How much to widen when toxicity doubles

Question

Your break-even spread is driven by adverse selection. Right now the informed fraction of your flow is $\alpha = 0.10$ , informed traders take about $d = \$ 0.30 $out of you, and you quote a half-spread of$ h = $0.03 $, exactly break-even. Then a news catalyst hits and the informed fraction jumps to$ \alpha = 0.20$.

If you leave your quotes unchanged, what's your P&L per fill? How much must you widen to get back to break-even?

Accepted Answer

The break-even half-spread just covers the adverse-selection cost per fill, which is a = \alpha d. At the original state: a{	ext{old}} = 0.10 	imes 0.30 = \0.03 = h. \quad\checkmark 	ext{ (break-even)} Toxicity doubles. Now \alpha = 0.20, so the cost per fill becomes a{	ext{new}} = 0.20 	imes 0.30 = \0.06, while you're still collecting only h = \0.03. If you don't move, 	ext{net per fill} = h - a{	ext{new}} = 0.03 - 0.06 = -\0.03. You flip from break-even to losing 3 cents a fill, and worse, toxic regimes usually come with higher fill rates on the toxic side, so the bleed compounds. Ho…

How much to widen when toxicity doubles

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