Measure losses below your target, not volatility alone. Paste returns, set MAR, view clear metrics. Download tables and PDFs to support faster investment reviews.
| Month | Return | Target | Shortfall | Shortfall² |
|---|---|---|---|---|
| 1 | 1.20% | 0.50% | 0.00% | 0.0000000000 |
| 2 | -0.60% | 0.50% | 1.10% | 0.0001210000 |
| 3 | 0.80% | 0.50% | 0.00% | 0.0000000000 |
| 4 | -1.10% | 0.50% | 1.60% | 0.0002560000 |
| 5 | 0.40% | 0.50% | 0.10% | 0.0000010000 |
Downside risk measures only returns that fall below a minimum acceptable return (MAR). If MAR is 0.50% per month, months above 0.50% contribute zero, while months under 0.50% create shortfalls. This aligns with goal-based investing, where the pain is missing a hurdle rather than often ordinary fluctuation around an average.
For each period, shortfall = max(0, MAR − r). The calculator squares each shortfall, then sums them across all observations. Dividing by n (population) or n−1 (sample) produces LPM2, the second lower partial moment around MAR. Squaring matters because a 1.00% miss contributes four times the penalty of a 0.50% miss. Using n−1 is helpful when you are estimating from a limited sample for a conservative variance.
Downside deviation is √LPM2, reported in the same units as the input returns. If the output is 0.80% per month, typical downside dispersion below MAR is about eight-tenths of a percent per month. To compare across frequencies, annualize by multiplying by √P, where P is periods per year (12 monthly, 52 weekly, 252 trading days). Changing MAR changes what is counted: raising MAR usually increases the number of shortfalls and the deviation.
The Sortino ratio replaces total volatility with downside deviation: (average return − MAR) ÷ downside deviation. If average return is 1.10% and MAR is 0.50%, the numerator is 0.60%. With 0.80% downside deviation, Sortino is 0.75. Larger ratios indicate more return per unit of downside risk. The calculator also displays average excess return over an optional risk-free rate for context, while keeping MAR as the downside threshold.
Shortfall probability shows how often returns miss MAR. If 3 of 12 months are below target, the rate is 25%. Average shortfall shows the typical gap during those below-target months, which helps compare strategies with similar deviations but different loss shapes. Together, downside deviation, shortfall probability, and average shortfall support risk budgeting, setting realistic targets, and documenting performance in an investment committee memo.
Downside deviation is the square root of LPM2, measuring dispersion of returns that fall below your target. Periods above the target do not increase it, so it focuses on harmful variability rather than total volatility.
Use a hurdle that matches your objective, such as 0% for loss-only risk, a monthly savings goal, or a required portfolio return. Keep the target consistent when comparing strategies.
Yes. Paste values separated by commas, spaces, or new lines. Select whether they are in percent (1.2) or decimal (0.012) so the calculator converts units correctly.
Using n treats your data as the full population and typically gives a slightly smaller variance. Using n−1 is the sample estimator, often used when data is limited and you want a more conservative estimate.
First compute per-period downside deviation from the squared shortfalls. Then multiply by the square root of periods per year, such as √12 for monthly or √252 for trading-day data.
Sharpe uses total volatility, which penalizes upside swings. Sortino uses downside deviation, so it emphasizes downside protection when upside variability is acceptable for your strategy.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.