Implement Probabilistic Sharpe Ratio (PSR)

[miron]

For annual probabilistic sharpe ratio, a dataframe sample of yearly returns (yearly log returns) over at least 2 years is needed:
Algo().assets_close().resample('Y')
Consider daily/weekly/monthly returns.

pct_change() returns to log returns:
np.log1p(df['Yearly Returns']

@staticmethod
def psr(df, benchmark=0):
    sharpe = stats['Sharpe']
    skew = scipy.stats.skew(df['Yearly Returns'])
    kurtosis = scipy.stats.kurtosis(df['Yearly Returns'])
    n = len(df)
    sigma_sr = np.sqrt(
        (1/(n-1)) * (1 + 0.5*sharpe**2 - skew*sharpe+(kurtosis/4)*sharpe**2))
    ratio = (sharpe - benchmark) / sigma_sr
    psr = scipy.stats.norm.cdf(ratio)
    return psr