Treynor Ratio Calculator
Print| Excess Return per Unit Beta | 0.00% |
When evaluating fund performance, measuring gross returns alone is misleading; a portfolio manager might achieve high returns simply by taking on excessive market risk. While the Sharpe Ratio measures total volatility, the Treynor Ratio (also known as the reward-to-volatility ratio) evaluates excess returns relative specifically to systematic risk (market risk measured by Beta).
Our free Treynor Ratio Calculator helps investors and wealth managers analyze how effectively a portfolio or mutual fund compensates investors for taking on un-diversifiable market exposure.
How to Calculate the Treynor Ratio
The Treynor Ratio applies the Capital Asset Pricing Model (CAPM) framework, assuming that in a fully diversified portfolio, unsystematic (company-specific) risk has been eliminated, leaving only systematic market sensitivity (Beta).
The Treynor Ratio Formula:
Treynor Ratio = (Rₚ - R_f) / βₚ
- Rₚ: Actual or expected Portfolio Return (expressed as a percentage).
- R_f: Risk-Free Rate of Return (e.g., yield on 10-year U.S. Treasury bonds).
- βₚ: Portfolio Beta (measuring sensitivity to benchmark market movements).
Step-by-Step Calculation Example
Consider an actively managed large-cap mutual fund that achieved an annual return of 14.5% over the past year. The current risk-free rate is 3.5%. The fund’s regression analysis indicates a Beta (β) of 1.10 (indicating 10% more volatility than the broad S&P 500 benchmark).
Let’s calculate the fund’s Treynor Ratio:
Excess Return (Rₚ - R_f) = 14.5% - 3.5% = 11.0%
Treynor Ratio = 11.0% / 1.10 = 10.00% (or 0.100)
| Performance Variable | Fund Value | Financial Interpretation |
|---|---|---|
| Portfolio Annual Return (Rₚ) | 14.5% | Total annual realized return |
| Risk-Free Rate (R_f) | 3.5% | Baseline safe yield (U.S. Treasuries) |
| Portfolio Excess Return | +11.0% | Net return generated above risk-free rate |
| Portfolio Beta (βₚ) | 1.10 | Systematic risk exposure relative to market |
| Treynor Ratio Score | 10.00% (0.100) | Generates 10.0% excess return per unit of Beta |
Frequently Asked Questions (FAQ)
What is the difference between the Treynor Ratio and the Sharpe Ratio?
The main difference is the risk measure used in the denominator. The Sharpe Ratio uses total risk (standard deviation), making it ideal for non-diversified single portfolios. The Treynor Ratio uses systematic risk (Beta), making it ideal for comparing fully diversified sub-components of a broader investment portfolio.
What is a good Treynor Ratio?
A higher Treynor Ratio indicates superior risk-adjusted performance. However, because Treynor ratios depend on the prevailing risk-free interest rate environment and market equity risk premium, they are best evaluated by comparing multiple competing funds or managers operating within the same asset class.
Can the Treynor Ratio be negative?
Yes. A negative Treynor Ratio occurs when a portfolio’s total return is less than the risk-free rate (resulting in negative excess return), indicating that the investor would have been better off holding risk-free government bonds.