Treynor Ratio
Calculate the Treynor ratio: T = (Rp - Rf) / beta.
Measure risk-adjusted return using systematic risk instead of total volatility.
The Formula
The Treynor ratio measures the risk-adjusted return of a portfolio relative to its systematic risk, expressed as beta (β). Named after Jack Treynor, one of the pioneers of modern portfolio theory, it was introduced in 1965 as a way to evaluate how efficiently a portfolio compensates investors for the market risk they accept. Unlike the Sharpe ratio, which uses total volatility (standard deviation), the Treynor ratio uses only beta — the portion of risk that cannot be eliminated through diversification.
The numerator, Rp − Rf, is the excess return of the portfolio above the risk-free rate. The risk-free rate is typically the yield on short-term government bonds such as U.S. Treasury bills. This excess return represents the compensation investors receive for taking on investment risk rather than simply holding a risk-free asset.
The denominator, βp, is the portfolio beta — a measure of how sensitive the portfolio is to movements in the overall market. A beta of 1.0 means the portfolio moves in line with the market. A beta above 1.0 means the portfolio amplifies market moves, and a beta below 1.0 means it is less sensitive. By dividing by beta, the Treynor ratio normalizes performance by market risk exposure only.
A higher Treynor ratio indicates better risk-adjusted performance. The ratio is most meaningful when comparing well-diversified portfolios, where unsystematic (company-specific) risk has already been largely eliminated. For undiversified portfolios or individual stocks, the Sharpe ratio — which accounts for total risk — is often more appropriate. The Treynor ratio is widely used by professional fund managers and institutional investors to rank portfolio managers operating at similar levels of market exposure.
Variables
| Symbol | Meaning | Unit |
|---|---|---|
| T | Treynor ratio — risk-adjusted return per unit of market risk | dimensionless |
| Rp | Portfolio return — annualized return of the investment | % |
| Rf | Risk-free rate — return on a risk-free asset like Treasury bills | % |
| βp | Portfolio beta — sensitivity of portfolio returns to market movements | dimensionless |
Example 1
A portfolio returned 14% annually. The risk-free rate is 3% and the portfolio beta is 1.2. What is the Treynor ratio?
Excess return = 14% − 3% = 11%
T = 11% / 1.2 = 9.17%
Treynor ratio = 9.17% (strong risk-adjusted return for the level of market risk taken)
Example 2
Fund A returned 16% with beta 1.5. Fund B returned 12% with beta 0.8. Risk-free rate is 4%. Which fund has the better Treynor ratio?
Fund A: T = (16% − 4%) / 1.5 = 12% / 1.5 = 8.0%
Fund B: T = (12% − 4%) / 0.8 = 8% / 0.8 = 10.0%
Fund B has the higher Treynor ratio (10.0% vs 8.0%), meaning it earned more return per unit of market risk
When to Use It
The Treynor ratio is best suited for:
- Comparing well-diversified portfolios where unsystematic risk is minimal
- Evaluating mutual funds and ETFs that track broad market indices
- Ranking portfolio managers with similar investment mandates
- Assessing how much excess return a fund earns for each unit of market exposure
- Situations where beta is the more relevant risk measure than standard deviation
- Institutional performance attribution and manager selection processes