Trading Fees and Efficiency in Limit Order Markets Jean-Edouard Colliard1 1

Thierry Foucault2

Paris School of Economics 2

HEC Paris

12th Symposium on Finance, Banking and Insurance, December 16th, 2011.

Plan

Introduction

Model

Implications

Conclusion

Plan

Introduction

Model

Implications

Conclusion

Background

NYSEArca BATS EDGX Nasdaq Nasdaq OMX PSX Nasdaq OMX BX

Make Fee -21 -27 -29 -20 -13 14

Take Fee 30 28 30 30 18 -18

Exchange Fee 9 1 1 10 5 -4

March 2010 (in cents/1000 shares)-Tape A

CESR, April 1st 2010: ”Micro-structural issues of the European equity markets” 1. What are the impacts of current fee structures on trading platforms, participants, their trading strategies and the wider market and its efficiency? 2. Is there a role for regulators to play in the fee structures? Is there room for regulatory intervention in the determination of exchange fees or should we just rely on intermarket competition?

Contribution

Theoretical model of a limit order market where: I

Traders have access to different trading platforms and an OTC market.

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Platforms charge different trading fees to makers and takers.

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Traders’ orders are affected by trading fees and determine prices.

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Fees are set by platforms to maximize profit.

Main results: lower total trading fees can decrease the trading rate and harm investors. The socially optimal trading fee can be positive. The breakdown of fees between makers and takers is neutral.

Fees and the trading rate

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Traders are heterogeneous in terms of waiting costs. ”Patient traders” submit limit orders and gain more.

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Makers can strategically use orders with a low fill rate, exploit impatient traders.

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Higher fees affect patient traders more than impatient traders in equilibrium, hence higher fees reduce ex post heterogeneity, and can reduce rent-seeking strategies.

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Thus a positive fee can be optimal, too much competition between trading platforms can be harmful and decrease the trading rate.

Fees and spreads

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Spreads are positively affected by total fees and make fees, negatively by take fees.

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Total trading costs increase in total fees but are unaffected by the breakdown of fees. ”Cum fee spread”: (A∗ − fta ) − (B ∗ + fta ) = S ∗ + 2fta

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Lower make fees with higher take fees make prices ”look good” but have no fundamental impact on trades.

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Neutrality result ⇒ small frictions are enough to tip the balance.

Related literature

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Competition for order flow: Pagano 1989, Glosten 1994, Hendershott and Mendelson 2000, Parlour and Seppi 2003, Foucault and Menkveld 2008 (...). No maker/taker choice.

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Competition between markets: Yavas 1992, Gehrig 1993, Rust and Hall 2003 (...). Trading fees given or absent.

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⇒ we lack a theory for the supply of trading services.

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Degryse, van Achter, Wuyts 2010.

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Empirical: Malinova and Park 2011, Declerck and Moinas 2010.

Plan

Introduction

Model

Implications

Conclusion

Agents

I I

˜. Market for a zero-coupon bond that pays v0 at a random date T Buyers and sellers arrive sequentially and can trade one unit. 1. Buyers have a value vH = v0 + L. 2. Sellers have a value vL = v0 − L.

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Investors value execution speed: 1. Patient traders discount future payoffs by δH . 2. Impatient traders discount future payoffs by δL .

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All investors have a deadline of one period to execute their trade.

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Competitive dealers have a value v0 and execution costs λ ⇒ spread 2λ on the dealer market.

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4 possible types of investors:

Buyer

Seller

Fraction

Patient

π/2

π/2

π

Impatient

(1 − π)/2

(1 − π)/2

(1 − π)

Fraction

50%

50%

Strategies

Since orders stay in the book for only one period, the book is always either ”full” (one order) or empty. Traders choose between: I

(if there is a matching order in the book) Submitting a market order (M), executed against the limit order in the book, and paying fta to the platform.

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Submitting a limit order (L), accepted either by all traders of the opposite side (1/2) or only by impatient traders ( 1−π 2 ). In case of execution the trader has to pay fma to the platform. In case of non-execution he can use the dealer market in last resort.

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Going directly to the dealer market (D) and get L − λ.

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Direct trade brings 2L minus waiting costs, compared to L − λ.

Market structure

How do we solve the model? We first take fees as given and study investors’ decisions. Knowing these decisions, a monopoly platform selects the level of fees ex ante, or duopolists compete in fees. Upon arrival in the market, an investor’s trade-off is the following: I

Aggressive limit order, high execution probability : bad price, waiting costs, low probability to end up trading in the dealer market.

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Soft limit order, low execution probability : best price, waiting costs, high probability to end up trading in the dealer market.

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Market order : bad price, immediacy. Only possible if there is a matching order in the book.

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Dealer market: worst price, immediacy, always possible.

Markov perfect equilibrium: find the strategy of each type of player in each state of the order book. Gives 5 logically consistent equilibrium types.

Equilibrium Proposition For each parameter values, there is a unique Markov Perfect Equilibrium. The type of equilibrium is determined by dealers’ half-spread λ and trading fees f¯ as on the graph below.

Example: Type #3 equilibrium

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Impatient investors use the dealer market if they don’t submit a market order ⇒ B ∗ − vL − fta = L − λ.

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A patient maker has to leave a surplus of exactly L − λ to a taker. The patient maker (buyer) gets: V ∗ (δH )

1+π 1−π (vH − fma − B ∗ ) + δH (L − λ) 2 2 1−π 1+π δH (vH − vL − (fma + fta ) − (L − λ)) + δH (L − λ) 2 2

= δH =

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Notice that V ∗ (δH ) only depends on f¯ = fma + fta .

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Equilibrium condition: a patient buyer prefers targeting an impatient rather than a patient seller, V ∗ (δH ) ≥ L − λ and V ∗ (δL ) ≤ L − λ.

Competition between a platform and dealers

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We compute the trading rate, stationary probability that a market order is executed on the platform. Monopoly platform’s objective: max TR(f¯, λ) × f¯

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When the dealer market becomes more efficient (smaller λ), the matchmaker reduces its fee.

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Competition from the dealer market however is in general not enough to drive the matchmaker’s fee to zero unless λ is small. Why?

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1. For sufficiently high values of λ, trades in the LOM generates a greater surplus (order processing cost > waiting cost). 2. The matchmaker can therefore capture part of this surplus while still maintaining traders’ incentives to use the limit order market.

Competition between two platforms and dealers

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The platforms coexist (both attracts trades) if they have the same total fee (fma,1 + fta,1 = fma,2 + fta,2 ). Otherwise the platform with the smallest total fee attracts all trading.

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Whether the platforms coexist or not, the equilibrium for fixed fees has the same properties as in the single platform case.

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Competition among matchmakers drives the total fee to zero.

Plan

Introduction

Model

Implications

Conclusion

Trading rate Main point: the trading rate and traders’ welfare can increase when higher fees lead to a switch from type 3 to type 4.

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In a type 3 equilibrium patient traders target only impatient traders and extract a rent. Strategic behavior leading to a low trading rate and low welfare.

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A key reason for this behavior is the heterogeneity between patient and impatient traders: an impatient taker must be left with L − λ, a patient trader with V ∗ (δH ) > L − λ.

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Remember we have: V ∗ (δH ) = δH

I

I


1+π 1−π 2L − f¯ − (L − λ) + δH (L − λ) 2 2

Increasing f¯ decreases V ∗ (δH ) more than V ∗ (δL ) ⇒ heterogeneity decreases ⇒ targeting patient traders becomes more profitable. For a high enough f¯, switch to a UP SI equilibrium. High fees curb patient makers’ rent-seeking behavior.

Fees can be too low

We compute the aggregate welfare for traders in the different equilibria and show the following:

Corollary For some values of λ such that small fees lead to a type 3 equilibrium, increasing fees can improve welfare. Otherwise f¯ = 0 is optimal for investors.

Corollary For all values of the parameters, investors are better off with access to two competing matchmakers rather than a single matchmaker. Increasing fees curbs the rent-seeking behavior. The monopolist matchmaker always avoids the type 3 equilibrium, but extracts too much surplus from traders.

Investor’s Welfare Zero Trading Fee Trading Fee: f 3 (λ) + 

Difference (%)

λ

0.81 0.82 0.85 0.88 0.90

0.33 0.32 0.30 0.27 0.26

0.36 0.34 0.29 0.23 0.19

9% 8.5% -2.2% -17% -25%

Should limit order markets coexist with OTC markets?

Corollary For intermediate values of λ, investors’ welfare can be higher with competing matchmakers and no dealer/OTC markets than with a hybrid structure. Counter-intuitive as without dealers makers get 0 in case of non-execution. ⇒ makes it very costly to have a non-executed limit order ⇒ extracting rent by using orders with a low fill rate becomes too risky.

Investor’s Welfare Hybrid LOM Only

DM Only

Order Processing Cost: λ

0.2 0.5 0.7 0.82 0.99

0.82 0.60 0.45 0.32 0.35

0.35 0.35 0.35 0.35 0.35

0.8 0.5 0.3 0.18 0.01

Fees and spreads

% % Total Fee % Take Fee %-Make Fee&-Total = Take Fee

Make Fee

Traded spread

Cum fee spread

& (not one for one) % (not one for one) Depends

% % %

&

Unchanged

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Easier to test than effects on welfare. See Malinova and Park 2011.

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The correct measure of trading costs is the cum fee spread Spread + 2fta .

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Negative fma and positive fta make prices ”look good”, without any effect on trading costs and welfare.

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Important assumptions: routing decisions based on cum fees prices (but trade-through rules are based on raw prices!), zero tick size. Conjecture: when one of these assumptions do not hold the breakdown of fees matters, Foucault, Kadan and Kandel 2011.

Entry and market share

Corollary Suppose that initially only one matchmaker coexists with a dealer market. Entry of a new matchmaker will reduce the trading rate in the consolidated order market and increase the market share of the dealer market for intermediate values of λ, and otherwise has the opposite or no effect.

Plan

Introduction

Model

Implications

Conclusion

Conclusion (1/2)

Why trading fees matter: I

General focus on the breakdown of fees leads to neglect the effect of total fees. Implicit assumption: only straightforward effects. But this is a strategic situation!

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Erroneous belief: you need makers to have takers, this is a two-sided market hence such a structure is natural.

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Fees control the market power of ”makers”, who compete with dealers.

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Higher fees can limit rent-seeking behavior.

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Proof that it matters: higher fees can increase welfare, even without taking into account the platform’s profits.

Conclusion (2/2)

Market structure determines fees and investors’ welfare: I

The monopolist competes with dealers to attract trades. More competitive dealers curb the monopolist’s market power and are always good for welfare with a monopoly LOM.

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With a duopoly market power is always zero. Then more competitive dealers may decrease total investors’ welfare as it becomes less interesting to submit limit orders with high execution probability. Having no dealers at all can be better.

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Duopoly is better for investors than monopoly.

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The optimal market structure can feature competing platforms, a dealer market and a floor on trading fees (difficult to set in practice).