Sortino Ratio Calculator
Risk-adjusted return that penalises only downside volatility.
Overview
The Sortino ratio, developed by Frank Sortino in the 1980s, is a risk-adjusted return measure that improves on the Sharpe ratio by penalising only the volatility investors actually fear: downside moves. The Sharpe ratio treats large upside surprises as risk because standard deviation does not distinguish direction. The Sortino fix replaces total volatility with downside deviation — the standard deviation of returns below a target threshold, usually zero or the risk-free rate.
In practical use, the Sortino ratio shines on strategies with positive skew: trend-following, long-volatility, or option-like exposures that have small frequent losses and occasional large wins. Those strategies score poorly on Sharpe because their winning months blow up the volatility figure. The Sortino corrects that by recognizing that an upside outlier is a feature, not a bug. The metric pairs naturally with the Sharpe ratio: comparing the two reveals whether a strategy's volatility is symmetric or skewed.
How it works
Pick a minimum acceptable return (MAR) — commonly zero, or the periodic risk-free rate. For each periodic return r_i, compute the downside deviation: (r_i − MAR) if negative, otherwise zero. Downside deviation is sqrt(Σ (min(0, r_i − MAR))^2 / n). Periodic Sortino is (mean(r_i) − MAR) / downside_deviation. Annualize by multiplying by √(periods_per_year) — the same convention as the Sharpe ratio. The result is the excess return per unit of downside risk.
Examples
- Monthly returns averaging 1.2% with overall standard deviation of 5% but only 3% downside deviation, MAR 0: monthly Sortino =
1.2 / 3 = 0.40; annualized =0.40 × √12 ≈ 1.39. Sharpe over the same set would be1.2 / 5 = 0.24annualized to 0.83. - A trend-following CTA with 10% annual return, 14% volatility, 8% downside deviation: Sortino ≈ 1.25 versus Sharpe ≈ 0.71. The Sortino better reflects investor experience.
- A pure short-volatility strategy with 7% return and 4% downside deviation: Sortino 1.75 — strong, but the small downside-deviation reading should be scrutinized for tail risk hidden by short histories.
- A balanced 60/40 portfolio averaging 8% with 6% downside deviation: Sortino ≈ 1.33.
FAQ
Should I always use Sortino instead of Sharpe?
Use both. Sharpe is the lingua franca; Sortino adds context where return distributions are skewed.
What MAR should I pick?
Zero is most common. Use the risk-free rate to align with Sharpe; use a target return for liability-driven investors.
Why does my Sortino look so much better than my Sharpe?
Because your strategy has positive skew — frequent small wins and occasional large gains. That widens the gap between total and downside volatility.
Is downside deviation the same as semi-variance?
Effectively yes — Sortino uses the square root of semi-variance below the MAR.
Does Sortino capture tail risk?
Partially. It penalises the magnitude of below-MAR returns but does not specifically isolate fat tails; pair with VaR or expected shortfall for that.