Need For Speed?

Low Latency Trading and Adverse Selection

Albert J. Menkveld and Marius A. Zoican ∗

April 22, 2013

- very preliminary and incomplete. comments and suggestions are welcome -

First version: 1 February 2013

∗Both authors are affiliated with VU University Amsterdam, the Tinbergen Institute and Duisenberg Schoolof Finance. Address: FEWEB, De Boelelaan 1105, 1081 HV Amsterdam, Netherlands. Albert Menkveld can becontacted at albertjmenkveld@gmail.com. Marius Zoican can be contacted at m.a.zoican@vu.nl. The authors wouldlike to extend their gratitude to EMCF for data sponsoring this project. We have greatly benefited from discussionsonthis research with Istvan Barra, Alejandro Bernales, Peter Hoffmann, Olga Lebedeva, Emiliano Pagnotta and BartYueshen Zhou. Albert Menkveld gratefully acknowledges NWO for a VIDI grant. Marius Zoican additionally thanksthe participants from the Tinbergen Institute and DSF Brown Bag Seminars for insightful comments.

1

Need For Speed? Low Latency Trading and Adverse Selection

Abstract

This paper investigates the impact of market-wide low latency trading technologies on

informational asymmetries between traders. It develops a model with two types of high-frequency

traders: market makers (HFT-M) and ”bandits” (HFT-B), who profit by trading on stale quotes.

The HFTs endogenously decide on information acquisition. Competitive HFT market-makers

face higher adverse selection risks when latency drops, as the conditional probability of a liquidity

motivated trade decreases. In equilibrium, they will charge higher spreads to compensate for

the additional risk. Lower market latencies also provide incentives for market makers to gather

information. Informed market makers reduce expected losses on stale quotes while still attracting

liquidity demand from uninformed traders. We find empirical support for the model implications:

the adverse selection component of the bid-ask spread increases by 15% (0.35 bps) on NASDAQ

OMX after introducing low-latency technology. The effect is stronger in more volatile securities.

Keywords: market microstructure, trading speed, information asymmetry, high frequency

trading

JEL Codes: G11, G12, G14

2

1 Introduction

Market venues have invested considerable effort and financial resources in recent years to improve

the speed with which traders can submit limit or market orders. Pagnotta and Philippon (2011)

list the most important low-latency investments around the globe from 2008 to 2012: for example,

in 2009, NYSE reduced its latency to 5 down from 150 milliseconds. Similar investments were

undertaken by stock exchanges in Tokyo, Singapore, London or Johannesburg. As of October 2012,

the fastest trading system in the world belongs to ALGO Technologies, with a round trip latency of

16 microseconds. The trading world already faces the lower bound of the speed of light as potentially

binding1.

Hasbrouck and Saar (2010) define trading latency as ”the time it takes to observe a market event

(e.g., a new bid price in the limit order book), through the time it takes to analyze this event and send

an order to the exchange that responds to the event”. This paper is primarily focused on changes in

the latter component of market latency, which depends on the trading platform’s technology rather

than the individual traders’ algorithms. Hence, in this paper, we define by ”market latency” the

time it takes an order to reach the market and confirmation is received back by the trader. For the

high frequency traders, who usually co-locate their computers with the venue’s servers, the latency

is already very low (a few milliseconds), and any improvement in market latency is likely to have a

large impact on trading times. On the other hand, for lower frequency traders, such a drop would

likely have little effect on their market access times.

The main research focus of this paper is analysing the effects of low latency-trading on the

information asymmetries across traders, adverse selection risks, spreads and ultimately social welfare.

Foucault (2012) argues that ”the jury is still out” on this issue, as the ultimate effect of low-latency

trading on adverse selection depends on HFT specialisation. In low-latency environments, high-

frequency market-makers are able to quickly update the quotes before better informed speculators

can trade against them. On the other hand, high-frequency speculators symmetrically improve

their ability to reach the market faster, thus being equally able to act on information as the market

maker.

The net effect on information asymmetries is non-trivial as the HFT sector does not specialise

only in passive or speculative strategies. The Securities and Exchange Commission identify various

strategies of high frequency traders, including passive market-making , directional trading, arbitrag-

ing, and structural trading - taking advantage of market frictions (”vulnerabilities”) such as stale

quotes2. Hagstromer and Norden (2013) find supporting evidence of order type specialisation among

1See How Low Can You Go?, HFT Review, April 20102 See SEC Concept Release on Equity Market Structure

3

high frequency traders on the Swedish markets; Baron, Brogaard, and Kirilenko (2012) additionally

show that these strategies are persistent through time.

In our model, we model the complexity of the environment by assuming high frequency traders

engage both in market-making activities as well as speculating short-term trends. We allow for

the fast market maker to endogenously decide to become informed or not. In this respect, the

paper extends the implications of Foucault, Hombert, and Rosu (2012) who investigate latency

effects when market-makers are both slow and uninformed. We ask what would happen to spreads,

information acquisition and welfare if the market suddenly offers a new technology that improve the

HFTs’ reaction time even further - regardless of their strategy.

We build a limit order market model with costly monitoring, endogenous information acquisition

and deterministic market latency. We extend Foucault, Roell, and Sandas (2003) by allowing for

trader heterogeneity (between HFT and non-HFT) in the time necessary to reach the market and

then studying the equilibrium as we widen the gap between the two categories’ market response

times.

In the competitive equilibrium, HFT market makers earn zero rents and face a larger conditional

probability of meeting an informed trader - hence a higher adverse selection risk. The additional risk

is partly compensated by larger spreads, and partly by market markets withdrawing quotes. The

unconditional probability of a liquidity trader (assumed to be a market taker) realising a trade is

falling for larger market speeds, as the market is increasingly dominated by high-frequency traders.

This result is robust to changing the competition on the market between the dealers; we consider

the polar cases of Bertrand competition and a monopolist dealer.

To empirically identify the effect of lower market latency on trading outcomes and adverse

selection, we use as an instrument the introduction of the INET Core Technology on NASDAQ

OMX (the incumbent market in the Nordics) on February 8, 2010. Prior to this event, NASDAQ

OMX had a round-trip latency of 2.5 ms, lagging behind its competitors: Chi-X Europe with 0.400

ms or BATS with 0.270 ms. The new technology allowed NASDAQ OMX to reduce its round-trip

latency 10 times, to 0.250 ms, effectively making the incumbent market the fastest venue for Nordic

securities.

This paper focuses on the precise channel between market latency and adverse selection given

trading environment with exogenous order types. A potential extension in future versions of the paper

is to endogenize the make/take decision of high frequency traders and study the interaction between

such choices and market latency, especially through competition between limit order submitters.

The structure of trading fees with limit order rebates is also an important factor influencing the

endogenous order type decision. In our current model, spreads fall when limit orders are allowed to

execute at lower latencies than market orders - which generates a positive welfare effect in periods

4

of little volatility.

The rest of the paper is structured as follows: Section 2 briefly reviews the literature on the

advantages and disadvantage of low-latency trading. Section 3 develops a theoretical model of the

market using a competitive dealer assumption (Bertrand-like competition). We find that the optimal

spread increases with market speed, whereas welfare is reduced. The perfect competition assumption

is relaxed in Section 4, where we consider a monopolist dealer who can freely maximise his profits,

and we obtain the same qualitative results. In Section 5 we present the dataset, formulate the

econometric specification testable hypotheses of the model, and an identification strategy based on

a natural experiment. Section 6 discusses the empirical results. Section 7 concludes.

2 Related Literature

The academic literature has brought forward a number of arguments in favour of low latency trading.

Faster access to the market is argued to lead to competitive liquidity supply - as in Hendershott,

Jones, and Menkveld (2011). Limit order submitters are able to react quicker on each other’s quotes,

and the risk of being undercut by a different passive trader before a market order arrives is larger.

This reduces the market power of a limit order submitter and provides the incentives to set tighter

spreads. However, as Biais, Foucault, and Moinas (2013) also argue, the algorithmic trading proxy

in Hendershott, Jones, and Menkveld (2011) could capture changes that go beyond fast trading - for

instance, algorithmic trading might have lowered search costs across markets. 3

A second advantage of trading speed is that low latency trading can result in better price

discovery - as argued by Hendershott and Riordan (2011). Improving the reaction times to new

information implies that quotes and trading prices are also incorporating innovations faster.

Pagnotta and Philippon (2011) claim that speed can be used as an instrument by markets to

vertically differentiate in trading speed and attract different clienteles. Hence, fast markets would

charge a premium to the traders with volatile private values, who value speed most. The other

market participants, with a low preference for speed, would be able to use the slower market’s

services for a lower fee.

On the other hand, low latency trading may also have negative effects for the markets. High

frequency traders with better information can have an unfair advantage in adversely selecting other

market participants, especially since they can process news faster - see Foucault, Hombert, and

Rosu (2012). Several papers point out to the positive relationship between adverse selection and

3 A Swedish government report - see Finansinspektionen Report 2012, states than 24 companies use algorithms totrade, while only 3 use high frequency trading in the operations. Thus, there is a clear distinction in practice betweenalgorithmic and HF trading, with the latter being a strictly smaller subset of the first.

5

high frequency trading. Hendershott and Riordan (2011) find a larger permanent impact of higher

frequency market orders compared with slower ones. The price impact is actually found large enough

to overcome the bid-ask spread. In the same line, Baron, Brogaard, and Kirilenko (2012) show

that high frequency traders earn short-time profits through aggressive orders, which is consistent

with adversely selecting other market participants. Brogaard, Hendershott, and Riordan (2012)

also find results consistent with low-latency traders imposing adverse selection costs on the other

market participants. Biais, Foucault, and Moinas (2013) develop a theoretical model of low-latency

trading showing that when some agents become fast, all traders incur higher adverse selection costs.

Hoffmann (2010) focuses on adverse selection differentials across market venues. He finds that

the adverse selection component is larger on the entrant venues, and positively related to market

volatility.

Furthermore, there is an ongoing debate about the possibility of low-latency trading inducing

unnecessary market volatility, leading to events such as the Flash Crash. However, evidence so far

leans against the hypothesis that high frequency traders were responsible for the Flash Crash of

May 2010 -Kirilenko, Kyle, Samadi, and Tuzun (2011).

Compared to Jovanovic and Menkveld (2011), this paper focuses on the informational aspects

of faster markets. We endogenize the arrival times to capture the latency changes but we fix the

order type by assuming liquidity traders to be takers. We also explicitly introduce high frequency

traders who trade only on information (as in Foucault, Roell, and Sandas (2003)), rather than for a

market-making reason.

In low-latency environments, both liquidity suppliers and demanders (potentially with better

information) take less time to access the market: limit orders submitters can withdraw/update quotes

faster before being adversely selected, whereas speculators can act quicker on private signals and

earn rents by adversely selecting the market makers. Our contribution is to analyse the implications

of this symmetry in latency innovations between different types of high-frequency traders engaged

in passive and short-term speculative strategies.

3 Market Latency with a Competitive Market Maker

In this section, we develop a model of costly monitoring in a limit order market with stochastic times

to market, based on Foucault, Roell, and Sandas (2003), to generate hypotheses than can be tested

empirically. We are interested how a drop in market latency, affecting mostly both high-frequency

market-makers and speculators influences information acquisition by dealers, adverse selection

probabilities, bid-ask spreads and welfare.

6

3.1 Primitives

This section presents the model’s primitives. Extensive motivation for these primitives is left to

subsection 3.2.

3.1.1 Asset and market

There is a single risky asset in the economy, with a stochastic value v. Define τ as an exponential

random variable with mean 1α and N (t) = It>τ . The dynamics of the asset value are given by the

following process:

v (t) = v (0) + Y ×N (t) (1)

In equation 1, Y is a random variable capturing the size and sign of news. When a jump in the

asset value occurs, it can either be interpreted as good or bad news of magnitude σ, where σ > 1.

Hence, the distribution of Σ is given by: P (Y = σ) = P (Y = −σ) = 12 . After a jump at time t, the

asset value is: vt+ = vt− ± σ.

One can think about the asset dynamics as a compound Poisson jump process with intensity α,

truncated after the first arrival: once the first jump occurs, there are no further changes in the asset

value.

The asset is traded on a limit order market with price priority - the largest bid and smallest ask

execute first.

3.1.2 Agents

In the market for the risky asset, there are 2 types of high-frequency risk-neutral agents: a

representative competitive market maker: HFT-M, who posts limit orders, and a representative

speculator or ”bandit”: HFT-B, who can post market orders - in the terminology of Foucault, Roell,

and Sandas (2003)). There is also a representative low frequency trader (LFT) who experiences

liquidity shocks at random times. The HFTs arrive to market with a deterministic delay ∆H ,

whereas the LFT has a deterministic delay of ∆L.

The high frequency traders have no private valuation for the asset and are risk neutral. HFT-B

has no monitoring costs and perfectly observes the asset value at any time t, whereas HFT-M can

invest in a monitoring technology allowing perfect tracking of the asset value by paying a positive

cost c (the difference between the monitoring costs is motivated in subsection 3.2).

The LFT has additional private values for the asset uniformly distributed between [−θ, θ], such

that θ < σ, but no technology to track jumps in the asset before the HFTs do4. The LFT receives a

4The liquidity trader observes the information after the HFTs (they are an order of magnitude slower)

7

liquidity shock according to a Poisson process with intensity µ.

Both HFT have a reservation utility of 0 (can decide to not participate on the market).

The competitive market-maker HFT-M earns his reservation utility - his participation constraint

holds strictly, as in Bertrand competition.

3.1.3 Timeline

Monitoring Stage (T=0) The market-maker chooses whether to acquire information (and pay

the fixed cost c) - strategy I, or stay uninformed (thus saving the fixed investment) - strategy U .

The bandit makes a similar decision, but has zero costs of monitoring. It follows immediately from

the assumptions that it is optimal for him to always monitor the news process.

Quoting Stage (T=1) The value of the asset is publicly observable (the initial condition for the

Poisson process): v0. The market-maker posts bid and ask quotes for the asset. As in Foucault,

Roell, and Sandas (2003), the bid quote is set to v0 − s and the ask quote is v0 + s, where s is the

half spread. Since HFT-M is risk neutral (has no inventory concerns) and the liquidity traders are

uniformly distributed and they are informed only at T = 3, s = sa = sb5

Trading Stage (T=2) The trading game starts once quotes are posted in the market and runs

in continuous time until a quote is either consumed or withdrawn. Thus, three events can happen:

1. The LFT receives a liquidity shock arrives to the market before any news and executes a

market order f his private value θi is larger than the half-spread |θi| ≥ s.

2. There is news before the LFT arrives to the market. Then, either:

(a) The LFT executes a market order before any HFT arrives to the market (during the ∆H

interval - HFT latency)

(b) If the LFT does not trade in the ∆H interval following news, an HFT would arrive to

the market first:

i. With probability γ, HFT-M arrives before HFT-B and he will withdraw the stale

quotes to avoid a loss.

ii. With probability 1− γ, HFT-B is first and he will execute a market order to make a

profit on the stale quote.

5As Foucault, Roell, and Sandas (2003) argues, since the problem is symmetric, sa 6= sb would make no difference.

8

For the remainder of the paper, we will take γ = 12 : conditional on an HFT arriving first

after news, the HFT-M and HFT-B arrivals are equiprobable.

The game tree and utility functions associated with this model is presented in Figure 1:

[Figure 1 here]

3.1.4 Strategy Spaces

The market maker and the bandit have 3 possible actions, presented in the following table. In

addition, the dealer chooses the equilibrium spread corresponding to each of these pure strategies:

there is a one-to-one correspondence between the set of strategies below (excluding s) and the

set of dealer strategies including the spread. This stems from the fact that, as we prove in the

next subsection, the optimal monitoring strategy for the bandit is always to purchase information.

Hence, between T0 and T1, the information set of the dealer is unchanged, which is equivalent to

the monitoring and spread decisions being taken at the same time.

Strategy Monitoring Decision after asset value jump

IR become Informed Rush to market

IN become Informed Do Not Rush to market

UN become Uninformed

3.2 Discussion of the assumptions

The trading environment, asset value dynamics and trader types are largely based on Foucault, Roell,

and Sandas (2003). We change the focus from externalities to the market speed game, and thus we

do not model the interactions between dealers. Hence, we build our model around a ”representative”

HFT from each type: one bandit and one market maker. We can think of the representative high

frequency traders as the aggregate of a continuum of HFT-M and HFT-B.

The perfect competition assumption, which assumes that market makers constantly undercut

each other until there are no profit opportunities in expectations is relaxed in the next section,

where we consider the opposite polar case: a monopolist HFT-M who can extract maximum rents

from liquidity traders. Our main results are qualitatively robust with respect to this change of the

competitive environment.

Since we abstract from externalities among dealers, which in Foucault, Roell, and Sandas (2003)

were necessary to keep the spreads from exploding, we introduce a private value distribution for

9

the liquidity traders, leading to a downward sloping demand function, as in Ho and Stoll (1983) or

Hendershott and Menkveld (2011). This ensures that the dealer cannot completely eliminate the

adverse selection risk through spreads, as he will then lose all profitable trading opportunities with

the liquidity traders.

Monitoring strategies are decided upon before the trading starts, as in Foucault, Roell, and Sandas

(2003), but discrete in the effort/signal probability set {cost,P (Information)} ∈ {{0, 0} , {c, 1}}.We argue that investments in monitoring algorithms are done in larger update batches (a fixed cost

c) than being fine-tuned for each trade.

We model our game with the HFT-B having zero monitoring cost. This assumption is meant

to capture the idea that while any bandit can act on a signal and adversely select the dealer, the

market maker has to monitor the news and defend against all bandits. Our model can be thought

of a reduced version for the following environment: a ”representative” bandit stands in front of many

speculators who might observe a signal with low frequency. If there are enough of these ”bandits”,

then a representative HFT-B will obtain such a signal at high frequency. When deciding upon

monitoring, the dealer has to be able to outsmart any speculator if he was to avoid adverse selection.

Our results are robust to relaxing the assumption of γ = 12 to any γ ∈ [0, 1). The comparative

statics with respect to the HFT latency (∆H) are qualitatively the same for any interior probability

γ. The results are strongest for the case γ = 0. This corresponds to the situation when the HFT-M

cannot use any information to update his quotes, so he is practically an uninformed market-maker (as

in Foucault, Hombert, and Rosu (2012) for example). The other extreme, when γ = 1 corresponds

to the case where the HFT-B can never speculate on information; this is a trivial case where there

is no adverse selection and therefore the latency is irrelevant to the model.

3.3 Expected Payoffs of HFTs

3.3.1 Irrelevance of the LFT market delay ∆L

We define the private value process of the LFTs by N ′ (t) - a Poisson process with intensity µ. Then

the LFT market arrival process can be defined as M (t) where it holds that:

M (t+ ∆L) = N ′ (t) (2)

Thus, if a liquidity trader receives his private value at time t (jump in the N ′(t) process), it

will arrive on the market at time t + ∆L (a jump in the M(t) process). It is trivial that if the

inter-arrival jump time in the N ′ process is exponentially distributed, then the same property holds

for the M(t) process, as all arrival times are shifted by the same deterministic quantity.

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Lemma 1. The market arrival process of the liquidity traders is equivalent in distribution to a

Poisson process of intensity µ if the private value shock process starts at least ∆L before the quotes

are posted. Hence, the deterministic delay ∆L is irrelevant for the distribution of LFT market

arrival times.

Proof. See appendix A.

3.3.2 Outcomes of the game

We consider now all the potential outcomes of the game and their respective probabilities, as well as

payoffs for the HF traders.

LFT arrival before news If a LFT arrives at τLFT before any jump in asset value, he will trade

if his private value exceeds the half-spread in absolute value. Since both news and market arrival of

liquidity traders can be modelled as Poisson processes with intensities α and µ, the probability of

this outcome is given by:

P {τLFT < τNews} =µ

µ+ α(3)

Given the game ends with a LFT arrival, the market marker earns in expectation s (1− s) - the

half spread times the probability of trade and the HFT-B earns 0 (no trade).

LFT arrival after news The probability of the jump in asset value arriving first is the complement

of the previous outcome:

P {τLFT > τNews} =α

µ+ α(4)

Given this event, there are 3 potential outcomes:

No LFT arrives in ∆H , HFT-M withdraws quote This outcome is only possible if HFT-

M monitors the asset value. The probability of no jump in M(t) during an interval of ∆H is given by

exp (−µ∆H), from the proprieties of Poisson processes. Conditional on it, HFT-M has a probability

of 12 of arriving before the bandit and withdrawing his quote - we prove in the following section that

HFT-B has IR as a dominant strategy. The full probability of the outcome is thus given by:

P (HFT −M first) =α

µ+ α︸ ︷︷ ︸News beforeLFT

× exp (−µ∆H)︸ ︷︷ ︸HFT first

× 1

2︸︷︷︸HFT−M first

(5)

11

In this case, both the market marker and the bandit earn zero profits.

No LFT arrives in ∆H , HFT-B executes market order In the case HFT-M monitors

the news, the outcome probability is symmetrical to HFT-M arriving first to the market:

P (HFT −M first) =α

µ+ α︸ ︷︷ ︸News beforeLFT

× exp (−µ∆H)︸ ︷︷ ︸HFT first

× 1

2︸︷︷︸HFT−B first

(6)

In the case HFT-M is uninformed, the outcome probability is double, since there is no more

competition between the bandit and the market-maker to arrive on the market.

Given the game ends with a HFT-B arrival, the bandit gains σ − s (the extent to which the

quote is stale) whereas the market-maker loses the same amount.

One LFT arrives in ∆H , LFT executes market order The probability of a jump in M(t)

during an interval of ∆H is given by 1− exp (−µ∆H). The outcome probability is thus:

P (HFT −M first) =α

µ+ α︸ ︷︷ ︸News beforeLFT

× (1− exp (−µ∆H))︸ ︷︷ ︸LFT first

(7)

The payoffs in this case are identical with the first outcome described: the market marker earns

in expectation s (1− s) - the half spread times the probability of trade and the HFT-B earns 0 (no

trade).

3.4 Dominated/Dominating Strategies

In this subsection, we seek to restrict the strategy spaces of the market maker and bandit, by

eliminating the strategies which are not optimal and cannot be part of an equilibrium under any

parameter values.

3.4.1 The ”Bandit” : HFT-B

We begin by analysing the HFT-B’s dominated strategies. We show that the bandit’s optimal

strategy is to always monitor and always submit a market order after news. With costless information,

this is intuitive: the bandit does not risk any losses and faces a positive probability of earning an

adverse selection profit - hence he has the incentive to post a market order if the dealer’s quotes no

longer reflect the asset’s true value.

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Lemma 2. (1) The bandit will always choose to monitor and submit a market order after news

arrive to market - strategy IR is a strictly dominant strategy, for any s < σ.

(2) The bandit will never rush to the market if s ≥ σ.

Proof. See appendix A.

The first result is natural since the HFT-B can obtain information costlessly. Remaining

uninformed and taking an action is equivalent then to monitoring and taking the same action

(practically not acting on information). Thus, HFT-B cannot be worse off if he monitors and

potentially he can become better off by switching his rush/do not rush decision.

The second result implies that the bandit has a single unique strategy: always post a market

order when the quote available allows him to make a profit - when the value of the asset changes

before the market maker gets to update his quotes. The worst case scenario is that he will not

arrive first at the market and thus miss the opportunity. When there are no news, HFT-B has no

incentive to post market orders, as he has no private value for the asset and thus no incentive to

pay the spread.

The intuition for the final part of the lemma is that the potential adverse selection profit for

HFT-B is the difference between the size of the news and the stale half-spread, thus σ − s. If this

quantity is negative, the bandit ends up paying more in trading costs than he will earn by the

change in asset value.

3.4.2 The Market-Maker: HFT-M

Lemma 3. (1) For the HFT-M, the strategy IN is strictly dominated in the monitoring-trading

subgame. That is, the market-maker will never choose to pay for information and then never rush

to withdraw his quotes. (2) It is never optimal for the dealer to set a half-spread s ≥ 1 or s = 0.

Hence, the half-spread strategy space is reduced from R+ to (0, 1).

The market-maker’s positive cost deters him from monitoring if his strategy is to not to act

on the information bought. Monitoring is only useful in a separating equilibrium: HFT-M takes a

different action if there is news than if there is no new information.

In the third part, we claim that the market-maker will never set a spread so high that it will drive

out all the demand from liquidity traders - his only rationale for being in the market. Since private

values never exceed 1 in absolute value, any higher spread will deter the liquidity traders from

posting market orders. Conversely, a spread of 0 will give HFT-M no profits, while still exposing

him to adverse selection risk from the bandit.

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3.5 Equilibrium results under Bertrand competition

Using Lemmas 2-3, we know that the equilibrium of the game is of the general form:

• at T = 0: the bandit always monitors the news. The market maker can either monitor or not.

• at T = 1: HFT-M sets a half-spread s ∈ (0, 1)

• at T = 2: HFT-B always rushes to the market after news, never if there are no news. If the

market-maker monitored at T = 0, he will behave in the same manner as the bandit.

The market maker’s utility functions for the 2 remaining potentially optimal HFT-M strategies

are as follows:

IR : EUHFT−M =µ

µ+ αs (1− s)+ α

µ+ α

[1

2exp (−µ∆H) (s− σ) + (1− exp (−µ∆H)) s (1− s)

]−c

(8)

UN : EUHFT−M =µ

µ+ αs (1− s) +

α

µ+ α[exp (−µ∆H) (s− σ) + (1− exp (−µ∆H)) s (1− s)]

(9)

Both these functions are strictly concave in s (negative second derivatives):

∂2EU(IR)

∂s2=∂2EU(UN)

∂s2= 2

(α

α+ µexp (−µ∆H)− 1

)< 0 (10)

and thus admit a single maximum. Note that for both strategies, the expected utility for s = 1

is larger than the expected utility for s = 0 (zero profits from liquidity traders, but a smaller loss if

adverse selection occurs).

Equilibrium Result We will show that for high enough latencies (small ∆H) and positive

information costs (c > 0), the equilibrium spread will be set at the lowest value which makes the

UN strategy break off - the smallest solution on (0, 1) of the equation EUD (s|UN,α, σ, c,∆H) = 0:

s∗UN(C) = min0<s<1

{s|EUHFT−M (s|UN,α, σ, c,∆H) = 0} (11)

No market-maker can set a lower spread and earn a positive profit, under any non-dominated

strategy available. As the market latency drops (∆H decreases), the adverse selection risks increases

and the IR strategy becomes profitable even for spreads lower than s∗UN(C). Hence, competitor

14

market-makers have an incentive to undercut s∗UN(C), which is no longer a ”competition proof”

spread. The new equilibrium spread will now be given by the value which makes the informed

strategy break off:

s∗IR(C) = min0<s<1

{s|EUHFT−M (s|IR, α, σ, c,∆H) = 0} (12)

Further, it can be proven that if they exist, both equilibrium competitive spreads are increasing

in the HFT market latency (decreasing in the delay):∂s∗

UN(C)

∂∆H< 0 and

∂s∗IR(C)

∂∆H< 0.

3.5.1 Optimal spreads under competition

To study which strategy is actually chosen in equilibrium, we introduce a new concept, the

competition-proof spread.

Definition 1. We define as the competition-proof spread a spread sCP set by HFT-M such that

there is no s < sCP that can undercut it and allow a market-maker to earn positive expected profits,

regardless of the strategy he is choosing: EUHFT−M (s|·, ·) ≥ 0.

In other words, a market-maker cannot set a strategy (UN or IR) and a spread such that it

undercuts the competition-proof spread and still at least break even. This new concept is illustrated

for some parameter values and different k in Figure 2.

[Figure 2 here]

In equilibrium, with Bertrand competition for a single market order, the spread set on the

market will be the competition-proof spread, the smallest spread possible that makes a strategy

break even. Were a HFT-M to set a higher spread, a competitor could either make a profit by

posting a lower spread and using the same information/market rush strategy or select another

strategy and make a non-negative profit. Hence, the equilibrium spread will either be s∗UN(C) or

s∗IR(C) or the market will break down (the utility function is negative for spreads in (0, 1) regardless

of the strategy considered).

Lemma 4. For each of the UN and IR market maker strategies, either both or none of the solutions

to the equation EUHFT−M (s) = 0 are on the interval (0, 1). In the latter case, the strategies are

strictly dominated by not participating on the market.

Proof. Note that EUHFT−M (0) < 0 and EUHFT−M (1) < 0 for both strategies. Hence, if the strictly

concave utility function has a root between 0 and 1, it has to hold that the other root is also on the

15

same interval. Hence, either none or both solutions to the equations are on (0, 1). If there is no root

on this interval, the utility function is always negative and hence dominated by posting no quote at

all.

Corollary 1. The competitive spread for each strategy is smaller than the monopoly spread.

Proof. If there is a root of the equation EUHFT−M (s) = 0 on (0, 1) then both solutions are on this

interval. Hence, the maximum of the function is reached also on (0, 1) and the smallest root is

logically lower than the argument that maximises the function.

Corollary 1 is a natural result: the competitive spread is lower than the one a market-maker can

post when it can extract rents due to monopoly power. Having stated these results, we can turn to

the potential equilibrium spreads of the trading game.

First, we define an adverse selection risk function A (α, µ,∆H):

Definition 2. We define the function A (α, µ,∆H) = αµ+α exp (−µ∆H). Note that A expresses the

probability of HFT-M being adversely selected by a bandit when uninformed, as well as double the

adverse selection probability if he is monitoring the news. Also, it is trivial to check that:

1. A (α, µ,∆H) is strictly decreasing in ∆H

2. A (α, µ,∆H) is strictly decreasing in µ

3. A (α, µ,∆H) is strictly increasing in α

4. In the limit: lim∆H→∞A (α, µ,∆H) = 0 and lim∆H→0A (α, µ,∆H) = αµ+α

5. For any combination of parameters it holds that: 0 ≤ A (α, µ,∆H) ≤ 1

The optimal spreads for any given strategy can be easily expressed in terms of the function A,

as detailed in Proposition 1:

Proposition 1. The strategy-contingent potential equilibrium spreads are, for the uninformed

market-maker (UN) strategy:

s∗UN(C) =1−

√1− 4A (α, µ,∆H) (1−A (α, µ,∆H))σ

2 (1−A (α, µ,∆H))(13)

and for the informed strategy IR:

s∗IR(C) =1− A2 −

√(1− A2

)2 − 4 (1−A)(A

2 σ + c)

2 (1−A)(14)

16

The actual equilibrium spread is the minimum of the two: s∗(C) = min(s∗UN(C), s

∗IR(C)

).

Proof. Solving the equations EUHFT−M (s|UN,α, σ, c,∆H) = 0 and EUD (s|IR, α, σ, c,∆H) = 0

and taking the minimum solutions.

We prove next that the spreads given in equations 13 and 14 are larger when the market latency

of high-frequency traders decreases, due to increased adverse selection risks. We state thus the

following lemma:

Lemma 5. The strategy-contingent potential equilibrium spreads s∗UN(C) and s∗IR(C) are increasing

in the market latency or equivalently decreasing with ∆H .

Proof. See appendix A.

If the deterministic HFT time to market ∆H is large enough for some fixed cost c of information,

then the uninformed (UN) HFT-M strategy is always preferred. If the latency drops, the informed

IR strategy may become optimal.

Lower market latencies and larger news intensities α relax the condition that needs to hold for

information gathering by market makers to be an equilibrium, whereas higher information costs c

are tightening it. We state the following important lemmas:

Lemma 6. For any trading speed and monitoring costs that satisfy c > σ2A (α, µ,∆H), being

uninformed and never rushing to market is the optimal strategy of the competitive HFT-M.

Proof. See appendix A

The next proposition summarises the condition under which monitoring is an optimal for HFT-M

and shows there is an unique latency below which monitoring is always optimal for the market-maker.

Proposition 2. The informed strategy IR is optimal for the market-maker and the equilibrium

spread is s∗IR(C) if the following condition holds:

A (α, µ,∆H)

2

(σ − s∗IR(C)

)− c ≥ 0 (15)

The above restriction is relaxed if ∆H drops and tightened if c increases. Also, if there is any

∆H ∈ R+ for which this condition holds, there is an unique threshold ∆CH > 0 such that it is true for

any ∆H < ∆CH . If the condition holds with equality, then the market-maker is indifferent between

the UN and IR strategies and any mixed strategy between the two.

Proof. See appendix A

17

3.5.2 Welfare

The welfare benchmark we are considering is the situation where all private values are realised. That

is, each liquidity trader who arrives at the market is willing to trade and will sell the asset if he has

a negative private value θi respectively buy it conditional on a positive private value. That is, the

social planner will set the probability of a trade P (trade) = 1 and the spread s = 0 (otherwise there

will be liquidity traders unwilling to exchange the asset). Under these conditions, the maximum

welfare is given by the expectation of the absolute private value. Applying Bayes’ rule, we have:

WelfareFirstBest = E [|θi|] = E [θi|θi ≥ 0]P (θi ≥ 0) + E [−θi|θi < 0]P (θi < 0) (16)

Knowing θi is uniformly distributed on [−1, 1], we compute the first best as:

WelfareFirstBest = E [|θi|] =1

2× 1

2+

1

2× 1

2=

1

2(17)

In our model, the welfare will be given by the probability of a trade with a liquidity agent times

the expectation of its private value.

WelfareCModel = P (F onmarket)×P (F trades)×E [|θi| |trade]− cI (EU [IRN ] > EU [UN ]) (18)

This value is the benchmark we should use to analyse the effect market speed is having on

welfare through adverse selection rationales. In our model, welfare will be given by:

WelfareCModel =

(

µµ+α + α

µ+α exp (−µ∆H))× (1− s∗UN(C))

(1+s∗UN(C)

)

2 , ∆H > ∆CH(

µµ+α + α

µ+α exp (−µ∆H))× (1− s∗IR(C))

(1+s∗IR(C)

)

2 − c, ∆H ≤ ∆CH

(19)

Generally, as both the spreads s∗UN and s∗IR are decreasing in ∆H and the probability of a

liquidity trader arriving first also has a similar behaviour, this would lead to lower welfare as market

speed rises.

[Figure 3 here]

At the threshold point ∆CH , when HFT-M starts monitoring, there are 2 effects on welfare,

summarised in the table below:

18

Effects of Trading Speed on Welfare (Competitive Case) at ∆H = ∆CH

No. Agent Effect on Welfare Influence (+/-) Total Effect

1 LFT lower trade probability Welfare↘ Negative

2 HFT-M monitoring costs Welfare↘ Negative

According to the results in Figure 3 robust to various other parameter specifications, welfare

drops as we decrease latency. At the threshold ∆CH where the competitive dealer switches the

strategy, there is a downward jump in welfare due to monitoring costs.

4 Market Latency with a Monopolist Market Maker

The analysis in sections 3 focused on the case of a competitive market maker. In this section, we

show that the same qualitative results hold if we allow for HFT-M to have market power and earn

positive expected profits. We are considering the opposite polar case, that of a monopolist HFT-M,

than can set s in the quoting stage of the original game (T = 1) to maximise its profits.

4.1 Optimal Spreads with a Monopolist HFT-M

The market-maker will select the monitoring strategy as well as the spread that maximises his profit.

Conditional of choosing any of the IR or UN strategies (note that the others are still dominated

under the results in lemmas 2 to 3), he will choose the corresponding spread that maximises the

expected utility.

Note that the expected utility functions are strictly concave and, for all un-dominated strategies,

the expected utility for s = 1 is larger than the expected utility for s = 0 (zero profits from liquidity

traders, but a smaller loss if adverse selection occurs). Hence, searching for the maximum of the

utility functions on s ∈ (0, 1) it will occur either at an interior point, when the first order condition

is zero, or at s = 1. If the maximum is at s = 1, then the maximum utility is negative (only adverse

selection losses).

Solving the first order conditions of the utility functions, we find that:

s∗IR(M) =2−A

4 (1−A); s∗UN(M) =

1

2 (1−A)(20)

Lemma 7. All interior optimal half-spreads s∗(M) are decreasing in the HFT latency, ∆H and in

the probability of news, α.

Proof. First derivatives of s∗(M) with respect to ∆H and α are strictly negative, respectively positive.

19

Lemma 8. The level of the half-spread, for a given ∆H and α, is always larger for the UN strategy

than for the IR strategy. That is, s∗UN(M) > s∗IR(M), for any given ∆H and α.

Proof. Immediate mathematic calculation.

4.2 Equilibrium

In equilibrium, HFT-M compares the maximum payoff he can get from each strategy (UN , IR or

stopping the game) and sets the optimal quote for that particular strategy, as a function of the

primitive parameters α, σ,∆H , µ and c.

For ∆H →∞ (intuitively, the probability of a liquidity trader arriving first is equal to 1), the UN

strategy yields the maximum payoff (basically there is no adverse selection risk, nor any successful

opportunity for the dealer to withdraw the quote, were he to wish so).

As speed increases, the gains from monitoring also rise to offset the adverse selection risks. For

very low latencies, the risk of being picked off is so large that the HFT-M cannot set any feasible

spread (s < 1) and the market breaks down. The result is stated in the following lemma:

Lemma 9. For ∆H < 1µ ln

(3α

2(α+µ)

), the market breaks down as both the optimal spreads for the

UN and IN strategy are larger than 1 - and attract no LFT demand.

Proof. Immediate calculation shows that for A ≥ 23 we have that s∗IR(M) > 1 and for A ≥ 1

2 we have

that s∗UN(M) > 1. Since ∂A∂∆HFT

< 0, any latency lower than the threshold ∆HFT = A−1(

23

)will

render both optimal quotes unfeasible. Computing the inverse function of A yields the mentioned

latency threshold of 1µ ln

(3α

2(α+µ)

).

4.2.1 Equilibrium Dealer Discrete Strategy Choice

Proposition 3. In the case of a monopolist market maker, the IR strategy is optimal if and only if

the following condition holds:

2A2 − 16c (1−A) + 8σA (1−A) ≥ 0 (21)

For ∆H →∞, the UN strategy is always optimal for HFT-M. The condition (21) is monotonically

relaxed as ∆H decreases. Hence, there can be at most one latency switching point ∆MH below which

monitoring becomes optimal. The existence condition of such a threshold requires that α is large

enough relative to µ:

4α

α+ µ+ 16c+ 8σ

µ− αα+ µ

> 0

20

If the condition holds with equality, then HFT-M is indifferent between the UN and IR strategies

and any mixed strategy between the two.

Proof. See appendix A

We find in equilibrium is that for lower market speeds, the market-maker always starts by not

monitoring and never trying to withdraw his quotes. The adverse selection risk increases with lower

latencies, which HFT-M accommodates through setting a higher spread. At some speed threshold

∆MH , the adverse selection risk becomes so large that the market-maker becomes willing to monitor

the news. At this speed, the probability he will trade with a LFT conditional on news becomes so

low that the monitoring costs are lower than the expected losses he will make from being adversely

selected.

Switching from UN to IR - Market Maker’s Tradeoff

Gains for Dealer Losses for Dealer

LFT arrives first: (1− s) s↗ monitoring costs c

News arrives first:

P (trade−HFT −B)↘News arrives first:

P (trade− F )↘

As the equilibrium spreads are lower for IR, the market maker will earn more in expectation

conditional he meets a LFT. (s(1− s) is decreasing in s for s ≥ 12 , the frictionless monopoly quote).

The equilibrium results for the HFT-M’s choice are presented in Figures 4.

[Figure 4 here]

In the terminology of our game, the optimal strategy of HFT-M has the following form:

HFT −M →

(UN, s∗UN ) ∆H > ∆MH (α, c, σ, µ)

(IR, s∗IR) ∆H ≤ ∆MH (α, c, σ, µ)

(22)

4.2.2 Comparative Statics for ∆MH

The speed threshold ∆MH is decreasing in the market volatility parameters α and σ and increasing

in the information costs c. This is intuitive: in less volatile markets, information asymmetries

manifest with a lower frequency which makes paying the information costs suboptimal unless the

loss conditional on being adversely selected increases (with market speed). In a similar fashion,

lower costs to obtain information make the dealer monitor even when the adverse selection risk is

not as high (for a higher ∆MH ).

21

4.2.3 Welfare

The welfare benchmark we are considering is the situation where all private values are realised, as

in the competitive model. However though, we need to change the benchmark from the first best

to a frictionless monopoly, as we are increasing the market power of the dealer, which is bound to

reduce welfare.

Without the adverse selection problem, the dealer will simply maximise his monopoly profit and

set a spread of 12 (solve max s(1 − s) =⇒ s∗Mon = 1

2). In this case, a liquidity trader will accept

the terms with probability 12 and the expected value of his private value, in absolute terms will be

1+s∗Mon2 = 3

4 . Hence, the monopoly welfare is given by:

WelfareMonopoly =1

2×

1 + s∗Mon

2= 0.375 (23)

This value is the benchmark we should use to analyse the effect market speed is having on

welfare through adverse selection rationales. In our model, welfare will be given by:

WelfareMModel =

(

µµ+α + α

µ+α exp (−µ∆H))× (1− s∗UN(M))

(1+s∗UN(M)

)

2 , ∆H > ∆MH(

µµ+α + α

µ+α exp (−µ∆H))× (1− s∗IR(M))

(1+s∗IR(M)

)

2 − c, ∆H ≤ ∆MH

(24)

Again, both the spreads s∗UN(M) and s∗IRN(M) are decreasing in ∆H and the probability of a

liquidity trader arriving first increases in ∆H : which lead to lower welfare as market speed increases,

at least as long as the dealer does not switch strategies (see figure 5).

At the threshold point ∆MH , when HFT-M starts monitoring, there are 3 effects on welfare,

summarised in the table below:

Effects of Trading Speed on Welfare (Monopoly) at ∆H = ∆MH

No. Agent Effect on Welfare Influence (+/-) Total Effect

1 Liquidity lower spreads Welfare↗ Positive

(1+2)

2 Liquidity lower trade probability Welfare↘ Positive

(1+2)

3 Dealer monitoring costs Welfare↘ Negative

(1+2+3)

The lower spreads benefit is stronger that the loss from lower trade probability with the liquidity

traders, which generates positive welfare for the liquidity traders when the dealer starts monitoring.

22

However, after we include the dealer’s costs, the total effect is negative, which leads to an even lower

welfare after monitoring becomes optimal for the dealer.

4.3 Model Predictions

For both the perfect competitive and monopolistic market maker, the model’s equilibrium spread

(for both the competitive and monopoly settings) is increasing in the HFT speed parameter ∆H , as

well as the intensity of news α. Also, the effect of market latency on the model equilibrium spread

is stronger if σ is larger. In the model, there is no other friction determining the spreads apart from

the information asymmetry. Hence, our predictions are formulated in terms of the adverse selection

component of the spread:

1. A drop in market latency will result in larger adverse selection costs on limit orders submitted

by HFT: ∆H ↓−→ s ↑

2. The intensity of news arrival results in larger adverse selection costs: α ↑−→ s ↑

3. The effect of a drop in market latency is larger for more volatile stocks:∣∣∣ ∂s∂∆H

∣∣∣ is increasing in

σ (see proof of Lemma 5)

5 Empirical Strategy

5.1 Dataset

Trade Data The trade data for this project is provided by the European Multilateral Clearing

Facility (henceforth EMCF) and consists of detailed individual trade information on equities from

Sweden, Denmark and Finland. The period spanned by our dataset is of 1 year, from September

1st, 2009 to September 10th, 2010. Due to the fact that up to October 19th, 2009 only a small part

of the trades were cleared through EMCF (who launched mandatory CCP services from that point

onwards), we have decided to exclude from analysis the first month covered as unrepresentative,

and focus on the remaining 11 months.

As a central counterparty institution, EMCF stands ready to become a third party in all the

trades - by buying the security from the original seller and then selling it to the original buyer. This

is known as novation process, in which 2 contracts (between EMCF and both parties) are created

instead of a single one between buyer and seller. Hence, data on all executed trades is available at

EMCF, including agency stamps: whether one of the original parties executed the trade for a client

23

or for its own account. More information on the EMCF central counterparty operation is included

in the Internet supplements of this paper 6.

The dataset contains information on approximately 70 million trades, including date and time

stamps 7, trader ID (anonymised), transaction price, quantity, sign of the transaction, trading

platform and whether the trade was executed on its own account or for a client (principal trade or

agent trade). Each of the trades takes place either on NASDAQ OMX (the incumbent market prior

to 2007) or on one of the new (entrant) markets, such as Chi-X, BATS Europe, NASDAQ Europe,

Burgundy or Quote MTF. For a snapshot of the dataset and the type of variables we use in this

paper, see Appendix D.

Order Book Data Information on the available quotes for all the stocks in the sample on all

markets is collected from the Thomson Reuters Tick History database, through SIRCA. At the

millisecond level, there are approximately 2.2 billion data points. This represents information on the

top of the order book for all exchanges: best bid and ask prices and the quantities demanded/supplied.

Since the trade data is available at the level of seconds, we have selected the last quote in each

second to match the trade and order book datasets.

Complementary Data Information from the main EMCF dataset is complemented by metadata

on each of the securities, obtained from Datastream - number of shares outstanding and ISIN codes,

as well as daily exchange rates between Euro and Swedish/Danish Krona. All trading prices are

converted to Euros at the daily exchange rate to provide comparability across stocks. Data on

intraday market volatility (on the OMX Nordic 40 index high and low daily prices) is obtained via

the Thomson Reuters Tick History (TRTH) system, for the days in the EMCF sample.

The universe of our sample consist of 226 traders being active in 242 stocks. The average trader

is present on the market in 157 out of 228 days and trades in about a third of the available stocks.

The average trade value over the full dataset was approximately 20.62 thousand Euro.

Variables We aggregate the data up to three hierarchical levels: first, we build a stock-day panel

with information on average price, daily volume, daily volatility, market capitalisation and stock

fragmentation and effective spreads on incumbent and entrant markets. Then, for each stock-day,

we look at the trader IDs which were active in that particular security (third aggregation level). We

build thus a multi-level panel with 3 dimensions: a stock-day panel extended in the cross-sectional

dimensions of traders. In the remainder of the paper, we index days by t, securities by i and traders

6See document http://db.tt/l03D3h2V7converted to standard GMT, including hours, minutes and seconds

24

by j.

The list of variable definitions and comments on their measurement are provided in Appendix

C. There we also present a table with variable short-names, for ease of exposition. The final

stock-day-trader-agency multilevel panel has approximately 1.7 million observations.

5.2 Measurement and model specification

Measuring the model spread Absent any inventory or order processing costs, the positive

spread in our model stems only from the adverse selection component (and dealer’s market power in

the monopoly setting). Hence, the dependent variable for testing is the adverse selection component

of the spread, computed as in Hendershott, Jones, and Menkveld (2011) and Hoffmann (2010). For

each trade, define: pt is the transaction price and mt is the prevailing midpoint at the transaction

time; the sign indicator qt takes the value qt = 1 for buys and qt = −1 for sell transactions (taking

the market taker perspective). The effective spread then is defined as the percentage deviation from

the midpoint:

ES = qtpt −mt

mt(25)

Assuming the market maker will close his position on average in∆ = 5 min, we decompose ES

in an adverse selection and a realised spread component. The adverse selection component then

measures whether and by how much the price moved against the quote submitter in the period

immediately following the trade:

ES = qtmt+∆ −mt

mt︸ ︷︷ ︸AS

+ qtpt −mt+∆

mt︸ ︷︷ ︸RS

(26)

Volatility Volatility is measured by 2 variables: we capture the dynamics of systemic risk by the

daily range based volatility of OMX Nordic 40 Index (σMktt ) and the cross-section of risk by the

idiosyncratic risk for each security (σIDi ). The idiosyncratic risk is computed as the estimate of

residual variance from regressing daily stock returns on daily index returns in the year following the

event (February 2010-February 2011).

Identification strategy We use the introduction of the INET technology on NASDAQ OMX on

February 8, 2010 as an instrument for an exogenous change in market speed. The latency dropped

ten times, from 2.5 ms to 250 µs. The market speed jump is captured by a time dummy DEvent,

which takes value 1 after February 8, 2010.

25

To allow for heterogenous effects between high- and low- frequency traders (for identification

details, see subsection 6.2), we define a new dummy variable: DHFT , which takes value 1 for HFT

accounts and 0 otherwise.

Econometric Model The benchmark model is a fixed-effects panel linear regression, estimated

by least squares. We regress the adverse selection component of the spread (expressed in bps)

aggregated across stocks, traders and days on event dummies, HFT dummies, their interaction,

volatility variables and stock-specific fixed effects. We choose the most conservative standard errors,

double-clustered at stock and day level, following the methodology in Petersen (2009). The equation

is given by:

ASijt = β0DLFTEvent + β1D

HFTEvent + β2DHFT + β3σ

Mktt + β4σ

IDi DEvent + β5 log V oltrad + δi + εijt (27)

Hypotheses We test the following hypotheses:

1. H10 : β1 > 0 and H2

0 : β0 > 0. The adverse selection component of the bid-ask spread increases

once the market latency drops, both for high and low frequency traders. This is the main

result of Lemmas 5 and 7 (under different competition assumptions, it holds that ∂s∗

∂k > 0 )

2. H30 : β3 > 0. The adverse selection component of the bid-ask spread increases in more volatile

periods (in the model, ∂s∗

∂α > 0 - Lemma 7 ).

3. H40 : β4 > 0. The effect of market speed on adverse selection is larger for riskier stocks. Under

both competition settings, the marginal effect of speed on spreads increasing in α: ∂2s∗

∂k∂α > 0.

6 Results

6.1 Summary Statistics

The volume-weighted means of adverse selection spread components for all trades are reported in

Table 1, separately for the periods before and after INET was introduced on NASDAQ OMX.

[Table 1 here]

Plotting the distribution of adverse selection averages for each stock, day and trader in the

sample on NASDAQ OMX, before and after the INET was introduced, we observe that the centre of

26

the probability mass shifts to the right in the second part of the sample. This finding is consistent

with larger mean adverse selection costs which are not due to an increase in the number of ”tail”

adverse selection events (which would be the case for instance if the period after INET would have

included days with extraordinary volatility in some stocks at least).

[Figure 6 here]

6.2 High Frequency Traders Identification

To identify high frequency traders in our dataset, we follow Kirilenko, Kyle, Samadi, and Tuzun

(2011) and, for each stock and day in our sample, we highlight the trader accounts who simultaneously

fulfil the following 3 conditions across all markets. Then, we compute a ”HFT ratio” by dividing

the number of stock × days when a particular trader behaved as a HFT to the total number of

appearances in the sample.

1. The account traded more than 10 contracts on a given stock in a given day.

2. The average of the absolute value of the end-of-day net position, expressed as a fraction of the

account’s total trading volume for the day is not more than 5%

3. The average of the square root of the sum of squared deviations of the minute-end net contract

holdings from the net contract holdings at the end of the day, expressed as a fraction of an

account’s total contract trading volume during that day, is not more that 1.5%. ”Contract

holdings” are defined as the net number of contracts bought or sold from the beginning of the

day until the end of the minute for which the calculation is made.

We find in total 7 trader accounts that have a pronounced HFT profile compared to the

mass of traders. Among those, only 4 accounts trade on NASDAQ OMX, while 3 use exclusively

alternative markets such as Chi-X or BATS Europe. The identified HFTs account for 5.43% of the

total NASDAQ OMX volume (denominated in Euro), with one particular account being strongly

dominating (4.91% of the total NASDAQ OMX volume and the third trader in the market by

volume, as well 90% of the total HFT volume).

[Figure 7 here]

27

6.3 Estimation Results

Table 2 shows the results of the empirical analysis, estimating the equation:

ASijt = β0DLFTEvent + β1D

HFTEvent + β2DHFT + β3σ

Mktt + β4σ

IDi DEvent + β5 log V oltrad + δi + εijt (28)

We consider different symmetric estimation windows around the INET implementation: 2 months

(December 8, 2009 - April 8, 2010), 3 months (November 8, 2009 - May 8, 2010) and 4 months

(October 19, 2009 - June 8, 2010).

[Table 2 here]

The empirical findings are summarised below:

1. We find that the drop in market latency has a positive significant effect on adverse selection

of approximately 0.4 bps (approximately 7%). Without distinguishing between high- and low-

frequency traders, this effect is strongly significant for all windows considered, in specification

with or without other control variables.

2. When allowing for separate effects between high frequency and low frequency traders, we find

an increase in the adverse selection spread component for LFT of approximately the same

magnitude (0.4 bps), which is significant and persistent across all time windows considered

(β1 > 0).

3. For the HFT, the effect is also significant and positive for 2 months after the event date

(about 0.55 bps), but it declines as we move further away from the event date - while

becoming statistically insignificant 4 months after the implementation date. This could point

to monitoring technology adjustments.

4. We find a positive and significant relationship between adverse selection and the volatility of

the index. A standard deviation increase in market volatility leads to a 0.27-0.36 bps increase

in the adverse selection component of the spread. We find thus empirical support for H30 .

5. The increase in the adverse selection is larger for securities with larger idiosyncratic risk. A

standard deviation increase in idiosyncratic risk leads to a 0.44 bps additional market latency

effect on adverse selection spread components. We find thus empirical support for H40 .

6. Before the INET implementation, HFTs have much lower adverse selection costs than LFTs:

between 3-3.5 bps, very strongly significant and consistent across all model specifications.

28

Placebo Analysis We test the relationship between the adverse selection spread component and

the event date for the other markets Nordic securities are traded on (the largest of which are Chi-X

Europe and BATS). These constitute a placebo group, as there was no similar speed improvement

on any other market during the same period.The results for a symmetric 2-months event window

around the event date are presented in Table 3. Note the event coefficients are no longer statistically

significant, regardless if we consider HFT and LFT separately or not.

[Table 3 here]

7 Concluding Remarks

This paper studies the effects on adverse selection and information asymmetries of the lower latency

technologies implemented by trading venues. We focus on symmetric and exogenous technology

improvements across HFT traders, regardless whether they act as market-makers trying to capture

the spread or as speculators earning profits on short-term price trends.

For empirical identification, we use a natural experiment in the Nordic markets. In February

2010, NASDAQ OMX implemented the INET technology, which reduced round-trip latencies tenfold.

We find that adverse selection increased by 15% on NASDAQ OMX following the latency drop,

after controlling for market volatility, volume and realised spreads. On the other trading venues,

adverse selection dropped in the post-event period, which might indicate the migration of informed

speculators from the slower to the faster market.

To explain our results, we develop a costly-monitoring theoretical model of the limit order market.

We find that lower market latencies lead to most market interactions to take place between high

frequency traders. This phenomenon, the “crowding-out” of low-frequency (liquidity) traders results

in larger adverse selection risks. Consequently, wider spreads are set to compensate the extra risk,

but also market-makers will improve their monitoring levels (when they do, spreads actually drop in

equilibrium). As the latency is reduced indefinitely, there are no more monitoring investments to be

undertaken by market-makers or speculators. Trading becomes increasingly more a zero-sum game

between high-frequency traders, leading to a lower trade to quotes ratio (due to quote withdrawals)

and lower welfare gains, as liquidity traders get to realise their private values less often.

An alternative policy to a symmetric latency drop between limit and market orders, stipulating

that only the limit orders should benefit from lower latencies will reduce the adverse selection risks

and result in tighter spreads, as the speculators no longer benefit from the faster trading.

29

Table 1: Adverse selection spread components on NASDAQ OMX. We report volume-weightedmeans of AS components for all trades in Nordic markets. The interquartile range is provided inparantheses.

Window Before INET After INET ∆(%)

Panel A: Adverse Selection Spread Component (bps)

1 month 2.59(2.32−2.79)

2.71(2.26−3.01)

4.63%

2 months 2.42(2.16−2.69)

2.62(2.16−2.95)

8.26%

4 months 2.60(2.17−2.89)

2.73(2.20−3.19)

5.38%

Panel B: OMX Nordic 40 Daily Volatility

1 month 1.04%(0.72−1.30)

0.94%(0.64−1.13)

−9.61%

2 months 0.88%(0.63−1.08)

0.88%(0.62−1.06)

−0.01%

4 months 0.98%(0.66−1.33)

0.98(0.63−1.31)

−0.05%

Panel C: Average Daily Volume Traded (EUR million)

1 month 2605.63(2314.35−2672.85)

2215.54(1973.25−2282.24)

−14.97%

2 months 2120.95(1632.14−2508.74)

2226.99(1999.90−2440.97)

4.99%

4 months 1956.77(1631.30−2283.53)

2577.56(2075.13−2899.43)

31.72%

30

Table 2: Adverse selection costs in basis points is regressed on event dummies/ event dummiesinteracted with the trader type (HFT / LFT). In several specifications, we also allow for the INETeffect to vary in the cross-section of stocks with the idiosyncratic volatility of the security. Multipleevent windows are considered: from 2 months to 4 months around the INET implementation.Volatility and volume measures are standardized to have mean zero and variance one. We usedouble-clustered standard errors (as in Petersen (2009)) and stock-specific FE.

Panel A: NASDAQ OMX (2 months around event date)

Variable (1) (2) (3) (4) (5)

DLFTEvent − − 0.372∗∗

2.280.562∗∗∗

3.490.551∗∗∗

3.47

DHFTEvent − − 0.558

2.47

∗∗ 0.767∗∗∗3.17

0.754∗∗∗3.29

DHFT − − −3.625∗∗∗−19.14

−3.241∗∗∗−16.82

−3.145∗∗∗−16.3

DEvent 0.351∗∗2.22

0.525∗∗∗3.43

− − −σMktt − 0.257∗∗∗

2.92− 0.274∗∗∗

2.920.254∗∗

2.89

σIDi ×DEvent − − − 0.441∗∗∗4.61

−log V oltrad − −0.913∗∗∗

−8.27−0.832∗∗∗−7.65

−0.862∗∗∗−7.79

No. Obs. 288909 288909 288909 288909 288909

Panel B: Window around event - 3 months

Variable (1) (2) (3) (4) (5)

DLFTEvent − − 0.435∗∗∗

2.990.561∗∗∗

4.040.553∗∗∗

4.05

DHFTEvent − − 0.452∗∗

2.160.644∗∗

2.640.637∗∗∗

2.91

DHFT − − −3.718∗∗∗−19.71

−3.339∗∗∗−17.51

−3.294∗∗∗−17.17

DEvent 0.419∗∗∗2.97

0.532∗∗∗4.05

− − −σMktt − 0.342∗∗∗

4.61− 0.341∗∗∗

4.510.338∗∗∗

4.57

σIDi ×DEvent − − − 0.449∗∗∗4.08

−log V oltrad − −0.857∗∗∗

−9.06− −0.791∗∗∗

−8.59−0.806∗∗∗−8.57

No. Obs. 446819 446819 446819 446819 446819

Panel C: Window around event - 4 months

Variable (1) (2) (3) (4) (5)

DLFTEvent − − 0.417∗∗∗

3.110.446∗∗∗

3.550.443∗∗∗

3.56

DHFTEvent − − −0.144

−0.59−0.023−0.09

−0.039−0.16

DHFT − −3.442∗∗∗−17.25

−3.104∗∗∗−15.57

−3.002∗∗∗−15.02

DEvent 0.394∗∗∗2.97

0.408∗∗∗3.34

− − −σMktt − 0.366∗∗∗

5.74− 0.366

5.710.362∗∗∗

5.72

σIDi ×DEvent − − − 0.434∗∗∗4.52

−log V oltrad − −0.862∗∗∗

−10.16− −0.784∗∗∗

−9.53−0.808∗∗∗−9.61

No. Obs. 566841 566841 566841 566841 566841

31

Table 3: Placebo Analysis: Adverse selection (bps) on alternative markets (other than NASDAQOMX) is regressed on event dummies/ event dummies interacted with the trader type (HFT / LFT).In several specifications, we also allow for the INET effect to vary in the cross-section of stockswith the idiosyncratic volatility of the security. We consider a 2 months window around the INETimplementation. Volatility and volume measures are standardized to have mean zero and varianceone. We use double-clustered standard errors (as in Petersen (2009)) and stock-specific FE.

Variable (1) (2) (3) (4) (5)

DLFTEvent 0.189

1.250.184

1.130.176

1.14

DHFTEvent −0.171

−0.87−0.212−0.89

−0.184−0.77

DHFT −0.255−1.22

−1.636∗∗∗−6.74

−1.576∗∗∗−6.53

DEvent −0.007−0.01

0.1671.11

− − −

σMktt 0.277∗∗∗

2.440.328∗∗∗

2.980.273∗∗∗

2.41

σIDi ×DEvent − −0.032−0.13

−

log V oltrad −0.487∗∗∗−4.6

−0.468∗∗∗−4.23

−0.452∗∗∗−4.29

R2 1.06% 1.1% 1.11% 1.13% 0.67%No. Obs. 141853 141853 141853 141853 141853

32

HFT-M

mon

itors(paysc)

not

mon

itor

(pays0)HFT-M

HFT-M

quotes

s

quotes

s

endgame

endgame

New

s

∆H

LFT

executesmarketorder

HFT-B

executesmarketorder

New

s

∆H

New

s

∆H

HFT-M

withdrawsquotes

LFT

executesmarketorder

New

s

(I)

(II)

(III)

(IV)

Pre-Trading

TradingOutcomes

Fig

ure

1:M

odel

Tim

ing

33

0.2 0.4 0.6 0.8 1.0Half Spread

-0.10

-0.05

0.05

0.10

0.15

HFT-M Utility

UN Strategy

IR Strategy

Cannot profitably undercut UN(competition proof)

Strategy UN is profitable at lower spreads than IR break-even spread.

(a) Dealer’s Utility Functions - ∆H = 1.5

0.2 0.4 0.6 0.8 1.0Half Spread

-0.20

-0.15

-0.10

-0.05

0.05

HFT-M Utility

UN Strategy

IR Strategy

Cannot profitably undercut IR(competition proof)

Strategy IR is profitable at lower spreads than UN break-even spread.

(b) Dealer’s Utility Functions - ∆H = 0.5

Figure 2: Dealer’s utility functions for the UR and IR strategies. We take α = 0.2, µ = 0.65, σ = 1.4and c = 0.07. Note that in the first panel, with lower market speed (∆H = 1.5), the break-evenspread from the informed strategy can always be profitably undercut by choosing not to acquireinformation. As the latency drops (second panel, ∆H = 0.5), the situation is reversed and thecompetition-proof spread becomes the break-even spread of the informed (IR strategy).

34

15 10 5Market Latency HInverted ScaleL

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Optimal Half-Spread

Monopolist HFT-M

Bertrand Competition

Switch to monitoring (competition)

Switch to monitoring (monopoly)

Market breakdown (competition)

(a) Comparison of equilibrium half-spreads against market latency for competitive and monopolymarket-makers (Parameter calibration: α = 0.2, µ = 0.25, σ = 1.25 and c = 0.025)

15 10 5Market Latency HInverted ScaleL

0.2

0.3

0.4

0.5Welfare

Monopolist HFT-M

Bertrand Competition

Switch to monitoring (competition)

Switch to monitoring (monopoly)

Market breakdown (competition)

(b) Comparison of welfare against market latency for competitive and monopoly market-makers(Parameter calibration: α = 0.2, µ = 0.25, σ = 1.25 and c = 0.025))

Figure 3: Equilbrium Spreads, Welfare and Market Speed in the competitive and monopolymarket-makers environments

35

15 10 5 2Market Latency HInverted ScaleL

0.05

0.10

0.15

0.20

Dealer Utility

IR Strategy

UN Strategy

Strategy Switch Threshold for HFT-M

(a) Low News Intensity (α = 0.2, µ = 0.25, σ = 1.25, c = 0.025)

15 10 5 2Market Latency HInverted ScaleL

-0.10

-0.05

0.05

0.10

0.15

0.20

Dealer Utility

IR Strategy

UN Strategy

Strategy Switch Threshold for HFT-M

(b) High News Intensity (α = 1.0, µ = 0.25, σ = 1.25, c = 0.025)

Figure 4: HFT-M’s choice between strategies in the monopoly case: expected utilities as a functionof market latency. We also include different news intensity (α) regimes to illustrate the relationshipbetween the strategy switching point and the frequency of news.36

15 10 5 2Market Latency HInverted ScaleL

0.54

0.56

0.58

0.60

0.62

Half-Spread

alpha=0.2, c=0.05

alpha=0.3, c=0.025

alpha=0.2, c=0.025

Market-maker starts monitoring: spread drops

(a) Optimal equilibrium spreads

15 10 5 2Market Latency HInverted ScaleL

0.25

0.30

0.35

Welfare

alpha=0.2, c=0.05

alpha=0.3, c=0.025

alpha=0.2, c=0.025

Market-maker starts monitoring

(b) Welfare

Figure 5: Equilibrium spreads and welfare under monopolist HFT-M for various news intensitiesand information cost parameters 37

Figure 6: Distribution of adverse selection averaged at stock-day-trader levels. The blue solid linecorresponds to the distribution before February 8, 2010 whereas the red dotted line corresponds tothe post-event distribution. Note the shift to the right of the probability mass following the INETevent.

38

Figure 7: HFT Profiles and Trading Aggressiveness. Each dot stands for a trader account. HFTprofiles (between 0 and 1) are measured as the proportion of the number of stock × days an accountsimultaneously passes the three Kirilenko, Kyle, Samadi, and Tuzun (2011) HFT criteria in the totalnumber appearances in the sample. Aggressiveness is simply measured as the proportion of marketorder executed volume in total traded volume, for each trader account. The size of the dots isproportional to the Euro-denominated volume traded on NASDAQ OMX by each particular agent.

39

A Proofs of Lemmas and Propositions

Lemma 1

Proof. It can be proven that the increments of M(t) and N(t) have the same distribution. From

the properties of the Poisson processes, we can write for any s < t and k ∈ {0, 1, 2...}:

P{N ′(t)−N ′(s) = k

}=µk (t− s)k

k!exp (−µ (t− s)) (29)

Similarly, for M(t), we have:

P {M(t)−M(s) = k} = P{N ′(t−∆L)−N ′(s−∆L) = k

}=µk (t− s)k

k!exp (−µ (t− s)) (30)

The previous relations holds because the interval (s−∆L, t−∆L) has the same length as (s, t):

P{N2(t−∆L)−N2(s−∆L) = k

}=µk (t−∆L − s+ ∆L)k

k!exp (−µ (t−∆L − s+ ∆L)) (31)

Lemma 2:

Part 1

Proof. If the bandit does not monitor the news (strategy UN) or monitors the asset value but does

not submit a market order (strategy IN), he will earn an expected payoff of 0 (no trade and no

monitoring cost). It is enough then to show that for s < σ, the expected payoff from strategy IR is

larger than zero. If the market-maker also monitors the news, the payoff of HFT-B is given by the

following expression:

ΠHFT−B =1

2× α

α+ µexp−µ∆H (σ − s) > 0 (32)

The expression (σ − s) is the profit conditional on arriving first to the market. The probability

of the HFT-B arriving first to the market is given by 3 components: αα+µ - the probability there is a

value jump before an LFT consumes the quote; exp−µ∆H - the probability that there are no LFTs

arriving in the interval from observing the jump to market arrival and 12 - the probability HFT-B

arrives before HFT-M.

If the market-maker does not monitor the news (or does not rush to market after a jump), the

payoff of HFT-B is as follows:

40

ΠHFT−B =α

α+ µexp−µ∆H (σ − s) > 0 (33)

The components of the profit are the same as before, except that the probability of HFT-B

arrives before HFT-M is now equal to 1 rather than 12 . Hence, IR a strictly dominant strategy for

the bandit.

Part 2

If s > σ, we see from the proof of Part 1 that the profit from the strategy IR is negative,

regardless of HFT-M’s strategy. Hence, it is optimal for the bandit to never act on information, as

the spread is larger than the potential benefit from the stale quote.

Lemma 3:

Part 1

Proof. With strictly positive monitoring costs, the strategy IN is strictly dominated by UN . This

is natural, since paying for information and not acting contingent on the value jumps yields a lower

payoff than not paying for information, with the difference being exactly the cost of obtaining the

information. Formally:

EUHFT−M [IN ] = EUHFT−M [UN ]− c

Part 2

We consider 2 possible cases: s ∈ [1, σ]and s ≥ σ, making use of the fact that σ > 1. Note that

for s ≥ 1, there are no liquidity traders willing to trade.

If s ∈ [1, σ] and there are news, then the bandit will rush to the market. If the bandit reaches

the market first, the dealer has a negative payoff s− σ < 0, whereas if the market-maker is first to

the market, he gains 0. No trade with liquidity agents will occur now, and the market-maker is

(weakly) worse off than ending the game.

If s > σ, both the bandit and the liquidity traders will stay off the market and HFT-M’s payoff

is 0. If s = 0, the gain he makes from liquidity traders is zero, whereas the losses he can incur from

the bandit are maximised (−σ).

Hence, in order for the dealer to earn a positive payoff, it should always set the half spread in

the interval (0, 1), which is the conclusion required.

Lemma 5.

41

Proof. We start with the optimal spread for the uninformed strategy (s∗UN(C)). To show this function

is decreasing in ∆H it is enough to show that∂s∗

UN(C)

∂A(∆H ,·) > 0, since by the chain rule we have that:

∂s∗UN(C)

∂∆H=

∂s∗UN(C)

∂A (∆H , ·)× ∂A (∆H , ·)

∂∆H︸ ︷︷ ︸<0

We have that:

∂s∗UN(C)

∂A=

√1− 4A (1−A)σ − 2 (1−A)σ

2 (1−A)2√

1− 4A (1−A)σ

Proving∂s∗

UN(C)(k)

∂A > 0 is equivalent to showing:

√1− 4A (1−A)σ − 1 + 2 (1−A)σ > 0

If the UN strategy yields positive utility, we have that:

s∗UN(C) < 1⇐⇒ 2 (1−A) > 1−√

1− 4A (1−A)σ

Thus, we have that:

√1− 4A (1−A)σ + 2 (1−A)σ >

√1− 4A (1−A)σ (σ − 1) > 0

which is true given our parameter restrictions.

Next, we turn to the IR equilibrium spread. Similarly, we need to prove only that∂s∗

IR(C)

∂A(∆H ,·) > 0,

that is:

∂s∗IR(C)

∂A=A− 2 + 8c (1−A) + 4σ (1−A) + 2

√(1− A2

)2 − 4 (1−A)(A

2 σ + c)

8 (1−A)2√(

1− A2)2 − 4 (1−A)

(A2 σ + c

) > 0

Proving∂s∗

IR(C)(k)

∂A > 0 is equivalent to showing:

A− 2 + 8c (1−A) + 4σ (1−A) + 2

√(1− A

2

)2

− 4 (1−A)

(A2σ + c

)> 0

If the IR strategy yields positive utility, we have that:

42

s∗IRN(C) < 1⇐⇒ A− 2 + 2

√(1− A

2

)2

− 4 (1−A)

(A2σ + c

)> A− 1 (34)

Then, after some algebraic manipulation, we only have to show that:

8c (1−A) + 4 (σ − 1) (1−A) ≥ 0 (35)

which again is true given our parameter restrictions (we know σ > 1 and A < 1).

Lemma 6.

Proof. We note first that the slope of the IR utility function is always larger than the slope of UN .

Simple algebraic manipulation of the first derivatives for the expected utility functions yields:

SlopeIR − SlopeUN =

[1− A

2− 2s (1−A)

]− [1− 2s (1−A)] = −A

2< 0 (36)

If EUHFT−M (s = 0|UN) > EUHFT−M (s = 0|IR) and since the UN utility grows faster than

the IR utility, then the smallest solution of EUHFT−M (s) = 0 will be for the uninformed, UN

strategy. Hence, the UN strategy is optimal.

The condition EUHFT−M (s = 0|UN) > EUHFT−M (s = 0|IR) is equivalent to −σA > −σ2A− c,

which can be written as: c > σ2A. This completes the proof.

Proposition 2.

Proof. For IR to be optimal it needs to hold that s∗IR(C) ≤ s∗UN(C) - the first root of IR utility

function is smaller than the first root of UN expected utility. Since in the proof of lemma 6 we have

shown that the UN utility is growing faster on the increasing section, the condition s∗IRN(C) > s∗UN(C)

is equivalent with the condition that the IR utility is always above UN in the negative quadrants:

EUHFT−M (s|IR) > EUHFT−M (s|UN), ∀s < s∗IR(C). (37)

This condition is equivalent to:

EUHFT−M (s|IR)− EUHFT−M (s|UN) ≥ 0⇐⇒ A2

(σ − s)− c ≥ 0 , ∀s ∈(

0, s∗IR(C)

)The inequality above is monotonically decreasing in s, so if it holds for the largest s in the

domain - s∗IR(C), it will hold for all lower values of the half spread. The sufficient condition is thus:

43

A2

(σ − s∗IR(C)

)− c ≥ 0 (38)

As s∗IR(C) is increasing in c (see definition), it is easy to see the condition is tightened for higher

values of the cost (the LHS is decreasing in the monitoring cost).

The condition states that:

IRCOptimal (α, µ,∆H , c, σ) =A (α, µ,∆H)

2

(σ − s∗IR(C)

)− c ≥ 0 (39)

We will prove that the condition is monotonically relaxed as ∆H decreases, under the assumption

s∗IR(C) exists and it is a feasible strategy (0 ≤ s∗IR(C) ≤ 1). If that is the case and there exists a

∆CH corresponding to a s∗IR(C) for which the condition (39) holds with equality, it will hold for all

∆H < ∆CH . The first derivative of (39) is given by:

∂IRCOptimal∂∆H

=1

2

[−σµA+ s∗IR(C)µA−A

∂s∗IR(C)

∂A∂A∂∆H

]=

1

2

[µA(s∗IR(C) − σ

)+ µA2

∂s∗IR(C)

∂A

](40)

Since µ and A are strictly positive, proving∂IRC

Optimal

∂∆H< 0 is equivalent to showing that:

s∗IR(C) − σ +A∂s∗IR(C)

∂A< 0 (41)

For expositional purposes, we make the following notation: B =

√(1− A2

)2 − 4 (1−A)(A

2 σ + c).

Remember that in the proof of Lemma 5 we found that:

s∗IR(C) =1− A2 −B

2(1−A);∂s∗IR(C)

∂A=A− 2 + 8c (1−A) + 4σ (1−A) + 2B

8 (A− 1)2 B(42)

Existence of s∗IR(C) ∈ R implies(1− A2

)2− 4 (1−A)(A

2 σ + c)> 0. This imposes a lower bound

on the cost term in∂s∗

IR(C)

∂A :

8 (1−A) c ≤ 2

(1− A

2

)2

− 4σ (1−A)A (43)

Hence, it holds that:

∂s∗IR(C)

∂A≤A− 2 + 2

(1− A2

)2+ 4σ (1−A)2 + 2B

8 (A− 1)2 B(44)

44

The condition s∗IR(C) > 0 imposes that: 2B < 2−A, so we can redefine the upper bound from

above:

∂s∗IR(C)

∂A≤

12 (2−A)2 + 4σ (1−A)2

8 (A− 1)2 B≤ 1

2σ

1

B(45)

The condition s∗IR(C) < 1 imposes that: 2B > 3A−2, equivalent to: 12B ≤

13A−2 . Hence, putting

these results together (and σ > 1), we have that:

s∗IR(C) − σ +A∂s∗IR(C)

∂A≤ 1− σ +

A3A− 2

σ = 1− σ(

2A− 2

3A− 2

)≤ A

3A− 2≤ 0 , ∀A ≤ 2

3(46)

Since we prove in Lemma 9 that the market breaks down for A ≤ 12 , the condition

∂IRCOptimal

∂∆H≤ 0

holds in any non-trivial equilibrium situation when the market maker posts any quotes at all.

Proposition 3

Proof. The HFT-M expected utility functions for both IR and UN strategies, evaluated at the

optimal spreads s∗IR(M) and s∗UN(M) are given by:

EUHFT−M (IR) =4 (1−A) +A2 + 16c (A− 1) + 8σA (A− 1)

16 (1−A)(47)

EUHFT−M (UN) =4 +A2 (16σ − 1)− 16Aσ

16 (1−A)(48)

Hence, we have that EUHFT−M (IR) ≥ EUHFT−M (UN) if and only if the following holds:

IRMOptimal (α, µ,∆H , c, σ) = 2A2 − 16c (1−A) + 8σ (1−A)A ≥ 0 (49)

We note that the derivative with respect to the cost is negative - larger monitoring costs tighten

the condition under which the informed strategy becomes optimal:

∂IRMOptimal∂c

= −16 (1−A) < 0

The derivative with respect to ∆H is given by:

∂IRMOptimal∂∆H

=∂IRMOptimal

∂A∂A∂∆H

= (4A+ 16c+ 8σ (1− 2A))∂A∂∆H

≤ 0 (50)

45

The previous holds for any A ≤ 12 - when the market does not break down, since we know that

∂A∂∆H

< 0.

For ∆H →∞ we have that the uninformed strategy is always optimal:

lim∆H→∞

IRMOptimal = −16c < 0

For ∆H → 0 we have that:

lim∆H→0

IRMOptimal = −(

4α

α+ µ+ 16c+ 8σ

µ− αα+ µ

)µ

If it holds that 4 αα+µ + 16c+ 8σ µ−αα+µ > 0 (for α sufficiently large relative to µ), there exists a

latency threshold ∆MH such that for all ∆H < ∆M

H the market maker chooses to be informed and for

all ∆H > ∆MH the market maker chooses to remain uninformed. The monotonicity of the optimality

condition assures the uniqueness of this threshold.

B Econometric Methodology Details

The models are estimated by Panel Ordinary Least Squares, by introducing a dummy variable

for each stock (to control for stock fixed effect) and for each trader (controlling thus for trader

intercepts). Since in our sample we have 242 stocks and 262 traders, this is equivalent to introducing

504 new parameters. However, due to the fact that we have over 1 million observations over time,

this estimation is feasible from the point of view of the sufficiency of the degrees of freedom.

Compared to random effects models, fixed effects linear models have the primary advantage of

not making a strong exogeneity assumption of a random factor relative to the included regressors

(see for instance Hsiao (2003) and Baltagi (2008)). If the panel is long enough, this approach yields

consistent and efficient estimates provided the model is true, with very little assumptions.

The least squares dummy variable approach (LSDV) is not a parsimonious model, due to the large

number of parameters, but it is computationally easier than a maximum likelihood optimisation over

more than 500 parameters. On the other hand, for models that have a limited dependent variable

(such as the volume share sent to entrant markets), the OLS approach might yield inconsistent and

biased estimates. Hence, maximum likelihood approaches are necessary for this type of variables.

46

C Variable Definitions and Measurement

The list of variable short-names used throughout this paper is presented in the table below. This

section describes how these variables are computed and provides relevant literature to motivate the

choice for different measurements.

Variable definitions and short labels

Variable Short Name Definition Levels

Adverse Selection AS Adverse Selection component of the bid-ask spread SD, SDTVolatility Range σ intraday volatility using high/low price SD(Absolute) Trade Imbalance (A)TI (absolute) scaled difference buys - sells SDTAverage Trade Size AvTr Volume divided by number of trades SDTAgency Profile AgPr Ratio client volume / total volume SDTAverage Price P Volume-weighted trading price SDMarket Capitalisation MktCap Shares outstanding x average price SDAggressive Trading AGG market order volume in total volume SDTEffective Spread ES volume-weighted half-spread per stock-day SD

Security specific measures To the fragmentation metrics defined before, we define average

prices and market capitalisation for a particular stock. The average price traded during the day is

computed by taking all trade prices and weighting them by transactions volume; for a certain day t,

with effective trading times τ , we have:

Pt =

∑τ∈t (Priceτ ×Quantityτ )∑

τ∈tQuantityτ(51)

The market capitalisation of a stock (MkCap) is defined on a daily basis, by multiplying the

number of stocks outstanding with the average price during that day.

Measurement for daily return volatility There are 3 main measures for the intraday return

volatility in the finance literature, as reviewed in Patton (2011): the squared daily returns, the

realised volatility measure (seeAndersen, Bollerslev, Diebold, and Labys (2003)) and the intra-daily

range (first proposed by Parkinson (1980)). The squared daily returns is the most naive option of

the three, since it does not take into account the variation in prices during the day - it is possible

that, after wide fluctuations, the closing price is not very different from the opening price, which

would incorrectly lead to an estimated volatility smaller than the real value.

The realised volatility measure is defined as the sum of n squared returns computed from

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transaction prices over the day (RVt =∑n

i=1 r2it). This is an unbiased estimator of the true volatility

if the stock price follows a geometric Brownian motion (Patton (2011)) and has a lower variance

than the squared return. If the grid we are sampling prices from is fine enough, the realised volatility

comes arbitrarily close to the true volatility. However though, in the presence of microstructure

noise, the observed price is not equal to the true price process (there is a bid-ask bounce, since some

trades take place at the bid quote, others at the ask quote) - and the realised volatility measure can

thus overestimate the true volatility - see Alizadeh, Brandt, and Diebold (2002).

The volatility measure we choose to use in this paper is the scaled intra-daily range, defined as:

σt =1

2√

ln (2)ln

(supi {pit}infi {pit}

)(52)

The intra-daily range is considerably easier to compute - since we only need 2 prices for each

day: the highest and the lowest one. This is a unbiased estimator of the true volatility, just like

the realised volatility (the scaling factor 1

2√

ln(2)ensures unbiasedness under a geometric brownian

motion DGP for the prices). The efficiency is considerably higher than for daily squared return, and

close to the efficiency of realised volatility, computed with a 2 hour sampling interval (Andersen,

Bollerslev, Diebold, and Labys (2003)). Alizadeh, Brandt, and Diebold (2002) show that this

measure is more robust to the presence of microstructure noise, thus being potentially a superior

estimate in real-world situation.

This measure is computed both at individual stock level, from the EMCF dataset, as well as

market wide, using the OMX Nordic 40 index as a proxy for the Scandinavian markets.

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D Appendix: Snapshot of the dataset

Sample Data Snapshot. There are 8 possible platforms: XHEL (Nasdaq OMX Helsinki), XSTO(Nasdaq OMX Stockholm), XCSE (Nasdaq OMX Copenhagen), CHIX (Chi-X Europe), NURO(Nasdaq Europe), BATS (BATE Euope), QMTF (Quote MTF) and BURG (Burgundy). AGNTstands for client trade, whereas PRCP stands for principal (own trade). Dates are formated as1yymmdd, to facilitate comparison across decades (2009-2010).

Platform Time Date Price Quantity TraderID

Origin Buy/Sell Currency Symbol Maker/Taker

XHEL 90001 1090901 9.59 8300 150002 AGNT S EUR NOKI 1...CHIX 90014 1090901 9.57 724 140001 PRCP B EUR NOKI -1...BATE 101014 1101003 9.81 901 300001 PRCP S DKK MAERS 1

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