Markets: A Rigorous Course

M05 · Problem 18 ★★ Check

ORB and multiple testing

A trader backtests an opening-range-breakout strategy on three years of data across 5 range lengths, 4 stop rules, 3 universes and 2 exit times, and reports the best variant's annualised Sharpe of 2.0. Assume the variants are independent and none has an edge, and that the standard error of an annualised Sharpe over 3 years is about 1/31/\sqrt3. Using the expected maximum of NN standard normals (M04: E[max⁡]≈(1−γE)Φ−1(1−1/N)+γEΦ−1(1−1/(Ne))E[\max] \approx (1-\gamma_E)\Phi^{-1}(1 - 1/N) + \gamma_E\Phi^{-1}(1 - 1/(Ne))), compute the expected best Sharpe under the null. How impressive is 2.0? What else would you require before trading it in India?

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