Definition
The Sortino ratio is a variation of the Sharpe ratio that divides excess return by downside deviation, which counts only returns below a chosen minimum acceptable return (MAR). It penalizes harmful volatility rather than all volatility.
How it works
Downside deviation takes each period's shortfall below the MAR (zero if the return is at or above it), squares the shortfalls, averages them across all periods and takes the square root. Periods above the MAR contribute a zero shortfall but still count in the number of periods n.
As with Sharpe, the return, MAR and downside deviation must use the same period unit, and a periodic ratio is annualized with √(periods per year) only under independence assumptions. Results are sensitive to the MAR and to how many bad periods the sample contains.
Formula / convention
Sortino = (R(p) − MAR) ÷ DD; DD = √(Σ min(0, r(i) − MAR)² ÷ n), all in the same period unit
Illustrative example
Illustrative: five monthly returns are +3%, −2%, +1%, −4% and +5%, with MAR = 0% per month. The mean is 0.6%; the squared shortfalls are 4 (for −2%) and 16 (for −4%), so downside deviation = √(20 ÷ 5) = 2.0% and the monthly Sortino is 0.6 ÷ 2.0 = 0.30, or about 0.30 × √12 ≈ 1.04 annualized.
What to watch for
With only a handful of below-target periods, downside deviation rests on very few observations and can be unstable. A Sortino ratio above the Sharpe ratio does not prove a strategy is safe; it may simply have had few large losses in the sample.