Treynor Ratio Calculator
Calculate the Treynor ratio to measure risk-adjusted returns based on systematic risk (beta). The Treynor ratio shows how much excess return you earn for each unit of systematic risk taken.
Treynor Ratio Results
Risk Analysis
Treynor Ratio Benchmarks
Excellent: > 5%
Good: 2-5%
Fair: 0-2%
Poor: < 0%
Note: Higher is better
Understanding the Treynor Ratio
The Treynor ratio, developed by Jack Treynor, measures the risk-adjusted performance of an investment portfolio by considering only systematic risk (beta). It shows how much excess return an investment generates per unit of systematic risk.
Treynor Ratio Formula
The Treynor ratio is calculated as:
Treynor Ratio = (R_p - R_f) ÷ ß_p
Where: R_p = portfolio return, R_f = risk-free rate, ß_p = portfolio beta
Key Differences from Sharpe Ratio
| Aspect | Sharpe Ratio | Treynor Ratio |
|---|---|---|
| Risk Measure | Total volatility | Systematic risk (beta) |
| Risk Type | Diversifiable + systematic | Systematic only |
| Portfolio Type | Any portfolio | Market-related portfolios |
| Best Use | Individual securities | Mutual funds, portfolios |
Interpreting Treynor Ratios
| Treynor Ratio | Performance Level | Interpretation |
|---|---|---|
| > 5% | Excellent | Strong systematic risk-adjusted returns |
| 2-5% | Good | Acceptable systematic risk performance |
| 0-2% | Fair | Average systematic risk efficiency |
| < 0% | Poor | Underperforming systematic risk |
Beta and Systematic Risk
Beta measures how much a security moves relative to the market. A beta of 1 means the security moves with the market, while a beta greater than 1 means it's more volatile.
- ß = 1: Moves with the market (average systematic risk)
- ß > 1: More volatile than market (high systematic risk)
- ß < 1: Less volatile than market (low systematic risk)
- ß = 0: No correlation with market (no systematic risk)
- ß < 0: Moves opposite to market (negative systematic risk)
Applications
- Mutual Fund Evaluation: Compare fund performance relative to market risk
- Portfolio Management: Assess systematic risk efficiency
- Asset Allocation: Determine optimal market exposure
- Performance Attribution: Understand sources of excess returns
- Risk Management: Evaluate market risk compensation
Advantages
- Relevant Risk: Focuses on non-diversifiable risk
- CAPM Foundation: Based on modern portfolio theory
- Comparability: Easy to compare across different investments
- Market Focus: Emphasizes market-related performance
- Practical Use: Widely used by institutional investors
Limitations
- Beta Stability: Betas can change over time
- Market Assumption: Assumes market is efficient
- Single Factor: Only considers market risk
- Data Requirements: Needs historical return data
- Short-term Focus: May not reflect long-term performance
Treynor Ratio in Practice
The Treynor ratio is particularly useful for evaluating portfolios that are well-diversified, as it focuses on the risk that cannot be eliminated through diversification.
- Institutional Investors: Use for pension fund evaluation
- Fund Managers: Performance measurement tool
- Portfolio Optimization: Risk-return analysis
- Benchmarking: Compare against market indices
Tip: The Treynor ratio is most appropriate for well-diversified portfolios where unsystematic risk has been largely eliminated. Use it to evaluate how efficiently a portfolio is compensated for its market risk exposure.