Break-even half-spread under adverse selection

MediumExpected Value Market Making & Betting Games~4m

You post a symmetric quote a half-spread $s$ (in dollars) either side of the fair mid. Your flow is $80\%$ uninformed - they cross the spread, so each such fill earns you exactly $s$ . The other $20\%$ is informed: they only trade when the fair value is about to jump $3.00 against your fill, so each informed fill loses you $(3.00 - s)$ . On top of that, every fill pays a flat $0.05 clearing fee. What is the smallest half-spread $s$ (in dollars) at which your expected P&L per fill is non-negative?

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Write $E[\text{P\&L}]$ as a function of $s$ : the $s$ -terms from both flow types combine.
Set the expectation to zero; the floor is expected adverse-selection cost plus the fee.

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0.65 (± 0.001)

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Break-even half-spread under adverse selection

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