Back out the informed fraction from the spread

Question

A stock's near-term value is either VH = 101 or VL = 99, equally likely, so midpoint \mu = 100 and half-gap \delta = 1. You observe the market quoting a half-spread of \0.20 (bid 99.80, ask 100.20). If the whole spread were pure adverse selection, what fraction of the flow is informed? Then redo it assuming a fixed order-processing cost of \0.05 per side.

Accepted Answer

In the Glosten-Milgrom model with equal priors, the break-even half-spread is exactly the adverse-selection term \alpha\delta. Invert it: 	ext{half-spread} = \alpha\delta \;\Rightarrow\; \alpha = \frac{	ext{half-spread}}{\delta} = \frac{0.20}{1} = 0.20. So if adverse selection is the only thing driving the spread, about 20\% of the arriving flow is informed. Every fifth trade, on average, comes from someone who knows which way the value will resolve, and that alone justifies quoting 0.20 away from fair value on each side. Now add a processing cost. Real half-spreads are the sum of three pie…

Back out the informed fraction from the spread

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