6.9.6 Advanced Extensions

Basic Prerequisites: 03 · Maker-Taker Fees & Rebates and 04 · Competition & the Race to Zero.

---

1. Intuition & Practical Objective

Once the market maker’s economics is decomposed (spread, adverse selection, inventory, fees, rebates), market structure becomes a set of knobs on that decomposition - and regulators, exchanges, and brokers all turn them. This page connects the theory to the three structural features that most shape a modern maker’s P&L: access-fee caps and tick-size rules, and payment for order flow (PFOF), plus the empirical unit economics of one HFT firm (Menkveld 2013).

The practical objective: given a proposed rule change, predict which term of the P&L it moves, in which direction, and by how much. If you can do that, you can read a regulatory consultation as a P&L statement.

The one-sentence essence. “Access fees, tick size, and order-flow payments are not abstractions - each one lands on a specific line of the maker’s P&L, and the equilibrium response is a re-quote, not a windfall.”

---

2. Mathematical Ground Truth & Derivations

2.1 Access-fee cap

US equity venues may charge no more than the access fee cap on a per-share basis for NMS stocks priced at or above $1.00 - historically $0.0030/share (SEC Rule 610, Reg NMS). This directly bounds the take fee in the cum-fee spread:

$$f_t\le f_t^{\max }=\$0.0030.$$

Two consequences follow from Page 03’s identity $S^{\text{cum}}=S^{\text{net}}+2f_{\text{net}}$:

• Because the cap binds only on the take side, a venue can still pay an arbitrarily large maker rebate $r$ - but only by charging takers up to the cap, so $f_{\text{net}}\ge f_t^{\max }-r$, i.e. a large rebate forces a positive net fee.
• The rebate’s pass-through into the raw quote is governed by the tick (Page 03): a venue with a coarse tick can pay a large rebate without it fully tightening the raw spread - the rebate is then partly captured as maker rent rather than being fully passed to takers (Malinova & Park 2015; Foucault, Kadan & Kandel 2013).

2.2 Tick-size rules

The tick $\tau$ sets the finest quote and therefore the floor on the realised edge, $e_{\min }=\tau /2+r$ (Page 04). A tick-size rule is a direct lever on liquidity-supplier rents:

• Coarse tick ($\tau$ large): $e_{\min }$ high; competition cannot erode maker rents; spreads are wide but liquidity is deep and stable.
• Fine tick ($\tau$ small): $e_{\min }$ low; competition drives spreads down toward the cost floor ($\lambda +c_{\text{inv}}$); spreads are tight but depth at the touch thins and makers may exit if $\tau <{\tau }^{\min }=2(\lambda -r)$.

The empirical testbed is the SEC Tick Size Pilot (2016–2018): a randomized program that widened the tick to $0.05 for a set of small-cap (low-capitalization, low-volume) stocks, with control groups, precisely to test whether a wider tick improved liquidity provision. The theory above predicts the mechanism: a coarse tick raises $e_{\min }$ and the residual rent $R_{\tau }$, encouraging quoting.

2.3 Payment for order flow (PFOF)

PFOF is a payment from a wholesaler / market maker to a retail broker for the right to execute the broker’s order flow. It is economically distinct from maker-taker fees (which flow exchange → maker), but it lands on the same P&L statement, from the wholesaler’s side:

$${\pi }_{\text{wholesaler}}=\underset{\text{effective half-spread}}{\underbrace{h^{\text{eff}}}}-\underset{\text{PFOF to broker}}{\underbrace{p}}-\underset{\text{adverse selection}}{\underbrace{{\lambda }_{\text{retail}}}}-\underset{\text{tech, clearing, reg.}}{\underbrace{c_{\text{other}}}},$$

where $h^{\text{eff}}$ is the effective spread the wholesaler captures on the internalised trade.

The economics turn on ${\lambda }_{\text{retail}}$ being small: retail flow is famously uninformed (it does not systematically trade on news), so a wholesaler is willing to pay real money for it - the payment is essentially the price of acquiring low-adverse-selection flow. Setting ${\pi }_{\text{wholesaler}}=0$ gives the maximum sustainable PFOF:

$$\boxed{p^{\star }=h^{\text{eff}}-{\lambda }_{\text{retail}}-c_{\text{other}}.}$$

PFOF grew to dominate US retail execution: by 2009, internalised trades accounted for about 17% of total US equity trading volume (SEC 2010, cited in Colliard & Foucault 2012, fn. 4), and the share has risen since. It is the single largest structural feature distinguishing US equity market making from most others.

2.4 The unit economics of an HFT maker (Menkveld 2013)

Menkveld’s anatomy of one large HFT market-making firm gives the empirical calibration of the whole folder: spread revenue and passive-order profitability are the gross revenue lines; inventory cost (and the passive-order slippage from adverse selection) is the dominant cost line. The desk operates with very high volume and razor-thin per-share edges - exactly the $e\to$ floor regime of Page 04.

---

3. Computational Implementation - PFOF break-even and the rule levers

Standard library only. We compute the maximum sustainable PFOF for a wholesaler and show the P&L at realistic payments, then tabulate the effect of the access-fee cap and tick size on the maker’s edge floor.

Three solid results.

• The maximum sustainable PFOF is $0.0050/share (0.5¢); at that payment the wholesaler earns exactly zero, and any higher payment requires a wider effective spread or cheaper technology - which is why PFOF ultimately shows up as a retail execution-quality question, not merely a routing question.
• The access-fee cap ($0.0030$) bounds the fee component of the cum-fee spread at $2\times 0.0030=0.0060$ - real but small relative to the raw spread; it constrains the fee channel, not the spread channel.
• The tick lever is dominant and highly non-linear: the SEC pilot’s $0.05 tick would lift the maker’s edge floor to $0.0270$ and the protected rent $R_{\tau }$ to $+0.0210$ - 21× the rent at a $0.01 tick ($+0.0010$) and 4× the daily half-spread itself. A tick-size rule is, quantitatively, a liquidity-supplier subsidy far larger than any rebate schedule.

---

4. Failure Modes & First-Principles Breakdowns

1. Regulating the fee and ignoring the tick. The access-fee cap bounds one term of the cum-fee spread; the tick bounds the whole spread. Policy debate that treats them separately mis-sizes the effect - the tick lever dominates (see the table: $\tau =0.05$ gives $R_{\tau }=+0.0210$ vs a fee cap worth at most $0.0060$ of spread).
2. Reading PFOF as pure conflict-of-interest. PFOF is a price for uninformed flow. It is a real conflict (the broker’s incentive is routing economics, not execution quality), but the analytical question is whether ${\lambda }_{\text{retail}}$ stays low - if retail flow becomes informed or the wholesaler’s effective spread compresses, $p^{\star }$ collapses and the payment structure becomes untenable.
3. Confusing maker-taker and PFOF. Maker-taker: exchange pays maker, taker pays exchange (bilateral, venue-level). PFOF: maker/wholesaler pays broker, broker routes (bilateral, firm-level, off-venue). They can coexist and compound a maker’s per-share economics (minus a rebate and minus a PFOF).
4. Assuming rebate pass-through. Malinova & Park (2015): the TSX maker rebate moved posted quotes but left taker cum-fee costs unchanged; the visible effect was a change in retail order aggressiveness. A regulator expecting the rebate to visibly tighten the spread finds a re-pricing, not a welfare gain.
5. Fixed-cost creep. Message-rate market-data fees scale with quoting intensity, so a venue that increases quoting via a coarse tick simultaneously raises every maker’s $C$ - the break-even count $N^{\star }=eQ/C$ can fall even as $e$ rises.

---

5. References

• Colliard & Foucault (2012), RFS 25(11)
• Malinova & Park (2015), JF 70(2)
• Foucault, Kadan & Kandel (2013), JF 68(1)
• Menkveld (2013), JFM 16(4)
• SEC (2010), Concept Release on Equity Market Structure
• Malinova & Park (2015) and Anand, McCormick & Serban on PFOF economics (cited in MP 2015).

---

6. Connected Graph Bridges

• Back: 05 · Failure Modes & Practice
• Hub: Index Hub
• Cross-pillar / sibling: LOB Mechanics & L3 · Adverse Selection & Glosten–Milgrom · Inventory Management & Quote Skewing