Backing out how toxic your flow is

Question

You quote a half-spread of h = \0.03 (you earn 3 cents versus the mid on each fill). But you notice the price moves an average of \0.05 against you over the minute after each fill. You believe informed traders, when they trade, have an edge of about d = \0.25 (the eventual move they're trading toward), while uninformed flow is random. Estimate the fraction of your flow that is informed, and whether you're profitable.

Accepted Answer

Break each fill's expected P&L into two pieces. You always collect the half-spread h. Against that, you suffer an adverse-selection cost a, the average amount the price drifts against you after a fill. That drift is caused by the informed fraction: if a fraction \alpha of your counterparties are informed and, when informed, take about d out of you, then the average post-fill move against you is a = \alpha\,d. You measured a = \0.05 and you believe d = \0.25, so \alpha = \frac{a}{d} = \frac{0.05}{0.25} = 0.20. About 20\% of your flow is informed, that's your toxicity estimate. (The other 80\% …

Backing out how toxic your flow is

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