hard · Market Microstructure adverse-selection
Consider the PIN (Probability of Informed Trading) model of Easley-O'Hara: information events occur with probability α, are bad news with probability δ, informed traders arrive at rate μ on event days, and uninformed buyers and sellers arrive at rates varepsilon_b and varepsilon_s. A researcher computes PIN = αμ / (αμ + varepsilon_b + varepsilon_s) and uses it as a measure of adverse selection. Two stocks have IDENTICAL estimated PIN, but Stock A has high α with low μ while Stock B has low α with high μ.
Which conclusion about the implied price impact of an unexpected buy order is correct?
- Both stocks have the same unconditional PIN but Stock B's order imbalance is more diagnostic on event days, so a single unexpected buy moves Stock B's price more despite equal PIN.
- Equal PIN implies strictly equal price impact for any incoming order by mathematical construction, since PIN is the sufficient statistic for adverse-selection price response.
- Stock A has the higher price impact overall because its larger event frequency α means any given order is more likely to fall on an actual information event day for that specific stock.
- Neither order has price impact because the unconditional buy probability already incorporates the informed component, leaving the posterior unchanged.
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