Treynor Ratio Calculator
Calculate the Treynor Ratio to evaluate your portfolio’s risk-adjusted returns relative to market risk.
How to Calculate Treynor Ratio: Complete Guide with Examples
What is the Treynor Ratio?
The Treynor Ratio (also called the reward-to-volatility ratio) is a performance metric that measures the excess return generated by a portfolio per unit of systematic risk (beta). Developed by economist Jack Treynor, this ratio helps investors evaluate how well a portfolio compensates them for taking on market risk.
Treynor Ratio Formula
The formula for calculating the Treynor Ratio is:
Treynor Ratio = (Portfolio Return – Risk-Free Rate) / Portfolio Beta (β)
Key Components Explained
- Portfolio Return: The actual return achieved by the investment portfolio over a specific period.
- Risk-Free Rate: Typically represented by government bond yields (e.g., 10-year Treasury yield).
- Portfolio Beta (β): Measures the portfolio’s volatility relative to the market. A beta of 1 means the portfolio moves with the market.
Step-by-Step Calculation Example
Let’s calculate the Treynor Ratio for a portfolio with:
- Annual return: 15%
- Risk-free rate: 3%
- Portfolio beta: 1.2
Applying the formula:
(15% – 3%) / 1.2 = 12% / 1.2 = 10.00
Interpreting Treynor Ratio Results
| Treynor Ratio Value | Interpretation | Investment Quality |
|---|---|---|
| > 1.0 | Excellent risk-adjusted returns | High quality |
| 0.5 – 1.0 | Good performance | Above average |
| 0 – 0.5 | Average performance | Market equivalent |
| < 0 | Poor performance | Below market |
Treynor Ratio vs. Sharpe Ratio
| Metric | Risk Measure | Best For | Formula |
|---|---|---|---|
| Treynor Ratio | Systematic risk (beta) | Diversified portfolios | (Rp – Rf) / β |
| Sharpe Ratio | Total risk (standard deviation) | Individual assets | (Rp – Rf) / σ |
Practical Applications
- Portfolio Comparison: Compare different portfolios’ risk-adjusted returns
- Performance Benchmarking: Evaluate fund managers against market indices
- Asset Allocation: Optimize portfolio construction based on risk tolerance
- Investment Selection: Identify undervalued assets with high risk-adjusted returns
Limitations to Consider
- Relies on historical data which may not predict future performance
- Assumes beta accurately represents systematic risk
- Sensitive to the choice of risk-free rate
- Doesn’t account for unsystematic risk
Real-World Example: Comparing Two Mutual Funds
Let’s compare Fund A and Fund B using their Treynor Ratios:
| Metric | Fund A | Fund B |
|---|---|---|
| Annual Return | 12.5% | 14.2% |
| Beta | 0.95 | 1.30 |
| Risk-Free Rate | 2.0% | 2.0% |
| Treynor Ratio | 11.05 | 9.38 |
Despite Fund B having higher absolute returns, Fund A demonstrates better risk-adjusted performance with a higher Treynor Ratio (11.05 vs 9.38), making it the more efficient investment choice.