Trader Positions and Marketwide Liquidity Demand
 

Esen Onur, John S. Roberts, and Tugkan Tuzun∗

September 19, 2017

ABSTRACT

In electronic, liquid markets, traders frequently change their positions. The

distribution of these trader position changes carries important information about

liquidity demand in the market. From this distribution of trader position-changes,

we construct a marketwide measure for intraday liquidity demand that does not

necessarily depend on aggressive trading. Using a rich regulatory dataset on S&P

500 E-mini futures and 10-year Treasury futures markets, we show that this liquidity demand measure has a positive impact on prices. We then decompose

our measure of liquidity demand into three components: aggressive, passive and

mixed liquidity demand. Passive liquidity demand also has an impact on prices;

a one standard deviation increase in passive liquidity demand is associated with

0.5 tick rise in prices for S&P 500 E-mini futures. In addition, we find that new

information is incorporated into the prices when passive liquidity demanders take

positions. By providing direct evidence, we contribute to the growing literature

on the impact of passive limit orders.

JEL classification: G10, G130, G140.
 

Keywords: Liquidity, Passive Trading, Price Impact.
 

∗The research presented in this paper was co-authored by Esen Onur, and John Roberts, CFTC

employees who wrote this paper in their official capacity, and Tugkan Tuzun, a Federal Reserve Board

economist detailed to the CFTC who also wrote this paper in his official capacity. The Office of the

Chief Economist and CFTC economists and consultants produce original research on a broad range

of topics relevant to the CFTCs mandate to regulate commodity futures markets, commodity options

markets, and the expanded mandate to regulate the swaps markets pursuant to the Dodd-Frank Wall

Street Reform and Consumer Protection Act. These papers are often presented at conferences and

many of these papers are later published by peer-review and other scholarly outlets. The analyses and

conclusions expressed in this paper are those of the authors and do not reflect the views of Federal

Reserve Board, Federal Reserve System, their respective staff, other members of the Office of CFTC

Chief Economist, other Commission staff, or the Commission itself. This paper was previously entitled

“Demand for Intraday Risk Transfer”.
I. Introduction

One objective of financial markets is to facilitate risk transfer between market participants. The party that initiates risk transfer is deemed the liquidity demander, and its

counterparty is deemed as the liquidity supplier. Empirically, liquidity demanders are

often identified as the side of trades that use marketable orders. However, given recent

advances in financial markets, there are various reasons to challenge this definition.

Electronification of financial markets has made the determination of liquidity demanders more complicated for two reasons. First, high frequency traders have increased

the amount of intraday intermediation in financial markets. As opposed to traditional

market makers who provide immediacy, these new types of intraday intermediaries can

demand immediacy as part of their intraday intermediation role. Indeed, they take the

aggressive side of the trade about half of the time, contributing to aggressive trading,

but they do not take on large positions (Kirilenko et al., 2017). As a result, it is not clear

whether a measure of aggressive imbalance, such as the difference between aggressive

buy and sell volume, can accurately capture which side of the trade is taking position in

the market. Second, following the increasing use of electronic limit order books, where

every trader can submit limit orders, it has been recognized that informed traders strategically use passive limit orders to take positions (Collin-Dufresne and Fos, 2015; Easley,

de Prado and O’Hara, 2016) . In fact, Easley, de Prado and O’Hara (2016) point out

that informed traders cannot simply be equated to traders who use marketable orders as

they change positions. Therefore, the imbalance of aggressive buy and sell trades (e.g.

order flow) may not be a precise indicator of underlying information, especially after the

electronification of financial markets.

In this paper, we introduce a new measure for marketwide liquidity demand based

on information present in trader positions regardless of their aggressiveness. It is im1
 
portant to note that liquidity demand, which is expressed by trader positions, does not
 

necessarily coincide with demand for immediacy, as the passive side of transactions can

also be demanding liquidity if passive transactions are used for taking large positions.

In fact, traders often recognize a trade-off between demanding immediacy and getting a

favorable execution price. Imagine a trader with long-lived information who decides to

take a sizable position in an electronic limit order market. He does not need immediacy

and patiently uses passive orders to reduce his transaction cost by taking the other side

of immediacy demanding traders. When this trader tries to achieve his trading objective, he is likely to trade against a number of counterparties, who will experience smaller

changes in their net positions.

This scenario is important for two reasons. First, this patient position taker demands

liquidity but not immediacy. Traders on the aggressive side of the trades are satisfying

his liquidity demand. Second, because the passive side of the transactions is fulfilled

by this informed trader, it is his passive positioning that brings information to the

market. Overall, this scenario highlights the difference between liquidity demand, which

is generated by traders desire to build positions, and immediacy demand, which is mainly

generated by traders’ patience.

Our measure, which is aimed at capturing net liquidity demand in the market, is

the skewness of intraday position changes across market participants. Intuitively, the

skewness measure captures the imbalance between traders with large positions, who demand liquidity, and traders with small positions, who supply liquidity. It is important

to note that this measure is based on position information rather than on trade information because traders can reach their desired position by several trade executions to

minimize transaction costs (Bertsimas and Lo, 1998). This characterization of trading

is especially true for limit order book markets, because the increased electronification

of such markets has also facilitated order splitting, causing a majority of trades to be

2
 
clustered at small sizes (Chordia, Roll and Subrahmanyam, 2011; Kyle, Obizhaeva and
 

Tuzun, 2016; O’hara, Yao and Ye, 2014). With the clustered trade sizes, individual

trades contain little information about trader positions. As a result, trader positions

rather than transactions could better capture the true liquidity demand in the market.

We have two main findings. First, our skewness measure has impact on prices even

after controlling for the demand for immediacy, as captured by the imbalance between

aggressive buy and sell trades. Using trade execution information, we decompose this

measure into three components: passive, aggressive, and mixed terms. This decomposition allows us to examine the differential impact of passive and aggressive positioning.

We find that passive positioning has impact on prices. Second, we also show that this

passive positioning incorporates information into prices and reduces market liquidity.

This finding is consistent with theories of adverse selection (e.g. Glosten and Milgrom

(1985) in the sense that when immediacy providers are taking positions, the market

becomes less liquid, allowing them to compensate their counterparties. It is well established that immediacy demanders pay a premium when they trade (e.g. Grossman and

Miller (1988)). Our results suggest that immediacy providers also pay a premium if they

are taking positions.

The rest of the paper is organized as follows. Section 2 describes the literature.

Section 3 introduces a simple model to illustrate our intuition for the new measure of

intraday liquidity demand. Section 4 introduces data and the measures we construct.

Section 5 presents analysis and findings, and Section 6 concludes.

II. Literature

Researchers have recognized that aggressive trading may not equate to liquidity demand and, hence, passive trading may not equate to liquidity supply. Menkveld (2015)

3
 
highlights the need for a better measure of liquidity supply and demand that does not
 

condition on immediacy. Biais, Declerck and Moinas (2016) argue that proprietary

traders can provide liquidity even if they are aggressively trading.

The closest paper to ours is Easley, de Prado and O’Hara (2016). They develop a

bulk volume trade classification and show that this measure can detect informational

trading better than order flow. Our measure of liquidity demand differs from theirs

in that ours captures the position build-up of large traders on one side of the market

without taking signal from price changes. Instead, we study the effect of our measure

on prices. But, consistent with their results, we also find that passive trading lowers

market liquidity, suggesting that passive orders carry information.

Bloomfield, O’Hara and Saar (2005) use an experimental design to argue that informed traders use both market and limit orders to fully capitalize on their information.

Collin-Dufresne and Fos (2015) show that activist investors, who arguably have private

information prefer to use limit orders to trade patiently. These patient activist traders

inherently demand liquidity but do not demand immediacy. Hence, it may not be possible to quantify the effect of informed patient traders by only analyzing the immediacy

demand in the market. We contribute to this line of research by showing that traders

can also affect prices when they build positions through immediacy provision without

aggressively trading.

Researchers often proxy for liquidity demand in limit order markets with immediacy

demand, determined by classifying trades using the Lee and Ready (1991) algorithm.

Hasbrouck (1991a,b) analyze the price impact and information content of immediacy demanding trades. Chordia, Roll and Subrahmanyam (2002) study the relationship among

aggressive trading, market returns and liquidity. They show that daily order flow affects

market returns. Sarkar and Schwartz (2009) introduce a measure of correlation between

the numbers of buyer- and seller-initiated trades, which they call market sidedness. They

4
 
show that this measure is an indication of disagreements and can predict more volatility
 

and lower bid-ask spreads. On the other hand, Hautsch and Huang (2012) estimate the

price impact of incoming passive orders. Our approach mainly differs from theirs in

that our estimation focuses on the impact of position build-up through executed passive

orders.

Our skewness measure is naturally related to the literature on the distributional

properties of trader positions. Kyle and Obizhaeva (2017) develop a framework where

the distribution of positions, along with transaction costs, market resiliency, and pricing

accuracy, is shown to be constant across stocks when measured per unit of business

time. Andersen et al. (2015) extend this idea to intraday dynamics of number of trades,

trade size and trading volume in the S&P 500 E-mini futures market. More recently,

Duffie and Zhu (2017) show that allowing a mechanism through which investors can

trade large quantities at a price that is not affected by their price pressure improves

allocative efficiency.

III. Trader Positions and Liquidity Demand

To illustrate how our measure of liquidity demand relates to the higher moments of

trader position distribution, specifically the skewness, we introduce a simple model of

trading.

Assume that there is a risky asset with zero net supply and that there are two types

of traders: noise traders and liquidity providers. 1 There are N risk averse liquidity

providers with a profit function defined as follows.

Π(Xi) = Xi(V − P1) − δXi

γ+1

1For simplicity, we are not modelling an informed trader. However, the main results of this model

still hold if an informed trader is added.

5
 
The profit of liquidity providers is a function of the size of position they take, X, the
 

price at which price they can liquidate their position, P1, and the fundamental value of

the asset V. If the price of the asset at its expected fair value at time t=0 (E(V ) = P0),

then −XiΔP is the expected revenue from providing liquidity. Assume γ is a positive

odd number, then Π(.) is a concave function. It is costly to provide liquidity for the

risky asset and δXi

γ+1 is the cost of accepting risk. The demand function of liquidity

providers can be obtained from their profit function.

Π'

(Xi) = −ΔP − δ(γ + 1)Xi

γ = 0 (1)

ΔP = −δ(γ + 1)Xi

γ (2)

ΔP 1

X γ i = −( ) (3) δ(γ + 1)

Summing across all liquidity providers, we get

δ(γ + 1) N

N

Xγ ΔP = − i (4) N

i=1

A noise trader receives a shock to trade Y units of the risky asset and demand

liquidity. Then, the market clearing condition suggests that the sum of all positions in

the market is zero.

N

N

Y + Xi = 0 (5)

i=1

Substituting (3) into the market clearing condition, we obtain the relationship between Y and ΔP.

6
 
ΔP = (γ + 1)δ(

Y )

γ (6) N

Equation (4) shows the relationship between liquidity providers and price while equation (6) shows the relationship between the liquidity demanding noise trader and the

price. In electronic limit order books where everyone can submit limit orders, it may

not be possible to distinguish traders who demand liquidity from traders who respond

to this liquidity demand. Hence, price equations (4) and (6) cannot be estimated without identification assumptions about the trading behavior of liquidity demanders and

suppliers. Traditionally, traders on the passive (immediacy-providing) side of trades are

assumed to be liquidity providers. We propose a specification that does not rely on immediacy demand to identify liquidity providers and demanders. This specification can

)γ−1 be obtained by multiplying (4) by −( N

1 and summing with equation (6).

(γ + 1)δ N

N

ΔP = (Nγ−1 − N)

[Y γ + Xi

γ

] (7)

i=1
 

 N [Y γ + Xγ

] is the sum of γth power of all trader position changes. i=1 i

To illustrate the intuition of this equation, imagine that 100 traders each buy one

contract each and 100 traders each sell one contract. In this scenario, exactly 100 contracts exchange hands. Imagine a different situation where 1 trader buys 100 contracts

and 100 traders each sell 1 contract, selling a total of 100 contracts. Because exactly

100 contracts again exchanged hands, the amount of position change in both situations

is the same. However, the side that trades more than the average quantity in absolute

terms demands liquidity, hence liquidity demand is balanced between buyers and sellers in the first situation while a buyer is demanding liquidity in the second situation.

The skewness (γ= 3) of intraday position changes can capture the differences between

these situations; it is zero in the first situation and positive in the second situation.

7
 
Importantly, the skewness of intraday trader positions does not use a measure of aggressiveness and, therefore, does not depend on immediacy demand. It is also important to

note that liquidity providers each take smaller positions than their large counterparties,

so the number of liquidity providers is always higher than the number of liquidity demanders. Because liquidity suppliers trade against price movements, this intuition suggests

that prices should move in the opposite direction of the higher number of traders. For

example, if the number of sellers is higher than the number of buyers, the price will

increase.

IV. Data and Measures Used

We use intraday audit-trail transaction level data of E-mini S&P 500 and 10-year Treasury futures markets. The contracts are settled at expiration dates in March, June,

September, and December of each year. The contract with the nearest expiration date,

which attracts the majority of trading activity, is called the front-month contract. Our

sample is from January 2015 to August 2016 and includes detailed account-level data

from the U.S. Commodity Futures Trading Commission on all front-month transactions.

The data set contains information about counterparties, whether the trade was buyer- or

seller-initiated, the trade size (in terms of contracts), and prices, as well as time-stamps

indicating transaction time stamps to the millisecond.

Individual position changes have information on the amount of liquidity demanded

and supplied in the market. For one-minute intervals, we aggregate total buy and sell

volume for each trader to calculate their net position changes. In our analysis, we use

the distributional properties of position changes at one-minute intervals. We choose oneminute intervals for two reasons.2. First, we would like to show that position changes

2In unreported results, we repeat our analysis with 5-minute and 10-minute intervals. The results

8
 
affect prices at very high frequencies. However, at the highest frequency, event time, the
 

skewness measure cannot be calculated because for each transaction, the skewness of

the position change distribution is mechanically zero. Second, we would like to calculate

our skewness measure at frequencies comparable to investment horizons of intraday

intermediaries. Kirilenko et al. (2017) show that market makers and high-frequency

traders liquidate half of their positions within about three and two minutes, respectively.

Hence, one-minute intervals should include position changes of traders who demand and

supply liquidity intraday.

Figure 1 shows the distribution of one-minute position changes observed in these two

markets for the entire sample. Because position changes tend to cluster around zero,

we partition the distribution into two parts: (1) position changes between -10 and 10

contracts, and (2) position changes greater than 10 contracts and less than -10 contracts.

The charts on the left plot the position changes between -10 and 10 contracts. There are

no zero position changes, as we do not include traders who do not change their positions

within one minute even if they trade during that time frame. For the S&P 500 E-mini

futures, position changes at 1 and -1 contracts each account for about 20% of the position

changes. Hence, about 40% of all position changes are 1 contracts in this market. For

the 10-year Treasury futures, position changes at 1 and -1 contracts are each 9% of the

position changes distribution, about half of their respective shares in the S&P 500 E-mini

futures. The charts on the right plot the position changes of greater than 10 contracts

and fewer than -10 contracts. In both markets, the frequencies of large positive and

negative position changes decay monotonically with spikes in even contracts such as 20,

25, 50, 60, 75, and 100. Some portion of the spike in 100 contracts is due to the fact that

for the purpose of illustration, we mark the position changes greater than 100 contracts

to 100 contracts and the position changes less than -100 contracts to -100 contracts.

are qualitatively identical.

9
 
The position change distributions in both markets appear to be symmetric during our
 

sample period. The mean of the distribution of position changes is always zero, as the

sum of all position changes is zero. Therefore, it is straightforward to calculate higher

moments of this distribution.

Figure 2 explores the relationship of skewness, computed for one-minute intervals,

with various measures of market activity. In addition to skewness, we compute the

number of traders, total volume, price volatility (defined as the maximum observed

price minus the minimum observed price), and price change (defined as the end price

minus the start price). Our skewness measure is the Fisher-Pearson skewness coefficient

of the trader position change distribution.3 The price changes are calculated in number

of ticks.4 The order flow is the difference of buyer- and seller- initiated volume measured

in 1,000 contracts. We split the sample of intervals into 10 groups based on our skewness

value, where the first group indicates a skewness value between 1 and 0.80, the second

indicates a skewness value between 0.80 and 0.60, and so on. The first row shows

the average number of short traders (red) and long traders (blue) by skewness group.

Price changes increase monotonically from the smallest skewness group to the largest.

As skewness increases, the number of long traders decreases and the number of short

traders increases. Consistent with our intuition in the previous section, this relationship

suggests that price changes are negatively correlated with the number of long traders

and positively correlated with the number of short traders.

Average volume and price volatility show a similar pattern: They are largest at

the extreme skewness groups (groups 1 and 10), with large averages also observed in

the lowest skewness groups (groups 5 and 6). The price changes are higher for higher

3In unreported results, in addition to skewness, we add other odd moments of the positions change

distribution. Among the odd moments, skewness measure has the highest explanatory power for prices.

4The tick size is 0.25 index points in the E-mini S&P 500 contract and 1/64 in the 10-year Treasury

futures contract.

10
 
skewness groups. Prices increase (decrease) the most for the most positively (negatively)

skewed intervals.

Table I summarizes the statistics for price changes, order flow, and the skewness

measure in the E-mini market. The mean and median of these variables are slightly

negative, but very close to zero. A mean value of zero skewness suggests that, on

average, the net marketwide liquidity demand is zero and traders take comparable short

and long positions consistent with our results in Figure 1. The standard deviation of

minute-by- minute price changes is about 3 ticks. The standard deviations of order flow

and skewness are 0.79 and 4.43, respectively. The correlations of skewness with price

changes and order flow are 0.31 and 0.41, respectively.

Table II reports the same statistics for the 10-year Treasury futures. Similarly, the

mean and median of price change, order flow, and skewness are very close to zero, but

their standard deviations suggest that albeit small, there is variation in these variables.

Once again, skewness is highly correlated with price changes and order flow. Although

skewness is highly correlated with order flow, it is important to analyze whether and

how much additional effect skewness has on price changes.

V. Analysis and Findings

In this section, we analyze the relationship between the price changes and the marketwide liquidity demand captured by the skewness of the distribution of intraday position changes. The skewness measure captures the asymmetry in the sizes of short and

long position changes, and this measure has a large value when few traders in the market have relatively large position changes. It is well-documented that trades that are

aggressive and that therefore demand immediacy have impact on prices.5 Our skewness

5Hasbrouck (1991b), Chordia, Roll and Subrahmanyam (2002), and others document the impact of

aggressive transactions on prices.

11
 
measure is different than order flow because it measures the amount of position build-up
 

regardless of its immediacy.

Aggresssive trades cannot completely capture liquidity demand for three reasons.

First, traders split their orders to avoid detection. Order shredding makes trade size an

inaccurate measure of the intended position changes of traders. Second, with increased

electronification, there is significant volume related to intermediation. In other words,

intermediaries trade large volumes but do not take significant positions. Third, in electronic limit order markets, traders can use a mixture of passive and aggressive orders to

trade and build their intraday positions. For example, in Figure 3, we show that large

traders are not always aggressive traders. This figure plots the aggressiveness ratios for

one-minute position changes averaged across days. The box plots in Figure 3 show the

maximum, 75th percentile, median, 25th percentile and minimum of this average aggressiveness ratio for various levels of position changes. Once again, we divide the position

changes into two groups. The box plots on the left show the absolute position changes

of 1 through 1000 rounded by 25. The box plots on the right show the absolute position

changes of 1000 through 5000 rounded by 100. For the S&P 500 E-mini futures, the

median value of average aggressiveness is less than 40% for the smallest position change

group, 25 contracts. This value increases to over 70% for 400 contracts, but starts to

decline for larger position changes in the box plot to the right. For example, position

changes of greater than 4000 contracts generally have less than a 60% aggressiveness

ratio. Similarly, for the 10-year Treasury futures contract, the median aggressiveness

ratio increases initially but starts declining after 2000 contracts. The median aggressiveness ratio for position changes over 2000 contracts are generally below 40%. The

aggressiveness ratios presented especially for the very large position changes are far below 1, suggesting that traders take positions with a mixture of aggressive and passive

orders, which motivates a deeper investigation into the impact of aggressive and passive

12
 
position changes on prices and market liquidity.
 

A. Sorting Returns

We start our analysis with a two-way sorting of returns. We create eight buckets for

order flow and eight buckets for our skewness measure. In terms of bucket numberings,

+4 (−4) represents the most positive (negative) order flow or skewness bucket. For

the S&P 500 E-mini and 10-year Treasury futures markets, we report a total of 64

bucket combinations for which we measure price changes. Tables III and IV show how

each bucket combinations is related to price changes. Table III presents the statistics

associated with S&P 500 E-mini futures and Table IV presents the ones associated with

10-year Treasury futures.

As shown in Table III, within each order flow bucket, price changes in the S&P 500

E-mini futures are increasing as skewness goes from its lowest bucket to its highest. In

other words, a higher measure of skewness is associated with higher price change for a

given amount of order flow. The tests in the two rightmost columns show the difference

in price change levels between the lowest and the highest skewness buckets (+4 and

-4), for each order flow bucket. For the S&P 500 E-mini futures market, the difference

in price change of these buckets varies between 1.06 and 2.29 ticks. The t-statistics

associated with each difference measure shows that all are statistically significant.

Similarly, price changes of 10-year Treasury futures in Table IV are increasing as

skewness increases within each order flow group. The difference between the largest and

smallest skewness buckets varies between 0.13 and 0.54 ticks. While these differences

are smaller than those in E-mini, t- statistics indicate that they are all statistically

significant. In addition, given that standard deviation of price changes is significantly

bigger for E-mini futures than 10-year Treasury futures, it is natural to expect smaller

13
 
price changes for 10-year Treasury futures.
 

B. Liquidity Demand and Prices

We present analysis of OLS regression results in this section. We regress price changes

measured in number of ticks, on order flow and our measure of liquidity demand- skewness of position change distribution.

 Pt = α + λOFt + βSkewt + εt (8) TickSize

Table V summarizes the results from the regression above. We run the regression

separately for S&P 500 E-mini futures and 10-year Treasury futures. First, we show

univariate regressions with skewness as the only explanatory power and then add order

flow to the regression to control for the demand for immediacy. When prices are regressed

on skewness alone, the coefficients on the skewness measure are statistically significant

with 0.27 ticks for the S&P 500 E-mini futures and 0.11 ticks for the 10-year Treasury

futures. When the order flow variable is included in these regressions, the magnitudes

of these coefficients decrease to 0.1 for the S&P 500 E-mini futures but increase to 0.6

for the 10-year Treasury futures. They continue to be statistically significant.

These results are also economically significant. A one standard deviation increase in

the skewness measure increases prices 0.44 ticks in the S&P 500 E-mini futures and 0.12

ticks in the 10-year Treasury futures market. These results suggest that our liquidity

demand measure has an impact on prices even after controlling for the demand for

immediacy.

14
 
 

C. Components of Liquidity Demand

Summary statistics and the regression results suggest that order flow and skewness

measures are correlated. In this subsection, we decompose our skewness measure into

three components to isolate the component of our liquidity demand that does not demand

immediacy. The position change of each trader can be separated into aggressive and

passive position changes.

Xi = Xi,Agg + Xi,Pass (9)

Hence, the third moment of the position change distribution can be written as a

function of aggressive and passive position changes.

Nn N N N n n n

X3 X3 (Xi,Agg + Xi,Pass)

3 = i,Agg + i,Pass + 3 Xi,AggXi,Pass(Xi,Agg + Xi,Pass)

i=1 i=1 i=1 i=1

(10)

The first component is the liquidity demand with only aggressive trading. The second

is the liquidity demand with only passive trading. The third is the liquidity demand

with a mix of aggressive and passive trading. These components represent the extent

to which trader positions are built through passive versus aggressive trading. After we

decompose our skewness measure, we run the following regression

Pt + β2SkewPass + β3SkewM ixed = α + λOFt + β1Skewt

Agg

t t + εt (11) TickSize

The results are displayed in Table VI. We first regress the price changes on the

three components of skewness. For the S&P 500 E-mini futures, the coefficients of

the passive, aggressive and mixed components are 0.23, -0.05, and 0.16, respectively.

These coefficients are all statistically significant. The negative coefficient on the passive

15
 
skewness could appear counter intuitive at first. However, traders who take positions by
 

trading passively necessitates order flow trading against their orders in the book. The

passive skewness is likely capturing the inverse of immediacy demand if it is included

in the regression without the order flow variable. To address this issue, we include

order flow variable in the regression. When order flow is included in the regression, the

coefficient on the passive skewness increases to 0.1 and the coefficient on the aggressive

skewness decreases to 0.05. Similarly, when order flow is included in the regression for

the 10-year Treasury futures, the coefficient on the passive skewness increases from -0.04

to 0.01, and the coefficient on the aggressive skewness decreases from 0.08 to 0.03.

These results have interesting interpretations for aggressive and passive trading.

First, order flow can mostly capture the information in the aggressive liquidity demand.

Second, the passive skewness measure has a positive impact on prices after controlling

for order flow. This positive impact suggests that for a given level of order flow, passive

traders pay a premium to trade against the incoming order flow. This price premium

suggests that passive traders demand liquidity if they are building positions. Third, a

one standard deviation increase in passive skewness increases prices 0.54 ticks in the

S&P 500 E-mini futures, 18% of one-minute price volatility. Yet, one standard deviation increase in the passive skewness measure increases prices 0.03 ticks in the 10-year

futures, 3% of one-minute price volatility. The effect of passive skewness appears to be

smaller for the 10-year Treasury futures, but it is still economically important.

D. Information in Passive Trading

We design a structural vector auto-regression (SVAR) to assess whether the components

of the skewness measure contribute to price discovery. This SVAR specification is related

to the recent extensions of Hasbrouck (1991b) in Fleming and Mizrach (2009), and in

16
 
Brogaard, Hendershott and Riordan (2015). While these studies estimate their model

in event time, our data are in one-minute frequency. In our setting, order flow and

skewness measures are allowed to affect prices for up to 10 minutes.

⎡ ⎤

Yt =
 

⎢

⎢

⎢

⎢

⎢

⎢

⎢

⎢

⎢

⎢

⎣
 

ΔPt

OFt

Agg Skew

⎥

⎥

⎥

⎥

⎥

⎥

⎥

⎥

⎥

⎥

⎦
 

(12) t

SkewPass

t

SkewM ixed

t

⎡ ⎤

⎢

⎢

⎢

⎢

⎢

⎢

⎢

⎢

⎢

⎢

⎣
 

1 −β −δ −γ −θ
 

0 1 0 0 0
 

0 0 1 0 0

0 0 0 1 0

0 0 0 0 1

⎥

⎥

⎥

⎥

⎥

⎥

⎥

⎥

⎥

⎥

⎦
 

N

10

Yt = α + λiYt−i + ft (13)

i=1

For brevity, we only report the impulse response function results of prices. The

cumulative impulse response function of prices in response to a one standard deviation

shock is plotted in the Figure 4. As expected, order flow has a large and permanent

impact on prices. A one standard deviation shock to order flow increases prices by about

2 ticks in the S&P 500 E- mini futures and 0.5 ticks in the 10-year Treasury futures.

Consistent with our results in the previous subsection, we find that passive skewness

has a positive impact on prices. Our measure of passive skewness has a permanent price

impact of 0.5 ticks in the S&P 500 E-mini futures and 0.05 ticks in the 10-year Treasury

futures. The impact of mixed skewness on prices is slightly lower but also permanent. If

traders who have long-lived information use passive orders to build their positions, their

information may not be fully incorporated into prices within minutes. The patience of

17
 
passive traders might help explain why the effects of passive and mixed skewness on
 

prices are smaller than the order flow effect.

E. Impact on Market Liquidity

In this subsection, we analyze the effect of our skewness measure on market liquidity.

Classical theories of market liquidity suggest that market liquidity deteriorates in the

presence of informed trading (Glosten and Milgrom, 1985; Kyle, 1985). In general,

liquidity providers make the market less liquid to compensate themselves for trading

against informed traders. If the traders are building positions for informational reasons,

then we expect our skewness measure to decrease market liquidity.

Measuring changes in market liquidity is difficult, however, as one has to separate

out the changes in the market liquidity due to volatility. Furthermore, in deep markets

such as the E-mini S&P Futures and 10-year Treasury markets, the effective spread is

often one tick regardless of changes in the depth of the limit order book. Following

Easley, de Prado and O’Hara (2016), we use the high-low spread estimator of Corwin

and Schultz (2012), which filters out the spread component due to market volatility.

This procedure allows us to concentrate on the spread component that relates to market

liquidity.

Table VII summarizes the sample statistics of the Corwin-Schultz spread estimator

for one minute intervals for the S&P 500 E-mini futures and the 10-year Treasury futures

markets. For both markets, this spread estimator shows considerable variation. While

5th and 25th percentiles of the spread are zero, the 75th and 95th percentiles go from

2.37 basis points to 4.9 basis points for the E-mini, and from 1.2 basis points to 1.81

basis points for the 10-year Treasury futures.

The effect of the skewness measure on the spread estimator shows the impact of

18
 
position imbalance on market liquidity. To investigate this relationship, we regress the
 

Corwin-Schultz spread estimator on the absolute value of the skewness measure and the

absolute value of the order flow.

Table VIII reports the results of this regression. The coefficient on the order flow is

-0.34 for the E-mini and -0.05 for the 10-year Treasury futures. These coefficients are

both statistically significant. In contrast, the coefficient on the skewness measure in the

E-mini is 0.01 and statistically significant while it is statistically indistinguishable from

zero in the 10-year Treasury Futures. The negative coefficient on the order flow could

suggest that aggressive order flow could come from uninformed traders, consistent with

the findings of Easley, de Prado and O’Hara (2016). When we decompose the skewness measure into its components, the coefficients of the aggressive, passive, and mixed

skewness measures are 0.005, 0.03, and 0.02, respectively, and statistically significant for

the E-mini. For the 10-year Treasury, the coefficient on the passive skewness measure is

0.003 and is statistically significant.

Hence, in both markets, building positions with passive orders decreases market

liquidity. Passive liquidity demand impacts market liquidity, as predicted by the classical

theories of market liquidity. Furthermore, in the E-mini, the coefficients on the aggressive

and mixed skewness are positive and significant, suggesting that position build-up by

both aggressive and mixed orders also lowers market liquidity.

VI. Conclusion

The electronification of financial markets has led to a number of important changes in

the way trading takes place. First, in electronic limit order books, every trader can easily

submit passive limit orders and provide immediacy while still following his long-term

investment strategy. Second, traders are increasingly relying on order shredding, which

19
 
leads to smaller and clustered trade sizes. Traders following this behavior leave little
 

evidence in transactions data when they build their positions. Third, with the rise of

algorithmic trading, there has been a longer chain of intermediation between buyers and

sellers, resulting in higher trading volume. As opposed to traditional market makers who

provide immediacy, new types of intraday intermediaries often demand immediacy but

keep negligible positions. These developments make immediacy demand an imperfect

measure for position accumulation by traders or their liquidity demand.

Our measure of intraday liquidity demand, skewness of the intraday trader position

change distribution, is aimed at capturing large position changes in the cross-section

of traders without conditioning on their immediacy demand. Traders use a mixture of

aggressive and passive trades to achieve their desired positions. Our skewness measure

makes it possible to separately quantify the effects of passive and aggressive trading on

prices separately. We find that passive trading has an impact on prices when it is used

to build positions in the market. This positioning also incorporates information into

prices and makes the market less liquid.

Our results have important implications. Many studies use algorithms such as LeeReady to identify the initiating side of transactions in databases where the aggressor

side of the trade is not readily available to researchers. Hence, order flow is already a

noisy measure of traders aggressive trading. Our study shows that even in databases

where the aggressor side of the transaction is accurately identified, order flow cannot

fully reflect traders’ intentions. It is also important to note that because our skewness

measure is related to position build-up on one side of the market, there are more traders

on the opposite side of this positioning. Hence, our results can also suggest that prices

tend to move against the side that has the highest number of traders. In this context,

traders herd on the liquidity providing side of the market.

20
 
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Biais, Bruno, Fany Declerck, and Sophie Moinas. 2016. “Who supplies liquidity,

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Hasbrouck, Joel. 1991a. “Measuring the information content of stock trades.” The

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22
 
Figure 1: Distributions of One-Minute Net Position Changes
 

-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

Position Change

0%

5%

10%

15%

20%

Sample Percentage

-100 -92 -84 -76 -68 -60 -52 -44 -36 -28 -20 -12 -4 4 12 20 28 36 44 52 60 68 76 84 92 100

Position Change

0.0%

0.2%

0.4%

0.6%

Sample Percentage

(a) ES: Net Position Changes 1 to 10 (b) ES: Net Position Changes 11 to 100

-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

Position Change

0%

2%

4%

6%

8%

10%

Sample Percentage

-100 -92 -84 -76 -68 -60 -52 -44 -36 -28 -20 -12 -4 4 12 20 28 36 44 52 60 68 76 84 92 100

Position Change

0.0%

0.2%

0.4%

0.6%

0.8%

1.0%

Sample Percentage

(c) 10Yr: Net Position Changes 1 to 10 (d) 10Yr: Net Position Changes 11 to 100

The figure shows the distribution of one-minute position changes observed in the E-mini S&P 500 and

10-year Treasury futures markets for the entire sample. The charts on the left plot the position changes

between -10 and 10 contracts. The charts on the right plot the position changes of greater than 10

contracts and fewer than -10 contracts.

23
 
Figure 2: E-Mini S&P 500 and 10-Year Treasury Futures Sample Stats by Skew Group
 

Price Change Price Range Volume Trader Count

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.950

0.975

1.000

1.025

1.050

3,000

3,200

3,400

3,600

3,800

75

100

125

150 Long Short

1 2 3 4 5 6 7 8 9 10

Skew Group

(a) ES

Price Change Price Range Volume Trader Count

-0.010

-0.005

0.000

0.005

0.010

0.019

0.020

0.021

0.022

1,600

1,700

1,800

1,900

10

20

30

40

50

60

Long Short

1 2 3 4 5 6 7 8 9 10

Skew Group

(b) 10Yr0

The figure shows sample statistics for one-minute intervals for E-mini S&P 500 and 10-year Treasury

futures contracts. All statistics are presented across skewness groups, where the first group includes

skewness values between 1 and .80; the second group includes skewness values between .80 and .60, and

so on. The top panel displays statistics for S&P 500 E-mini futures contracts and the bottom panel

displays statistics for the 10-year Treasury futures contracts. The first rows show average trader counts

for traders who are net short (red) and net long (blue). The second rows show average volume, third

rows display average price volatility (max price min price) and the fourth rows display average trade

price change. 24
Figure 3: Aggressiveness Ratios for Position Changes for S&P 500 E-mini and 10-year
 

Treasury Futures
 

0 200 400 600 800 1000

Position Change

0%

20%

40%

60%

80%

100%

Share of Aggressive Volume

1000 2000 3000 4000 5000

Position Change

0%

20%

40%

60%

80%

100%

Share of Aggressive Volume

(a) ES: Set 1 (b) ES: Set 2

0 200 400 600 800 1000

Position Change

0%

20%

40%

60%

80%

100%

Share of Aggressive Volume

1000 2000 3000 4000 5000

Position Change

0%

20%

40%

60%

80%

100%

Share of Aggressive Volume

(c) 10Yr: Set 1 (d) 10Yr: Set 2

The figure plots the box plots of aggressiveness ratios for one-minute position changes averaged across

days. The box plots show the maximum, 75th percentile, median, 25th percentile and minimum of this

average aggressiveness ratio for various levels of position changes. The charts on the left plot absolute

position changes of 1 through 1000, rounded by 25. The box plots on the right plot the absolute position

changes of 1000 through 5000, rounded by 100.

25
 
Figure 4: Cumulative Impulse Response Functions
 

2 4 6 8 10

Minutes

0.0

0.5

1.0

1.5

2.0

Accumulated Response of Price Change

Price Change Order Flow Agg Skew Pass Skew Mixed Skew

(a) ES

2 4 6 8 10

Minutes

0.0

0.2

0.4

0.6

0.8

Accumulated Response of Price Change

Price Change Order Flow Agg Skew Pass Skew Mixed Skew

(b) 10Yr

The figure shows graphs that plot the change in prices (in number of ticks) for following 10 minutes in

response to a one standard deviation shock to prices, order flow, aggressive skewness, passive skewness

and mixed skewness variables.

26
 
Table I: E-Mini S&P 500 Futures
 

Panel A: Summary Statistics

Mean Median 25th Pctl 75th Pctl Std Dev N

Price Change 0.01 0.00 -1.00 1.00 2.96 155,394

Order Flow -0.01 -0.01 -0.34 0.32 0.79 155,394

Skewness -0.04 -0.04 -2.69 2.61 4.43 155,394

Panel B: Correlations

Price Change Order Flow Skewness

Price Change 1.00 0.68

<.0001

0.40

<.0001

Order Flow 0.68

<.0001

1.00 0.41

<.0001

Skewness 0.40

<.0001

0.41

<.0001

1.00

The table shows the summary statistics for the S&P 500 E-mini futures market.

Panel A reports the mean, median, quartiles, standard deviation of price changes,

order flow and skewness measures calculated at one-minute intervals. Price change

is in number of ticks (0.25 points), and order flow is the difference between aggressive buy and sell volume scaled in 1000 contracts. Skewness is the Fisher-Pearson

population skewness coefficient of the trader position change distribution. Panel B

reports the correlations coefficients among price change, order flow and skewness

measures.

27
 
Table II: 10-Year Treasury Futures
 

Panel A: Summary Statistics

Mean Median 25th Pctl 75th Pctl Std Dev N

Price Change 0.00 0.00 -1.00 1.00 1.09 142,844

Order Flow 0.00 0.00 -0.32 0.33 0.83 142,844

Skewness 0.00 0.01 -1.86 1.86 2.99 142,844

Panel B: Correlations

Price Change Order Flow Skewness

Price Change 1.00 0.51

<.0001

0.31

<.0001

Order Flow 0.51

<.0001

1.00 0.41

<.0001

Skewness 0.31

<.0001

0.41

<.0001

1.00

The table shows the summary statistics for the 10-year Treasury futures market.

Panel A reports the mean, median, and standard deviation of price changes, order

flow and skewness measures calculated at one-minute intervals. Price change is in

number of ticks (1/64 points), and order flow is the difference between aggressive

buy and sell volume in 1000 contracts. Skewness is the Fisher-Pearson population

skewness coefficient of the trader position change distribution. Panel B reports the

correlations coefficients among price change, order flow, and skewness measures.

28
 
Table III: Price Changes by Skewness and Order Flow Groups– S&P 500 E-

Order Flow Skewness Groups 

Groups −4 −3 −2 −1 +1 +2 +

−4 -3.98 -3.58 -3.39 -3.12 -3.16 -2.66 -2.−3 -1.82 -1.74 -1.68 -1.50 -1.30 -1.15 -0.−2 -1.10 -0.98 -0.90 -0.81 -0.63 -0.50 -0.−1 -0.63 -0.48 -0.37 -0.26 -0.13 -0.03 0.

+1 -0.40 -0.08 0.08 0.26 0.34 0.44 0.

+2 -0.12 0.47 0.57 0.75 0.84 0.93 1.+3 0.27 1.05 1.18 1.38 1.71 1.78 1.+4 1.95 2.69 2.74 3.13 3.18 3.37 3.

29The table shows the price changes in number of ticks for different skewness and order flow 

E-mini futures. Each observation for the skewness and order flow variables are arranged intfrom the lowest, represented by −4, to the highest, represented by +4. The last two column

for the tests of equality between price changes in the lowest and highest skewness groups.
Table IV: Price Changes by Skewness and Order Flow Groups– 10-Year Trea

Order Flow Skewness Groups 

Groups −4 −3 −2 −1 +1 +2 +

−4 -1.05 -1.01 -0.96 -0.85 -0.82 -0.76 -0.−3 -0.54 -0.54 -0.55 -0.46 -0.48 -0.42 -0.−2 -0.29 -0.25 -0.22 -0.21 -0.18 -0.21 -0.−1 -0.09 -0.08 -0.06 -0.06 -0.05 -0.06 0.

+1 0.01 0.08 0.05 0.06 0.04 0.05 0.+2 0.05 0.18 0.22 0.22 0.22 0.24 0.+3 0.24 0.35 0.46 0.45 0.52 0.53 0.+4 0.52 0.76 0.75 0.83 0.97 0.98 1.

30The table shows the price changes in number of ticks for different skewness and order flow 

Treasury futures. Each observation for the skewness and order flow variables are arranged infrom the lowest, represented by −4, to the highest, represented by +4. The last two column

for the tests of equality between price changes in the lowest and highest skewness groups.
 

Table V: Regression Results: Skewness Measure
 

E-mini S&P 500 Futures 10-year Treasury Futures

Intercept 0.02 0.02 0.00 0.00

2.37 4.54 0.98 0.87

Skewness 0.27 0.10 0.11 0.60

140.66 56.69 109.28 103.26

Order Flow 2.32 0.04

168.23 40.33

N 155,394 155,394 142,841 142,841

Adj-R2(%) 16.27 48.17 9.72 27.08

The table reports the regression results of price changes in number of ticks on order

flow and skewness of the position change distribution in S&P 500 E-mini and 10­

year Treasury futures markets. t-statistics are calculated from White standard

errors.

Pt = α + λOFt + βSkewt + εt TickSize

31
 
 

Table VI: Regression Results: Disaggregated Skewness
 

E-mini S&P 500 Futures 10-year Treasury Futures

Intercept 0.02 0.03 0.00 0.00

2.98 5.14 1.75 1.06

Agg Skewness 0.23 0.05 0.08 0.03

128.83 26.63 79.65 26.57

Pass Skewness -0.05 0.10 -0.04 0.01

-23.95 51.45 -32.08 10.23

Mixed Skewness 0.16 0.04 0.02 0.03

30.85 11.50 8.22 11.28

Order Flow 2.70 0.60

136.95 66.19

N 155,394 155,394 142,841 142,841

Adj-R2(%) 25.69 49.02 18.26 26.74

The table reports the regression results of price changes in number of ticks on order

flow and aggressive, passive and mixed skewness measure of the position change

distribution in S&P 500 E-mini and 10-year Treasury futures markets. t-statistics

are calculated from White standard errors.

Pt Agg + β2SkewPass + β3SkewM ixed = α + λOFt + β1Skewt t t + εt TickSize

32
 
Table VII: High-Low Spread Estimator
 

E-Mini S&P 500 Futures 10-Year Treasury Futures
 

P5 0.00 0.00

P25 0.00 0.00

Median 0.71 0.69

Mean 1.45 0.66

P75 2.37 1.20

P95 4.90 1.81

Std Dev 1.86 0.68

N 155,394 142,844

The table reports the summary statistics of the Corwin-Schultz (2012) spread

estimator for the S&P 500 E-mini futures market and the 10-year Treasury futures

market. The summary statistics include 5th, 25th, 50th (median), 75th , 95th

percentiles as well as the mean and standard deviation of this spread estimator.

33
 
Table VIII: Regression Results: Bid-Ask Spread
 

E-mini S&P 500 Futures 10-year Treasury Futures

Intercept 0.02 0.03 0.00 0.00

2.98 5.14 1.75 1.06

Lag H-L Spread 0.11 0.11 0.13 0.13

22.72 22.48 38.65 38.65

abs(Order Flow) -0.34 -0.40 -0.05 -0.06

-41.34 -42.33 -17.07 -14.99

abs(Skewness) 0.01 0.00

5.56 -0.56

abs(Agg Skewness) 0.005 0.000

2.69 -0.31

abs(Pass Skewness) 0.03 0.003

15.65 2.63

abs(Mixed Skewness) 0.02 -0.004

5.82 -2.48

N 155,394 155,394 142,841 142,841

Adj-R2(%) 2.23 2.50 1.81 1.82

The table reports the regression results of the Corwin-Schultz spread estimator

on its lag, the absolute value of the order flow, and the absolute values of the

skewness measure and its components for the S&P 500 E-mini futures and 10-year

Treasury futures markets. t-statistics are calculated from White standard errors.

34