Tick Size Constraints, High Frequency Trading, and Liquidity1
First Draft: November 18, 2012
This draft: July 7, 2014
Chen Yao and Mao Ye
1
Chen 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: [email protected]. Telephone: 217-244-0474. We thank Jim
Angel, Shmuel Baruch, Robert Battalio, Dan Bernhardt, Jonathan Brogaard, Jeffery Brown, 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, Pankaj Jain, Tim Johnson, Charles Jones, Andrew
Karolyi, Nolan Miller, Katya Malinova, Steward Mayhew, 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, 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, AFA 2014 meeting
(Philadelphia), NBER market microstructure meeting 2013, 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 2013, and the 9th Central Bank
Workshop on the Microstructure of Financial Markets 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, and Chao Zi for their
excellent research assistance.
1
Abstract
This paper argues that constraints on price competition imposed by tick size regulation
have a causal impact on HFT liquidity provision. Non-high-frequency traders (non-HFTers) are
2.62 times more likely than HFTers to provide the best prices, thereby establishing price priority.
One-penny minimum tick size for all stocks priced above $1, however, results in larger relative
tick size for low-priced stocks, which constrains non-HFTers from providing better prices but
help HFTers’ to establish time priority. We find HFT liquidity provision is more active for stocks
with large relative tick size and lower information asymmetry. For twin ETFs tracking the same
index, HFT is more active for the low priced one. The diff-in-diff test shows an ETF has a
decline in liquidity and increase in HFT activity after split relative to a non-splitting ETF
tracking the same index, whereas reverse splits increases liquidity but decreases HFT activity.
Profit of liquidity provision is higher for low priced stocks.
2
The literature on high frequency trading (HFT) identifies two overarching effects of
speed competition. 1) Price competition effect: speed allows high frequency traders (HFTers) to
be the low cost provider of liquidity; 2) Information effect: speed enables HFTers to trade on
advance information and adversely select slow traders (Jones (2013) and Biais and Foucault
(2014)). We further the HFT literature by establishing another channel for speed competition:
tick size constraints. In this view, speed competition neither facilitates price competition nor is it
necessarily used to adversely select other traders, but enables HFTers to achieve time priority
over non-HFTers when price competition is constrained. The purpose of this paper is to
demonstrate the causal impact of tick size regulation on HFT, particularly its liquidity supplying
behavior. This novel perspective on HFT, in turn, leads to a new insight for the policy debate on
market structure: current policy debate focuses on whether and how to pursue additional
regulation on HFT, our paper, demonstrates that HFT can be a response to existing regulation.
An important yet often neglected assumption for Walrasian equilibrium is infinitely
divisible price. In reality, price competition is constrained by tick size regulation. SEC rule 612
(the Minimum Pricing Increment) of regulation NMS prohibits stock exchanges from displaying,
ranking, or accepting quotations, orders, or indications of interest in any NMS stock priced in an
increment smaller than $0.01 if the quotation, order, or indication of interest is priced equal to or
greater than $1.00 per share.2 A recent study by Credit Suisse demonstrates that this one-penny
tick size is surprisingly binding for large stocks with low price: 50% of S&P stocks priced below
$100 per share have one-penny quoted spreads (Avramovic, 2012). The clustering of quoted
spreads on one penny suggests that many low priced liquidity stocks should have a natural bidask spread of less than one penny. The minimum pricing increment rule imposes a floor on the
lowest price for liquidity in the public exchange, and a surplus (supply exceeds demand) rises as
2
There are some limited exemptions such as the Retail Price Improvement (RPI) Program and mid-point peg orders.
3
a natural response to a binding price floor. Rockoff (2008) summarizes four possible responses
when controls prevent the price systems from rationing supply: queuing, black markets, evading,
and rationing. HFT liquidity provision is an application of this general economic principle. We
observe speed competition as a form of queuing through which traders with high speed capacity
compete for the front of the queue at a constrained price.
A binding tick size is not restricted to the scenario of one-cent spread. The constraints
exist wherever one trader’s ability to provide a better price is hindered by the tick size, for tick
size stops traders from bidding the securities price up or down to their marginal valuation. The
uniform tick size of one-cent implies that relative tick size, or the inverse of the nominal price, is
higher for stocks with lower price. For example, in January 2010, Citi group had a nominal price
level around $3.3, and a relative tick size as high as 30-basis point, which is greater than the
average daily return of Citi. This relative tick size is 18 times wider than that of HSBC, which
has a nominal price around $59. Traders, who would have differentiated themselves in the price
of liquidity under small relative tick size, may be forced to quote the same price when the
relative tick size is large. When traders quote the same price, speed generally serves as the
secondary priority rule to allocate supply in current U.S. market. As a result, a large relative tick
size generates two interrelated effects: it hinders price competition and encourages speed
competition.
We find that traders are more likely to quote identical prices for low priced stocks,
indicating that stocks with a large relative tick size indeed undergo more constrained price
competition. To identify the pattern, we categorize the provision of best price in the limit order
books into three types: 1) supplied by HFTers only, 2) supplied by non-HFTers only, and 3)
supplied by both. For large stocks with low prices, HFTers and non-HFTers both quote the best
4
price 95.9% of the time, and the priority of liquidity supplying is determined by the ability to
submit the orders at the top of the queue. A small relative size, however, encourages price
competition. The best quotes from HFTers and non-HFTers are the same only 45.5% of the time
for large stocks with high prices, indicating that HFTers and non-HFTers differentiate in price
54.5% of time.
The price competition channel of HFT believes that speed advantage enables HFTers to
provide better price of liquidity. Two recent surveys by Biais and Foucault (2014) and Jones
(2013) summarize three channels for speed to improve the price: avoiding adverse selection
(Hendershott, Jones and Menkveld (2011)), better management of inventory (Brogaard,
Hagströmer, Norden and Riordan (2013)) and low cost of operation (Biais and Foucault (2014)).
Opposite to this common belief, we find that non-HTFers are the more frequent providers of best
quotes. First, the likelihood of non-HFTers as unique providers of best price is 2.62 times more
than that of HFTers. More direct evidence involves test using relative tick size. Suppose speed
encourages better price of liquidity, HFTers should take a more important role as the unique
providers of best price for stocks with smaller relative tick size, for which reduces constraints to
undercut price. Our empirical results, however, indicate the opposite: HFTers are less likely to be
the unique providers of best price relative to non-HFTers as relative tick size decreases. This
result is surprising, because a recent editorial by Chordia, Goyal, Lehmann and Saar (2013)
raises the concern that “HFTers use their speed advantage to crowd out non-HFT liquidity
provision when the tick size is small and moving in front of standing limit orders is inexpensive.”
Our results, however, show that non-HFTers are more likely to move in front of the price queue
when relative tick size is small. In addition, the market share of non-HFTers is the highest for
stocks with the lowest relative tick size, both in terms of depth provided by non-HFTers and
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volume with non-HFTers as liquidity providers. As relative size increases, non-HFTers face
constraints to undercut HFTers, and HFTers have the comparative advantage to establish time
priority at constrained price. Indeed, O’Hara, Saar and Zhong (2013) find that HFTers are likely
to improve NBBO when relative tick size is large. Our results indicate that such an improvement
cannot simply be the indication for price competition, because non-HFTers also intend to provide
the same best price, but HFTers’ speed advantage help them to be the first to improve NBBO.
The existing literature does not differentiate two scenarios: 1) Both HFTers and non-HFTers are
willing to provide the best price, but HFTers have the speed advantage to post the order at the
top of the queue. 2) HFTer can provide better price than non-HFTers. HFTers improve NBBO in
both cases, but the first case renders speed competition and the second case generates price
competition. To draw the conclusion that who is the prominent best quote provider, we need to
examine whether one type of traders is more likely to provide better price than the other type,
particularly when the constraints for price competition is not binding.
The causal impact of relative tick size on HFT is further demonstrated using the two
identifications: twin ETFs tracking the same underlying indices and the diff-in-diff analysis
using ETF splits/reverse splits.3 The twin ETF test finds that low priced ETF within the index
group experiences more HFT activity. Because the twin-ETFs share the same underlying, such
differences can be ascribed to their heterogeneity in relative tick size. This result is further
strengthened by diff-in-diff test using ETF splits/reverse splits as exogenous shocks to relative
tick size, with ETFs tracking the same index but experiencing no splits/reverse splits as the
control group. We find that HFT activity in the splitting ETFs increases relative to the control
group, whereas reverse splits reduces HFT activity.
3
Though some indices are with more than two tracking ETFs, we use the phrase “twin ETFs” for brevity.
6
The test based on ETFs differentiates the tick size constraints channel of HFT from the
information channel. 4 We acknowledge the importance of the information channel, but our
results demonstrate an additional, non-informational channel of speed competition. Low priced
ETFs should not have more information than their high priced twins that track the same indices,
but the former have more HFT activity. Similarly, ETFs splits/reverse splits should not increase
the information content of affected ETFs relative to their controls, but splits result in an increase
in HFT activity whereas reverse splits reduces HFT activity. All these results imply a noninformational channel that drives HFT activity. In addition, we find that HFTers have a lower
share of market making relative to non-HFTers for stocks with higher probability of informed
trading (PIN). The result suggest that HFTers does not have comparative advantage to provide
liquidity for stocks with higher information asymmetry. Instead, HFTers are more active for
stocks with higher relative tick size and lower information asymmetry. Considering the fact that
information asymmetry is a major determinant of bid-ask spread (Glosten and Milgrom (1985)
and Easley and O’Hara (1987)), these results also lend supports to tick size constraints
hypothesis: HFT liquidity providers have comparative advantage in stocks whose natural bid ask
spread is lower relative to the tick size.
Proponents of increasing tick size argue that a wider tick size increases liquidity (Grant
Thornton, 2012). We show, however, a wider relative tick size decreases liquidity. The results on
liquidity, in turn, facilitate the understanding on the economic mechanism to drive the HFT
results. Split should not change the economic fundamentals of an ETF relative to its non-splitting
pair. Therefore, the proportional spread, or the transaction costs for a fixed dollar amount, should
4
The information channel has been modeled extensively (Biais, Foucault and Moinas (2013), Martinez and Rosu
(2011) and Foucault, Hombert, and Rosu (2012)). The empirical work focuses on the type of information used by
high frequency trader, such as dislocation of different financial instruments that track the same index (Budish,
Cramton and Shim, 2013), order flow (Hirschey (2013) and Brogaard, Hendershott and Riordan (2013)).
7
not change after splits if there are no tick size constraints. Therefore, nominal spread should
decrease in the same ratio as the decline of nominal price, keeping the proportional spread
unchanged. We find that nominal quoted spread decreases after the split, but the decrease of
spread is less than the decrease of nominal price, rendering an increase of proportional quoted
spread. Apparently, the wider relative tick size after the splits prevents the nominal spread from
fully adjusting. The higher proportional spread is also associated with a higher depth at the
constrained spread, or a longer queue to provide liquidity at the new best price on a coarser grid.
The effective spread, or the real transaction cost faced by liquidity demanders, increases after
splits. Therefore, we confirm the results of Schultz (2000) and Kadapakkam, Krishnamurthy, and
Tse (2005) that splits harms liquidity, but the control group in our sample provides a cleaner
identification for endogeneity. Our main contribution to the literature on tick size, however, is to
showing an increase in relative tick size leads to a change of HFT behaviors. Splits increase the
proportional quoted spread as well as the length of the queue to supply liquidity, which
encourage speed competition at the constrained price. Therefore, splits harms liquidity but
increases HFT activity. Reverse splits, on the other hand, has opposite effects. The increases in
nominal spread after reverse splits are less than the increase in nominal price, leading to a
decline in proportional spread. Also, a finer grid implies liquidity providers who were forced to
quote the same price before the reverse split can now differentiate themselves by quoting
different prices, resulting in a decrease in the queue to provide liquidity at the best price. A
decrease in the quoted spread and the depth to provide liquidity at best price also comes with a
decrease in HFT activity.
The results on splits/reverse splits are also interesting to audience broader than market
structure. In classical corporate finance textbooks, splits are used to increase liquidity whereas
8
reverse splits are either used to comply the minimum price per share requirement or to go dark
through reducing the number of small shareholders. In current market, however, reverse splits
increase liquidity. Rather than increase liquidity, splits enhance speed competition to provide
liquidity. The question on HFT is appealing to general finance audience since it generates direct
real impact. Traditionally, the real impact of market microstructure originates from the liquidity
channel: market structure impact liquidity, liquidity can affect asset return, and asset return can
affect cost of capital and allocation of real resources. Speed competition, however, directly
affects allocation of real resources as well as talents: we have witness aggressive investment in
speed such as co-location, cable connecting New York and London and microwave towers
between New York and Chicago as well as competition for top programmers. The current
literature ascribes this arms race to the rent from information channel: speed allows for faster
access to information.5 Policy debate focuses on whether such advance access to information is
unfair or even illegal. We are the first to show such profit can come from non-information
channel. First, a large relative tick size leads to higher profit of providing liquidity, which is
predicted by Foucault, Pagano and Roell (2013). Second, the profit of market making is higher
for HFTers than non-HFTers, and the results are more prominent if inventory is cleared at shorter
horizon. This result is consistent with Sandas (2001) that time priority leads to higher rents:
traders at the front of the queue have higher profit than traders at the end of the queue. Both
results are robust after controlling for information asymmetry. Our results indicate that speed
may generate rents without incurring adverse selection.
5
The information can be dislocation of financial instruments tracking the same index (Budish, Cramton and Shim,
2013), order flow (Hirschey (2013) and Brogaard, Hendershott and Riordan (2013)), macro news announcements
and market wide price movements (Brogaard, Hendershott and Riordan (2013)) or information created by HFT
through exploratory trading (Clark-Joseph, 2014).
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Our tick size channel offers unique insights on recent policy debates on HFT. Current
debate focuses on whether additional regulation is required for HFT, and if so, how to pursue it.
Our paper is the first one to point out that HFT can be a market design responses to existing
regulation. Therefore, one possible solution is deregulation instead of more regulation. At the
minimum, we believe the first step to pursue additional regulation is to evaluate current
regulation.
We are concerned that the U.S. regulation is moving to an opposite direction. The
Jumpstart Our Business Startups Act (the JOBS Act) encourages the SEC to examine the
possibility of increasing tick size, and a pilot program to increase the tick size to 5 cents for
small stocks has been announced. 6 Our results suggest that SEC should also consider pilot
program to decrease tick size for low priced liquid stocks. Proponents of increasing tick size
argue that a wider tick size controls the growth of HFT (Grant Thornton, 2012), but our results
indicate that wider tick size can encourage HFT. The second argument for increasing tick size is
that a wider tick size increases liquidity, but we show that a large relative tick size reduces
liquidity. The final argument to increase tick size is that it increases market-making revenue and
supports sell-side equity research and, eventually, increases the number of IPOs (Grant
Thornton, 2012). Economic theories suggest that constrained prices should facilitate non-price
competition, 7 but we doubt that non-price competition would take the form of providing better
research, especially when speed exists as a more direct form of non-price competition.
This paper is organized as follows. Section 1 discusses hypothesis for this paper as well
as empirical strategy to test them. Section 2 describes the data used in the study. Section 3
presents preliminary result between relative tick size and HFT liquidity provision using double
6
7
SEC Provides Details of 5-Cent Tick Test, Wall Street Journal, June 25, 2014.
Airlines, for example, offer better service when price competition is constrained (Douglas and Miller, 1974).
10
sorting. Section 4 examines the determinants of HFT liquidity provision using regression
analysis. Section 5 provides a robustness check on the causal relation between relative tick size,
liquidity and HFT using twin ETFs and diff-in-diff test. Section 6 concludes the paper and
discusses the policy implications.
1. Testable Hypothesis and Empirical Design
In this paper we first test whether the speed advantage of HFTers allow them to provide
better prices of liquidity. The test result is fundamental to price competition channel, for which
believes that HFTers provide liquidity at lower cost, as they have lower operation cost (Biais and
Foucault, 2014), lower risk of being adversely selected due to their speed advantages
(Hendershott, Jones and Menkveld, 2011), and better inventory management skills (Brogaard,
Hagstromer, Norden and Riordan, 2013). So here is our first hypothesis.
Hypothesis 1: HFTers quote better prices than non-HFTers.
Surprisingly, this hypothesis has not been directly tested despite its vital importance. One
reason for this omission is that existing empirical evidence seems to support hypothesis 1. First,
Hendershott and Riordan (2013) suggest that HFT are more likely to improve the best bid and
offer (BBO), and O’Hara, Saar and Zhong (2013) show they are more likely to improve BBO
when relative tick size is large. However, the literature has not distinguished two different cases.
In the first case, both HFTers and non-HFTers would like to improve BBO. HFTers are faster to
put their order on top of the queue, while non-HFTers join the BBO after the HFTers. In the
second case, HFTers are the only providers of the best price and non-HFTers neither match nor
undercut the price. HFTers are the first to improve BBO in both cases, but only the second case
support price competition hypothesis, because the first case relates to pure speed competition.
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The second reason for this omission is because existing literature find that exogenous speed
improvement increases liquidity (Hendershott, Jones and Menkveld (2011), Boehmer, Fong and
Wu (2013) and Brogaard, Hagstromer, Norden and Riordan (2013)). However, the technology
shocks in these experiments are all at millisecond level or second level, whereas speed at our
sample is at nanosecond level. A companion paper by Gai, Yao and Ye (2013) finds that speed
enhancement does not improve liquidity. More importantly, there are distinct differences
between speed improvement increasing liquidity and the traders with higher speed improving
liquidity, because the price improvement may come from traders that become relative slower.
Slow traders lose time priority when they quote the same price as fast trader, which give them
higher incentive to undercut the price and achieve price priority. Direct test of this hypothesis
needs account level data around technology shock, which is not available for our study.
However, our results that non-HFTers are better providers of liquidity indicates the possibility
for such an interpretation.
The second hypothesis of this paper is closely related to the first one. Suppose HFTers
are better providers of liquidity, their market share of liquidity provision should increase when
tick size decreases, because a finer tick size reduces the constraints for HFTers to be the unique
providers of best price. A recent survey by Chordia, Goyal, Lehmann and Saar (2013), therefore,
raises the concern that non-HFTers may be crowd out by HFTers when the tick size is small. The
crowd out effect can be summarized in the second hypothesis.
Hypothesis 2: HFTers have larger market share of liquidity provision relative to nonHFTers when relative tick size is small.
Hypothesis 1 and 2 are both conjectures related to the price competition channel. The tick
constraints channel differs fundamentally from the price competition channel: price competition
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channel consider that speed competition encourages price competition, but tick size constraints
channel consider speed competition is a consequence of constrained price competition. The main
hypothesis of this paper is that lower nominal price, or larger relative tick size, leads to more
HFT market marking, which can be considered as the alternative for hypothesis 2.
Hypothesis 2a: a larger relative tick size causes more HFT liquidity provision.
Hypothesis 2a is the main causal relationship we aim to establish for this paper. The key
challenge to claim this causal relationship is to address endogeneity originating from
simultaneity bias or omitted variables (Roberts and Whited, 2011). Simultaneity bias occurs
when the dependent variable (y) and the independent variable (x) are determined in equilibrium
so that it can plausibly be argued either that x causes y or that y causes x. One goal of this paper
is to demonstrate that lower nominal price, or larger relative tick size, leads to more HFT market
making. The simultaneity bias arises when HFT market making leads to lower nominal price, or
when both HFT market making and nominal price are determined in equilibrium. Such a reverse
causality is unlikely to exist in reality: we are not aware any literature or argument that HFT
market making have a first order effect to reduce the nominal price. 8 In addition, the diff-in-diff
test presented in section 7 addresses the concern of simultaneity bias.
Biases induced by omit variables arise from excluding observable or unobservable
variables that 1) correlated with nominal price and 2) have explanatory power to HFT market
making. These criteria provide us two lines to search for the independent variables to be
included: the nominal share price literature and the literature on the determinants of the HFT
market making. Interestingly, a recent paper by Benartzi, Michaely, Thaler, and Weld (2009)
8
There is an indirect channel that HFT market making can affect price: HFT market making may affect liquidity,
and liquidity may affect asset prices. Current literature show that high frequency trading either has no impact on
liquidity (Gai, Yao and Ye (2013) or improve liquidity (Hendershott, Jones and Menkveld, 2011). In the first case,
the liquidity channel breaks down. In the second case, higher liquidity leads to lower return or higher nominal price,
which is opposite to what we find.
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argues that nominal share price is nearly orthogonal to the firm fundamentals, and that several
popular hypotheses of nominal prices such as marketability hypothesis, the pay-to-play
hypothesis, or signaling hypothesis cannot explain nominal prices. The only cross-sectional
result they established is that large firms have higher prices. 9 This finding dramatically reduce
the number of variables that need to be controlled, because it implies that the impact of nominal
price on HFT market marking can be estimated consistently after controlling for market cap.
The preliminary analysis presented in section 3 is based on the double sorting first on market cap
and then on price. The regression analysis in section 4 controls for more variables that may
impact nominal price or HFT market making.
Section 5 provides two clean tests for hypothesis 2a based on ETFs. The first test
compares HFT activity of twin ETFs tracking the same index but with heterogeneous nominal
price. The index fixed effect, therefore, controls for both observable and unobservable factors
that affect HFT activity through their common underlying fundamental. The results are further
strengthened in our second test involving diff-in-diff analysis using splits/reverse splits as
exogenous shock to nominal price, where the ETF splits/reverse splits are the pilot group and the
non-split ETFs that track the same index are the control group.
ETF tests are particularly interesting not only because they are exogenous, but also
because it differentiates tick size constraints hypothesis from information based explanation.
ETFs tracking the same index should have same fundamental information, either with or without
splits/reverser splits. Therefore, the variation in HFT activity under ETF tests should not be
driven by information. We acknowledge the importance of information channel, and the diversity
of high frequency traders (Hagstromer and Norden (2013)) implies that there should be more
9
They also find that firm splits when its price deviates from the other firms in the same industry. However, there are
no splits in our 117 NASDAQ HFT sample.
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than one driver of HFT activity. The purpose of this paper is to reveal important new channel
overlooked by the literature.
The ETF tests also provide a clean environment to indentify the impact of splits/reverse
splits on liquidity, which is an interesting result by itself. Some classical textbooks, such as Berk
and DeMarzo (2013) states splits can increase liquidity whereas Ross, while Westerfield and
Jaffe (2013) claim that split can decreases liquidity. The authors make the inferences from the
literature, which finds mixed results on the impact of split on liquidity. One possibility for the
inconclusiveness is the counterfactual: it is hard to know what happens to the firm if it does not
split. We contribute to this literature by finding securities with identical fundamentals but do not
split. Our tick size constraints hypothesis implies that splits should increases proportional quoted
spread because a larger relative tick size constrains price competition. However, the depth at best
price should increases because constrained price competition leads to a longer queue to provide
liquidity. An increase in quoted spread and depth renders ambiguous prediction on effective
spread, or the transaction cost by liquidity demanders: an increase in quoted spread implies that
transaction cost should be reduced for small traders, but an increase in depth at best price implies
that large orders may get better execution. Here we conjecture that effective spread should also
increases after split, because Foucault, Pagano and Roell (2013) predicts that cumulative depth
should be independent of tick size, though depth at best price may increase in tick size. Also, our
tick size constraints hypothesis also implies that HFT market making activity should increase
after splits. Therefore, we have our third hypothesis:
Hypothesis 3: Splits increase quoted spread, depth and effective spread as well as HFT
market making activity; reverse splits reduces quoted spread, depth and effective spread as well
as HFT market making activity.
15
The hypothesis on reverse splits is the mirror image of splits under tick size constraints
hypothesis. This hypothesis is intriguing because it indicate that reverse splits can be used to
increase liquidity and control speed competition in market making.
The fourth hypothesis also involves both price competition channel and information
channel. The literature knows that speed advantage of HFTers to avoid adverse selection by
quickly withdraw its quotes, but it is not clear whether such an advantage increases or decreases
HFTers’ share of market making relative to non-HFTers for stocks with higher information
asymmetry. On one hand, the ability to avoid adverse selection can enable HFTers to maintain a
tighter bid-ask spread in normal times (price competition channel), which enable HFTers to play
a more prominent role in market making for stocks with higher probability of informed trading.
The tick size constraints channel, however, indicate the opposite. The information based models
often predict 0 bid-ask spread when there is no informed liquidity demanders (Glosten and
Milgrom (1985)) and Easley and O’Hara (1987)). Without information asymmetry, tick size
provides pure profit opportunity for market making, and speed may serves as the way to allocate
the profits. An increase in information asymmetry leads to an increase in bid ask spread relative
to tick size, which reduces the value of speed competition. We state the hypothesis 4 under price
competition channel, with this competition forces as the alternative.
Hypothesis 4: HFTers provide more liquidity for stocks with higher information
asymmetry.
The final ingredient of this paper relates to the profits of HFTers. It is important
because these profits are the drivers of arms race in speed, which involves the investments for
both sources and talents. One fundamental question for finance is whether activities in financial
markets are just side slow or it affects the real decision on resource allocation. The traditional
16
channel for market microstructure to affect real decision is the liquidity channel: market structure
matters for liquidity (O’Hara, 2003), liquidity affects asset return (Pastor and Stambaugh
(2003)), Acharya and Pedersen (2005) and Amihud and Mendelson (1986)) and asset return
affects cost of capital and real decision. Speed competition attracts the attention of broader
finance and economics audience because it has a direct real impact. A recent article in the
Financial Times estimates that a 1-millisecond advantage is worth up to $100 million in annual
gains.10 Therefore, “investment banks and proprietary trading firms spend millions to shave ever
smaller slivers of time off their activities.” 11 This investment involves resources, such as the
cable between New York and London or Microwave towers between New York and Chicago, or
talents, such as the search for top programmers. The common belief is the profits are from fast
access for information, and this paper aims to show that profits can come from tick size, a noninformational source. This hypothesis is motivated by theoretical predictions by Foucault,
Pagano and Roell (2013) and Sandas (2001). Foucault, Pagano and Roell (2013) demonstrates
that profit of market making increases in tick size and Sandas (2001) show that time priority
leads to higher profits: traders at the front of the queue have higher profit than traders at the end
of the queue. Therefore, we have our 5th hypothesis.
Hypothesis 5: Profit of market making increases in tick size, and HFTers have higher
profit than non-HFTers.
2. Data and Institutional Details
This paper uses three main datasets: a NASDAQ HFT dataset, NASDAQ TotalViewITCH with a nanosecond time stamp and Bloomberg. We supplement our liquidity measure
using daily TAQ data with a millisecond time stamp. CRSP and Compustat are also used to
10
“Speed fails to impress long-term investors,” Financial Times, September 22, 2011.
11
“Wall Street’s Need for Trading Speed: The Nanosecond Age,” Wall Street Journal, June 14, 2011.
17
calculate the characteristics of stocks. The sample period for our analysis is October, 2010 unless
indicated otherwise.
2.1 Sample of stocks and NASDAQ HFT data
The NASDAQ HFT dataset provides information on limit-order books and trades for 120
stocks selected by Hendershott and Riordan. The original sample includes 40 large stocks from
the 1000 largest Russell 3000 stocks, 40 medium stocks from stocks ranked from 1001–2000,
and 40 small stocks from Russell 2001–3000. Among these stocks, 60 are listed on the
NASDAQ and 60 are listed on the NYSE. Because the sample was selected in early 2010, three
stocks disappeared from our sample period. Panel A of Table 1 contains the summary statistics
of the 117 stock samples.
Insert Table 1 About Here
The limit-order book data offer one-minute snapshots of the book with an indicator that
breaks out liquidity providers into HFTers and non-HFTers at each price level, which facilitates
the analysis of best quotes and depth provided by HFTers and non-HFTers. The trade file
provides information on whether the traders involved in each trade are HFTers or non-HFTers.
In particular, trades in the dataset are categorized into four types, using the following
abbreviations: “HH”: HFTers who take liquidity from other HFTers; “HN”: HFTers who take
liquidity from non-HFTers; “NH”: non-HFTers who take liquidity from HFTers; and “NN”: nonHFTers who take liquidity from other non-HFTers.
One limitation of NASDAQ HFT data is that it identifies a firm as a high frequency
trading firm if it engages only in proprietary trading, which implies that HFT desks from brokerdealers are not classified as HFT firms. This exclusion, however, has little impact on our
research question: we are interested in the behavior differences between the fastest traders
18
aiming to achieve time priority and traders who are not as fast as the former. Our conversation
with NASDAQ indicates that the excluded HFTers tend to be slower. One reason is purely
technical: the HFT desks not clearly identified share their infrastructure with non-HFT business,
which reduces their speed relative to other firms focusing exclusively on HFT.
2.2 Sample of stocks and NASDAQ HFT data
To clearly identify the causal impact of relative tick size on HFT liquidity provision, we
introduce two identifications: twin Exchange-Traded Funds (ETFs) and diff-in-diff test of ETFs
split. The first test involves using twin ETFs which track the same underlying index, but are
traded at different nominal prices. We start the collection of these Twin ETFs from Bloomberg
terminal. Though Bloomberg provide the ticker names for ETFs, for some ETFs, it misses
information for their underlying indexes, or records underlying indexes differently for ETF
tracking the same index. 12 As a result, we supplement Bloomberg with hand collected
information from ETF Database (http://etfdb.com/indexes/), an authoritative ETF information
website. The website classifies indexes into nine categories and we hand collect the cases where
the indexes are tracked by more than one ETF. The combined sample has 65 ETFs that track 28
indexes. Because our focus is HFT, we impose a minimum of 100 trades per day, which leads to
18 ETFs in 8 pairs.
For brevity, we refer them as twin ETFs, despite that some indexes have
more than 2 ETFs.
Our diff-in-diff test uses ETFs that have undergone splits/reverse splits, and takes them as
the pilot group, whereas ETFs that do not split but track the same indexes are used as control
12
For example, Bloomberg records the underlying index of IVV as SPTR and that of SPY as SPX, but both are
famous ETFs that track S&P 500. The difference between SPTR and SPX are in that SPTR assumes reinvestment of
dividends and capital gains while SPX does not. However, in constructing the ETF SPY, iShares, the ETF issuer,
assumes reinvestment of dividends and capital gains to avoid the drop of ETF price once a company in the index
pays out dividend, which is then consistent with that of IVV. So they are theoretically tracking S&P 500 in the same
way.
19
group. Splits/reverse splits are frequent events among leveraged ETFs, which positively or
negatively amplify the daily returns of underlying indexes.13 These ETFs are majorly issued by
Proshares and Direxion, and often appear in pairs that track the same index but in opposite
directions. For example, ETFs SPXL and SPXS are both tracking S&P 500, but SPXL amplifies
the index by 300% while SPXS by -300%. The amplification effect results in frequent
divergence of their nominal prices, and the issuers often use split/reverse split to keep their
nominal prices align with each other. We search the Bloomberg and ETF Database to collect the
information for leveraged ETFs pairs that track the same index and with the same multiplier, and
the data is then merged with CRSP to identify their splitting/reverse splitting activities. We
indentify 5 splits and 21 reverse splits from January 2010 to November 2011 after the 100-trade
cut-off. Reverse splits occur more frequently, because the issuers are often concerned about the
higher trading cost of low priced ETFs.14 This concern is formally confirmed in section 5, but is
at odds with the recent claim of Grant Thornton (2012) that large tick size increases liquidity.
Since NASDAQ HFT dataset does not provide HFT information for ETFs, we compute
the HFT activities based on methodologies introduced by Hasbrouck and Saar (2013) using
NASDAQ ITCH data, which is a series of messages that describe orders added to, removed
from, or executed on the NASDAQ. We also use ITCH data to construct a limit order book with
nanosecond resolution, which is the foundation to calculate liquidity. Detailed information on
how to link these messages can be found in Gai, Yao, and Ye (2013) and Gai, Choi, O’Neal, Ye,
and Sinkovits (2013).
3. Double Sorting
13
We only find one split and one reverse split for non leverage ETFs that track the same index, but the result is also
consistent with our hypothesis.
14 Why has ProShares decided to reverse split the shares of these funds?
(http://www.proshares.com/resources/reverse_split_faqs.html)
20
The original 120 stocks selected by Hendershott and Riordan include 40 large stocks
from the 1000 largest Russell 3000 stocks, 40 medium stocks from stocks ranked from 1001–
2000, and 40 small stocks from Russell 3000 stocks 2001–3000. A natural way to conduct the
analysis is to sort the stocks 3-by-3 based on the market cap and the price level of the stock. We
therefore sort the 117 stocks first into small, medium, and large groups based on the average
market cap of September 2010, and each group is further subdivided into low, medium, and high
sub-groups based on the average closing price of September 2010.
3.1. Who Provides Best Price?
A fundamental question on the HFT literature is whether speed advantage of HFTers
enables them to provide better price of liquidity relative to Non-HFTers. The price competition
channel believes that speed competition encourages price competition because it helps HFTers to
avoid adverse selection (Hendershott, Jones and Menkveld, 2011) and manage their inventory
(Brogaard, Hagstromer, Norden and Riordan, 2013). The literature, however, overlooks the
possibility that speed competition may discourage price competition. U.S. market follows pricetime priority. HFTers can achieve time priority when they quote the same price as non-HFTers,
which gives them less incentive to undercut the price; non-HFTers are less likely to be on the top
of the queue when they quote the same price as HFTers, which gives them higher incentive to
improve the price. Whether such an incentive is strong enough so that non-HFTers take a
prominent role in providing best quotes is a crucial question, which summarized in our
hypothesis 1 in section 1.
The test strategy for hypothesis 1 involves relative tick size: suppose non-HFTers are
more likely to quote better price, they should be more likely to be the unique provider of best
price as relative tick sizes decreases. A large relative tick size hinders price competition and
21
forces traders with better price to quote the same price as the traders with worse price. Small
relative tick size encourages price differentiation and alleviates the constraints to establish price
priority.
The one-minute snapshots of the limit-order book in NASDAQ high-frequency book data
indicates the depth provided by both HFTers and non-HFTers at each ask and bid price. Our
analysis starts by categorizing the best price (bid or ask are treated independently)in these 391
minute-by-minute snapshots for each stock and each day into three groups: 1) both HFTers and
non-HFTers display the best price, 2) only HFTers display the best price and 3) only non-HFTers
display the best price. 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. The results are
presented in Table 2. Column 1 presents the percent of time that HFTers are unique providers of
the best quotes, column 2 presents the percent of time that non-HFTers are unique providers of
the best quotes, and column 3 presents the percent of time that both are on the best quotes.
Column 1, 2 and 3 sum to 100 percent. Column 4 presents the ratio where non-HFTers are the
unique providers of best price relative to where HFTers are the unique providers of the best price
(Column 3/Column 2). Column 5, defined as column 2 minus column 1, is the differences in
percentage between non-HFTers as the unique providers of best price and HFTers as the unique
providers of best price, and the statistics inference based on 21 daily observations is
demonstrated in column 6.
Table 2 shows that HFTers and non-HFTers are more likely to quote the same price when
relative tick size is large: for low-priced large-cap stocks, HFTers and Non-HFTers are both on
the best price 95.9% of the time. Therefore, there is less price differentiation with a large relative
tick size. A reduction in relative tick size encourages price competition, and HFTers and Non-
22
HFTers quote the same best price 45.5% of time for high-priced large stocks. Therefore, price
priority is sufficient to differentiate HFTers and non-HFTers 54.5% of time for high-priced large
stocks, but price priority is sufficient only 4.1% of time for low-priced large stocks, suggesting
95.9% of time, time priority is needed to break the tie in quotes price. This evidence suggests
that price competition is indeed more constrained for stocks with large relative tick size; a large
relative tick size hinders price competition and encourages speed competition.
Insert Table 2 about Here
A more intriguing result is exhibited in column 4: non-HFTers are more likely to display
the best price than HFTers. The last row of Column 4 shows that Non-HFTers are 2.62 times
more likely to display better prices than HFTers. More convincing evidence involves the pattern
across different relative tick size. As relative tick size decreases, non-HFTers take a more and
more prominent role than HFTers in providing best price, which implies non-HFTers are more
likely to jump ahead of the price queue when the relative tick size is small. This result is contrast
to the common belief that a smaller relative tick size leads to penny-jumping behavior of HFTers
because stepping in front of standing limit orders is inexpensive (Chordia, Goyal, Lehmann and
Saar (2013)). Surprisingly, we show that a smaller tick size increases the likelihood of nonHFTers to jump ahead of price queue relative to HFTers.
The first row of Table 2 demonstrates that non-HFTers are also more likely to offer better
prices than HFTers for low-priced large stocks (2.5% vs. 1.6%). The difference (0.9%) is
statistically significant but economically trivial, because 95.9% of the time they quote the same
price. Therefore, time priority determines execution sequence. It is natural to expect that HFTers
have comparative advantage to establish time priority when price competition is constrained, and
a recent paper by O’Hara, Saar and Zhong (2013) found that HFTers take on an increasing share
23
of limit orders that improve the best price when relative tick size is large. Combining our results
with O’Hara, Saar and Zhong (2013), the evidence suggests that HFTers are more likely to
improve NBBO when non-HFTers also want to quote the same price, except non-HFTers do not
have speed advantage to be on top of the queue to improve the quote. This competition is more
related to speed instead of price. To summarize, a small relative tick size facilitates non-HFTers
to achieve price priority, and a large relative tick size leads non-HFTers and HFTers to quote the
same price, helping HFTers to establish time priority. This intuition helps to understand the
results in section 3.3, which shows that share of volume with HFTers as liquidity providers are
the highest for low priced stocks.
3.2. Best Depth Provided by HFT and Non-HFT
This section analyzes best depth, or the quantity provided by each type of traders at the
best price, which offers two robustness checks to the results established in Section 3.1. First, if
non-HFTers only provide trivial amount of depth when they are the unique providers of the best
price, the results based on the frequency of best quotes exaggerate the impact of non-HFTers.
Second, the previous section excludes the case where both HFTers and non-HFTers provide the
best price. This omitted case can be considered by this section. Suppose both are at best depth,
their relative contribution to the best depth is determined by the number of shares they offer.
Denote
the
depth
provided
by
HFTers
and
non-HFTers
as
{HFTdepthitm,
NonHFTdepthitm}, where i is the stock, t is the date, and m is the time of day. We provide two
ways of aggregating the HFT liquidity provision for stocks in each portfolio.
The share-weighted average first sums the HFT liquidity provision for all stocks in the
portfolio and then divide the number by the total liquidity provision for all stocks in the portfolio
for each day.
24
The average depths from HFTers and non-HFTers for stock i on day t are:
𝑀
𝑀
𝑖=1
𝑖=1
1
1
𝐻𝐹𝑇𝑑𝑒𝑝𝑡ℎ𝑖𝑡 = ∑ 𝐻𝐹𝑇𝑑𝑒𝑝𝑡ℎ𝑖𝑡𝑚 and 𝑁𝑜𝑛𝐻𝐹𝑇𝑑𝑒𝑝𝑡ℎ𝑖𝑡 = ∑ 𝑁𝑜𝑛𝐻𝐹𝑇𝑑𝑒𝑝𝑡ℎ𝑖𝑡𝑚
𝑀
𝑀
(1)
The depth provided by HFTers relative to the total depth of portfolio J on day t is:
𝑆𝑊𝐻𝐹𝑇𝑑𝑒𝑝𝑡ℎ𝑠ℎ𝑎𝑟𝑒𝐽𝑡 =
∑𝑖∈𝐽 𝐻𝐹𝑇𝑑𝑒𝑝𝑡ℎ𝑖𝑡
∑𝑖∈𝐽(𝐻𝐹𝑇𝑑𝑒𝑝𝑡ℎ𝑖𝑡 + 𝑁𝑜𝑛𝐻𝐹𝑇𝑑𝑒𝑝𝑡ℎ𝑖𝑡 )
(2)
Stocks with larger depth provided by HFTers have greater weight in share-weighted
measure. An alternative measure is equal-weighted average, whereby each stock has the same
weight. For each stock i and day t,
𝐻𝐹𝑇𝑑𝑒𝑝𝑡ℎ𝑠ℎ𝑎𝑟𝑒𝑖𝑡 =
𝐻𝐹𝑇𝑑𝑒𝑝𝑡ℎ𝑖𝑡
𝐻𝐹𝑇𝑑𝑒𝑝𝑡ℎ𝑖𝑡 + 𝑁𝑜𝑛𝐻𝐹𝑇𝑑𝑒𝑝𝑡ℎ𝑖𝑡
(3)
Next, suppose there are N stocks in portfolio J; the equal-weighted HFT liquidity
provision is defined as:
1
𝐸𝑊𝐻𝐹𝑇𝑑𝑒𝑝𝑡ℎ𝑠ℎ𝑎𝑟𝑒𝐽𝑡 = 𝑁 ∑𝑁
𝑖=1 𝐻𝐹𝑇𝑑𝑒𝑝𝑡ℎ𝑖𝑡
(4)
Table 3 presents results based on 21 daily observations of SWHFTdepthshare (Panel A)
and EWHFTdepthshare (Panel B) for each portfolio. Panel A shows that the depth provided by
HFTers increases monotonically with relative tick size. The share-weighted depth from HFTers
is as high as 55.66% for large stocks with large relative tick size, while the figure is only 35.07%
for large stocks with small relative tick size. The difference is 20.59% and the t-statistics based
on 21 observations runs as high as 22.10. Panel B shows that the equal-weighted depth
percentage provided by HFTers is 43.10% for mid-cap stocks with large relative tick size, while
the figure is 24.79% for mid-cap stocks with small relative tick size. The difference is 18.30%
with a t-statistics of 30.28. As the percent of depth offered by non-HFTers are 1 minus the
25
percent of depth offered by HFTers, Table 3 shows that a smaller tick size increases the percent
of depth offered by non-HFTers relative to HFTers. Taking together, section 3.1 shows that a
smaller tick size is associated with higher chance that non-HFTers offer the best price, and this
section demonstrates that the same pattern holds true for the quantity of shares offered at the best
price.
Insert Table 3 about Here
3.3 Tick Size Constraints and Volume
Section 3.1 and 3.2 show that non-HFTers are more likely to quote better prices to
achieve price priority over HFTers, partially when relative tick size is small. A large relative tick
size, however, discourages price differentiation and these two types of traders are more likely to
quote the same price, leading time priority to determine the execution sequence. Although our
data do not provide the information on the queue of liquidity provision, it is natural to believe
that speed competition at constrained price favors HFTers, who can quickly post orders at the top
of the queue. The results on volume provide additional evidence consistent with this claim: the
volume with HFTers as liquidity providers increases with relative tick size, and the number is the
highest for the portfolio in which HFTers and non-HFTers quote the same price 95.9% of the
time.
NASDAQ high-frequency data indicate, for each trade, the maker and taker of liquidity.
The same as the previous section, we sort the stocks 3-by-3 first based on the market cap and
then the price level of the stock. Table 4 presents the percentage of volume with HFTers as the
liquidity providers in two ways: volume-weighted and equal-weighted. Recall that NHit, HHit,
HNit, and NNit are the four types of share volume for stock i on each day t. For each portfolio J,
26
the volume-weighted share with HFTers as liquidity providers relative to total volume is defined
as:
𝑉𝑊𝐻𝐹𝑇𝑙𝑖𝑞𝑢𝑖𝑑𝑖𝑡𝑦𝑠ℎ𝑎𝑟𝑒𝐽𝑡 =
∑𝑖∈𝐽(𝑁𝐻𝑖𝑡 +𝐻𝐻𝑖𝑡 )
∑𝑖∈𝐽 𝑁𝐻𝑖𝑡 +𝐻𝐻𝑖𝑡 + 𝐻𝑁𝑖𝑡 + 𝑁𝑁𝑖𝑡 )
(5)
The equal-weighted percentage of volume with HFT liquidity providers is defined in two
steps. For each stock i and day t, the percentage of volume with HFT as the liquidity providers is
𝐻𝐹𝑇𝑙𝑖𝑞𝑢𝑖𝑑𝑖𝑡𝑦𝑠ℎ𝑎𝑟𝑒𝑖𝑡 =
𝑁𝐻𝑖𝑡 + 𝐻𝐻𝑖𝑡
𝑁𝐻𝑖𝑡 + 𝐻𝐻𝑖𝑡 + 𝐻𝑁𝑖𝑡 + 𝑁𝑁𝑖𝑡
(6)
Next, suppose there are N stocks in portfolio J; equal-weighted percentage of volume
with HFT as the liquidity providers is defined as:
1
𝐸𝑊𝐻𝐹𝑇𝑙𝑖𝑞𝑢𝑖𝑑𝑖𝑡𝑦𝑠ℎ𝑎𝑟𝑒𝐽𝑡 = 𝑁 ∑𝑁
𝑖=1 𝐻𝐹𝑇𝑙𝑖𝑞𝑢𝑖𝑑𝑖𝑡𝑦𝑣𝑜𝑙𝑢𝑚𝑒𝑠ℎ𝑎𝑟𝑒𝑖𝑡
(7)
Panel A of Table 4 demonstrates the results on volume-weighted average and Panel B
presents the results on equal-weighted average. Both panels demonstrate a clear pattern that
volume with HFT liquidity providers increases in relative tick size. For example, Panel A shows
that 49.96% of the volume is due to HFT liquidity providers for large stocks with large relative
tick size, but only 35.93% of the volume is due to HFT liquidity providers for large stocks with
small relative tick size. The difference is 14.03% with a t-statistics result of 15.54 for 21
observations. Panel B shows that mid-cap stocks with large relative tick size represent 35.57%
of volume with HFT liquidity provision, a percentage that decreases to 22.92% for mid-cap
stocks with small relative tick size. The difference is 12.65% with a t-statistics result of 22.65.
Across all 3 by 3 observations, volume with HFTers as liqudidity providers is the highest for
large stocks with large relative tick size, where HFTers and non-HFTers quote the same price
96.9% of time (Table 3). In summary, our results show that HFT liquidity provision is more
27
active for stocks with large relative tick size, or stocks that face more tightly constrained price
competition.
Insert Table 4 about Here
4
Regression Analysis
As a robustness check, we perform multivariate regression analysis including additional
control variables that may impact nominal price or HFT market making. A sufficient condition
for the omitted variable bias to rise is that the missing variables have correlation with both
nominal price and HFT market making. As this is the first paper to link nominal price literature
and HFT liquidity, we are not aware any papers that have touched upon the variables correlated
with both nominal price and HFT. Therefore, we start from the necessary condition that omitted
variables correlated with at least one of these two variables. Our search for control variables is
guided by the nominal price literature and HFT literature.
4.1. Control Variables
The nominal price literature suggests that industry norm is important in choosing nominal
price. Benartzi, Michaely, Thaler, and Weld (2009) find that a firm may split/reverse if its price
deviates from the industry average. The advantage of regression analysis is that we can control
this unobservable variable using industry fixed effect, where industry is classified using Fama
and French 48 industry. Though Benartzi, Michaely, Thaler, and Weld (2009) pronounces other
hypothesis unable to explain nominal prices, as a robustness check, we still take five lines of
literature on nominal price into consideration when searching for control variables. The summary
of these variables and their construction is in Table 1.
28
The first line of literature is on optimal tick size hypotheses, which argues that firms
choose the optimal tick size through split/reverse split (Angel (1997)).
Optimal tick size
hypotheses implies that the regression of HFT market making on relative tick size would lead to
spurious results, because firm characteristics can determine both high frequency market making
and the relative tick size. However, optimal tick size hypothesis has been rejected by the
following experiment. If firms chooses their optimal relative tick size, we should observe firm
aggressively splitting their stocks when the tick size changed from 1/8 to 1/16 and then to 1 cent,
however, this did not happen in reality. Nevertheless, we include idiosyncratic risk, number of
analyst that may affect the choice of optimal tick size from this literature in the regression.15
The marketability hypothesis argues that lower price appeals to individual traders. Test of
this hypothesis find mixed results: some papers find individuals prefer low-priced stocks (Dyl
and Elliott (2006)), whereas Lakonishok and Lev (1987) find no long term relationship between
nominal price and retail ownership and Byun and Rozeff (2003) suggest that if there are any
short-term effects, they are very small. Nevertheless, we include the measure of small investor
ownership suggested by Dyl and Elliott (2006), which is equal to the logarithm of average book
value of equity per shareholder.16
The signaling hypothesis states that firm use stock splits to signal good news. The
empirical literature, however, does not come to a conclusion on whether splits are used as a
signal and if so, what types of news that firms intend to signal. In addition, the 117 stock in our
15 Angel also argues that the relative tick size also depends on whether a firm is in the regulated industry, and this
effect has been taken care of by including industry by time fixed effect. Angel uses firm book value as a control for
size, which is similar to market cap that has already been controlled. When book value is included as an additional
control, results are similar.
16
We also include 1 minus the percentage institutional holding as another measure of individual ownership and the
results are similar. The other proxy for retail traders is the trade size (Schultz, 2000) and Kadapakkam,
Krishnamurthy and Tse (2005), where small trades are assumed to come from small traders. O’Hara, Yao and Ye
(2013), however shows that small trades are more likely to come from high frequency traders.
29
sample do not split. Though our ETF sample contains splits, these splits can be regarded as noninformation driven, particularly when compared with ETFs that track the same index but do not
split.
The remaining two literatures on nominal do not suggest additional control variables for
our analysis. The catering hypothesis by Barker, Greenwood, and Wurgler (2009) discusses
time-series variations in stock prices: firms split when investors place higher valuations on lowpriced firms and vice versa, but our analysis focus on the cross-sectional variation. Campbell,
Hilscher, and Szilagyi (2008) find that extreme low price predicts distress risk, but the 117 firms
in our sample are far from default, and the distress risk should not affect the ETFs in our sample.
We then introduce additional control variables from the HFT literature. One particular
interesting control variable is information asymmetry, because it can affect HFT liquidity
provision in both directions. The literature has the consensus that speed advantage allows
HFTers to reduce the pick-off risk by cancelling their quotes before being adversely selected, but
it does not predict whether HFTers have a higher or lower market share for stocks with higher
probability of informed trading. On one hand, HFTers may take a more prominent role in
liquidity provision for stocks of higher probability of informed trading, because their ability to
avoid adverse selection enable them to quote a tighter bid-ask spread in normal times, which
increases their market share. On the other hand, frequent cancellation due to information
asymmetry may reduce market share of liquidity provision. Existing literature shows that HFTers
withdraw from the market during extreme information asymmetry (Kirilenko, Kyle, Samadi,
Tuzun (2011) and Easley, De Prado and O’Hara (2012), but it is not clear whether asymmetry
information impacts HFT liquidity providers more than non-HFT liquidity providers in normal
times. More importantly, the tick size constraints channel implies that HFT should provide less
30
liquidity for stocks with higher information asymmetry. The information based model in market
microstructure implies that natural bid ask spread is zero under no information asymmetry
(Glosten and Milgrom (1985) and Easley and O’Hara (1987)). Under this extreme scenario, the
rent for liquidity provision is equal to the tick size. An increase in information asymmetry would
increase the natural bid-ask spread, or reduces the ratio of relative tick size to natural bid-ask
spread, leading to a decrease of the rents. Therefore, an increase in information asymmetry
reduces rents created by relative size and thereby the value of speed competition.
To summarize, economic suggest forces increasing as well force decreasing the market
share of HFT liquidity provision. That which forces is more compelling is an empirical question,
which is the hypothess 4 we aim to test. The measure of information asymmetry is the
probability of informed trading (PIN) by Easley, Kiefer and O’Hara (1996). Turnover and
volatility are also included in our regression following the analysis by Hendershott, Jones and
Menkveld (2011) on algorithmic trading. We also include past return to examine the impact of
return on HFT market making.17 The method of calculating the variables from HFT literature is
also summarized in Table 1.
4.2 Regression Results on HFT Liquidity Provision.
The regression specification is
𝑦𝑖,𝑡 = 𝑢𝑗,𝑡 + 𝛽 × 𝑟𝑒𝑙𝑎𝑡𝑖𝑣𝑒𝑡𝑖𝑐𝑘𝑖,𝑡 + Γ × 𝑋𝑖,𝑡 +𝜖𝑖,𝑡
(8)
where 𝑦𝑖,𝑡 is the daily percent of depth provided by HFTers (HFTdepth) or percent of volume
with HFTers as liquidity providers (HFTvolume) for each stock i on date t. 𝑢𝑗,𝑡 is the industry by
17
We thank Laura Starks and an anonymous reviewer for Texas Finance Festival for the suggestion to add past
return.
31
time fixed effects. 18 The key variables of interest, relativetickit, is the the daily inverse of the
stock price. 𝑋𝑖,𝑡 are the control variables discussed in table 1, including PIN as the proxy for
information asymmetry.
Insert Table 5 about here
Table 5 confirms that HFTdepth and HFTvolume both increases in relative tick size,
which are consistent with our tick size constraints hypothesis. Large cap stocks also have higher
HFTdepth and HFTvolume. Column 3 shows that the sign for retail trading is mixed: more retail
trading leads to a decrease in HFTdepth but an increase in HFTvolume. Column 4 indicates that
firm age is the only variable that predicts both HFTdepth and HFTvolume under relative tick size
hypothesis: HFTers tend to provide more liquidity for older firms. Column 5 shows that HFTers
provide less liquidity for firms with higher PIN. Interestingly, Column 6 shows that HFT
provides less liquidity for firms with higher past return. The result is also consistent with tick
size constraints hypothesis, because a higher past return leads to higher stock price, thus a lower
relative tick size. Nevertheless, the result is only significant in column 7 of panel A, probably
because monthly return do not have a first order impact on nominal price. Finally, column 7,
which includes all the variables in column 1 to 6, shows that HFTvolume increases in turnover
but decreases in idiosyncratic risk. Older firms have both higher HFTvolume and HFTdepth,
whereas firms with higher PIN have lower HFTvolume and HFTdepth.
Column 5 and 7 show that a higher PIN, alone or combined with other control variables,
leads to less HFTvolume and HFTdepth. This intriguing result suggests that the speed advantage
for HFTers to update their quotes does not lead to a higher market share of HFTers for stocks
18
We do not includes firm fixed effect because the focus of this paper is to understand the cross-sectional variation
in HFT market making activity, and firm fixed effect defeat this purpose (Roberts and Whited (2011)).
32
with higher information asymmetry. The results are hard to justify using information hypothesis,
but lead additional support to tick size constraints hypothesis. The main take-way from Table 5
is that HFTers concentrate their activity on stocks with large relative tick size and lower
information asymmetry. Considering the fact that information asymmetry is a major determinant
of natural bid-ask spread, this result suggest that HFTers traders focus on stocks whose relative
tick size is large relative to their natural bid-ask spread.
5
Identifications Using ETFs
Double sorting and multivariate regression analysis reveals that stocks with larger
relative tick sizes attract more HFT liquidity provision. As a robustness check, this session offers
two clean identifications for the causal impact of relative tick size on HFT activity: twin ETFs
and diff-in-diff test using ETF splits. The same identification strategy also facilitates the analysis
of the causal relationship between relative tick size and liquidity. The question of liquidity is not
only important by itself, but also offers additional economic insights to understand the
relationship between relative tick size and HFT.
The twin ETFs test uses ETFs tracking the same index but with different nominal price. 19
This test is motivated by the seminal work by Ashenfelter and Krueger (1994) that uses twin
brothers to examine the impact of return to education. In their test, family fixed effect removes
unobservable but identical underlying abilities. Complement to the previous analysis in which
observable differences are controlled for, the index fixed effects control for unobservable factors
that affect HFT through underlying fundamentals.
19
In reality, ETFs that track the same index may have slightly different portfolios due to tracking error, but the
slight difference between holdings should not be a determinant for HFT activity.
33
The diff-in-diff test use the splits/reverse splits of leveraged ETFs as exogenous shocks to
the relative tick size. We use leveraged ETEs because splits/reverse splits are much more
frequent for leveraged ETFs than for regular ETFs. 20 Leveraged ETFs are a type of ETFs that
amplifies returns of an underlying index. They usually appear in pairs that track the same index
but in opposite directions: bull ETFs offer 2x or 3x return of the underlying index, and bear ETFs
offer -2x or -3x return of the underlying index. The bear and bull ETFs for the same index are
usually issued by the same company at similar prices when they are first issued, but large
cumulative movements of an index results in the divergence of the nominal price. The issuers of
leveraged ETF usually use splits/reverse splits to align the nominal price of the bull and bear
ETFs. These exogenous shocks of relative tick size facilitates our diff-in-diff analysis using the
ETFs that do not split as control group. Technically, the main difference between bear and bull
ETFs tracking the same index is their opposite returns, which is controlled in the regression
analysis. Plus, the opposite return should have little impact on market making activity, because
market making implies the presence on both long and short side of the same security. Also,
HFTers usually end the day with nearly zero inventory.
The twin-ETF and diff-in-diff tests yield the same economic linkage among relative tick
size, liquidity and HFT activity. Large tick size increases quoted spread, because it constrains
price competition. The depth at the best price increases in relative tick size, suggesting the queue
to supply the liquidity elongated at constrained price. From the theoretical argument by Foucault,
Pagano and Roell (2013) that the gain from being at the head of the queue increases in tick size,
we conjecture that time priority becomes more important. Indeed, we find HFT activity increases
20
In our sample period, only one ETF in our twin-ETF sample has split, and one has reverse split, and we find the
ETF split/reverse split increase/decrease HFT activity relative to its non-split twin, both of which are consistent with
the tick size constraints hypothesis.
34
in relative size. We also find that effective spread, or the cost of transaction for liquidity
demander, increases in relative tick size. Therefore, a larger relative tick size results in more
constrained price competition and intense speed competition, and it also harms liquidity.21
The session proceeds as follows. Section 5.1 illustrates how HFT activity and liquidity
are measured.
Section 5.2 presents the results for twin ETF test, and the diff-in-diff test in
section 5.3.
5.1 Measure of HFT Activity and Liquidity
Because the NASDAQ HFT data set does not provide HFT information for ETFS, we use
“strategic runs”, proposed by Hasbrouck and Saar (2013), as a proxy for HFT market making
activity. A strategic run is a series of submissions, cancellations and executions that are likely to
be parts of an algorithmic strategy. The link between submissions, cancellations and executions
are constructed based on four criteria: (1) reference numbers are provided by data distributors
that link limit orders with their subsequent cancellations or executions. (2) We have a more
updated version of the data relative to Hasbrouck and Saar (2013). Therefore, if a trader chooses
to use the “U” (update) message to cancel an order and add another one, we know the addition
and cancellation comes from the same trader. (3) The “U” message contains message for both
cancellation and addition, but the traders can choose to cancel an order and add another one
without using “U” message. In this case, we need to decide whether a cancellation can be linked
to the subsequent resubmission of either a limit order or market order. Following Hasbrouck and
Saar (2013), we impute such a link when an cancellation is followed within 100 ms by a limit
order submission with the same size and same direction or by an execution of a limit order with
21
We should be cautious about these results not be interpreted as evidence for HFT harming liquidity, but a larger
tick size increases HFT activity as well as transaction cost.
35
the same size but opposite direction (this means a market order with same size and same
direction was resent to the market). (4) If a limit order is partially executed and the remainder is
cancelled, we apply second criteria based on the cancelled quantity. We then keep all the runs
with 10 messages or more following Hasbrouck and Saar (2013). Finally, RunsInProcess is the
time-weighted average of the number of strategic runs with 10 or more messages. To construct
that, we sum the time length of all strategic runs for a stock in each day and then divide it by the
total trading time of the day.
We then test whether RunsInProcess is a good proxy for HFT market making activity by
computing the correlation between RunsInProcess and HFT market making activity and the
results are displayed in Table 6. The cross-sectional correlation is as high as 0.765.
RunsInProcess also have a correlation of 0.283 with HFT market taking activity, indicating
RunsInProcess also capture some liquidity taking activity of HFT. However, the lower
correlation for taking implies that RunsInProcess is a better proxy for making than for taking.
Indeed, pure submissions of market orders are not considered as strategic runs, because all “runs”
start with limit orders. The 10 message cut-off further reduces the possibility that a strategic run
comes for a liquidity taking HFT or an agency algorithm that help its customers to break large
orders into smaller pieces. Finally, because RunsInProcess weight the strategic runs by time, it
increases the impact of patient liquidity providing algorithms that stay on the book and waiting
for liquidity demanders. Impatient liquidity demand algorithms may also use limit orders, but
those limit orders tend to switch to market orders after a shorter time horizon, which reduces the
impact of liquidity demand algorithms in the time weighted average.
Insert Table 6 About Here
36
We use try the correlation test for several other measures of HFT activity such as quoteto-trade ratio (Angel, Harris and Spatt, 2010 and 2013), message ratio (Hendershott, Jones and
Menkveld (2011) and Boehmer, Fong and Wu (2012)) and cancellation ratio (Hagströmer and
Norder (2013)), all of which are based on the intuition that HFT tends to cannel more orders than
Non-HFT. Surprisingly, these measures have either 0 or negative correlation with HFT market
making. This do not disqualify them as excellent proxies to distinguish trader types if the
comparison is within the same security (Hagströmer and Norder (2013)), neither does our result
suggest these three variables are poor measures of HFT activity across time series, but we should
be cautious about applying them to cross-sectional data. For given security, traders with high
message to trade ratio tends to be HFTers, particularly HFTers engage in market making
(Hagströmer and Norder (2013) and Bias and Foucault (2014)). As the HFTers activity increases
for a security across the time, we also tend to see a higher message to trade ratio in time series.
However, relative tick size can play an important role when compare stock cross-sectionally. A
large relative tick size attracts HFTers to be on the top of the queue, but once HFTers place an
order in the queue, they are less likely to cannel the order, since the position in the queue will be
lost if they do so. A smaller relative tick size discourages HFTers, but HFTers tend to cancel
frequently because a smaller relative tick size implies more price movement and competition.
Therefore, one side contribution of our paper is that we should be cautious in interpreting the
results that use these three measures for cross-sectional comparison. RunsInProcess, one the
other hand, combines speed, cancellation and persistence of the strategy, and has strength to
measure HFT market making activity in cross-section. A higher RunsInProcess implies three
factors: fast response (within 100 ms), frequent cancellation (10 messages or more) and persist
interest in supplying liquidity (stay in the queue to provide liquidity conditional on fast and
37
frequent cancellation). Therefore, RunsInProcesshas a very higher correlation with crosssectional variation in HFT market marking activity, and we use it as a proxy for HFT market
making henceforth.
Stock market liquidity is defined as the ability to trade a security quickly at a price close
to its consensus value (Foucault, Pagano, and Röell, 2013). 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 comes from a message-by-message
limit-order book we construct, in which any order addition, execution, or cancellation leads to a
new record of the limit-order book. The construction is implemented by the Gordon
Supercomputer in the San Diego Supercomputing Center. A discussion of efficient construction
of limit-order books using supercomputers can be found in Gai, Choi, O’Neal, Ye, and Sinkovits
(2013).
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 ask and bid. In addition to earning the quoted spread, a
market maker also obtains a rebate from each executed share from NASDAQ. Therefore, we
compute two other measures of the quoted spread: Qspreadadj and pQspreadadj, which are
spreads adjusted by the liquidity supplier’s rebate.22 Specifically,
𝑄𝑠𝑝𝑟𝑒𝑎𝑑𝑎𝑑𝑗𝑖,𝑡 = 𝑄𝑠𝑝𝑟𝑒𝑎𝑑𝑖,𝑡 + 2 ∗ 𝑙𝑖𝑞𝑢𝑖𝑑𝑖𝑡𝑦 𝑚𝑎𝑘𝑒𝑟 𝑟𝑒𝑏𝑎𝑡𝑒
(9)
𝑝𝑄𝑠𝑝𝑟𝑒𝑎𝑑𝑎𝑑𝑗𝑖,𝑡 = (𝑄𝑠𝑝𝑟𝑒𝑎𝑑𝑖,𝑡 + 2 ∗ 𝑙𝑖𝑞𝑢𝑖𝑑𝑖𝑡𝑦 𝑚𝑎𝑘𝑒𝑟 𝑟𝑒𝑏𝑎𝑡𝑒)/𝑚𝑖𝑑𝑝𝑜𝑖𝑛𝑡𝑖𝑡
(10)
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.
22
38
All these four quoted spreads are weighted by its quote duration to obtain the daily timeweighted average for each stock.
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. The effective spread measures the actual transaction costs for liquidity demanders.
However, a liquidity demander in NASDAQ also pays the taker fee.23 Therefore, we compute the
fee-adjusted effective spread and the fee-adjusted proportional effective spread.
𝐸𝑠𝑝𝑟𝑒𝑎𝑑𝑎𝑑𝑗𝑖𝑡 = 𝐸𝑠𝑝𝑟𝑒𝑎𝑑𝑖𝑡 + 2 ∗ 𝑙𝑖𝑞𝑢𝑖𝑑𝑖𝑡𝑦 𝑡𝑎𝑘𝑒𝑟 𝑓𝑒𝑒
(11)
𝑝𝐸𝑠𝑝𝑟𝑒𝑎𝑑𝑎𝑑𝑗𝑖𝑡 = (𝐸𝑠𝑝𝑟𝑒𝑎𝑑𝑖𝑡 + 2 ∗ 𝑙𝑖𝑞𝑢𝑖𝑑𝑖𝑡𝑦 𝑡𝑎𝑘𝑒𝑟 𝑓𝑒𝑒)/𝑚𝑖𝑑𝑝𝑜𝑖𝑛𝑡𝑖𝑡
(12)
Our main measures of depth are the depth at the best bid and offer and depth within 10
cents of the best bid and offer (Hasbrouck and Saar, 2013).
5.2 Twin ETFs Test
The twin-ETF test uses ETFs that tracking the same index to examine the impact of
relative tick size on HFT and liquidity. Index by time fixed effects control for both observables
and unobservable characteristics that affects the HFT activity or liquidity.24
Denote 𝑦𝑖,𝑡,𝑗 as the HFT activity or liquidity measure for ETF j in index i at day t and
𝑢𝑖,𝑡 as index by time fixed effect. Regression compares the differences for HFT activity or
24
We choose interactive index by time fixed effects instead of individual index fixed effect and time fixed effect to
allow the time fixed effect to differ across index for each day.
39
liquidity between ETFs tracking the same index I, which is explained by their differences in
relative tick size and market cap.25
𝑦𝑖,𝑡,𝑗 = 𝑢𝑖,𝑡 + 𝛽 × 𝑟𝑒𝑙𝑎𝑡𝑖𝑣𝑒𝑡𝑖𝑐𝑘𝑖,𝑡,𝑗 + 𝜌 × 𝑙𝑜𝑔𝑚𝑘𝑡𝑐𝑎𝑝𝑖,𝑡,𝑗 +𝜖𝑖,𝑡,𝑗
(13)
Table 7 displays the results. For all regression specifications, we find ETFs with larger
cap have lower spread, more depth and HFT activity. The key variable of interest is relative tick
size, which is presented in the first row.
Insert Table 7 About Here
Column 1 and 2 show that nominal spread is lower for ETFs with higher relative tick size
or lower price. However, they also have higher proportional spread, particularly after fee
adjustment. Indeed, the fee is the same for all securities, implying a higher proportional fee for
low priced ETFs. In this sense, the fees in NASDAQ have the similar economic impact as tick
size.26 The fact that lowed price ETFs has lower nominal spread and higher proportional spread
is particularly interesting. Without tick size constraints, two ETFs tracking the same index
should have the same proportional spread. This implies that their nominal spread should be at
the same proportion to their prices. For example, suppose that the price of the low priced ETF is
½ of the higher priced ETF, the nominal spread of the low priced ETF should only be ½ of that
of the high priced ETF, reflecting the same transaction cost measured in proportion. Our results
suggests that low priced ETFs do have lower nominal spread, but the nominal spread does not
decrease less than the nominal price, leading to a higher proportional spread. One possibility is
25
We measure market cap as the price of the ETF multiplied by its shares outstanding in CRSP. We aware that
CRSP may update shares outstanding of ETFs with delay, but this small discrepancy in shares outstanding has little
impact for our purposes. Option matrix updates the shares outstanding with less delay, but results in loss of pairs in
our sample.
26
NASDAQ is a maker/taker market, which subsidizes liquidity makers and charges liquidity takers. The impact of
the fee in taker/maker market (market subsidizes liquidity takers and charges liquidity makers) can be different. See
Yao and Ye (2014) for a discussion on the market with inverted fee.
40
that the coarse tick size for the low priced ETFs prevents the nominal spread from fully adjusting.
For example, suppose we have a $50 ETF with 3 penny natural quoted spread, implying a 1.5
penny natural quoted spread for a $25 ETF tracking the same index. However, 1.5 penny is not
allowed by the 1 penny tick size, and quoting 1 cent spread loses money, leading to a 2 penny
spread. This intuition follows for more general case where natural spread is not an integer and
the proof is available upon request. Overall, a large relative tick size constrains traders’ ability to
undercut price, leading to a wider proportional quoted spread for low priced ETFs relative to
high priced ETFs.
Column 5 reveals that a large relative tick size results in more depth provided at the best
bid and ask, implying that a longer queue to provide liquidity at the best price. The result follows
the same intuition as the first 4 columns. A large relative tick size for low priced ETFs implies
that traders who are able to quote different prices under a finer grid may have to quote the same
price, which increases the queue at the best price.
Taking together, an increase in relative tick size constrains price competition but
elongates the queue to provide liquidity at constrained price. Column 6 show HFT activity also is
higher for ETFs with relative tick size. Such a difference cannot be ascribed to information,
because the low priced and high priced ETFs should have the same information because of their
common underlying. We argue the source of the difference is due to tick size constraints. ETFs
with lower price have higher proportional spread and longer queue to provide liquidity at
constrained price, and speed competition play a prominent role when price competition is more
constrained.
The literature generally considers that securities with lower quoted spread and higher
depth as more liquid. Because the low priced ETF have both higher quoted spread and depth, the
41
key variable of interest turns to the effective spread, the measure for the actual transaction cost
for liquidity demanders. Column 7-10 shows that the nominal effective spread is lower for ETFs
with large relative tick size, but their proportional effective spread is higher. The result is also
stronger for effective spread adjusted for the taker fee, because the uniform taker fee implies a
higher proportional fee for ETFs with lower price. Column 11 shows EFT with larger relative
tick size have more HFT activities. In summary, we show that a large relative tick size leads to
less liquidity as well as more HFT activity. We should be cautious that our results should not be
used as evidence for HFTers harming liquidity. We argue that it is large relative tick size leads to
both a reduction of liquidity and an increase in HFT activity.
5.3 Diff-in-Diff Test Using Leveraged ETFs Splits
This section establishes the causal relationship between relative tick size and HFT
activity using the diff-in-diff test. ETF splits provide us with a cleaner environment to examine
the impact of relative tick size than stock splits do, since stocks splits may not be regarded as
exogenous event. For example, Brennan and Copeland (1988) argues that undervalued firms use
stock splits to signal the quality and strength of their future prospects. In their model, splits are
credible signals because they are costly. The splits for ETFs, however, are much less likely to be
motivated by information. Even if there are any informed related splits, it can be controlled by
ETFs that track the same index but do not spilt.
The regression specification for the diff-in-diff test is as follows:
𝑦𝑖,𝑡,𝑗 = 𝑢𝑖,𝑡 + 𝛾𝑗 + 𝜌 × 𝐷𝑖,𝑡,𝑗 + 𝜃 × 𝑟𝑒𝑡𝑢𝑟𝑛𝑖,𝑡,𝑗 + 𝜖𝑖,𝑡,𝑗
(14)
where 𝑦𝑖,𝑡,𝑗 is HFT activity or liquidity measure for ETF j in index i at time t. 𝑢𝑖𝑡 , the index by
time fixed effects, controls for the time trend that may affect each index. The new element 𝛾𝑗 , is
42
the ETF fixed effect that absorbs the time invariant differences between two leverage ETFs
tracking the same index. After controlling index by time and ETF fixed effects, the only real
differences between the bull and bear ETFs that track the same indexes are returns, 𝑟𝑒𝑡𝑢𝑟𝑛𝑖𝑗𝑡 .
𝐷𝑖𝑗𝑡 , the treatment dummy, equals to 0 for the control group. For the treatment group, the
treatment dummy equals to 0 before the split/reverse split and equal to 1 after the split/reverse
split. Therefore, coefficient 𝜌 captures the treatment effect. The leveraged bull ETF is in the
treatment group, and leveraged bear ETF is in the control group if leveraged bull ETF splits, and
vice versa.
Panel A of Table 8 reports the splits results. Column 1 and 2 show that nominal spread
decreases by 9.7 cents after splits. However, the proportional quoted spread increases by 1 basis
point after split, and the quoted spread increases by 1.22 basis points. The increase after
adjusting the fee is higher because the fixed nominal fee implies a higher proportional fee after
splits. Without the friction of an increased relative tick size, we would expect nominal spread to
decrease in the same ratio as the decrease of the nominal price, keeping the proportional spread
unchanged. Our results indicate that the nominal quoted spread does not adjust to the same
proportion as the decrease in nominal price, and we argue the large relative tick size after the
splits prevent the full adjustment. The results for proportional spread are more significant after
adjusting for the fee, because the homogenous fee leads to a higher proportional fee post-split.
Column 5 shows that the average dollar depth increases by 150,000 dollars, though the result is
not significant due to the small number of split ETFs. The nominal effective spread decreases by
5.4 cents after split, but the proportional effective spread, or the transaction cost for a fixed dollar
amount of transaction, increases by 1 basis point. Again, we observe an increase in HFT activity
along with an increase of proportional spread and depth. We argue it is because an increase in
43
tick size constraints leads to wider proportional spread and the queue to provide liquidity, which
in turn generates more HFT activity.
Insert Table 8 About Here
Panel B reports the results on reverse splits. Column 1-2 shows that reverse splits
increase the quoted spread by 1.2 cents, but the proportional quoted spread decreases by 2.6 basis
points (Column 3) and 5.01 basis points after adjusting the fee (Column 4). Again, suppose there
is no friction, the proportional quoted spread, or the cost to transact a fixed dollar amount, should
not change, which implies an increase of quoted spread at the same proportion to the increase in
price. Column 1 and 3 indicate that the increase in quoted spread is less than the increase in price,
leading to an increase in proportional quoted spread. Column 2 and 4 demonstrates that maker
fee further amplifies the effect, because fixed maker fee leads to a reduction in the proportional
fee. We ascribes this result to the reduction of relative tick size after the reverse split. Reverse
splits create new possible level of proportional spread for fixed nominal spread, which
encourages price competition. For example, for a stock with 5 dollars, the first nominal tick of 1
cent implies a proportional tick of 20 basis point, and the second nominal tick implies a
proportional tick of 40 basis points. A 1-for-5 reverse split reduces the first proportional tick to 4
basis points, the second one 8 basis points… and 20 basis points is the fifth proportional tick
after the reverse splits. The finer grid suggests that the proportional spread should be noincreasing after reverse split, and we find a reduction in proportional spread. The depth at the
best price decreases by 3 million dollars, implying a shorter queue to provide liquidity at less
constrained price. This result, along with the reduction in proportional quoted spread, is the
evidence that traders who were forced to quote the same price under large relative tick size can
44
now choose to differentiate themselves by price, leading to a reduction in depth at the new but
less constrained best price.
Columns 7 and 8 shows an increase in effective spread by 0.7 cents, but Column 9-10
shows a reduction in proportional spread of 2.91 basis points and 5.35 basis point after adjust for
the fee. The results show that transaction cost by liquidity demanders falls after reverse splits.
Column 11 reports a reduction in HFT activity after the reverse splits, and the intuition follows
the results established in previous sessions. A reduction in relative tick size enhances price
competition and reduces the queue to supply liquidity at the constrained best price, which
weakens the incentives to be at the top of the queue at constrained price. Therefore, we see less
HFT activity after reverse splits.
In summary, we find that splits decreases liquidity whereas reverse splits increases
liquidity. The results is intriguing by itself, because classic finance textbooks argue that firm
uses splits to increase liquidity whereas reverse splits are generally used to avoid delisting or to
go dark by reducing the number of small shareholders (Ross, Westerfield and Jaffe, 2008). We
show, however, split reduces liquidity whereas reverse splits increases liquidity. We also find
that splits attracts HFT activity whereas reverse splits reduce HFT activity. Again, these results
should not be interpreted as negative impact of HFTers on liquidity, because our results are
based on exogenous shocks on tick size but not HFT activity. Therefore, the correct economic
interpretation is a large relative tick size reduces liquidity but attracts HFTers. Our results,
however, do reveal the importance of including relative tick in the analysis of both liquidity and
HFT activity, because endogeneity may arise if we omit nominal price.
45
6. Conclusion
We contribute to the literature of HFT by providing a tick size based explanation of speed
competition in liquidity provision. Contrary to the common belief that HFTers provide liquidity
at lower cost, we find that Non-HFTers play a more prominent role in providing liquidity at
better prices than HFTers do, particularly when relative tick size is small. An increase in relative
tick size, however, constrains non-HFTers’ abilities to undercut price and helps HFTers to
achieve price priority when they quote the same price as non-HFTers. As a consequence, HFTers
provide a larger fraction of liquidity for low priced stock in which one cent uniform tick size
implies a larger relative tick size. For ETFs tracking the same index, HFTers are more active in
the lower priced ETFs. In addition, splits increase HFT activity along with increases in quoted
spread and the queue to provide liquidity; reverse splits decrease quoted spread and depth and
also results in a decrease of HFT activity.
Also, we find that HFTers are less active in market making for stocks with higher PIN,
suggesting that fast access to information does not render market making HFTers a more
prominent role in liquidity provision with higher probability of informed trading. HFTers
specialize in stocks with larger relative tick size and lower information asymmetry, or stocks
with large tick size relative to natural bid-ask spread, because these are the stocks where speed
competition is more important.
The tick size constraints channel also provides new possibility to explain the results of
existing literature. The literature on HFT finds that speed improvement increases liquidity and
the common belief for the source of improvement is from traders with higher speed, which is at
odds with the results of current paper. There are two possibilities to explain this discrepancy.
One possibility is that the existing literature on speed is based on technology shocks at
46
millisecond or second range, whereas speed competition in our sample is at nano-seconds level
(Gai, Yao and Ye, 2013) implying a diminishing return of
speed (Jones, 2013). A more
intriguing conjecture is that liquidity improvement may come from traders who do not improve
their speed in those technology shocks. Traders with speed improvement have time priority over
traders who do not, which may give the latter the incentive to jump ahead of the price queue.
Therefore traders who pay the technology enhancement enjoy time priority and less need to
undercut the price, whereas traders can also choose not to pay but have more needs to undercut
the price. A test for this conjecture based on account level data will be very interesting.
The tick size constraints channel also provides new insights on policy debate on HFT.
The current policy debate focuses on whether additional regulation is required on HFT, and if so
how to pursue it. Our paper points to a new direction: HFT may simply be a consequence of
existing regulation on tick size and one possible policy solution is deregulation instead of more
regulation. At the minimum, we firmly believe the first step to pursue additional regulation is the
due diligence to evaluate the impact of existing regulation on HFT.
This paper provides empirical evidence linking tick size regulation and HFT, which
provides a benchmark to evaluate the economic consequences of increasing tick size. The JOBS
Act encourages the SEC to examine the possibility of increasing tick size, and a pilot program is
under way for less liquid stocks. Proponents of wider tick size have offered three rationales for
this position (Grant Thornton, 2012). First, wider tick size controls the growth of HFT. Second,
wider tick size should increase liquidity. Our paper shows that wider tick size encourages HFT
without improving liquidity. The third argument to increase tick size is that wider tick size
increases market-making revenue, supports sell-side equity research, and increases the number of
IPOs. The economic argument that controlling price leads to non-price competition is valid, but
47
we doubt that non-price competition would take the form of stock research or more IPO. The
causal impact of tick size on IPO has never been proved by academic research, but speed
competition under constrained price competition is well established by this paper. A recent
article in the Wall Street Journal states that “investment banks and proprietary trading firms
spend millions to shave ever smaller slivers of time off their activities . . . [as] the race for the
lowest ‘latency’ [continues], some market participants are even talking about picoseconds—
trillionths of a second.”27 We believe one of the drivers for such aggressive investment is the
desire to establish time priority when price competition is constrained, and the rents originating
in tick size constraints facilitate such arms race.
Our paper can be extended in various ways. First, current theoretical work on speed
competition focuses on the role of information. Our paper points out another channel for speed
competition: tick size constraints. Models using discrete prices can be constructed to indicate the
value of speed and the impact of tick size constraints on market quality. Second, speed
competition is not the only market design response to tick size constraints. In a companion paper,
we examine the causal impact of tick size constraints on taker/maker fee market or the market
that charges liquidity providers but subsidize liquidity demanders (Yao and Ye, 2014). The
literature on market microstructure focuses on liquidity and price discovery under certain market
design, but market design is also endogenous, and it is fruitful to examine why certain market
design exists in the first place. Finally, the SEC recently announced a pilot program for
increasing tick size for a number of small stocks, believing that tick size may need to be wider
for less liquid stocks. We encourage SEC to consider decreasing tick size for liquid stocks in the
pilot program, particularly large stocks with lower price.
27
“Wall Street’s Need for Trading Speed: The Nanosecond Age,” Wall Street Journal, June 14, 2011.
48
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51
Table 1. Summary Statistics
This table presents the summary statistics of all stocks and ETFs we use in this paper. Panel A presents
the summary statistics of stocks in NASDAQ HFT sample. Panel B presents the summary statistics of
non-leverage ETF sample, which we use in the twin ETFs test. Panel C presents the summary statistics of
leveraged ETF sample, which we use in the diff-in-diff test. The variable definitions are as follows:
HFTdepth (in pcg) is the percentage of depth at the best bid/ask provided by HFTers. HFTvolume (in pcg)
is the percentage of trading volume with HFTers as liquidity providers. 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 daily price range, that is, high minus low,
proposed by Parkinson (1980). logbvaverage is the logarithm of average book value of equity per
shareholder at the end of previous year, that is, December 2009. idiorisk is the variance of 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 the 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 past
one month return. PIN is the probability of informed trading. return is the contemporaneous daily return
Qtspd represents time-weighted quoted spread. pQtspd represents time-weighted proportional quoted
spread. Qtspdadj and pQtspdadj represent the time-weighted quoted spread and time-weighted proportional
quoted spread after adjustment for fee. SEffspd represents size-weighted effective spread and pSEffspd
represents size-weighted proportional effective spread. SEffspdadj and pSEffspdadj represent size-weighted
effective spread and size-weighted proportional effective spread after adjustment for fee. Depth1
represents the time-weighted dollar depth at the best bid and ask. Depth10 represents the time-weighted
dollar depth within 10 cents from the best bid and ask. RunsInProcess is the proxy for HFT market
making activity.
Mean
Median
Std.
Min.
Max.
Panel A. NASDAQ HFT Sample
HFTdepth (in pcg)
0.321
0.298
0.166
0.006
0.744
HFTvolume (in pcg)
0.285
0.273
0.134
0.000
0.728
tickrelative
0.048
0.034
0.038
0.002
0.192
logmcap
22.010
21.473
1.893
19.371
26.399
turnover
2.367
1.801
2.179
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
0.017
0.001
0.139
age (in 1k days)
9.751
7.671
7.839
0.945
30.955
numAnalyst
13.731
12.000
10.048
1.000
48.000
pastreturn
0.105
0.096
0.073
-0.077
0.336
PIN
0.118
0.111
0.052
0.021
0.275
Panel B. Twin ETF Sample
tickrelative
0.021
0.015
0.018
0.007
0.078
logmcap
21.970
22.740
2.312
17.107
25.139
52
Qtspd (in cent)
2.667
2.035
2.016
1.007
12.900
pQtspd (in bps)
5.414
2.810
5.884
0.832
31.889
Qtspdadj (in cent)
3.257
2.625
2.016
1.597
13.490
pQtspdadj (in bps)
6.664
3.426
6.372
1.280
33.680
SEffspd (in cent)
1.986
1.412
1.434
0.000
8.178
pSEffspd (in bps)
3.997
1.995
4.043
0.000
19.347
SEffspdadj (in cent)
2.586
2.012
1.434
0.600
8.778
pSEffspdadj (in bps)
5.267
2.835
4.667
1.148
21.158
Depth1 (in mn)
0.978
0.416
1.454
0.044
9.194
Depth10 (in mn)
11.684
3.859
20.650
0.267
103.756
RunsInProcess (in .1sec)
8.366
2.412
13.269
0.097
65.499
Panel C. Leveraged ETF Sample
Mean
Median
Treatment
Control
Treatment
Control
Split Sample
return
0
-0.001
0.006
-0.005
Qtspd (in cent)
15.133
2.010
13.884
1.940
pQtspd (in bps)
12.113
9.939
10.910
10.150
Qtspdadj (in cent)
15.723
2.600
14.474
2.530
pQtspdadj (in bps)
12.659
13.112
11.362
13.406
SEffspd (in cent)
8.946
1.496
7.892
1.345
pSEffspd (in bps)
7.150
7.614
6.301
7.089
SEffspdadj (in cent)
9.546
2.096
8.492
1.945
pSEffspdadj (in bps)
7.705
10.840
6.812
9.955
Depth1 (in mn)
0.181
0.180
0.133
0.119
Depth10 (in mn)
0.491
1.136
0.412
0.790
RunsInProcess (in .1sec)
1.488
3.491
1.345
1.375
Reverse Split Sample
return
-0.001
-0.001
0
0.001
Qtspd (in cent)
2.863
1.565
4.494
2.536
pQtspd (in bps)
11.026
9.647
8.762
8.011
Qtspdadj (in cent)
3.453
2.155
5.084
3.126
pQtspdadj (in bps)
14.803
13.492
10.620
9.621
SEffspd (in cent)
2.103
1.265
3.086
1.842
pSEffspd (in bps)
8.974
7.930
6.437
5.434
SEffspdadj (in cent)
2.703
1.865
3.686
2.442
pSEffspdadj (in bps)
12.815
11.312
8.326
7.130
Depth1 (in mn)
0.698
0.129
0.305
0.081
Depth10 (in mn)
5.834
2.277
3.434
1.378
RunsInProcess (in .1sec)
7.661
4.796
5.614
3.305
53
Table 2. Who Provides the Best Quotes?
This table displays the percentage of time HFTers and non-HFTers provide the best bid and ask quotes to
the NASDAQ limit-order book. The sample includes 117 stocks in 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 HFTers
are the sole providers of the best quotes, the percentage of time that non-HFTers are the sole providers of
the best quotes and the percentage of time that both provide the best quotes. Column (1) presents the
average percentage of time that HFTers are the sole providers of the best quotes and column (2) presents
the average percentage of time that non-HFTers are the sole providers of the best quotes. Column (3)
presents the average percentage of time that both HFTers and non-HFTers provide the best quotes.
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 of column (5) based on 21 daily observations are
presented in column (6). *, ** and *** represent statistical significance at the 10%, 5%, and 1% level,
respectively.
Large Cap
Middle Cap
Small Cap
Total
(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
(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
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
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
15.4%
41.7%
42.9%
2.62
26.3%***
18.31
54
Table 3. Market Share of BBO Depth Provided by HFTers
This table presents percentage of depth at NASDAQ best bid and offer (BBO) provided by HFTers. 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
presents share-weighted BBO depth provided by HFTers and Panel B presents equal-weighted BBO
depth provided by HFTers. To calculate the share-weighted average for each portfolio on each day, we
aggregate the number of shares provided by HFTers at BBO and then divide it by the total number of
shares at BBO for that portfolio. Panel A presents the average daily share-weighted BBO depth provided
by HFTers. t-statistics are calculated based on the 21 daily observations. To calculate the equal-weighted
average, we first compute, for each stock on each day, the depth provided by HFTers relative to total
depth. The daily equal-weighted average for each portfolio is the average of the percentage of depth
provided by HFTers for stocks in the portfolio. Panel B presents the average daily equal-weighted BBO
depth provided by HFTers. t-statistics are calculated based on 21 daily observations. *, ** and ***
represent statistical significance of large-minus-small differences at the 10%, 5%, and 1% level,
respectively.
Panel A: Percentage of BBO Depth Provided by High-frequency Traders (Share-weighted)
Large
Medium
Small
Large-Small
Relative Tick Size
Relative Tick Size
Relative Tick Size
Relative Tick Size
(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
t-stat
Panel B: Percentage of BBO Depth Provided by High-frequency Traders (Equal-weighted)
Large
Medium
Small
Large-Small
Relative Tick Size
Relative Tick Size
Relative Tick Size
Relative Tick Size
(Low Price)
(Medium Price)
(High Price)
(Low-High Price)
Large Cap
50.22%
42.70%
30.81%
19.41%***
30.55
Middle Cap
43.10%
26.37%
24.79%
18.30%***
30.28
Small Cap
22.64%
25.48%
21.04%
1.59%
1.50
L-S Cap
27.58%***
17.22%***
9.77%***
t-statistics
28.70
20.59
16.86
55
t-stat
Table 4. Percentage of Volume with HFTers as the Liquidity Providers
This table presents the trading volume percentage due to HFTers as liquidity providers. 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 presents the
volume-weighted percent of volume due to HFT liquidity providers and Panel B presents the equalweighted percent of volume due to HFT liquidity providers. To calculate the volume-weighted average
for each portfolio on each day, we aggregate volume due to HFT liquidity providers and then divide that
figure by the total volume for that portfolio. Panel A presents the average daily volume-weighted
percentage of trading volume due to HFT liquidity providers. t-statistics are calculated based on 21 daily
observations. To calculate the equal-weighted average, we first compute the percentage of volume due to
HFT liquidity providers for each stock on each day. The daily equal-weighted average for each portfolio
is the average of the percentage of volume due to HFT liquidity providers for stocks in the portfolio.
Panel B presents the average daily equal-weighted percentage of trading volume due to HFT liquidity
providers. t-statistics are calculated based on 21 daily observations. *, ** and *** represent statistical
significance at the 10%, 5%, and 1% level of large-minus-small differences, respectively.
Panel A: Percentage of Trading Provided by High-frequency Liquidity Providers (Volume-weighted)
Large
Medium
Small
Large-Small
Relative Tick Size
Relative Tick Size
Relative Tick Size
Relative Tick Size
(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
t-stat
Panel B: Percentage of Trading Provided by High-frequency Liquidity Providers (Equal-weighted)
Large
Medium
Small
Large-Small
Relative Tick Size
Relative Tick Size
Relative Tick Size
Relative Tick Size
(Low Price)
(Medium Price)
(High Price)
(Low-High Price)
Large Cap
46.25%
36.61%
32.89%
13.35%***
25.35
Middle Cap
35.57%
23.47%
22.92%
12.65%***
22.65
Small Cap
19.15%
18.61%
18.02%
1.13%
1.37
L-S Cap
27.10%***
17.99%***
14.88%***
t-statistics
44.70
25.44
21.25
56
t-stat
Table 5. HFT Liquidity Provision
This table presents the regression result of HFT liquidity provision on relative tick size (reciprocal of price), market capitalization and other control variables.
The regression uses NASDAQ HFT data sample as of October 2010 and merge it with all the other variables calculated from databases including CRSP,
COMPUSTAT, etc. Column (1)-(7) present results of daily percentage of depth provided by HFTers. Column (8)-(14) present results of daily percentage of
trading volume with HFTers as liquidity providers. Industry*time high-dimensional fixed effect is adopted in the regression analysis. t-statistics are shown in
parenthesis; *, ** and *** denotes statistical significance at 10%, 5% and 1% respectively.
57
Dep. Var
tickrelative
logmcap
HFTdepth (in percentage)
HFTvolume (in percentage)
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
(10)
(11)
(12)
(13)
(14)
0.678***
0.691***
0.674***
0.691***
0.641***
0.677***
0.653***
0.937***
0.933***
0.943***
0.992***
0.893***
0.937***
0.950***
(7.03)
(7.13)
(6.99)
(6.89)
(6.65)
(7.03)
(6.52)
(14.13)
(14.09)
(14.24)
(14.20)
(13.59)
(14.12)
(13.89)
0.038***
0.038***
0.038***
0.032***
0.032***
0.038***
0.023***
0.051***
0.049***
0.051***
0.042***
0.044***
0.051***
0.032***
(18.50)
(17.12)
(18.41)
(8.18)
(13.11)
(18.32)
(5.54)
(35.57)
(32.50)
(35.76)
(15.23)
(25.94)
(35.42)
turnover
volatility
(11.08)
0.001
0.001
0.01***
0.01***
(0.38)
(0.55)
(5.67)
(5.27)
-0.496
-0.268
-0.414
-0.209
(-0.70)
(-1.55)
(-1.27)
logbvaverage
(-0.80)
-0.003*
0.002
0.00***
0.01***
(-1.80)
(1.21)
(3.30)
(4.77)
idiorisk
-0.290
age
numAnalyst
-0.314
-0.49***
-0.55***
(-1.48)
(-1.61)
(-3.62)
(-4.11)
0.01***
0.01***
0.00***
0.00***
(8.27)
(8.55)
(4.36)
(6.64)
-0.00
-0.00
0.00***
0.00**
(-1.23)
(2.62)
(-1.11)
PIN
(2.41)
-0.36***
-0.44***
-0.42***
-0.41***
(-4.46)
(-5.44)
(-7.73)
(-7.55)
pastreturn
-0.069
-0.12***
-0.007
-0.035
(-1.53)
(-2.66)
(-0.23)
(-1.16)
-0.57***
-0.55***
-0.53***
-0.46***
-0.39***
-0.56***
-0.23**
-0.88***
-0.85***
-0.93***
-0.71***
-0.68***
-0.88***
-0.53***
(-11.37)
(-10.29)
(-9.72)
(-5.83)
(-6.17)
(-10.96)
(-2.46)
(-25.64)
(-23.30)
(-24.88)
(-12.92)
(-15.54)
(-25.23)
(-8.29)
R
0.402
0.403
0.403
0.426
0.408
0.403
0.436
0.565
0.572
0.567
0.573
0.577
0.565
0.596
N
Ind.*time FE
2268
Y
2268
Y
2268
Y
2268
Y
2268
Y
2268
Y
2268
Y
2268
Y
2268
Y
2268
Y
2268
Y
2268
Y
2268
Y
2268
Y
Const.
2
58
Table 6. Correlation Test
This table presents the cross-sectional correlation between HFT proxies and the HFT activity measures
which is calculated from NASDAQ HFT dataset. The HFT activity measures include HFT liquidity
making depth, HFT liquidity making volume and HFT liquidity taking volume. The HFT proxies include
RunsInProcess, calculated before dividing it by regular trading time in 0.1 second (from 9:30a.m to
4:00p.m), Trading Volume (in $100) to Message Ratio, and Quote to Trade Ratio. P-values are shown
under correlation coefficients; *, ** and *** denotes statistical significance at 10%, 5% and 1%
respectively.
HFT Measures
HFTdepth (liq. making)
HFTvolume (liq. making)
HFTvolume (liq. taking)
RunsInProcess
0.650***
0.765***
0.283
<.0001
<.0001
0.002
-0.031
0.252***
0.274
0.7403
0.0061
0.003
-0.385***
-0.390***
-0.082
<.0001
<.0001
0.378
Trading Vol. (in $100)
/ Message Ratio
Quote / Trade Ratio
59
Table 7. Twin ETFs Test
This table regresses liquidity measures and HFT measure on relative tick size (reciprocal of price) and market capitalization. It is based on daily
observations in October 2010. After merging with market quality and HFT measures, we also deleted illiquid ETFs that have less than 100
average consolidated number of trades in all trading platforms as of the sample period, which has finally left us with 8 ETF pairs that track the
same market index. Index*time high-dimensional fixed effect is adopted in the regression analysis. t-statistics are shown in parenthesis; *, **
and *** denotes statistical significance at 10%, 5% and 1% respectively.
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
(10)
(11)
Qtspd
pQtspd
Qtspdadj
pQtspdadj
Depth1
Depth10
SEffspd
pSEffspd
SEffspdadj
pSEffspdadj
RunInProc
(in cent)
(in bps)
(in cent)
(in bps)
(in mn)
(in mn)
(in cent)
(in bps)
(in cent)
(in bps)
(in .1sec)
-23.407***
88.178***
-23.407***
147.178***
76.215***
652.383***
-27.353***
78.292***
-27.353***
138.292***
36.543***
(-17.76)
(27.08)
(-17.76)
(45.20)
(20.81)
(14.43)
(-7.21)
(31.20)
(-7.21)
(55.11)
(4.00)
-0.356***
-0.745***
-0.356***
-0.745***
0.243***
5.026***
-0.209***
-0.381***
-0.209***
-0.381***
3.254***
(-13.74)
(-13.04)
(-13.74)
(-13.04)
(10.69)
(8.05)
(-8.69)
(-10.09)
(-8.69)
(-10.09)
(7.88)
10.05***
17.92***
10.64***
17.92***
-5.31***
-119.93***
6.26***
9.17***
6.86***
9.17***
-74.56***
(15.02)
(13.19)
(15.90)
(13.19)
(-9.83)
(-8.25)
(10.80)
(10.33)
(11.84)
(10.33)
(-7.76)
R2
0.914
0.903
0.914
0.917
0.824
0.604
0.811
0.915
0.811
0.936
0.560
N
378
378
378
378
378
378
378
378
378
378
378
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
tickrelative
logmcap
Constant
Ind.*time FE
60
Table 8. Diff-in-Diff Test Using Leveraged ETF Splits
This table present results of diff-in-diff test using leveraged ETF split (and reverse-split) events. It is based on leverage ETFs splits during 2010
and 2011. We merged the sample with ma rket quality and HFT proxy measures and then deleted illiquid ETF samples that have less than 100
average consolidated number of trades in all trading platforms as of the sample period, which has finally left us with 5 treatment ETFs in the split
sample and 21 treatment ETFs in the reverse-split sample. The first big column on the right present results belonging to the ETF split sample,
while the second big column present results belonging to the ETF reverse-split sample. Panel A reports the results for split and Panel B reports the
results for reverse splits. Both index*time high-dimensional fixed effect and ETF fixed effect are adopted in the regression analysis. t-statistics are
Panel A. Split Sample
Dummytreatment
return
Constant
2
R
N
Ind.*time FE
ETF FE
(1)
Qtspd
(in cent)
(2)
pQtspd
(in bps)
(3)
Qtspdadj
(in cent)
(4)
pQtspdadj
(in bps)
(5)
Depth1
(in mn)
(6)
Depth10
(in mn)
(7)
SEffspd
(in cent)
(8)
pSEffspd
(in bps)
(9)
SEffspdadj
(in cent)
(10)
pSEffspdadj
(in bps)
(11)
RunInProc
(in .1sec)
-9.697***
1.007*
-9.697***
1.220**
0.015
0.334***
-5.355***
0.853**
-5.355***
1.069**
0.350***
(-16.02)
(1.94)
(-16.02)
(2.29)
(1.39)
(3.50)
(-12.05)
(2.11)
(-12.05)
(2.57)
(3.42)
-8.880**
-6.698**
-8.880**
-7.862**
-0.009
-0.326
-4.808*
-5.092**
-4.808*
-6.275**
-0.396
(-2.40)
(-2.11)
(-2.40)
(-2.41)
(-0.13)
(-0.56)
(-1.77)
(-2.06)
(-1.77)
(-2.46)
(-0.63)
10.062***
14.484***
10.652***
16.383***
0.129***
0.462**
5.520***
6.787***
6.120***
8.718***
1.856***
(8.39)
(14.06)
(8.88)
(15.52)
(6.23)
(2.45)
(6.27)
(8.47)
(6.95)
(10.56)
(9.15)
0.910
607
Y
Y
0.742
607
Y
Y
0.910
607
Y
Y
0.718
607
Y
Y
0.915
607
Y
Y
0.811
607
Y
Y
0.868
607
Y
Y
0.635
607
Y
Y
0.868
607
Y
Y
0.729
607
Y
Y
0.978
607
Y
Y
61
Panel B. Reverse Split Sample
Dummytreatment
return
Constant
R2
N
Ind.*time FE
ETF FE
(1)
Qtspd
(in cent)
(2)
pQtspd
(in bps)
(3)
Qtspdadj
(in cent)
(4)
pQtspdadj
(in bps)
(5)
Depth1
(in mn)
(6)
Depth10
(in mn)
(7)
SEffspd
(in cent)
(8)
pSEffspd
(in bps)
(9)
SEffspdadj
(in cent)
(10)
pSEffspdadj
(in bps)
(11)
RunInProc
(in .1sec)
1.175***
-2.608***
1.175***
-5.011***
-0.321***
-0.006
0.701***
-2.905***
0.701***
-5.348***
-3.187***
(8.41)
(-13.48)
(8.41)
(-18.43)
(-6.02)
(-0.61)
(5.96)
(-12.22)
(5.96)
(-17.08)
(-9.77)
-1.648
-3.622**
-1.648
-4.452**
0.878**
0.094
-1.030
-2.183
-1.030
-3.028
2.243
(-1.56)
(-2.48)
(-1.56)
(-2.17)
(2.19)
(1.30)
(-1.16)
(-1.22)
(-1.16)
(-1.28)
(0.91)
3.190***
9.260***
3.780***
12.193***
0.547***
0.152***
2.297***
7.360***
2.897***
10.343***
6.718***
(8.79)
(18.42)
(10.41)
(17.26)
(3.95)
(6.12)
(7.51)
(11.92)
(9.48)
(12.71)
(7.92)
0.834
607
Y
Y
0.883
607
Y
Y
0.834
607
Y
Y
0.856
607
Y
Y
0.787
607
Y
Y
0.888
607
Y
Y
0.768
607
Y
Y
0.784
607
Y
Y
0.768
607
Y
Y
0.797
607
Y
Y
0.850
607
Y
Y
62