Hong Life CalculatorsUnderstanding the Treynor ratio calculator — concept and principle
The Treynor ratio measures how much excess return a portfolio earned for each unit of market risk (beta). This calculator compares two portfolios with each other and with the market, and shows the return CAPM would predict for portfolio A.
How it is calculated
- Treynor ratio T = (Rp − Rf) ÷ βp.
- Market Treynor ratio = Rm − Rf (the market's beta is 1).
- CAPM predicted return = Rf + β × (Rm − Rf).
- The portfolio with the higher ratio earned more excess return per unit of beta.
The principle
Jack Treynor proposed in 1965 that investors in a well-diversified portfolio care mostly about market (systematic) risk, because diversification removes the rest. Dividing the excess return by beta shows the reward per unit of that risk. Unlike the Sharpe ratio, which divides by total volatility, the Treynor ratio ignores risk that diversification removes, so it suits well-diversified portfolios or funds held as part of a larger portfolio.
Worked example
Default inputs: A returns 11% with beta 1.2; B returns 8% with beta 0.7; risk-free 4%; market 9%.
- Excess return of A = 11 − 4 = 7%; Treynor A = 7 ÷ 1.2 ≈ 5.83.
- Treynor B = (8 − 4) ÷ 0.7 ≈ 5.71.
- Market Treynor = 9 − 4 = 5.
- Portfolio A ranks higher, and A beats the market per unit of beta.
- CAPM predicted return for A = 4 + 1.2 × 5 = 10%, below its actual 11%.
| Portfolio A beta | Treynor ratio — portfolio A |
|---|---|
| 0.3 | 23.33 |
| 0.6 | 11.67 |
| 0.9 | 7.78 |
| 1.2 | 5.83 |
| 1.5 | 4.67 |
| 1.8 | 3.89 |
| 2.4 | 2.92 |
How to read the result
A higher ratio means better reward for market risk. A ratio above the market's means the portfolio would plot above the security market line, which is equivalent to a positive Jensen's alpha. Use the same period for returns and beta, and compare portfolios against the same benchmark.
Common mistakes
- Using the Treynor ratio for a concentrated portfolio where unsystematic risk matters.
- Mixing annual returns with a beta estimated on another period.
- Interpreting the ratio when beta is negative or near zero.
- Comparing ratios computed with different risk-free rates.
Frequently asked questions
What is a good Treynor ratio?
One higher than the market's (Rm − Rf) and higher than comparable portfolios over the same period.
How is the Treynor ratio different from the Sharpe ratio?
Treynor divides by beta (market risk); Sharpe divides by standard deviation (total risk).
When should I use the Treynor ratio?
For diversified portfolios or when a fund is one part of a larger diversified holding.
Sources: Treynor, J. L. (1965). How to Rate Management of Investment Funds. Harvard Business Review, 43(1). · Bodie, Kane & Marcus, Investments (portfolio performance evaluation)