middlemen in limit-order markets1 - semantic scholar · 2015-07-28 · control sample as they had...

Electronic copy available at: http://ssrn.com/abstract=1624329

(preliminary and incomplete)

Middlemen in Limit-Order Markets1

Boyan Jovanovic and Albert J. Menkveld

first version: June 30, 2010

this version: May 19, 2011

1Boyan Jovanovic, Department of Economics, New York University, 19 West 4th Street, New York, NY, USA,tel +1 212 998 8900, fax +1 212 995 4186, [email protected]. Albert J. Menkveld, VU University Amsterdam,FEWEB, De Boelelaan 1105, 1081 HV, Amsterdam, Netherlands, tel +31 20 598 6130, fax +31 20 598 6020,[email protected] and TI Duisenberg School of Finance. We thank Robert Engle, Thierry Foucault,Phil Haile, Joel Hasbrouck, Terrence Hendershott, Johannes Horner, Charles Jones, Lasse Pedersen, Emiliano Pag-notta, and seminar or conference participants at the Autoriteit Financiele markten (AFM), Autorite Marches Financiers,Deutsche Borse, City U London, Dutch Central Bank, European Securities and Markets Authority (ESMA), KC FED,Universita Cattolica del Sacro Cuore, U Paris Dauphine, Queen Mary U, SED Meeting Montreal, St. Louis FED,and Yale for comments. We are grateful to both Euronext and Chi-X for acting as data sponsor and to Sean Flynnand Bernard Hosman for invaluable research assistance. Jovanovic thanks the Kauffman Foundation for support andMenkveld gratefully acknowledges Robert Engle for sponsoring him NYU visit in 08/11, VU University Amsterdamfor a VU talent grant, and NWO for a VIDI grant.

mailto:[email protected]

mailto:[email protected]

Electronic copy available at: http://ssrn.com/abstract=1624329

Abstract

Middlemen in Limit-Order Markets

A limit-order market enables an early seller to trade with a late buyer by leaving a price quote. But, public

news in the interarrival period creates adverse selection for the seller and therefore hampers trade. High-

frequency traders/machines (HFT) might restore trade by bringing the capacity to quickly update quotes

on news. A theoretical model shows that HFT entry can indeed increase welfare, but it might just as well

destroy it. Empirically HFT entry coincided with a 13% reduction in the effective bid-ask spread and an

unchanged trade frequency.

(for slides click http://goo.gl/RjzDt)

(for the internet appendix click http://goo.gl/xvQuN)

http://goo.gl/RjzDt

http://goo.gl/xvQuN

[insert Figure 1 here]

Successful entry of new limit-order markets has changed the industry of securities trading. Figure 1 illus-

trates how the NYSE had an 80% market share in its listed stocks in 2003, yet only 25% in 2011. Technology

facilitated the entry of cheap and fast electronic limit-order markets. BATS is an example of a successful

entrant market. It started in June 2005, picked up significant market share in 2007, and gradually grew to

a 10% share in 2011. Europe showed a parallel trend. Chi-X started in April 2007 and captured a 15%

market share in European equity trading. The London Stock Exchange, an incumbent, saw its market share

plummet from 30% in 2008 to 20% in 2011.

Coincidentally, high-frequency traders (HFTs) have become the most active participants in equity markets.

The Securities and Exchange Commission (SEC) published a policy document that refers to HFT as “one of

the most significant market structure developments in recent years. . . it typically is used to refer to profes-

sional traders acting in a proprietary capacity. . . characteristics often attributed to proprietary firms engaged

in HFT are. . . the use of extraordinarily high-speed and sophisticated computer programs for generating,

routing, and executing orders. . . very short time- frames for establishing and liquidating positions. . . ending

the trading day in as close to a flat position as possible. . . estimates of HFT volume in the equity markets

vary widely, though they typically are 50% of total volume or higher (SEC (2010, p.45)).”1 High-frequency

traders are therefore naturally thought of as middlemen in particular due to the proprietary nature of their

trading and the short holding period (milliseconds, seconds, minutes, or at most hours).

This paper studies how high-frequency trading might affect investor welfare in limit-order markets both

theoretically and empirically. A limit order is a pre-commitment to buy or sell a given amount of shares at

a pre-specified price. Limit orders arrive at the market and, if possible, are either matched with an existing

limit order or added to the stack of limit orders known as the limit order book (see Parlour and Seppi (2008)

for a survey). An important reason for the success of this type of electronic markets is that they provide a

cost-efficient way to match investors who are spaced out in time. In classic human-intermediated markets

such matching requires middlemen who need compensation (see, e.g., Grossman and Miller (1988)). In

limit-order markets matching seems possible without middlemen.

1The Committee of European Securities Regulators (CESR) published a similar discussion document where HFT is a focusarea; it solicits research as the HFT chapter’s title is: “The impact of High Frequency Trading (HFT) on market structure is still notfully understood (CESR (2010, p.31)).

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Trade in limit-order markets without middlemen is hampered by a winner’s curse if the late investor is likely

to be better-informed (inherent to being the late investor) on the (common) value of the asset than the early

investor. For example, there might have been a press release on the stock in the interarrival period. The

early investor’s limit order is adversely selected; it is more likely to execute if the information was good,

less likely if it was bad. A rational early investor is fully aware of such risk and prices in an ‘adverse

selection cost’ (see Glosten and Milgrom (1985)) which reduces the likelihood of trade and destroys social

value as some natural re-allocations from low to high private value investors do not happen.

A competitive sector of middlemen — high-frequency traders — might reduce the informational friction,

and thus improve welfare, as the nature of their operation is information technology driven. To the extent that

the information between two investor arrivals is hard, machine-processable information the early investor,

say a seller, might instead of submitting a limit sell order — thus effectively post a price — pass off him asset

to a middleman who can post a price and quickly update it on incoming hard information thus reducing the

adverse selection risk. Examples of hard information are price changes in the market index, same-industry

stocks, oil etc.2 The extent to which this alternative route to the late investor improves welfare is the central

objective of our study.

Middlemen might increase the informational friction if their hard information was unknown to the late

investor and there was therefore no winner’s curse to begin with (at least with respect to this type of infor-

mation). In this case middlemen destroy welfare. The model section of the paper provides a single unified

analysis of this ugly face of the middleman’s along with its friendly face discussed in the previous paragraph.

The model fills the empty intersection of the literature on middlemen in human-intermediated markets and

the literature on limit-order order markets without middlemen. The middlemen literature assumes an in-

formation asymmetry where, rather than better informed, middlemen are uninformed which was natural for

markets where humans intermediate (see, e.g., Glosten and Milgrom (1985) and Kyle (1985)). Foucault,

Roell, and Sandas (2003) introduce costly monitoring ability for liquidity suppliers and analyze optimal

intensity. The most related limit-order models analyze how adverse selection risk affects the choice of an

arriving agent to choose between a limit and a market order (see, e.g., Hollifield, Miller, Sandås, and Slive

(2006) and Goettler, Parlour, and Rajan (2009)). They do not consider the entry of middlemen.

The empirical part analyzes the advent of middlemen by exploiting the introduction of an HFT-friendly

2See Petersen (2004) for the distinction between hard and soft information.

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trading venue as an instrument. Chi-X started trading Dutch index stocks on April 16, 2007. Unlike the

incumbent market, Euronext, it did not charge limit order modifications, nor executions. Quite the contrary,

limit orders that led to execution received a rebate. The first 77 trading days of 2007 and 2008 are compared

to establish a ‘treatment’ effect. To control for time effects, Belgian index stocks serve as an ‘untreated’

control sample as they had not yet been introduced in Chi-X, yet were trading in Euronext under the same

rules as Dutch stocks.

Post Chi-X, a middleman has entered for Dutch stocks who trades primarily passive (i.e., through limit

orders). One new broker ID (not present in the pre-entry sample) trades very frequently — it is present

in roughly every third trade in Chi-X and in every twelfth trade in Euronext. It is particularly active on

days when most of a stock’s price movement is explained by the index — the R2 of a single-factor CAPM

explains 45% of time variation in middleman participation. What makes this broker an HFT, though, is

that its net position over the trading day is zero almost half of the sample days. A further finding is that

75-80% of its trades were passive. These observations provide empirical support for our theory which

characterizes middlemen as cost-efficient intermediaries. They minimize adverse selection cost by quickly

updating quotes on incoming hard information.

A diff-in-diff analysis (post- minus pre-entry, treated minus untreated) shows that middlemen entry is ac-

companied by an increase in liquidity supply, yet it did not change the number of trades. Post-entry realized

volatility is 64% higher for (treated) Dutch stocks, which is the same order of magnitude as the 69% higher

volatility for the (untreated) Belgian stocks. This is a reassuring result as it is unlikely that low-frequency

volatility is affected by HFT entry. The diff-in-diff analysis finds a significant 13% reduction in the effective

bid-ask spread, i.e., it increased 13% less for Dutch stocks as compared to Belgian stocks. The number of

trades appears to be unaffected by middlemen entry as it increased by a modest and insignificant 3% for

Dutch stocks relative to Belgian stocks.

The diff-in-diff results should be interpreted with care due to potential endogenous timing and selection

bias. Chi-X might have decided to start the system on April 16, 2007, and select Dutch stocks because

these stocks at that time showed particularly high activity and large spreads. If these were transitory effects,

the subsequent volume decline and spread reduction are to be expected irrespective of HFT entry. We

plan to study the size of transitory effects to verify whether (i) timing was indeed endogenous (spread and

volume were temporarily high on April 16, 2007) and (ii) whether the size of these effects could explain the

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magnitude of the reported treatment effect.

The empirical findings add to a growing literature on high-frequency trading. Brogaard (2010) studies

trading of 26 NASDAQ-labeled HFT firms in the NASDAQ market in 2008-2010. In the aggregate, he

concludes that HFT tends to improve market quality. Kirilenko, Kyle, Samadi, and Tuzun (2010) study the

behavior of high-frequency traders in the E-mini S&P 500 stock index futures on May 6, the day of the flash

crash. Menkveld (2011) provides an in-depth empirical analysis of a high-frequency trader’s profitability

through a decomposition of its trading revenue and an analysis of the capital tied up in the operation through

margin calls.

The paper also fits into a broader literature on algorithmic or automated trading. Foucault and Menkveld

(2008) study smart routers that investors use to benefit from liquidity supply in multiple markets. Hen-

dershott, Jones, and Menkveld (2011) show that algorithmic trading (AT) causally improves liquidity and

makes quotes more informative. Chaboud, Chiquoine, Hjalmarsson, and Vega (2009) relate AT to volatil-

ity and find little relation. Hendershott and Riordan (2009) find that both AT demanding liquidity and AT

supplying liquidity makes prices more efficient. Hasbrouck and Saar (2010) study low-latency trading or

“market activity in the millisecond environment” in NASDAQ’s electronic limit order book ‘Single Book’

in 2007 and 2008 and find that increased low-latency trading is associated with improved market quality.

More broadly, our findings contribute to the literature on middlemen in search markets. In Rubinstein

and Wolinsky (1987) and Masters (2007) middlemen may improve allocations because they speed up the

meeting process. Rents are divided via Nash bargaining. Hosios condition and optimality obtain when

numbers are endogenous. In our model, however, market participation is exogenous. Our paper is closer to

Li (1996) in which where middlemen have an advantage in terms of information in a lemons model. The

contrast is (i) that the quality of the traded good is exogenous, and (ii) that the information is not about

independent values but, rather, common values, which we believe to be at the heart of evaluating welfare

effects of HFTs who specialized in speed to minimize being adversely selected on public information. A

unique feature of limit order markets is that late investors cherry pick take-it-or-leave-it offers (i.e., limit

orders) of early investors, leaving the latter with a winner’s curse problem. Closer to home are models on

search in decentralized markets, e.g., Duffie, Garleanu, and Pedersen (2005), Lagos, Rocheteau, and Weill

(2009), and Duffie, Malamud, and Manso (2009).

The remainder of the manuscript is structured as follows. Section 1 develops the model. Section 2 presents

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empirical results. Section 3 concludes.

1 Model

The model features two investors who are spaced out in time: an early-arriving (potential) seller (S) who

owns the asset and a late-arriving (potential) buyer (B) who does not own the asset (cf. Grossman and Miller

(1988)). Eventually middlemen or machines (M) are introduced which, by their very nature, can stay in the

market indefinitely (i.e., at no cost). The agents (S, B, and M) have available to them a limit order market to

potentially effectuate a trade and therefore a transfer of the asset. All agents in the model are risk-neutral. An

overview of all notation and what the various variables are a modeling device for is included as Appendix I.

S values the asset at x+ z, and B values it at y+ z. The private values x and y are drawn independently from a

common distribution with CDF F. The common value (innovation) z is drawn from a distribution with CDF

G.

The common value z is itself composed of two independent components:

z = zh + zs

The superscripts denote machine-processable ‘hard’ information and its complement, ‘soft’ information (cf.

Petersen (2004)).

The game may also include a number of middlemen or machines (M) that all have a zero private value for

the asset. In other words, each M’s valuation of the asset is just z. M always know zh because they can track

this machine-processable information at high frequencies. They do not know zs which, by its very nature,

requires human skill to process. It is important to note that machines have zero opportunity cost and are

therefore assumed to always be in the market (unlike S or B for whom it is costly to stay in the market).

The two components are, by definition, orthogonal which implies that σ2z = σ

2h + σ

2s . Let

α Bσ2

h

σ2h + σ

2s

(1)

denote the relative importance of hard information.

5


The informational structure of the game is depicted in Panel A of Figure 2. Private values are observed

only by the agents themselves. The hard common value zh is always observed by the middlemen, but only

observed with probability λ by the buyer. The buyer is more likely to be informed on common values than

the seller by the mere virtue of arriving late. The soft common value zs is observed only by the buyer.

1.1 The game without middlemen

This section develops the structure of the game in which M are absent. The game consists of two periods:

1. S observes (only) x, posts an ask ps (x), and leaves.

2. B arrives, observes y and zs, and observes zh with probability λ. This probability of observing zh is

independent of zh and zs.

Note that a bid by B is excluded as by the time that B can post it, S is gone.

As S can only condition him ask price p on him private value x, this price is uncorrelated with z and both of

its components. B accepts iff y + z > p with probability λ

y + zs > p with probability 1 − λ(2)

In the event of a sale, S receives p. On the other hand, if z ≤ p − y, S receives x + z. Conditioning on y, S’s

expected return is:

λ

(p[1 −G (p − y)

]+

∫ p−y

−∞(x + z) g (z) dz

)+ (1 − λ)

(p[1 −Gs (p − y)

]+

∫ p−y

−∞(x + z) gs (z) dz

)(3)

where

g (z) =∫ ∞

−∞gh (

z − z′)

gs (z′) dz′ (4)

is the density of z, gh is the density of zh, and gs the density of zs.

Note that in the process B conditions on z and which creates a winner’s curse for S. That is, if him ask quote

is ‘successful’ and wins a trade he is cursed as, conditioning on the event of a trade the expectation of z is

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positive. She is more likely to sell on good news (positive z) than on bad news (negative z). The seller is

adversely selected by the buyer.

Evidently, (3) makes S optimally choose p as follows:

v(x, gλ

)≡ max

p

∫ ∞

−∞

[p[1 −Gλ (p − y)

]+

∫ p−y

−∞(x + z) gλ (z) dz

]dF (y) (5)

where, for all z, Gλ B λG + (1 − λ) Gs and gλ B λg + (1 − λ) gs.

When is the winner’s curse absent? The winner’s curse is absent in two situations which differ in

what they imply for the role of an informed M. First, there may be no common value of either type, i.e.,

σ2z = σ

2h + σ

2s = 0. In this straightforward case M neither help nor hurt – they are irrelevant and would not

be able to make money by trading, as will be shown in the next subsection.

More significant, however, is the case

σ2s = λ = 0, coupled with σ2

h > 0 (6)

In this case, only zh matters and neither S nor B is aware of it. There is therefore no adverse selection

problem in the market to begin with; the decision rule (2) reduces to ‘ buy iff y > p’, and (5) reduces to

maxp

{p[1 − F (p)

]+ xF (p)

}(7)

If M is not in the market, the ask price that maximized this expression would be an equilibrium.

How M might introduce a winner’s curse. Potential entry by a single M dramatically changes the

equilibrium, provided that S and B are aware of M’s presence in the wings. When σ2h > 0, any equilibrium

– and particularly the equilibrium implicit in (7) – is vulnerable to entry of M who, knowing zh, would wish

to buy the security whenever zh > p, leaving S or B with the security in states where zh < p and creating,

in other words, a winner’s curse problem for both S and B. An opportunistic M can thus reduce welfare by

placing market orders in states that favor him.

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1.2 The game with middlemen

High-frequency traders are most realistically modeled as a sector of competitive middlemen. This setting is

therefore very different from what was described in the previous paragraph. Competition forces M to place

limit orders to buy (i.e., bid prices) of their own. These bids are not vulnerable to a winner’s curse caused

by zh because M all know zh and can incorporate its realization into their bids. Indeed, it will turn out that

competitive M will help most when σ2h is large relative to σ2

s , which is to say when α in equation (1) is large.

The game is set up to reflect the fact that S is (i) slow and (ii) cannot stay in the market (at zero cost).

Therefore S can only take one action while he is in the market, i.e., he can either post an ask or accept a bid.

Panel B of Figure 2 graphically illustrates the following sequential structure of the game:

Period 1. S arrives and can take only one action: either post an ask or accept a bid.

1. S observes x and (maybe) posts an ask pS . Simultaneously, M post competitive bids.

2. If S did not post an ask he can accept a M bid. If he rejects it, the game ends.

3. If S did post an ask (and therefore foregoes being able accept an M’s bid), the M accept or reject it.

4. S leaves

Period 2. B arrives.

1. B observes zh that is revealed through M’s bids. B also observes y and zs.

2. If M bought the asset from S, he now tries to sell it to B.

3. If the M rejected the ask that S posted, the ask is now available for B, and B takes it iff y + z > pS .

Under these assumptions, we shall now show that M compete each other out of all rents that might be

derived from knowing zh and from being fast. Competitive bids by M in period 1.1 allow both S and B to

infer zh and, as a result, unless S has posted an ask, the adverse selection on zh disappears.

One consequence of this is that, regardless of λ, B is able to get information on zh and therefore gets to know

both components of z. The parameter λ thus affects only the game in which M are absent.

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1.2.1 The second period sub-game between M and B

As B infers zh from competitive bidding by the middlemen in period 1, this hard information is common

knowledge between them in the period 2 subgame when M owns the asset and posts an ask price for B. B

takes this ask price pM(zh), shortened to pM , and trade occurs iff

y + zs + zh > pM (8)

Now let

p B pM − zh (9)

Then trade takes place if

zs > p − y (10)

So M’s value of holding the security is

zh + vM

where

vM ≡ maxp

∫ ∞

−∞

[p[1 −Gs (p − y)

]+

∫ p−y

−∞zgs (z) dz

]dF (y) (11)

That is, M faces a winner’s curse itself induced by B’s privately knowledge of zs. As the size of soft

information (σ2s) grows, M’s value of holding the asset (vM) tends to zero.

Lemma 1

vM = v(0, gs)

Proof. The RHS of (5) and the RHS of (11) differ only with respect to the distribution gλ (z) on the one hand

and gs (z) on the other. It is, in other words, the same function of g.

1.2.2 The first period choice for S to post an ask price or not

S knows neither zs nor zh. Posting an ask price in period 1 therefore exposes him to a winner’s curse on

common value components (as will be shown below in equation (16)). Therefore he may prefer not to post

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an ask as it avoids the winner’s curse. She cannot avoid it altogether as even instead of posting accepting

M’s bid exposes him indirectly to a winner’s curse over zs because M are exposed to it and their bid will

reflect that exposure. M’s exposure reduces vM in the formulas below, when the size of soft information

(σ2s) increases. Let us compare him expected payoff under the two strategies.

If S does not post an ask. In this case S essentially avoids a zh winner’s curse on him ask price (as there

effectively always is a zs curse that he is exposed to). Instead, he has the option to accept a middleman’s bid

which we expect to be a particularly attractive option if the size of hard information (σ2h) is relatively large.

If S does not post an ask, he rationally anticipates the competitive M’s bid to be:

pM = zh + vM

which reveals zh to him.3

Now S has the option to accept or reject. Now aware of zh he accepts the bid iff

x + zh + E(zs) < zh + vM ⇔ x < vM (12)

as E (zs) = 0. M therefore obtains the asset iff (12) holds and thus with probability:

F(vM

)(13)

When deciding whether or not to post an ask S does not know zh. If he decides not to post an ask, S’s

expected utility conditional on x is:

U (x) ≡ max(x, vM

)(14)

Differentiating U (x) for x , vM yields:

U′ (x) = I{x>vM} = Pr (no trade | x) (15)

3Note that S observing M’s bid, turning around, and posting an ask price himself is explicitly ruled out. The reason is S is tooslow for two actions. This is modeling device to capture a machine’s ability to process vast amounts of information quickly andupdate ask quotes to avoid the winner’s curse. If S willingly passes off the asset to the middleman he essentially buys its ability toavoid the curse on hard information.

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where I{.} is the indicator function.


Figure 3 illustrates U (x), the value to S of not posting.

If S does post an ask. In this case S fully exposes himself to the winner’s curse. We expect this option to be

particularly attractive when the size of hard information (σ2h) is small. The value of this option is developed

in this subsection and graphed as V (x) in Figure 3.

Let us first discuss the special case of no hard information (σ2h = 0). S is now able to extract the same rents

from B as M could in the second-period subgame; he collects vM in expectation. The conjectured value

graph of posting an optimal ask is depicted in Figure 3 as V(x | σ2h = 0). It crosses the vertical axis exactly

at vM. We therefore conjecture that the strategy post is better for S than not-post for private values x ≥ 0.

As for the general case with hard information, if S posts an ask pS (x) it will be accepted if either a M or the

B values the security more, i.e., if:

pS (x) < max(zh + vM, y + zs + zh

)= zh +max

(vM, y + zs

)≡ zh + ϕ

(y + zs) (16)

M can act before B arrives and they therefore have the first take on the offer. When pS < zh + vM, any M

that is lucky enough to snap up the offer makes positive expected rents. Thus if pS is in the money for M,

one of them will snap it up. If, however, pS > zh + vM then the ask pS remains in the order book and is

available for B when he shows up. B will accept the offer if pS < y + zs + zh.

Leading up to S’s optimization problem, condition (16) is more easily expressed as:

zh > p −max(vM, y + zs

)

11

Anticipating these optimal responses by M and B, S chooses pS to solve:

V (x) ≡ maxp

∫ p[1 −Gh

(p −max

(vM, y + zs

))]+∫ p−max(vM ,y+zs)

−∞

(x + zs + zh

)dGh

(zh

) dGs (zs) dF (y) (17)

Differentiating (17), using the envelope theorem, and simplifying yields:

V ′ (x) = Pr(zh + ϕ

(y + zs) ≤ pS (x)

)> 0 (18)

where pS (x) is the optimal policy for S and V is convex.

This expression is completely analogous to (15); the derivative V ′ (x) is equal to the probability of no trade

conditional on x. More explicitly:

V ′ (x) =∫

Gh (ps (x) − ϕ (y + zs)) dGs (zs) dF (y) (19)

Moreover, limx→∞ V ′ (x) = 1 and V ′ (x) < 1 as illustrated in Figure 3.

If pS (x) is differentiable, we may use the chain rule to conclude that

V ′′ (x) =∂pS (x)∂x

·∫

gh (ps (x) − ϕ (y + zs)) dGs (zs) dF (y) > 0

because (still to be shown), pS is strictly increasing in x.

S’s decision whether or not to post. This choice problem is illustrated in Figure 3. The optimal decision

depends on x. S posts iff

V (x) ≥ U (x) (20)

Let

A = {x | (20) holds} (21)

be the set of private values x for which S posts an ask price.

As V (x) > x, (20) holds for x = vM . Therefore the intersection of V and U occurs at a value of x below vM.

Moreover, (19) shows that V ′ > 0 any intersection of U and V therefore must:

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1. be unique and

2. occur at a value of x, say a, that is smaller than vM in which case it satisfies

vM = V (a) (22)

The set A therefore is:

A = {x | (20) holds} = [a,∞)

Finally, since V (x) > x, (22) implies that

x < A⇒ x < vM

which proves

Proposition 1 If S does not post then S accepts M’s bid with probability 1.

This proposition effectively removes the lowest branch of the tree depicted in Panel B of Figure 2.

1.3 The model’s implications for how middlemen presence affects the trading game

This section develops the implications of the presence of middlemen in the trading game between S and B.

It is focused on the number of trades, the distance between transacted bid and ask prices (referred to as the

‘effective bid-ask spread’), and most importantly welfare. The trade and price implications are developed

in order to calibrate the model to the data. Also, the conjectured relationship of more active middlemen on

relatively more hard information as opposed to soft information (i.e., a higher α) is developed as it will be

tested in the data (see, e.g., Figure 8).

1.3.1 The game without middlemen

Trades. The expected number of trades in the case without middlemen is:

TNM =

∫ ∞

−∞

∫ ∞

−∞

(1 −Gλ

[pS (x) − y

])dF (x) dF (y)

13

Effective bid-ask spread. In the game without M there are no bids, there is only an ask pS (x) which solves

(5). A bid can be obtained, however, if the arrivals of S and B are reversed where the late investor (now S)

retains the informational advantages. Let pB (y) denote B’s bid then the bid-ask spread is naturally defined

as:

Spread =∫ ∞

−∞pS (x) dF (x) −

∫ ∞

−∞pB (y) dF (y) (23)

In an internet appendix — the http address in on the abstract page — it is shown that with symmetry of the

densities f , gh, and gs one obtains the following result:

Proposition 2 For (x, y) satisfying F (x) = 1 − F (y):

pS (x) − x = y − pB (y) (24)

Spread = 2∫ ∞

−∞

[pS (x) − x

]dF (x) (25)

A standard measure in data analysis is the effective spread which effectively samples the bid-ask spread only

at the time of trade. The model equivalent for this ex-post measure interacts the bid or ask price quote with

a trade dummy and sums over (x, y, z):

Effective spread =1

TNM

∫ ∞

−∞

∫ ∞

−∞

[pS (x) − x

] (1 −Gλ

[pS (x) − y

])dF (x) dF (y) .

Welfare. Welfare in this case is the expectation of the sum of each investors private value interacted with a

dummy that is one if the investor is the final owner, zero otherwise:

WNM = E(xI{S owns} + yI{B owns}

)(26)

=

∫ ∞

−∞

(∫ ∞

−∞

[xGλ

[pS (x) − y

]+ y

(1 −Gλ

[pS (x) − y

])]dF (x) dF (y)

)

The common value z drops out as it is zero in expectation. It is not as innocuous as it seems as it drives who

ultimately ends up holding the asset.

14

1.3.2 The game with middlemen

Trades. If S posts an ask price (i.e., x ∈ A), M has the first take on it (as M is fast) and gets the asset iff the

price is below M’s reservation value, i.e., iff:

pS < zh + vM (27)

As pS (x) is strictly increasing in x and thus invertible, the probability that M gets the asset is:

F[(

pS)−1 (

zh + vM)]≡ qS M (28)

where(pS

)−1denotes the inverse function of pS (x). This expression mirrors (13).

If S posts an ask (x ∈ A), the number of trades is:

TA(x, y, zh, zs

)=

0 if pS (x) > max(zh + vM , y + zh + zs

)1 if

pS (x) > zh + vM and pS (x) < y + zh + zs or

pS (x) < zh + vM and pM > y + zh + zs

2 if pS (x) < zh + vM and pM < y + zh + zs

(29)

If S does not post an ask (x < A), the number of trades is:

TÃ(x, y, zh, zs

)=

0 if x > vM

1 if x < vM and pM > y + zh + zs

2 if x < vM and pM < y + zh + zs

(30)

The expected total number trades therefore is:

TM = E (TA + TÃ)

=

∫(TA + TÃ) dF (x) dF (y) dGh

(zh

)dGs (zs)

which is the (unconditional) expectation over the four mutually independent shocks. The only trades that M

do not participate in are those for zh + vM < pS (x) < y + zh + zs.

15

Effective bid-ask spread. The only bids in the game with M are those by M in the first period of the game.

They all bid zh + vM where vM is given by the LHS of (11). The average ‘effective’ bid is therefore:

pbid = vM (31)

as trade does not depend on zh.

The game features three potential ask prices:

1. pask = pM if x < A, M’s ask price solves (11),

2. pask = pS (x) if x ∈ A, S’s ask price solves (17),

3. pask = pM if x ∈ A and the first ask price is snapped up by M which then posts the ask pM for B.

The set A does not depend on zh; the selection therefore is only on x. The effective ask is now obtained by

averaging these ask prices multiplied by a trade event dummy over(x, zh

):

pask =1

TM{pF (a)

[1 − F (p)

]+

∫ [∫ ∞

apS (x) I{pS(x)<zh+max(vM ,y+zs)}dF (x)

]dF (y) dGh

(zh

)dGs (zs)

+

∫ [∫ ∞

a

(pM + zh

)I{pS (x)<zh+vM ∩ pM<y+zh+zs}dF (x)

]dF (y) dGh

(zh

)dGs (zs) } (32)

where p is defined in (9) for E(pM

)= p. The top line of (32) captures sales by S to either M or B; the

bottom line captures sales by M to B.

The effective bid-ask spread in the game with M therefore is:

Effective Spread = pask − vM

Welfare. The common value z drops out again from the welfare equation but its two components critically

determine who ends up owning the asset. Welfare itself is a weighted average of welfare in the event that S

posts (x ∈ A) and welfare in the event that S does not (x < A). The second case is easier, so we start with it.

16

The contribution to expected welfare of x < A is:

WNP ≡∫{∼A∩(zh+vM ,∞)}

xdF (x) +∫{∼A∩(−∞,zh+vM)}

dF (x)∫ ∞

−∞

(∫pM−zs

ydF (y))

dGs (zs) (33)

where pM is defined in (11). If M ends up with the asset welfare is zero.

In the case that S posts an ask (x ∈ A) welfare is:

WP ≡∫{A∩(pS (x)>max(zh+vM ,y+zs+zh))}

xdF (x) +∫{A∩(pS (x)<max(zh+vM ,y+zs+zh))}

dF (x) D

where D is the welfare obtained if S parts with the asset. Once again, if M ends up with the asset welfare is

zero. In fact, welfare y is collected in one of following two mutually exclusive events:

(pS (x) ≤ zh + vM and y + zs + zh ≥ pM

)≡ D1

(x, y, zh, zs

)with p defined in (9) or:

zh + vM < pS (x) ≤ y + zs + zh ≡ D2(x, y, zh, zs

)Therefore:

D =∫

D1∪D2

ydF (x) dF (y) dGh(zh

)dGs (zs)

The welfare for the case with middlemen is becomes:

WM = WP +WN P

1.4 Parameter choices and the welfare effect of middlemen

This section first calibrates parameters to fit salient features of the data and uses these to discuss the welfare

effect of middlemen.

1.4.1 Parameter choices

Private values are chosen to be normally distributed, i.e., x, y ∼ N(µ, σ2).

17

The private-value dispersion parameter σ. Private value variance is fixed at π to fix the first-best welfare

gains from trade to one. That is, relative to autarky, the expected gains from trade among S and B equal one

unit. Therefore all variables will be measured in ‘gain-from-trade’ units.

The variance parameter π is obtained as follows (cf. Clark (1961, equation (2))):

E max (x, y) − E (x) = µ +σ√π− µ (34)

The mean private value parameter µ. The welfare analysis compares the regime with M to the one

without M. The introduction of M might ‘artificially’ raise welfare as a zero-private-value agent is added

to the trade economy. That is, the social planner would assign the asset to M in case both S and B are on a

negative private value draw. To suppress this effect µ is chosen to make this a small probability event, i.e.,:

Pr {max (x, y) < 0} = F (0)2 =

[Φ

(− µσ

)]2= 0.01 (35)

where Φ is the standard normal CDF. As the private value variance was set to π this implies: µ = 2.27.

The relative size of hard information parameter α. The total common value innovation is measured in

the data as the long-term price change in between trades. A proxy for how much of this is hard information

is ‘hard’ is obtained by identifying the part that is correlated with a change in the index futures midquote in

the same time interval (although, admittedly, this is a lower bound as M might exploit other correlated price

series). Essentially, the relative size of hard information is the R2 of a regression of stock return on the index

return (for details we refer to the discussion of Table 4. Panel B of Table 4 implies: α = 4.02/9.47 = 0.42.

The relative size of common value versus private value θ (and therefore σ2z ). As private value variance

σ2 was fixed at π the common value variance is best described as its size relative to private value variance

which is captured by the parameter θ:

θ :=σ2

z

π

The parameter θ is estimated in two ways. One way is based on one of the strongest empirical results which

is that middlemen particicpation increases with the relative size of hard information (cf. Figure 8). The

18

slope of the fitted least-squares line is: 0.10. The model equivalent of middlemen participation τ is:

τ :=TM −

∫ [∫A I{pS (x)>zh+vM and pS (x)<y+zh+zs}dF (x)

]dF (y) dGh

(zh

)dGs (zs) ,

TM(36)

The parameter θ is estimated as the solution to:

θ1 = arg minθ

(τ (θ, α = 1) − τ (θ, α = 0) − 0.10)2

The model-implied relationship between M participation and θ is plotted as the top graph of Figure 4.

A second way to estimate θ is to fit the markup charged by S relative to adverse selection component in

the regime without M. In the data, the period without M identifies this markup as the ratio of the effective

spread and its adverse selection component which is, on average, 2.61/1.89=1.38 in the pre-event period (cf.

Table 6). The parameters (θ,λ) for which the model-implied relative markup equals the observed markup

are established as the solution to:

(θ2, λ) = arg minθ,λ

E(pS (x) − x | y + zλ > pS (x)

)E

(zλ | y + zλ > pS (x)

) − 1.38

2

(37)

subject to zλ having the CDF

Gλ = λN(0, σ2

z

)+ (1 − λ) N

(0, ασ2

z

)which is a mixture of two normal distributions where α = 0.42 (cf. earlier discussion).

The complete list of parameter choices is summarized below.

pre-set estimated

parameter µ σ2 α θ1 (θ2,λ)

value 2.27 3.14 0.42 0.27 (2.63,0)

1.4.2 How middlemen affect welfare

This section discusses how the entry of middlemen affects welfare in the trading game between S and B.

It first discusses how they might improve welfare by assuming maximum information asymmetry between

19

S and B to begin with, i.e., setting λ = 1. It then analyzes how they might destroy welfare by potentially

creating adverse selection rather than solving it, i.e., λ < 1.

How might M improve welfare? The effect of middlemen entry is analyzed by plotting welfare for the

regime with middlemen against welfare in the regime without middlemen. It is plotted as a function of

either the relative size of hard information in total common value information, α, and as a function of the

relative size of common value variation vs. private value variation, θ. Generally, we find that the entry of M

increases welfare in both these parameters (as expected), α and θ, but increasing θ raises the welfare increase

more than increasing α.

Let us now discuss the effect of each parameters in turn.


Raising α. The bottom panel of Figure 4 graphs the realized gains from trade (welfare) as a function of

α where θ is kept fixed at its estimate of 0.27(= θ1). The green dashed line shows the first-best gains from

trade which is slightly above one (which is to be expected given the introduction of M as a third agent,

see discussion of (34)). A comparison of the top and bottom panels of Figure 4 shows that M participation

is correlated with welfare, as is to be expected. The gains are positive but small – about two percent of

maximum welfare — and they rise only slightly with α.


Raising θ. Figure 5 shows that M participation (top panel) and the welfare gains due to M entry (bottom

panel) both increase with θ.

How might M reduce welfare? Figures 4 and 5 show a uniformly positive effect of M on welfare, which

begs the question of whether there are parameter values for which the entry of M destroys welfare. Prima

facie, the model might generate a welfare-reducing effect of M only when λ is close to zero, which is to say,

only when B is unaware of zh in which case there is no adverse selection unless M is in the game.

When θ rises, the markup (pS (x) − x) rises in order to undo the increase in adverse selection. We generated

a version of Figure 5 in which, when increasing θ, we simultaneously reduce λ so as to keep the absolute

20

informational advantage of B constant in the no-M regime. Figure 5 conditions on hypothetical values of

θ and evaluates welfare in the absence of M under the value of λ that produces the closest model fit to the

criterion in the RHS of (37). Let welfare without M be defined as w (θ, λ) , and let welfare with M be defined

as w (θ). Note that the parameter λ does not affect outcomes in the M regime because B can reverse-engineer

zh from the bids by M in the first period. Figure 6 plots w (θ, λ (θ)) , w (θ) where

λ (θ) := arg minλ

(RHS of (37))

s.t. z ∼ λN (0, θπ) + (1 − λ) N (0, αθπ)

This calculation answers the question: Given a hypothetical amount of total adverse selection (θπ), what

information structure (λ) among buyers matches best the markup charged relative to the adverse selection

that an uninformed seller faces in the game without M?


Figure 6 shows that θ has to be high before M actually harm welfare. For these θ’s we find that λ(θ) = 0

which means that if M is absent there is no adverse selection. As a result, welfare does indeed become

higher for the no M regime. However, the estimated θs or, rather, the range of θs that our estimates imply

as being reasonable all suggest a positive role of M. The two estimates of θ implied by the values of σ2z (1)

and σ2z (2) in the above Table are θ1 = 0.27 and θ2 = 2.63 respectively. For θs in that range, the effect of M

on welfare is positive as Figure 6 shows.

2 Empirical results

2.1 Background

The European Union aimed to create a level playing field in investment services when it introduced the

Markets in Financial Instruments Directive (MIFID) on November 1, 2007. For markets, MIFID created

competition between national exchanges and it allowed new markets to enter.

21

Instinet pre-empted MIFID when it launched the trading platform Chi-X (Chi-X) on April 16, 2007, for

Dutch and German index stocks.4 At the end of 2007, it allowed a consortium of the world largest brokers to

participate in equity through minority stakes.5 Before Chi-X Instinet had successfully introduced the product

as ‘Island’ in the U.S. which distinguished itself from others through fast-execution and subsidization of

passive orders (see fee discussion below). Eventually Instinet sold the U.S. license to NASDAQ but kept the

international license which led to Chi-X.

In the first 77 trading days of 2008, our sample period, Chi-X traded British, Dutch, French, German, and

Swiss local index stocks. It had captured 4.7% of all trades and was particularly strong in Dutch stocks with

a share of 13.6%. Volume-wise, Chi-X overall market share was 3.1% and its Dutch share was 8.4%. Chi-X

started off particularly strong for the stocks studied in this manuscript.

Prior to Chi-X entry, Euronext was by far the main venue for trade in Dutch stocks. Its trading platform ran

in much the same way as the Chi-X platform and competition focused on fees and speed (see discussion

below). Dutch stocks also traded as ADRs in the U.S. and in the Xetra system run by the German Stock

Exchange. They did not yet trade in NASDAQ OMX, Turquoise, or BATS-Europe which entered later on a

business model similar to Chi-X: subsidies on passive orders and a fast system.

The broker identified as a middleman in this study was a substantial participant in Chi-X. In our sample

period, it participated in 10.8 million of the 99.2 million Chi-X trades. It was particularly active in Dutch

stocks with participation in 1.7 million out of 8.6 million Chi-X trades.

Fee structure. In our sample period, Chi-X did not charge for limit order submissions and cancellations.

Quite the opposite, it paid 0.2 basis points if the order becomes the passive side of a trade. If however

the order is ‘marketable’ and executes against a standing limit order upon arrival it gets charged 0.3 basis

points. For example, in the stock of limit sell orders in the book, the one with the lowest price becomes

the prevailing ‘ask’ quote. If a limit buy order arrives with a price (weakly) higher than this ask price, it

immediately executes against this limit sell and a transaction is recorded. For simplicity, in this example

it is assumed that orders are of the same size. For a detailed description of the generic limit-order market

mechanism we refer to Biais, Hillion, and Spatt (1995).

4“Chi-X Successfully Begins Full Equity Trading, Clearing and Settlement,” Chi-X press release, April 16, 2007.5These brokers were: BNP Paribas, Citadel, Citi, Credit Suisse, Fortis, Getco Europe, Ltd, Goldman Sachs, Lehman Brothers,

Merrill Lynch, Morgan Stanley, Optiver, Societe Generale and UBS (op. cit. footnote 7).

22

Euronext on the other hand charges a fixed fee of e1.20 per trade which for an average size trade of

∼e25,000 (see Table 1) is effectively 0.48 basis points. Highly active brokers benefit from volume dis-

counts that can bring the fixed fee down to e0.99 per trade (∼0.40 basis points). In addition, Euronext

charges an ‘ad valorem’ fee of 0.05 basis points. The act of submitting an order or cancelling it is not

charged (i.e., only executions get charged without an aggressive/passive distinction). But, if on a daily basis

the cancellation-to-trade ratio exceeds 5, all orders above the threshold get charged a e0.10 fee (∼0.04 basis

points).

In terms of post-trade costs, Chi-X clears and settles through EMCF which claims to be over 50% cheaper

than other European clearing houses including the ones used by Euronext.6

System speed. In a April 7, 2008 press release Chi-X celebrates its first anniversary. It claims to run one

of the fastest platforms in the industry with a system response time (often referred to as ‘latency’) of two

milliseconds. This is “up to 10 times faster than the fastest European primary exchange.”7

Overall, Chi-X appears to be particularly friendly venue for the middleman type that is central to the theory.

Its fees are lowest across the board and particularly low for a strategy that relies on passive orders that get

cancelled and resubmitted upon the arrival of public news. Its speed advantage allows one to do so quick

enough in order not to be picked off.

2.2 Data, Approach, and Summary statistics

Data. The main sample consists of trade and quote data on Dutch index stocks for both Chi-X and Euronext

from January 1 through April 23, 2008. The quote data consist of best bid and ask price and the associated

depth. The trade data contain transaction price, size, and an anonymized broker ID for both sides of the

transaction. The broker ID anonymization is done for each market separately and broker IDs can therefore

not be matched across markets — say the first market uses 1,2,3,. . . and the second one uses a,b,c,. . . . The

time stamp is to the second in Euronext and to the millisecond in Chi-X. In the analysis, Chi-X data is

aggregated to the second in order to create a fair comparison across markets.

In a final analysis we aim to identify the net effect of middlemen introduction through a difference-in-

6See, “EMCF cuts clearing fees”, The Trade News, 4/24/08.7“Chi-X Europe Celebrates First Anniversary,” Chi-X press release, April 7, 2008.

23

difference analysis (see Section 2.6). The instrument is essentially the introduction of Chi-X and the advent

of the identified middleman to the market. A first step in identifying such effect is to collect and analyze

the exact same data for Euronext in the first 77 trading days in 2007 when there was no Chi-X, nor was the

middleman broker ID active in the Euronext data (comparing the same period in 2007 and 2008 avoids the

impact of calendar effects).8 This is the ‘treated’ sample. To control for all that changed comparing 2007

with 2008, Belgian index stocks are analyzed as the ‘untreated’ sample as Chi-X had not yet been introduced

(as a matter of fact, Chi-X introduced Belgian stocks on April 24, 2008 which motivates the choice of our

main sample period). Other than the absence of Chi-X, Belgian stocks traded in the same way as Dutch

stocks as Euronext operated its trading system across its four markets (Belgium, France, the Netherlands,

and Portugal). In terms of the actual data, the Belgian sample only differs from the Dutch sample in that it

lacks broker IDs on transactions.

The list of all stocks that are analyzed in this study is included as an appendix. It contains security name,

isin code, and weight in the local index.

Finally, a dataset with quotes from the highly active index futures market is used to track changes in both

the Dutch AEX index AEX and the Belgian BEL20 index.

Approach. The analysis was done in two steps (i) to make it feasible (the entire dataset contains roughly

100 million event records) and (ii) to do proper statistical inference. The first step calculates all variables of

interest for each stock-day. For example, it calculates the time-weighted quoted half spread (ask minus bid

divided by two) for Heineken on January 2, 2008. To make activity measures comparable across stocks, we

convert, e.g., the number of shares traded to aeamount by multiplying it with the average transaction price in

the sample period. The second step is a panel data analysis on the ‘box’ with all stock-day results. Standard

errors are based on residuals that are clustered by day so as to avoid ‘double counting’ in the presence of

commonality and to explicitly recognize heteroskedasticity. The results are presented as weighted-averages

across stocks where the weight corresponds to the stock’s weight in the local index (see appendix with the

list of all stocks). Also, results are reported separately for large and small stocks where the cutoff is the

median index weight.

[insert Table 1 here]8This makes the pre-entry period run through April 20, 2007. This appears at odds with the Chi-X effective date of April 16,

2007, but in the data no trade materialized in the Chi-X system until after April 20, 2007.

24

Summary statistics. Table 1 presents summary statistics to illustrate Chi-X role in the trading of Dutch

stocks. It leads to a couple of observations.

1. Chi-X managed to obtain a nontrivial market share within one year of its existence. Chi-X’ share of

overall volume is 8.4% its share of trades is 13.6%. Its performance is particularly strong for large

stocks.

2. The use of Chi-X in addition to Euronext leads to a substantial improvement of liquidity supply. The

average quoted half spread is 3.70 basis points for Euronext and 5.09 basis points for Chi-X. Average

depth is e108,100 for Euronext and e48,500 for Chi-X. The wider spread and lower depth in Chi-X

does not necessarily imply that investors who demand liquidity/immediacy only focus on Euronext.

The results are, for example, consistent with Chi-X always having a strictly better price on one side of

the market, i.e., a strictly lower ask or a strictly higher bid. To assess Chi-X’ contribution to liquidity

supply one might calculate the lowest ask across markets minus the highest bid — the inside spread

— and compare it to the Euronext spread. The inside spread is, effectively, what investors with ‘smart

routers’ pay (see Foucault and Menkveld (2008)).

The inside spread however might lead one to overestimates liquidity supply improvement as the av-

erage Chi-X depth is lower than Euronext depth. To control for depth, we define the ‘generalized’

inside spread which adjusts both the bid and the ask quote for potentially better prices in Chi-X. For

example, the adjusted ask is e29.995 if the Euronext ask is e30.00 with depth e100,000 and the

Chi-X’ ask is e29.99 with depth e50,000. The generalized inside spread is a conservative measure

as it calculated for transaction sizes that consume full Euronext depth; smaller transaction sizes imply

an even tighter spread.

The generalized inside spread is 2.86 basis points, which is a significant 1.02 basis points (-23%)

lower than the Euronext-only spread of 3.70 basis points. A conservative t-value of this differential

assumes perfect correlation and therefore equals 3.92. The differential is statistically significant for

both large stocks (-24%) and small stocks (-16%).

3. A standard effective spread decomposition shows that, by far, its largest component is adverse selec-

tion (91%) which thus supports the focus on information asymmetry in the theoretical model. The

effective spread is defined as the transaction price minus the midquote — the average of the bid and

ask quote — at the time of trade. It can be decomposed into a component that is compensation for

25

being adversely selected and the orthogonal component which is gross profit to the passive order

submitter. A standard decomposition relies on ‘waiting out’ the time it takes until prices reflect the

long-term information in the trade (see, e.g., Glosten (1987)) which we set to 30 minutes. Overall,

we find that the average effective spread is 3.04 basis points which is the sum of a significant 2.78 ad-

verse selection (91%) and an insignificant 0.26 basis points gross profit (9%). The adverse-selection

component is higher for small stocks.

2.3 Caught on tape! a middleman

The anonymization scheme by market makes simple matching of broker IDs across markets impossible.

Instead, we match pairs of broker IDs and find that one combination (say broker 7 and broker d) achieves

mean-reversion in net position within the day. Also, both broker IDs trade very frequently. It thus matches

the SEC’s defition of ‘high frequency trader’ and appears to fit the profile of the middleman in our main

theory.


Figure 7 illustrates the middleman’s trading by plotting inventory in ING stock throughout January 30, 2008

assuming he starts off at zero. This inventory at any particular point in time is thus defined as the number of

shares bought minus the number of shares sold since the start of the trading day. The two top graphs plot this

inventory by market and show that the middleman is quite active and runs into positions of almost 40,000

shares. Yet, these time series also appear nonstationary which, by market, would not qualify these broker

IDs as middlemen. But, if summed across markets, which is the bottom graph, the pattern does exhibit

high-frequency mean-reversion and it seems that we did catch a middleman. Although hard to see from the

graph, the inventory at the end of the day is exactly zero shares.

[insert Table 2 here]

In Table 2, Panels A and B generate statistics in support of the conjecture that the broker IDs underlying

Figure 7 represent a middleman. Panel A reports that on almost half (0.46) of the stock-days in the sample

the middleman’s change in inventory across the day is exactly zero. On average, this daily inventory change

26

is e-56,000. Panel B shows that the middleman trades 1.40 times per minute in Euronext and 0.96 times per

minute in Chi-X. She trades an average e32,000 per minute in Euronext and e21,000 per minute in Chi-X.

The average open-to-close inventory change is therefore of the same magnitude as the amount he trades in a

minute which supports strong inventory mean-reversion. She is a substantial market participant as, based on

these numbers, he is a counterparty in every third trade in Chi-X (35.6%) and every fourteenth trade (7.7%)

in Euronext. Disaggregating across small and large stocks, it appears him participation rate is the same in

Chi-X but substantially lower in Euronext. She also seems less eager to carry positions overnight as the

fraction of days with a zero inventory change is 0.60 as opposed to 0.33 for large stocks.

Panel C of Table 2 reports that most often the middleman is at the passive side of a transaction. In Chi-X,

78.8% of him transactions was another broker’s aggressive order executing against him limit orders waiting

in the book. In Euronext, it was slightly lower, 74.0%. The standard errors, 0.7% and 1.0% respectively,

show that this is a structural pattern as the distance to 50% is statistically significant. This predominant use

of passive orders in addition to the inventory mean-reversion is consistent with dynamic inventory control

models that have been proposed for market makers (see, e.g., Ho and Stoll (1981), Amihud and Mendelson

(1980), and Hendershott and Menkveld (2010)). These models predict an intermediary to skew him quotes

opposite to the direction of him inventory in order to mean-revert. This could explain why Chi-X quotes,

where our middleman is in every third trade, often features strictly better prices on one side of the market

only (see the discussion on the ‘generalized inside spread’ in Section 2.2). Interestingly, disaggregation

across large and small stocks shows that the middleman is less passive for small stocks in Euronext (52.7%)

which, along with him high fraction of days that he ‘goes home flat’, indicates that he often willingly pays

the half spread to keep inventory close to zero.

Panel D of Table 2 reveals adverse selection is a relatively smaller component of the effective spread when

the middleman is on the passive side of the trade relative to when he is not. The panel conditions the

effective spread decomposition on whether or not the middleman was on the passive side of the trade.

The middleman effective spread is 3.47% on average, which is significantly higher than the nonmiddleman

effective spread of 2.96$ (conservative t-value is 3.92). The adverse-selection cost, however, is 2.75 basis

points for middleman trades which is not significantly different from the 2.81 basis points for nonmiddleman

trades. The remainder is gross profits to the passive side of the trade or so-call realized spread. It is 0.72

basis points for middleman trades which is significantly higher than the 0.15 basis points for nonmiddleman

trades (t value is 1.97). Testing against zero reveals that gross profits are only significantly positive if the

27

middleman is on the passive side of the trade. In relative terms, adverse selection is 79% of the effective

spread for middleman trades vs. 95% for nonmiddleman trades. We note that this result should not be

interpreted as evidence that the middleman is bad for the market as he appears to have significantly positive

gross profits on him passive orders. First off, trading conditions might be worse when the middleman is on

the passive side, e.g., volatility might be higher — Section 2.5 will provide evidence for this conjecture.

But, any judgement on whether the middleman is good or bad for liquidity supply or trading in general is

deferred until the diff-in-diff analysis of Section 2.6.

2.4 Information-processing speed

This section studies the theory’s conjecture that the middleman has superior information-processing speed

which makes him a cost-efficient limit-order submitter. The idea is that a fast computer with enormous

processing power can follow all relevant public news and quickly cancel and resubmit limit orders to reflect

it. This reduces the adverse-selection cost associated with limit orders. The theory captures this idea by

allowing the middleman to condition him price on the common value innovation z.

The middleman’s ability to avoid picking-off risk in real markets is not perfect as not all (public) information

is ‘hard’. We believe the middleman is particularly well-positioned to quickly do the ‘statistics’ and infer-

ence a security’s change in fundamental value by tracking price series that correlate with it, e.g., the index

level, same industry stocks, foreign exchange rate, etc. We label such information ‘hard’ information. The

middleman is at a disadvantage for ‘soft’ information which is, for example, an assessment of the quality of

a new management team, the value of a new patent, etc.

The econometric challenge is to test the prediction that the middleman’s quotes reveal hard information on

a stock’s fundamental value before anyone can pick him off. A data limitation is that him quotes are not

observed. Instead, we conjecture that Chi-X quotes are more revealing of middleman quotes than Euronext

quotes as Chi-X is the most friendly venue for their activity (see passive order and speed discussion in

Section 2.1). The identified middleman’s higher participation rate in Chi-X supports it. Midquotes in the

highly active index futures market are used to trace an important piece of hard information that matters for

a security’s fundamental value.

We believe the most appropriate analysis of whether Chi-X (read: middlemen) quotes are more likely to

28

reflect hard information inbetween trades requires a cointegration model that identifies the information in

the trade. But, leading up to such model we first perform two analyses on the raw data to measure (i) the

speeed with which both markets’ quotes reveal index futures information and (ii) to what extent their quote

updates inbetween trades correlate with the long-term information in the trade.


Simple raw data analysis. Table 3 shows that Chi-X quotes are more responsive to changes in the Dutch

index futures market than are Euronext quotes. A natural and simple approach is to consider all events where

the index future midquote changes and count how often a stock midquote adjusts in the same second. This

comparison, however, includes ‘mechanical’ stock midquote changes that are the result of executions that

knock off stale quotes rather than the result of quote updates. It is for this reason that the analysis further

conditions down on index changes that are not accompanied by stock transactions one second before, during,

or one second after the change. The results show that same-second Chi-X stock quote updates happen three

times more often than Euronext quote updates and their correlation with the index change is significantly

more positive. Both these observations are statistically significant.


Panel A of Table 4 shows that Chi-X quote updates appear more informed than Euronext quote updates.

First, midquote changes strictly inbetween trades are calculated9, i.e., the log midquote one second after

trade (t-1) is subtracted from the log midquote one second prior to trade t (prices are expressed as log prices

whenever price changes are analyzed throughout the study). These are then correlated with the long-term

information revealed in the trade interval which is proxied by transaction price (t+10) minus transaction

price (t-1). This correlation is 0.050 for Chi-X quote updates which is significantly higher than the Euronext

correlation of 0.013. A drawback of this approach is that it does not recognize and strip out transient effects

in quotes due to, e.g., dynamic inventory control. And, it cannot assess to what extent an informational

advantage reflects ‘hard’ information. This is why we turn to a cointegration approach.

A cointegration model. A cointegration model is proposed to gauge quote update informativeness in

both the Euronext and the Chi-X market. The approach extends Hasbrouck (1995) to include the market9The transaction clock used in this table aggregates across markets; it does not distinguish between Chi-X and Euronext trades.

29

index so that quote informativeness can be decomposed into an index-correlated part (hard information)

and a remainder part (which arguably is a mix of hard and soft information). This enables us to quantify

Chi-X quote informativeness and compare it to Euronext quote informativeness. Moreover, it allows for to

decompose any such differential into an index and a nonindex differential to test the conjecture that Chi-X

quote informativeness is particularly strong for hard information.

The cointegration model is defined as:

∆pt B [indext midquote euronextt− midquote chi xt− trade pricet]′ (38)

where t runs over the transaction clock, t− indicates that the quote snapshot is taken one second prior to the

transaction, index is the midquote price in the local index futures, trade pricet is the transaction price, and

midquote Xt− indicates the midquote price in market X.

pt = φ1∆pt−1 + φ2∆pt−2 + · · · + β(A′pt−1) + εt (39)

β′ =

0 β22 β32 β42

0 β21 β31 β41

A′ =

0 1 −1 0

0 1 0 −1

The vector error correction term βA′pt−1 in equation (39) reflects the presence of two random walks, one

associated with the market index and the other with the security’s ‘efficient price’. This common efficient

price disciplines differentials across both midquote price series and the trade price series to be stationary

with mean zero. Price changes are assumed to be covariance stationary which implies that they can be

expressed as a vector moving average (VMA):

∆pt = θ1εt−1 + θ2εt−2 + · · · = θ(L)εt (40)

where L is the lag operator. The two random walks now show up in the coefficient polynomial θ(L) evaluated

at 1 which reflects the long-term response of prices to an error term impulse. This matrix has rank 2, i.e.,

the second, third, and fourth row are equal as all three are security prices that in the long-term agree on what

the current shock’s impact is on the efficient price. A useful econometric proxy for this efficient price is the

best long-term linear forecast of prices conditional on all historical price information up until and including

30

time t:

ft B limt→∞

E∗[pt+k|pt, pt−1, . . . ] (41)

where the asterisk indicates that it is the best linear forecast. Hasbrouck (2007, Ch.8) shows that the forecast

innovation from (t-1) to t for the efficient price is:

∆ ft = [θ(1)]2εt (42)

where [.]i indicates ‘the ith row of the matrix in brackets’.

The forecast innovations ∆ ft are a natural measure for the theory’s common value changes in between trades

and linear projections allows for further analysis of these common-value innovations. For ease of exposition,

let Px(y) be the best linear projection of the random variable y on random variable x. In regression terms,

Px(y) B x′β (43)

where β is the coefficient of a standard linear regression of y on x. The projections allow for the following

analysis.

1. Quote informativeness inbetween is naturally measured by the variance of the efficient price projection

onto the quote innovation, e.g., var(Pe(∆ ft)) where Pe projects onto the Euronext quote innovation

[ε]2. In other words, how much information in the intertrade interval can be learned from obtaining

a market’s quote update? This measure is zero in a Glosten and Milgrom (1985) type of model and

equal to the full ∆ ft variance if liquidity demanders are uninformed.

2. The variance of efficient price changes (as measured by ∆ ft) and its projection onto quote innovations

can be decomposed into an index-correlated component (hard information) and an orthogonal com-

ponent. For example, var(Pm ◦Pe(∆ ft)) where m corresponds to [ε]1 indicates how much of Euronext

quote informativeness reflects the index innovation. If Euronext quote updates are uncorrelated with

index innovations this measure is zero. P−m is defined to be the orthogonal part, i.e., y = (Pm+P−m)(y)

by construction.

Panel B of Table 4 provide empirical support for Chi-X quotes being significantly more informative on hard

information. The proxy for such information is the index-correlated part of efficient price changes which

31

amounts to 42% (=100%*4.02/9.48). By Roll’s standards these firms are large and this percentage cor-

responds to him finding that most large U.S. firm are in the 40% to 50% range (see Roll (1988, p.545)).

Projecting efficient price changes onto Euronext and Chi-X quotes reveals that Chi-X quotes are more infor-

mative (3.83 vs 3.54 basis points squared) but this difference is not significant. If, however, this differential

is decomposed into index and nonindex components, Chi-X is significantly more informative on the index

component (0.30 vs. 0.05 basis points squared with a t value of 5.0 for the differential).

Disaggregating according to large and small stocks reveals a cross-sectional heterogeneity as Chi-X quotes

are significantly more informative for large stocks, but significantly less informative for small stocks. For

large stocks, Chi-X quote innovations reveal 3.70 basis points squared of the intertrade innovation which

is a significant 28% higher than the 2.90 basis points squared for Euronext. For small stocks on the other

hand, Chi-X quote updates reveal 4.60 basis points squared which a significant 37% lower than Euronext

the informativeness of Euronext quote updates. Decomposing according to index and nonindex information

reveals that Chi-X quote appear significantly more informative on the index part for both types of stocks,

but are significantly less informative on the nonindex for small stocks. For large stocks the nonindex part is

not significantly different across markets (although Chi-X informativeness is slightly higher for this part).

2.5 Middleman participation: which stocks and when?


This section studies middleman participation in both the cross-section (through ‘between’ correlations) and

in the time dimension (through ‘within’ correlations). Table 5 presents these correlations of various trading

variables which lead to the following observations.

[insert Figures 8 here]

The relative size of hard information as proxied by the ‘R2 of a single factor CAPM’ correlates positively

with middleman trade participation (0.67 between and 0.46 within) and Chi-X share of trades (0.64 between

and 0.23 within). Figure 8 illustrates the 0.46 within correlation by plotting middleman participation against

the size of hard information. It reveals that this strong correlation does not appear to be driven by outliers

32

and is based on considerable time variation in both variables, double-digit percentages. The increase in

Chi-X share of trades is not surprising given that it is a middleman’s preferred habitat (low fees and a

fast system). The table also shows that middleman participation correlates positively with Chi-X trade

share (0.89 between and 0.41 within) which is further evidence that the relationship between Chi-X and

middlemen appears symbiotic.


The differential between Chi-X and Euronext price-quote informativeness correlates positively with the

relative amount of hard information (0.64 between and 0.23 within). A market’s price-quote informativeness

is defined as the predictive power of midquote price changes for the amount of information that is revealed

inbetween trades. The methodology is based on linear projections (Pe − Pi)(∆ f ) and a cointegration model

(see Section 2.4). Figure 9 illustrates the cross-sectional relationship by plotting the size of hard information

against both market’s price-quote informativeness for each stock. The black dots represent Chi-X, the white

dots represent Euronext, and dot size corresponds to stock’s overall volume. The graph leads to the following

two observations. First, black dots appear to be above white dots on the right-hand side of the graph, below

them on the left-hand side. This illustrates the positive between-correlation of hard information size and

Chi-X minus Euronext price-quote informativeness. Second, dot size is generally larger on the right-hand

side of the graph. Hard information is relatively more important for active stocks.


Figure 10 replots Figure 9 but decomposes price-quote informativeness into an index-related part (top graph)

and an orthogonal part (bottom graph). It illustrates that Chi-X price-quote informativeness is higher than

Euronext quote informativeness across all stocks for the hard information (black dots are generally above

with dots in the top graph) and results are mixed for the nonindex part which is likely to be a combination of

hard and soft information. The latter result illustrates that it is not only index information that drives Chi-X

quote efficiency.

33

2.6 The counterfactual: what if middlemen had not been introduced?

As we cannot rerun trading in the first 77 days of 2008 without Chi-X and the identified middleman, we

revert to a diff-in-diff approach as a second best. As discussed in Section 2.2, additional data have been

collected to create a pre-event sample of the first 77 trading days of 2007 to compare before and after Chi-X

introduction. This difference for the ‘treated’ sample is then compared to the difference for an untreated

sample of Belgian stocks. Belgium is a natural choice as it a neighboring country whose stocks also trade in

the Euronext system. The difference in difference (‘∆ Dutch - ∆ Belgian’) identifies a treatment effect.


The diff-in-diff results of Table 6 (Panel A) reveal that Chi-X introduction raises liquidity supply, does not

affect the number of trades, and lowers trading volume. Before discussing these results, we like to point out

that the comparison across Dutch and Belgian stocks is not perfect as the latter typically trade less actively,

3.71 vs. 11.05 trades per minute in the post-event period. Yet, volatility increase is comparable across

markets; realized volatility increases slightly less for Dutch stocks (64% vs. 69%) whereas the increase of

intertrade volatility based on the cointegration model is not significantly different across markets (41% vs

39%). Bearing this in mind, the table leads to the following observations:

1. The generalized inside spread which equals the Euronext spread in the absence of Chi-X has in-

creased by 35% in Belgian stocks (reflecting the higher volatility), yet stayed put for Dutch stocks

(0%). The treatment effect is a significant 35%. Depth at this quote has declined by 13% more

for Dutch stocks but we consider this effect to be second order as this decrease does not undo the

large price discount. If one were to transact the 13% at one tick behind the best price quote this

implies a 175% worse price10 and the overall effect is thus still a spread improvement of 100%*(1-

(0.87*0.65+0.13*0.65*1.75))=29%. The significant treatment effect of minus 13% for effective spread

further supports a general increase in liquidity supply on the introduction of Chi-X/ middlemen.

2. The number of trades in Dutch stock increases by 53% which is not significantly different from the in-

crease of 55% witnessed for Belgian stocks. The number of trades in Dutch stocks has been corrected

10This calculation is based on a one cent tick size and an average share price of ∼e20 which imply a 5 basis points worse priceon a one tick move. This is a 175% increase relative to the 2.86 basis points average half spread (see Table 1).

34

for double-counting of trades due to the presence of the new middleman that has been identified (see

Table 2). In other words, if a security that in the past traded directly between investor A and B now

travels via the middleman this would artificially inflate trade activity.

3. Volume increases by only 5% for Dutch stocks, which is a significant 15% less than the 21% increase

in Belgian stocks. Again, this volume was corrected for double-counting.

3 Conclusion

We model high-frequency traders in electronic markets. We base this conclusion on the introduction of

Chi-X, an HFT-hospitable market, and on being able to compare the post Chi-X entry change in the trading

of Dutch stocks which do trade on Chi-X, and similar Belgian stocks that do not. We showed evidence that

middlemen are better informed about recent news than the average investor, in that their reaction times were

faster and in the right direction.

Being better informed, middlemen still can make a positive or a negative contribution to welfare. On the

one hand, they can raise welfare by solving a pre-existing adverse-selection problem. In that case their entry

should be accompanied by a rise in trade and a fall in bid-ask spreads. On the negative side, they can create

or exacerbate a pre-existing adverse-selection problem in which case bid-ask spreads should rise and trade

declines.

Our evidence on the welfare contribution of middlemen is mixed. On the one hand, middlemen’s participa-

tion lowers the effective bid-ask spreads but, on the other, it does not affect the number of trades. The net

effect is therefore uncertain.

Our theoretical analysis and the mixed evidence on welfare suggest that there is room for optimal market

design. Regulators and market operators should think carefully about how adverse-selection risk affects the

various participants. For example, the speed privilege that HFTs can buy into, co-location, might require a

differentiated order-fee schedule. Passive orders submitted through this pipe might optimally be rewarded

more whereas aggressive orders might have to be charged more. The reason is that passive orders come with

the positive externality of liquidity supply to others whereas aggressive orders have a negative externality of

creating adverse selection for non-co-located participants. The latter is, in spirit, similar to the old NYSE

35

market structure where specialists were not allowed to have a live data feed of market-index information

into their system. Also, markets might want to enable limit-order submitters to peg their order to, e.g., the

market index (cf. Black (1995)).

36

Appendix I: Variable/parameter description and modeling device discussion

Variables:

variable meaningM middleman/machine, a representation of high-frequency traders

S seller, an investor who owns the asset and arrives early

B buyer, an investor like S except that he does not own the asset and arrives late (no overlapwith S)

x,y private value of asset ownership for S and B, respectively

z=zh+zs common value innovation of asset ownership produced in between arrival of S and B

zh, zs zh is hard information, i.e., “quantitative, easy to store and transmit in impersonal ways,” ;zs is soft information; zh is known by M and potentially partially by B; zs is known by Bonly

Parameters:

parameter description modeling device for. . .σ2

x=σ2y=σ

2=π

µx=µy=µ

mean and variance of indepen-dent normally distributed pri-vate valus of ownership for Sand B, respectively

M private value of ownership is set to zero; vari-ance of private value is set to π so that expectedsocial value of optimal re-allocation is standard-ized to one (E max(x, y) − µ = σ√

π); µ captures

expected social loss of M ownership relative toinvestor ownership (by construction expressed inunits of social value of re-allocation as the latterwas set to equal 1)

σ2z variance of normally distributed

common value innovation zsize of winner’s curse (adverse selection) frictionin the absence of M

λ probability that B observes hardinformation zh

extent to which M participation produces socialvalue (might be negative for small λ)

α relative size of hard informationin z

relative size on how informed M is on z

θ relative size of common valuevariance (σ2

z ) relative to privatevalue variance (σ2

x)

relative size of the informational friction

37

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38

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40

Table 1: Summary statistics

This table provides summary statistics on a sample of 14 Dutch index stocks that trade both in theincumbent market Euronext and in the entrant Chi-X (Chi-X). The sample runs from Jan 1, 2008 throughApril 23, 2008. The table reports weighted averages where weights are based on a stock’s local indexweight. Time-clustered standard errors account for commonality and heteroskedasticity and are reported inparentheses.

variable (units) large small allEuronext volume (e1000/min) 524.4

(19.9)128.1

(4.3)466.6(17.4)

Chi-X volume (e1000/min) 49.4(2.0)

4.5(0.2)

42.8(1.8)

Chi-X share volume (%) 8.6 3.4 8.4

Euronext #trades (/min) 19.03(0.62)

9.30(0.21)

17.61(0.55)

Chi-X #trades (/min) 3.16(0.12)

0.57(0.03)

2.78(0.10)

Chi-X share #trades (%) 14.2 5.7 13.6

Euronext time-weighted quoted half spread (basis points) 3.47(0.07)

5.00(0.14)

3.70(0.08)

Chi-X time-weighted quoted half spread (basis points) 3.44(0.10)

14.76(0.98)

5.09(0.20)

time-weighted generalized inside half spreada (basis points) 2.63(0.18)

4.20(0.24)

2.86(0.18)

Euronext time-weighted quoted depth (e1000) 121.4(2.4)

30.6(0.3)

108.1(2.0)

Chi-X time-weighted quoted depth (e1000) 53.3(1.2)

21.0(1.1)

48.5(1.0)

trade-weighted effective half spread (basis points) 2.89(0.06)

3.90(0.10)

3.04(0.06)

trade-weighted adverse selection, 30 min (basis points) 2.62(0.14)

3.74(0.21)

2.78(0.14)

trade-weighted realized spread, 30 min (basis points) 0.28(0.14)

0.16(0.17)

0.26(0.13)

N=1078 (14 stocks, 77 days)a: defined as a Chi-X adjusted Euronext half spread in the sense that it is the cost of demanding the full Euronext depthbut re-routing (part of) the order to Chi-X if Chi-X has strictly better prices; it is a ‘generalized’ inside spread since itcontrols for depth; for example, the adjusted ask is e29.995 if the Euronext ask is e30.00 with depth e100,000 and theChi-X’ ask is e29.99 with depth e50,000

41

Table 2: Caught on tape! a middleman

This table produces statistics on middleman trading for Dutch index stocks from January 1 through April 23,2008. The middleman is discovered as a combination of an anonymous Chi-X broker ID and an anonymousEuronext broker ID that achieves high-frequency trading and mean-reversion in inventory across markets.Figure 7 plots middleman inventory for a single stock on a representative day to illustrate him trading. Time-clustered standard errors account for commonality and heteroskedasticity and are reported in parentheses.

large small allPanel A: middleman inventoryaverage net change in middleman inventory (e1000) −75.6

(93.3)55.1(19.6)

−56.5(79.8)

standard deviation net change in middleman inventory (e1000) 1, 417.2(186.7)

298.4(33.5)

1, 314.6(172.3)

fraction of days with zero net change in inventory 0.33 0.60 0.46

Panel B: middleman activitymiddleman Euronext volume (e1000/min) 36.8

(1.8)4.3(0.3)

32.0(1.6)

middleman Chi-X volume (e1000/min) 24.2(1.8)

1.9(0.2)

21.0(1.6)

middleman Euronext #trades (/min) 1.56(0.07)

0.43(0.03)

1.40(0.06)

middleman Chi-X #trades (/min) 1.09(0.08)

0.19(0.02)

0.96(0.07)

middleman participation rate Euronext trades (%) 8.2(0.3)

4.8(0.3)

7.7(0.3)

middleman participation rate Chi-X trades (%) 35.7(1.8)

35.2(2.3)

35.6(1.8)

Panel C: middleman order typesmiddleman relative use of passive orders in Euronext (%) 78.6

(0.8)53.5(2.7)

74.9(0.9)

middleman relative use of passive orders in Chi-X (%) 76.9(0.5)

84.8(0.8)

78.0(0.5)

Panel D: middleman vs nonmiddleman effective spread and its decompositionmiddleman trade-weighted effective half spread (basis points) 3.25

(0.06)4.72(0.11)

3.47(0.07)

nonmiddleman trade-weighted effective half spread (basis points) 2.81(0.06)

3.81(0.10)

2.96(0.06)

middleman trade-weighted adverse selection, 30 min (basis points) 2.54(0.17)

3.98(0.66)

2.75(0.17)

nonmiddleman trade-weighted adverse selection, 30 min (basis points) 2.64(0.15)

3.78(0.21)

2.81(0.14)

middleman trade-weighted realized spread, 30 min (basis points) 0.72(0.17)

0.74(0.62)

0.72(0.16)

nonmiddleman trade-weighted realized spread, 30 min (basis points) 0.17(0.14)

0.03(0.17)

0.15(0.13)

N=1078 (14 stocks, 77 days)

42

Table 3: Speed comparison across markets

This table compares Euronext and Chi-X in terms of how quickly their price quotes for stocks reflectschanges in the Dutch local index (AEX) future. A natural approach is to consider all events where the indexfuture midquote (the average of the bid and ask quote) changes and count how often the stock midquote isadjusted in the same second. This comparison, however, includes ‘mechanical’ stock midquote changes thatare the result of executions that knock off stale quotes rather than quote updates. It is for this reason thatthe analysis further conditions down on index future midquote updates that show no stock transactions onesecond before, during, or one second after the index futures quote update. The sample Dutch index consistsof Dutch index stocks from January 1 through April 23, 2008. Time-clustered standard errors account forcommonality and heteroskedasticity and are reported in parentheses.

large small allcount of Euronext and index futures quote change in same second (/day) 426

(24)637(40)

457(25)

count of Chi-X and index futures quote change in same second (/day) 1256(52)

1257(58)

1256(50)

correlation Euronext quote change and index futures quote change 0.33(0.01)

0.16(0.01)

0.31(0.01)

correlation Chi-X quote change and index futures quote change 0.46(0.02)

0.15(0.01)

0.41(0.01)

14 stocks, 77 days

43

Table 4: Euronext and Chi-X quote informativeness

This table analyzes to what extent midquote (the average of the bid and ask quote) updates inbetween tradesreveal the information that arrives in the intertrade intervals. The observation clock runs in transaction time.Panel A correlates log midquote changes strictly inbetween trades with the information revealed in the tradeinterval which is proxied by the the log trade price (t+10) minus log trade price (t-1). Panel B is based oncointegration model which stacks all price series of interest into a single price vector

∆pt B [indext midquote euronextt− midquote chi xt− trade pricet]′

where t runs over the transaction clock, t− indicates that the quote snapshot is taken one second prior tothe transaction, index is the midquote in the local index futures, trade pricet is the transaction price, andmidquote Xt− indicates the midquote in market X. The price series is modeled as a vector error correctionmodel (VECM) to capture cointegration:

pt = φ1∆pt−1 + φ2∆pt−2 + · · · + β(A′pt−1) + εt

β′ =

(0 β22 β32 β420 β21 β31 β41

)A′ =

(0 1 −1 00 1 0 −1

)The βA′pt−1 reflects the presence of two random walks, one associated with the market index and the otherwith the security’s ‘efficient price’ which is naturally defined as

ft B limt→∞

E∗[pt+k|pt, pt−1, . . . ]

where the asterisk indicates that it is the best linear forecast (see Hasbrouck (2007, Ch.8)). The extent towhich Chi-X and Euronext quotes reveal efficient prices and whether it is the index or the nonindex compo-nent is established through linear projection of ∆ ft on the price innovation vector εt where Pm denotes a pro-jection on the first element which captures the market-index innovation (and P−m is its residual), Pe projectsonto the second element which is the Euronext quote innovation, and Pc projects onto the third elementwhich is the Chi-X quote innovation. The sample Dutch index consists of Dutch index stocks from January1 through April 23, 2008. Time-clustered standard errors account for commonality and heteroskedasticityand are reported in parentheses.

large small allPanel A: correlations based on raw dataa

correlation Euronext midquote return and long-term price impact of (signed) trade 0.007(0.003)

0.046(0.003)

0.013(0.003)

correlation Chi-X midquote return and long-term price impact of (signed) trade 0.052(0.004)

0.039(0.003)

0.050(0.003)

Panel B: cointegration analysisa

overall efficient price innovationvariance efficient price innovation inbetween trades, ∆ f 8.19

(0.49)16.98(1.16)

9.47(0.58)

variance efficient price innovation correlated with market index, Pm(∆ f ) 3.74(0.28)

5.66(0.51)

4.02(0.30)

variance efficient price orthogonal to market index, P−m(∆ f ) 4.45(0.28)

11.32(0.75)

5.45(0.33)

- continued on next page -

44

- continued from previous page -large small all

efficient price innovation correlated with the Euronext midquote returnvariance efficient price innovation inbetween trades, Pe(∆ f ) 2.90

(0.17)7.25(0.45)

3.54(0.21)

variance efficient price innovation correlated with market index, Pm ◦ Pe(∆ f ) 0.05(0.00)

0.08(0.01)

0.05(0.00)

variance efficient price orthogonal to market index, P−m ◦ Pe(∆ f ) 2.85(0.17)

7.18(0.45)

3.48(0.21)

efficient price innovation correlated with the Chi-X midquote returnvariance efficient price innovation inbetween trades, Pc(∆ f ) 3.70

(0.17)4.60(0.44)

3.83(0.20)

variance efficient price innovation correlated with market index, Pm ◦ Pc(∆ f ) 0.33(0.02)

0.14(0.02)

0.30(0.02)

variance efficient price orthogonal to market index, P−m ◦ Pc(∆ f ) 3.37(0.16)

4.47(0.43)

3.53(0.19)

14 stocks, 77 daysa: based on midquotes that are sampled strictly inbetween trades (i.e. one second after the last trade and one second ahead ofthe next trade) in order to avoid spurious correlation due a trade knocking off the best bid or ask quote

45

Tabl

e5:

Cor

rela

tion

daily

vari

able

s

Thi

sta

ble

pres

ents

corr

elat

ions

fora

pane

ldat

aset

oftr

adin

gva

riab

les

that

are

calc

ulat

edby

stoc

k-da

y.It

dist

ingu

ishe

d‘b

etw

een’

and

‘with

in’

corr

elat

ions

whi

chst

udy

vari

able

inte

rdep

ende

nce

inth

ecr

oss-

sect

ion

and

thro

ugh

time,

resp

ectiv

ely.

The

with

inco

rrel

atio

nis

base

don

time

mea

ns:

x i=

1 T∑ T t=

1x i

t.T

hebe

twee

nco

rrel

atio

nis

base

don

day

t’sde

viat

ion

rela

tive

toth

etim

em

ean:

x∗ it=

x it−

x i.T

hesa

mpl

eD

utch

inde

xco

nsis

tsof

Dut

chin

dex

stoc

ksfr

omJa

nuar

y1

thro

ugh

Apr

il23

,200

8.St

anda

rder

rors

are

repo

rted

inpa

rent

hese

s(w

ithin

corr

elat

ion

stan

dard

erro

rsac

coun

tfor

com

mon

ality

and

hete

rosk

edas

ticity

).

vari

able

(uni

ts)

corr

type

vari

ance

effpr

ice

inno

va-

tion

mid

dle-

man

part

ic-

ipat

ion

rate

#tra

des

Chi

-Xsh

are

#tra

des

mid

dle-

man

rela

tive

use

ofpa

ssiv

eor

ders

Chi

-Xm

inus

Eu-

rone

xtqu

ote

info

rma-

tiven

ess,

(Pc−

Pe)

(∆f)

rela

tive

size

inde

xco

mpo

nent

a(%

)be

twee

nb−0.5

0(0.2

7)0.

67∗

(0.2

7)0.

55∗

(0.2

7)0.

75∗∗

(0.2

7)0.

07(0.2

7)0.

64∗

(0.2

7)w

ithin

c0.

13(0.1

0)0.

46∗∗

(0.0

5)−0.0

9(0.0

8)0.

13∗∗

(0.0

4)0.

04(0.0

7)0.

23∗∗

(0.0

8)

vari

ance

effpr

ice

inno

vatio

nin

betw

een

trad

es,∆

fbe

twee

nb−0.7

3∗∗

(0.2

7)−0.6

2∗(0.2

7)−0.6

1∗(0.2

7)−0.6

4∗(0.2

7)−0.8

8∗∗

(0.2

7)w

ithin

c0.

15∗∗

(0.0

5)0.

55∗∗

(0.1

2)−0.1

5∗(0.0

7)0.

03(0.0

6)−0.0

4(0.0

8)

mid

dlem

anpa

rtic

ipat

ion

rate

(%)

betw

eenb

0.64∗

(0.2

7)0.

89∗∗

(0.2

7)0.

53∗

(0.2

7)0.

78∗∗

(0.2

7)

with

inc

0.11∗

(0.0

5)0.

41∗∗

(0.0

5)0.

08(0.0

5)0.

20∗∗

(0.0

5)

#tra

des

(/m

in)

betw

eenb

0.73∗∗

(0.2

7)0.

34(0.2

7)0.

40(0.2

7)w

ithin

c0.

01(0.0

6)−0.0

5(0.0

7)−0.2

9∗∗

(0.0

6)

Chi

-Xsh

are

#tra

des

(%)

betw

eenb

0.23

(0.2

7)0.

67∗

(0.2

7)w

ithin

c−0.1

5∗∗

(0.0

5)0.

05(0.0

4)

mid

dlem

anre

lativ

eus

eof

pass

ive

orde

rs(%

)be

twee

nb0.

52∗

(0.2

7)w

ithin

c−0.0

2(0.0

4)

14st

ocks

,77

days

a :siz

eof

the

inde

xco

mpo

nent

inth

eeffi

cien

tpri

cein

nova

tion

b :bas

edon

the

time

mea

ns:

x i=

1 T

∑ T t=1

x it

c :bas

edon

day

t’sde

viat

ion

rela

tive

toth

etim

em

ean:

x∗ it=

x it−

x i∗ /∗∗

:sig

nific

anta

ta95/9

9%le

vel

46

Tabl

e6:

Diff

-in-d

iffan

alys

istr

adin

gva

riab

les

Thi

sta

ble

com

pare

str

adin

gva

riab

les

base

don

Dut

chin

dex

stoc

ksbe

fore

and

afte

rth

ein

trod

uctio

nof

Chi

-Xan

dth

ead

vent

ofm

iddl

emen

(e.g

.,th

eID

ofth

em

iddl

eman

we

iden

tified

inTa

ble

2di

dap

pear

inth

epr

e-ev

ent

peri

od).

Itco

mpa

res

the

first

77tr

adin

gda

ysof

2007

(thr

ough

Apr

il20

)an

d20

08(t

hrou

ghA

pril

23).

Thi

sse

rves

asth

e‘t

reat

ed’

sam

ple.

The

sam

eco

mpa

riso

nis

done

for

Bel

gian

inde

xst

ocks

whi

chcr

eate

san

‘unt

reat

ed’

sam

ple

asC

hi-X

had

not

yet

been

intr

oduc

ed.

Bel

gium

isa

natu

ral

choi

ceas

ita

neig

hbor

ing

coun

try

who

sest

ocks

also

trad

ein

the

Eur

onex

tsys

tem

.A

diff

-in-

diff

anal

ysis

then

iden

tifies

the

trea

tmen

teff

ect.

The

perc

enta

gech

ange

was

dete

rmin

edba

sed

onth

elo

gse

ries

.Ti

me-

clus

tere

dst

anda

rder

rors

acco

untf

orco

mm

onal

ityan

dhe

tero

sked

astic

ityan

dar

ere

port

edin

pare

nthe

ses.

vari

able

(uni

ts)

Net

herl

ands/‘

trea

ted’

Bel

gium/‘

untr

eate

d’diff

-in-

diff

a

pre

post

∆pr

epo

st∆

∆∆

Pane

lA:F

ulls

ampl

e20

-min

real

ized

vola

tility

(bp/

min

)3.

9(0.1

)7.

6(0.3

)64

%∗∗

(4%

)4.

1(0.1

)8.

3(0.4

)69

%∗∗

(4%

)−4

%∗

(2%

)

vola

tility

effici

entp

rice

inno

vatio

nin

betw

een

trad

es,∆

f(b

p)1.

9(0.0

)2.

9(0.1

)41

%∗∗

(3%

)3.

5(0.1

)5.

0(0.1

)39

%∗∗

(3%

)2% (2

%)

time-

wei

ghte

dge

nera

lized

insi

deha

lfsp

read

a(b

asis

poin

ts)

2.93

(0.0

3)2.

86(0.1

8)0% (2

%)

5.00

(0.0

8)6.

86(0.1

6)35

%∗∗

(2%

)−3

5%∗∗

(2%

)

time-

wei

ghte

dqu

oted

dept

h(e

1000

)21

3(2

)10

8(2

)−6

2%∗∗

(2%

)67 (1

)46 (0

)−4

9%∗∗

(2%

)−1

3%∗∗

(2%

)

trad

e-w

eigh

ted

effec

tive

half

spre

ad(b

asis

poin

ts)

2.61

(0.0

2)3.

04(0.0

6)13

%∗∗

(2%

)3.

99(0.0

7)5.

07(0.1

2)27

%∗∗

(2%

)−1

3%∗∗

(1%

)

trad

e-w

eigh

ted

adve

rse

sele

ctio

n,30

min

(bas

ispo

ints

)1.

89(0.0

9)2.

78(0.1

4)32

%∗∗

(6%

)3.

16(0.1

1)5.

23(0.2

2)54

%∗∗

(5%

)−2

1%∗∗

(7%

)

#tra

des

(/m

in)

11.0

5(0.3

4)20.3

9(0.6

3)59

%∗∗

(3%

)3.

71(0.1

2)6.

89(0.2

1)55

%∗∗

(3%

)3% (2

%)

#tra

des

afte

rrem

ovin

gm

iddl

eman

’str

ades

(/m

in)

11.0

5(0.3

4)19.8

0(0.6

1)56

%∗∗

(3%

)3.

71(0.1

2)6.

89(0.2

1)55

%∗∗

(3%

)0% (2

%)

volu

me

(e10

00/m

in)

446

(16)

509

(18)

10%∗

(4%

)72 (2

)10

0(4

)21

%∗∗

(4%

)−1

0%∗∗

(2%

)

volu

me

afte

rrem

ovin

gm

iddl

eman

’svo

lum

e(e

1000/m

in)

446

(16)

496

(18)

8% (4%

)72 (2

)10

0(4

)21

%∗∗

(4%

)−1

3%∗∗

(2%

)

#obs

erva

tions

4746

,14+

18=

32st

ocks

,77+

77=

154

days

a :defi

ned

asth

eN

ethe

rlan

dsdiff

eren

tial(

post

min

uspr

e)m

inus

the

Bel

gium

diff

eren

tial

∗ /∗∗

:sig

nific

anta

ta95/9

9%le

vel(

only

appl

ied

todiff

eren

tials

)

47

Figure 1: Market fragmentation

These graphs illustrate the entry of new markets and the subsequent fragmentation of trading. The topgraph presents the total entrant share of EUR volume in Europe-listed stocks as well as the largest entrant(Chi-X) share and the largest incumbent (London Stock Exchange) share. The bottom graph presents thetotal entrant share of share volume in NYSE-listed stocks as well as a large entrant (BATS) share and theincumbent (NYSE) share. The data sources for these graphs are Barclays Capital Equity Research andFederation of European Securities Exchanges.

Jan-03 Jan-04 Jan-05 Jan-06 Jan-07 Jan-08 Jan-09 Jan-10 Jan-110

10

20

30

40

50

60

70

80

90

%

U.S. trading in NYSE-listed equities

total entrant share

BATS (entrant) share

NYSE (incumbent) share

Jan-08 May-08 Sep-08 Jan-09 May-09 Sep-09 Jan-10 May-10 Sep-10 Jan-110

5

10

15

20

25

30

35

%

European trading in Europe-listed equities

total entrant share

Chi-X (entrant) share

LSE (incumbent) share

48

Figure 2: Structure of the game

This figure illustrates the game between the seller S, the middleman M, and the buyer B. Panel A illustratesthe informational structure. Panel B depicts the various steps in the game.

panel A: information structure

private

value

x y

zh

SB

private

value

common

value

zs

MM

hard

common

value

soft

z

with

prob

λ

panel B: steps in the game

B rejects

S owns

S owns

S posts pS(x)

M bids pM(zh)

S does not post

M bids pM(zh)

M rejects

M posts pM(zh)

B rejects

S owns

M acceptsB accepts

B owns

B rejects

M ownsS accepts

S rejects S owns

S owns

S owns

49

Figure 3: The posting decision for the seller

This figure depicts the value function for S when he posts and for when he does not post a price, U (x) andV (x) respectively.

private value seller (x)

total value seller

U(x)

V (x |σ2

h>> 0)

V (x |σ2

h= 0)

vM

vM

a

50

Figure 4: Middlemen participation and welfare vs. the relative size of hard information

These figures illustrate how middlemen participation (top) and welfare (bottom) change with the relativesize of hard information. The alpha parameter measures how much of the common value variance is hardinformation. The remaining parameters are set to: λ = 1, µ = 2.27, θ = 0.27.

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0alpha, relative size common value innovation

0.48

0.50

0.52

0.54

0.56

0.58

0.60

mid

dle

man p

art

icip

ati

on in t

rades

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0alpha, relative size hard information

0.65

0.70

0.75

0.80

0.85

0.90

0.95

1.00

1.05

welfare no middleman

with middleman

first best

51

Figure 5: Middlemen participation and welfare vs. the size of the informational friction

These figures illustrate how middlemen participation (top) and welfare (bottom) change with the size of theinformational friction. The theta parameter describes how large the common value variance is relative toprivate value variance. The remaining parameters are set to: λ = 1, µ = 2.27, α = 0.42.

0 1 2 3 4 5theta, relative size common value innovation

0.45

0.50

0.55

0.60

0.65

0.70

0.75

0.80

0.85

0.90

mid

dle

man p

art

icip

ati

on in t

rades


0.2

0.4

0.6

0.8

1.0

welfare no middleman

with middleman

first best

52

Figure 6: Middlemen participation and welfare vs. the size of the informational friction (2)

This figure illustrates how welfare changes with the size of the informational friction while keeping theinformational asymmetry fixed in the no middleman case. The theta parameter describes how large thecommon value variance is relative to private value variance. The remaining parameters are set to: µ =2.27, α = 0.42.


0.2

0.4

0.6

0.8

1.0

welfare

(advers

e s

ele

ctio

n n

o m

iddle

man c

ase

unch

anged)

no middleman

with middleman

first best

53

Figure 7: Middleman inventory

These graphs plot the middleman’s intraday inventory for ING stock on January 30 starting him offwith zeroshares (by assumption). They plot inventory both by market (top two graphs) and aggregated across markets(bottom graph). The middleman is discovered as a combination of an anonymous Chi-X broker ID andan anonymous Euronext broker ID that achieves high-frequency trading and mean-reversion in inventoryacross markets. The graphs illustrate this trading pattern for one stock-day and Table 2 produces middlemanstatistics for the full sample.

-40000

-35000

-30000

-25000

-20000

-15000

-10000

-5000

0

5000

09:0

0:00

10:0

0:00

11:0

0:00

12:0

0:00

13:0

0:00

14:0

0:00

15:0

0:00

16:0

0:00

17:0

0:00

18:0

0:00

units

:sha

res

middleman’s Euronext inventory

-5000

0

5000

10000

15000

20000

25000

30000

35000

40000

09:0

0:00

10:0

0:00

11:0

0:00

12:0

0:00

13:0

0:00

14:0

0:00

15:0

0:00

16:0

0:00

17:0

0:00

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0:00

units

:sha

res

middleman’s Chi-X inventory

-15000

-10000

-5000

0

5000

10000

15000

09:0

0:00

10:0

0:00

11:0

0:00

12:0

0:00

13:0

0:00

14:0

0:00

15:0

0:00

16:0

0:00

17:0

0:00

18:0

0:00

units

:sha

res

middleman’s inventory aggregated across markets

54

Figu

re8:

Scat

ter

plot

ofm

iddl

eman

activ

ityve

rsus

amou

ntof

hard

info

rmat

ion

Thi

sfigu

reco

ntai

nsa

scat

terp

loto

fthe

trad

epa

rtic

ipat

ion

byth

eid

entifi

edm

iddl

eman

(see

Tabl

e2)

agai

nsta

prox

yfo

rthe

rela

tive

impo

rtan

ceof

‘har

d’in

form

atio

nde

fined

asan

ypu

blic

info

rmat

ion

that

can

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oces

sed

bym

achi

nes

(e.g

.,pr

ice

chan

ges

inth

ein

dex

futu

res,

sam

ein

dust

ryst

ocks

,for

eign

exch

ange

rate

).T

heco

njec

ture

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atm

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emen

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atin

gw

ithfa

stm

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nes

have

aned

gew

hen

such

info

rmat

ion

isa

larg

erpa

rtof

tota

linf

orm

atio

n.A

prox

yfo

rthe

rela

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size

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rdin

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atio

nis

the

‘R2 ’o

fare

gres

sion

ofst

ock

retu

rnon

inde

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turn

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his

prox

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cons

truc

ted

fore

ach

stoc

k-da

yin

the

sam

ple

base

don

the

coin

tegr

atio

nm

odel

resu

ltsof

Tabl

e4.

Mid

dlem

antr

ade

part

icip

atio

nis

also

calc

ulat

edfo

rea

chst

ock-

day.

Bot

hva

riab

les

are

dem

eane

dby

stoc

kto

only

focu

son

the

time

vari

atio

n(a

ndno

thav

eth

ere

sults

bedr

iven

byun

obse

rved

hete

roge

neity

acro

ssst

ocks

).T

hesc

atte

rplo

toft

hese

seri

esth

usill

ustr

ates

the

with

inco

rrel

atio

npr

esen

ted

inTa

ble

5.

-10-5 0 5 10

15

20 -5

0-4

0-3

0-2

0-1

0 0

10

20

30

40

50

60

middleman participation in trades, demeaned by stock (%)

rela

tive

size

inde

x co

mpo

nent

in e

ffici

ent p

rice

inno

vatio

n, d

emea

ned

by s

tock

(%

)

55

Figu

re9:

Chi

-Xan

dE

uron

extp

rice

-quo

tein

form

ativ

enes

sin

the

cros

s-se

ctio

n

Thi

sfig

ure

grap

hsC

hi-X

and

Eur

onex

tpri

ce-q

uote

info

rmat

iven

ess

agai

nsta

prox

yfo

rth

ere

lativ

eim

port

ance

of‘h

ard’

info

rmat

ion

defin

edas

any

publ

icin

form

atio

nth

atca

nbe

proc

esse

dby

mac

hine

s(e

.g.,

pric

ech

ange

sin

the

inde

xfu

ture

s,sa

me

indu

stry

stoc

ks,f

orei

gnex

chan

gera

te).

Pric

equ

ote

info

rmat

iven

ess

isde

fined

asth

epr

edic

tive

pow

erof

mid

quot

e(a

vera

geof

the

bid

and

ask

quot

e)pr

ice

chan

ges

for

the

amou

ntof

info

rmat

ion

that

isre

veal

edin

betw

een

trad

es.

The

met

hodo

logy

isba

sed

onlin

ear

proj

ectio

ns(P

e−

Pi)(∆

f)an

da

coin

tegr

atio

nm

odel

(see

Sect

ion

2.4)

.T

heva

riab

les

are

calc

ulat

edas

aver

ages

per

stoc

kan

dth

egr

aphs

repr

esen

tdis

pers

ion

inth

ecr

oss-

sect

ion.

The

size

ofth

edo

tcor

resp

onds

toav

erag

est

ock

volu

me.

0 1 2 3 4 5

15

20

25

30

35

40

45

50

55

60

(bp)

rela

tive

size

of i

ndex

com

pone

nt in

effi

cien

t pric

e in

nova

tion

(%)

Eur

onex

t mid

quot

e pr

ice

upda

te in

form

ativ

enes

sC

hi-X

mid

quot

e pr

ice

upda

te in

form

ativ

enes

s

56

Figure 10: Price quote informativeness: index vs nonindex component

This figure decomposes the bottom graph of Figure 9 into the price-quote informativeness of the index-correlated component of the predictability and an orthogonal component.

0

1

2

3

4

5

15 20 25 30 35 40 45 50 55 60

(bp)

relative size of index component in efficient price innovation (%)

Euronext midquote price update informativeness on index componentChi-X midquote price update informativeness on index component

0

1

2

3

4

5

15 20 25 30 35 40 45 50 55 60

(bp)

relative size of nonindex component in efficient price innovation (%)

Euronext midquote price update informativeness on nonindex componentChi-X midquote price update informativeness on nonindex component

57

middlemen in limit-order markets1 - semantic scholar · 2015-07-28 · control sample as they had...

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