Front-running and post-trade transparency

Transcription

1 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. 1 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

2 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 ac- 2

3 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 p t 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 x t to maximize the risk-neutral objective [ ] T E p t x t. (2) t=1 3

4 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 y t to maximize the CARA objective [ ( )] T E exp Y T ν + p t y t, (3) where Y t = t τ=1 y τ is the dealers inventory at the end of period t. Dealers begin the game with zero inventory of the asset, Y 0 = 0. There is one liquidity trader agent that chooses signed trades z t. 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 z t from a normal distribution, t=1 z t N (0, σ z ) (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 z t to maximize the risk-neutral objective function [ ] T E p t z t (5) t=1 s.t. Z T = Q, where Z t = t τ=1 z τ 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 h t = {p τ } t 1 τ=1 and the dealers initial inventory Y 0. 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 = {z t } T t=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 x t and z t are interpreted as market orders, and the sum of 4

5 market orders is interpreted as the order flow. 4 The dealers y t 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 p t competitively. Then the dealers choose to fill a quantity of the posted orders y t. Last the order flow and the dealers fill is executed at the price p t. 3 Equilibrium Definition A competitive equilibrium is a sequence of prices and trades {p t, x t, y t, z t } T t=1 for which x t and y t maximize (2) and (3), and if the liquidity trader is a block trader z t maximizes (5), and prices motivate dealers to fill unmatched orders, y t = x t + z t. Proposition 1 The equilibrium price sequence (in both model versions) is p t = σy t = σ (Y t 1 + x t + z t ) (8) All proofs are in the appendix. The prices exhibit a time-varying inventory premium, which is the difference between the equilibrium prices p t 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 z t is drawn using (4). Proposition 2 The front runner s equilibrium market order sequence is x t = α t Y t 1 α t z t + α t where α t = 1/(T + 2 t) and β τ = T + 1 τ. T τ=t+1 β τ z τ (9) 4 For a discussion of the definitions of market order and order flow, see Harris (2003). 5 Due to the interpretation of y t as a filled order, the sign of the dealers trades is inverted: positive y t are dealer sells. The convention keeps all signs in the model positive. 5

6 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 z τ = 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, x t = z 1 /(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 z τ = 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 α t (z T Y t 1 ), which guides Y t 1 to the value z T at rate α t, and hence guides the price toward σz T. 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 t 1 and t 2. Now the front runner trades off the transaction costs necessary to move the time-t 1 price toward its ideal with the transaction costs necessary to move the time-t 2 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 [ p t h t ]) = sgn ( p t 1 ) (10) and prices exhibit a reversal if the equality does not hold. Proposition 3 For some quantity γ t < 1 given in the appendix, for times t < T prices exhibit momentum if and if not, they exhibit a reversal. p t 1 > γ t p t 2 (11) 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

7 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 z t 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

8 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 y t affects future prices. The dealers final-period value function (with market-clearing condition) is { U T (Y T 1 ) = max exp ( (YT 1 + y T )ν + p T y T ) } pt s.t. y T = x T + z T y T = exp ( YT 2 1σ/2 ) exp ( (x T + z T ) 2 σ/2 ) 8

9 so the market-clearing price p T is as given in (8). Solving backward, the period-t value function is { U t (Y t 1 ) = max max EU t+1 (Y t ) } pt s.t. y t = x t + z t y t y t+1 = exp ( Yt 1σ/2 2 ) ( E exp ) T τ=t (x τ + z τ ) 2 σ/2 for which the period-t price is as given in (8). The value functions are globally concave in the choice variable y t, so equilibrium prices are unique. Proposition 2 Proof Guess the front runner s value function has a quadratic form, ˆV t (Y t 1 ) = A t Y 2 t 1 + Y t 1 T τ=t B t,τ z τ + C t where C t includes all terms that have derivatives with respect to x t equal to 0. Maximize the value function substituting the quadratic form, { V t (Y t 1 ) = max pt x t + ˆV t+1 (Y t ) } x t = ( T τ=t+1 B t+1,τ z τ + ( Y t 1 + z t ) σ ) 2 / 4(σ At+1 ) = ˆV t (Y t 1 ) which identifies the system of difference equations A t = σ σ 4 σ A t+1 B t,τ = 2A t B t+1,τ, t < τ and boundary values B τ,τ = 2A t. The front runner s final-period value function is V T (Y T 1 ) = max x T { p T x T } = (Y T 1 + z T ) 2 σ/4 which identifies boundary value A T = σ/4. Hence the coefficients equal A t = α t β t σ/2 for t T B t,τ = α t β τ σ for t τ T. The market order at time t is the argmax of ˆV t using control x t. Proposition 3 Proof Prices p t yield a noisy signal s t of present and future order flows, s t = p t /(σα t ) β t Y t 1 = T τ=t β τ z τ = s t+1 + β t z t, that is ordered by Blackwell s criterion for the ordering of information structures (Blackwell and Girschick, 1954). Given p t and Y t 1 the history h t is uninformative about z τ for τ t. 9

10 Using the signal-slope coefficients λ t,τ = cov (p t, z τ ) var (p t ) σ 2 α t β τ 6β τ 1 = σ 3 αt 2 T = i=t β2 β i t (1 + 2β t ) σ, the posterior means of future liquidity flows z τ, τ t, can be written E [z τ p t ] = λ t,τ (p t E [p t Y t 1 ]) = λ t,τ (p t (1 α t )p t 1 ), where the second expectation is taken conditional on only Y t 1 using Blackwell s ordering. The posterior mean of p t is E [ p t h t ] = δ 1 p t 1 δ 2 p t 2 where δ 1 = 1 6/(2T + 5 2t) and δ 2 = 1 6/(T + 3 t) + 6/(2T + 5 2t). The term γ t mentioned in the statement of the proposition satisfies γ t = δ 1 /δ 2. The term δ 1 > 0 only for t < T, so (11) holds for t < T. Proposition 4 Proof The dealers problem does not change substantially, so p t = σy t 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 Y t = Y t 1 + x t +(N 1) x t +z t, where x t is the market order of the other runners held constant. Maximizing the same value function form as in proposition 2, { V t (Y t 1 ) = max pt x t + q ˆV t+1 (Y t ) } x t ( (σ qa) σ(y t 1 + z t ) + qn ) 2 k τ=1 B τ z t+τ = (σ + N(σ 2qA)) 2 = ˆV t (Y t 1 ), in which x t has already been set to the arg max. The maximum identifies the system of difference equations and boundary conditions, A t (N) = A T (N) = σ 2 (σ A t+1 ) (σ + N(σ 2A t+1 )) 2 B t,τ (N) = 2NA tb t+1,τ σ σ 2 (N + 1) 2 B τ,τ (N) = 2A τ C t = C t+1 + A t (σz t + T τ=t NB t,τ z τ /σ) 2 For the proof I employ the substitution A t = σ 2 ɛ for some ɛ (0, σ 2 ). The ɛ satisfies its bounds because if A t+1 (0, σ 2 ) then A t does too, and A T = σ/(n +1) 2. The proof is that if A t+1 = σ 2 ˆɛ, 0 < A t = σ 2 10 σ 2 σ/2+ɛ (σ/2+nˆɛ) 2 < σ 2.

11 Total rents equal NA t (N)Yt 2 T + NY t τ=t B t(n)z t + NC t (N). First NA T (N) is obviously decreasing in N. The term NA t (N) is decreasing in N since NA t (N) = N σ2 (σ/2+ɛ) (σ+4nɛ) 2 (N+1)σ 2 (σ/2+ɛ) (N+1)(σ 2 +4Nɛσ+16N 2 ɛ 2 ) 2 (σ/2+ɛ) σ = N > (N + 1) (σ 2 +4(N+1)ɛσ+16(N+1) 2 ɛ 2 ) = (N + 1)A t (N + 1). It follows immediately that NB τ,τ (N) is decreasing in N. Since NB t (N) is composed of τ t multiples of A t and N, it is decreasing in N. Since NC t is composed of terms NA t (N) and NB t,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 W t (Y t, Z t ) the block trader s value function. If there is no runner, it is easy to solve for W : W t (Y t, Z t ) = σy t Z t σz 2 t /(2α t β t ) If there is a front runner, guess the runner s value function V t (Z t, Y t ) and the block trader s value function W t (Z t, Y t ) both have quadratic forms, ˆV t (Y t, Z t ) = A t Y 2 t + B t Z t Y t + C t Z 2 t Ŵ t (Y t, Z t ) = D t Y 2 t + E t Z t Y t + F t Z 2 t and as before solve for the system of difference equations that govern the values of A t, B t, C t, D t, E t, and F t. The system is 6 F t 1 = (o t + 4F 2 t j t + m t i t n 2 t )σ/c 2 t C t 1 = (B 2 t f t + 2B t e t f t + e 2 t f t C t d 2 t )σ/c 2 t B t 1 = 2(C t a t d t + B t b t f t + b t e t f t )σ/c 2 t E t 1 = 2(C t + i t )(4F t h t l t n t )σ/c 2 t D t 1 = (C t + i t )(4D t F t l 2 t )σ/c 2 t A t 1 = (C t a 2 t + b 2 t A t b 2 t )σ/c 2 t 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 W 1 to Ŵ1 for various game lengths T. Since the dealer starts with no inventory, comparing the two reduces to comparing σα t β t /2 to F t. The graph below compares the two. 6 Define constants a t = 1 2D t + E t, b t = 1 + E t 2F t, c t = 3 + 2D t 3E t + 4F t + B ta t + 2A tb t, d t = 3 + 2A t + 2D t E t, e t = E t 2F t, f t = A t 1, g t = 2A t + E t 1, h t = A t + D t 1, i t = D t E t 1, j t = 2A t + D t 2, k t = 2A t + D t 3, l t = 1 + E t, m t = F t(e 2 t + 2B tg t + 4E tj t 4D tk t), n t = B t + E t, o t = (3 2A t) 2 F t. 11

12 References D. Bernhardt and B. Taub. Front-running dynamics. Journal of Economic Theory, 138(1): , D. Blackwell and M.A. Girschick. A Theory of Games and Statistical Decisions. Wiley, M.J. Fishman and F.A. Longstaff. Dual trading in futures markets. Journal of Finance, pages , L. Harris. Trading and exchanges: Market microstructure for practitioners. Oxford University Press, USA, A.S. Kyle. Continuous auctions and insider trading. Econometrica: Journal of the Econometric Society, pages , J.M. Poterba and L.H. Summers. Mean reversion in stock prices* 1:: Evidence and implications. Journal of Financial Economics, 22(1):27 59, A. Röell. Dual-capacity trading and the quality of the market. Journal of Financial Intermediation, 1(2): , A. Sarkar. Dual trading: winners, losers, and market impact. Journal of Financial Intermediation, 4(1):77 93,