• Single asset, no asymmetric information
• Investors value it at either +V (buyers) or -V (sellers)
  • Arrive asynchronously (one per period)

• Trading:
  • Post limit orders or trade with market orders
  • Several simplifying assumptions (limit orders good for one period, one limit order/one lot at a time, etc.)
  • Maker-taker exchange:
    • taker fee for market orders
    • maker rebate for limit orders

• "maker-taker": pay taker fees on market orders & receive maker rebates on limit order trades
  • e.g., because they access the exchange directly or b/c or the "tiered plan"
• "flat-fee": pay fixed/flat broker commission
  • competitive broker, charges the average of the fees
  • same fixed fee, no matter the type of order

• weighted by the probabilities of "flat fee" investors trading with market vs. limit orders
• flat fees = average exchange fees incurred by the broker

• fee for limit orders
• assumed <0 (rebate)

• fee for market orders
• assumed > 0 

maker fee < flat fee < taker fee

ask

bid

bid$+$flat fee

bid$-$maker rebate

flat fee buyer: get spread/2 - flat fee

maker-taker buyer: get spread/2 + maker rebate

Ceteris paribus:

• limit orders are more attractive for "maker-taker" traders than for "flat-fee" traders 

 "Maker-taker" traders post better quotes

$\Rightarrow$ for a given limit order book state

1. When a "maker-taker" trader prefers trading with with a market order to submitting own limit order, so does the "flat-fee" investor.
2. When a "flat-fee" investor prefers to use a limit order, so does the "maker-taker" trader

• "Maker-taker" and "flat-fee" traders are willing to accept different prices

Earn a smaller spread but with a larger probability

Earn a larger spread but with a smaller probability

• $\Rightarrow$ can choose to price limit orders in two ways:
  • at "narrow" spreads $\to$ next period, all traders on the right side of the market send market orders
  • at "wide" spreads $\to$ next period, only "flat-fee" traders send market orders and "maker-taker" traders prefer to post own limit orders

• (Almost) all traders are "maker-taker"
  • $\to$ need to send limit orders that are attractive enough to these
  • $\to$ all traders submit limit orders at "narrow spreads" 
  • $\to$ all traders use market orders whenever there is an order in the limit order book on the "right side of the market"

• For larger fractions of flat-fee investors ($\lambda>\lambda_1)$:
  • maker-taker traders do not trade against flat-fee trader limit orders (spreads are too wide)
  • $\to$ lower volume & unrealized gains from trade
  • $\to$ maker-taker/asymmetric fees are detrimental to welfare 

Establishing causality from historical data is challenging

• Lower fee asymmetry (i.e., smaller difference between the taker and the maker fees) $\Rightarrow$ larger $\lambda's$
  • $\Rightarrow$ larger $\lambda_1$ $\to$ larger "no distortion" region

• As maker-taker fees change:
  •  thresholds change
  • may switch across different equilibria types
  • $\to$ non-monotonic effects on
    • market quality
    • trading volume

• narrow spreads
• all use market orders

Type 1

Type 3

Type 5

only flat-fee investors use market orders

• MT: market orders only when spreads are narrow
• FF: market orders for all spreads

Highest

Volume

Broker:

client limit orders

client marketable orders

Problem:

• long queue & low exec probability
• trade after Exchange 2 limit orders 
• adverse selection

• Any asymmetry between maker and taker fees may distort routing! 
  • Not just rebates!