Tick Size Constraints, High-Frequency Trading, and Liquidity

Chen Yao and Mao Ye1

January 20, 2015

Abstract

We argue that the uniform one-cent tick size imposed by SEC rule 612 drives speed

competition in liquidity provision for low-priced securities. A large relative tick size (one

cent divided by price) constrains price competition, creates higher revenue in liquidity

provision, and encourages HFTs to achieve time priority over non-HFTs at constrained prices.

Our difference-in-differences test using splits/reverse splits as exogenous shocks

demonstrates that a large relative tick size harms liquidity and encourages HFT liquidity

provision. These results undermine the rationale for maintaining a uniform tick size and the

recent policy proposal to increase the tick size to five cents.

1Chen Yao is from the University of Warwick and Mao Ye is from the University of Illinois at Urbana-Champaign. Please send all correspondence to Mao Ye: University of Illinois at Urbana-Champaign, 340 Wohlers Hall, 1206 South 6th Street, Champaign, IL, 61820. E-mail: maoye@illinois.edu. Telephone: 217-244-0474. We thank Jim Angel, Shmuel Baruch, Robert Battalio, Dan Bernhardt, Jonathan Brogaard, Jeffery Brown, Eric Budish, John Campbell, John Cochrane, Amy Edwards, Robert Frank, Thierry Foucault, Harry Feng, Slava Fos, George Gao, Paul Gao, Arie Gozluklu, Joel Hasbrouck, Frank Hathaway, Terry Hendershott, Björn Hagströmer, Yesol Huh, Pankaj Jain, Tim Johnson, Charles Jones, Andrew Karolyi, Nolan Miller, Katya Malinova, Steward Mayhew, Albert Menkveld, Maureen O’Hara, Neil Pearson, Richard Payne, Andreas Park, Josh Pollet, Ioanid Rosu, Gideon Saar, Ronnie Sadka, Jeff Smith, Duane Seppi, Chester Spatt, Clara Vega, Haoxiang Zhu, an anonymous reviewer for the FMA Napa Conference, and seminar participants at the University of Illinois, the SEC, CFTC/American University, the University of Memphis, the University of Toronto, HEC Paris, the AFA 2014 meeting (Philadelphia), the NBER market microstructure meeting 2013, the Midway Market Design Workshop (Chicago Booth), the 8th Annual MARC meeting, the 6th annual Hedge Fund Conference, the Financial Intermediation Research Society Conference 2013, the 3rd MSUFCU Conference on Financial Institutions and Investments, the Northern Finance Association Annual Meeting 2013, The Warwick Frontiers of Finance Conference, the China International Conference in Finance, the 9th Central Bank Workshop on the Microstructure of Financial Markets, and Market Microstructure: Confronting many Viewpoints Conference in Paris for their helpful suggestions. We also thank NASDAQ OMX for providing the research data. This research is supported by National Science Foundation grant 1352936. This work also uses the Extreme Science and Engineering Discovery Environment (XSEDE), which is supported by National Science Foundation grant number OCI-1053575. We thank Robert Sinkovits and Choi Dongju of the San Diego Supercomputer Center and David O’Neal of the Pittsburgh Supercomputer Center for their assistance with supercomputing, which was made possible through the XSEDE Extended Collaborative Support Service (ECSS) program. We also thank Jiading Gai, Chenzhe Tian, Rukai Lou, Tao Feng, Yingjie Yu, Hao Xu and Chao Zi for their excellent research assistance.

1

The literature on high-frequency trading (HFT) identifies two overarching effects of

speed competition: 1) price competition effect: speed allows high-frequency traders (HFTs)

to be the low-cost providers of liquidity; 2) information effect: speed enables HFTs to trade

on advance information and adversely select slow traders (Jones (2013) and Biais and

Foucault (2014)). We contribute to the HFT literature by establishing the tick size constraints

as a new channel for speed competition. From this perspective, speed enables HFTs to

achieve time priority over non-HFTs when price competition is constrained. We argue that

the resulting arms race in speed is a natural consequence of the uniform one-cent tick size

imposed by SEC 612 of regulation NMS, which hinders price competition, generates rents for

liquidity provision, and encourages speed competition to establish time priority at constrained

prices, particularly for securities with a low price or a large relative tick size. This newly

identified channel for HFT leads, in turn, to a new perspective on the policy debate on market

structure: the current policy debate focuses on whether and how to pursue additional

regulation of HFT; our paper, however, demonstrates that HFT can be a response to an

existing regulation.

The main economic mechanism examined in this paper involves a trade-off for

liquidity providers between establishing price and establishing time priority with regard to

the relative tick size. The NASDAQ market studied in this paper is organized as an electronic

limit-order book whereby liquidity is provided by limit orders. The execution precedence of

displayed limit orders follows a price/time priority rule. Price priority means that limit orders

offering better terms of trade—limit sells at lower prices and limit buys at higher prices—

execute ahead of limit orders at worse prices. Time priority means that limit orders at the

same price are executed in the order which they are submitted. Time priority rewards first-

movers who provide liquidity at a given price. SEC rule 612 (the Minimum Pricing

Increment) of regulation NMS restrict the pricing increment to be no smaller than $0.01 if the

security is priced equal to or greater than $1.00 per share. The uniform one-cent tick size

implies that the cost of establishing price priority over existing limit orders increases with the

relative tick size. For example, holding all else equal, the cost of establishing price priority

over existing limit orders for a $5 stock (with a relative tick size of 20bps) is twenty times

greater than that for $100 stocks (with a relative tick size of 1bps). A large relative tick size

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can generate three interrelated effects: 1) it hinders price competition on the part of liquidity

providers by imposing a high cost on establishing price priority, and thus it leads liquidity

providers, who would have differentiated themselves by quoting at different prices under a

small relative tick size, to quote the same price. 2) It generates higher rents for liquidity

provision as it stops liquidity providers from bidding the securities to their marginal

valuation. 3) It encourages speed competition on the part of liquidity providers to establish

time priority, as the precedence of execution for limit orders at the same price is determined

by time of submission.

We find that a small relative tick size encourages non-HFTs to establish price priority

over HFTs. We first show that HFTs and non-HFTs are more likely to differentiate on the

best quotes they provide when the relative tick size is small, indicating that, for these cases,

the price priority rule is sufficient to determine the liquidity provision precedence between

HFTs and non-HFTs. More importantly, stocks with a smaller relative tick size are associated

with higher incidences of non-HFTs establishing best quotes relative to that of HFTs. A large

relative tick size, on the other hand, encourages HFTs to establish time priority over non-

HFTs. For instance, for large stocks with a large relative tick size, HFTs and non-HFTs

coincide on the best quotes they provide as much as 95.9% of the time, indicating that for

these incidences, the time priority rule needs to be deployed to determine the execution

sequence. We show that HFTs enjoy a higher percentage of trading volume due to their limit

orders’ obtaining time priority over price priority than do non-HFTs. The time priority of

HFTs here refers to that non-HFTs display the same quotes at the time of the execution of

HFT orders, but HFTs win execution priority over non-HFTs. As the relative tick size

increases, the difference between HFTs’ and non-HFTs’ percentage of trading volume due to

time priority widens. The comparative advantage that HFTs enjoy by establishing time

priority drives the main results of our paper: the proportion of liquidity provided by HFTs

relative to that of non-HFTs increases with the relative tick size.

Proponents of widening the tick size argue that increasing the tick size would control

the growth of HFT and increase liquidity (Weild, Kim and Newport (2012), but we find that

an increase in the tick size harms liquidity and encourages HFT liquidity provision. The

causal impact of the relative tick size on liquidity and HFT liquidity provision is

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demonstrated using a difference-in-differences test. The test uses ETF splits/reverse splits as

exogenous shocks to relative tick sizes. The control group involves ETFs that track the same

index, but do not experience splits/reverse splits. We first show that an increase in the relative

tick size after splits harms liquidity. The proportional quotes spread widens; the quoted depth

at the best price increases, but the proportional effective spread, or the actual transaction cost

for liquidity demanders, increases. The impact of splits on liquidity is an important question

that has met with mixed results in the literature (Berk and Demarzo (2013)). We contribute to

this literature by studying the question in a clean setting in which securities with identical

fundamentals but with no splits are used as controls. The results for liquidity also facilitate

the understanding of the economic mechanism underlining the tick size constraints channel.

Stock splits lead to a coarser price grid in a proportional sense, so traders operating at

different price levels before splits may quote the same price after splits. This mechanism

leads to an increase in the proportional spread and the length of the queue to supply liquidity

at the more constrained best bid and offer (BBO). As a result, splits favor HFTs since they

discourage price competition while encouraging speed competition. Reverse splits, on the

other hand, create a finer price grid in the proportional sense, which implies that liquidity

providers who were constrained at the same price can now differentiate themselves by prices,

thus shortening the queue at the best quote. As a result, reverse splits encourage price

competition while discouraging speed competition in liquidity-providing activities. We also

find that reverse splits increase liquidity. We caution that the negative correlation between

HFT liquidity providing activity and liquidity after splits/reverse splits should not be

interpreted as implying that HFTs harm liquidity, because the shock is imposed on the

relative tick size but not HFT activity. Our results do indicate, however, that the effect of the

relative tick size should be taken into account in future studies of HFT on liquidity.

We contribute to the burgeoning literature on HFT by establishing tick size

constraints as a new channel for speed competition. The price competition channel argues

that a speed advantage enables faster traders to provide better quotes, or speed competition

results in price competition. However, the price competition channel cannot explain why

HFT liquidity provision is more active for stocks with large relative tick sizes, as we find that

a large relative tick size is not associated with more incidences in which HFTs establish price

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priority relative to non-HFTs. The evidence is instead consistent with the tick size constraints

channel, as we find that a large relative tick size leads HFTs and non-HFTs to quote the same

price and helps HFTs establish time priority. More surprisingly, we find that a reduction in

the tick size increases the proportion of best quotes provided by non-HFTs relative to HFTs,

implying that non-HFTs are more likely to provide better quotes when the tick size

constraints are less binding.

As regards the information channel, the literature has documented that quicker access

or quicker response to information generates rents and arms races to exploit such rents (Biais,

Foucault and Moinas (2013) and Budish, Cramton and Shim (2013)). This paper finds that

rents can also be extracted from the tick size: specifically, stocks with a larger tick size have

higher revenue in liquidity provision per dollar volume. It is natural to expect that both HFTs

and non-HFTs have higher incentives to supply liquidity for low-priced stocks, because their

large relative tick sizes increase revenue from limit orders and cost for market orders.

However, the speed advantage of HFTs implies that for limit orders at the same price, orders

from HFTs are more likely to be executed due to their ability to establish time priority.

Therefore, speed allocates the rents created from the tick size. The findings are consistent

with an argument offered by the CEO of the HFT firm Tradeworx, Manoj Narang, who said

that “the finer the trading increment the more important price priority becomes relative to

time priority. In other words, if the market was designed to trade at continuous (vs. discrete)

non-penny increments you could always win a trade by quoting the best price and the speed

game would be non-existent.”2 We argue that the tick size is one of the drivers of the arms

race in speed, which in turn can directly impact the real economy by reallocating physical

and human capital resources to industries specialized in latency reduction.

More broadly, our paper contributes to the long-standing body of literature that

examines the impact of price controls. Rockoff (2008) summarizes four possible responses

when controls prevent prices from adjusting to natural levels: queuing, black markets,

evading, and rationing. We observe speed competition as a form of queuing through which

traders with the capacity to trade at high speeds compete for a position at the front of the

2 See Credit Suisee’s HFT 101 with Tradeworx, by Ashley Serrao, Christian Bolu, Dina Shin, and Peter Tiletnick.

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queue. This economic intuition provides insights into the policy debate on HFT as well as

tick size. Current policy debates on HFT focus on whether additional regulation is required

for HFT. We argue, however, that HFT is a natural response to an existing regulation. We

question the rationale of uniform tick size, as it generates a heterogeneous incentive to

engage in price and speed competition for stocks with different relative tick sizes. We also

question the recent initiative to increase the tick size, which is encouraged by the Jumpstart

Our Business Startups Act (the JOBS Act). The plan for a pilot program that increases the

tick size of 1200 small stocks to five cents has been proposed for comments.3 Proponents of

increasing the tick size first argue that an increase in the tick size would control the growth of

HFT and improve liquidity, which is at odds with our empirical evidence. Another argument

for increasing the tick size is that a larger tick size increases market-making revenue and

supports sell-side equity research and, eventually, increases the number of IPOs (Weild, Kim

and Newport, 2012). Economic theories suggest that constrained prices should facilitate non-

price competition, but we doubt that non-price competition would take the form of competing

on providing the best research, especially when speed exists as a more direct form of non-

price competition. We suggest that the SEC consider running a pilot program that decreases

the tick size for large stocks in addition to the current pilot program that would involve

increasing the tick size to five cents for small stocks.

This paper is organized as follows. Section I discusses the study’s hypotheses as well

as the empirical strategy for testing them. Section II describes the data used in the study.

Section III presents preliminary results pertaining to the relationship between the relative tick

size and the proportion of liquidity provided by HFTs using double sorting. Section IV

examines the determinants of HFT liquidity provision and revenue using regression analysis.

Section V examines causal relationships between the relative tick size, liquidity, and HFT

using a difference-in-differences test. Section VI provides additional robustness checks of our

results. Section VII concludes the paper and discusses the policy implications.

3 http://www.sec.gov/rules/sro/nms/2014/34-73511.pdf

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I. Testable hypothesis and empirical design

The main hypothesis of this paper is that a lower nominal price, or a larger relative

tick size, leads to a larger proportion of liquidity provided by HFTs relative to the liquidity

provided by non-HFTs.

Hypothesis 1: An increase in the relative tick size increases the proportion of trading

volume with HFTs as liquidity providers relative to the volume with non-HFTs as liquidity

providers.

The economic mechanism behind hypothesis 1 pertains to the trade-off between price

priority and time priority. A large relative tick size hinders traders from bidding securities to

their marginal valuations. Liquidity providers, who were able to differentiate themselves by

quoting differential prices under a small relative tick size, may have to quote the same prices

under a large relative tick size. The precedence of liquidity provision regarding quotes at the

same prices is determined by time priority, a comparative advantage enjoyed by HFTs. It is

important to note that an increase in the relative tick size may increase the incentive to submit

limit orders for both HFTs and non-HFTs, but non-HFTs are less likely to establish time

priority when they quote the same price as HFTs. Therefore, non-HFTs are “crowded out” if

they are less likely to post the order at the top of the queue.

Note as well that hypothesis 1 would not necessarily be true if a speed advantage also

helped HFTs establish price priority. If HFTs could quote better prices than non-HFTs, their

ability to offer strictly better prices would be less binding with a small relative tick size.

Therefore, a reduction in the relative tick size might increase the proportion of liquidity

provided by HFTs. This notion is reflected in a recent editorial report by Chordia, Goyal,

Lehmann, and Saar (2013) that “HFTs use their speed advantage to crowd out liquidity

provision when the tick size is small and stepping in front of standing limit orders is

inexpensive.” The price competition channel has established three mechanisms through

which HFTs are able to provide better prices for liquidity than non-HFTs: HFTs have lower

operations costs (Carrion (2013)) and their speed advantage reduces adverse selection risk

(Hendershott, Jones and Menkveld (2011)) or facilitates better inventory management

(Brogaard, Hagströmer, Nordén and Riordan (2014)). These three mechanisms suggest that

HFTs can establish price priority when the tick size constraints are less binding. A less

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benevolent possibility for the ability of HFTs to provide more liquidity when the relative tick

size is small is that they can conduct penny jumping (or quote matching), a practice that

involves stepping ahead of existing limit orders by slightly undercutting their prices. Harris

(2003) mentions that penny jumping is more profitable with a small tick size, and traders who

engage in penny jumping must respond to changes in market conditions faster than passive

traders who they run in front of, so penny jumpers tend to be computerized traders in screen-

based markets.4 Therefore, whether a large relative tick size would increase the proportion of

liquidity provided by HFTs relative to the proportion provided by non-HFTs remains an

empirical question.

Motivated by the argument presented above, our paper further investigates whether a

speed advantage facilitates the establishment of price priority for HFTs, especially when the

relative tick size is small, which leads to hypothesis 2:

Hypothesis 2: The smaller the relative tick size, the higher the probability that the

best quote is provided by HFTs rather than non-HFTs.

The key challenge in testing the tick size constraints hypothesis lies in addressing

possible endogeneity originating from omitted variables or simultaneity bias (Roberts and

Whited, (2012)). Biases induced by omitted variables arise from excluding observable or

unobservable variables that are 1) correlated with the nominal price and 2) have explanatory

power for HFT liquidity provision. Interestingly, in a recent paper Benartzi, Michaely,

Thaler, and Weld (2009) find that the average nominal price for a share of stock on the New

York Stock Exchange has remained roughly constant since the Great Depression. They also

find that several popular hypotheses pertaining to nominal prices, such as the marketability

hypothesis, the pay-to-play hypothesis (or optimal tick size hypothesis), and the signaling

hypothesis, cannot explain nominal prices. Particularly, they do not find that firms actively

manage their nominal price to achieve optimal relative tick size. If firms could choose their

optimal relative tick sizes, they would aggressively split their stocks when the tick size

changes from 1/8 to 1/16 and then to one cent. Such aggressive splits have not occurred in

reality. The main cross-sectional result Benartzi, Michaely, Thaler, and Weld (2009)

4 Lawrence Harris, Trading and Exchanges: Market Microstructure for Practitioners, (Oxford University Press, Oxford), 250.

8

established is that large firms have higher prices. 5 This finding provides the empirical

grounding for our double-sorting test examining the cross-sectional variation in proportional

HFT liquidity-providing activity with respect to the relative tick size in each market cap

category. In addition, to examine how the relative tick size affects the proportion of HFT

liquidity-providing activity related to the total liquidity-providing activity, we perform a

multivariate regression controlling for other variables that may impact the nominal price or

HFT liquidity provision. Notably, we further develop a clean difference-in-differences

specification to test this hypothesis. The test uses splits/reverse splits as exogenous shocks to

the nominal prices of ETFs, where the ETFs that split/reverse split are in the treatment group

and ETFs that track the same index but do not split/reverse split are in the control group.

In our scenario, simultaneity bias arises when an increase in the proportion of

liquidity provided by HFTs leads to a lower nominal price, or when both the proportion of

HFT liquidity provision and the nominal price are determined in equilibrium. Such a case of

reverse causality is unlikely to exist in reality: to the best of our knowledge, no evidence

indicates that HFT liquidity provision has the first-order effect of reducing the nominal price.

In addition, the difference-in-differences test involving ETFs splits/reserve splits alleviates

the simultaneity bias concern.

The difference-in-differences test is particularly interesting not only because the

shocks are exogenous but also because the change in HFT activity after splits/reverse splits

relative to control group activity should not be driven by informational factors. We

acknowledge the importance of the information channel, and the diversity of HFTs

(Hagströmer and Nordén, (2013)) implies that HFT activities can be driven by any of several

factors. However, ETFs tracking the same index have the same fundamental information, and

this identification strategy allows us to establish the tick size constraints channel as one

additional driver of speed competition in addition to information.6

5 Benartzi, Michaely, Thaler, and Weld (2009) also find that a firm splits when its price deviates from those of other firms in the same industry. However, there are no splits in our 117 NASDAQ HFT sample. Also, it is not clear how the price of other firms in the same industry is determined. We control for the industry by time fixed effects in the regression section. 6 Certainly, one can argue that when the relative tick size is larger, the information about the depletion of the depth at the best quotes becomes more important. See Foucault, Kadan and Kandel (2013).

9

The textbook in corporate finance by Berk and Demarzo (2013) states that the

literature finds mixed results on the impact of splits on liquidity. Our difference-in-

differences test contributes to this literature by studying the question in a clean setting in

which securities with identical fundamentals but with no splits/reverse splits are used as

controls. Our conjecture regarding liquidity is motivated by the theoretical argument of

Foucault, Pagano, and Röell (2013), which shows that a large tick size increases the spread as

well as the depth at a given price level. Therefore, we have our third hypothesis:

Hypothesis 3: Splits increase the quoted spread, depth at the best price, and effective

spread as well as HFT liquidity-providing activity; reverse splits reduce the quoted spread,

depth at the best price, and effective spread as well as HFT liquidity-providing activity.

The hypothesis pertaining to reverse splits is the mirror image of the hypothesis

pertaining to splits under tick size constraints.

The final hypothesis relates to revenues taken by HFTs. One fundamental question in

finance is whether activities in financial markets affect real resource-allocation decisions.

The literature has revealed several indirect mechanisms through which the market

microstructure affects real decisions. 7 Speed competition attracts the attention of a broader

finance and economics audience because of its direct impact on real resource allocation. A

recent article in the Financial Times estimates that a 1-millisecond advantage is worth up to

$100 million in annual gains.8 The common belief is that profits are generated by quick

access to information. The policy debate, as a consequence, focuses on the fairness and

legitimacy of HFTs having ready access to information. Our paper takes a different route: we

argue that regulating the tick size can also lead rents to faster traders and drive the arms race

in speed. Harris (1994) and Foucault, Pagano, and Röell (2013) argue that market-making

profits increase with the tick size. Anshuman and Kalay (1998) argues that all economic rents

from the spread are eliminated in equilibrium by competing liquidity providers with

7 One line of research relates market microstructure to asset pricing, which identifies three channels: liquidity, information risk, and ambiguity (O’Hara (2003);; Easley and O’Hara (2010)). The other related strand of the literature connects liquidity and price discovery to corporate decisions. For liquidity on corporate investment, see Fang, Noe, and Tice (2009) and Ellul and Pagano (2006), among others. Bolton and von Thadden (1998) and Maug (1998) associate liquidity with corporate governance. Bond, Edmans and Goldstein (2011) offer a useful survey on the informational effects of market prices on firms. 8 “Speed fails to impress long-term investors,” Financial Times, September 22, 2011.

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continuous price. The tick size creates positive expected revenue by posing a barrier to such

competition. The above argument leads to our fourth hypothesis:

Hypothesis 4: Liquidity-providing revenue increases with the tick size.

Notice that both HFTs and non-HFTs should have stronger incentives to submit limit

orders for low-priced stocks if the revenue from limit orders increases with the relative tick

size, but HFTs’ speed advantage gives them a comparative advantage for establishing time

priority.

II. Data and institutional details

This paper uses three main datasets: a NASDAQ HFT dataset, the NASDAQ

TotalView-ITCH with a nanosecond time stamp, and Bloomberg. CRSP, Compustat and

I/B/E/S are also used to calculate stock characteristics. The sample period is October 2010

unless indicated otherwise.

A. Sample of stocks and NASDAQ HFT data

The NASDAQ HFT dataset provides information on limit-order book snapshots and

trades for 117 stocks selected by Hendershott and Riordan. The original sample includes 40

large stocks from the 1000 largest Russell 3000 stocks, 40 medium stocks ranked from 1001–

2000, and 40 small stocks ranked from 2001–3000. Among these stocks, 60 are listed on the

NASDAQ and 60 are listed on the NYSE. Since the sample was selected in early 2010, three

of the 120 stocks were delisted before the sample period (BARE, CHTT and KTII). Panel A

of Table I contains the summary statistics for the 117 stocks.

Insert Table I about Here

The limit-order book data offer one-minute snapshots of the book from 9:30 a.m. to

4:00 p.m. for each sample date and stock. The displayed liquidity for each of these 391

snapshots is classified into two types: liquidity provided by HFTs and liquidity provided by

non-HFTs. This paper focuses on analyzing the displayed quotes from HFTs and non-HFTs

at the best bid and ask.9 The trade file provides information on whether the traders involved

9 At each price level, hidden orders have lower priority than displayed orders, even if the hidden orders were entered before displayed orders.

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in each trade are HFTs or non-HFTs. In particular, trades in the dataset are categorized into

four types, using the following abbreviations: “HH”: HFTs who take liquidity from other

HFTs;; “HN”: HFTs who take liquidity from non-HFTs;; “NH”: non-HFTs who take liquidity

from HFTs;; and “NN”: non-HFTs who take liquidity from other non-HFTs. Therefore, the

trade data allow us to break out trading volume into two types: volume due to liquidity

provision from HFTs and volume due to liquidity provision from non-HFTs.

NASDAQ data is the best publicly available HFT data on the U.S. equity market, but

it suffers from three limitations. Nevertheless, as we illustrate below, the data limitations are

unlikely to affect the findings in this paper.

The first limitation of the data is that the NASDAQ identifies a firm as an HFT firm if

it engages only in proprietary trading. HFT desks in large and integrated firms (e.g., Goldman

Sachs and Morgan Stanley) may be excluded because these institutions also act as brokers for

customers and engage in proprietary low-frequency strategies, so their orders cannot be

uniquely identified as HFT or non-HFT business. One other omission involves orders from

small HFTs that route their orders through these integrated firms (Brogaard, Hendershott and

Riordan (2014)). Nevertheless, the inclusion of some HFTs in the non-HFT group tends to

bias the estimate of their differences towards zero. NASDAQ HFT data thus underestimate

the true differences between HFTs and non-HFTs and attenuate our findings. The fact that we

still detect economically and statically significant differences between their activities

demonstrates the robustness of our results.

Second, the data contain information on NASDAQ trading only, not on other

exchanges. As Battalio, Corwin, and Jennings (2014), Yao and Ye (2014) and Chao, Yao and

Ye (2014) indicate, one way to establish price priority over standing limit orders on the

NASDAQ is to submit a limit order at the same price to a taker/maker market.10 For two limit

orders at the same price, one submitted to the NASDAQ and the other submitted to a

taker/maker market, if liquidity takers consider the liquidity rebate, the one submitted to the

taker/maker market has price priority over the one submitted to the NASDAQ. However, the

exclusion of other exchanges is unlikely to affect our argument regarding the economic trade- 10 EDGA and the Boston Stock Exchange are two examples of taker/maker markets. On the NASDAQ market, liquidity providers are subsidized, but liquidity takers are charged in the exchange, while in a taker/maker market liquidity providers are charged while liquidity takers are subsidized.

12

off between price priority and time priority for stocks with heterogeneous price levels. To see

this, consider the following two facts: 1) The minimum price variation in a taker/maker

market is one cent as well for stocks above $1. In percentage terms, the minimum variation is

higher for lower-priced stocks, and the cost to establish price priority within a taker/maker

market decreases with the price. 2) The cost of establishing price priority by moving an order

from NASDAQ to a taker/maker market is higher for low-priced stocks, because the make-

take fee of given exchanges are also uniform for stocks priced above $1. For example, in

October 2010, the most active liquidity provider obtained a rebate of 0.295 cents for limit

orders on the NASDAQ, whereas liquidity providers needed to pay 0.02 cents per share for

limit orders on the Boston Stock Exchange. Therefore, the cost of establishing price priority

by posting an order at the same price on the Boston Stock Exchange is 0.315 cents for stocks

priced above $1. In percentage terms, the cost is higher for lower-priced stocks. In this

regard, the fee and rebate function similarly to the tick size. In short, the economic trade-off

captured in this paper holds within markets as well across markets, and the existence of

taker/maker markets should not confound the economic argument of this paper.

Finally, data based on snapshots do not provide a dynamic view of the limit-order

book. This prevents us from separating the presence of the best quotes in the limit-order book

that are due to one trader’s actively improving quotes from those that are due to other traders’

passively withdrawing from the best quotes. Fortunately, the NASDAQ also provides us with

five days of data based on all quote updates from HFTs and non-HFTs from February 22,

2010 through February 26, 2010. The robustness checks in section VI using this small data

sample show consistent results.

B. Sample of stocks and NASDAQ ITCH data

We use a difference-in-differences approach to clearly identify the causal impact of

the relative tick size on HFT liquidity provision. The test uses leveraged ETFs that have

undergone splits/reverse splits as the pilot group, and uses leveraged ETFs that track the same

indexes and do not split/reverse split in our sample period as the control group. Leveraged

ETFs are issued prominently by Proshares and Direxion, and often appear in pairs that track

the same index but in opposite directions. For example, the ETFs SPXL and SPXS both track

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the S&P 500, but SPXL amplifies S&P 500 returns by 300% while SPXS does so by -300%.

These twin leveraged ETFs usually have similar nominal prices when launched for IPOs, but

the return amplification results in frequent divergence of their nominal prices after issuance.

The issuers often use splits/reverse splits to keep their nominal prices aligned with each other.

We search Bloomberg Database to collect information on leveraged ETF pairs that

track the same index with an identical multiplier, and the data are then merged with CRSP to

identify their splitting/reverse splitting events. We identify 11 splits and 33 reverse splits

from January 2010 through December 2013.11 Reverse splits occur more frequently, because

their issuers are often concerned about the higher trading cost of low-priced ETFs.12 Our

empirical analysis provides evidence that supports this concern.

Since the NASDAQ HFT dataset does not provide HFT information for ETFs, we

compute HFT activities based on methodologies introduced by Hasbrouck and Saar (2013)

using NASDAQ-ITCH data. We also use ITCH data to construct a limit-order book at

nanosecond-scale resolution, upon which the calculation of liquidity is based. Details on how

to link these messages can be found in Gai, Yao, and Ye (2013) and Gai, Choi, O’Neal, Ye,

and Sinkovits (2013). Summary statistics for leveraged ETFs are presented in Panel B of

Table I.

III. Double sorting

Our preliminary analysis starts with examining the cross-sectional pattern of liquidity

provision with respect to the relative tick size in each market cap category. We sort the 117

stocks first into small, medium, and large groups based on the average market cap in

September 2010, and each group is further divided into low, medium, and high sub-groups

based on the average closing price in September 2010. Section III.A presents the results for

the provision of best quotes by HFTs and non-HFTs with respect to the relative tick size, and

Section III.B presents the percentage of volume with HFTs as liquidity providers with respect

to the relative tick size.

11 To ensure sufficient trading volume in these ETFs, we use leveraged ETFs that experience at least 50 trades each day. 12 “Why has ProShares decided to reverse split the shares of these funds?” (http://www.proshares.com/resources/reverse_split_faqs.html)

14

A. Provision of the Best Quotes

The uniform one-cent tick size hinders price competition involving liquidity providers,

particularly for stocks with low prices, or stocks with large relative tick sizes. It is natural to

expect that a small relative tick size facilitates price differentiations between non-HFTs and

HFTs, but it is not clear in the literature whether a smaller tick size leads HFTs to establish

strictly better prices than non-HFTs do or vice versa. The price competition channel has

established three mechanisms through which HFTs are able to provide better prices for

liquidity than non-HFTs: HFTs have lower operational costs (Carrion (2013)), and their

speed advantage either reduces adverse selection risk (Hendershott, Jones and Menkveld

(2011)) or facilitates better inventory management (Brogaard, Hagströmer, Nordén and

Riordan (2014)). Holding all other things equal, these three mechanisms suggest that the

presence of HFTs as unique providers of best quotes relative to slow traders would increase,

or at least not decrease, with the reduction in the relative tick size, because the constraints on

offering strictly better prices is less binding with a small relative tick size. Also, a small

relative tick size may facilitate penny-jumping from HFTs, which can also increase the

presence of HFTs in the best quotes.

The one-minute snapshots of the limit-order book in the NASDAQ high-frequency

book enable us to examine the providers of the best quotes with respect to the relative tick

size. The data indicate the depth provided by both HFTs and non-HFTs at each bid and ask

price. Our analysis starts by categorizing the best price (the bid and the ask are treated

independently) in these 391 minute-by-minute snapshots for each stock and each day into

three groups according to the following criteria: 1) the best price is displayed by HFTs only,

2) the best price is displayed by non-HFTs only, and 3) the best price is displayed by both

HFTs and non-HFTs. The number is then averaged across all the stocks in each portfolio for

each day, resulting in 21 daily observations for each of the 3-by-3 portfolios. Column 1 of

Table II presents the percentages of time that HFTs are unique providers of the best quotes,

Column 2 presents the percentages of time that non-HFTs are unique providers of the best

quotes, and column 3 presents the percentages of time that HFTs and non-HFTs both display

the best quotes. Columns 1, 2, and 3 sum to 100 percent. Column 4 demonstrates the ratio of

column 2 to column 1. Column 5, defined as column 2 minus column 1, shows the

15

differences in percentage between non-HFTs as unique providers of the best price and HFTs

as unique providers of the best price. Column 6 contains the statistical inferences for column

4 based on 21 daily observations.

Insert Table II about Here

Table II shows that HFTs and non-HFTs are more likely to quote identical prices for

stocks with large relative tick sizes. The best quotes provided by HFTs and non-HFTs are the

same 95.9% of the time for low-priced large stocks, while best quotes provided by HFTs and

non-HFTs are the same only 45.5% of time for high-priced large stocks. In other words, price

priority is sufficient to differentiate two types of traders only 4.1% of the time for low-priced

large stocks, but it is sufficient 54.5% of the time for high-priced large stocks. This result

implies that a large relative tick size is associated with a lower level of price differentiation.

This evidence is consistent with the notion that price competition is more constrained for

stocks with a large relative tick size.

Surprisingly, we find that, as the relative tick size decreases, non-HFTs play an

increasingly more prominent role than HFTs in providing the best price, though the pattern is

not monotonic for small stocks (columns 5 and 6). The evidence does not support hypothesis

2 that the smaller the relative tick size, the higher the probability that the best quote is

provided by HFTs rather than non-HFTs.13

A recent paper by O’Hara, Saar, and Zhong (2013) finds that HFT is more likely to

improve the BBO for stocks with large relative tick sizes than for stocks with small relative

tick sizes. Their paper differs from ours from two perspectives. First, O’Hara, Saar, and

Zhong (2013) examine the cross-sectional variation of HFTs within their own group, while

we compare the activity of HFTs with that of non-HFTs. Second, and more importantly, our

13 The main purpose of the current paper is to empirically document the comparative advantage of HFTs over non-HFT in terms of price or time priority. Formal modeling of the rationale that makes non-HFTs more willing to establish price priority is beyond the scope of the paper. Nevertheless, we offer the following two possibilities. First, a speed advantage may reduce HFTs’ incentives to improve quotes. The U.S. market prioritizes price over time. HFTs can achieve time priority when they quote the same price as non-HFTs, which reduces their incentive to undercut the price; non-HFTs are likely to lose time priority when they quote the same price as HFTs, which gives them a greater incentive to improve the price to gain price priority. Second, a recent paper by Frazzini, Israel, and Moskowitz (2012) suggests that a large fundamental institutional investor designs trading algorithms to provide rather than demand liquidity. These natural buyers or sellers can offer more aggressive limit orders when price competition is less constrained.

16

paper focuses on the trade-off between price priority and time priority. The fact that HFTs are

more likely to be the first to improve the BBO does not necessarily imply that they are more

likely to establish price priority. To the best of our knowledge, the literature does not

distinguish between the following two scenarios. In the first scenario, both HFTs and non-

HFTs concurrently intend to improve the BBO, but HFTs move faster and thus gain the first

place in the queue for the new BBO, while non-HFTs join the queue for the new BBO after

HFTs do. In the second scenario, only HFTs intend to improve the BBO, and non-HFTs

neither match nor undercut that price. HFTs improve the BBO in both cases, but only the

second case entails price competition, whereas the first case pertains to speed competition

between HFTs and non-HFTs. Therefore, to draw a conclusion about who is the best quote

provider, we need to examine the chances that one type of trader provides a better price than

the other type, particularly when the constraints on price competition are less binding.

Table II presents the presence of HFT and non-HFT on the best quotes and, as a

robustness check, we also examine the best depth, or the quantity provided at the best price in

Table III. We denote the displayed depth provided by HFTs and non-HFTs as HFTdepthitm,

NonHFTdepthitm, where i is the stock, t is the date, and m is the time of day. The share-

weighted average first sums the HFT liquidity provision for all stocks in the portfolio and

then divides the number by the total liquidity provision for all stocks in the portfolio for each

day.14

The average depths from HFTs and non-HFTs for stock i on day t are:

𝐻𝐹𝑇𝑑𝑒𝑝𝑡ℎ = 1𝑀 𝐻𝐹𝑇𝑑𝑒𝑝𝑡ℎ

𝑁𝑜𝑛𝐻𝐹𝑇𝑑𝑒𝑝𝑡ℎ = 1𝑀 𝑁𝑜𝑛𝐻𝐹𝑇𝑑𝑒𝑝𝑡ℎ

(1)

The depth provided by HFTs relative to the total depth of portfolio J on day t is:

14 The depth result is share-weighted. We also try equal-weighted depth and the results are similar.

17

𝐻𝐹𝑇𝑑𝑒𝑝𝑡ℎ𝑠ℎ𝑎𝑟𝑒 = ∑ 𝐻𝐹𝑇𝑑𝑒𝑝𝑡ℎ∈∑ (𝐻𝐹𝑇𝑑𝑒𝑝𝑡ℎ + 𝑁𝑜𝑛𝐻𝐹𝑇𝑑𝑒𝑝𝑡ℎ )∈

(2)

Table III shows the average percentage of depth at the BBO provided by HFTs for

each of the market cap–by–relative tick size portfolios. The result indicates that the

percentage of depth provided by HFTs increases monotonically with the relative tick size.

The depth from HFTs runs as high as 55.66% for large stocks with large relative tick sizes,

while the figure is only 35.07% for large stocks with small relative tick sizes. The difference

is 20.59% and the t-statistic based on the 21 observations runs as high as 22.10. The depth

percentage provided by HFTs is 39.73% for mid-cap stocks with large relative tick sizes,

while the figure is 24.61% for mid-cap stocks with small relative tick sizes. The difference is

15.13% with a t-statistic of 22.88. As the percentage of depth at the BBO offered by non-

HFTs is 1 minus the percentage of depth at the BBO offered by HFTs, it is easy to see that

stocks with a smaller relative tick size have a larger ratio of depth at the BBO offered by non-

HFTs to that offered by HFTs.

Insert Table III about Here

B. Tick size constraints and volume

NASDAQ high-frequency data indicate, for each trade, the maker and taker of

liquidity. Recall that NHit, HHit, HNit, and NNit are the four types of share volumes for stock i

on each day t. For each portfolio J on day t, the volume with HFTs as liquidity providers

relative to total volume is defined as:15

𝐻𝐹𝑇𝑙𝑖𝑞𝑚𝑎𝑘𝑒 = ∑ (𝑁𝐻∈ +𝐻𝐻 )∑ (𝑁𝐻∈ +𝐻𝐻 +𝐻𝑁 + 𝑁𝑁 ) (3)

Table IV shows the average percentage of volume with HFTs as liquidity providers

for each of the market cap–by–relative tick size portfolios. The result demonstrates that the

volume with HFTs as liquidity providers increases with the relative tick size. For example,

about half of the volume is due to HFTs’ being liquidity providers for large stocks with large

relative tick sizes, but only 35.93% of the volume is due to HFTs’ being liquidity providers

15 The equal-weighted average yields similar results. As a falsification test, in section VI.B we also perform double sorting for the percentage of volume with HFTs as liquidity takers.

18

for large stocks with small relative tick sizes. The difference is 14.03% with a t-statistic of

15.54 for the 21 observations.

Insert Table IV about Here

The pattern documented in table IV cannot be explained by the price competition

channel. Table II shows that HFTs have the lowest probability to establish price priority for

stocks with large relative tick sizes. For example, HFTs are the unique best quote providers

only 1.6% of the time (the first row of table II) for large stocks with large relative tick size.

However, table IV shows that proportion of volume with HFTs as liquidity providers is the

highest for this portfolio. The pattern is nevertheless consistent with the tick size constraints

channel: non-HFTs and HFTs quote the same price 95.9% of the time for large stocks with

large relative tick size, where time priority plays a prime role in determining the execution

sequence. As the relative tick size decreases, the volume with non-HFTs as liquidity

providers increases, which also dovetails with the result shown in Table II that a small

relative tick size facilitates non-HFTs to establish price priority. Section VI.B provides

further evidence that HFTs are more likely to establish time priority than non-HFTs,

especially when the relative tick size is large.

IV. Regression analysis

The multivariate regressions in this section further confirm that a large relative tick

size results in a higher percentage of liquidity provided by HFTs. We control for additional

variables to overcome omitted variable bias. A sufficient condition for omitted variable bias

to occur is that the missing variables are correlated with both the nominal price and HFT

liquidity provision. We address the issue of omitted variables based on the necessary

condition, and control for variables that can be potentially correlated with either the nominal

price or HFT liquidity provision.16 We also demonstrate in this section that revenues taken

for liquidity provision are also higher for stocks with large relative tick sizes.

16 To the best of our knowledge, the literature has not documented any variables correlated with both the nominal price and HFT liquidity provision.

19

A. Control variables

The nominal price literature suggests that the industry norm is important in choosing

the nominal price. Benartzi, Michaely, Thaler, and Weld (2009) find that a firm may

split/reverse split if its price deviates from the industry average. We control for this average

using an industry fixed effect, whereby industries are classified using the Fama–French

classification of 48 industries. Although Benartzi, Michaely, Thaler, and Weld (2009) argue

that other hypotheses cannot explain nominal prices, to run a robustness check we

nevertheless take five lines of studies in the nominal price literature into consideration, three

of which suggest additional control variables for our analysis.17 The summary of control

variables from these hypotheses is presented in Table I.

The optimal tick size hypothesis argues that firms choose the optimal tick size

through splits/reverse splits (Angel (1997)). Anshuman and Kalay (2002) also build a

theoretical model to demonstrate the existence of optimal tick size under certain parameter

values. This hypothesis implies that firm characteristics can determine both HFT liquidity

provision and the relative tick size. However, the optimal tick size hypothesis has been

rejected in the following experiments. We have not seen that firms aggressively split their

stocks to maintain their optimal relative tick size when the nominal tick size changes from

1/8 to 1/16 and then to one cent. (Benartzi, Michaely, Thaler, and Weld (2009)). Nevertheless,

we include the idiosyncratic risk, and the number of analysts that may affect the choice of the

optimal tick size, from this study.18

The marketability hypothesis argues that a lower price appeals to individual traders.

Tests of this hypothesis yield mixed results.19 Nevertheless, we include the measure of small

17Two other lines of research do not suggest additional variables to control for in our study. The catering hypothesis proposed by Baker, Greenwood, and Wurgler (2009) discusses time-series variations in stock prices: firms split when investors place higher valuations on low-priced firms and vice versa, but our analysis focuses on cross-sectional variation. Campbell, Hilscher, and Szilagyi (2008) find that an extremely low price predicts distress risk, but the 117 firms in our sample are far from default, and the distress risk should not affect the the ETFs sample in Section V. 18 Angel (1997) also argues that the relative tick size also depends on whether a firm is in a regulated industry, and this effect has been taken care of by including an industry-by-time fixed effect. It uses firm book value as a control for size, which is similar to the market cap for which we have controlled. When book value is included as an additional control, the results are similar. 19 Some papers find that individuals prefer low-priced stocks (Dyl and Elliott,( 2006)), whereas Lakonishok and Lev (1987) find no long-term relationship between nominal prices and retail ownership. Byun and Rozeff (2003) suggest that if there are any short-term effects of low prices, they are very small.

20

investor ownership suggested by Dyl and Elliott (2006), which is equal to the logarithm of

the average book value of equity per shareholder.

The signaling hypothesis states that firms use stock splits to signal good news. The

empirical literature, however, does not reach a definitive conclusion as to whether splits serve

as a signal or, if so, what types of news prompt firms to signal.20 In addition, the 117 stocks

in our sample do not split during our sample period. Nevertheless, we use the probability of

informed trading (PIN) proposed by Easley, Kiefer, O’Hara and Paperman (1996) to control

for information asymmetry.

We then include additional control variables from the HFT literature in our regression,

such as turnover and volatility following Hendershott, Jones, and Menkveld (2011). The

literature has reached a consensus that HFTs’ speed advantage allows them to reduce the

pick-off risk by canceling their quotes before being adversely selected, but it is intriguing to

further examine whether HFTs take a higher or lower market share for stocks with higher

PINs. Therefore, in addition to its role as a proxy for the signaling hypothesis, the coefficient

estimate for the PIN also sheds light on the activeness of HFT on stocks with higher

asymmetric information. The regression also includes past returns as the independent variable

to examine the impact of returns on HFT liquidity provision. 21 The method used for

calculating the variables from the HFT literature is also summarized in Table I.

B. Regression results for HFT liquidity provision.

The regression specification is

𝐻𝐹𝑇𝑣𝑜𝑙𝑢𝑚𝑒 , = 𝑢 , + 𝛽 × 𝑡𝑖𝑐𝑘 , + Γ × 𝑋 , +𝜖 , (4) where 𝐻𝐹𝑇𝑣𝑜𝑙𝑢𝑚𝑒 , is the proportion of volume with HFTs as liquidity providers,

calculated as the volume with HFTs as the liquidity providers over the total trading volume

for stock i on date t.22 𝑢 , is the industry-by-time fixed effect.23 The key variable of interest,

𝑡𝑖𝑐𝑘 , , is the daily inverse of the stock price for stock i. 𝑋 , are the control variables 20 See Brennan and Copeland (1988), Lakonishok and Lev (1987), and Kalay and Kronlund (2013). 21 We thank an anonymous reviewer for the Texas Finance Festival for the suggestion of adding past returns. 22 We also analyze who provides the best price using multinomial logit and probit models and obtain similar results. The results are not reported but are available upon request. 23 We do not include firm fixed effects because the focus of this paper is on understanding the cross-sectional variation in HFT market-making activity, and firm fixed effects defeat this purpose (Roberts and Whited (2012)).

21

presented in Table I. The results are presented in table V. Column 1 presents the results for

the effect of the relative tick size with market cap as a control variable. Column 2–6 include

additional control variables from each hypothesis discussed in Section IV.A. Column 2

controls for variables that affects HFT; column 3 includes the control variable suggested by

the marketability hypothesis; column 4 contains control variables from the relative tick size

hypothesis; column 5 controls PIN for information asymmetry and column 6 controls for past

returns. Column 7 incorporates control variables from all hypotheses.

Insert Table V about here

Table V confirms that HFTvolume increases with the relative tick size, consistent with

our tick size constraints hypothesis. For example, column 7 show that a one-standard-

deviation increase in the relative tick size is associated with a 3.7% increase in the percentage

of volume with HFTs as liquidity providers (0.956*0.039), representing 13% of the increase

relative to the mean of HFTvolume ((0.956*0.039)/0.28). The table also shows that stocks

with larger market caps have higher percentages of liquidity provided by HFTs. The

insignificant coefficients before other variables do not necessarily imply that these variables

have no impact on the absolute magnitude of the liquidity provision of HFTs, but should be

interpreted as implying that these variables have no statistically significant impact on the

ratio of HFT liquidity provision to total volume.

Columns 5 and 7 show that a higher PIN, alone or combined with other control

variables, reduces HFTvolume. This intriguing result suggests that HFTs do not participate in

liquidity provision to a greater extent relative to non-HFTs for stocks with higher information

asymmetry. The main takeaway from Table V is that HFTs concentrate their activity on

stocks with large relative tick sizes and lower information asymmetry relative to non-HFTs.

C. Relative tick size and revenues

The fact that speed competition is more intense for stocks with large relative tick sizes

suggests that revenue from liquidity provision is higher for these stocks (hypothesis 4). We

22

examine revenue instead of profits because our calculation cannot include all costs of

liquidity provision such as investment in infrastructure or human capital.24

Our revenue measure comes from Brogaard, Hendershott, and Riordan (2014),

Menkveld (2013), and Baron, Brogaard, and Kirilenko (2014). The HFT liquidity provision

revenue for an individual stock for a certain time interval v is defined as

𝜋 = −(𝐻𝐹𝑇 ) + 𝐼𝑁𝑉 × 𝑃 (5)

The revenue comes from two components. The first term, ∑ −(𝐻𝐹𝑇 ), captures total cash

flows throughout interval v, with n indicating each of the N transactions within each

interval.25 The second term, often referred as “positioning profit,” cumulates value changes

associated with net position. In our analysis, the inventory cumulated in interval v,

𝐼𝑁𝑉_𝐻𝐹𝑇 , is assumed to be cleared at the end of the interval midpoint quote 𝑃 . The

revenue measure depends on the frequency of inventory clearance. Brogaard, Hendershott

and Riordan (2014) assume that inventory is cleared daily at the closing midpoint. There is

also empirical evidence showing that the inventory of HFTs crosses zero multiple times

within the day. For example, Brogaard, Hagströmer, Nordén and Riordan (2014) finds that

the inventory of fast HFTs can cross zero 13.316 times per day. Kirilenko, Kyle, Samadi, and

Tuzun (2014) estimate that HFTs reduce half of their net holdings in 137 seconds. Therefore,

we calculate the revenue taking v at varying lengths: one-minute, five-minute, 30-minute and

one-day lengths, respectively.

Since we are interested in the market marking profit per dollar volume per day, we

calculate the unit profit as:

𝑈𝑛𝑖𝑡𝑅𝑒𝑣𝑒𝑛𝑢𝑒 = ∑ 𝜋 /𝐷𝑜𝑙𝑉𝑜𝑙 (6)

where v is the total number of intervals for each trading day and 𝐷𝑜𝑙𝑉𝑜𝑙 is the total dollar

volume with HFTs as liquidity providers for each stock on each day. For example, if the

24 Menkveld (2013) and Baron, Brogaard and Kirilenko (2014) estimate capital employed by HFTs in their sample 25 We also add a liquidity rebate when calculating the first part of the profit. NASDAQ has a complex fee structure and we use a fee of 0.295 cents per share, but the results are similar at other fee levels.

23

interval v is taken to be 30 minutes long, cash flows are calculated for each of the 30-minute

intervals and inventories accumulated are emptied at the end of the 30-minute interval; the

total number of intervals V equals 13.

We test hypothesis 4 using the following specification.

𝑈𝑛𝑖𝑡𝑅𝑒𝑣𝑒𝑛𝑢𝑒 , , = 𝛽 × 𝐻𝐹𝑇𝑑𝑢𝑚𝑚𝑦 , , + 𝛽 × 𝑡𝑖𝑐𝑘 ,

+𝑢 , + Γ × 𝑋 , +𝜖 , , (7) In the specification, 𝑈𝑛𝑖𝑡𝑅𝑒𝑣𝑒𝑛𝑢𝑒 , , is the unit revenue for each stock i on date t for

trader type n assuming inventory cleared at frequency v. We have two daily observations for

each stock at each frequency v: a unit revenue for HFTs and a unit revenue for non-HFTs.

These unit variables are affected by a number of controls (𝑋 , ) and two key variables of

interest: relative tick size and HFT dummy. 𝐻𝐹𝑇𝑑𝑢𝑚𝑚𝑦 , , equals 1 for the unit revenue of

HFTs and 0 otherwise. 𝑡𝑖𝑐𝑘 , , is the relative tick size of stock i at day t. 𝑢 , is the

industry-by-time fixed effect. 𝑋 , are control variables presented in Table I.

Table VI shows that the unit revenue for HFTs is higher than that for non-HFTs if the

inventory is cleared at one minute, five minutes or 30 minutes. For example, if inventory is

clearer at every 30 minutes, the unit revenue of HFT is 0.42 basis points higher than that of

the non-HFT. The economic and statistical significance of the HFTdummy increases with the

frequency of inventory clearance. Indeed, one important feature of HFTs is their “very short

time-frames for establishing and liquidating positions” SEC (2010).

The main result in Table VI is that the unit revenue for liquidity provision increases

with the relative tick size. For example, column 3 shows that a one-standard-deviation

increase in the relative tick size is associated with a 0.72 basis-point increase in the unit

revenue measure. Therefore, both HFTs and non-HFTs should have a stronger incentive to

provide liquidity for low-priced stocks, because their large relative tick sizes increase revenue

from limit orders and cost for market orders. However, the speed advantage enables HFTs to

establish time priority and thus they are able to obtain the higher rents created by large

relative tick sizes. Indeed, the previous sections show that HFT liquidity provision is more

active for stocks with larger relative tick sizes, and this section reveals that stocks with large

relative tick sizes yield greater revenue from liquidity provision. Combining these two

24

results, our paper reveals that speed advantage allows HFTs to take a larger market share for

stocks with higher rents from liquidity provision.

Insert Table VI about Here

Our results pertaining to revenue also shed light on policymaking. The usual

interpretation of the revenue of HFTs is that it is due to their information advantage. Such an

interpretation generates debate on the legitimacy of their information (Hu, Pan and Wang

(2013)). Our paper takes a different route on this debate. Our results suggest that rents can

also be extracted from the tick size regulation, and speed serves as the mechanism for

allocating the rents. The rents still exist even if we impose restrictions on HFT. Assume the

extreme scenario in which HFTs are banned: the rent still rewards whoever can post an order

at the front of the limit-order book, especially for stocks with large relative tick sizes. Also,

the recent policy proposal to increase the tick size to five cents would increase the rents,

which can drive another round of speed competition.

V. Identifications using ETFs

This section examines the causal impact of the relative tick size on HFT liquidity-

providing activity (hypothesis 1) using a difference-in-differences test. The same

identification strategy also facilitates the analysis of the causal relationship between the

relative tick size and liquidity (hypothesis 3). The question of liquidity is not only important

in its own right, but it also offers additional economic insights to help us understand the

relationship between the relative tick size and the proportion of liquidity provided by HFTs.

Section V.A illustrates how the proportion of the liquidity provided by HFTs and market

liquidity are measured. Section V.B presents the difference-in-differences test using the

splits/reverse splits of leveraged ETFs as exogenous shocks to the relative tick size.

A. Measure of HFT activity and liquidity

The NASDAQ HFT dataset does not contain HFT information for ETFs. Therefore,

we use NASDAQ-ITCH data to construct a proxy for the proportion of HFT liquidity

provision. The standard proxy for the absolute level of HFT activity is the “strategic run”

25

proposed by Hasbrouck and Saar (2013).26 Hasbrouck and Saar (2013) find that strategic run

has a very high correlation with the level of HFT activity. As our paper focuses on the HFTs

liquidity-providing activity relative to the total liquidity-providing activity, we normalize the

HFT activity by the total trading volume. We construct a variable, RelativeRun, which is

equal to the log value of strategic run divided by the log value of dollar volume in NASDAQ

market.27

Table VII demonstrates that RelativeRun is a good proxy for the proportion of

liquidity provided by HFTs. We calculate RelativeRun for the 117 stocks using ITCH data

and compare it with the proportion of liquidity provided by HFTs calculated using NASDAQ

HFT data. Table VII presents the cross-sectional correlation between RelativeRun and the

percentage of trading volume with HFTs as liquidity providers, HFTvolume (making). The

Pearson correlation is as high as 0.837 and the spearman correlation is as high as 0.835. The

correlations are much higher than two other widely used HFT proxies: the quote-to-trade

ratio (Angel, Harris and Spatt (2010 and 2013)) and negative dollar volume divided by total

number of messages (Hendershott, Jones, and Menkeveld (2011) and Boehmer, Fong, and

Wu (2013)), both of which are based on the intuition that HFTs tend to cancel more orders

than non-HFTs. Surprisingly, these two measures have negative cross-sectional correlations

with the proportion of liquidity provided by HFTs.28 One additional contribution of our paper

26 A strategic run is a series of submissions, cancellations, and executions that are likely to form an algorithmic strategy. The link between submissions, cancellations, and executions are constructed based on three criteria: (1) Limit orders with their subsequent cancellations or executions are linked by reference numbers provided by data distributors. (2) When an inference is needed to decide whether a cancellation is linked to either a subsequent submission of a nonmarketable limit order or a subsequent execution that occurs when the same order is re-sent to the market priced to be marketable, we follow Hasbrouck and Saar (2013), and infer such a link when a cancellation is followed within 100 milliseconds by a limit-order submission of the same size and same direction or by an execution of a limit order of the same size but in the opposite direction. (3) If a limit order is partially executed and the remainder is cancelled, we apply criterion (2) based on the canceled quantity. Strategic run is the sum of the time length of all strategic runs with 10 or more messages divided by the total trading time of that day (Hasbrouck and Saar (2013)). 27 We use log form so that the results are less sensitive to outliers (Wooldridge (2006)). 28 These two measures can be good proxies for distinguishing trader types if the comparison is made within the same security or to measure time-series variation in HFT activity. However, using these two proxies in cross-sectional comparison can be misleading because of the relative tick size. The statement by Manoj Narang, CEO of the HFT firm Tradeworx explains why HFT activity can be negatively correlated with cancellation rates: “The wider the trading increment, the more size starts aggregating at each price level and the more ties you have in prices as there are fewer prices to be at. This elevates the importance of time priority becomes relative to price priority thereby making the role of speed more important. In addition, wider trading increments also reduce cancellation rates as the fair price of a security can now fluctuate in a wider band.”

26

is that we put forward the notion of carefully interpreting results that use quote-to-trade ratios

and negative dollar volume divided by total number of messages in cross-sectional

comparisons. Despite the common intuition that HFTs tend to cancel more orders than non-

HFTs, HFT activity can be negatively correlated with cancellation.

Table VII show that RelativeRun has a positive correlation with the proportion of

liquidity taken by HFTs (HFTvolume (taking)), calculated as percentage of trading volume

with HFTs are the liquidity takers. The result indicates that RelativeRun may also capture

some liquidity-taking activity on the part of HFTs. However, its high correlation with HFT

liquidity-making activity and its low correlation with HFT liquidity-taking activity imply that

it is a better proxy for liquidity-making activities than for liquidity-taking activities. 29

Therefore, we use RelativeRun as a proxy for liquidity-making, though we are aware that it

may capture liquidity-taking HFT activity to a small degree.

Insert Table VII about Here

Stock market liquidity is defined as the ability to trade a security quickly at a price

that is close to its consensus value (Foucault, Pagano, and Röell (2013)). The spread is the

transaction cost faced by traders, and is often measured by the quoted bid-ask spread or the

trade-based effective spread. Depth reflects the market’s ability to absorb large orders with

minimal price impact, and is often measured by the quoted depth. These liquidity measures

come from a message-by-message limit-order book we construct from ITCH data.30

The quoted spread (Qspread) is measured as the difference between the best bid and

ask at any given time. The proportional quoted spread (pQspread) is defined as the quoted

spread divided by the midpoint of the best bid and best ask prices. In addition to earning the

quoted spread, a liquidity provider also obtains a rebate from each executed share from the

29 RelativeRun can be a better proxy for liquidity making than for liquidity taking for the following reasons. Pure submissions of market orders are not considered strategic runs, because all “runs” start with limit orders. The 10 message cut-off and the time weight also increase the correlation of RelativeRun with patient liquidity-providing algorithms. Impatient liquidity-demanding algorithms may use limit orders, but these algorithms are more likely to switch to market orders once the initial limit orders fail to be executed. Therefore, strategic runs that arise from liquidity-demanding algorithms should contain fewer messages. Even if they contain more than 10 messages, it is natural to expect that they span a shorter period of time and carry lower time weight in RelativeRun. 30 We are aware that measures from a limit-order book are not sufficient for statics liquidity. See Jones and Lipson (2001) for a discussion.

27

NASDAQ. Therefore, we compute two other measures of the quoted spread: Qspreadadj and

pQspreadadj, which are spreads adjusted by the liquidity supplier’s rebate.31 Specifically,

𝑄𝑠𝑝𝑟𝑒𝑎𝑑 , = 𝑄𝑠𝑝𝑟𝑒𝑎𝑑 , + 2 ∗ 𝑙𝑖𝑞𝑢𝑖𝑑𝑖𝑡𝑦 𝑚𝑎𝑘𝑒𝑟 𝑟𝑒𝑏𝑎𝑡𝑒 (8) 𝑝𝑄𝑠𝑝𝑟𝑒𝑎𝑑 , = (𝑄𝑠𝑝𝑟𝑒𝑎𝑑 , + 2 ∗ 𝑙𝑖𝑞𝑢𝑖𝑑𝑖𝑡𝑦 𝑚𝑎𝑘𝑒𝑟 𝑟𝑒𝑏𝑎𝑡𝑒)/𝑚𝑖𝑑𝑝𝑜𝑖𝑛𝑡 (9)

All four of these quoted spreads are weighted by the duration of a quote to obtain the daily

time-weighted average for each stock.

Our main measures of depth are the time-weighted average of displayed dollar depth

at the BBO. The effective spread measures the cost of trading against the actual supply of

liquidity (SEC (2012)). The effective spread (Espread) for a buy is defined as twice the

difference between the trade price and the midpoint of the best bid and ask price. The

effective spread for a sell is defined as twice the difference between the midpoints of the best

bid and ask and the trade price. The proportional effective spread (pEspread) is defined as the

effective spread divided by the midpoint. Also, a liquidity demander on the NASDAQ pays

the taker fee.32 Therefore, we compute the fee-adjusted effective spread and the fee-adjusted

proportional effective spread:

𝐸𝑠𝑝𝑟𝑒𝑎𝑑 = 𝐸𝑠𝑝𝑟𝑒𝑎𝑑 + 2 ∗ 𝑙𝑖𝑞𝑢𝑖𝑑𝑖𝑡𝑦 𝑡𝑎𝑘𝑒𝑟 𝑓𝑒𝑒 (10) 𝑝𝐸𝑠𝑝𝑟𝑒𝑎𝑑 = (𝐸𝑠𝑝𝑟𝑒𝑎𝑑 + 2 ∗ 𝑙𝑖𝑞𝑢𝑖𝑑𝑖𝑡𝑦 𝑡𝑎𝑘𝑒𝑟 𝑓𝑒𝑒)/𝑚𝑖𝑑𝑝𝑜𝑖𝑛𝑡 (11)

B. Difference-in-Differences test using leveraged ETF splits

This section uses a difference-in-differences test to establish the causal relationship

between the relative tick size, market liquidity, and the percentage of HFT liquidity provision.

ETF splits provide us with a cleaner environment than stock splits, allowing us to isolate the

effects of the tick size constraints. Stock splits may be motivated by information (Grinblatt,

Masulis, and Titman (1984), Brennan and Hughes (1991), Ikenberry, Rankine and Stice

(1996)), but the ETF splits are much less likely to be motivated by informational reasons and,

even if they are, their pairs that track the same index but do not split, provide an ideal control.

Among ETFs, splits/reverse splits are more frequent for leveraged ETFs. The bear-and-bull

31 For each stock on each day, the liquidity maker’s rebate is 0.295 cents per execution, but the results are qualitatively similar at other rebate levels. 32 We set the taker fee at 0.3 cents per share.

28

leveraged ETFs for the same index are usually issued by the same company at similar IPO

prices, but large cumulative movements of an index result in the divergence of nominal

prices. The issuers of leveraged ETFs usually conduct splits/reverse splits to align the

nominal prices of bull-and-bear ETFs.

The regression specification for the difference-in-differences test is:

𝑦 , , = 𝑢 , + 𝛾 , + 𝜌 × 𝐷 , , + 𝜃 × 𝑟𝑒𝑡𝑢𝑟𝑛 , , + 𝜖 , , (12) where 𝑦 , , is HFT liquidity-providing activity or the liquidity measure for ETF j in index i at

time t. 𝑢 , , the index-by-time fixed effects, controls for the time trend that may affect each

index. 𝛾 , are ETF fixed effects that absorb the time-invariant differences between two

leveraged ETFs that track the same index i. One such time-invariant difference is the

divergence of nominal prices before the splits/reverse splits. After controlling for index-by-

time and ETF fixed effects, the only major differences between the bull-and-bear ETFs that

track the same indexes are returns in each period, 𝑟𝑒𝑡𝑢𝑟𝑛 , , . The key variable in this

regression is 𝐷 , , , the treatment dummy, which equals 0 for the control group. For the

treatment group, the treatment dummy equals 0 before splits/reverse splits and 1 after

splits/reverse splits. Therefore, coefficient 𝜌 captures the treatment effect. The leveraged bull

ETF is in the treatment group, and the leveraged bear ETF is in the control group if the

leveraged bull ETF splits, and vice versa.

To derive an unbiased estimate of coefficient 𝜌, the actual split/reverse split must be

uncorrelated with the error term in equation (12). This does not mean that the actual

split/reverse split must be exogenous. Equation (12) includes an index-by-time fixed effect,

an ETF fixed effect, and a contemptuous ETF return. The estimate of coefficient 𝜌 remains

unbiased even if the actual split/reverse split is related to these particular explanatory

variables. Two stylized facts are then important for establishing the unbiasedness of 𝜌.

First, the motivation for ETF splits/reverse splits is transparent. The issuer of ETFs

tends to align the nominal price of the twin leveraged ETFs, so they decide to split an ETF

when it has a drastically higher nominal price than its pair, or reverse-split an ETF when it

has a drastically lower nominal price than its pair. Such a difference in price can be captured

by the ETF fixed effect, and the estimate of coefficient 𝜌 remains unbiased. In fact, as we

29

control for both index-by-time fixed effects and ETF fixed effects, the estimation will be

biased only if the actual split/reverse split is somehow related to the contemporaneous

idiosyncratic shocks to the percentage of HFT liquidity-provision activity (Hendershott,

Jones and Menkveld (2011)).

It is then helpful to notice that the schedule for executing a split/reverse split is

predetermined and announced well before the actual split/reverse split. Our event window is

five days before and five days after the actual splits, and the event window sits after the

announcement of the splits. 33 Thus it seems highly unlikely that the split/reverse split

schedule could be correlated with idiosyncratic shocks to HFT liquidity provision in the

future (Hendershott, Jones and Menkveld (2011)). Also, a closer examination of these

announcements reveals that fund companies often conduct multiple splits/reverse splits on the

same day for ETFs tracking diversified underlying assets.34 Such a diversified sample further

mitigates the concern that the split decision is correlated with ETF specific idiosyncratic

shocks.

Panel A of Table VIII reports the splits results. Quoted spreads without rebate

adjustment (Columns 1) and with rebate adjustment (Columns 2) both decrease by 10.565

cents following splits. Column 3 shows that the proportional quoted spread increases by

2.129 basis points. Without the relative tick size frictions, we would expect the nominal

quoted spread to decrease by the same percentage as the nominal price, keeping the

proportional spread unchanged. However, with the increased relative tick size, the percentage

decrease in the nominal quoted spread is less than the percentage decrease in the nominal

price,35 which leads to an increase in the proportional quoted spread. Column 4 shows that

the proportional quoted spread with rebate adjustment experiences an even larger increase

(3.804 basis points). Indeed, the liquidity rebate is held constant during these events, which

implies a higher rebate per stock price after splits. In this sense, the economic impact of a

33 Using a longer time window creates overlap between the pre-announcement and pre-split periods, but we find similar results. 34 For example, the announcement made on April 9, 2010 involves splits ranging from oil, gas, gold, real estate, financial stocks, and basic materials to Chinese indices. 35 Technically, the nominal stock price may also be subject to tick size constraints, but the magnitude of the relative tick size has a greater impact on the nominal quoted spread than on nominal price, because the nominal price is much higher than the nominal quoted spread.

30

liquidity rebate resembles that of the tick size, the inclusion of which leads to a further

increase in the proportional quoted spread.

Column 5 shows that the average dollar depth at the BBO increases by 45,000 dollars.

A large relative tick size after splits implies that traders who were able to quote a range of

prices under a finer grid may have to quote the same price under a coarser grid, which

lengthens the queue at the best price. The literature generally agrees that securities with lower

quoted spreads and greater depth are more liquid. Because splits lead to higher quoted

spreads and greater depth, the key variable of interest turns out to be the effective spread, the

measure of the actual transaction costs incurred by liquidity demanders. The nominal

effective spread decreases by 6.826 cents following a split, but the proportional effective

spread, or the transaction cost for a fixed transaction dollar amount, increases by 2.073 basis

points and, after fee adjustment, 3.777 basis points. Therefore, we find that liquidity

decreases as the cost of actual transactions increases. This result is consistent with the

findings of Conroy, Harris and Benet (1990), Schultz (2000) and Kadapakkam,

Krishnamurthy, and Tse (2005) that splits harm liquidity, but the ETFs tracking the same

index provides an ideal control group for cleaner identification.

Our main results in panel A are presented in Column 10, which shows an increase in

the proportion of HFT liquidity-providing activity in the treatment group after splits relative

to the control group. Since the analysis has controlled for the index-by-time fixed effect, an

increase in the proportion of HFT liquidity-providing activity cannot be attributed to the

change in the underlying fundamentals of the leveraged ETF. Specifically, the increased HFT

activity cannot be ascribed to information events, because the treatment and control groups

have the same underlying information. The ETF fixed effects and the return variable further

control for other possible differences between ETFs in the same pair.36 We argue that the

increase in HFT liquidity-provision activity is driven by changes in the relative tick size.

Following the same intuition as discussed previously, splits lead to coarser price grids, which

can force traders who have quoted different prices before splits to quote the same price after

splits, thus causing an increase in the length of the queue at the new but more constrained 36 One such example is the clientele effect. For example, short sellers may prefer a bear ETF because of the short sale constraints for the bull ETF. The ETF fixed effects also control for other differences between the control and treatment groups before the splits/reverse splits, such as their divergence in nominal price.

31

best price. Once liquidity providers are in the same price queue, the time priority rule

determines the execution sequence, which intensifies speed competition. Taken as a whole,

splits encourage HFT liquidity provision, as a large relative tick size impedes price

competition while encouraging speed competition.

Insert Table VIII about Here

Panel B shows that reverse splits generate a pattern that is the opposite of that of splits.

Columns 1–4 show that the quoted spread increases but the proportional quoted spread

decreases after reverse splits. The patterns hold with or without rebate adjustment. We

ascribe this result to the reduction in the relative tick size following the reverse split. Given a

fixed nominal spread, after reverse splits, the proportional spread has new incremental units;

the newly added units of increment encourage price differentiation. The depth at the best

price decreases by 374,000 dollars, implying a shorter queue to provide liquidity. This result,

along with the reduction in the proportional quoted spread, constitutes evidence that traders

who were forced to quote the same price can now choose to differentiate themselves by price,

leading to a reduction in depth offered at the new BBO. Columns 6–9 show that the effective

spread increases but the proportional effective spread decreases, suggesting that the

transaction cost for liquidity demanders falls after reverse splits. Column 10 reports a

reduction in HFT activity following reverse splits. A reduction in the relative tick size

enhances price competition and reduces the queue for supplying liquidity, which weakens the

incentives to be at the top of the queue at the constrained price. Therefore, we see less HFT

liquidity-providing activity following reverse splits.

In summary, we find that splits decrease liquidity whereas reverse splits increase

liquidity. We also find that splits attract HFT liquidity-providing activity whereas reverse

splits reduces HFT liquidity-providing activity. These results should not be interpreted to

mean that HFTs have a negative impact on liquidity provision, because the tests are based on

exogenous shocks to the tick size but not HFT activity. The correct economic interpretation is

that a large relative tick size reduces liquidity but attracts HFT liquidity provision. Our results,

however, do reveal the importance of controlling for the relative tick size when considering

the causal relationship between HFT liquidity provision activity and liquidity.

32

VI. Robustness Tests

This section provides several robustness checks for the main results presented in

previous sections. Section VI.A checks the validity of alternative hypotheses to explain the

prevalence of HFT’s as liquidity providers on stocks with large relative tick sizes. Section

VI.B provides additional evidence pertaining to the comparison of price and time priority

based on a sample of data that provides all the quote updates from HFTs and non-HFTs from

February 22, 2010 through February 26, 2010. This small sample of data provides a dynamic

view of the market. We are able to provide additional evidence that HFTs enjoy higher

percentages of volume due to limit orders establishing time priority relative to non-HFTs,

especially when the relative tick size is large. Using the same dataset, Section VI.B also

addresses the concern that the presence of non-HFTs regarding the best quotes is due to HFTs’

canceling or executing orders instead of non-HFTs actively improving the quotes.

A. Cross-sectional variation of HFT activity on liquidity taking

Concerns may arise if HFTs prefer low-priced stocks for reasons other than their large

relative tick sizes. For example, HFTs may prefer low-priced stocks because with them they

can trade the same number of shares with less capital, or HFTs may be the counterparts of

less sophisticated traders and less sophisticated traders may favor low-priced stocks. These

incentives, however, affect not only HFTs’ liquidity-providing behavior but also their

liquidity-taking behavior. Thus, if these motivations drive the cross-sectional variation of

HFT liquidity provision, we should observe that HFT liquidity taking and HFT’s activities

overall display the same cross-sectional pattern as that of HFT liquidity-providing activity.

This section checks the validity of these alternative hypotheses as well as of other hypotheses

that have similar effects on liquidity provision and liquidity taking.37

37 We are aware that the make-take fee structure is a possible mechanism for generating alternative liquidity-making and taking patterns. Because the maker rebate and take fee are also uniform for stocks priced above $1, the rebate and fees are higher in percentage for stocks with lower prices. However, as discussed in section II, the economic mechanism underlying the fee is the same as the relative tick size, which is the trade-off between price and time priority.

33

We follow the methodology in Table IV, and use the Nasdaq HFT trade file for 117

stocks in Oct 2010 to compute the volume with HFTs as liquidity takers relative to total

volume for each portfolio J on day t:

𝐻𝐹𝑇𝑙𝑖𝑞𝑡𝑎𝑘𝑒 = ∑ (𝐻𝑁∈ +𝐻𝐻 )∑ (𝑁𝐻∈ +𝐻𝐻 + 𝐻𝑁 + 𝑁𝑁 ) (13)

In addition, we compute the volume with HFTs engaged either as liquidity providers or

liquidity takers relative to total volume for each portfolio J on day t:

𝐻𝐹𝑇𝑙𝑖𝑞𝑏𝑜𝑡ℎ = ∑ (𝐻𝑁∈ + 𝑁𝐻 +𝐻𝐻 )∑ (𝑁𝐻∈ +𝐻𝐻 + 𝐻𝑁 + 𝑁𝑁 ) (14)

Table IX Panel A shows the average trading volume percentage due to HFT liquidity

takers for each of the market cap–by–relative tick size portfolios. The result demonstrates

that the percentage of volume with HFTs as liquidity takers decreases with the relative tick

size. If HFTs’ preference for low-priced stocks is driven by low capital requirements or a less

sophisticated clientele, it is unlikely that we would observe that the HFT liquidity-making

and liquidity-taking activities display opposite cross-sectional variations with respect to the

relative tick size.

Panel B of table IX reveals an interesting pattern for overall HFT activity. Although

HFT liquidity-providing and liquidity-taking activities have opposite cross-sectional

variations with respect to the relative tick size, the overall HFT activity follows the same

cross-sectional variation as the HFT liquidity-making activity for large- and medium-sized

stocks, while following the same cross-sectional variation as the HFT liquidity-taking activity

for small-sized stocks. This result can be driven by varying dispersions of HFT liquidity-

making and liquidity-taking activities for stocks of varying market caps. For example, for

large-sized stocks, the HFT liquidity-making activity for stocks with large relative tick sizes

is 14.03% higher than that for stocks with small relative tick sizes (Table IV), but HFT

liquidity-taking activity for stocks with large relative tick sizes is only 4.17% lower than that

for stocks with small relative tick sizes (Panel A of Table IX). The difference in percentage

can contribute to the increasing share of overall HFT activity with respect to relative tick

sizes for large stocks. The same reasoning can be applied to medium- and small-sized stocks.

Insert Table IX about Here

34

In summary, the HFT activity overall does not exhibit a clear relationship with the

relative tick size since HFT liquidity-providing and liquidity-taking activities exhibit the

opposite cross-sectional variations with respect to the relative tick size. Proponents of a wider

tick size argue that a large tick size would control the growth of HFT (Weild, Kim, and

Newport (2012)). This argument is not consistent with the results displayed in Table IX.

Trading volumes of large- and medium-sized stocks tend to be larger than those of small-

sized stocks; thus if we take the market as a whole, a larger tick size is associated with higher

overall HFT activity.

B. Additional robustness check on price v.s. time priority

The tick size constraints channel argues that speed enables HFTs to achieve time

priority over non-HFTs when price priority is unable to differentiate two types of traders due

to the tick size regulation. The previous sections have established two results. First, a large

relative tick size is associated with higher frequency of incidences in which the best quotes

provided by HFTs and non-HFTs quotes are the same, while a small relative tick size is

associated with higher frequency of incidents in which the best quotes are uniquely provided

by non-HFTs relative to HFTs. Second, the portfolio in which HFTs serve most actively as

the liquidity providers for executed orders is also the portfolio in which HFTs and non-HFTs

provide the same best quotes the majority of the time when HFTs enjoy their comparative

advantage in establishing time priority over non-HFTs. These two results are established

using snapshots of limit-order books and executed trades, and thus are susceptible to two

criticisms. The first criticism corresponds to the speed competition between HFTs and non-

HFTs. Although the result that HFTs enjoy time priority over non-HFTs when the two types

of traders quote the same price is very much to be expected, and the result from the

percentage of volume with HFTs as the liquidity providers is consistent this claim, the nature

of the data we deploy in previous sections prevents us from providing direct evidence for this

claim. The second criticism corresponds to the price competition between HFTs and non-

HFTs. The data cannot discriminate whether the presence of non-HFTs in the best quotes is

due to non-HFTs’ actively undercutting HFTs or to HFTs’ withdrawing from best quotes.

35

Fortunately, NASDAQ provides us with five days of a sample that allows us to

dynamically examine the limit-order book. We use this sample to address the two concerns

mentioned above. Section VI.B.1 describes the data. Section VI.B.2 examines whether HFTs

are more likely to establish time priority than non-HFTs, and also tests how such a difference

in establishing time priority varies with the relative tick size. Section VI.B.3 examines

whether non-HFTs are more likely to actively establish price priority by undercutting HFTs.

B.1. Data

The NASDAQ top-of-book data contain the collective best HFT–displayed quotes,

the collective best non-HFT–displayed quotes, and their corresponding aggregate sizes. There

is a data record any time there was a change in either the HFT or non-HFT quote. The data is

available only for the week of Feb 22–26, 2010, so we use the data mainly for a robustness

check instead of showing the results in the main section. The sample for our analysis contains

the same 117 stocks as in the previous sections.

For each record, we are able to differentiate whether the change to the top-of-book is

made by an order added to the book or by an order that has disappeared from the book. An

order can disappear from the limit-order book by being either executed or canceled. Since the

NASDAQ also provides trading records with trade identifiers (HH, HN, NH, NN) for the 117

stocks during this sample period, we match the top-of-book data and the trade data by

millisecond timestamp, sign of the order (trade), price of the order (trade), size of the order

(trade), and type of liquidity providers (HFTs or non-HFTs). We classify the ones that we

identify as having disappeared from the limit-order book and matches that can be found in the

trade data as executions of displayed orders.

B.2. Time priority of HFT traders

Although the top-of-book limit-order data do not provide information on the time

precedence queue at each price, we are still able to infer whether an order is executed due to

time priority or price priority. If, at the time of execution, only a unique type of trader (HFT

or non-HFT) provides quotes at the execution price, we classify this trade as executed

because its liquidity provider has price priority. If, at the time of execution, both HFTs and

36

non-HFTs provide quotes at the execution price, we classify this trade as executed because its

liquidity provider has time priority. This can be supported by the reasoning that although the

other type of trader provides liquidity at the same price as the executed order, displayed

orders from the other type of trader fail to be executed because they have lower (time)

priority. By this classification, each trade from displayed orders is classified into one of the

four types: 1) the liquidity-providing HFT has price priority, 2) the liquidity-providing HFT

has time priority, 3) the liquidity-providing non-HFT has price priority, and 4) the liquidity-

providing non-HFT has time priority.

To test which type of trader is more likely to have time priority over the other type,

and how this relation changes with the relative tick size, we perform the following regression:

𝑇𝑖𝑚𝑒 𝑃𝑟𝑖𝑜𝑟𝑖𝑡𝑦 , , = 𝛽 × 𝐻𝐹𝑇𝑑𝑢𝑚𝑚𝑦 , , + 𝛽 × 𝑡𝑖𝑐𝑘 , + 𝛽 × 𝑡𝑖𝑐𝑘 , × 𝐻𝐹𝑇𝑑𝑢𝑚𝑚𝑦 , , +𝑢 , + Γ × 𝑋 , +𝜖 , , (15)

In the specification, 𝑇𝑖𝑚𝑒 𝑃𝑟𝑖𝑜𝑟𝑖𝑡𝑦 , , is the proportion of volume due to the liquidity

provider having time priority, calculated as the volume due to the liquidity provider having

time priority over the liquidity provider’s total volume, for stock i on date t of liquidity

provider type n.38 We have two daily observations for each stock: one for HFTs and one for

non-HFTs. The dependent variable is impacted by control variables (𝑋 , ) and three key

variables of interest: relative tick size, an HFT dummy, and their

interaction. 𝐻𝐹𝑇𝑑𝑢𝑚𝑚𝑦 , , equals 1 for HFTs and 0 otherwise. 𝑡𝑖𝑐𝑘 , is the relative

tick size of stock i at day t minus the average of the relative tick size of the sample. We

demean the relative tick size to facilitate the interpretation of 𝛽 , which captures the

difference between HFTs and non-HFTs for stocks with the average relative tick size. 39 𝛽

measures the relationship between the dependent variable and relative tick size for non-HFTs.

The interaction term 𝑡𝑖𝑐𝑘 , × 𝐻𝐹𝑇𝑑𝑢𝑚𝑚𝑦 , , . captures the differences between HFTs

and non-HFTs’ percentage of volume due to having time priority for stocks with different

relative tick sizes. 𝑢 , is the industry-by-time fixed effect. 𝑋 , are control variables presented

in Table I.

38 The number is defined as missing if the trading volume from liquidity provider type n is 0 for stock i on date t. 39 Without demeaning the data, 𝛽 is interpreted as the difference in profit between HFTs and non-HFTs for stocks with zero tick size, or infinite price.

37

Table X shows that the larger the relative tick size, the higher the percentage of

volume due to liquidity providers with time priority. The table also shows that HFTs enjoy a

higher percentage of volume due to achieving time priority than that enjoyed by non-HFTs.

For a stock with average tick size, HFT has about 8% more trades due to time priority than

that for non-HFTs. Note that the larger the relative tick size, the larger the difference between

HFT’s percentage of volume due to obtaining time priority and non-HFTs’ percentage of

volume due to obtaining time priority, as the positive significant coefficient of the interaction

term between the relative tick size and the HFT dummy variable indicates.

Insert Table X about Here

In summary, an increase in the relative tick increases the proportion of the dollar

volume due to time priority, and HFTs enjoy a higher proportion of the dollar volume due to

time priority than non-HFTs, especially when the relative tick size is large. All findings are

consistent with the tick size constraints hypothesis.

B.3. Active update of quotes

Using a minute-by-minute snapshot of the limit-order book, Table II shows that as the

relative tick size goes down, the best quotes are more likely to be provided by non-HFTs

relative to HFTs. Blume and Goldstein (1997) distinguish the active from the passive ways in

which an order can become the best bid (or ask). The first, the active way, is by actively

posting a bid (or ask) within the spread and thereby narrowing the spread. The second, the

passive way, is through lowering the collective best quotes or through the collective

withdrawal of other orders at the best quotes, thus leaving the remaining order at the very

best bid (or ask). Since orders actively improving the BBO or orders passively canceled or

executed can both affect the state of the limit-order book, one concern regarding the finding

in Table II is that the finding is due to orders which passively change the top-of-book limit

order. For example, the best quotes established by non-HFTs may simply be stale quotes, or

when non-HFTs fail to update their quotes when there is an information event. To address

this concern, we focus exclusively on orders which actively improve the BBO, and examine

how their activities vary with the relative tick size.

38

We use NASDAQ top-of-book displayed limit orders for the week of Feb. 22–26,

2010 to calculate the dollar size of each order which actively improves BBO for the 117

stocks on each day. For each update in the top-of-book, we check whether the best bid price

after the top-of-book update is higher than the previous best bid price, or whether the best ask

price after the top-of-book update is lower than the previous ask price. If so, we regard the

BBO as having been actively improved. Since the data allow us to identify the types of

traders who actively improve the BBO, we aggregate the dollar sizes for all orders that

actively improved BBO for HFTs and non-HFTs, respectively.40 The specification of the

regression is as follows:

𝐷𝑜𝑙𝑙𝑎𝑟𝑆𝑖𝑧𝑒 , = 𝛽 × 𝑡𝑖𝑐𝑘 , + Γ × 𝑋 , + 𝑢 , +𝜖 , (16)

where 𝐷𝑜𝑙𝑙𝑎𝑟𝑆𝑖𝑧𝑒 , is the proportional difference between non-HFTs’ and HFTs’

aggregate dollar size of orders that actively improve the BBO. This is calculated as

for stock i on date t, where 𝐷𝑜𝑙𝑆𝑖𝑧𝑒 denotes the aggregate dollar size

of orders that improve the BBO for liquidity provider type j. The variable of interest, 𝛽,

measures how the percentage difference between HFTs’ and non-HFTs’ active dollar size

improvement varies with the relative tick size. 𝑢 , is the industry-by-time fixed effect. 𝑋 ,

are the control variables presented in Table I.

Table XI displays the regression output. The result shows that a decrease in the

relative tick size leads to an increase in the percentage of active dollar size improvement from

non-HFTs relative to HFTs. Therefore, our result that the proportion of liquidity provided by

non-HFTs relative to that of HFTs decreases with the relative tick size is robust even when

only active improvement of quotes is taken into account.

Insert Table XI about Here

40 When weighted by size, the case in which traders improve the best quotes by only 1 share carries less weight. The aggregated dollar size is not weighted by time. This is due to the fact that for those orders, the duration of their remaining in the limit-order book cannot be determined. The top-of-book data provide the information on the cumulative depth, but without the information on order ID.

39

VII. Conclusion

We contribute to the HFT literature by providing a tick size–based explanation of

speed competition in liquidity provision. We find that a large relative tick size constrains

price competition and generates higher revenue for liquidity provision. The constrained price

competition also helps HFTs achieve time priority when they quote the same price as non-

HFTs. As a consequence, HFTs provide a larger fraction of liquidity for low-priced stocks in

which a one-cent uniform tick size implies a larger relative tick size. We argue that such a

cross-sectional pattern cannot be explained by either of two existing HFT channels: the price

competition channel or the information channel.

The tick size constraints channel provides new insights into the policy debate over

HFT. The current policy debate focuses on whether additional regulation is required and, if

so, how to pursue it. Our paper points in a new direction: HFT may simply be a consequence

of the existing tick size regulation. One possible policy solution would be tick size

deregulation instead of additional regulation. Specifically, our paper questions the uniform

tick size rationale, which generates a heterogeneous relative tick size.

This paper also questions the rationale to increase the tick size. The JOBS Act

encourages the SEC to examine the possibility of increasing the tick size, and a pilot program

is under way for less liquid stocks. Proponents of a larger tick size have offered three

rationales for this position (Weild, Kim and Newport (2012)). First, a larger tick size should

control the growth of HFT, and second, a larger tick size should increase liquidity. Our paper

shows that a larger tick size encourages HFT without improving liquidity. The third

argument for increasing tick size is that a larger tick size would lead to more IPOs. However,

the causal impact of the tick size on IPOs has not been proved by academic research using

clean identification. We believe that an increase in the tick size would create more rents for

traders who establish time priority, and would fuel another round of the arms race in speed.

Our paper has several limitations. First, we show that non-HFTs are more likely to

establish price priority than HFTs when the relative tick size is small. However, our data do

not provide the identity of the non-HFTs who undercut the price of HFTs. One such

possibility is that some non-HFTs in the sample are fundamental investors who use limit

orders to minimize their transaction costs, and they can afford more aggregative limit orders

40

because they are natural buyers or sellers of a security. This conjecture can be tested with

account-level data. Second, we consider only displayed orders in our analysis because hidden

orders have lower execution priority than displayed orders at the same price. It would be

interesting to examine the use of hidden orders by HFTs and non-HFTs.

Our paper could be extended in various ways. First, the extant literature on HFT finds

that technological shocks that enhance trading speed improve liquidity. It is commonly

believed that liquidity improvement arises from traders with higher speed. However, this

paper finds that non-HFTs provide larger proportion of best quotes relative to that of HFTs

when the relative tick size is small. An intriguing conjecture is that liquidity improvement

can arise from traders who choose not to upgrade in the face of technology shocks. Slow

traders lose time priority when competing with faster traders and thus they have stronger

incentives to undercut the price; on the other hand, faster traders enjoy the speed advantage

for establishing time priority and thus they have weaker incentives to improve quotes. It

would be interesting to test this conjecture using account-level data. Second, current

theoretical work on speed competition focuses on the role of information. Models using

discrete prices can be constructed to indicate the value of speed and the impact of tick size

constraints on market quality. Third, speed competition is not the only market design

response to tick size constraints (Buti, Consonni, Rindi, Wen and Werner (2014) and Chao,

Yao and Ye (2014)). The literature on market microstructure focuses on liquidity and price

discovery under certain market designs, but market design is also endogenous, and it should

prove fruitful for examining why certain market designs exist in the first place. Finally, the

SEC recently announced a pilot program for increasing the tick size for a number of small

stocks, believing that the tick size may need to be wider for less liquid stocks. We encourage

the SEC to consider decreasing the tick size for liquid stocks in the pilot program,

particularly for large stocks with lower prices.

41

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46

Table I. Summary Statistics This table presents the summary statistics for the various samples used in this paper. Panel A presents the summary statistics for stocks contained in the NASDAQ HFT sample in October 2010. Panel B provides the summary statistics for the leveraged ETF sample used in the difference-in-differences test, in which the event window is 5 days before splits/reverse splits from 2010 through 2013. Panel C lists the summary statistics for stocks in the NASDAQ HFT sample from February 22, 2010 through February 26, 2010 used in the robustness test section. All the variables are measured for each stock per day unless otherwise indicated. HFTvolume is the trading volume with HFTs as liquidity providers over the total trading volume. tickrelative is the reciprocal of price. logmcap is the log value of market capitalization. turnover is the annualized share turnover. volatility is the standard deviation of open-to-close returns based on the daily price range, that is, high minus low, proposed by Parkinson (1980). logbvaverage is the logarithm of the average book value of equity per shareholder at the end of the previous year (December 2009). idiorisk is the variance on the residual from a 60-month beta regression using the CRSP Value Weighted Index. age (in 1k days) is the length of time for which price information is available for a firm on the CRSP monthly file. numAnalyst is the number of analysts providing one-year earnings forecasts calculated from I/B/E/S. pastreturn is the monthly return for each stock in September 2010. PIN is the probability of informed trading. UnitRevenue is the revenue for liquidity provision per dollar volume. return is the contemporaneous daily return. Qtspd represents the time-weighted quoted spread. pQtspd represents the time-weighted proportional quoted spread. Qtspdadj and pQtspdadj represent the time-weighted quoted spread and the time-weighted proportional quoted spread after adjusting for fees. SEffspd represents the size-weighted effective spread and pSEffspd represents the size-weighted proportional effective spread. SEffspdadj and pSEffspdadj represent the size-weighted effective spread and the size-weighted proportional effective spread after adjusting for fees. Depth represents the sum of the time-weighted dollar depth at the best bid and ask. RelativeRun is the proxy for percentage of liquidity provided by HFTs.

Mean Median Std. Min. Max. Panel A. NASDAQ HFT Sample

HFTvolume 0.28 0.267 0.135 0 0.728 tickrelative 0.05 0.036 0.039 0.002 0.192 logmcap 21.891 21.402 1.885 19.371 26.399 turnover 2.293 1.744 2.136 0.074 33.301 volatility 0.015 0.013 0.009 0.002 0.099 logbvaverage 13.148 13.196 2.112 8.822 17.881

idiorisk 0.013 0.008 0.016 0.001 0.139 age (in 1k days) 9.617 7.565 7.737 0.945 30.955 numAnalyst 13.545 11 9.92 1 48 pastreturn 0.105 0.096 0.071 -0.077 0.336 PIN 0.12 0.115 0.051 0.021 0.275 UnitRevenue (in bps)

1-min Interval 0.57 0.2 3.33 -32.87 88.89

47

5-min Interval 0.38 0.2 4.17 -29.81 145.62 30-min Interval 0.47 0.36 6.43 -69.21 145.62 Daily Closing 1.4 1.28 18.54 -323.38 215.43

Panel B. Leveraged ETF Sample

return 0 0 0.04 -0.25 0.25 Qtspd (in cent) 4.93 2.55 5.48 1.00 33.88 pQtspd (in bps) 10.56 9.76 5.84 1.77 33.17 Qtspdadj (in cent) 5.52 3.14 5.48 1.59 34.47 pQtspdadj (in bps) 13.11 11.87 7.19 2.44 44.67

SEffspd (in cent) 3.47 1.79 3.98 0.67 32.90 pSEffspd (in bps) 7.95 6.89 4.89 1.50 34.81 SEffspdadj (in cent) 4.07 2.39 3.98 1.27 33.50 pSEffspdadj (in bps) 10.54 9.05 6.67 2.16 43.28 Depth (in mn dollars) 0.35 0.11 0.87 0.01 6.99 RelativeRun 0.22 0.22 0.05 0.03 0.38

48

Table II. Who Provides the Best Quotes? This table displays the percentages of time that the best bid and ask quotes to the NASDAQ limit-order book are provided by HFTs and non-HFTs, respectively. The sample includes 117 stocks in the NASDAQ HFT data from October 2010. Stocks are sorted first into 3-by-3 portfolios by average market cap and then by average price from September 2010. For each portfolio and each trading day, we calculate the percentage of time that the best quotes are provided uniquely by HFTs, the percentage of time that the best quotes are provided by uniquely non-HFTs, and the percentage of time that the best quotes are provided by both HFTs and non-HFTs. Column (1) presents the average percentage of time that the best quotes are provided uniquely by HFTs, column (2) presents the average percentage of time that the best quotes are provided uniquely by non-HFTs, and column (3) presents the percentage of time that the best quotes are provided by both HFTs and non-HFTs. Column (4) shows the ratio of column (2) figures to column (1) figures. Column (5) shows the difference between column (1) figures and (2) figures. t-statistics for column (5) based on 21 daily observations are presented in column (6). *, **, and *** represent statistical significance at the 10%, 5%, and 1% levels, respectively.

(1) (2) (3) (4) (5) (6)

Relative Tick Size HFT Only

Non-HFT Only

HFT & Non-HFT Ratio Non-HFT

minus HFT t-stat

Large Cap

Large (Low Price) 1.6% 2.5% 95.9% 1.55 0.9%*** 7.27

Medium (Medium Price) 11.9% 18.6% 69.6% 1.57 6.7%*** 14.01

Small (High Price) 16.8% 37.7% 45.5% 2.25 20.9%*** 37.81

Middle Cap

Large (Low Price) 18.0% 15.2% 66.8% 0.84 -2.9%*** -3.52

Medium (Medium Price) 20.0% 56.6% 23.4% 2.83 36.6%*** 36.03

Small (High Price) 20.7% 63.7% 15.7% 3.08 43.0%*** 67.15

Small Cap

Large (Low Price) 11.3% 54.7% 34.1% 4.86 43.4%*** 27.55

Medium (Medium Price) 20.2% 55.8% 24.0% 2.77 35.7%*** 30.11

Small (High Price) 18.6% 70.7% 10.7% 3.80 52.1%*** 66.79

Total 15.4% 41.7% 42.9% 2.62 26.3%*** 18.31

49

Table III. Market Share of BBO Depth Provided by HFTs This table presents the percentages of depth at the NASDAQ best bid and offer (BBO) provided by HFTs. The sample includes 117 stocks in NASDAQ HFT data from October 2010. The stocks are sorted first by average market cap and then by average price in September 2010. To calculate the share-weighted average for each portfolio on each day, we aggregate the number of shares provided by HFTs at the BBO and then divide it by the total number of shares at the BBO for that portfolio. t-statistics are calculated based on 21 daily observations. *, ** and *** represent statistical significance of large-minus-small differences at the 10%, 5%, and 1% levels, respectively.

Large Medium Small Large-Small

Relative Tick Size Relative Tick Size Relative Tick Size Relative Tick Size t-stat

(Low Price) (Medium Price) (High Price) (Low-High Price)

Large Cap 55.66% 45.44% 35.07% 20.59%*** 22.10

Middle Cap 39.73% 29.24% 24.61% 15.13%*** 22.88

Small Cap 25.78% 23.02% 20.78% 5.00%*** 3.18

L-S Cap 29.88%*** 22.43%*** 14.29%***

t-statistics 18.84 17.92 16.80

50

Table IV. Percentage of Volume with HFTs as the Liquidity Providers This table presents the trading volume percentage due to HFTs as liquidity providers. The sample includes 117 stocks in the NASDAQ HFT data from October 2010. The stocks are sorted first by average market cap and then by average price in September 2010 into 3-by-3 portfolios. To calculate the volume-weighted average for each portfolio on each day, we aggregate the volumes due to HFT liquidity providers and then divide that figure by the total volume for that portfolio. t-statistics are calculated based on 21 daily observations. *, **, and *** represent statistical significance at the 10%, 5%, and 1% levels of large-minus-small differences, respectively.

Large Medium Small Large-Small

Relative Tick Size Relative Tick Size Relative Tick Size Relative Tick Size t-stat

(Low Price) (Medium Price) (High Price) (Low-High Price)

Large Cap 49.96% 38.23% 35.93% 14.03%*** 15.54

Middle Cap 39.30% 24.03% 24.33% 14.97%*** 18.74

Small Cap 24.11% 18.88% 18.49% 5.62%*** 5.38

L-S Cap 25.84%*** 19.35%*** 17.43%***

t-statistics 21.33 21.76 18.22

51

Table V. HFT Liquidity Provision This table presents the results of the regression of percentage of trading volume with HFTs as liquidity providers on the relative tick size. The regression uses the NASDAQ HFT data sample as of October 2010. The regression specification is:

𝐻𝐹𝑇𝑣𝑜𝑙𝑢𝑚𝑒 , = 𝑢 , + 𝛽 × 𝑡𝑖𝑐𝑘 , + Γ × 𝑋 , +𝜖 , where 𝐻𝐹𝑇𝑣𝑜𝑙𝑢𝑚𝑒 , is the trading volume with HFTs as the liquidity provider over total trading volume for stock i on date t. 𝑡𝑖𝑐𝑘 , is the inverse of the stock price for stock i on day t. 𝑢 , represents industry-by-time fixed effects. The definitions of the control variables 𝑋 , are presented in Table 1. We report estimated coefficients and heteroskedasticity robust standard errors, clustered by firm. Standard errors are in parentheses. ***, **, and * indicate the statistical significance at the 1%, 5%, and 10% levels. Dep. Variable HFTvolume

(1) (2) (3) (4) (5) (6) (7)

tickrelative 1.034*** 1.035*** 0.943*** 1.074** 0.982*** 1.033*** 0.956***

(0.38) (0.37) (0.34) (0.42) (0.37) (0.38) (0.36) logmcap 0.054*** 0.051*** 0.051*** 0.047*** 0.046*** 0.054*** 0.031***

(0.01) (0.01) (0.01) (0.01) (0.01) (0.01) (0.01) turnover 0.008** 0.007**

(0.00) (0.00) volatility -0.719 -0.536

(0.64) (0.59) logbvaverage 0.003 0.005

(0.00) (0.00) idiorisk -0.359 -0.547

(0.63) (0.46) age 0.002 0.003*

(0.00) (0.00) numAnalyst 0.001 0.001

(0.00) (0.00) PIN -0.469** -0.407*

(0.22) (0.21)

pastreturn -0.013 -0.034 (0.11) (0.09)

R2 0.613 0.622 0.634 0.618 0.626 0.613 0.664 N 2352 2352 2268 2352 2352 2352 2268 Industry*time FE Y Y Y Y Y Y Y

52

Table VI. Tick size and Liquidity Provision Revenue This table presents the regression of the unit revenue of liquidity provision on the relative tick size. The regression uses the NASDAQ HFT sample as of October 2010.The regression specification is:

𝑈𝑛𝑖𝑡𝑅𝑒𝑣𝑒𝑛𝑢𝑒 , , = 𝛽 × 𝑡𝑖𝑐𝑘 , + 𝛽 × 𝐻𝐹𝑇𝑑𝑢𝑚𝑚𝑦 , , + 𝑢 , + Γ × 𝑋 , + 𝜖 , , Columns (1)–(4) present regression results for daily unit profit measured on the assumption that inventories are emptied at one-minute, five-minute, 30-minute intervals and at daily closing. 𝑡𝑖𝑐𝑘 , is the inverse of the stock price for stock i on day t. 𝐻𝐹𝑇𝑑𝑢𝑚𝑚𝑦 , , is equal to 1 if the revenue measure is from HFTs and 0 otherwise. 𝑢 , represents the industry-by-time fixed effects. The definitions of the control variables 𝑋 , are presented in Table 1. We report estimated coefficients and heteroskedasticity robust standard errors, clustered by firm. Standard errors are in parentheses. ***, **, and * indicate the statistical significance at the 1%, 5%, and 10% levels. Dep. Variable Unit Revenue (in bps) (1) (2) (3) (4) 1-min Interval 5-min Interval 30-min Interval Daily Closing

tickrelative 20.125*** 19.024*** 18.677*** 21.561

(4.68) (4.21) (4.25) (17.55)

HFTdummy 0.828*** 0.761*** 0.420** -0.093

(0.13) (0.14) (0.17) (0.52)

logmcap -0.268 -0.160 -0.129 -0.233

(0.17) (0.16) (0.16) (0.51)

turnover -0.113** -0.085 0.038 -0.178

(0.05) (0.07) (0.09) (0.20)

volatility -0.807 -19.509 -91.450*** -179.865**

(14.92) (21.25) (22.08) (73.51)

logbvaverage 0.029 0.036 0.017 0.314

(0.07) (0.08) (0.07) (0.19)

idiorisk -3.551 2.883 11.624** 26.079

(7.79) (6.03) (5.02) (20.86)

age 0.005 -0.008 -0.028* -0.033

(0.02) (0.02) (0.02) (0.05)

numAnalyst 0.042* 0.040** 0.033* 0.063

(0.02) (0.02) (0.02) (0.06)

PIN 0.604 0.797 2.895 9.835

(3.05) (3.15) (3.47) (8.87)

pastreturn -2.409 -1.658 1.373 9.321*

(2.06) (1.72) (1.95) (5.59)

R2 0.260 0.219 0.214 0.194

N 4484 4484 4484 4484

Industry*time FE Y Y Y Y

53

Table VII. Correlation Test for the Proxy of the Percent of HFT Activity This table presents the cross-sectional correlations between the proxies for the percentage of liquidity provided by HFTs and the HFT activity calculated from the NASDAQ HFT dataset. The HFT activity measures include the percentage of volume with HFTs as liquidity providers, HFTvolume (making), and the percentage of volume with HFTs as liquidity takers, HFTvolume (taking). The proxy for the percentage of liquidity provided by HFTs include RelativeRun, Quote-to-Trade Ratio and the Dollar Volume (in $100)–to–Message Ratio multiplied by -1. P-values are shown under correlation coefficients; *, **, and *** denote statistical significance at the 10%, 5% and 1% levels, respectively.

HFT Measures HFTvolume (making) HFTvolume (taking)

Panel A. Pearson Correlation

RelativeRun 0.837 0.377

<.0001 <.0001

Quote / Trade Ratio -0.390 -0.082

<.0001 0.378

-Trading Vol. (in $100) / Message Ratio -0.252 -0.274

0.006 0.003

Panel B. Spearman Correlation

RelativeRun 0.835 0.361

<.0001 <.0001

Quote / Trade Ratio -0.589 -0.154

<.0001 0.0969

-Trading Vol. (in $100) / Message Ratio -0.554 -0.506

<.0001 <.0001

54

Table VIII. Difference-in-differences Test Using Leveraged ETF Splits (Reverse Splits) This table presents the results of difference-in-differences tests using leveraged ETF split (and reverse split) events from 2010 to 2013. The event windows are 5 days before and 5 days after the events. The regression specification is:

𝑦 , , = 𝑢 , + 𝛾 , + 𝜌 × 𝐷 , , + 𝜃 × 𝑟𝑒𝑡𝑢𝑟𝑛 , , + 𝜖 , , 𝑢 , is the index by time fixed effects and 𝛾 , is the ETF fixed effects for ETF j of index i. The treatment dummy 𝐷 , equals 0 for the control group. For the treatment group, 𝐷 equals 0 before splits/reverse splits and 1 after the splits/reverse splits. Returni,t,j is the return for ETF j of index i on day t. Qtspd represents the time-weighted quoted spread. pQtspd represents the time-weighted proportional quoted spread. Qtspdadj and pQtspdadj represent the time-weighted quoted spread and the time-weighted proportional quoted spread after adjusting for fees. SEffspd represents the size-weighted effective spread and pSEffspd represents the size-weighted proportional effective spread. SEffspdadj and pSEffspdadj represent the size-weighted effective spread and the size-weighted proportional effective spread after adjusting for fees. Depth represents the time-weighted dollar depth at the BBO in millions of dollars. RelativeRun is the proxy of the percentage of liquidity provided by HFTs. We report estimated coefficients and heteroskedasticity robust standard errors, clustered by ETFs. Standard errors are in parentheses. ***, **, and * indicate the statistical significance at the 1%, 5%, and 10% levels. Panel A. Split Sample

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

Qtspd Qtspdadj pQtspd pQtspdadj Depth SEffspd SEffspdadj pSEffspd pSEffspdadj RelativeRun (in cent) (in cent) (in bps) (in bps) (in mn) (in cent) (in cent) (in bps) (in bps)

𝐷 -10.565*** -10.565*** 2.129* 3.804*** 0.045 -6.826*** -6.826*** 2.073** 3.777** 0.008*

(2.17) (2.17) (1.07) (1.33) (0.05) (1.59) (1.59) (0.91) (1.42) (0.00)

return -8.451*** -8.451*** -9.417*** -10.060*** 0.037 -4.671*** -4.671*** -5.103** -5.757* -0.016

(1.07) (1.07) (1.44) (2.29) (0.03) (0.67) (0.67) (2.07) (3.12) (0.01) R2 0.950 0.950 0.957 0.952 0.956 0.932 0.932 0.929 0.926 0.964 N 220 220 220 220 220 220 220 220 220 220 Index*time FE Y Y Y Y Y Y Y Y Y Y ETF FE Y Y Y Y Y Y Y Y Y Y

55

Panel B. Reverse Split Sample

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

Qtspd Qtspdadj pQtspd pQtspdadj Depth SEffspd SEffspdadj pSEffspd pSEffspdadj RelativeRun

(in cent) (in cent) (in bps) (in bps) (in mn) (in cent) (in cent) (in bps) (in bps)

𝐷 1.415** 1.415** -3.822*** -6.917*** -0.374** 0.837* 0.837* -4.088*** -7.235*** -0.016**

(0.66) (0.66) (0.79) (1.38) (0.17) (0.46) (0.46) (0.87) (1.48) (0.01)

return 0.076 0.076 -7.758*** -10.672*** 0.877 2.498 2.498 -0.768 -3.731 -0.038

(3.05) (3.05) (2.25) (3.43) (0.73) (1.71) (1.71) (2.82) (4.37) (0.03)

R2 0.908 0.908 0.932 0.896 0.780 0.867 0.867 0.845 0.842 0.897 N 660 660 660 660 660 660 660 660 660 660 Index*time FE Y Y Y Y Y Y Y Y Y Y ETF FE Y Y Y Y Y Y Y Y Y Y

56

Table IX. Percentage of Volume with HFTs as the Liquidity Takers and Percentage of Volume with HFTs as the Liquidity Takers or Liquidity Makers This table presents the trading volume percentage with HFTs as liquidity takers and trading volume percentage with HFTs as liquidity providers or liquidity takers. The sample includes 117 stocks in NASDAQ HFT data from October 2010. The stocks are sorted first by average market cap and then by average price from September 2010 into 3-by-3 portfolios. Panel A displays the volume-weighted percentage of trading volume with HFTs as liquidity takers. To calculate the volume-weighted average for each portfolio on each day, we aggregate the volumes with HFTs as liquidity takers and then divide that figure by the total volume for that portfolio. Panel B displays the volume-weighted percentage of trading volume with HFTs engaged as either liquidity providers or takers. To calculate the volume-weighted average for each portfolio on each day, we aggregate the volumes due to HFT liquidity providers or HFT liquidity takers and then divide that figure by the total volume for that portfolio.t-statistics are calculated based on 21 daily observations. *, **, and *** represent statistical significance at the 10%, 5%, and 1% levels of large-minus-small differences, respectively.

Large Medium Small Large-Small

Relative Tick Size Relative Tick Size Relative Tick Size Relative Tick Size t-stat

(Low Price) (Medium Price) (High Price) (Low-High Price)

Panel A. Percentage of Trading Volume with High-frequency Traders as Liquidity Takers

Large Cap 44.11% 47.57% 48.28% -4.17%*** -5.31

Middle Cap 39.19% 42.40% 46.97% -7.78%*** -6.25

Small Cap 27.65% 33.36% 39.64% -11.99%*** -10.69

L-S Cap 16.46%*** 14.21%*** 8.64%***

t-statistics 13.76 13.04 8.47

Panel B. Percentage of Trading Volume with High-frequency Traders as Liquidity Makers or Takers

Large Cap 73.72% 69.03% 68.14% 5.58%*** 9.30

Middle Cap 64.46% 57.39% 61.45% 3.01%** 2.55

Small Cap 45.61% 46.51% 51.41% -5.80%*** -3.92

L-S Cap 28.11%*** 22.53%*** 16.73%***

t-statistics 20.03 18.75 15.13

57

Table X. Dollar Volume due to Time Priority with Respect to Tick Size This table presents the regressions of the proportion of dollar volume due to limit orders having time priority on the relative tick size. The regression uses the NASDAQ HFT data sample of February 22–26, 2010.The regression specification is:

𝑇𝑖𝑚𝑒 𝑃𝑟𝑖𝑜𝑟𝑖𝑡𝑦 , , = 𝛽 × 𝐻𝐹𝑇𝑑𝑢𝑚𝑚𝑦 , , + 𝛽 × 𝑡𝑖𝑐𝑘 , +𝛽 × 𝐻𝐹𝑇𝑑𝑢𝑚𝑚𝑦 , , × 𝑡𝑖𝑐𝑘 , + 𝑢 , + Γ × 𝑋 , +𝜖 , ,

𝑇𝑖𝑚𝑒 𝑃𝑟𝑖𝑜𝑟𝑖𝑡𝑦 , , is the volume due to the liquidity provider having time priority over the liquidity provider’s total volume for stock i on date t of liquidity provider type n. 𝑡𝑖𝑐𝑘 , is the daily inverse of the stock price. 𝐻𝐹𝑇𝑑𝑢𝑚𝑚𝑦 , , equals 1 if the revenue measure is from HFTs and 0 otherwise. 𝑢 , represents the industry-by-time fixed effects. The definitions of the control variables 𝑋 , are presented in Table 1. We report estimated coefficients and heteroskedasticity robust standard errors, clustered by firm. Standard errors are in parentheses. ***, **, and * indicate the statistical significance at the 1%, 5%, and 10% levels.

Dep. Variable Volume Due to Time Priority (1) (2) (3) (4) (5) (6) (7)

tickrelative 3.069*** 3.231*** 3.075*** 3.407*** 3.089*** 3.073*** 3.529*** (0.47) (0.49) (0.49) (0.56) (0.49) (0.47) (0.61) HFTdummy 0.083*** 0.083*** 0.082*** 0.082*** 0.083*** 0.083*** 0.081*** (0.01) (0.01) (0.01) (0.01) (0.01) (0.01) (0.01) tickrelative*HFTdummy 0.551** 0.551** 0.590** 0.571** 0.556** 0.552** 0.613** (0.28) (0.28) (0.29) (0.28) (0.28) (0.28) (0.30) logmcap 0.098*** 0.092*** 0.095*** 0.059*** 0.094*** 0.099*** 0.051*** (0.01) (0.01) (0.01) (0.02) (0.01) (0.01) (0.02) turnover 0.009* 0.008* (0.01) (0.00) volatility -3.963*** -3.506*** (1.32) (1.32) logbvaverage -0.007 0.000 (0.01) (0.01) idiorisk -1.134 -1.064 (0.86) (1.24) age 0.006*** 0.006*** (0.00) (0.00) numAnalyst 0.007* 0.006* (0.00) (0.00) pin -0.282 -0.271 (0.34) (0.32) pastreturn -0.073 -0.006 (0.16) (0.15) R2 0.644 0.655 0.655 0.685 0.647 0.645 0.699 N 1154 1154 1094 1144 1154 1154 1084 Industry*time FE Y Y Y Y Y Y Y

58

Table XI. Active Quote Improvement This table presents the regression of the proportional difference between non-HFTs’ and HFTs’ dollar sizes of orders which actively improve the NASDAQ BBO on the relative tick size. The regression uses the NASDAQ HFT data sample as of February 22–26, 2010. The regression specification is:

𝐷𝑜𝑙𝑙𝑎𝑟𝑆𝑖𝑧𝑒 , = 𝛽 × 𝑡𝑖𝑐𝑘 , + Γ × 𝑋 , + 𝑢 , +𝜖 , where 𝐷𝑜𝑙𝑙𝑎𝑟𝑆𝑖𝑧𝑒 , is non-HFTs' minus HFTs’ dollar sizes of orders which actively improve the NASDAQ BBO over the sum of the two terms for stock i on day t. 𝑡𝑖𝑐𝑘 , is the daily inverse of the stock price. 𝑢 , represents the industry-by-time fixed effects. The definitions of the control variables 𝑋 , are presented in Table 1. We report estimated coefficients and heteroskedasticity robust standard errors, clustered by firm. Standard errors are in parentheses. ***, **, and * indicate the statistical significance at the 1%, 5%, and 10% level. Dep. Variable non-HFTs Minus HFTs’ Active Quote Improvement

(1) (2) (3) (4) (5) (6) (7) tickrelative -2.434** -2.499** -2.170** -2.267** -2.437** -2.374** -2.105* (0.97) (0.97) (1.00) (1.11) (0.99) (0.95) (1.18) logmcap -0.117*** -0.111*** -0.109*** -0.118*** -0.101*** -0.115*** -0.084* (0.02) (0.02) (0.02) (0.04) (0.03) (0.02) (0.04) turnover -0.015 -0.012 (0.01) (0.01) volatility 2.462 2.563 (3.80) (3.71) logbvaverage -0.019 -0.028 (0.02) (0.02) idiorisk 0.004 -0.210 (1.17) (1.56) age -0.002 -0.005 (0.01) (0.01) numAnalyst 0.003 0.003 (0.01) (0.01) pin 0.866 1.071 (0.70) (0.71) pastreturn -0.305 -0.202 (0.38) (0.41) R2 0.459 0.464 0.477 0.450 0.468 0.462 0.487 N 585 585 555 580 585 585 550 Industry*time FE Y Y Y Y Y Y Y