Break-even half-spread from toxic flow

MediumProbability Expected Value Market Making & Betting Games~3m

You quote a market symmetric around fair value, capturing a half-spread $h$ on every uninformed fill. But $20\%$ of your flow is informed, and each informed fill loses you a fixed $4. What half-spread $h$ makes you break even per fill (in dollars, to two decimals)?

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Break-even per fill: $(1-f)h - fL = 0$ .
$h = fL/(1-f) = (0.2\times 4)/0.8$ ; you collect $h$ only on uninformed fills.

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Break-even half-spread from toxic flow

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