📊 Sortino Ratio

The Sortino ratio is a modification of the Sharpe ratio that only penalizes downside volatility. It recognizes that investors are primarily concerned with losses, not with upside surprises.

🔢 Formula

\[ So = \frac{R_p - R_f}{\sigma_d} \]

where:

\(R_p\) = portfolio return (annualized)
\(R_f\) = risk-free rate (or minimum acceptable return)
\(\sigma_d\) = downside deviation (annualized)

📐 Downside Deviation

\[ \sigma_d = \sqrt{\frac{1}{N} \sum_{i=1}^{N} \min(R_i - R_f, 0)^2} \]

Only returns below the threshold contribute to downside deviation. Returns above the threshold contribute zero.

💡 Interpretation

Sortino Ratio	Quality
\(< 0\)	Returns below the threshold
\(0 - 1.0\)	Moderate downside-adjusted return
\(1.0 - 2.0\)	Good
\(> 2.0\)	Excellent downside risk management

Numerical example

Portfolio return: 12%, Risk-free rate: 3%, Downside deviation: 10%

\[So = \frac{0.12 - 0.03}{0.10} = 0.90\]

Compare with Sharpe (if total σ = 15%): \(S = 0.60\). The Sortino is higher because upside volatility is excluded.

📊 Sharpe vs Sortino

Aspect	Sharpe	Sortino
Risk measure	Total standard deviation	Downside deviation only
Penalizes upside?	Yes ❌	No ✅
Best for	Symmetric return distributions	Asymmetric / skewed returns
Example	Broad market index	Options strategies, concentrated portfolios

🔑 When to Prefer Sortino

Skewed distributions: Strategies that have occasional large gains but controlled losses
Options-based portfolios: Inherently asymmetric payoffs
Growth stocks: Tend to have positively skewed return distributions
Any investor who cares about downside risk more than total risk

⚠️ Limitations

Small sample bias

Downside deviation requires sufficient data points below the threshold. With few negative returns (e.g., short bull market periods), the estimate becomes unreliable and the Sortino ratio can be misleadingly high.

📐 Sharpe Ratio — Total volatility variant
📊 Volatility — Understanding standard deviation
📈 Max Drawdown — Another downside-focused metric