Definition 12.16Quantitative Methods · الفصل 12 — Testing and Multiple Testing
For a Sharpe ratioSR (per period) estimated from n returns with skewness γ3 and kurtosis γ4, the probability that the true ratio exceeds SR0 is approximately
Φ((SR−SR0)n−1/1−γ3SR+4γ4−1SR2).
The deflated Sharpe ratio (Bailey and López de Prado, 2014) is this probability with SR0 the expected maximum of N null Sharpe ratios of variance V: SR0=V((1−γE)Φ−1(1−1/N)+γEΦ−1(1−1/(Ne))), γE the Euler–Mascheroni constant.