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Capacity with a square-root impact law

Challenge, about 10 minutes. Question R231.

For a fixed trade schedule, expected alpha is 10 bps per dollar traded. Other costs are 2 bps and impact is 4√(A/25) bps, where A is fund capital in millions. Under this assumed model, what is the largest A with nonnegative expected net return?

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Answer: 100 USD millions

  1. Break-even requires 10=2+4√(A/25), so √(A/25)=2. Squaring gives A/25=4 and A=$100 million. This is a model-based capacity bound.

Interview shortcut. Set alpha = costs + impact: 10 = 2 + 4√(A/25).

In the app this has a follow-up where one thing about the setup changes. Try the follow-up.

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