Glosten & Milgrom (1985)

Citation: Glosten, L. R., & Milgrom, P. R. (1985). “Bid, Ask and Transaction Prices in a Specialist Market with Heterogeneously Informed Traders.” Journal of Financial Economics.

Glosten and Milgrom’s 1985 paper provides a foundational model of how bid-ask spreads arise from information asymmetry. The central insight is that market makers face adverse selection: some traders know more than the market maker, and the market maker must protect against this by widening the spread.

The setup involves a market maker (specialist) who posts bid and ask prices at which they are willing to buy or sell. Traders arrive sequentially and are of two types:

1) Informed traders who know the true asset value 2) Uninformed (liquidity) traders who trade for exogenous reasons

The market maker cannot distinguish the two types. They only observe whether a trader wants to buy or sell.

flowchart LR
  IT[Informed trader] -->|Buys if value > ask| MM[Market maker]
  IT -->|Sells if value < bid| MM
  UT[Uninformed trader] -->|Buys or sells randomly| MM
  MM -->|Sets bid and ask| SP[Spread]

The key result is that the bid-ask spread compensates the market maker for losses to informed traders. When an informed trader arrives:

• If they buy, it’s because the asset is worth more than the ask price → the market maker sells too cheap
• If they sell, it’s because the asset is worth less than the bid price → the market maker buys too expensive

The market maker loses money on average to informed traders. To break even overall, they must profit on trades with uninformed traders. The spread creates this profit: the ask is above the expected value, and the bid is below it. The wider the spread, the more protection against adverse selection.

flowchart TD
  subgraph Spread Determinants
    PI[More informed traders] --> WS[Wider spread]
    HV[Higher volatility / info precision] --> WS
    ML[More liquidity traders] --> NS[Narrower spread]
  end
  WS --> IL[Lower liquidity]
  NS --> HL[Higher liquidity]

A crucial insight is that prices are a martingale (follow a random walk). Each trade reveals information. If a buy order arrives, the market maker revises upward their estimate of the asset’s value (since the trade is more likely to have come from an informed buyer). If a sell order arrives, they revise downward. Prices thus converge toward true value through the sequence of trades.

Key implications:

1) The spread is the cost of adverse selection. It is not a “markup” in the retail sense but a statistical necessity. Market makers who don’t charge it will be picked off by informed traders and go bankrupt.

2) Liquidity and information asymmetry are inversely related. Assets with more informed trading have wider spreads and less liquidity. This explains why spreads are wider for small stocks (more information asymmetry) than for large stocks.

3) Prices become informative through trading. Even though informed traders profit, their trades cause prices to move toward true values. The market maker’s losses are society’s gain in price accuracy.

4) No-trade results are possible. If information asymmetry is too severe, spreads become so wide that uninformed traders refuse to participate. Markets can break down entirely when adverse selection is extreme.

The Glosten-Milgrom model complements Kyle (1985) by focusing on the bid-ask spread rather than price impact. Together, they form the theoretical core of market microstructure: Kyle explains how informed traders behave, while Glosten-Milgrom explains how market makers respond. Both show that information asymmetry is central to understanding market liquidity.

Bid-ask spreads arise endogenously from adverse selection. The spread is a direct measure of information asymmetry: market makers widen it to survive against informed traders. Prices become informative through trading itself, as order flow reveals what no one will say.