7Fees, Rebates and Venue Economics

The same stock is bid at the same price on two exchanges. One pays the resting order a rebate and has twenty thousand shares queued ahead; the other charges the resting order a fee and has eight hundred. A trader who wants to be filled should pay to stand in the short line. Exchange fees are a few hundredths of a cent per share, but the spread of a liquid stock is one cent, and the fee split between the side that rests and the side that takes changes where orders go, how long queues are and who gets picked off. This chapter prices orders net of fees, shows when the split of a fee matters, and runs two venues of the exchange simulator side by side, one maker-taker and one inverted, to measure what a rebate buys.

7.1 Maker-taker, inverted and flat pricing

Under maker-taker pricing (One Quant Book 1, chapter 9) the venue pays the resting side a rebate and charges the taking side a fee; an inverted venue (taker-maker) does the reverse. Both earn the difference.

Flat pricing is the norm for futures, where the exchange charges each side a fee per contract, and in many equity markets outside the United States; maker-taker and inverted pricing are how US equity exchanges compete for the two sides of the order flow within a fee cap on taking displayed quotes. The two Cboe venues of the box are the chapter’s running example; the simulation uses their standard rates.

7.2 Fee-adjusted prices and the effective tick

A buyer who takes 1 000 shares at 20.00 pays USD 20.0030 a share on the maker-taker venue and USD 19.9998 on the inverted one: USD 3.20 less on the inverted venue at the same quoted price. The fee differences create prices between the ticks.

With the two Cboe take fees, 0.30 and $-0.02$ cents, the fee-adjusted asks of a one-cent stock sit alternately 0.32 and 0.68 cents apart: a quote on the inverted venue is a price improvement of 0.32 cents that the one-cent tick forbids on any single venue (Figure 7.1). Chao, Yao and Ye (2019) argue that this is why a discrete tick fragments US stock exchanges and disperses their fee structures: venues differentiate by fees because they cannot by price.

A taker compares venues on fee-adjusted prices and a router splits a marketable order across them in that order.

def route_take(quotes, side: int, qty: int) -> list[tuple]:
    """quotes: (venue, price, displayed qty, take fee) on the side being taken (asks for a buy, bids for a sell)."""
    order = sorted(quotes, key=lambda q: fee_adjusted(q[1], side, q[3]) * side)
    out, left = [], qty
    for venue, price, avail, _ in order:
        if left <= 0:
            break
        q = min(avail, left)
        if q > 0:
            out.append((venue, price, q))
            left -= q
    return out

7.3 Is the fee split neutral?

Moving 0.20 cents from the take fee (0.30 to 0.10) to the make side (a 0.16 rebate becomes a 0.04 fee) shows the difference. Without a tick, an ask at 10.01 moves to 10.012: the taker still pays 10.013 all-in and the maker still nets 10.0116. On a one-cent grid the ask must stay at 10.01 (the taker now pays 10.011, the maker loses 0.2 cents) or jump to 10.02 (the taker pays 10.021). When quotes cannot move, the rent goes to queue position instead: makers compete by joining queues, and the fee split decides how long the queues are. Colliard and Foucault (2012) model how the level and split of fees change fill rates and spreads; Foucault, Kadan and Kandel (2013) explain maker-taker pricing by the speed at which the two sides react. On the Toronto Stock Exchange, Malinova and Park (2015) found that posted quotes adjusted to a change in the fee split and liquidity demanders’ costs, fees included, did not change, while posted spreads narrowed and aggressive orders became more frequent.

7.4 Tiers and the venue’s business

A venue’s revenue from trading is the difference between what takers pay and what makers receive, times its volume; its members’ rates depend on volume tiers (One Quant Book 1, chapter 29), which give the largest liquidity providers the largest rebates and make volume thresholds into cliffs. Trading fees are only part of the business: market data and connectivity are sold to the same members.

The simulation builds the choice that tiers and fees create. Two engines of firm.exchsim run one stock with a one-cent tick: MT with BZX’s standard rates, INV with BYX’s. A small reactive market supplies the flow: an efficient price $P^\ast$ that moves one tick at random times; limit orders that join the best or rest a few ticks behind and cancel at a constant rate, and at once with probability one half when $P^\ast$ jumps through them; noise market orders; and informed market orders at a rate proportional to the distance between $P^\ast$ and the mid. Each limit order goes to MT or INV with probability one half. A fee-aware taker routes by fee-adjusted price (Listing 7.1), so at equal prices it takes INV’s queue first; a fee-blind one takes the larger displayed queue first, as a router that looks only at size would. Each case runs three seeds of two hours.

    def market(t: float, side: int, qty: int, informed: bool):
        state["informed"] = informed
        quotes = [(v.name, p, v.book.visible_qty(-side, p), v.take * 10_000)
                  for v in ven.values() for p in v.book.prices(-side)[:5]]
        if rng.random() >= f.aware:          # fee-blind: the larger displayed size first
            quotes = [(n, p, q, -1e-9 * q) for n, p, q, _ in quotes]
        for name, p, qq in route_take(quotes, side, qty):
            state["cl"] += 1
            o = IN["O"](state["cl"], 1, "BS"[side < 0], qq, p, "I", "Y", "N", 0, 0, 0, "N", 0)
            run(ven[name], t, 2, o)

When every taker is fee-aware, the inverted venue is the front of a consolidated queue and the maker-taker venue its back. INV takes 77% of the volume. Its limit orders receive a fill for 28.2% of the shares posted, after a median 4.6 seconds, against 8.4% after 8.8 seconds on MT, where the queue at the best is longer (910 shares a side on average, against 510). Fills on MT come when INV’s queue has been exhausted, which is when the flow is large or informed: the mid moves 0.63 cents against an MT fill within 30 seconds, 0.13 against an INV fill (standard errors 0.04). The capture is the same on both, 0.54 cents. Net of adverse selection, an MT fill is worth $-0.09$ cents before the rebate and an INV fill 0.40 cents before the fee.

What does a posted share earn? Its value is the filled share times capture less adverse selection less the make fee. With every taker fee-aware, a share posted on MT is worth 0.006 cents and one on INV 0.057 (the difference has a standard error of 0.009): the rebate does not pay for the back of the queue. For a provider to be indifferent, MT would have to pay a rebate of 0.77 cents, more than twice its 0.30-cent take fee: no maker-taker venue can buy that queue. With half of the takers fee-blind, MT’s queue is hit first by those who look at size, and the ranking reverses: 0.052 cents on MT against 0.028 on INV (standard error 0.006), and the indifferent make fee on MT is about zero (0.006 cents), so the 0.16-cent rebate is more than MT needs. With no fee-aware taker, MT’s posted share is worth 0.074 against 0.015. How takers route decides what a rebate buys.

7.5 Evidence from fee experiments

The SEC tried to measure fees as the tick size pilot had measured the tick. It adopted the Transaction Fee Pilot, Rule 610T, on December 19, 2018: 1 460 randomly selected stocks in two test groups, one with a cap of USD 0.0010 on exchange transaction fees (the cap then in force, set in 2005, was USD 0.0030) and one in which exchanges could not pay rebates, and every other stock in a control group. Exchanges challenged the rule, and the D.C. Circuit vacated it on June 16, 2020, before it started. The evidence therefore comes from changes that venues made themselves and from routing data. Malinova and Park’s Toronto study is one; Battalio, Corwin and Jennings (2016) found retail brokers that sent limit orders to the venues paying the largest rebates and a negative relation between limit order execution quality and the rebate level, the conflict Angel, Harris and Spatt had described. Their finding is the empirical side of the simulation: an order placed for its rebate stands at the back of the consolidated queue.

7.6 Tutorial: the rebate that bought a queue

7.7 Build: fees and venue choice

7.8 Exercises

7.9 Problem: The Rebate That Bought a Queue

7.10 Interview questions