Sortino Ratio
Like Sharpe but penalizes only downside volatility -- when and why to prefer it.
What is the Sortino Ratio?
The Sortino ratio measures how much return a strategy earned for the amount of downside risk it took. It is similar to the Sharpe ratio, but with one key difference: instead of penalizing all volatility, it only penalizes volatility from losses.
The Sharpe ratio treats a +5% candle and a -5% candle as equally "risky" because both are far from the mean. The Sortino ratio recognizes that the +5% candle is a good thing. It only counts the -5% candle as risk. This makes the Sortino ratio a better fit for strategies that have occasional large gains.
How It's Calculated
The Sortino ratio replaces standard deviation (used by the Sharpe ratio) with "downside deviation" -- a measure of volatility that only considers returns below zero.
In plain English: divide the average return by the downside deviation, then annualize the result. The less downside volatility a strategy has for a given return, the higher the Sortino ratio.
What is Downside Deviation?
Downside deviation is like standard deviation, but it only measures how spread out the losses are. Here is how it works:
Take each candle's return. If the return is negative, keep it. If the return is positive or zero, replace it with zero -- it does not count as risk. Then square all the values, average them across all candles (including the ones you zeroed out), and take the square root.
Worked Examples
Consider 5 candle returns with a mix of gains and losses:
+3%, -1%, +3%, -1%, +2%
Step 1: Replace positive returns with zero.
0, -1, 0, -1, 0
Step 2: Square each value.
0, 1, 0, 1, 0
Step 3: Average across all 5 candles and take the square root.
Mean of squared values: (0 + 1 + 0 + 1 + 0) / 5 = 2 / 5 = 0.4
Downside deviation: sqrt(0.4) = 0.63%
For comparison, the standard deviation of these returns (using N-1) is 2.05%. The downside deviation is much smaller because it ignores the upside volatility from the +3% and +2% candles -- only the two -1% candles contribute to it.
A strategy runs for 252 daily candles on a stock. Across all 252 candles, the mean return is 0.05% per candle and the downside deviation is 0.5%.
Step 1: Divide the mean by the downside deviation.
0.05 / 0.5 = 0.1
Step 2: Annualize by multiplying by sqrt(252) = 15.87.
Sortino = 0.1 * 15.87 = 1.59
For comparison, if this same strategy had a standard deviation of 0.8%, its Sharpe ratio would be (0.05 / 0.8) * 15.87 = 0.99. The Sortino ratio is higher because it uses the smaller downside deviation (0.5%) instead of the total standard deviation (0.8%). The upside volatility that dragged down the Sharpe ratio is ignored.
Two strategies both run for 252 daily candles and both average +0.08% per candle. Their total volatility is different, but their downside volatility is the same:
- Strategy A: standard deviation 1.5%, downside deviation 0.6%. The high total volatility comes from occasional large winning candles.
- Strategy B: standard deviation 0.8%, downside deviation 0.6%. Returns are more symmetric -- gains and losses are similar in size.
Sharpe ratios (penalizes all volatility):
Strategy A: (0.08 / 1.5) * 15.87 = 0.85
Strategy B: (0.08 / 0.8) * 15.87 = 1.59
Sortino ratios (penalizes only downside):
Strategy A: (0.08 / 0.6) * 15.87 = 2.12
Strategy B: (0.08 / 0.6) * 15.87 = 2.12
The Sharpe ratio makes Strategy A look worse because its large winning candles increase total volatility. The Sortino ratio treats both strategies the same because their downside risk is identical. Neither is "wrong" -- they answer different questions about the same data.
Reading Your Results
The Sortino ratio is interpreted the same way as the Sharpe ratio -- higher is better. However, the Sortino ratio is typically higher than the Sharpe ratio for the same strategy because downside deviation is usually smaller than total standard deviation. The ranges below provide rough orientation, but what counts as "good" varies by asset, timeframe, and strategy type.
Things to Watch Out For
Sortino is annualized
Like the Sharpe ratio, the Sortino ratio is multiplied by the square root of candles per year. Short backtests with few candles can produce inflated Sortino ratios, especially if the few negative candles happen to be small. Longer backtests produce more stable estimates. See Statistical Significance & Trade Count and Timeframes & Data for more on why short backtests can mislead.
Few losing candles can inflate the Sortino ratio
If a strategy has very few negative candles, the downside deviation is very small, which pushes the Sortino ratio very high. This does not necessarily mean the strategy is safe -- it may just mean the backtest period did not include conditions that would produce losses.
Leverage changes the Sortino ratio
If your strategy uses leverage, both returns and downside deviation are amplified. As with the Sharpe ratio, the ratio itself should stay roughly the same in theory, but portfolio wipeouts from leverage can change the result. Simula calculates the Sortino ratio for each leverage level separately.
Related Metrics
Sharpe Ratio -- uses total standard deviation instead of downside deviation. The Sharpe ratio penalizes all volatility equally, while the Sortino ratio focuses only on downside risk.
Calmar Ratio -- divides annualized return by max drawdown. Where the Sortino ratio uses downside deviation (the typical bad candle), the Calmar ratio uses the worst cumulative decline.
Volatility -- the annualized standard deviation of all returns. Comparing volatility with downside deviation shows how much of a strategy's total volatility comes from the downside.