Match numerator and downside denominator
Subtract the per-period target from each return and average those excess returns. Downside deviation is sqrt(mean(min(return − target, 0)²)), with the mean taken across every observation. Annualized Sortino equals mean periodic excess return ÷ periodic downside deviation × sqrt(periods per year). Using percentage points consistently gives the same ratio as converting both components to decimals. The target and input return series must describe matching periods.
Work through a monthly return sample
Consider hypothetical monthly returns of 2%, −1%, 3%, and −2%, with a zero target and 12 periods per year. Mean return is 0.5% per month. Downside deviation is approximately 1.1180% because squared shortfalls are averaged over all four returns. The annualized ratio is 0.5 ÷ 1.1180 × sqrt(12), approximately 1.5492. Changing the target changes both the average excess return and the measured downside deviation.
Handle zero downside and unstable samples
When every return meets or exceeds the target, downside deviation is zero and the ratio is undefined. An undefined result should not be presented as a finite score or automatic evidence of superior performance. Short samples can make the ratio unstable, and the square-root scaling does not account for serial dependence. Compare ratios only when frequency, target, annualization, and treatment of missing data agree. A negative numerator produces a negative ratio when downside deviation is positive.