6.9.5 Failure Modes & Practice

Basic Prerequisites: 02 · Market-Maker P&L and 04 · Competition & the Race to Zero.

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1. Intuition & Practical Objective

Every market-making desk in the world is a version of the same bet: capture the spread faster than you get picked off and before your inventory kills you. The economics is clean paper; the P&L is decided by five specific ways the paper breaks. This page names them for a desk manager and a student alike, so that each failure is recognisable before it shows up as a drawdown.

The five ways a market-making desk dies:

1. Rebate-driven distortion - you keep quoting to earn the rebate after your true edge has gone negative; the subsidy masks the loss.
2. Competition eroding the edge - $N\to N^{\star }$ compresses your per-share profit toward zero; the survivor is whoever has the lowest fixed cost.
3. Inventory blowups - one-sided (informed) flow turns inventory into a trending, levered position that breaches financing limits.
4. Adverse selection mis-estimated - the maker quotes to the wrong $\lambda$ and the winner’s curse compounds.
5. Fixed-cost escalation - message-rate data fees and latency spend grow while fills-per-quote fall, moving $N^{\star }$ against you.

The one-sentence essence. “A rebate can keep a losing maker quoting, a thicket of competitors can erode a winning one to zero, and a one-sided fill burst can turn a hedged book into an unhedged bet - in that order of subtlety.”

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2. Mathematical Ground Truth & Derivations

2.1 Rebate-driven distortion: the rebate buys tolerance for toxicity

Use the Glosten–Milgrom per-trade result (see GM - 05): with $V_H-V_L=2$ (a $\pm 1$ move about the mid), the expected adverse-selection cost per trade is $\pi$, the informed fraction. Adding the rebate, the maker’s per-trade P&L is

$$\mathbb{E}[{\pi }_{\text{trade}}]=h+r-\pi .$$

Break-even informs the toxicity tolerance:

$$\boxed{{\pi }^{\star }=h+r.}$$

A rebate of $r$ raises the toxicity the maker can survive by exactly $r$:

$$\Delta {\pi }^{\star }=r.$$

This is the failure. The rebate does not make a bad market good; it makes a bad maker survive longer in a market he should leave. A maker who should exit at $\pi >{\pi }^{\star }$ instead keeps quoting, bleeding $r$ per trade less than he otherwise would - the loss is masked, not removed. Regulators reading “rebates improve liquidity” must ask whether the additional liquidity is good or merely persistent.

2.2 Inventory blowups: the random walk with a levered boundary

Inventory $q_t$ accumulates fill-by-fill. Under balanced flow it is a zero-drift random walk: $\mathbb{E}[q_t]=0$, $\text{sd}(q_t)\propto \sqrt{t}$. Under informed one-sided flow it acquires a drift: $q_t\approx (2p-1)t$ where $p$ is the buy-probability. The maker’s loss from carrying inventory scales with the variance of the terminal mark,

$$\text{inventory P\&L}\sim -\frac{1}{2}{\gamma }_{\text{risk}}{\sigma }^2{q}^2,$$

which is quadratic in $q$ (the Avellaneda–Stoikov penalty). A blowup is therefore a self-accelerating process: the more one-sided the flow, the larger $|q|$, the larger the required reserve, the more leverage - until a financing or risk-limit boundary is breached. Hasbrouck (2007) Ch 11 notes the ruin channel is precisely this levered inventory + credit withdrawal (Brunnermeier–Pedersen 2005), not the spread.

2.3 Edge erosion and cost escalation

From Page 04, ${\pi }_N=eQ/N-C$. Two degradations act simultaneously:

• $N$ rises (more competitors enter), dividing $Q$.
• $C$ rises (message-rate data fees, latency hardware), so each entrant needs more edge to justify staying.

Combined, the survivable edge rises while the achievable edge falls - the two curves cross, and that crossing is the exit of the marginal desk.

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3. Computational Implementation - the failure modes in numbers

Standard library only. Part 1 shows the rebate raising the toxicity tolerance and masking a genuine loss. Part 2 shows inventory under balanced vs. toxic flow.

Three solid results.

• The rebate raises the toxicity the desk tolerates one-for-one with $r$: ${\pi }^{\star }=0.0100\to 0.0120\to 0.0140$. At $r=0.004$ the desk looks break-even - but it is quoting into a market it cannot beat; the rebate has converted a $-0.004$/trade loss into a $0.000$ line. The subsidy masked the failure; it did not fix it.
• Inventory under balanced flow stays bounded ($|q|\le 150$ over $10,000$ fills, growing like $\sqrt{t}$), while a shift to $p=0.65$ produces a terminal inventory of $3002$ - a 20× larger position at the risk limit, purely from flow composition, not from the spread.
• Because the inventory penalty goes as $q^2$, the toxic case’s risk charge is roughly $20^2=400$× the balanced case’s. This is a leverage failure, and it is the one that ends desks.

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4. Failure Modes & First-Principles Breakdowns

1. The rebate masks, it does not cure. $r$ shifts the break-even toxicity ${\pi }^{\star }=h+r$ rightward. A desk that survives on the rebate is a desk that has been made persistent, not made good. Cutting the rebate reveals the loss instantly (the $+0.0000\to -0.0040$ jump above).
2. Inventory blowups are flow-composition events, not price events. The $3002$-share toxic-book inventory above was generated with the same price process as the balanced case; only the fill direction bias changed. Risk systems that monitor volatility but not order-flow imbalance (see Order Flow Imbalance) are blind to the actual trigger.
3. Quadratic inventory risk is invisible in linear TCA. A per-share inventory cost of $0.001$ looks harmless; the true $\frac{1}{2}\gamma {\sigma }^2{q}^2$ charge is what breaches limits. Always reconcile the linearised $c_{\text{inv}}$ against the convex penalty at the 99th percentile of $|q|$.
4. Edge erosion is silent and continuous. No single day shows a collapse; $e\to 0$ over months as entrants arrive and costs rise. The desk discovers it only when the quarterly rebate-tier true-up reveals it was paying to trade.
5. Adverse selection clustering. Informed flow arrives in bursts, so $\lambda$ is autocorrelated, not i.i.d. A maker who sizes reserve against the average $\lambda$ will have exactly the wrong amount of capital precisely when it is needed (VPIN, Toxic Order Flow).

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5. References

• Glosten & Milgrom (1985), JFE 14
• Hasbrouck (2007)
• Menkveld (2013), JFM 16(4)
• Malinova & Park (2015), JF 70(2)
• Brunnermeier & Pedersen (2009), Market liquidity and funding liquidity, RFS 22(6)

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6. Connected Graph Bridges

• Back: 04 · Competition & the Race to Zero
• Forward: 06 · Advanced Extensions
• Siblings: GM - 05 · Failure Modes · Toxic Order Flow & VPIN · Inventory Management & Quote Skewing
• Hub: Index Hub