Semi-Variance measures only the variance of returns that fall below the mean — capturing the downside risk while ignoring the upside volatility that investors welcome.
Semi-Variance = (1/n) × Σ min(0, Ri − R̄)², where only below-mean returns are included in the sum. It's a more intuitive risk measure for investors because it ignores positive surprises (good news) and focuses entirely on negative deviations from the target. Semi-Variance is the foundation for Semi-Standard Deviation (√Semi-Variance), which is used in Sortino Ratio calculations when MAR = mean return.
Standard deviation treats a +20% surprise and a -20% surprise with equal concern. Semi-Variance says: 'Only worry about the -20% side.' It measures only the downside deviations from the average return — because as an investor, you don't mind being surprised on the upside, but you very much mind being surprised on the downside. Semi-Variance gives a risk measure that aligns with actual investor psychology.
Calculate mean return R̄.
For each period where Ri < R̄: compute (Ri − R̄)².
For periods where Ri ≥ R̄: contribute zero.
Average all squared deviations (including zeros) → Semi-Variance.
Semi-Std Dev = √Semi-Variance → used in Sortino Ratio when MAR = R̄.