Sharpe Ratio vs. Sortino Ratio
Sharpe Ratio vs. Sortino Ratio
Which Risk-Adjusted Return Metric Actually Matters?
Comparing investments fairly requires adjusting returns for risk. Two portfolios might deliver identical returns, but if one experiences twice the volatility, it is less attractive. The Sharpe and Sortino ratios are the most widely used metrics for measuring risk-adjusted returns. However, they measure "risk" differently. The Sharpe ratio penalizes all volatility equally—both upside surprise and downside disaster. The Sortino ratio penalizes only downside volatility, rewarding portfolios with asymmetric return profiles (high upside, low downside). For investors who care more about losses than gains, the Sortino ratio is more intuitive. For investors focused on consistency, the Sharpe ratio is appropriate. This article explores both metrics, their calculations, their trade-offs, and guidance on when to use each.
Quick definition: The Sharpe ratio measures excess return per unit of total volatility; the Sortino ratio measures excess return per unit of downside volatility only. Sortino ratios are higher for portfolios with positive skew (good upside, bad downside protection).
Key takeaways
- Sharpe ratio = (return - risk-free rate) / standard deviation; penalizes all volatility equally
- Sortino ratio = (return - risk-free rate) / downside deviation; penalizes only downside volatility
- Sortino ratios exceed Sharpe ratios for portfolios with positive skew (upside outweighs downside)
- Sharpe is standard for academic comparisons; Sortino is more intuitive for downside-focused investors
- Both ratios improve with higher returns and lower risk; trade-offs between the two are common
The Sharpe Ratio: Total Volatility Penalty
The Sharpe ratio, developed by Nobel laureate William Sharpe, compares a portfolio's excess return (return above a risk-free rate) to its total volatility (standard deviation):
Sharpe Ratio = (Portfolio Return - Risk-Free Rate) / Portfolio Standard Deviation
Example calculation:
Suppose:
- Your portfolio returned 10% annually
- Risk-free rate (Treasury yield) is 4%
- Portfolio standard deviation is 12%
Sharpe = (0.10 - 0.04) / 0.12 = 0.06 / 0.12 = 0.50
This portfolio has a Sharpe ratio of 0.50. Interpretation: for every 1% of volatility accepted, the portfolio delivered 0.5% of excess return above the risk-free rate.
Benchmark context:
- Sharpe ratio below 0.5 = poor risk-adjusted returns
- Sharpe ratio 0.5–1.0 = moderate risk-adjusted returns
- Sharpe ratio 1.0–2.0 = good risk-adjusted returns
- Sharpe ratio above 2.0 = exceptional risk-adjusted returns
The S&P 500 historically delivers a Sharpe ratio of approximately 0.4–0.6, depending on the period. Most active managers underperform this benchmark on a risk-adjusted basis.
The Sortino Ratio: Downside Volatility Only
The Sortino ratio, developed by Frank Sortino, modifies the Sharpe formula by replacing total volatility with "downside deviation"—the volatility of returns below a target threshold, typically zero (negative returns only).
Sortino Ratio = (Portfolio Return - Target Return) / Downside Deviation
Where downside deviation is calculated as:
Downside Deviation = sqrt(sum of max(0, target - return)^2 / number of periods)
This calculation includes only periods where returns fell below the target; positive return periods are ignored.
Example with the same portfolio:
Suppose the portfolio's monthly returns over 36 months were:
Month 1-10: +1% each (up months)
Month 11-15: 0% (flat months)
Month 16-20: -1% each (down months)
Month 21-36: +0.5% each (mixed recovery)
- Average monthly return: 0.43% (annualized: 5.1%)
- Standard deviation (all returns): 0.79% monthly (annualized: 2.7%)
- Downside deviation (only negative returns): 0.5% monthly (annualized: 1.73%)
Using the Sortino formula with 0% target:
Sortino = (0.051 - 0.04) / 0.0173 = 0.011 / 0.0173 = 0.636
Compare to Sharpe:
Sharpe = (0.051 - 0.04) / 0.027 = 0.011 / 0.027 = 0.407
The Sortino ratio (0.636) exceeds the Sharpe ratio (0.407) because the portfolio's downside volatility (1.73%) is much lower than its total volatility (2.7%). This portfolio is skewed positively—upside exceeds downside.
The Key Difference: Upside vs. Downside
The fundamental difference between Sharpe and Sortino is whether volatility is symmetrical:
Sharpe ratio assumes volatility is symmetrical. A portfolio that rises ±10% per year contributes equally to its Sharpe ratio as a portfolio that rises 0% and falls -10%. Both have 10% volatility. However, from an investor's perspective, rising ±10% is preferable to rising 0%/falling -10% because upside is favorable and downside is not.
Sortino ratio rewards upside volatility. A portfolio that rises ±10% per year will have higher Sortino than Sharpe because the 10% upside volatility does not penalize the ratio (only downside does). This is more intuitive: investors like upside surprises and dislike downside ones.
Real example: Consider two portfolios over a year:
Portfolio A: +8%, -2%, +5%, -1%, +9%, -3%, +7%, +4%, +6%, +2%, +5%, +3%
- Total return: 5%
- Standard deviation: 4.8%
- Downside deviation: 2.1%
Portfolio B: +15%, +10%, +5%, +0%, -5%, -10%, -15%, -10%, -5%, +0%, +5%, +10%
- Total return: 0%
- Standard deviation: 10.0%
- Downside deviation: 9.2%
Using a 4% risk-free rate:
Portfolio A Sharpe: (5% - 4%) / 4.8% = 0.21 Portfolio A Sortino: (5% - 4%) / 2.1% = 0.48
Portfolio B Sharpe: (0% - 4%) / 10.0% = -0.40 Portfolio B Sortino: (0% - 4%) / 9.2% = -0.43
Portfolio A clearly dominates Portfolio B. Sharpe captures this (0.21 vs. -0.40). Sortino also captures it (0.48 vs. -0.43), but the difference is smaller because both portfolios experienced significant downside. Sortino's advantage is clearer when comparing portfolios with similar returns but different downside exposure.
Measuring Downside Deviation
Downside deviation is the crux of Sortino. To calculate it:
Step 1: Choose a target return (usually 0% or the risk-free rate)
Step 2: For each return period (month or quarter), calculate how far below the target it fell (or zero if it exceeded the target)
Step 3: Square each shortfall
Step 4: Average the squared shortfalls and take the square root
Example: Monthly returns = +2%, -3%, +1%, -5%, +4% Target = 0%
Shortfalls: 0%, 3%, 0%, 5%, 0%
Squared shortfalls: 0, 9, 0, 25, 0
Average: 34/5 = 6.8
Downside deviation = sqrt(6.8) = 2.6%
If this portfolio's standard deviation (all returns) is 3.5%, the downside deviation (2.6%) is lower, meaning the portfolio has positive skew—more upside than downside.
Real-World Comparison: Factor-Based Strategies
Suppose you are evaluating three investment strategies:
Strategy 1: Dividend-focused (low volatility)
- Annual return: 8%
- Standard deviation: 6%
- Downside deviation: 3%
- Sharpe (risk-free = 3%): (8% - 3%) / 6% = 0.833
- Sortino: (8% - 3%) / 3% = 1.67
Strategy 2: Balanced growth
- Annual return: 9%
- Standard deviation: 10%
- Downside deviation: 6%
- Sharpe: (9% - 3%) / 10% = 0.60
- Sortino: (9% - 3%) / 6% = 1.0
Strategy 3: Growth with upside skew
- Annual return: 11%
- Standard deviation: 12%
- Downside deviation: 5%
- Sharpe: (11% - 3%) / 12% = 0.667
- Sortino: (11% - 3%) / 5% = 1.6
Analysis by Sharpe: Strategy 1 (0.833) dominates Strategy 2 (0.60) and Strategy 3 (0.667). The low-volatility dividend strategy appears superior.
Analysis by Sortino: Strategy 3 (1.6) dominates Strategy 1 (1.67 is close) and Strategy 2 (1.0). Strategy 3 looks nearly as attractive as Strategy 1 because its downside volatility is exceptional despite high total volatility.
Interpretation: If you are indifferent between upside and downside swings, Sharpe suggests Strategy 1. If you dislike downside but appreciate upside, Sortino suggests Strategy 3. The choice depends on your risk preferences.
When to Use Sharpe vs. Sortino
Use Sharpe ratio when:
- Evaluating passive index portfolios or strategies expected to have symmetrical return distributions
- Comparing across different asset classes (stocks, bonds, commodities) where upside and downside are similarly important
- Making academic or institutional comparisons (Sharpe is the standard)
- You care about consistency rather than downside protection specifically
Use Sortino ratio when:
- Evaluating alternative strategies (hedge funds, factors) that often have asymmetrical returns
- You strongly dislike losses but welcome upside surprises
- Evaluating portfolios with options or downside-hedging strategies that artificially limit downside
- You want intuitive "loss-only risk" metrics
Practical recommendation: Use both. Calculate Sharpe for standard comparisons, but also calculate Sortino to understand whether return advantage comes from lower downside volatility (preferable) or lower upside volatility (less preferable). If two strategies have similar Sharpe ratios but different Sortinos, the one with higher Sortino is superior because its returns come from capturing upside rather than dampening volatility.
Common Mistakes
Mistake 1: Choosing a strategy because of one high Sortino ratio. A strategy that limits downside through options or shorting calls might show excellent Sortino ratios. However, these strategies often cap upside, reducing returns. Compare Sortino carefully—if it is high because downside is limited at the cost of upside, total return may be insufficient.
Mistake 2: Using the wrong target return for Sortino. If you use 0% as the target but 4% is a realistic minimum return you need, your downside deviation calculation misses meaningful shortfalls. Use a realistic minimum-acceptable return as the target.
Mistake 3: Ignoring correlation between risk-adjusted metrics. Sortino and Sharpe are highly correlated; a strategy with high Sharpe almost always has high Sortino. The moments when they diverge are interesting (high Sharpe, low Sortino = high upside volatility; low Sharpe, high Sortino = low downside volatility), but they are not tools for discovering hidden insight. Use them as confirmatory metrics, not discovery tools.
Mistake 4: Assuming Sortino ratios are comparable across different risk-free rates or target returns. If you calculate Sortino using 0% target and a colleague calculates using 3% target, the ratios are not directly comparable. Standardize target returns when comparing.
Mistake 5: Treating high Sortino as guaranteed downside protection. A high Sortino ratio means historical downside volatility was low, but this does not mean downside is permanently low. Market regimes change; downside volatility in crisis periods often exceeds historical norms. Sortino reflects past performance; stress-test expected future downside.
FAQ
What is a "good" Sortino ratio?
Generally, a Sortino ratio above 1.0 is considered good; above 2.0 is excellent. However, this depends on context. A low-volatility strategy might deliver a Sortino of 0.5 and still be attractive for conservative investors. A hedge fund with a 3.0 Sortino attracts capital easily, but fees often compress that advantage. Benchmark against peers and your specific return target rather than absolute thresholds.
How do I calculate these ratios in Excel?
For Sharpe: = (average return - risk-free rate) / STDEV(all returns)
For Sortino: = (average return - risk-free rate) / STDEV(IF(returns < target, returns, 0))
The second formula requires array input (Ctrl+Shift+Enter on Windows, Cmd+Shift+Enter on Mac).
Why do hedge funds report Sortino instead of Sharpe?
Because many hedge fund strategies have downside-protection mechanisms (stops, collars, short positions) that reduce downside volatility without eliminating upside. This creates high Sortino ratios that look more attractive than Sharpe. Investors should calculate both and understand which is genuinely driving superior risk-adjusted returns: lower downside or higher returns.
Can a portfolio have a negative Sharpe but positive Sortino?
Yes. If a portfolio underperforms the risk-free rate due to downside losses but had some positive upside months, downside deviation might be lower than total volatility. For example, a strategy that loses 2% annually might have negative Sharpe but positive Sortino if gains in winning months exceeded losses in losing months. This is unusual but possible.
How often should I recalculate Sharpe and Sortino?
Quarterly at minimum. Rolling Sharpe and Sortino (calculated over a rolling 3-year window) are useful for detecting regime changes. If a strategy's Sharpe ratio drops from 0.8 to 0.3 over a quarter, something has changed—either market conditions or strategy performance. Investigate.
Are there other risk-adjusted return metrics I should know?
Yes. Information ratio measures excess return versus a benchmark per unit of tracking error. Calmar ratio measures annual return divided by maximum drawdown. Omega ratio measures the probability-weighted upside relative to downside. Each answers different questions. Start with Sharpe and Sortino, then expand to others if needed.
Related concepts
- Calculating Portfolio Standard Deviation
- Beta vs. Volatility: Not the Same Thing
- What is Value at Risk
Summary
The Sharpe ratio measures excess return per unit of total volatility; the Sortino ratio measures excess return per unit of downside volatility only. For portfolios with symmetrical return distributions, both metrics align closely. For portfolios with asymmetrical returns (high upside, low downside), Sortino ratios exceed Sharpe ratios, rewarding favorable skew. Sharpe is the institutional standard for comparing strategies; Sortino is more intuitive for investors focused on downside protection. Neither metric is perfect—both rely on historical volatility and assume past distributions continue into the future. Use both metrics to triangulate whether a strategy's apparent advantage comes from higher returns (good), lower downside volatility (good), or lower upside volatility (less compelling). Combine risk-adjusted return metrics with absolute return targets and drawdown tolerance for complete portfolio assessment.