT HFT HFT NHFT NHFT NHFT HFT NHFT Display HiddenDisplay Hidden All Display Hidden All Diff Diff Diff Diff

Without Rebates -0.292 1.139 0.149 -0.769 1.281 -0.292 1.316 2.026 0.422 -0.024(-0.57) (2.53) (0.44) (-1.79) (2.24) (-0.84) (1.62) (2.73) (0.94) (-0.04)

With Rebates 0.181 1.418 0.606 -0.278 1.559 0.168 1.118 1.813 0.404 -0.026(0.35) (3.15) (1.77) (-0.65) (2.71) (0.48) (1.37) (2.43) (0.90) (-0.04)

57

Table 13: Probability Score of HFTs Trading Against HiddenLiquidityThis tables reports the frequencies of different types of deman-der - liquidity supply type trade pairs to see if the strategiesof HFT liquidity demanders interact more with hidden liquid-ity than the strategies of NHFT liquidity demanders. It uses amodel from Chabound et al. (2014) to examine whether the fre-quency of HFT demand - hidden supply or NHFT demand - hid-den supply differs from theoretical probabilities generated basedon the assumption that traders’ activities are independent. Thetable reports Rhidden, a difference in the ratio of probabilitiesin which HFT and NHFT liquidity demanders interact with dis-played and hidden liquidity. Rhidden will equal 0 if HFTs takeliquidity from hidden orders at the same rate that NHFTs takeliquidity from hidden orders, therefore their interactions withhidden and displayed orders would be independent. If Rhiddenis less than 0, then either HFTs are better at executing againsthidden liquidity than by chance or NHFTs are better at execut-ing against displayed liquidity than by chance. The table alsoreports results for RhiddenHFT and RhiddenNHFT, which aresimilar measures analyzing the interaction of HFT and NHFTliquidity demand with hidden liquidity supplied by HFTs andNHFTs, respectively. The ratios are calculated for each stock-day by counting the frequencies of each type of transactionsthat occur during the stock-day. The table reports the averagefrom the pooled sample of stock-days. The t-statistics reportedare calculated using standard errors double clustered by stockand day, using the techniques of Thompson (2011). The tablealso reports the percentage of stock-days for which the value isgreater than 0 and the percentage of stock-days for which thevalues are not-missing. A missing value would be generated ifone of the types transactions used in the calculation did notoccur during the stock-day.

Percent obs Percent obsVariable Mean t-stat greater 0 Non-missingRhidden -0.293 -5.13 39.8% 98.0%

RhiddenHFT -0.110 -1.82 48.2% 75.9%RhiddenNHFT -0.324 -6.38 34.2% 97.3%

58

Figure 1: Percentage of Depth Hidden in NASDAQ Limit Order Book During the Trading DayThis figure plots the percent of NASDAQ limit order book depth that is hidden and the percentage oflimit order book depth supplied by HFTs and NHFTs that is hidden throughout the day. Hidden ispercentage of shares in the 10 best prices on the bid and ask side of the NASDAQ limit order that ishidden during each half-hour interval. HFT and NHFT Hidden are the percentage of shares supplied byHFTs or NHFTs in the NASDAQ limit order book that are hidden during each half-hour interval. Hiddenpercentages are calculated by dividing the sum of all hidden shares in the limit order book during eachhalf-hour interval by the sum of all shares, hidden and displayed, in the limit order book. Percentages arefirst calculated for each half-hour interval during each stock-day. For each stock, each half-hour intervalis then averaged across all days. The figure plots the cross-sectional mean from stock averages for eachhalf-hour intervals.,

59

Appendix A

Supplemental Tables

60

Table A.1: Determinants of Hidden Volume in the Limit Order BookThis table presents analysis using linear regression models to examine the determinants of the percentage of HFTand NHFT volume that is hidden in the NASDAQ limit order book. Nasdaq Quote information from the 10 bestprice levels on the bid and ask side of the limit order book are aggregated into the following price groups: at pricesinside the best displayed quotes, prices at and inside the best displayed quotes, and prices above the best displayedquotes (Above). The percentage of hidden liquidity for each trader type in each price group is calculated for eachstock-day by summing up across all limit order book snapshots the total dollar value (shares times price) of hiddenliquidity supplied by the trader type in the limit order book price group and dividing it by the total dollar valueof liquidity (displayed plus hidden) supplied by the trader type in the same price group. The percentage of hiddenliquidity for Inside the Best Displayed Quotes is calculated by dividing the total dollar value of hidden liquidityinside the best displayed quotes by the total dollar value of liquidity supplied Inside and At the Best Quotes.Hidden liquidity results are presented in 3 panels: Panel A examines prices inside the best displayed quotes, PanelB examines prices inside and at the best displayed quotes, and Panel C examines prices above the best displayedquotes. Dependent variables in each panel are the percentage of hidden dollar volume for all traders supplyingliquidity (All Hidden), the percentage of hidden dollar volume for HFTs supplying liquidity (HFT Hidden), thepercentage of hidden dollar volume for NHFTs supplying liquidity (NHFT Hidden), and the difference between thepercentage of hidden dollar volume for HFTs supplying liquidity and the percentage of hidden dollar volume forNHFTs supplying liquidity (Diff Hidden).Explanatory variables are the percentage of NASDAQ dollar trading volume in which HFTs trade, the percentage ofNASDAQ dollar trading volume for which HFTs demanded liquidity, and the percentage of NASDAQ dollar tradingvolume for which HFTs supplied liquidity, the log of total dollar trading volume reported by all exchanges, the logof the stock’s closing price, the percentage of total dollar trading volume that is traded on NASDAQ, the stock’spositive abnormal return, the stock’s negative abnormal return, the positive CRSP daily value weighted marketreturn, the negative CRSP daily value weighted market return, the daily opening value of VIX, the volatility of5 minute NBBO midpoint returns, the average depth at the NBBO inside quotes, the average NBBO percentagespread, the average number of displayed shares added to the NASDAQ limit order book each minute that improvethe best displayed bid or offer, the number of displayed shares added to the book at the best displayed bid or offer,the number of displayed shares added to the book at prices worse than the best displayed bid or offer, the averagenumber of displayed shares canceled from the limit order book each minute at the best displayed bid or offer, thenumber of displayed shares canceled from the book at prices worse than the best displayed bid or offer, and thestock’s probability of informed trading (PIN). The stock’s abnormal return is the difference between the stock’sdaily return and the expected return from a model that is estimated by regressing the daily returns of each stockon a 5 factor model that includes the Carhart 4 factor model and the Pastor-Stambaugh liquidity factor. Abnormalreturns and market returns are separated out into positive and negative returns to account for possible asymmetriceffects of positive and negative information. If the return is positive (negative) on the stock-day, then the positive(negative) return variable is equal to the return value (minus the return value) and the negative (positive) returnis equal to zero. NASDAQ ITCH addition and cancellation variables are normalized by dividing by the averagenumber of shares traded on NASDAQ each minute. All explanatory variables are standardized so the coefficientscan be interpreted as the percentage increase in the use of hidden liquidity for a one standard deviation increasein the explanatory variable. Parenthesis report standard errors double clustered by stock and day. ***, **, and *indicate significance at the 1%, 5%, and 10% level, respectively.

61

Tabl

eA

.1:

Det

erm

inan

tsof

Hid

den

Volu

me

inth

eLi

mit

Ord

erB

ook:

Pane

lAIn

side

Disp

laye

dQ

uote

s

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

Varia

ble

All

Hid

den

HFT

Hid

den

NH

FTH

idde

nD

iffH

idde

nH

FTVo

lum

e%

-1.7

5***

-1.0

5-2

.36*

**1.

32(0

.39)

(0.8

5)(0

.33)

(0.8

5)H

FTD

eman

dVo

lum

e%

-0.4

20.

36-0

.44

0.81

(0.3

2)(0

.78)

(0.3

1)(0

.76)

HFT

Supp

lyVo

lum

e%

-1.9

8***

-2.1

0**

-2.8

5***

0.75

(0.5

4)(0

.96)

(0.3

8)(0

.97)

Log

Dai

lyTr

adin

gVo

lum

e-6

.47*

**-5

.60*

**-8

.97*

**-7

.54*

**-5

.67*

**-4

.32*

**-3

.30*

-3.2

2(1

.09)

(1.2

2)(2

.11)

(2.3

1)(0

.75)

(0.7

5)(1

.79)

(2.1

0)Lo

gPr

ice

11.2

2***

10.6

3***

18.4

6***

17.4

9***

8.34

***

7.41

***

10.1

3***

10.0

7***

(1.2

2)(1

.34)

(1.8

8)(2

.09)

(0.7

9)(0

.83)

(1.4

3)(1

.66)

Nas

daq

%D

olla

rVo

lum

e-2

.69*

**-2

.64*

**-0

.02

0.06

-3.2

6***

-3.1

8***

3.24

***

3.24

***

(0.3

4)(0

.34)

(0.7

8)(0

.78)

(0.3

2)(0

.31)

(0.7

2)(0

.72)

Pos

Adj

Ret

-0.0

7-0

.05

0.02

0.05

-0.2

6-0

.24

0.29

0.29

(0.2

7)(0

.27)

(0.4

6)(0

.45)

(0.2

6)(0

.26)

(0.4

2)(0

.42)

Neg

Adj

Ret

0.30

0.30

0.41

0.41

0.07

0.07

0.34

0.34

(0.3

7)(0

.37)

(0.5

4)(0

.55)

(0.3

2)(0

.32)

(0.5

3)(0

.53)

Pos

Mar

ket

Ret

0.16

0.17

-2.6

9**

-2.6

7**

0.71

0.73

-3.4

0***

-3.4

0***

(0.5

4)(0

.49)

(1.3

3)(1

.27)

(0.5

2)(0

.46)

(1.3

0)(1

.30)

Neg

Mar

ket

Ret

0.39

*0.

39*

0.50

0.51

0.28

0.28

0.23

0.23

(0.2

2)(0

.22)

(0.8

1)(0

.83)

(0.2

4)(0

.22)

(0.8

5)(0

.85)

Ope

ning

VIX

0.96

***

0.84

***

1.79

***

1.60

**0.

71**

*0.

53**

1.08

1.07

(0.2

3)(0

.23)

(0.6

4)(0

.66)

(0.2

3)(0

.22)

(0.6

7)(0

.69)

Taq

MP

Vola

tility

3.35

***

3.11

***

6.15

***

5.75

***

2.56

***

2.17

***

3.60

***

3.57

***

(0.5

4)(0

.57)

(0.9

7)(1

.00)

(0.4

2)(0

.44)

(0.8

6)(0

.90)

NB

BO

Dep

th1.

24*

1.21

*3.

11**

3.06

**0.

650.

602.

46**

*2.

45**

*(0

.68)

(0.6

9)(1

.34)

(1.3

6)(0

.49)

(0.5

1)(0

.93)

(0.9

4)N

BB

OSp

read

%2.

26**

*2.

55**

*6.

31**

*6.

78**

*0.

641.

09**

5.67

***

5.69

***

(0.7

3)(0

.72)

(1.5

6)(1

.58)

(0.4

9)(0

.44)

(1.2

8)(1

.36)

Shar

esA

ddA

ggre

ssiv

e-2

.90

-3.3

42.

992.

27-2

.08

-2.7

65.

075.

03(3

.26)

(3.2

4)(4

.19)

(4.1

7)(3

.17)

(3.1

5)(4

.06)

(4.0

1)Sh

ares

Add

At

Quo

te-2

.98

-3.2

9-0

.58

-1.0

9-2

.05

-2.5

41.

471.

44(2

.23)

(2.2

1)(2

.99)

(2.9

7)(2

.13)

(2.1

2)(2

.82)

(2.7

8)Sh

ares

Add

Abo

veQ

uote

-5.6

5-7

.69

7.56

4.21

-3.4

6-6

.63

11.0

210

.84

(6.7

7)(6

.85)

(9.5

9)(9

.96)

(7.4

4)(7

.54)

(10.

97)

(11.

00)

Shar

esC

ance

lAt

Quo

te5.

095.

64-0

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0.44

3.73

4.58

-4.1

8-4

.13

(3.8

1)(3

.77)

(5.0

4)(4

.96)

(3.6

7)(3

.64)

(4.9

0)(4

.81)

Shar

esC

ance

lAbo

veQ

uote

5.13

7.13

-7.0

3-3

.75

2.85

5.96

-9.8

9-9

.71

(7.0

3)(7

.14)

(9.8

8)(1

0.27

)(7

.77)

(7.8

9)(1

1.20

)(1

1.25

)PI

N-0

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81.

81**

2.02

**-0

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-0.7

72.

77**

*2.

79**

*(0

.89)

(0.9

0)(0

.89)

(0.9

0)(0

.78)

(0.7

7)(0

.80)

(0.8

0)C

onst

ant

12.9

9***

12.9

8***

17.9

5***

17.9

3***

12.0

2***

12.0

0***

5.94

***

5.93

***

(0.4

6)(0

.45)

(1.1

1)(1

.12)

(0.4

0)(0

.39)

(1.1

0)(1

.10)

Obs

erva

tions

4,27

54,

275

4,27

54,

275

4,27

54,

275

4,27

54,

275

R-s

quar

e0.

501

0.50

30.

614

0.61

50.

375

0.38

00.

369

0.36

9

62

Tabl

eA

.1:

Det

erm

inan

tsof

Hid

den

Volu

me

inth

eLi

mit

Ord

erB

ook:

Pane

lBIn

side

and

At

Disp

laye

dQ

uote

s

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

Varia

ble

All

Hid

den

HFT

Hid

den

NH

FTH

idde

nD

iffH

idde

nH

FTVo

lum

e%

-8.8

5***

-0.8

2-8

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**7.

69**

*(0

.76)

(1.1

3)(0

.83)

(1.5

4)H

FTD

eman

dVo

lum

e%

-2.5

7***

1.48

*-3

.45*

**4.

94**

*(0

.53)

(0.9

0)(0

.61)

(1.1

4)H

FTSu

pply

Volu

me

%-9

.31*

**-3

.44*

**-7

.48*

**4.

04**

(0.9

3)(1

.14)

(0.9

1)(1

.58)

Log

Dai

lyTr

adin

gVo

lum

e2.

165.

88**

*-1

0.16

***

-7.2

6***

8.29

***

10.4

0***

-18.

45**

*-1

7.66

***

(1.4

9)(1

.81)

(2.0

9)(2

.17)

(1.6

4)(1

.94)

(2.9

6)(3

.21)

Log

Pric

e7.

38**

*4.

84**

*20

.42*

**18

.44*

**1.

520.

0718

.90*

**18

.36*

**(1

.05)

(1.1

9)(1

.79)

(1.9

2)(0

.94)

(1.0

8)(2

.10)

(2.3

1)N

asda

q%

Dol

lar

Volu

me

0.15

0.36

0.16

0.32

-0.0

50.

070.

200.

25(0

.59)

(0.5

7)(0

.85)

(0.8

3)(0

.62)

(0.6

2)(1

.11)

(1.1

1)Po

sA

djR

et1.

60**

*1.

67**

*0.

410.

471.

55**

*1.

59**

*-1

.14*

*-1

.12*

*(0

.35)

(0.3

3)(0

.47)

(0.4

6)(0

.37)

(0.3

5)(0

.56)

(0.5

5)N

egA

djR

et2.

29**

*2.

30**

*1.

08*

1.09

*2.

07**

*2.

08**

*-0

.99

-0.9

9(0

.55)

(0.5

3)(0

.60)

(0.6

2)(0

.54)

(0.5

2)(0

.73)

(0.7

4)Po

sM

arke

tR

et-1

.52*

-1.4

6*-4

.22*

**-4

.18*

**-0

.11

-0.0

8-4

.11*

**-4

.10*

**(0

.88)

(0.8

2)(1

.13)

(1.0

4)(0

.97)

(0.9

7)(1

.48)

(1.4

6)N

egM

arke

tR

et-0

.38

-0.3

7-0

.04

-0.0

3-0

.35

-0.3

40.

310.

31(0

.56)

(0.5

6)(0

.78)

(0.8

4)(0

.57)

(0.5

8)(0

.76)

(0.7

7)O

peni

ngV

IX1.

54**

*1.

05*

2.57

***

2.19

***

1.13

**0.

841.

45*

1.34

(0.5

3)(0

.54)

(0.7

8)(0

.81)

(0.5

4)(0

.55)

(0.8

6)(0

.88)

Taq

MP

Vola

tility

2.04

***

0.99

6.96

***

6.14

***

0.00

-0.5

96.

96**

*6.

74**

*(0

.66)

(0.6

7)(1

.05)

(1.0

3)(0

.63)

(0.6

7)(1

.20)

(1.2

0)N

BB

OD

epth

-3.4

9***

-3.6

2***

1.80

1.70

-4.8

5***

-4.9

3***

6.66

***

6.63

***

(0.8

8)(0

.82)

(1.2

3)(1

.25)

(1.1

4)(1

.11)

(2.1

1)(2

.12)

NB

BO

Spre

ad%

1.35

**2.

59**

*4.

89**

*5.

85**

*0.

851.

55**

4.04

**4.

30**

(0.6

2)(0

.73)

(1.7

8)(1

.71)

(0.6

3)(0

.78)

(2.0

2)(2

.04)

Shar

esA

ddA

ggre

ssiv

e-4

.25

-6.1

2-3

.11

-4.5

8-4

.69

-5.7

61.

581.

18(5

.01)

(4.8

4)(5

.11)

(4.9

9)(4

.62)

(4.6

0)(6

.04)

(6.0

7)Sh

ares

Add

At

Quo

te-4

.72

-6.0

5*-6

.53*

-7.5

7**

-4.2

3-4

.99

-2.3

0-2

.58

(3.5

5)(3

.41)

(3.5

3)(3

.43)

(3.3

5)(3

.32)

(4.4

2)(4

.43)

Shar

esA

ddA

bove

Quo

te6.

04-2

.68

-2.2

5-9

.06

1.46

-3.5

0-3

.71

-5.5

6(1

1.18

)(1

0.78

)(1

1.77

)(1

2.07

)(1

1.84

)(1

1.86

)(1

6.84

)(1

7.26

)Sh

ares

Can

celA

tQ

uote

6.57

8.89

6.66

8.48

6.73

8.05

-0.0

70.

43(5

.96)

(5.7

4)(6

.19)

(5.9

6)(5

.52)

(5.4

9)(7

.20)

(7.2

1)Sh

ares

Can

celA

bove

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te-7

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1.47

2.87

9.55

-2.5

42.

335.

417.

22(1

1.61

)(1

1.18

)(1

2.22

)(1

2.53

)(1

2.26

)(1

2.27

)(1

7.46

)(1

7.87

)PI

N1.

021.

57*

2.30

*2.

73**

0.87

1.18

1.43

1.55

(0.8

7)(0

.89)

(1.2

0)(1

.22)

(0.7

7)(0

.79)

(1.3

0)(1

.31)

Con

stan

t42

.05*

**42

.00*

**30

.27*

**30

.23*

**45

.61*

**45

.58*

**-1

5.34

***

-15.

35**

*(0

.79)

(0.7

6)(1

.25)

(1.2

6)(0

.80)

(0.7

9)(1

.47)

(1.4

7)O

bser

vatio

ns4,

275

4,27

54,

275

4,27

54,

275

4,27

54,

275

4,27

5R

-squ

are

0.34

90.

364

0.50

50.

510

0.20

20.

207

0.32

60.

326

63

Tabl

eA

.1:

Det

erm

inan

tsof

Hid

den

Volu

me

inth

eLi

mit

Ord

erB

ook:

Pane

lCA

bove

Disp

laye

dQ

uote

s

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

Varia

ble

All

Hid

den

HFT

Hid

den

NH

FTH

idde

nD

iffH

idde

nH

FTVo

lum

e%

-3.9

7***

-2.7

6**

-4.2

4***

1.48

(0.6

8)(1

.34)

(0.7

2)(1

.57)

HFT

Dem

and

Volu

me

%-1

.50*

*-0

.65

-1.6

6**

1.01

(0.6

8)(1

.11)

(0.7

0)(1

.31)

HFT

Supp

lyVo

lum

e%

-3.6

5***

-3.1

2*-3

.82*

**0.

69(0

.95)

(1.7

1)(0

.81)

(1.9

0)Lo

gD

aily

Trad

ing

Volu

me

-8.7

0***

-7.5

6***

-20.

59**

*-1

9.22

***

-2.0

8-0

.94

-18.

51**

*-1

8.28

***

(1.3

7)(1

.58)

(2.3

5)(2

.93)

(1.3

9)(1

.54)

(2.5

9)(3

.36)

Log

Pric

e5.

82**

*5.

04**

*15

.60*

**14

.66*

**2.

28**

1.50

13.3

2***

13.1

6***

(1.2

5)(1

.47)

(2.4

5)(2

.73)

(0.9

7)(1

.19)

(2.4

3)(2

.81)

Nas

daq

%D

olla

rVo

lum

e-1

.17

-1.1

0-4

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**-4

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400.

47-5

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**-5

.36*

**(0

.75)

(0.7

5)(1

.18)

(1.2

0)(0

.62)

(0.6

2)(1

.24)

(1.2

6)Po

sA

djR

et0.

780.

80*

-0.3

6-0

.33

1.53

***

1.56

***

-1.8

9*-1

.89*

(0.4

8)(0

.48)

(0.9

0)(0

.90)

(0.5

4)(0

.53)

(1.1

0)(1

.10)

Neg

Adj

Ret

1.37

**1.

37**

0.46

0.46

1.67

**1.

67**

-1.2

1-1

.21

(0.5

9)(0

.59)

(0.9

5)(0

.94)

(0.6

6)(0

.65)

(1.1

2)(1

.12)

Pos

Mar

ket

Ret

-0.2

3-0

.21

-4.3

5***

-4.3

3***

1.82

1.84

-6.1

8***

-6.1

7***

(1.1

0)(1

.06)

(1.6

2)(1

.58)

(1.3

0)(1

.26)

(2.0

7)(2

.07)

Neg

Mar

ket

Ret

0.24

0.25

-0.1

3-0

.12

0.61

0.62

-0.7

4-0

.74

(0.6

6)(0

.64)

(0.8

2)(0

.82)

(1.0

0)(0

.98)

(1.4

9)(1

.50)

Ope

ning

VIX

0.28

0.13

-0.4

6-0

.64

1.02

0.87

-1.4

8-1

.51

(0.6

7)(0

.69)

(1.2

2)(1

.21)

(0.7

8)(0

.80)

(1.5

0)(1

.51)

Taq

MP

Vola

tility

2.60

***

2.27

***

7.95

***

7.56

***

0.18

-0.1

47.

77**

*7.

70**

*(0

.73)

(0.7

4)(1

.38)

(1.4

0)(0

.83)

(0.7

8)(1

.72)

(1.6

5)N

BB

OD

epth

1.09

1.05

2.02

1.97

0.71

0.67

1.31

1.30

(0.9

3)(0

.95)

(1.6

4)(1

.65)

(0.6

7)(0

.69)

(1.2

6)(1

.26)

NB

BO

Spre

ad%

-3.3

3***

-2.9

5***

-5.7

3***

-5.2

7***

-1.0

1-0

.63

-4.7

2**

-4.6

4**

(0.9

7)(0

.97)

(1.8

9)(1

.86)

(0.9

9)(1

.03)

(2.0

6)(1

.99)

Shar

esA

ddA

ggre

ssiv

e20

.47*

**19

.89*

**7.

987.

2822

.74*

**22

.16*

**-1

4.76

*-1

4.88

*(3

.92)

(3.9

2)(7

.65)

(7.5

9)(4

.02)

(4.0

3)(8

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(9.0

1)Sh

ares

Add

At

Quo

te13

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183.

6816

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**15

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2.09

*-1

2.17

*(3

.06)

(3.0

6)(5

.81)

(5.7

5)(3

.16)

(3.1

8)(6

.91)

(6.9

2)Sh

ares

Add

Abo

veQ

uote

41.4

3***

38.7

4***

16.6

913

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50.6

7***

47.9

9***

-33.

98-3

4.53

(9.8

5)(9

.44)

(18.

11)

(18.

02)

(11.

25)

(11.

13)

(23.

22)

(23.

72)

Shar

esC

ance

lAt

Quo

te-2

1.38

***

-20.

66**

*-5

.83

-4.9

6-2

6.17

***

-25.

46**

*20

.35*

20.4

9*(4

.79)

(4.8

2)(9

.35)

(9.2

7)(4

.89)

(4.9

3)(1

1.07

)(1

1.09

)Sh

ares

Can

celA

bove

Quo

te-4

5.80

***

-43.

15**

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96-5

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***

-49.

67**

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29.7

1(1

0.09

)(9

.70)

(18.

38)

(18.

30)

(11.

55)

(11.

41)

(23.

66)

(24.

13)

PIN

0.15

0.32

1.74

1.95

0.76

0.93

0.98

1.01

(1.1

4)(1

.12)

(1.4

7)(1

.55)

(1.0

8)(1

.06)

(1.6

4)(1

.73)

Con

stan

t25

.87*

**25

.86*

**31

.32*

**31

.30*

**21

.91*

**21

.90*

**9.

41**

*9.

40**

*(0

.94)

(0.9

4)(1

.85)

(1.8

6)(1

.11)

(1.1

0)(2

.42)

(2.4

3)O

bser

vatio

ns4,

275

4,27

54,

275

4,27

54,

275

4,27

54,

275

4,27

5R

-squ

are

0.31

60.

318

0.37

30.

374

0.16

70.

169

0.19

60.

196

64

Table A.2: Endogenous Determinants of Hidden TransactionsThis table presents analysis for the 2nd stage of a 2SLS regression examining the determinants of the percentageof HFT and NHFT volume that is hidden in transactions on NASDAQ. The percentage of Liquidity Supplied inTransactions is calculated for each stock-day by summing up the total dollar value of all transactions in which thetrader type supplied liquidity using hidden orders and dividing it by the total dollar value of all transactions inwhich the trader type supplied liquidity.The 2SLS is meant to control for endogeneity that may arise in the percentage of NASDAQ dollar trading volumein which HFTs trade. The instrument variables for each stock-day are based on the runs in process instrumentvariable utilized in Hasbrouck and Saar (2013). The instrument variables used in the first stage are the averagepercentage of NASDAQ dollar trading volume each day in which HFTs trade for stocks that are in the same marketcap group, the average percentage of NASDAQ dollar trading volume for which HFTs demanded liquidity for stocksthat are in the same market cap group, and the average percentage of NASDAQ dollar trading volume for whichHFTs supplied liquidity for stocks that are in the same market cap group. The stock for which the IV is beingcalculated, stocks in the same four digit SIC code, and stocks in the same index, if the stock for which the IVis being calculated is in the S and P 500 or NASDAQ 100 indices, are excluded from the average. Dependentvariables are the percentage of hidden dollar volume for all traders supplying liquidity (All Hidden), the percentageof hidden dollar volume for HFTs supplying liquidity (HFT Hidden), the percentage of hidden dollar volume forNHFTs supplying liquidity (NHFT Hidden), and the difference between the percentage of hidden dollar volume forHFTs supplying liquidity and the percentage of hidden dollar volume for NHFTs supplying liquidity (Diff Hidden).Explanatory variables are the fitted value for the percentage of NASDAQ dollar trading volume in which HFTtrades, the fitted values for the percentage of NASDAQ dollar trading volume in which HFTs demanded liquidity,the fitted values for the percentage of NASDAQ dollar trading volume in which HFTs supplied liquidity, the logof total dollar trading volume reported by all exchanges, the log of the stock’s closing price, the percentage oftotal dollar trading volume that is traded on NASDAQ, the stock’s positive abnormal return, the stock’s negativeabnormal return, the positive CRSP daily value weighted market return, the negative CRSP daily value weightedmarket return, the daily opening value of VIX, the volatility of 5 minute NBBO midpoint returns, the averagedepth at the NBBO inside quotes, the average NBBO percentage spread, the average number of displayed sharesadded to the NASDAQ limit order book each minute that improve the best displayed bid or offer, the number ofdisplayed shares added to the book at the best displayed bid or offer, the number of displayed shares added to thebook at prices worse than the best displayed bid or offer, the average number of displayed shares canceled from thelimit order book each minute at the best displayed bid or offer, the number of displayed shares canceled from thebook at prices worse than the best displayed bid or offer, and the stock’s probability of informed trading (PIN). Thestock’s abnormal return is the difference between the stock’s daily return and the expected return from a modelthat is estimated by regressing the daily returns of each stock on a 5 factor model that includes the Carhart 4factor model and the Pastor-Stambaugh liquidity factor. Abnormal returns and market returns are separated outinto positive and negative returns to account for possible asymmetric effects of positive and negative information.If the return is positive (negative) on the stock-day, then the positive (negative) return variable is equal to thereturn value (minus the return value) and the negative (positive) return is equal to zero. NASDAQ ITCH additionand cancellation variables are normalized by dividing by the average number of shares traded on NASDAQ eachminute. All explanatory variables are standardized so the coefficients can be interpreted as the percentage increasein the use of hidden liquidity for a one standard deviation increase in the explanatory variable. Parenthesis reportstandard errors double clustered by stock and day. ***, **, and * indicate significance at the 1%, 5%, and 10%level, respectively.

65

Tabl

eA

.2:

Endo

geno

usD

eter

min

ants

ofH

idde

nTr

ansa

ctio

ns

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

VAR

IAB

LES

All

Hid

den

HFT

Hid

den

NH

FTH

idde

nD

iffH

idde

nFi

tted

HFT

Volu

me

%-9

.51*

**-9

.13*

**-7

.89*

**-1

.23

(1.6

3)(2

.55)

(1.4

2)(2

.53)

Fitt

edH

FTD

eman

dVo

lum

e%

-5.5

0***

-7.2

4**

-4.9

8***

-2.2

4(1

.59)

(2.9

7)(1

.60)

(2.9

6)Fi

tted

HFT

Supp

lyVo

lum

e%

-5.8

9*-2

.38

-4.1

8**

1.79

(3.1

4)(5

.65)

(2.0

6)(5

.31)

Log

Dai

lyTr

adin

gVo

lum

e6.

25**

*6.

16*

1.81

-1.5

69.

02**

*8.

24**

*-7

.23*

**-9

.80*

(1.4

6)(3

.46)

(2.2

8)(6

.28)

(1.2

0)(3

.02)

(2.1

2)(5

.89)

Log

Pric

e3.

89**

*3.

94*

14.2

3***

16.4

5***

-0.7

1-0

.20

14.8

4***

16.5

4***

(0.8

4)(2

.03)

(1.6

9)(4

.11)

(0.4

7)(1

.70)

(1.4

4)(3

.82)

Nas

daq

%D

olla

rVo

lum

e-0

.10

-0.1

03.

04**

*2.

87**

*-0

.71*

*-0

.75*

*3.

80**

*3.

67**

*(0

.30)

(0.3

5)(0

.65)

(0.7

4)(0

.29)

(0.3

1)(0

.66)

(0.7

1)Po

sA

djR

et-0

.13

-0.1

3-0

.11

-0.1

4-0

.08

-0.0

90.

00-0

.02

(0.3

1)(0

.31)

(0.4

9)(0

.48)

(0.2

8)(0

.28)

(0.5

4)(0

.53)

Neg

Adj

Ret

-0.2

0-0

.20

-0.0

8-0

.06

-0.2

4-0

.23

0.20

0.21

(0.4

4)(0

.45)

(0.6

1)(0

.59)

(0.3

7)(0

.38)

(0.5

8)(0

.56)

Pos

Mar

ket

Ret

-0.6

1-0

.61

-2.6

5***

-2.6

6***

-0.1

9-0

.20

-2.4

5***

-2.4

6***

(0.6

2)(0

.62)

(0.9

6)(1

.01)

(0.5

6)(0

.56)

(0.7

9)(0

.82)

Neg

Mar

ket

Ret

-0.2

9-0

.29

-0.5

7-0

.56

-0.1

3-0

.12

-0.4

6-0

.44

(0.5

2)(0

.52)

(0.7

7)(0

.70)

(0.4

7)(0

.45)

(0.4

8)(0

.44)

Ope

ning

VIX

0.54

0.55

1.04

1.46

*0.

57*

0.66

0.46

0.79

(0.3

8)(0

.42)

(0.6

4)(0

.76)

(0.3

4)(0

.41)

(0.5

7)(0

.77)

Taq

MP

Vola

tility

1.02

**1.

054.

13**

*5.

06**

*-0

.25

-0.0

44.

34**

*5.

05**

*(0

.48)

(0.9

7)(0

.99)

(1.9

5)(0

.39)

(0.8

1)(0

.90)

(1.8

4)N

BB

OD

epth

-0.8

8**

-0.8

7**

1.60

1.71

-1.5

9***

-1.5

7***

3.21

***

3.29

***

(0.3

9)(0

.40)

(1.0

9)(1

.08)

(0.2

9)(0

.30)

(0.9

8)(0

.98)

NB

BO

Spre

ad%

2.90

***

2.87

***

6.50

***

5.38

***

1.79

***

1.54

4.84

***

3.99

*(0

.49)

(1.0

5)(1

.08)

(2.0

3)(0

.49)

(0.9

9)(1

.25)

(2.0

8)Sh

ares

Add

Agg

ress

ive

-11.

03**

*-1

0.99

**-1

6.23

***

-14.

25**

-6.6

2**

-6.1

6*-9

.72*

-8.2

1(3

.73)

(4.2

8)(5

.66)

(6.3

9)(3

.10)

(3.5

6)(5

.11)

(5.5

9)Sh

ares

Add

At

Quo

te-7

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**-7

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**-1

1.41

***

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01**

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1**

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9*-6

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*-5

.81

(2.6

0)(2

.93)

(3.7

7)(4

.28)

(2.2

6)(2

.52)

(3.4

7)(3

.81)

Shar

esA

ddA

bove

Quo

te-2

9.34

***

-29.

13**

-48.

82**

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0.19

*-2

1.37

**-1

9.37

*-2

7.69

**-2

1.09

(9.9

6)(1

2.97

)(1

5.03

)(2

0.71

)(8

.91)

(11.

14)

(13.

90)

(18.

49)

Shar

esC

ance

lAt

Quo

te13

.26*

**13

.20*

**18

.39*

**15

.97*

*8.

14**

7.59

*10

.41*

8.56

(4.3

7)(5

.02)

(6.4

0)(7

.37)

(3.6

9)(4

.21)

(5.8

4)(6

.48)

Shar

esC

ance

lAbo

veQ

uote

30.3

6***

30.1

6**

50.1

9***

41.6

4**

22.2

6**

20.2

8*28

.20*

21.6

7(1

0.33

)(1

3.28

)(1

5.64

)(2

1.22

)(9

.28)

(11.

44)

(14.

55)

(19.

02)

PIN

-0.1

1-0

.12

2.06

***

1.64

-0.0

6-0

.16

1.87

**1.

54(0

.59)

(0.7

4)(0

.78)

(1.0

8)(0

.50)

(0.6

4)(0

.76)

(0.9

9)C

onst

ant

18.6

2***

18.6

2***

16.8

2***

16.8

1***

20.3

2***

20.3

2***

-3.5

5***

-3.5

6***

(0.6

0)(0

.60)

(1.0

3)(1

.02)

(0.5

4)(0

.54)

(0.9

2)(0

.91)

Obs

erva

tions

4,27

54,

275

4,26

04,

260

4,27

54,

275

4,26

04,

260

R-s

quar

e0.

195

0.19

50.

473

0.46

90.

0380

0.03

650.

421

0.42

0

66

Table A.3: First Stage Intraday Determinants of Changes in Hidden VolumeThis table presents analysis of the first stage regressions for the 2SLS regressions examining the intraday determi-nants of changes in the percentage of HFT and NHFT volume that is hidden in the NASDAQ limit order book.The 2SLS is meant to control for endogeneity that may arise in the percentage of NASDAQ dollar trading volumein which HFTs trade. The instrument variables are based on the runs in process instrument variable utilized inHasbrouck and Saar (2013). The instrument variables used in the first stage are the change in the average NASDAQdollar trading volume for which HFTs demanded liquidity for stocks that are in the same market cap group andthe change in the average NASDAQ dollar trading volume for which HFTs supplied liquidity for stocks that are inthe same market cap group. The stock for which the IV is being calculated, stocks in the same four digit SIC code,and stocks in the same index, if the stock for which the IV is being calculated is in the S and P 500 or NASDAQ100 indices, are excluded from the average.In the first stage regressions, the dependent variables are the one minute change in the percentage of dollar tradingvolume for which HFTs demanded and supplied liquidity. Explanatory variables are the instrument variables forthe change in the average HFT liquidity demanding and supplying activity in other stocks, the change in the totaltrading volume of the stock across all US markets, the change in the percent of total stock trading volume that istraded on NASDAQ, the change in the total displayed depth at the best displayed quotes on NASDAQ, the changein the total displayed depth above the best displayed quotes on NASDAQ, the change in displayed shares added tothe NASDAQ limit order book that improve the best displayed bid or offer, the change in shares added at the bestdisplayed bid or offer, the change in shares added at prices worse than the best displayed bid or offer, the changein the shares canceled from the limit order book at the best displayed bid or offer, the change in shares canceledat prices worse than the best displayed bid or offer, the change in the five minute midpoint return volatility, thepositive quote midpoint return, the negative quote midpoint return, the change in the NBBO percentage spread,and the change in the NASDAQ displayed percentage spread. The positive (negative) quote midpoint return equalsthe one minute percentage change in the NBBO midpoint (minus the one minute percentage change in the NBBOmidpoint) if the midpoint return is positive (negative) and zero otherwise. All observations are at the minuteinterval and all variables are calculated as sums over the one minute period between limit order book snapshots.Before differencing, all variables are normalized so that each stock-day has a mean value of 0 and standard deviationof 1. Parenthesis report standard errors double clustered by stock and day. ***, **, and * indicate significance atthe 1%, 5%, and 10% level, respectively. The F-statistic reported is for a test on the excluded instrument in thefirst stage regression.

67

Table A.3: First Stage Intraday Determinants of Changes in Hidden Volume

(1) (2)VARIABLES HFT Demand Volume % HFT Supply Volume %IV Alt HFT Demand Volume % 0.0793*** -0.0141***

(0.0052) (0.0018)IV Alt HFT Supply Volume % -0.0087*** 0.0092***

(0.0022) (0.0017)Market Trading Volume -0.0589*** -0.0464***

(0.0055) (0.0041)NASDAQ % of Trading Volume -0.0260*** -0.1078***

(0.0070) (0.0085)NASDAQ Displayed Depth At Quote -0.0215*** -0.0011

(0.0017) (0.0021)NASDAQ Displayed Depth Above Quote -0.0046 0.0068***

(0.0028) (0.0024)Shares Add Aggressive 0.0095*** -0.0031

(0.0031) (0.0039)Shares Add At Quote 0.0346*** 0.0366***

(0.0032) (0.0058)Shares Add Above Quote -0.0080* 0.0030

(0.0048) (0.0046)Shares Cancel At Quote -0.0066 -0.0008

(0.0044) (0.0045)Shares Cancel Above Quote 0.0439*** 0.0160***

(0.0057) (0.0047)5 minute MP volatility 0.0397*** 0.0189***

(0.0028) (0.0031)Pos Midpoint Ret 0.0015 -0.0279***

(0.0031) (0.0048)Neg Midpoint Ret 0.0007 -0.0314***

(0.0033) (0.0047)NBBO Percent Spread 0.0105*** 0.0121***

(0.0024) (0.0016)NASDAQ Displayed Percent Spread 0.0210*** -0.0089***

(0.0018) (0.0027)Constant -0.0071*** 0.0222***

(0.0025) (0.0030)Observations 1,318,419 1,318,419R-squared 0.0094 0.0070F-stat 238.15 32.56

68