The Madhavan-Richardson-Roomans Model

The bid-ask spread compensates a market maker for two different risks, and they don't show up the same way in the data. Part of the spread just covers the fixed cost of running a quote — exchange fees, inventory bookkeeping — and this part doesn't move the market maker's own belief about fair value. The other part covers adverse selection: the fear that the person trading against you knows something you don't, which means every trade that hits your quote should make you revise that quote in the same direction. The Madhavan-Richardson-Roomans (MRR) model separates these two by watching how quote midpoints respond to signed trades over a short sequence of transactions.

The model treats the trade sign (buy = $+1$, sell = $-1$) as partly predictable from the last trade's sign — traders tend to cluster their own order flow — and regresses the change in quote midpoint on the current signed trade. The regression coefficient on that signed trade is the adverse-selection component: it measures how much of the trade's price impact is permanent, because it changed the market maker's fair-value estimate, versus transitory, because it was just the bounce between the bid and the ask.

For a stock with a 10-cent quoted spread, MRR might estimate that 6 cents is adverse selection and 4 cents is pure order-processing cost. That split matters operationally: a market maker facing mostly adverse selection needs to widen quotes or slow down when informed flow is suspected, while one facing mostly order-processing cost can compete on spread without much added risk.