Adverse Selection

Adverse selection is the loss a market maker expects because the counterparties most eager to trade are often the best informed.

1. The idea

Adverse selection arises because trade requests are not random: informed traders selectively trade against mispriced quotes, so on average a fill is bad news about the maker's current quote. This is a Bayesian updating problem — being hit on the bid is itself information suggesting fair value is lower than the maker thought.

The classic setup: a fraction $π$ of order flow comes from informed traders who know whether the true value is above or below the current quote and trade accordingly; the rest is noise, trading randomly. The maker should update the fair-value estimate immediately after any fill.

This logic explains why quotes widen in news-heavy or illiquid conditions (higher $π$ ), and why market makers pull quotes or widen sharply around scheduled information events.

2. Why it matters

Interviewers use adverse selection to test Bayesian reasoning: 'given you just got filled, what do you now believe about fair value?' is a direct Bayes'-theorem question.

3. Core mathematics

Posterior after a buy fill (Glosten-Milgrom style)

E [V ∣ buy at a] = a + (1 - π) \cdot 0 + π \cdot (informed value - a)

Simplified intuition; exact form depends on the value distribution

Bayes' rule for trader type given side

P (informed ∣ trade) = \frac{P ( trade ∣ informed ) P ( informed )}{P ( trade )}

4. How to recognize it

Think of this when…

Mentions informed vs. uninformed (noise) traders
Asks how a market maker should update fair value after a fill
References news events, insiders, or 'someone always seems to know'

5. Worked example

Worked example

True value $V$ is either $100$ (prob 0.5) or $102$ (prob 0.5). An informed trader always buys if $V = 102$ and never if $V = 100$ ; a noise trader buys with probability 0.5 regardless of $V$ . Informed and noise traders are equally likely to arrive. Given a buy order arrives, what is $P (V = 102)$ ?

1
P(buy | V=102): informed always buys (prob 1), noise buys with prob 0.5, each type arrives with prob 0.5.
$P (buy ∣ V = 102) = 0.5 (1) + 0.5 (0.5) = 0.75$
2
P(buy | V=100): informed never buys, noise buys with prob 0.5.
$P (buy ∣ V = 100) = 0.5 (0) + 0.5 (0.5) = 0.25$
3
Apply Bayes' rule with equal priors.
$P (V = 102 ∣ buy) = \frac{0.75 \times 0.5}{0.75 \times 0.5 + 0.25 \times 0.5} = \frac{0.375}{0.5}$
Answer: $P (V = 102 ∣ buy) = 0.75$ — a buy order is strong evidence of the higher value, so the maker should raise the ask.

6. Common mistakes

Treating all order flow as uninformative noise
Failing to update fair value after each fill before setting the next quote
Ignoring that adverse selection scales with position size — large informed orders are worse news than small ones

7. Quick check

Adverse selection is the loss a market maker expects because:

In the worked example, after observing a buy, the maker's estimate of fair value should:

8. Practice

18 QuantSolve questions use this concept.

Practice this concept

9. Related methods

Bayes' Theorem Conditional Expectation

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