Do High-Frequency Traders Anticipate Buying and Selling Pressure?

TLDR: The existence of an anticipatory trading channel through which HFTs may increase non-HFT trading costs is supported, and results are not fully explained by H FTs reacting faster to signals that non-hFTs also observe.

Abstract: This study tests the hypothesis that high-frequency traders (HFTs) identify patterns that allow them to anticipate and trade ahead of other investors’ order flow. HFTs’ aggressive purchases and sales lead those of other investors. The effect is consistently stronger for a subset of HFTs and at times when non-HFTs are hypothesized to be less focused on disguising order flow. These results are not fully explained by HFTs reacting faster to signals that non-HFTs also observe such as news, contrarian or trend-chasing behavior by non-HFTs, and trader misclassification. These findings support the existence of an anticipatory trading channel through which HFTs may increase non-HFT trading costs.

Figures

Figure 3: HFT Net Buying around the HFT Net Marketable Buying Sorts Cumulative standardized HFT net buying (HFTNB) around sorts on HFT net marketable buying (HFTNMB). The time t cumulative imbalance is the time t−1 cumulative imbalance plus the time t imbalance. Panel A plots aggregate HFTNB for stocks sorted on aggregate HFTNMB. Panel B plots HFTNB of three HFT groups (High, Mid, and Low) for stocks sorted by the High group’s HFTNMB. HFTs are sorted into groups by the coefficient on the first lag of the individual HFT’s HFTNMB in a regression of non-HFTNMB on ten lags of the HFT’s HFTNMB, non-HFTNMB, and returns estimated during the prior month. Table 5 provides more detail on the sorting procedure. Stocks are sorted into deciles each second based on HFT net marketable buying. Decile breakpoints are calculated from nonzero observations during the prior trading day. Stocks in decile ten are marked as those HFTs are buying and those in decile one are marked as those HFTs are selling. Portfolio means are calculated by first averaging across all observations for a day and then averaging across all days in the sample. Net marketable buying is shares bought in buyer-initiated trades minus shares sold in seller-initiated trades. Net buying is shares bought minus shares sold. Imbalances are divided by 20-day trailing average daily volume to make them comparable across stocks. In both panels, all HFTNB measures are divided by the standard deviation of aggregate HFTNB among all sample stocks that day to ease interpretation.

Figure 4: Non-HFT Price Impact with and without competition from HFTs

Table 4 Example Patterns Predicting non-HFT Net Marketable Buying and Returns This table reports two patterns that predict non-HFT net marketable buying (non-HFTNMB), HFT net marketable buying (HFTNMB), and NBBO midpoint returns in basis points (R). Stocks are sorted in second t into Buy and Sell portfolios based on values for second t−1 and accumulated values from seconds t−5 to t−1:

Figure 5: Persistence of Differences in Individual HFTs’ Prediction Ability

Figure 1: Cumulative HFT vs. non-HFT Net Marketable Buying.

Table 3 Intra-day VAR Estimates for Individual Stock-day Observations

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LBS Research Online
N Hirschey
Do High-Frequency Traders Anticipate Buying and Selling Pressure?
Article
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Hirschey, N
(2021)
Do High-Frequency Traders Anticipate Buying and Selling Pressure?
Management Science, 67 (6). pp. 3321-3345. ISSN 0025-1909
DOI: https://doi.org/10.1287/mnsc.2020.3608
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Do High-Frequency Traders Anticipate Buying and
Selling Pressure?
Nicholas Hirschey
*
London Business School
January 2020
Abstract: This study provides evidence that high-frequency traders (HFTs) identify patterns in
past trades and orders that allow them to anticipate and trade ahead of other investors’ order flow.
Specifically, HFTs’ aggressive purchases and sales lead those of other investors, and this effect is
stronger at times when it is more difficult for non-HFTs to disguise their order flow. Consistent
with some HFTs being more skilled or more focused on anticipatory strategies, I show that trades
from a subset of HFTs consistently predict non-HFT order flow the best. The results are not
explained by HFTs reacting faster to news or past returns, by contrarian or trend-chasing behavior
by non-HFTs, or by trader misclassification. These findings support the existence of an anticipatory
trading channel through which HFTs increase non-HFT trading costs.
*
Contact information: Department of Finance, London Business School, Regent’s Park, London NW1 4SA, United
Kingdom; Email: nhirschey@london.edu. I would like to thank NASDAQ OMX for providing the data and Frank
Hatheway, Claude Courbois, and Jeff Smith for many useful discussions about the data and market structure. I
would also like to thank Andres Almazan, Fernando Anjos, Robert Battalio, Johannes Breckenfelder, Carlos Carvalho,
Jonathan Cohn, Shane Corwin, Andres Donangelo, Cesare Fracassi, John Griffin, Terry Hendershott, Paul Irvine,
Pete Kyle, Richard Lowery, Tim Loughran, Jeffrey Pontiff, Mark Seasholes, Clemens Sialm, Laura Starks, Sheridan
Titman, and seminar participants at Boston College, the European Finance Association meeting, the Georgia Institute
of Technology, the Hong Kong University of Science and Technology, the London Business School, the London School
of Economics, Rice University, the University at Buffalo, the University of California Irvine, the University of Georgia,
Manchester Business School, the University of Melbourne, the University of Miami, the University of Notre Dame, the
University of Texas at Austin, and the Western Finance Association meeting for helpful comments and suggestions.

Investors and regulators have immense interest in the automated strategies used by high-frequency
traders (HFTs) and how they affect other investors. Liquidity provision by HFTs has clear benefits.
Yet HFTs make many informed trades; more than half their dollar volume on NASDAQ comes from
marketable trades that must predict returns to be profitable. The welfare consequences of this
informed trading are less clear. In particular, a prominent concern is that one way HFTs predict
returns is by using past trade and order data to learn which stocks non-HFTs are about to buy or
sell. This information is valuable because an HFT who infers a non-HFT is beginning to liquidate
a large position can sell shares now and profit when the price subsequently falls.
This paper examines these issues and provides the first evidence that one reason HFTs appear
informed is that they anticipate and trade ahead of non-HFT buying and selling pressure. Specifi-
cally, I analyze return and trade patterns around periods of intense marketable buying and selling
by HFTs. The imbalance between these marketable purchases and sales is a simple measure of
HFTs’ directional bets.
1
Anticipatory trading implies HFTs trade in the same direction as their
expectation of future non-HFT order flow. Consistent with HFTs using such a strategy, I show
that when HFTs sell a stock with marketable orders, this predicts future marketable selling by
non-HFTs and lower returns.
This strategy has important implications for liquidity and price efficiency. If a non-HFT is selling
to fund a liquidity shock, the HFT’s selling harms the non-HFT by depressing their liquidation
price (Brunnermeier and Pedersen 2005). If instead the non-HFT is selling because the stock is
overvalued, the HFT is effectively reverse engineering the non-HFT’s signal (Madrigal 1996, Yang
and Zhu 2019, Baldauf and Mollner 2020). Competition between the HFT and non-HFT to trade
on the signal causes prices to incorporate this information faster.
2
But it also implies moderated
benefits of HFT participation in price discovery, because some information arriving via HFT trades
would soon be incorporated into prices by non-HFTs anyway. Additionally, the competition lowers
non-HFT profits, which reduces their incentive to acquire information (Grossman and Stiglitz 1980,
1
A marketable limit order is functionally equivalent to a market order: a buy order with a limit price at or above
the best ask or a sell order with a limit price at or below the best bid at the time it enters the order book. NASDAQ
requires all orders to have a limit price, and a trade is initiated when a marketable limit order crosses either the best
bid or best ask.
2
Non-HFTs may at first trade less aggressively to hide from HFTs, slowing price adjustment. But once the HFT
has learned how the non-HFT is trading, competition between them ultimately pushes prices closer to fundamental
value (Madrigal 1996, Yang and Zhu 2019).
1

Stiglitz 2014, Weller 2018).
3
These concerns were the basis for Michael Lewis’s (2014) book, Flash
Boys, and the founding of the deliberately slowed down IEX trading platform.
The analysis in this paper uses an entire year of unique trade and trader-level data from the
NASDAQ Stock Market. It is an important sample for studying HFTs given NASDAQ was the
biggest U.S. exchange by volume and HFTs accounted for 40% of its dollar volume.
In tests where stocks are sorted by HFT net marketable buying at the one second horizon, non-
HFT net marketable buying for the stocks bought most aggressively by HFTs rises by a cumulative
65% of its one-second standard deviation over the following thirty seconds. For the median stock,
this equates to a 100 share HFT imbalance predicting non-HFTs to buy 13 more shares with
marketable orders than they sell. The figures for stocks HFTs sell most aggressively are similar,
but in the opposite direction. Turning to returns, future returns for stocks HFTs buy aggressively
are positive, while returns for stocks they sell aggressively are negative. The returns and non-HFT
trade imbalances predicted by these sorts persist for more than five minutes.
The sorts also show who provides liquidity to these marketable HFT trades. For the stocks
HFTs buy with marketable trades, their net buying is also positive in the surrounding seconds.
Thus at these times HFTs in aggregate take liquidity from non-HFTs.
The evidence is consistent with HFTs recognizing persistent informed non-HFT order flow in
real time. Since liquidity providers are slow to update their quotes, HFTs trade ahead of the
impending non-HFT order flow and associated price change to earn a profit. I provide two example
patterns that illustrate how HFTs could identify stocks with persistent order flow and prices that
update slowly. The examples are simple, interpretable, and use only past order flow and returns as
their inputs. Though HFTs use more sophisticated algorithms, the example patterns nonetheless
succeed in predicting future non-HFT order flow and returns. And HFT order flow in surrounding
seconds is consistent with the patterns capturing predictability used by HFTs.
I next examine whether some HFTs are more skilled at anticipating order flow. There is evidence
HFTs follow a variety of strategies (Boehmer, Li, and Saar 2018) and fast HFTs are more profitable
(Baron, Brogaard, Hagstr
¨
omer, and Kirilenko 2019). Consistent with HFTs having heterogenous
skills, there is persistence in which individual HFTs’ trades most strongly predict non-HFT order
3
These incentive effects arise when HFTs learn from the endogenous order flow of non-HFTs who pay a cost for
their signals. This is absent from models in which the speculative HFT’s trades do not affect the signal itself, such
as Foucault, Hombert, and Rosu (2016).
2

flow. I sort HFTs into three groups each month based on the size of coefficients from regressions
of non-HFT order flow on the HFTs’ lagged trading (excluding predictability from trend-chasing
by non-HFTs and serial correlation in non-HFT order flow). For HFTs in the top third the prior
month, a one-standard deviation shock to their net marketable buying predicts a cumulative change
in non-HFT net marketable buying equal to 14% of its one-second standard deviation over the next
30 seconds. This compares to an estimate of 2% for HFTs in the bottom third. These top HFTs’
trades are also more strongly correlated with future returns. This skill persistence result holds
regardless whether individual HFTs are sorted based on correlations with their net marketable
buying or total net buying (summing marketable and non-marketable trades).
These findings imply that large non-HFTs have an incentive to disguise their order flow, and
in reality we see them deploy execution algorithms to achieve this goal. Yet in the competition
between HFT and non-HFT algorithms, non-HFTs are at a disadvantage to the extent that they
are constrained by their desire to enter or exit their position. Dark pool operator ITG writes,
“some traders are more willing to increase fill rate at the expense of execution quality—the risk of
information leakage and impact”(ITG 2013). Indeed, I find the correlation between HFT and non-
HFT trades is stronger at times non-HFTs are impatient and thus less focused on disguising order
flow: at the market open, on days with high volume, and when trading illiquid or small-cap stocks.
This is consistent with Goldman Sachs’ acknowledgement their algorithms leak more information
in small-caps (Traders Magazine 2013).
I consider several explanations for marketable HFT trades leading marketable non-HFT trades.
The effect could be caused by HFTs reacting faster to a signal non-HFTs also observe (Von Beschwitz,
Keim, and Massa 2015, Chordia, Green, and Kottimukkalur 2018). But the most probable signals
they would both utilize in close succession do not fully explain the results (e.g., past returns, news
articles, analyst forecasts and recommendations, management guidance, and form 8-K filings). Con-
trols for returns also show the effect is not due to a reverse causality story in which HFT purchases
cause trend chasing non-HFTs to purchase shares as well. Another explanation is trade misclassi-
fication. Perhaps NASDAQ incorrectly labels some HFT trades as coming from non-HFTs. Then
the lead-lag result may be caused by trades from correctly labeled HFTs predicting those of incor-
rectly labled HFTs who follow similar strategies. I evaluate this explanation by comparing the way
HFT trading forecasts itself to how it forecasts non-HFT trading. Misclassification implies that
3

Frequently asked questions

Q1. What contributions have the authors mentioned in the paper "Do high-frequency traders anticipate buying and selling pressure?" ?

This study provides evidence that high-frequency traders ( HFTs ) identify patterns in past trades and orders that allow them to anticipate and trade ahead of other investors ’ order flow. This paper examines these issues and provides the first evidence that one reason HFTs appear informed is that they anticipate and trade ahead of non-HFT buying and selling pressure. I would also like to thank Andres Almazan, Fernando Anjos, Robert Battalio, Johannes Breckenfelder, Carlos Carvalho, Jonathan Cohn, Shane Corwin, Andres Donangelo, Cesare Fracassi, John Griffin, Terry Hendershott, Paul Irvine, Pete Kyle, Richard Lowery, Tim Loughran, Jeffrey Pontiff, Mark Seasholes, Clemens Sialm, Laura Starks, Sheridan Titman, and seminar participants at Boston College, the European Finance Association meeting, the Georgia Institute of Technology, the Hong Kong University of Science and Technology, the London Business School, the London School of Economics, Rice University, the University at Buffalo, the University of California Irvine, the University of Georgia, Manchester Business School, the University of Melbourne, the University of Miami, the University of Notre Dame, the University of Texas at Austin, and the Western Finance Association meeting for helpful comments and suggestions. 

Q2. What are the future works mentioned in the paper "Do high-frequency traders anticipate buying and selling pressure?" ?

Future research could provide more detail on which characteristics of past trades and orders allow HFTs to predict the stocks non-HFTs will buy and sell. 

Q3. Why is the post-sort spread larger in smaller stocks?

The larger post-sort spread in smaller stocks could be due to non-HFTs having a harder time disguising order flow when trading relatively illiquid stocks. 

Q4. What is the definition of net marketable buying imbalance?

A net marketable buying imbalance, defined as shares in buyer-initiated trades minus shares in seller-initiated trades, is a common measure of buying and selling pressure from the existing literature (e.g., Chordia, Roll, and Subrahmanyam 2002). 

Q5. How many basis points is the second estimate from the counterfactual?

The estimate from the counterfactual with no HFTs is 0.274 basis points the second of the shock and 0.743 basis points 30 seconds later. 

Q6. What is the lag one coefficient on non-HFT net marketable buying?

In the equation forecasting non-HFT net marketable buying, the lag one coefficient on HFT net marketable buying is 0.0007, rising to 0.0021 at lag two and then declining slowly to 0.0016 at lag ten. 

Q7. How many lags does the coefficient in the HFT regression show?

Using the VAR with 30 lags, Panel B shows the coefficient in the HFT regression is roughly zero by the fifteenth lag, while the coefficient in the non-HFT regression remains positive and significantly different from zero even after 30 lags. 

Q8. What is the downside to this method?

A downside to this method is that relying on data from a single exchange means it misses position changes caused by trades on other venues (Menkveld 2013, Reiss and Werner 1998).