Skip to main content

Documentation Index

Fetch the complete documentation index at: https://docs.chicago.global/llms.txt

Use this file to discover all available pages before exploring further.

Risk-adjusted returns measure investment performance relative to the risk taken to achieve those returns. A 15% return with 20% volatility may be worse than 10% return with 5% volatility.

​
Beginner

​
What It Means

Raw returns don’t tell the whole story. Risk-adjusted returns answer the question: “How much return did I get for each unit of risk I took?” Higher risk-adjusted returns mean more efficient use of risk.

​
Portfolio Example

PortfolioReturnVolatilityRisk-Adjusted?
Portfolio A15%20%Lower
Portfolio B12%8%Higher
Portfolio B is actually better - it generated nearly as much return with far less risk. You could leverage Portfolio B to match Portfolio A’s risk and get higher returns.

​
Why It Matters

Comparing raw returns is misleading. A hedge fund returning 20% with 40% volatility isn’t necessarily better than an index fund returning 10% with 15% volatility. Risk-adjusted metrics reveal true performance quality.

​
Advanced

​
Key Risk-Adjusted Metrics

MetricFormulaBest For
Sharpe Ratio(Return - Rf) / VolatilityGeneral comparison
Sortino Ratio(Return - Rf) / Downside DevDownside-focused
Treynor Ratio(Return - Rf) / BetaDiversified portfolios
Information RatioAlpha / Tracking ErrorActive managers
Calmar RatioReturn / Max DrawdownDrawdown-sensitive

​
Sharpe Ratio

The most common risk-adjusted measure: 
Sharpe Ratio = (Rp - Rf) / σp

Where:
- Rp = Portfolio return
- Rf = Risk-free rate
- σp = Portfolio volatility
SharpeInterpretation
Below 0.5Below average
0.5 - 1.0Good
1.0 - 1.5Very good
Above 1.5Excellent (rare)

​
Sortino Ratio

Focuses only on downside risk: 
Sortino Ratio = (Rp - Rf) / Downside Deviation

Downside Deviation = Only negative returns count
Sortino is often preferred because investors don’t mind upside volatility - only downside hurts. A stock that jumps 10% isn’t “risky” in any meaningful sense.

​
Calmar Ratio

Uses maximum drawdown as the risk measure: 
Calmar Ratio = Annual Return / |Maximum Drawdown|
CalmarInterpretation
Below 0.5Poor
0.5 - 1.0Acceptable
1.0 - 2.0Good
Above 2.0Excellent

​
Comparing Metrics

MetricRisk MeasureStrengthsWeaknesses
SharpeTotal volatilitySimple, universalPenalizes upside
SortinoDownside onlyMore intuitiveFewer data points
CalmarMax drawdownCaptures tail riskSingle worst event
InformationTracking errorActive management focusBenchmark dependent

​
Practical Application

When to use each metric:
  • Sharpe: Comparing any strategies against each other
  • Sortino: When you care specifically about losses
  • Calmar: When drawdowns are your primary concern
  • Information Ratio: Evaluating active managers vs. benchmark
  • Treynor: Comparing well-diversified portfolios

​
Limitations

  • Backward-Looking: Past risk-adjusted returns don’t guarantee future performance
  • Distribution Assumptions: Most assume normal returns (reality has fat tails)
  • Time Period Sensitive: Results vary significantly by measurement period
  • Gaming: Some strategies artificially inflate ratios (selling options, smoothing)
A high Sharpe Ratio from selling options or illiquid strategies may mask hidden tail risks. Always understand the source of risk-adjusted returns.

​
Related Terms

Sharpe Ratio

Most common measure

Volatility

The denominator in most metrics

Drawdown

Used in Calmar Ratio