6.9 Market-Maker Economics & Rebates

Basic Prerequisites: Adverse Selection & Glosten–Milgrom (what a fill costs) and Avellaneda–Stoikov & Optimal Quoting (what a quote should be). (these are the folder-level prerequisites for pages 02–06; page 01 states its own, smaller, entry requirements)

1. Intuition & Practical Objective

The market-making models in this pillar tell you what to quote. This folder asks the business question that sits underneath them: does the market-making trade actually make money, and who pays for it? A maker does not earn the quoted spread - he earns the quoted spread minus the informed traders who pick him off, minus the cost of carrying the inventory that accumulates, plus whatever the exchange pays him to post, minus whatever the exchange charges him to cross. Strip the P&L down to those five terms and the entire economics of the business is visible in one line.

This folder is the economic capstone of Pillar 6. It is a hub: (a) the fast formula lookup below gives the P&L decomposition, the rebate-adjusted spread, and the break-even conditions; (b) six sub-pages walk from zero intuition through the decomposition, maker-taker fees and rebates, the competition race to zero, the failure modes, and the regulatory/PFOF extensions.

The one-sentence essence. “A market maker’s per-share P&L is $π = (h + r) - λ - c_{inv}$ , where $h$ is the quoted half-spread, $r$ the exchange rebate, $λ$ the adverse-selection loss per share, and $c_{inv}$ the inventory cost - the quoted spread is gross revenue, and only the difference survives.”

2. Mathematical Ground Truth & Derivations

Quick-Reference Lookup (job #1). Formulas below are from Stoll (1978), Grossman & Miller (1988), Colliard & Foucault (2012, RFS 25(11)), Malinova & Park (2015, JF 70(2)), and Hasbrouck (2007) Ch 11–12, with the verified empirical anchors from those papers. Every number in the check column was re-executed and reproduced exactly (§3 and the sub-pages).

Notation: $h$ quoted half-spread ($/share), $r = ∣ f_{m} ∣ \geq 0$ maker rebate, $f_{t}$ take fee, $f_{m}$ make fee ( $f_{m} = - r$ under a rebate), $λ$ expected adverse-selection loss per share, $c_{inv}$ inventory cost per share, $S^{raw}$ raw quoted spread, $S^{cum}$ cum-fee spread, $N$ number of competing makers, $C$ fixed desk cost, $Q$ maker-side annual volume, $τ$ tick size.

Quantity	Formula	Verified anchor
MM P&L per share	$π = h + r - λ - c_{inv} - f_{take} \cdot 1 [taker]$	§3 (Page 02) reproduces $π = 0.005$ from $h = .010, r = .002, λ = .006, c_{inv} = .001$
Break-even half-spread	$h^{⋆} = λ + c_{inv} - r$	-
Rebate-adjusted raw half-spread	$h^{raw} = h^{net} - r$ (competitive neutrality)	CF 2012 Prop. 1: breakdown neutral at fixed total fee
Exchange net fee per share	$f_{net} = f_{t} + f_{m} = f_{t} - r$	NYSE Arca 2012: $0.30 -$ $0.21 = $0.09/round lot
Cum-fee spread (round trip, taker)	$S^{cum} = S^{raw} + 2 f_{t}$	$0.020 + 2 (0.003) = 0.026$
Maker’s net spread	$S^{net} = S^{raw} - 2 f_{m} = S^{raw} + 2 r$	-
Neutrality identity	$S^{cum} = S^{net} + 2 f_{net}$	$0.020 + 2 (0.003) = 0.026$ both ways
Competitive break-even maker count	$N^{⋆} = \frac{e Q}{C}$ with edge $e = h + r$	Page 04: $N^{⋆} = 7$ at $e =$ $.014, $Q = 1 0^{9}$ , $C =$ $2M
Tick floor on the race to zero	residual $= τ /2 + r - λ$	Page 04: $τ = .01, r = .002, λ = .006 \Rightarrow + 0.001$
Minimum viable tick	$τ^{m i n} = 2 (λ - r)$	$λ = .006, r = .002 \Rightarrow τ^{m i n} = 0.008$
Max sustainable PFOF	$p^{⋆} = h^{eff} - λ_{retail} - c_{other}$	Page 06: $p^{⋆} = 0.005$ at $h^{eff} = .008$

Critical caveat. The quoted spread is not the maker’s revenue, and the rebate is not free money. Under competition the rebate is largely passed through into a tighter raw quote (CF 2012), so measuring a maker’s edge from the posted spread alone double-counts the subsidy. Always compute the net spread $S^{raw} + 2 r$ before and the cum-fee spread the taker actually pays.

3. Computational Implementation - the P&L engine

Standard library only. This reproduces the headline numbers the sub-pages use: the per-share decomposition, the rebate neutrality check, and the break-even count.

4. Failure Modes & First-Principles Breakdowns

Hub signposts - the full analysis lives in 05 · Failure Modes & Practice. In one line each:

Rebate-driven distortion - a maker who quotes for the rebate rather than the edge keeps quoting through negative true edge; the subsidy masks the loss instead of removing it.
Competition eroding edge - $N \to N^{⋆}$ drives per-maker profit to zero; below the tick floor the residual is the only rent left, and only scale survives.
Inventory blowups - inventory is a random walk with a financing/limit boundary; the ruin channel is leverage + capital withdrawal, not the spread.
Spread ≠ revenue - the quoted spread overstates the maker’s take by exactly the adverse-selection component (Hasbrouck Ch 11).
Cum-fee illusion - moving the make/take breakdown at constant total fee changes the raw spread but not the taker’s cost (CF 2012); treating the raw spread as the policy target is a measurement error.

5. References

Stoll, Hans R. (1978), The supply of dealer services in securities markets, Journal of Finance 33(4)
Grossman & Miller (1988), Liquidity and market structure, Journal of Finance 43(3)
Colliard & Foucault (2012), Trading fees and efficiency in limit order markets, Review of Financial Studies 25(11), 3389–3421
Malinova & Park (2015), Subsidizing liquidity: the impact of make/take fees on market quality, Journal of Finance 70(2), 509–536
Hasbrouck, Jeffrey (2007), Empirical Market Microstructure
Menkveld, Albert J. (2013), High frequency trading and the new market makers, Journal of Financial Markets 16(4)
Foucault, Kadan & Kandel (2013), Liquidity cycles and make/take fees in electronic markets, Journal of Finance 68(1)

6. Connected Graph Bridges

Prerequisite models: Adverse Selection & Glosten–Milgrom · Avellaneda–Stoikov & Optimal Quoting
Sibling topics: Inventory Management & Quote Skewing · Spread Decomposition & the Roll Model · Toxic Order Flow & VPIN · Limit Order Book Mechanics & L3
Sub-pages (in-folder): 01 From Zero · 02 Market-Maker P&L · 03 Maker-Taker Fees & Rebates · 04 Competition & the Race to Zero · 05 Failure Modes & Practice · 06 Advanced Extensions

Beginner: start at 01 · Practitioner: start at 05

Kwant Atlas

Explorer

6.9 Market-Maker Economics & Rebates

1. Intuition & Practical Objective

2. Mathematical Ground Truth & Derivations

3. Computational Implementation - the P&L engine

4. Failure Modes & First-Principles Breakdowns

5. References

6. Connected Graph Bridges

6.9.1 From Zero

6.9.2 The Market-Maker P&L Decomposition

6.9.3 Maker-Taker Fees and Rebates

6.9.4 Competition and the Race to Zero

6.9.5 Failure Modes & Practice

6.9.6 Advanced Extensions