skfolio.measures.expected_max_sharpe_ratio#

skfolio.measures.expected_max_sharpe_ratio(n_trials, trial_sharpe_ratio_std, trial_sharpe_ratio_mean=0.0)[source]#

Approximate the expected maximum Sharpe ratio across independent trials.

When a strategy is selected as the best of several trials, its Sharpe ratio is the maximum of a sample and is therefore inflated by the selection itself.

The formula below approximates this expected maximum. It assumes that the trial Sharpe ratios are independent and follow the same normal distribution:

\[SR_0 = \mu + \sigma \left[(1 - \gamma) \, Z^{-1}\left(1 - \frac{1}{N}\right) + \gamma \, Z^{-1}\left(1 - \frac{1}{N e}\right)\right]\]

with \(N\) the number of trials, \(\mu\) and \(\sigma\) the mean and standard deviation of the trial Sharpe ratios, \(\gamma\) the Euler-Mascheroni constant, \(e\) Euler’s number and \(Z^{-1}\) the inverse standard normal CDF.

The Deflated Sharpe Ratio uses this benchmark with \(\mu = 0\), representing trials whose true Sharpe ratios are zero.

Parameters:

n_trialsfloat: Number of independent trials \(N\), which can be fractional when estimated as an effective trial count. Must be finite and at least 1.
trial_sharpe_ratio_stdfloat: Standard deviation \(\sigma\) of the trial Sharpe ratios, measuring how much they vary from one trial to another. Must be finite and non-negative.
trial_sharpe_ratio_meanfloat, default=0.0: Mean \(\mu\) of the Sharpe ratios across the trials.

Returns:

valuefloat: Approximate expected maximum Sharpe ratio, in the same per-period terms as trial_sharpe_ratio_std and trial_sharpe_ratio_mean.

Raises:

ValueError: If n_trials is not a finite real number greater than or equal to 1, or trial_sharpe_ratio_std is not a finite, non-negative real number.