How much toxic flow can your spread survive?

Question

You earn a 3-cent half-spread on every fill. When a fill turns out to be informed, the value moves an average of 15 cents against you. Some fraction p of your flow is informed. What fraction of informed flow makes you break even? Above that, are you profitable or not?

Accepted Answer

Set up the break-even. On every fill you collect the half-spread s = 0.03. A fraction p of fills are informed and cost you L = 0.15 each. Expected profit per fill: E[	ext{profit}] = s - p\,L = 0.03 - p(0.15). Set it to zero and solve for the break-even informed fraction: 0.03 - 0.15\,p = 0 \;\Longrightarrow\; p^ = \frac{s}{L} = \frac{0.03}{0.15} = 0.20. Interpretation. If exactly 20\% of your flow is informed, you break even. Below 20\% you profit; above 20\% every fill is a net loser: - At p = 0.10: E = 0.03 - 0.10(0.15) = 0.03 - 0.015 = +1.5 cents per fill, healthy. - At p = 0.30: E = 0.03…

How much toxic flow can your spread survive?

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