Risk & Performance
Sortino Ratio
Risk-adjusted return focusing only on downside volatility (losses), ignoring upside variability.
Formula
Sortino Ratio = (Rₚ − MAR) ÷ Downside Deviation
Variables
Rₚ- Portfolio return
MAR- Minimum acceptable return
Downside Deviation- Volatility of returns below MAR
Worked Example
Scenario: Portfolio returning 10% with 3% downside deviation and 8% target has Sortino = (10% − 8%) ÷ 3% = 0.67.
Steps:
- Identify portfolio return: 10%
- Set minimum acceptable return target: 8%
- Calculate only negative deviations below target
- Calculate standard deviation of negative returns: 3%
- Divide: (10% − 8%) ÷ 3% = 0.67
When to Use This Formula
- Evaluate downside-focused investment strategies
- Compare when upside volatility is less important than drawdown
- Assess hedge fund or alternative strategies
Limitations & Assumptions
- Target return selection is subjective
- Short samples may contain few downside observations
- Still compresses loss shape and timing into one number
Common Questions
Why can Sortino exceed Sharpe?
Because downside deviation is typically smaller than total volatility. If a portfolio has large gains and small losses, downside deviation is much lower.
Measuring return and risk
- Maximum drawdown formulaFormula
- Profit factor formulaFormula
- Win rate formulaFormula
- Risk-reward ratio formulaFormula
- Beta formulaFormula
Reference note: This is an educational mathematical reference. The formula's applicability depends on assumptions, market conditions, and use case. Always verify results independently and consult domain experts for decisions.