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Key Takeaways
- The Treynor ratio divides a portfolio return above the risk-free rate by its beta, expressing excess return per unit of systematic risk rather than per unit of total volatility.
- Use Treynor to compare excess return with market sensitivity, and measure residual risk and total volatility separately.
- The benchmark is the market risk premium, the market portfolio’s own Treynor ratio: a positive-beta portfolio that beats it plots above the security market line with positive CAPM alpha, and a negative beta reverses that test.
- At zero beta the ratio is undefined. For a negative beta, inspect the numerator and denominator together because division changes the sign.
- Compare Treynor, Sharpe and the underlying beta, volatility and regression residuals to understand their different rankings.
- Trust the ratio only as far as the beta: estimate it against a named benchmark and frequency, and check its standard error before you rank funds.
What is the Treynor ratio?
The Treynor ratio is a risk-adjusted return measure that divides a portfolio’s mean excess return over the risk-free rate by its beta against a market benchmark. It expresses excess return per unit of systematic, or market, risk rather than per unit of total volatility. It is also called the reward-to-volatility ratio or the Treynor measure.
How is the Treynor ratio calculated?
The calculation divides arithmetic mean excess return by beta against a market benchmark. Label the result’s horizon and units, periodic or annualized, decimals or percentage points, because 8.0 and 0.08 can be the same fund.
Beta is covariance with the market divided by market variance. Use a consistent return basis for the beta and performance comparison.
Formula
Treynor ratio = mean(portfolio return − risk-free return) ÷ portfolio beta- Use arithmetic mean returns at a consistent observation frequency, or their explicitly stated annualized convention.
- Use the matching risk-free holding-period return for the same currency and observation periods.
- Bp is the portfolio beta, the covariance of its returns with the market divided by the variance of the market.
- The ratio carries the numerator’s units: in percentage points Fund A reads 8.0, meaning 8 points of excess return per 1.0 of beta, and in decimals the same fund reads 0.08. Compare readings in one convention.
- With beta held fixed, annualizing a monthly arithmetic mean multiplies the ratio by 12; a beta re-estimated on annual returns can come out different, so name the beta’s return horizon.
- The natural benchmark is the market risk premium, E(Rm) − Rf, which is the Treynor ratio of the market portfolio because the market has a beta of 1.
Treynor ratio example: five portfolios
Use matched annualized arithmetic mean returns: 4% for the risk-free baseline and 9% for the market. A has 14% mean return, beta 1.25 and 20% volatility; B has 10%, beta 0.60 and 12% volatility; C has 14%, beta 0.50 and 30% volatility. Use excess-return volatility for the Sharpe comparison.
- Market benchmark: (9.0% − 4.0%) / 1.00 = 5.0, the Treynor ratio of the market portfolio
- Fund A: (14.0% − 4.0%) / 1.25 = 8.0
- Fund B: (10.0% − 4.0%) / 0.60 = 10.0
- Fund C: (14.0% − 4.0%) / 0.50 = 20.0
- Sharpe ratios on the same inputs: A is 10.0% / 20% = 0.50, B is 6.0% / 12% = 0.50, C is 10.0% / 30% = 0.33
Treynor is 8 for A, 10 for B and 20 for C, measured in annualized percentage points per unit of beta. Sharpe is 0.50, 0.50 and 0.33 respectively. C wins on Treynor but has the lowest Sharpe: its 30% volatility carries risk that beta leaves out, so size it on total volatility, not on its 0.50 beta.
The table gives B 10, C 20, D 100 and E −10 using the same units. D’s 100 comes from dividing by a 0.05 beta and E’s −10 from a negative beta, so read both through their alphas: 4.75% and 3.00%.
On Sharpe, which divides by total excess-return volatility instead of beta, A and B tie at 0.50 and C falls to 0.33.
Treynor ratio and CAPM alpha
At a 5% market premium, CAPM alpha is mean excess return minus beta × 5%. B and E both have 3% alpha even though their Treynor ratios are +10 and −10.
The exact identity is alpha = beta × (Treynor − market premium). For positive beta, exceeding the market premium corresponds to positive alpha; negative beta reverses that comparison.
Beta, residual risk and the Treynor ratio
In a one-market regression, a portfolio’s variance splits into market risk, beta squared times market variance, and residual risk; Treynor prices only the first. The residual holds other common factors as well as company-specific moves.
A small beta can still move in lockstep with the market: a portfolio with 5% in a market asset and 95% in a constant-return risk-free asset has beta 0.05 and perfect positive correlation with the market in that model.
Check the regression residuals and beta’s standard error. R-squared tells you how much of the variation the market explains; the standard error tells you how precisely beta is pinned down.
Annualizing the Treynor ratio and leverage
If beta is held fixed while monthly arithmetic mean excess return is annualized, multiply the Treynor ratio by 12. A beta re-estimated on annual returns can come out different, so annualize the mean or re-estimate beta, and say which.
Leverage leaves the ratio unchanged in the idealized model, because scaling excess returns scales beta by the same factor. A real leveraged position pays financing and trading costs, which lower it.
Treynor ratio vs Sharpe ratio
Use Treynor for return per unit of market risk, Sharpe for return per unit of total volatility and drawdown for the worst run in the value path, then check how each new position changes the combined portfolio’s exposures.
Limitations of the Treynor ratio
- Beta captures only market risk. Residual risk is left out, so C posts the highest Treynor ratio of A, B and C despite 30% volatility. Size a concentrated position on total volatility.
- Set the ratio aside near zero beta, where it becomes unstable and then undefined, and read a negative-beta fund through its alpha: E reads −10 beside a 3.00% alpha.
- Rank funds only on betas estimated the same way. The benchmark, return frequency and window all move beta, and its standard error sets how far to trust the ranking.
- Line up units and horizon first. 8.0 in percentage points and 0.08 in decimals are the same reading, and a monthly figure needs scaling before it meets an annual one.
- Check factor exposures beyond the market. In a one-market model, size, value or sector bets land in the residual, outside the ratio.
Bottom line
The Treynor ratio measures how much excess return a portfolio earned for each unit of market risk, which suits comparing diversified portfolios with the market premium. Use it with a well-estimated positive beta, and read it beside Sharpe, alpha and residual volatility so residual risk does not hide behind a low beta.
Clear answers
Frequently Asked Questions
Sources and Further Reading
- CFA Institute: Portfolio Risk and Return, Part II
- CFA Institute: Measures of Risk-Adjusted Return, Let's Not Forget Treynor and Jensen
- Investor.gov: Beginners' Guide to Asset Allocation, Diversification, and Rebalancing
How entries are sourced, calculated and updated: editorial methodology.