Spread vs adverse selection

Where the market maker’s P&L actually is: spread captured from uninformed flow, minus what the informed take. The whole game is quoting wide enough to be paid for the risk.

The idea

What is the market-making P&L decomposition?

Market-making P&L decomposes into five terms: gross spread capture (what you would earn if every fill were a noise trader and the price never moved), minus adverse-selection cost (informed fills that move against you), minus inventory and hedging cost (carrying and offsetting the position), minus fees, plus rebates. Net P&L is the sum, and each term is separately measurable.

The spread is your gross margin, not your profit. Out of the spread you earn, informed traders take a chunk back (they trade with you right before the price moves against you), the position you are left holding costs you to carry or hedge, the venue charges fees, and sometimes pays you a rebate. What is left is net.

Each term is per-fill or per-unit-time and measurable separately from your fills and the subsequent price path, which is exactly what performance attribution does for a quoting book. This is the accounting form of the market-making trilemma: spread capture is the reward leg, adverse selection is the counterparty-risk leg, inventory/hedging cost is the position-risk leg, and the fee and rebate terms are the venue's cost structure layered on top. The waterfall above walks each step from gross to net.

What is gross spread capture?

Gross spread capture is what a market maker would earn if every fill came from a noise trader and the price never moved against it: roughly the half-spread per fill, summed over fills. It is the headline number, the reason to quote at all, but it is an upper bound on profit, because real flow is partly informed and the price does move.

If you quote 99.99 / 100.01 around a mid of 100.00 and a noise trader hits your bid, you have bought 0.01 below fair value, and that 0.01 half-spread is gross capture. Do it on both sides and you capture the full 0.02 spread per round trip; multiply by fill rate and you have gross spread P&L per unit time. The realised versus effective spread distinction matters here: the quoted (effective) spread is what you post; the realised spread is what you actually keep after the price moves over some horizon. The gap between them is the adverse-selection term.

Gross capture scales with fill rate, which falls as you widen quotes: the $\lambda(\delta) = A e^{-\kappa\delta}$ decay from Avellaneda–Stoikov. So you cannot just widen the spread to earn more gross, because you fill less. The optimum is finite, which is the whole point of the A–S spread formula.

What is adverse selection, and why is being filled often bad news?

Adverse selection is the cost of trading with better-informed counterparties. A fraction of the flow is informed (it trades the right way just before the price moves) so the maker systematically buys right before prices fall and sells right before they rise. Because informed traders choose to hit your quote precisely when it is mispriced, a fill is disproportionately bad news.

Think about who chooses to lift your ask. A noise trader does it for liquidity reasons unrelated to value, which is good for you. An informed trader does it because your ask is cheap relative to where the price is going, which is bad for you. You cannot tell them apart at fill time; you only learn afterwards, when the price moves. On average your fills are tilted toward the trades you would rather not have made. This is the winner's curse of market making.

The signature is the markout curve: plot the mean P&L of your fills against the time elapsed since the fill. If your flow were pure noise it would be flat at the half-spread; under adverse selection it drifts negative: the price keeps moving against your fills for seconds-to-minutes afterwards, eating the spread you captured. The depth of that drift is your adverse-selection cost, in bps, and it is directly measurable.

The model behind it is Glosten–Milgrom (1985): the bid and ask are conditional expectations of value given the direction of the incoming order, so a buy order rationally raises the maker's value estimate and the spread exists precisely to cover the expected loss to informed flow. The informed fraction is PIN (PIN / VPIN); the manipulable toy is IX-ADVSEL on the adverse-selection page. This is why a better fair value and toxicity detection are worth real money: they shrink the adverse-selection term by letting you quote around where the price is actually going and pull or widen when the flow turns informed. That is the entire commercial point of Market Making II.

What is the inventory and hedging cost?

Even with skew, a maker carries residual inventory, and that position has price risk and a cost to hedge. The inventory cost is the expected loss from holding the position while it is marked to a moving market; the hedging cost is the spread, fees and impact paid to offset it in a correlated instrument. Both are netted out of gross spread.

Inventory you do not immediately flatten sits exposed to the market. Skew mean-reverts it, but the time it is held still costs you in expected variance, and if you hedge it instead you pay the hedge's spread, fees and market impact, plus basis risk. This is the third leg of the trilemma, now as a line item. The A–S spread's inventory term $\gamma\sigma^{2}(T-t)$ is exactly the maker pricing this cost into the quote: you widen to charge for the inventory risk you will bear. If your realised inventory cost exceeds what that term collected, your $\gamma$ (or your skew) was too low for the volatility you faced.

What is the break-even spread?

The break-even spread is the quoted spread at which gross capture exactly covers the leaks: primarily expected adverse-selection cost, plus inventory cost and net fees. Quote tighter than break-even and informed flow makes you net-negative; quote wider and you are profitable per fill but fill less. It is the floor every viable market maker must quote above.

There is a minimum spread below which you cannot profitably make a market, because the spread you would capture is smaller than what informed flow takes back plus your costs. Glosten–Milgrom (1985) makes this precise: the equilibrium spread is set so the maker breaks even against the informed fraction. Below it, you bleed.

In practice you estimate it empirically from your markout curve and your fee schedule: the adverse-selection term is the negative drift after fills; the fee term is your net maker-taker economics. A rebate lowers the break-even spread, sometimes below zero, which is the whole premise of rebate capture. The inventory term is your realised carry/hedge cost.

The honest implication: a tight headline spread is not a profitable spread. Two makers quoting the same spread can have opposite P&L if one faces toxic flow and the other does not. This is why a maker's edge is mostly in the inputs (fair value and toxicity) not in the spread number itself, and why whether HFT is still profitable in 2026 turns on who can keep the adverse-selection term small.

Worked example

A per-fill P&L attribution for a synthetic quoting bot over one session, as of a 2026 worked snapshot. Mid 100.00, quoted half-spread 0.05 (so quoted spread 0.10), 1,000 fills, markout horizon 30 s, fees and rebate per the figures below. All in price units per share; scale to your size.

Gross spread capture. 1,000 fills $\times$ 0.05 half-spread = +50.0. This is the headline: what you would keep if every fill were noise and the price never moved.

Adverse selection. The markout curve drifts from +0.05 at fill to $-0.02$ by 30 s, so the price moved against your fills by 0.07 on average, and most of the gross spread you "captured" was illusory. Attributing the round-trip drift per side, the net realised half-spread is about $0.05 - 0.035 \approx 0.015$, so adverse selection takes back roughly 1,000 $\times$ 0.035 = −35.0, leaving realised spread P&L near +15.0. (The exact split depends on how you attribute round-trip drift to each side; the point is that most of the gross spread leaked.)

Inventory & hedging cost. Residual inventory carried and partly hedged costs about −4.0 over the session (carry variance plus the hedge's spread and impact). Fees. 1,000 fills $\times$ 0.002 taker-equivalent fee on the hedging trades and any aggressive flattening = −2.0. Rebates. As a passive maker on a maker-taker venue, 1,000 fills $\times$ 0.001 rebate = +1.0.

The break-even spread here is the quoted spread at which net hits zero: roughly a quoted spread of about 0.08 given this flow's toxicity and fees; quote tighter and the same flow turns you net-negative. The numbers are illustrative and synthetic; real markouts, fees and rebates vary by venue and instrument (check the venue spec, as of 2026), and the round-trip-to-per-side attribution is a modelling choice. Measure your own markout curve before trusting any spread. Educational only, not investment advice; no P&L is promised.