Risk & Portfolio

Twelve monthly returns and a 3% risk-free rate. The Sharpe ratio is 0.78; the Sortino ratio, which only counts downside, is 1.31, because most of the volatility here was upside. The maximum drawdown was only 2.5%, so the Calmar ratio is 3.1. Three ratios, three impressions, from the same twelve numbers.

• Sharpe ratios from short samples are very noisy, and monthly returns that are autocorrelated (smoothed, illiquid assets) inflate them (Lo 2002).
• Trying many strategies and reporting the best inflates the Sharpe ratio; the deflated Sharpe ratio corrects for that (Bailey & López de Prado 2014).
• Calmar is normally measured over 36 months; one year’s drawdown is too short to say much.

r = np.array([2.1, -1.0, 3.2, 0.5, -2.5, 1.8, 0.9, -0.4, 2.6, -1.6, 1.4, 0.7]) / 100   # 12 months, made up
rf = 0.03 / 12
ex = r - rf
sharpe = ex.mean() / ex.std(ddof=1) * np.sqrt(12)
downside = np.sqrt((np.minimum(ex, 0) ** 2).mean()) * np.sqrt(12)
sortino = ex.mean() * 12 / downside
wealth = np.cumprod(1 + r)
mdd = (1 - wealth / np.maximum.accumulate(wealth)).max()
calmar = (wealth[-1] - 1) / mdd                            # one year, so the total return is the annual one

Assumes import numpy as np and import pandas as pd. Each snippet carries its own example numbers; the comments say which are made up or simulated.