Adverse selection in market making is the loss a market maker incurs when quoting to traders with superior private information. Glosten and Milgrom (1985) formalize this in Bid, Ask and Transaction Prices in a Specialist Market with Heterogeneously Informed Traders. A risk-neutral specialist quotes prices to a stream of informed and uninformed traders arriving one at a time. They prove that a positive bid-ask spread emerges even with zero transaction costs and zero expected specialist profit. The spread is the specialist's only defense against systematically losing to better-informed insiders.
What the Study Found
The specialist sets the ask at A_t = E[V|S_t, Z_t > A_t]. The bid is the symmetric B_t = E[V|S_t, Z_t < B_t]. The ask exceeds and the bid falls below the expected value E_t[V]. Transaction prices form a martingale relative to both specialist and public information, with E[p_{k+1}|S_k] = p_k. The adverse-selection component of the spread equals Ψ = E[V|S_t, Z>A] − E[V|S_t, Z<B]. Expected volume times average spread squared is bounded by the value's variance, E[N·Ψ̄²] ≤ 2·var(V)·y. When part of the spread reflects per-trade cost c, price changes show negative serial correlation. The coefficient is R = −β/(δ + β²), where β = 2c/(Ψ + 2c).
Methodology
The paper develops a theoretical sequential-trade model rather than an empirical dataset, so it has no sample or time period. A risk-neutral, competitive specialist sets bid and ask prices under a zero-expected-profit condition each period. Traders arrive one at a time and trade single units, split between informed insiders and uninformed liquidity traders. Each uninformed trader's time-preference parameter p governs supply and demand elasticity. Equilibrium prices are rational-expectations conditional expectations of value, with dynamics analyzed through martingale theory and Bayesian belief updating.
Key Statistics
| Metric | Finding | Context |
|---|---|---|
| Equilibrium ask / bid | A_t = E[V|S_t, Z_t > A_t]; B_t = E[V|S_t, Z_t < B_t] | Zero-expected-profit quotes (Eq. 4) |
| Transaction prices | E[p_{k+1}|S_k] = p_k | Prices form a martingale (Proposition 2) |
| Volume–spread bound | E[N·Ψ̄²] ≤ 2·var(V)·y | Spread bounded by value variance (Proposition 3) |
| Serial correlation | R = −β/(δ + β²), β = 2c/(Ψ + 2c) | Negative when cost share is positive (Eq. 6) |
| Assimilation time | ≈ proportional to 1/α² | Trades until insider info revealed, small α (Eq. 12) |
| Belief update | π+/(1−π+) = [π/(1−π)]·Factor | Bayesian update after each trade (Section 3) |
Why This Matters
The model gave market microstructure its account of the spread as a pure information cost, separable from inventory and order-processing costs. Because quotes adjust toward the asset's true value as orders arrive, the framework explains how private information gradually leaks into prices through trading itself. It also shows markets can shut down entirely when informed traders dominate, a warning about liquidity evaporating under extreme asymmetric information. The serial-correlation result gives empiricists a way to decompose observed spreads into their adverse-selection and cost components.