How to calculate the Sortino ratio
Sortino = (R_p − MAR) ÷ σ_d
σ_d = √( Σ min(0, rᵢ − MAR)² ÷ N )
The standard definition divides by all periods (N). Some texts — including the worked example in the Trading Metrics docs — divide only by the number of below-target periods, which gives a larger downside deviation and a lower ratio. The calculator supports both.
Worked example
- Twelve monthly returns: 2, 1, −1, 3, −2, 1, 4, 0, −3, 2, 1, 3 (%). Their mean is 11 ÷ 12 = 0.917%.
- Negative returns: −1, −2, −3. Squared sum = 14.
- Standard σ_d = √(14 ÷ 12) = 1.08% → Sortino = 0.917 ÷ 1.08 = 0.85.
- Dividing by the 3 negative months instead: σ_d = √(14 ÷ 3) = 2.16% → Sortino = 0.42.
How to interpret the Sortino ratio
Higher is better. When a strategy's Sortino ratio is much higher than its Sharpe ratio, its volatility comes mostly from upside moves — typical of trend-following systems with large winners. Similar values mean volatility is symmetric.
Limitations and common mistakes
- State which denominator you used — Sortino ratios calculated differently are not comparable.
- With few negative periods, downside deviation is estimated from very little data.