Liquidity Cycles and Make/take Fees in Electronic Markets

Liquidity Cycles and Make/take Fees in Electronic Markets Thierry Foucault, HEC Ohad Kadan, Ohlin School of Business Eugene Kandel, Hebrew University

Preliminary, Comments Welcome!

Liquidity Cycles and Make/take Fees in Electronic Markets Introduction

Motivations 1/2

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Make/take cycles in electronic markets.

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Alternation of two phases in limit order markets: 1. "Make-liquidity" phase: The limit order book …lls (competition among liquidity providers) 2. "Take-liquidity" phase: A trade takes place and consumes liquidity 3. The cycle restarts...

Liquidity Cycles and Make/take Fees in Electronic Markets Introduction

Example

Source: Biais, Hillion and Spatt, Journal of Finance, 1995.

Liquidity Cycles and Make/take Fees in Electronic Markets Introduction

Motivations 1/2

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=) Alternation of pro…t opportunities for liquidity providers and then liquidity takers. 1. Competition among "liquidity-makers" is similar to a race: importance of being …rst to supply liquidity after a transient decline liquidity. 2. Same thing for "liquidity-takers".

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=) Monitoring the market is important. 1. But monitoring is costly as it requires attention. 2. It is increasingly automated (algorithmic trading)=)Huge reduction in monitoring costs.

Liquidity Cycles and Make/take Fees in Electronic Markets Introduction

Example

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IBM brochure:

"Tackling latency: the algorithmic arms race".

Liquidity Cycles and Make/take Fees in Electronic Markets Introduction

Questions I

What is the nature of competition between (i) "liquidity-makers" and (ii) "liquidity-takers" in presence of monitoring costs?

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How does a reduction in monitoring cost change this competition and a¤ect the trading rate? How does it change the distribution of trading pro…ts between the two sides?

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What is the role of make/take fees in this context? 1. Trading platforms (e.g., ECNs in the U.S, Chi-X and Turquoise in Europe etc...) charge di¤erent fees on liquidity demanders and liquidity suppliers. 2. Why? Why subsidies for liquidity makers? Should "access" fees be capped as in RegNMS? Likely to become an issue in MiFID as well

Liquidity Cycles and Make/take Fees in Electronic Markets Introduction

Make/Take Fees-Examples

Platform BATS ($/share*100/tape A) NYSE ($/share*100/tape A) NYSEArca ($/share*100/tape A) Chi-X (bps) Turquoise (bps)

Make Fee -0.024 0 -0.028 -0.2 -0.15

Take Fee 0.025 0.008 0.029 0.3 0.35

Liquidity Cycles and Make/take Fees in Electronic Markets Introduction

Make/Take Fees and Algo Trading "It’s very easy to fall in love with the idea of maker-taker incentives, but hard to think through the consequences in terms of what that means for how public customers trade and how our markets work." Michael Bickford, senior vice president in charge of options at the American Stock Exchange. "It’s probably too soon to tell if the model is working. Algo trading is anticipated to grow, but whether that grows with or without a maker-taker model or is spurred on by that model has yet to be seen." Gary Katz, President of ISE. in "Options maker-taker markets gains steam", Traders Magazine, October 2007.

Liquidity Cycles and Make/take Fees in Electronic Markets Model

Model

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Market participants: two distinct specialized sides/sectors. 1. M market-makers: post quotes (e.g., high frequency electronic market-makers such as GETCO, ATD, Tradebot systems, Inc., Optiver). 2. N market-takers: hit quotes (e.g., brokers slicing orders).

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Gains from trade: L. 1. Market-makers value the security at v0 2. Market-takers value the security at v0 + L

Liquidity Cycles and Make/take Fees in Electronic Markets Model

Splitting gains from trade I

Prices must be on a grid with tick size ∆

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Market takers do not trade at a price larger than a = v0 + ∆/2 (e.g., v0 + ∆/2 < v0 + L).

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Order size restricted to nmax =1 share.

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Fees: parties to a transaction pay a total fee c to the "matchmaker" (the trading platform) 1. The market-maker pays cm ; get per trade: πm =

∆ 2

2. The market-taker pays ct = c πt = L

cm , cm ; get per trade: ∆ 2

ct .

Liquidity Cycles and Make/take Fees in Electronic Markets Model

Cycles

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Two states: 1. State E (low liquidity): The book is Empty: there is a pro…t opportunity (π m ) for a market-maker 2. State F (high liquidity): The book is Full: there is a pro…t opportunity (π t ) for a market-taker.

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Transitions: 1. From E to F: when a market-maker posts an o¤er. 2. From F to E: when a market-taker hits an o¤er.

Liquidity Cycles and Make/take Fees in Electronic Markets Model

Monitoring 1/2 I

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Each market-maker controls her monitoring intensity em it takes for her to become (λi ): it determines the time T aware that the book is in state E and posts an o¤er. Each market-taker controls his monitoring intensity (µi ): et it takes for him to become aware it determines the time T that the book is in state F and trades. Monitoring costs per unit of time: quadratic in monitoring intensities λi and µi : Cm (λi ) = Ct (µi ) =

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γ and β= "Monitoring Costs"

1 2 βλ 2 i 1 2 γµ 2 i

Liquidity Cycles and Make/take Fees in Electronic Markets Model

Monitoring 2/2 I

em and T et , have an exponential distribution Reaction times, T with parameters λi and µi .

Liquidity Cycles and Make/take Fees in Electronic Markets Model

Objective Functions I I

Market participants maximize their expected pro…t per unit of time. Reward-renewal theorem (Ross (1988))=) 1. Expected Pro…t Market-Makers: ¯ m λ µπ ¯ λ¯ ) = ¯i Πim (λi , µ, λ + µ¯

1 2 βλ 2 i

2. Expected Pro…t Market-Takers: ¯ t µ µπ ¯ λ¯ ) = ¯i Πjt (µi , µ, λ + µ¯ 3. Expected Pro…t Trading Platform: µ¯ λ¯ ¯λ + µ¯ I

( cm + c t )

Observe complementarity of both sides.

1 2 γµ 2 i

Liquidity Cycles and Make/take Fees in Electronic Markets Model

Timing and Equilibrium Concept

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Timing: 1. The trading platforms chooses its fee structure: cm , ct 2. Market participants choose their monitoring intensities 3. Rest of the game: the game is played forever on a continuous time line

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Nash equilibrium in monitoring intensities

Liquidity Cycles and Make/take Fees in Electronic Markets Model

Trading Activity for Fixed Fees

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Finding 1: Two equilibria: (i) one with low levels of monitoring and low trading rate and (ii) one with high levels of monitoring and high trading rate.

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Intuition: monitoring decisions of both sides are self-reinforcing.

Liquidity Cycles and Make/take Fees in Electronic Markets Model

Trading Activity for Fixed Fees

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Finding 2: In equilibrium, the trading rate increases in: 1. The number of participants on both sides. 2. The inverse of traders’monitoring costs (γ 3. Traders’expected pro…t per trade.

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1

and β

1

).

Implications: 1. Complementarities in participation decision (membership is important) 2. Improvements in monitoring technologies =) Burst in trading volume 3. The trading platform can control the trading rate through its fees.

Liquidity Cycles and Make/take Fees in Electronic Markets Model

Imbalanced Attention I

γπ (2M 1 )

Finding 3: If βπmt (2N 1 ) > 1 then the market-side monitors more intensively than the market-taking side.

Liquidity Cycles and Make/take Fees in Electronic Markets Model

Implications 1/2 I

Average reaction times after a large market order are not necessarily identical for the market-making side and the market-taking side.

1/λ

Offer : Market enters in state F

1/µ Trade : Market enters In State E I

Trade : market enters in State E.

=) O¤er an empirical way to identify some parameters.

Liquidity Cycles and Make/take Fees in Electronic Markets Model

Implications 2/2

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The side "short" of attention slows down the trading process=)Incentive for the trading platform to choose its fees so as to rebalance attention. That is: 1. Reduce the fee on the side short of attention (increase its bene…t per trade) 2. Increase the fee on the side long of attention (reduce its bene…t per trade)

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Is this intuition correct?

Liquidity Cycles and Make/take Fees in Electronic Markets Model

The role of make and take fees I

Objective of the trading platform: Maxfcm ,ct g (cm + ct ) | {z }

Margin per trade

µ¯ λ¯ λ¯ + µ¯ | {z }

Trading Rate

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Finding 4: For each level of its total fee (c), there is a breakdown of its fee between the two sides that maximizes the trading rate and thereby the trading platform revenue.

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Remark: In general, a ‡at fee (cm = ct ) is not optimal so that there is a make-take spread (cm ct 6= 0).

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Intuition: The platform should equalize the e¤ects of a marginal change in each fee on its trading volume by balancing the amount of attention on each side.

Liquidity Cycles and Make/take Fees in Electronic Markets Model

Example

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Suppose ∆ = 1; γ = 2; β = 1; c = 10%∆; L = 1; M = N = 1. µ¯ λ¯ Trading Rate ∂Vol ∂cm ∂Vol ∂ct

cm = ct = 0.05 0.06 0.088 0.0389 -0.98 -1.23.

cm = 0.088 0.072 0.085 0.039 -1.1 -1.1

Liquidity Cycles and Make/take Fees in Electronic Markets Model

Determinants of the make-take spread

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Let r =

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Finding 5: When M = N = 1, the optimal fee structure is:

γ β

cm =

1 2

∆

2(L

c) 1

1+r4

and ct = c

cm

Liquidity Cycles and Make/take Fees in Electronic Markets Model

Determinants of the Make-Take Spread

Tick Size Make-Take Spread >0 : MarketMakers are optimally charged more than market-takers

Make-Take Spread