6.9.4 Competition and the Race to Zero

Basic Prerequisites: 02 · Market-Maker P&L and 03 · Maker-Taker Fees & Rebates.

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1. Intuition & Practical Objective

Market making has famously no moat. A quote is a public, copyable price: the moment you post the best bid, any competitor can post a better one for free, and the customer takes whichever is cheapest. Lionel Harris’s line - “if you’re not the best, you’re the worst” - is the whole competitive dynamic. So why doesn’t the spread collapse to zero?

Three forces stop the collapse, and every one of them is a cost, not a barrier:

1. Adverse-selection cost $\lambda$. No one quotes inside the level at which informed traders start to eat them. This is the true, irreducible floor (Glosten–Milgrom).
2. Fixed costs $C$. Colocation, low-latency infrastructure, market-data licences, risk systems, and staff are large and lumpy. A desk needs enough volume to cover them, which caps how many desks the volume can feed.
3. The tick size $\tau$. You cannot quote finer than one tick. When the tick is coarse, competition runs out of room before the spread reaches the cost floor, leaving a residual rent.

This page turns “the race to zero” into arithmetic: a break-even count of competitors, and a tick floor that decides whether the race reaches the true cost, or stops short of it and leaves money on the table.

The one-sentence essence. “Competition compresses the maker’s edge toward the adverse-selection floor, but the tick size is a hard lower bound on the spread - so a coarse tick stops the race early and protects rents, while a fine tick lets the race overshoot into losses.”

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2. Mathematical Ground Truth & Derivations

2.1 Fixed-cost break-even of a desk

Let $e$ be the maker’s realised edge per share ($e=h+r$, the half-spread plus rebate actually earned after competition), $Q$ the maker-side annual volume (shares), and $C$ the desk’s annual fixed cost. With $N$ symmetric competing makers each capturing $Q/N$:

$${\pi }_N=\frac{eQ}{N}-C,\boxed{N^{\star }=\frac{eQ}{C}}$$

is the number of makers at which the industry just covers its fixed costs. Below $N^{\star }$ the industry earns rents; above it, competition is value-destroying and desks exit. This is Grossman & Miller (1988) and the “zero-profit” long-run condition made operational.

2.2 Compression and the tick floor

$e$ is not constant: as $N$ rises, quotes tighten and $e$ falls. The lower bound on the realised edge is set by the finest quote the tick permits. A two-sided quote at the touch has half-spread $\tau /2$, so

$$e_{\min }=\frac{\tau }{2}+r.$$

The race to zero therefore stops at $\max (\text{cost},e_{\min })$, where the cost floor is $\lambda$ (adverse selection; add $c_{\text{inv}}$ for inventory). Define the residual rent at the floor:

$$\boxed{R_{\tau }=\underset{e_{\min }}{\underbrace{\frac{\tau }{2}+r}}-\lambda }$$

• $R_{\tau }>0$ - the tick binds: competition cannot erode the surplus, makers keep a protected rent. (This is why exchanges with coarse ticks support profitable liquidity provisioning.)
• $R_{\tau }<0$ - the tick does not bind (or binds below cost): competition drives makers below their adverse-selection cost, the race “overshoots,” and desks lose money and withdraw - degrading liquidity until spreads widen again.

Minimum viable tick. Setting $R_{\tau }=0$ gives the smallest tick at which a rebate-funded maker can survive at the touch:

$${\tau }^{\min }=2(\lambda -r).$$

If $\tau <{\tau }^{\min }$, the tick is too small for the market to support a maker at the touch: the maker must either stand off the touch or exit. This is the analytical content of the SEC’s tick-size pilot and of every exchange’s “tick size protects liquidity” lobbying campaign.

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3. Computational Implementation - break-even count and the tick floor

Standard library only. Part 1 counts the competitors; Part 2 shows the tick deciding whether the race to zero overshoots or stops short.

Three solid results.

• At an edge of $0.014$/share the industry supports exactly $N^{\star }=7$ competitive makers; a tenth entrant loses $600,000$/year - the race to zero is a counting result, not a vague tendency.
• The minimum viable tick is $0.0080$: $\tau =0.002$ and $\tau =0.005$ leave makers below the adverse-selection cost (residual $-0.0030$ and $-0.0015$), while $\tau =0.010$ and $\tau =0.020$ leave positive rents ($+0.0010$ and $+0.0060$).
• Quadrupling the tick ($0.005\to 0.020$) converts a negative protected rent into a clearly positive one ($-0.0015\to +0.0060$, a swing of $0.0075=3\tau /2$) - the tick floor turns a losing no-rebate race into a profitable one: tick size is a liquidity subsidy the exchange cannot print on its own. That is the entire regulatory stakes of this page.

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4. Failure Modes & First-Principles Breakdowns

1. Assuming the race reaches the cost floor. It stops at the tick, not the cost. Under a coarse tick, spread ≠ cost, and the gap is a rent. Treating a wide spread as “adverse selection” when it is really tick protection misattributes the surplus (see 04 · Spread Decomposition).
2. Ignoring that $N$ is endogenous to $e$. $N^{\star }=eQ/C$ holds $e$ fixed; but new entrants lower $e$, which lowers $N^{\star }$ - a fixed point, not a one-shot count. In practice competition and compression run together until either the cost floor or the tick floor is hit.
3. Treating fixed costs as sunk. $C$ includes market-data and connectivity fees that scale with message rate, not with volume - so a maker whose quote-to-trade ratio rises (more cancels per fill) faces rising $C$ even at constant $Q$, squeezing $N^{\star }$ directly. This is a real modern pressure: proliferation of quoting raises costs faster than fills.
4. Fee-tier cliffs. Rebate tiers are step functions of monthly volume, so $e(N)$ is discontinuous: losing one tier can turn a profitable desk into a losing one without any change in $Q$ or $\lambda$.
5. Latency races are not the same race. A faster maker does not compete on price; he competes on position in the queue at a given price - picking off stale quotes. That is an arms race with a different zero (queue-position value), and conflating it with the price race understates the tech-cost component of $C$ (see LOB Mechanics).

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5. References

• Grossman & Miller (1988), Liquidity and market structure, JF 43(3)
• Glosten & Milgrom (1985), JFE 14
• Foucault, Kadan & Kandel (2013), Liquidity cycles and make/take fees, JF 68(1)
• Hasbrouck (2007)
• Menkveld (2013), JFM 16(4)

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6. Connected Graph Bridges

• Back: 03 · Maker-Taker Fees & Rebates
• Forward: 05 · Failure Modes & Practice · 06 · Advanced Extensions
• Inputs: Adverse Selection & Glosten–Milgrom (the $\lambda$ floor) · Inventory (adding $c_{\text{inv}}$ to the cost floor)
• Cross-pillar: Pillar 3 - the same zero-profit logic prices options (no-arbitrage).