βοΈ Treynor Ratio Calculator
Excess return per unit of market risk.
Treynor ratio
Estimates for planning only, not financial advice.
A portfolio returning 12 percent with a 3 percent risk-free rate and a beta of 1.2 has a Treynor ratio of 7.5. That is 7.5 percentage points of excess return per unit of market risk. Compare it against another fund's Treynor over the same period; the higher number delivered more compensation for the systematic risk taken.
How to Use This Calculator
Enter the portfolio's return for the period, the risk-free rate for the same period, and the portfolio beta. Use consistent annualization: annual returns with annual rf, monthly with monthly.
Enter total return for the period, dividends included. Fund fact sheets publish this.
Enter the risk-free rate: T-bill yield for the period is the standard proxy.
Enter beta vs the relevant benchmark. A diversified equity fund vs the S&P 500 is the classic setup.
The Formula
Treynor divides excess return by beta, systematic risk only, unlike Sharpe which divides by total volatility. The assumption: the portfolio is diversified, so idiosyncratic risk has been diversified away and only market risk deserves compensation. For a well-diversified fund that assumption holds; for a concentrated 5-stock portfolio it does not, and Sharpe is fairer.
Worked Example
Return 12 percent, rf 3 percent, beta 1.2. Excess: 9 percent. Treynor: 9 / 1.2 = 7.5. Fund B: return 10 percent, beta 0.8. Treynor: 7 / 0.8 = 8.75. Fund B wins on risk-adjusted terms despite the lower headline return: it earned nearly as much excess per unit of market risk with far less. Ranking by raw return would have picked the wrong fund.
Treynor vs Sharpe vs Sortino
| Ratio | Risk divisor | Best for |
|---|---|---|
| Treynor | Beta (systematic) | Diversified portfolios, fund ranking |
| Sharpe | Total volatility | Single assets, concentrated portfolios |
| Sortino | Downside deviation | Asymmetric strategies |
Use Treynor when comparing diversified funds against a benchmark, Sharpe when total risk matters to the holder, Sortino when upside volatility should not count. They often agree; when they disagree, the disagreement itself is informative about the return distribution. Our Sortino calculator covers the downside view.
What Treynor Misses
Beta is backward-looking and unstable: a fund's beta drifts with its holdings and market regimes. Treynor also assumes the CAPM world where only systematic risk is priced, and it says nothing about the magnitude of returns, only the ratio. A Treynor of 15 on a 4 percent excess return is less useful than a Treynor of 8 on a 12 percent excess if you need actual dollars. And like all historical ratios, it describes the past; a manager change or style drift voids the history.
Ranking Funds With Treynor: a Worked Screen
Build the comparison properly and Treynor earns its keep. Pull five large-cap funds' 5-year annualized returns, betas, and the 5-year T-bill average. Suppose Fund A returned 11 percent with beta 1.1, Fund B 10 percent with beta 0.85, and the risk-free rate was 2.5 percent. Treynor A: (11 - 2.5) / 1.1 = 7.7. Treynor B: (10 - 2.5) / 0.85 = 8.8. Fund B wins despite the lower headline return, and the gap is meaningful: it earned more per unit of market risk in every year of the sample.
Then stress-test the ranking. Recompute over 3-year and 10-year windows: if the order flips, the edge is regime-dependent, not skill. Check that betas are measured against the same benchmark over the same period; a mid-cap fund's beta against the S&P 500 is a different animal than against the Russell Midcap. And never rank on Treynor alone: add absolute return, max drawdown, expense ratio, and manager tenure. Treynor is the risk-adjustment column in a multi-column decision, not the decision.
Ranking Funds the Treynor Way
The Treynor ratio, excess return divided by beta, answers a specific question: how much return did this portfolio earn per unit of market risk taken? A fund with 12 percent return, 4 percent risk-free rate, and beta 1.2 scores (12-4)/1.2 = 6.67. Compare that against peers' Treynor ratios, not against raw returns: the fund that earned 14 percent with a beta of 1.8 (5.56) took its investors on a wilder ride for less compensation per unit of risk.
Know its limits before trusting it. Treynor assumes the portfolio is diversified, so idiosyncratic risk is irrelevant; for concentrated holdings, Sharpe is the honest metric. Beta itself is backward-looking and unstable, and a negative-beta or near-zero-beta fund produces nonsense ratios. Use Treynor as one screen among several: rank diversified equity funds by Treynor, cross-check with Sharpe and alpha, and beware any ranking that hinges on a single year's beta estimate. Ratios rank; judgment selects.
In practice, Treynor shines in manager selection. When a pension committee compares five large-cap managers, raw returns mislead because betas differ; Treynor puts them on one risk-adjusted scale. Pair it with upside/downside capture ratios to see whether the manager earns the Treynor score in up markets, down markets, or both. A high Treynor built entirely on bull-market beta is luck wearing a formula; a high Treynor with downside protection is skill worth paying for.
Estimates for planning only, not financial advice.
Frequently Asked Questions
What is the Treynor ratio?
Excess return divided by beta: (portfolio return minus risk-free rate) / beta. It measures compensation per unit of systematic (market) risk. A Treynor of 7.5 means 7.5 points of excess return per unit of beta. Higher is better when comparing funds.
How do you calculate the Treynor ratio?
Subtract the risk-free rate from the portfolio return, then divide by beta. With 12% return, 3% rf, and 1.2 beta: (12-3)/1.2 = 7.5. Use the same period for all three inputs. Mixing a 5-year return with a 1-year T-bill rate silently corrupts the ratio; annualize everything consistently.
What is the difference between Treynor and Sharpe ratio?
Treynor divides by beta (systematic risk only); Sharpe divides by total standard deviation (all volatility). Treynor suits diversified portfolios where idiosyncratic risk is diversified away; Sharpe suits concentrated holdings where total volatility is what the investor feels. When both rank funds the same way, the conclusion is solid; when they disagree, the return distribution holds the explanation.
What is a good Treynor ratio?
There is no absolute scale; it is a ranking tool. Compare funds over identical periods: the higher Treynor delivered more excess return per unit of market risk. Negative Treynor means the fund did not beat the risk-free rate. A Treynor of 8 versus 6 is meaningful; a Treynor of 8 versus 7.8 is noise, so demand clear separation before switching funds.
What beta should I use?
The portfolio's beta against the relevant benchmark (usually the S&P 500 for US equity funds), measured over the same period as the return. Fund fact sheets publish it. Mismatched periods or wrong benchmarks make the ratio meaningless. For a small-cap fund, use a small-cap benchmark beta; an S&P 500 beta misstates its systematic risk badly.
Can the Treynor ratio be negative?
Yes, when the portfolio underperforms the risk-free rate. A negative Treynor says the risk taken was not compensated at all. Rank negative-Treynor funds by magnitude: less negative lost less per unit of risk. But do not over-interpret small negatives over short periods; a single bad quarter can flip the sign without changing the fund's character.
Why does Treynor ignore unsystematic risk?
It assumes a diversified portfolio, where stock-specific risk washes out and only market risk remains. For concentrated portfolios that assumption fails, and Treynor overstates risk-adjusted performance, which is why Sharpe exists. A 10-stock portfolio with a great Treynor may simply have gotten lucky on idiosyncratic bets; Sharpe would penalize the concentration Treynor ignores.
Does Treynor work for bond funds?
Approximately, using a bond benchmark beta, but interest-rate risk dominates and beta against equities misleads. For bonds, excess return per unit of duration is usually the more honest risk adjustment. A bond fund's equity beta is often near zero, which would make its Treynor absurdly large; that absurdity is the signal to use a different metric.
How is Treynor related to alpha?
Jensen's alpha is the excess return above what beta predicts (the CAPM line); Treynor is the slope of the line from the risk-free rate through the portfolio. Positive alpha generally accompanies a Treynor above the market's, since the market's Treynor is the benchmark slope.
What are the limitations?
Beta instability, backward-looking inputs, the CAPM assumptions underneath, and no information about absolute return levels. Use it to rank diversified funds over identical periods, alongside absolute returns and drawdowns. A Treynor of 15 on a 4 percent excess return is less useful than 8 on a 12 percent excess if you need actual dollars.