Price Discovery without Trading: Evidence from Limit Orders

• Author: JONATHAN BROGAARD,TERRENCE HENDERSHOTT,RYAN RIORDAN
• DOI: http://doi.org/10.1111/jofi.12769
• Date: 01 August 2019
• Published date: 01 August 2019

THE JOURNAL OF FINANCE •VOL. LXXIV, NO. 4 •AUGUST 2019

Price Discovery without Trading: Evidence

from Limit Orders

JONATHAN BROGAARD, TERRENCE HENDERSHOTT, and RYAN RIORDAN∗

ABSTRACT

We analyze the contribution to price discovery of market and limit orders by high-

frequency traders (HFTs) and non-HFTs.While market orders have a larger individ-

ual price impact, limit orders are far more numerous. This results in price discovery

occurring predominantly through limit orders. HFTs submit the bulk of limit orders

and these limit orders provide most of the price discovery. Submissions of limit or-

ders and their contribution to price discovery fall with volatility due to changes in

HFTs’ behavior. Consistent with adverse selection arising from faster reactions to

public information, HFTs’ informational advantage is partially explained by public

information.

ACCORDING TO THE TRADITIONAL VIEW of price discovery, trades reveal investors’

private information while market makers’ quotes reflect public information

(see, e.g., Glosten and Milgrom, 1985; Kyle, 1985). Most stock exchanges and

financial markets have evolved into limit order books where there are no des-

ignated market makers and limit orders represent the bulk of activity. The-

oretical models of limit order books study informed traders’ choice between

market orders and limit orders. The market/limit order choice of informed and

uninformed investors determines the nature of price discovery and adverse

selection. In this paper, we use regulatory data that enable the classification

of limit orders and trades by high-frequency traders (HFTs) and non-HFTs

to systematically quantify the contribution to price discovery of market and

limit orders by HFTs and non-HFTs, primarily using a vector autoregression

(VAR;Hasbrouck, 1991a,1991b,1995). We then link these results to theoretical

models of limit order books.

∗Jonathan Brogaard is with David Eccles School of Business, University of Utah. Terrence

Hendershott is with Haas School of Business, University of California – Berkeley. Ryan Riordan

is with Smith School of Business, Queen’s University. The authors thank seminar participants

at the 2015 Cambridge Microstructure Theory and Application Workshop, Australia National

University, Baruch College, Boston College, Chinese University of Hong Kong, Goethe University,

Hong Kong University,Stockholm Business School, UC Santa Cruz HFT Workshop, and University

of Mannheim for helpful comments. The authors also thank Helen and Victoria asked not to be

thanked IIROC for providing data and comments. All errors are our own. This research was

supported by the Social Sciences and Humanities Research Council of Canada and the Norwegian

Finance Initiative. Hendershott has provided expert witness testimony in a variety of matters,

including an ongoing market manipulation case.

DOI: 10.1111/jofi.12769

1621

1622 The Journal of Finance R

The role of HFTs in adversely selecting non-HFTs is widely debated by aca-

demics, regulators, and investors, with concerns often focusing on HFTs using

market orders to “pick off” stale limit orders (Biais, Foucault, and Moinas,

2015; Budish, Cramton, and Shim, 2015; Foucault, Hombert, and Rosu, 2015;

Foucault, Kozhan, and Tham, 2017). Relatedly, most empirical literature on

price discovery focuses on the contribution of market orders (Hasbrouck, 1991a,

1991b; Brogaard, Hendershott, and Riordan, 2014).1We find, however, that

HFTs’ limit orders contribute more than twice as much to price discovery as

their market orders. In contrast, non-HFTs’ market orders contribute more

to price discovery than their limit orders. Comparing HFTs to non-HFTs, we

find that HFTs’ market orders are responsible for less price discovery than

non-HFTs’ market orders, while HFTs’ limit orders are responsible for twice as

much price discovery as non-HFTs’ limit orders. Overall, HFTs’ market orders

play a smaller role in price discovery while HFTs’ limit orders play a larger

role.2

Our results show that more aggressive orders have a higher price impact.3

Market orders, the most aggressive order type, have the highest impact, fol-

lowed by orders that change the national best bid and offer (NBBO), orders at

the NBBO, and orders behind the NBBO. Despite their lower individual price

impact, limit orders provide the majority of price discovery because they are

far more numerous: market orders represent less than 5% of messages.4Indi-

vidual HFT market orders contribute more to price discovery on average than

1Recent empirical literature examines the contribution of both market orders and limit orders to

price discovery.Among others, Hautsch and Huang (2012) quantify the impact of a limit order using

a cointegrated VAR. Cao, Hansch, and Wang (2009) and Cont, Kukanov, and Stoikov (2014)show

that order imbalances predict future price movements. Fleming, Mizrach, and Nguyen (2017)study

the price impact of market and limit orders in U.S. Treasury bonds using a VAR setup similar to

the one used here. These papers focus on the price impact of individual orders. In contrast, we focus

on decomposing the total amount of price discovery. In addition, our data identifying HFTs allow

us to examine whether orders placed by different traders play different roles in price discovery.

2These results do not necessarily imply that concerns about HFTs are unwarranted. HFTs’

market orders contribute some to price discovery and adverse selection. HFTs incorporating in-

formation with limit orders can also cause non-HFTs’ limit orders to be adversely selected, which

could in turn lead to excess intermediation if non-HFTs reduce their use of limit orders (Jovanovic

and Menkveld, 2015). However, the relative magnitudes of HFTs’ limit orders and market orders

in contributing to price discovery suggests that HFTs are not primarily using their information in

market orders to adversely select non-HFTs.

3A number of papers examine HFTs’ trading and price discovery. Brogaard, Hendershott, and

Riordan (2014) show that HFTs contribute to price discovery with market orders by trading in the

direction of future price changes. Carrion (2013) finds that market-wide information is incorporated

into prices quickly on days when HFTs trade more. Conrad, Wahal, and Xiang (2015) find that

high-frequency trading and quoting correlate with more efficient prices. Chaboud et al. (2014)

find that HFTs improve price efficiency through lower return autocorrelations and fewer arbitrage

opportunities. Chordia, Green, and Kottimukkalur (2018) show that high-frequency market orders

impound information quickly following macroeconomic announcements.

4Amessage refers to any instruction received by an exchange; a message includes marketable

orders, limit order placements, limit order cancellations, and limit order replacements. A limit

order refers to a nonmarketable instruction received by an exchange; a limit order includes limit

order placements, limit order cancellations, and limit order replacements.

Price Discovery without Trading 1623

non-HFT market orders. However, non-HFT market orders are three times

more likely, making them more important overall. HFT limit order submis-

sions and cancellations are both frequent and informative, leading HFT limit

orders to contribute roughly 30% of total price discovery versus roughly 15%

for non-HFTs.

That HFT limit order submissions have a positive price impact is seem-

ingly at odds with the results in Brogaard, Hendershott, and Riordan (2014)

that suggest HFTs’ liquidity-supplying trades have a negative price impact.5

However, the analysis in Brogaard, Hendershott, and Riordan (2014) relies on

executed trades and hence does not capture the effect of limit orders that do

not execute. For example, a limit order to buy will not execute if the price

increases. In this case the limit order contributes to price discovery without

trading. When a limit order executes, in contrast, its price impact is effectively

the opposite of the market order that it executes against. For example, when

a buy market order executes against a sell limit order, on average the efficient

price will increase. This leads to the buy market order having a positive price

impact and the sell limit order having a negative price impact upon execu-

tion. This is why Brogaard, Hendershott, and Riordan (2014) find that HFTs’

liquidity-supplying trades have a negative price impact. The price impact of

limit orders upon submission is the weighted average of the (negative) price

impact of the limit orders that execute and the (positive) price impact of the

limit orders that do not execute. Given that only 5% of limit orders execute, it

is not surprising that the average price impact for executed and nonexecuted

limit orders is positive.

Theoretical models of limit order books provide insights into the roles that

different orders by different traders play in price discovery (e.g., Goettler,

Parlour, and Rajan, 2009 [GPR]; Hoffmann, 2014).6These models focus on

traders’ choice between market orders and limit orders based on traders’ in-

formation and the state of the limit order book. Limit orders receive rather

than pay the bid-ask spread, but do not execute with certainty. Market orders

always execute, but pay the bid-ask spread. When information is more valu-

able and the spread is narrower, traders prefer market orders to limit orders.

5Brogaard, Hendershott, and Riordan (2014) show that HFTs contribute to price discovery

with market orders by trading in the direction of future price changes. They also find that HFTs’

liquidity-supplying trades are in the opposite direction of future price changes. Their results are

not necessarily inconsistent with the results presented here. We show that aggressive limit order

submissions and cancellations are associated with positive price impacts at the time of submission.

Brogaard, Hendershott, and Riordan (2014) show that orders submitted by HFTs that are not

subsequently cancelled and that execute against more aggressively priced incoming limit orders

are adversely selected.

6Other papers examine limit order trading by informed investors, but provide insights less

directly related to HFTs. Kaniel and Liu (2006) theoretically model the order choice of informed

traders. Consistent with GPR, their two-period model finds that informed traders are more likely

to submit limit orders. Bloomfield, O’Hara, and Saar (2005) conduct an experiment that includes

long-lived private information and show that informed trades submit more limit orders. Similarly,

Rosu (2019) shows that informed traders tend to use limit orders for moderate levels of mispricing

and market orders more extreme mispricing.