Reading the fill: adverse selection
MM · Chapter 311 min readAsked at Optiver, SIG, Jane Street, Hudson River Trading
Assumes Theoretical value, width and skew.
After this lesson you should be able to
- Explain why getting filled is itself information.
- Update a theoretical value after a trade, rather than only skewing for inventory.
- Say why a spread has to exist at all, even with no costs and no risk aversion.
You only get filled when someone wants the other side. Some of those people know something you do not, so a fill is evidence that your price was wrong in a particular direction. The spread exists to be paid for exactly that.
Definition 3.1
The core problem
Adverse selection — The tendency for the trades you win to be the ones you should have lost. You quote a market; the people who deal on it are disproportionately the ones whose information says your price is off.
Why this is not paranoia. Imagine ten people each hold a private estimate of something worth 100. You show 99 at 101. The person who deals is not a random one of the ten — it is whoever’s estimate is furthest from your price in the direction that makes dealing attractive. You have selected, by construction, for the counterparty most likely to be right against you. Nothing about that requires anyone to be acting in bad faith.
Proposition 3.2
A fill moves your estimate, not just your inventory
When someone lifts your offer, two things have happened: you are shorter, and you have learned that at least one participant thinks the value is above your ask. The first calls for skew. The second calls for moving your theoretical value up. They point the same way here, which is why the distinction is easy to miss — until the day they point opposite ways.
Holds when
- Weight the update by how informed you think the flow is. Against a counterparty who knows the answer, a fill is strong evidence; against random flow, it is almost none.
- Size matters: someone taking your full size tells you more than someone taking one lot.
| Reason | What moves | What it looks like after being lifted |
|---|---|---|
| Inventory — you are now short | The whole market moves up | You want to buy back |
| Information — they knew something | Your theoretical value moves up | The thing really is worth more |
| Both, which is the usual case | The market moves up more than either alone would justify | Requote well above where you were |
When the two disagree
Suppose you are already heavily short and someone hits your bid. Inventory says move up — you want to buy more. Information says move down — a seller thinks it is worth less than your bid. Which dominates depends on how informed you think that seller is, and saying so out loud is exactly the reasoning an interviewer is listening for.
Proposition 3.4
Why a spread exists at all
Even with no fees, no inventory risk and no risk aversion, a market maker quoting with zero spread loses money: the informed trades go against them and the uninformed trades are a coin flip. The spread is the compensation for trading against people who may know more. This is the Glosten–Milgrom result, and it is the reason "why not quote tighter?" has a real answer.
Holds when
- The more informed the flow, the wider the equilibrium spread.
- Venues that attract uninformed flow can support tighter markets, which is why retail order flow is valuable.
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