Front-running and post-trade transparency
Corey O. Garriott†
Bank of Canada
Post-trade transparency is thought to increase the potential for
costly front-running, but order management can circumvent frontrunning and can even make it welfare-improving. This weakens
the critique of efforts to increase post-trade transparency. Frontrunning is indeed harmful to traders who must transact at a
fixed and future time. Competition among front-runners improves welfare, and front-running tends to attract competition
since it causes observable price momentum.
Part of the business of professional trading is to construct a position
without disclosing the intention to do so. If it becomes obvious someone is
buying, others might buy to raise prices and then sell at them. The practice
of moving prices ahead of future flows and trading against the flows is called
front-running.1 Market participants who cannot disguise their trading intentions can suffer higher transactions prices; after the London whale incident
in 2012, Reuters wrote: “Whenever a trader has a large and known position,
the market is almost certain to move violently against that trader.”2
Financial institutions have used the potential for front-running to argue
against increasing post-trade transparency.3 They point out there is “information leakage” in the record of trade that can be used to infer their future
trading intentions and that if they are front run they are likely to supply
less liquidity.
In a trading game I present, information leaked to front runners is instead
good for market quality and for individual market participants. The game’s
front runner knows another market participant must transact a large “block”
quantity. The trader who must transact the block has the freedom to choose
the number and the timing of its transactions. If the block trader uses a good
order management strategy, it can circumvent front-running. The strategy
†
Contact: cgarriott@bankofcanada.ca. 234 Wellington St., Ottawa, Canada, K1N 5E6.
For a broker to trade ahead of its own clients’ orders is illegal in many jurisdictions,
but it is both legal and common for market participants to anticipate order flows by other
means, such as the history of trade. See Harris (2003, chap. 11, “Order Anticipators”)
2
“JP Morgan: When basis trades blow up.” Felix Salmon, 10 May 2012, Reuters.
3
For example, “OTC Derivatives Reform: A Discussion of OTC Markets in the Canadian Context.” CanDeal, June 2012.
1
1
is to distribute its trades in such a way as to motivate the supply of liquidity.
The presence of agents who have knowledge about future flows can hence
be welfare-improving. Front-running is costly to traders only if they must
trade at fixed and future times.
In the game, agents may buy and sell an asset in a dealer-intermediated
market. One of the agents present is a front runner. The front runner has
special information about future trading flows. If it knows the future flows
are to arrive at fixed and future times, the runner exploits its knowledge by
trading to move prices against the flows. The runner starts moving prices
immediately, well in advance of a future flow, because it pays equilibrium
transactions costs on which it can economize by trading incrementally. The
runner is successful in moving prices against future flows, and so it extracts
a rent.
In contrast, if the runner knows the future flows are to come not at fixed
future times but at times chosen by a “block trader” agent, who has an
exogenous need to construct a given block position, the runner’s presence
is instead welfare-improving. The runner would still like to push prices
against the block trader, but the block trader responds opportunistically.
The block trader distributes its trades through time in a way that motivates
the runner to supply liquidity. The strategy is (in part) to do the front
runner’s front-running for it, incentivizing the runner to trade against the
flows.
The policy implication is that traders (at least in this model’s market
structure) should not fear information leakage but in fact should prefer the
trading record be as transparent as possible so as to attract liquidity supply. Empirically some traders do in fact employ transparency to source
liquidity—whence the practice of sunshine trading, the announcement that
a particular agent is going to place a large trade. There are some caveats
to the model’s result. The model market is assumed to be intermediated by
anonymous and competitive dealers. If a block trader must trade bilaterally with one dealer in a noncompetitive setting, it is likely the block trader
would receive poor prices.
1.1
Contribution
The theoretical literature on front-running has focused on a conflict of interest posed by “dual trading” broker-dealers and brokers who internalize
(Röell 1990, Fishman and Longstaff 1992, Sarkar 1995). There could be a
conflict because dual-trading brokers often trade against their own clients.
But in some cases internalization in a competitive brokerage market can ac2
tually benefit uninformed traders. The reason is that verifiably uninformed
order flow is a commodity for which brokers compete. The older literature
did not endow agents with information about future flows. Bernhardt and
Taub (2008) did, and it is the paper most related to this one. They study
a two-period model in which the direction of liquidity trading persists. Liquidity traders are front-runned, and the runner extracts a rent. The case
that Bernhardt and Taub study is similar to the first case studied in this
paper, in which flows must arrive at a fixed future time.
Past literature has not focused on the time-series structure of frontrunning (and of avoiding being front-run), which is the focus here. In addition past literature studied running under the assumption of asymmetric
information about value, which was assumed because it enables the order
flow to impact prices. In contrast in this paper price impact derives from
limited capacity to bear risk, which dispenses with the need for private information about value. A pure-liquidity Kyle (1985) model is novel.
1.2
Structure of the paper
The model is defined in section two. Section three gives equilibrium outcomes under two different assumptions about what a front runner knows. In
the first version of the model (section 3.1) the front runner knows the order
flow will arrive at fixed future times. In the second version of the model
(section 3.2) the front runner knows future order flow is being managed by
a rational block trader who can choose the times and quantities at which it
trades. In section 4 the paper gives conclusions.
2
Model
There are T periods of trade indexed by t ∈ {1, 2, ..., T }.
There is one asset, infinitely divisible and in infinite supply. The asset
trades at price pt at time t. At the end of the game the asset pays a cash
dividend ν that is random and follows the normal distribution with constant
mean scaled to zero (without loss of generality),
ν ∼ N (0, σ).
(1)
There is one “front runner” agent. A front runner maximizes trading
profits by choosing signed trades xt to maximize the risk-neutral objective
" T
#
X
E −
p t xt .
(2)
t=1
3
There is a unit measure of “dealer” agents. They are infinitesimal, have
identical properties, and behave identically in equilibrium, so I do not index
them. They choose signed trades yt to maximize the CARA objective
"
!#
T
X
E − exp −YT ν +
,
(3)
pt yt
t=1
P
where Yt = tτ =1 yτ is the dealers’ inventory at the end of period t. Dealers
begin the game with zero inventory of the asset, Y0 = 0.
There is one “liquidity trader” agent that chooses signed trades zt . This
paper will study the model’s equilibrium outcome for two versions of the
liquidity trader. In the first version, the liquidity trader is a typical microstructure noise trader that draws zt from a normal distribution,
zt ∼ N (0, σz )
(4)
In the second version, the liquidity trader is a “block trader” who must
end the game with the inventory objective Q, which can be negative. The
block trader chooses signed trades zt to maximize the risk-neutral objective
function
" T
#
X
E −
pt zt
(5)
t=1
s.t. ZT = Q,
Pt
where Zt = τ =1 zτ is the block trader’s inventory at the end of period t.
The information sets are as follows. All agents in period t are aware of
the history of past prices ht = {pτ }t−1
τ =1 and the dealers’ initial inventory
Y0 . In addition, the runner has special knowledge about future flows in its
information set I. In the first version of the model, the version with a noise
trader, a runner knows the noise trader’s flows:
I = {zt }Tt=1 .
(6)
In the second version of the model, the version in which there is a block
trader, a runner knows the block trader’s inventory objective:
I = Q.
(7)
The mechanism of trade is the idealized Kyle (1985) batch-order market.
Accordingly xt and zt are interpreted as market orders, and the sum of
4
market orders is interpreted as the order flow.4 The dealers’ yt is interpreted
as orders filled by the dealers.5 The timing every period is as follows. First
the front runners and liquidity trader post market orders to the dealers.
Then the dealers form a price pt competitively. Then the dealers choose to
fill a quantity of the posted orders yt . Last the order flow and the dealers’
fill is executed at the price pt .
3
Equilibrium
Definition A competitive equilibrium is a sequence of prices and trades
{pt , xt , yt , zt }Tt=1 for which xt and yt maximize (2) and (3), and if the liquidity
trader is a block trader zt maximizes (5), and prices motivate dealers to fill
unmatched orders, yt = xt + zt .
Proposition 1 The equilibrium price sequence (in both model versions) is
pt = σYt
(8)
= σ (Yt−1 + xt + zt )
All proofs are in the appendix.
The prices exhibit a time-varying inventory premium, which is the difference between the equilibrium prices pt and E[ν]. The premium is an
inventory premium because the asset price increases with volatility if dealers are long whereas the price decreases with volatility if dealers are short.
The premium is linear in the dealers’ inventory and linearly increasing in
the order flow. The premium persists from period to period, compensating
dealers for bearing risk. Since prices increase linearly in the order flow, the
front runner pays a transactions cost that is quadratic.
3.1
Equilibrium with a noise trader
Suppose zt is drawn using (4).
Proposition 2 The front runner’s equilibrium market order sequence is
T
X
xt = −αt Yt−1 − αt zt + αt
β τ zτ
(9)
τ =t+1
where αt = 1/(T + 2 − t) and βτ = T + 1 − τ .
4
For a discussion of the definitions of market order and order flow, see Harris (2003).
Due to the interpretation of yt as a filled order, the sign of the dealers’ trades is
inverted: positive yt are dealer sells. The convention keeps all signs in the model positive.
5
5
To understand the front runner’s behavior, consider three extreme cases.
First suppose the noise trader only trades once and at the beginning of the
game, so zτ = 0 for τ > 1. In such a case the front runner has nothing
to front run, so it merely arbitrages the price toward E[ν]. It absorbs a
constant quantity of the dealers’ inventory every period, xt = −z1 /(T + 1).
The runner absorbs the dealers’ inventory incrementally and in equal pieces
rather than all at once so as to economize on the quadratic transaction costs.
Next suppose the noise trader only trades once but at the end of the
game, so zτ = 0 for τ < T . Now the front runner slowly moves prices
toward an ideal period-T execution price. Every period before T it trades a
constant quantity αt (zT − Yt−1 ), which guides Yt−1 to the value zT at rate
αt , and hence guides the price toward σzT . As before, the runner trades
incrementally so as to economize on the quadratic transaction costs.
Last suppose the noise trader only trades twice, at two different times t1
and t2 . Now the front runner trades off the transaction costs necessary to
move the time-t1 price toward its ideal with the transaction costs necessary
to move the time-t2 price toward its ideal.
Definition “Prices exhibit momentum” at time t if the sign of the price
change at time t − 1 is expected to persist in period t,
sgn (E [∆pt |ht ]) = sgn (∆pt−1 )
(10)
and “prices exhibit a reversal” if the equality does not hold.
Proposition 3 For some quantity γt < 1 given in the appendix, for times
t < T prices exhibit momentum if
|pt−1 | > γt |pt−2 |
(11)
and if not, they exhibit a reversal.
A peculiarity of the runner’s strategy against a noise trader is that the
strategy induces price momentum, i.e. a persistence in the first differences
of prices, which is empirically observable. Price momentum is an artifact of
the runner’s decision to trade incrementally and well in advance of future
flows. Since price momentum is observable to third parties it stands to
reason other agents might monitor the order flow for signs of front-running
and trade on the information. Front-running tactics suffer from their own
form of information leakage. The information leaked by a front-runner’s
own trading behavior would attract the entry of additional front-runners.
6
Proposition 4 The entry of additional runner agents is welfare-improving
for the noise trader (assuming the noise trader’s utility is increasing in
wealth).
Additional front runners are welfare-improving for the same reason that
additional Cournot oligopolists are welfare-improving. Multiple runners
would like to coordinate to split the surplus of front-running but their individual incentives are not sufficiently well-aligned to sustain cooperation.
Because their incentives to cooperate are weak they are more prone to arbitrage the price (and absorb dealer inventory) relative to the behavior of a
single, “monopolist” front-runner.
3.2
Equilibrium with a rational block trader
In contrast to section 3.1, suppose zt is instead chosen as the arg max of (5).
Proposition 5 The block trader prefers the runner agent be present.
The block trader benefits by the runner agent because it can induce the
runner agent to supply liquidity. The technique it uses to win liquidity from
the runner is to partition its orders into many small pieces.
It might seem the timing of flows should make a negligible difference
to the runner, who should be interested mostly in the total quantity. The
timing makes a difference because the block trader is doing the running
for the front runner. Suppose the block trader were to trade its entire
quantity in the last period of trade. The front runner would react as it
does in section 3.1, incrementally moving prices against the flow until the
final period, when it executes against the flow. Since prices are going to go
up anyway, the block trader may as well move prices itself because it can
construct some of its position along the way. In such a case the front runner
would do nothing until the final period.
In fact, the block trader goes a step further than moving prices for the
runner. If it trades more than the front runner would in order to move
prices, it can induce the front runner to supply it liquidity along the way,
which further reduces the block trader’s price impact. The dynamics of the
block trader’s strategy are presented in figure 1.
4
Conclusions
The model shows it is not obvious that information leakage about future
trading intentions is bad for a block trader or for market quality. One
7
common critique of increasing post-trade transparency—that it will cause
information leakage—is of questionable concern in market structure design
at least in market structures with dealers who compete for client orders.
Trading professionals are aware of countermeasures against front-running.
So why do many in the finance industry oppose increasing post-trade transparency? It is possible the industry opposes post-trade transparency not
because it leaks information about future trading intentions but because it
leaks commercial information, such as a company’s view on fundamentals
or the composition of its clientele, both of which are outside the scope of
this model. The protection of commercial information is a motive that is
less likely to arouse the sympathy of regulators.
The paper has an additional policy implication unrelated to post-trade
transparency. The model contributes to the explanations for the “excess
volatility” in stock prices by introducing dealer inventory as a pricing factor. Intermediaries move prices away from fundamentals as compensation
for bearing risky inventory. The price movements are akin to the “persistent,
but transitory, disparities between prices and fundamental values” observed
by Poterba and Summers (1988). Dealers’ inventories add variation in prices
that is not sourced from dividends, and front running can both amplify and
dampen the variations. The volatility of prices decreases as the market’s
risk-bearing capacity increases. Price movements associated with trading
are more volatile in markets that struggle to bear risk, so rulemakers should
carefully study the impact of rules such as the Volcker rule that discourage risk-bearing liquidity suppliers in core funding markets from holding
positions.
5
Appendix
Proposition 1
Proof It is necessary to solve backward in order to resolve expectations about the
price path including the way yt affects future prices. The dealers’ final-period value
function (with market-clearing condition) is
UT (YT −1 ) = max − exp (−(YT −1 + yT )ν + pT yT ) pT s.t. yT = xT + zT
yT
= − exp YT2−1 σ/2 exp −(xT + zT )2 σ/2
8
so the market-clearing price pT is as given in (8). Solving backward, the period-t
value function is
Ut (Yt−1 ) = max max EUt+1 (Yt ) pt s.t. yt = xt + zt
yt
yt+1
P
T
2
= − exp Yt−1
σ/2 E exp − τ =t (xτ + zτ )2 σ/2
for which the period-t price is as given in (8). The value functions are globally
concave in the choice variable yt , so equilibrium prices are unique.
Proposition 2
Proof Guess the front runner’s value function has a quadratic form,
PT
2
V̂t (Yt−1 ) = At Yt−1
+ Yt−1 τ =t Bt,τ zτ + Ct
where Ct includes all terms that have derivatives with respect to xt equal to 0.
Maximize the value function substituting the quadratic form,
Vt (Yt−1 ) = max − pt xt + V̂t+1 (Yt )
xt
2 PT
=
4(σ − At+1 ) = V̂t (Yt−1 )
τ =t+1 Bt+1,τ zτ + Yt−1 + zt σ
which identifies the system of difference equations
At =
σ
σ
4 σ − At+1
Bt,τ = 2At Bt+1,τ , t < τ
and boundary values Bτ,τ = 2At . The front runner’s final-period value function is
2
VT (YT −1 ) = max {−pT xT } = (YT −1 + zT ) σ/4
xT
which identifies boundary value AT = σ/4. Hence the coefficients equal
for t ≤ T
At = αt βt σ/2
for t ≤ τ ≤ T.
Bt,τ = αt βτ σ
The market order at time t is the argmax of V̂t using control xt .
Proposition 3
Proof Prices pt yield a noisy signal st of present and future order flows,
PT
st = pt /(σαt ) − βt Yt−1 = τ =t βτ zτ = st+1 + βt zt ,
that is ordered by Blackwell’s criterion for the ordering of information structures
(Blackwell and Girschick, 1954). Given pt and Yt−1 the history ht is uninformative
about zτ for τ ≥ t.
9
Using the signal-slope coefficients
λt,τ =
cov (pt , zτ )
σ 2 αt βτ
6βτ
1
=
,
PT 2 =
2
3
var (pt )
βt (1 + 2βt ) σ
σ αt i=t βi
the posterior means of future liquidity flows zτ , τ ≥ t, can be written
E [zτ |pt ] = λt,τ (pt − E [pt |Yt−1 ])
= λt,τ (pt − (1 − αt )pt−1 ) ,
where the second expectation is taken conditional on only Yt−1 using Blackwell’s
ordering. The posterior mean of ∆pt is
E [∆pt |ht ] = δ1 pt−1 − δ2 pt−2
where δ1 = 1 − 6/(2T + 5 − 2t) and δ2 = 1 − 6/(T + 3 − t) + 6/(2T + 5 − 2t). The
term γt mentioned in the statement of the proposition satisfies γt = δ1 /δ2 . The
term δ1 > 0 only for t < T , so (11) holds for t < T .
Proposition 4
Proof The dealers’ problem does not change substantially, so pt = σYt still.
It is sufficient to show the total rents extracted by N front runners is decreasing
in N . All rents are extracted from the noise trader since the dealers are competitive.
If the noise trader has any structure of utility that decreases in rent paid, it prefers
more runners.
From one front runner’s perspective, dealer inventory evolves as Yt = Yt−1 +
xt + (N − 1)x̄t + zt , where x̄t is the market order of the other runners held constant.
Maximizing the same value function form as in proposition 2,
Vt (Yt−1 ) = max − pt xt + q V̂t+1 (Yt )
xt
2
Pk
(σ − qA) σ(Yt−1 + zt ) + qN τ =1 Bτ zt+τ
=
= V̂t (Yt−1 ),
2
(σ + N (σ − 2qA))
in which x̄t has already been set to the arg max. The maximum identifies the
system of difference equations and boundary conditions,
σ 2 (σ − At+1 )
(σ + N (σ − 2At+1 ))2
σ2
AT (N ) =
(N + 1)2
At (N ) =
Bt,τ (N ) =
2N At Bt+1,τ
σ
Bτ,τ (N ) = 2Aτ
PT
2
τ =t N Bt,τ zτ /σ)
For the proof I employ the substitution At = σ2 − for some ∈ (0, σ2 ). The satisfies its bounds because if At+1 ∈ (0, σ2 ) then At does too, and AT = σ/(N +1)2 .
σ/2+
σ
The proof is that if At+1 = σ2 − ˆ, 0 < At = σ2 σ2 (σ/2+N
ˆ)2 < 2 .
Ct = Ct+1 + At (σzt +
10
PT
Total rents equal N At (N )Yt2 + N Yt τ =t Bt (N )zt + N Ct (N ). First N AT (N ) is
obviously decreasing in N . The term N At (N ) is decreasing in N since N At (N ) =
2
(σ/2+)
(N +1)σ 2 (σ/2+)
σ 2 (σ/2+)
N σ(σ+4N
)2 = N (N +1)(σ 2 +4N σ+16N 2 2 ) > (N + 1) (σ 2 +4(N +1)σ+16(N +1)2 2 ) = (N +
1)At (N + 1). It follows immediately that N Bτ,τ (N ) is decreasing in N . Since
N Bt (N ) is composed of τ − t multiples of At and N , it is decreasing in N . Since
N Ct is composed of terms N At (N ) and N Bt,τ (N ), it is decreasing in N .
Proposition 5
Although the agents’ value functions are identifiable in closed form, the difference
equation governing the value of their coefficients is not susceptible to proof. The
value function can be identified for games of finite length T computationally.
Proof Denote by Wt (Yt , Zt ) the block trader’s value function. If there is no runner,
it is easy to solve for W :
Wt (Yt , Zt ) = −σYt Zt − σZt2 /(2αt βt )
If there is a front runner, guess the runner’s value function Vt (Zt , Yt ) and the block
trader’s value function Wt (Zt , Yt ) both have quadratic forms,
V̂t (Yt , Zt ) = At Yt2 + Bt Zt Yt + Ct Zt2
Ŵt (Yt , Zt ) = Dt Yt2 + Et Zt Yt + Ft Zt2
and as before solve for the system of difference equations that govern the values of
At , Bt , Ct , Dt , Et , and Ft . The system is6
Ft−1 = (ot + 4Ft2 jt + mt − it n2t )σ/c2t
Et−1 = 2(Ct + it )(4Ft ht − lt nt )σ/c2t
Ct−1 = (Bt2 ft + 2Bt et ft + e2t ft − Ct d2t )σ/c2t
Dt−1 = (Ct + it )(4Dt Ft − lt2 )σ/c2t
Bt−1 = −2(Ct at dt + Bt bt ft + bt et ft )σ/c2t
At−1 = (Ct a2t + b2t − At b2t )σ/c2t
Clearly the system is too complicated to admit of general properties, but it is
easy to identify the value function coefficients computationally.
The object of interest is to compare the value funciton W1 to Ŵ1 for various game lengths T . Since the dealer starts with no inventory, comparing the
two reduces to comparing −σαt βt /2 to Ft . The graph below compares the two.
6
Define constants at = 1 − 2Dt + Et , bt = 1 + Et − 2Ft , ct = −3 + 2Dt − 3Et + 4Ft +
Bt at + 2At bt , dt = −3 + 2At + 2Dt − Et , et = Et − 2Ft , ft = At − 1, gt = 2At + Et − 1,
ht = At + Dt − 1, it = Dt − Et − 1, jt = 2At + Dt − 2, kt = 2At + Dt − 3, lt = 1 + Et ,
mt = −Ft (Et2 + 2Bt gt + 4Et jt − 4Dt kt ), nt = Bt + Et , ot = (3 − 2At )2 Ft .
11
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