Use all observations in the denominator
For each periodic return r and target t, calculate min(r − t, 0). Square those shortfalls, sum them, divide by the total observation count, and take the square root. Annualized downside deviation equals periodic downside deviation × sqrt(periods per year). Percentage inputs must be converted consistently to decimal returns during arithmetic. The target is per period; an annual target cannot be inserted directly into a field that expects a monthly or daily target.
Calculate a four-month example
For hypothetical monthly returns of 2%, −1%, 3%, and −2%, with a zero target, shortfalls are 0%, −1%, 0%, and −2%. Squared decimal shortfalls sum to 0.0005. Dividing by all four observations gives 0.000125, whose square root is approximately 1.1180% per month. Multiplying by sqrt(12) produces about 3.8730% annualized downside deviation under this convention.
Compare only matching conventions and periods
Dividing by only the negative observations would produce a different statistic. Keep the denominator convention, target, observation frequency, and annualization factor consistent when comparing portfolios. Missing periods should not silently become zero returns. If no return falls below the target, downside deviation is zero. The square-root annualization is a scaling convention that does not model serial dependence, changing volatility, or the severity of losses outside the observed sample.