Sortino Ratio: Beyond Volatility
The Sortino Ratio measures risk-adjusted return. It focuses solely on downside deviation. This differs from the Sharpe Ratio, which uses total standard deviation. Traders prefer the Sortino Ratio for strategies sensitive to negative returns. Mean reversion strategies often exhibit negative skewness. They experience frequent small gains and occasional large losses. The Sortino Ratio better captures this risk profile.
Calculate the Sortino Ratio as: (Portfolio Return - Minimum Acceptable Return) / Downside Deviation.
The Minimum Acceptable Return (MAR) is a threshold. It can be the risk-free rate, zero, or a specific target. Downside deviation measures the standard deviation of returns below the MAR.
Consider two hypothetical mean reversion strategies, 'Alpha' and 'Beta'. Both target an annual return of 15%. The risk-free rate is 3%.
Strategy Alpha:
- Annualized Return: 15%
- Standard Deviation: 10%
- Downside Deviation (below 3% MAR): 6%
Strategy Beta:
- Annualized Return: 15%
- Standard Deviation: 12%
- Downside Deviation (below 3% MAR): 5%
Sharpe Ratio for Alpha: (0.15 - 0.03) / 0.10 = 1.2 Sharpe Ratio for Beta: (0.15 - 0.03) / 0.12 = 1.0
Based on the Sharpe Ratio, Alpha appears superior. It has a higher risk-adjusted return.
Sortino Ratio for Alpha: (0.15 - 0.03) / 0.06 = 2.0 Sortino Ratio for Beta: (0.15 - 0.03) / 0.05 = 2.4
The Sortino Ratio reveals a different picture. Beta has a higher Sortino Ratio. It delivers the same return with less downside risk. This carries much weight for mean reversion strategies. Large drawdowns can decimate capital.
Calculating Downside Deviation
Downside deviation quantifies negative volatility. It only considers returns falling below the MAR. This provides a more accurate risk measure for strategies aiming to avoid losses.
Follow these steps to calculate downside deviation:
- Choose a Minimum Acceptable Return (MAR). Use the risk-free rate (e.g., 3-month Treasury bill yield). Or use zero for absolute return strategies.
- Collect historical daily or monthly returns for the strategy.
- Identify all returns below the MAR.
- For each return below MAR, calculate the difference: (MAR - Return). Square this difference.
- Sum the squared differences.
- Divide the sum by the number of observations. (Some practitioners divide by the total number of observations, others by the number of observations below MAR). Be consistent.
- Take the square root of the result. This is the downside deviation.
Example: Monthly returns for a mean reversion strategy over six months (MAR = 0.005, or 0.5% monthly).
| Month | Return | Below MAR? | (MAR - Return) | (MAR - Return)^2 |
|---|---|---|---|---|
| Jan | 0.012 | No | - | - |
| Feb | 0.003 | Yes | 0.002 | 0.000004 |
| Mar | 0.008 | No | - | - |
| Apr | -0.005 | Yes | 0.010 | 0.000100 |
| May | 0.006 | No | - | - |
| Jun | -0.002 | Yes | 0.007 | 0.000049 |
Sum of (MAR - Return)^2 = 0.000004 + 0.000100 + 0.000049 = 0.000153
Assuming we divide by the total number of observations (6): Downside Variance = 0.000153 / 6 = 0.0000255 Downside Deviation = sqrt(0.0000255) = 0.00505
This monthly downside deviation annualizes by multiplying by sqrt(12). Annualized Downside Deviation = 0.00505 * sqrt(12) = 0.01749 or 1.749%.*
A higher MAR makes downside deviation larger. A lower MAR reduces it. Selecting an appropriate MAR matters greatly.
Practical Application for Mean Reversion
Mean reversion strategies often display negative skewness. Their return distributions have a long left tail. They generate many small profits. They incur fewer, but larger, losses. The Sharpe Ratio penalizes all volatility equally. It does not distinguish between upside and downside.
Consider a strategy that trades SPY. It buys after a significant dip and sells after a bounce. From January 2010 to December 2020: Strategy A (aggressive):
- Annualized Return: 18%
- Annualized Standard Deviation: 15%
- Annualized Downside Deviation (MAR = 3%): 8%
Strategy B (conservative):
- Annualized Return: 14%
- Annualized Standard Deviation: 10%
- Annualized Downside Deviation (MAR = 3%): 6%
Sharpe Ratio for A: (0.18 - 0.03) / 0.15 = 1.0 Sharpe Ratio for B: (0.14 - 0.03) / 0.10 = 1.1
Strategy B appears better by Sharpe.
Sortino Ratio for A: (0.18 - 0.03) / 0.08 = 1.875 Sortino Ratio for B: (0.14 - 0.03) / 0.06 = 1.833
Strategy A now appears slightly better by Sortino. It generates higher returns with a manageable increase in downside risk. The higher total volatility (standard deviation) for Strategy A might come from larger positive spikes. The Sortino Ratio filters these out.
Traders use the Sortino Ratio to compare strategies with similar return objectives but different risk profiles. It helps in selecting strategies that align with loss aversion preferences. For a portfolio of mean reversion strategies, use the Sortino Ratio to allocate capital. Prioritize strategies with higher Sortino Ratios. This optimizes for downside protection.
A high Sortino Ratio indicates efficient capital deployment. It suggests the strategy generates returns without excessive exposure to negative events. A low Sortino Ratio implies the strategy takes on too much downside risk for its return. Adjust position sizing or entry/exit rules to improve the Sortino Ratio. Tighten stop-losses. Diversify across uncorrelated mean reversion signals.