# Treynor ratio

The Treynor ratio is a portfolio performance measure that divides a portfolio's excess return over the risk-free rate by its beta, the sensitivity of the portfolio's returns to market returns, so that the result reads as excess return earned per unit of systematic (market) risk.<sup>[1](https://link.springer.com/article/10.1057/s41260-025-00417-z)</sup><sup> • </sup><sup>[2](https://www.investopedia.com/terms/t/treynorratio.asp)</sup> Jack Treynor introduced it in 1965 as one of the earliest applications of the Capital Asset Pricing Model (CAPM) to the evaluation of fund managers.<sup>[3](https://pubs.aeaweb.org/doi/pdfplus/10.1257/0895330042162340)</sup>

| Key fact | Detail |
|---|---|
| Formula | Treynor ratio = ER / β, where ER is excess return over the risk-free rate and β is the regression coefficient from the Sharpe single index model<sup>[1](https://link.springer.com/article/10.1057/s41260-025-00417-z)</sup> |
| Beta definition | Covariance between portfolio and benchmark returns divided by the variance of benchmark returns; beta of 1 means the regression coefficient on benchmark returns is 1<sup>[4](https://rpc.cfainstitute.org/sites/default/files/-/media/documents/code/gips/measures-risk-adjusted-return.pdf)</sup> |
| Origin | Introduced by Jack Treynor in 1965; one of the earliest CAPM applications, alongside Sharpe's 1966 ratio and Jensen's 1968 alpha<sup>[3](https://pubs.aeaweb.org/doi/pdfplus/10.1257/0895330042162340)</sup> |
| Best use | Ranking well-diversified portfolios benchmarked to the same market index; a fully diversified portfolio is ranked identically by the Treynor and Sharpe ratios<sup>[4](https://rpc.cfainstitute.org/sites/default/files/-/media/documents/code/gips/measures-risk-adjusted-return.pdf)</sup> |
| Main blind spot | Ignores idiosyncratic (non-market) risk, so a poorly diversified portfolio with low beta but high total risk can look superior<sup>[4](https://rpc.cfainstitute.org/sites/default/files/-/media/documents/code/gips/measures-risk-adjusted-return.pdf)</sup> |
| Known failure modes | Misranks funds when excess returns are negative, when beta is negative, and is undefined at beta = 0<sup>[1](https://link.springer.com/article/10.1057/s41260-025-00417-z)</sup><sup> • </sup><sup>[5](https://wiki.fcontext.com/stocks/treynor-ratio/)</sup> |
| 2025 refinement | Modified Treynor Ratio, MTR = ER / (β + a)^(ER/\|ER\|), corrects rankings when excess returns are negative<sup>[1](https://link.springer.com/article/10.1057/s41260-025-00417-z)</sup> |

## Definition and formula

The ratio measures how much excess return an asset or portfolio produces per unit of systematic risk.<sup>[1](https://link.springer.com/article/10.1057/s41260-025-00417-z)</sup> In symbols,

\[ \mathrm{TR} = \frac{R_p - R_f}{\beta_p} \]

where \( R_p \) is the portfolio return over the measurement period, \( R_f \) the risk-free rate, and \( \beta_p \) the portfolio's beta. Beta is calculated as the covariance between the portfolio returns and the benchmark returns divided by the variance of the benchmark returns; a beta of 1 means the estimated sensitivity of the portfolio's returns to benchmark returns is 1.<sup>[4](https://rpc.cfainstitute.org/sites/default/files/-/media/documents/code/gips/measures-risk-adjusted-return.pdf)</sup> Beta measures the tendency of a portfolio's return to change in response to changes in the overall market's return.<sup>[2](https://www.investopedia.com/terms/t/treynorratio.asp)</sup>

The ratio's weakness with negative numbers is easiest to see in the worked example from the 2025 refinement paper. Two funds both have excess return of −1%; fund C has beta 0.5 and fund D has beta 1.5. Fund C is clearly the better choice because of its lower risk, yet it is assigned a lower Treynor Ratio value than fund D, −0.02 versus −0.00667, because dividing a negative number by a smaller beta makes it more negative.<sup>[1](https://link.springer.com/article/10.1057/s41260-025-00417-z)</sup>

## Origins and CAPM foundations

Treynor aimed to assess portfolio performance "with the market effect subtracted".<sup>[1](https://link.springer.com/article/10.1057/s41260-025-00417-z)</sup> The ratio sits within the CAPM framework pioneered by Treynor (1961), Sharpe (1964), Lintner (1965), and Mossin (1966), alongside Jensen's (1968) alpha and the Treynor–Black (1973) appraisal ratio.<sup>[1](https://link.springer.com/article/10.1057/s41260-025-00417-z)</sup> Treynor's CAPM foundations appear in two manuscripts, "Market Value, Time, and Risk" (1961) and "Toward a Theory of Market Value of Risky Assets" (1962), which circulated during the 1960s in mimeographed draft form but were never published in an academic or practitioner journal.<sup>[6](https://papers.ssrn.com/sol3/papers.cfm?abstract_id=447580)</sup>

[Performance measurement](https://www.edgepedia.org/performance-measurement) was one of the earliest applications of the CAPM, with Treynor's 1965 measure followed by Sharpe's 1966 ratio.<sup>[3](https://pubs.aeaweb.org/doi/pdfplus/10.1257/0895330042162340)</sup> Treynor himself disliked the formula that bears his name; in an email he wrote that a fund's market risk reflects the kind of stocks it owns, while its non-market risk reflects other factors, a distinction the ratio collapses.<sup>[7](https://tsgperformance.com/wp-content/uploads/2014/05/Jul08NL.pdf)</sup>

The measure inherits the CAPM's mean–variance assumptions, which may limit the usefulness of the Treynor ratio and the [Sharpe ratio](https://www.edgepedia.org/sharpe-ratio) for strategies with asymmetrical returns.<sup>[4](https://rpc.cfainstitute.org/sites/default/files/-/media/documents/code/gips/measures-risk-adjusted-return.pdf)</sup>

## How it compares with Sharpe, Sortino, and alpha

The Treynor ratio substitutes beta for standard deviation in the Sharpe ratio, scaling a portfolio's excess return over the risk-free rate by its market beta.<sup>[8](https://www.investopedia.com/ask/answers/010815/what-difference-between-sharpe-ratio-and-traynor-ratio.asp)</sup> The choice of risk denominator matches the investor's situation: per Scholz and Wilkens (2005), total-risk measures like the Sharpe ratio suit investors putting most of their capital in one fund, while systematic-risk measures like the Treynor ratio suit investors holding many funds, where unsystematic risk is diversified away.<sup>[1](https://link.springer.com/article/10.1057/s41260-025-00417-z)</sup>

**Divergence as a diagnostic.** A significant difference between a fund's Treynor and Sharpe rankings indicates a meaningful proportion of idiosyncratic risk relative to total risk; conversely, a fully diversified portfolio is ranked identically by the two ratios.<sup>[4](https://rpc.cfainstitute.org/sites/default/files/-/media/documents/code/gips/measures-risk-adjusted-return.pdf)</sup> Because the Treynor ratio does not capture idiosyncratic risk, it is most relevant for diversified portfolios, and a poorly diversified portfolio with low beta but higher total risk can appear to have a superior risk-adjusted return profile.<sup>[4](https://rpc.cfainstitute.org/sites/default/files/-/media/documents/code/gips/measures-risk-adjusted-return.pdf)</sup> Empirical work supports this convergence for diversified portfolios: in a 2020–2024 study of 11 large-cap Indonesian stocks, an optimized portfolio with expected return of 74.60% produced a Sharpe Ratio of 5.60 and a Treynor Ratio of 0.0697, and a paired t-test on the two rankings yielded p = 0.331, no statistically significant ranking difference.<sup>[9](https://ejurnal.undana.ac.id/index.php/JEM/article/view/26171)</sup>

The ratios also diverge in sign-dependent edge cases. With negative beta, the lower the excess return the higher the Treynor Ratio, an anomaly the Sharpe and [Information](https://www.edgepedia.org/information) ratios lack; only in the positive-excess-return, positive-beta quadrant does the ratio rank portfolios correctly.<sup>[1](https://link.springer.com/article/10.1057/s41260-025-00417-z)</sup>

The relationship to Jensen's alpha is family resemblance rather than arithmetic identity. Jensen's alpha, developed by Michael Jensen in 1968, is the excess return over the CAPM-expected return, expressed in basis points, and the alpha equation has been expanded to multifactor models including APT, the [Fama–French three-factor model](https://www.edgepedia.org/fama-french-three-factor-model), and the Carhart four-factor model.<sup>[4](https://rpc.cfainstitute.org/sites/default/files/-/media/documents/code/gips/measures-risk-adjusted-return.pdf)</sup>

Metric choice can be gamed. Sharpe and Treynor ratios are only weakly correlated with the information and Sortino ratios, so a fund manager who showcases a [Sortino ratio](https://www.edgepedia.org/sortino-ratio) without highlighting Sharpe or Treynor may be cherry-picking the metric on which they look best.<sup>[10](https://rpc.cfainstitute.org/blogs/enterprising-investor/2023/how-do-performance-metrics-correlate-might-fund-managers-cherry-pick)</sup>

## By the numbers

The Ibbotson 2011 report gives a long-horizon supply-side expected equity risk premium of 6.0 percent, derived as the historical equity risk premium minus a price-to-earnings adjustment using three-year average earnings.<sup>[11](https://psc.ky.gov/pscecf/2012-00222/rateintervention%40ag.ky.gov/10252012032043/Ibbotsoin_2011_Risk_Premia_Over_Time_Report_%2820110207135556%29.pdf)</sup> Damodaran's dataset provides historical annual US stock, bond, and bill returns from 1928 through 2022, the raw inputs for computing historical equity risk premium levels used in risk-adjusted return calculations.<sup>[12](https://pages.stern.nyu.edu/~adamodar/New_Home_Page/datafile/histret.html)</sup>

## Practical use and limitations

Both the Treynor ratio and Jensen's alpha are generally used to analyze past performance; insight into future performance depends on beta, which is based on historical price movements with limited predictability.<sup>[4](https://rpc.cfainstitute.org/sites/default/files/-/media/documents/code/gips/measures-risk-adjusted-return.pdf)</sup> Like the Sharpe ratio, the Treynor ratio is most effectively used as a ranking tool for portfolios benchmarked to the same market index.<sup>[4](https://rpc.cfainstitute.org/sites/default/files/-/media/documents/code/gips/measures-risk-adjusted-return.pdf)</sup> Software implementations exist in standard analytics libraries: the PerformanceAnalytics package for R computes the Treynor ratio as excess return over beta and also offers a modified Treynor ratio dividing by systematic risk instead.<sup>[13](https://timelyportfolio.github.io/PerformanceAnalytics/reference/TreynorRatio.html)</sup>

**Benchmark choice.** In a well-known study, Roll (1978) showed that even small changes in the proxy used for the market had large effects on risk-adjusted ratios; the R² between portfolio and benchmark (an R² of .80 means 80% of return variation relates to the benchmark) helps judge whether the benchmark is appropriate.<sup>[4](https://rpc.cfainstitute.org/sites/default/files/-/media/documents/code/gips/measures-risk-adjusted-return.pdf)</sup> A mismatched benchmark distorts beta directly: measuring a domestic large-cap fund's beta against the Russell 2000 Small Stock index would be inappropriate.<sup>[2](https://www.investopedia.com/terms/t/treynorratio.asp)</sup>

**Degenerate inputs.** At beta = 0 the ratio is undefined, and near zero it is unstable; with negative beta the sign logic inverts. A positive Treynor ratio means more measured excess return per unit of estimated market exposure, but it does not prove skill, forecast return, or capture total risk.<sup>[5](https://wiki.fcontext.com/stocks/treynor-ratio/)</sup> For statistical rigor, analytical formulas have been derived that yield confidence intervals on the Treynor index, with necessary and sufficient conditions for the index to be statistically different from zero.<sup>[14](https://ideas.repec.org/a/bla/jbfnac/v27y2000i1-2p127-154.html)</sup>

## References

1. [A Refinement to the Treynor Ratio, Journal of Asset Management (2025)](https://link.springer.com/article/10.1057/s41260-025-00417-z)
2. [Treynor Ratio: What It Is, What It Shows, Formula to Calculate It, Investopedia](https://www.investopedia.com/terms/t/treynorratio.asp)
3. [The Capital Asset Pricing Model, Journal of Economic Perspectives](https://pubs.aeaweb.org/doi/pdfplus/10.1257/0895330042162340)
4. [Measures of Risk-Adjusted Return, CFA Institute](https://rpc.cfainstitute.org/sites/default/files/-/media/documents/code/gips/measures-risk-adjusted-return.pdf)
5. [Treynor Ratio: Excess Return, Estimated Beta, and Comparable Risk Units, Financial Context Wiki](https://wiki.fcontext.com/stocks/treynor-ratio/)
6. [The Treynor Capital Asset Pricing Model, SSRN](https://papers.ssrn.com/sol3/papers.cfm?abstract_id=447580)
7. [Newsletter quoting Jack Treynor on the ratio bearing his name, TSG Performance](https://tsgperformance.com/wp-content/uploads/2014/05/Jul08NL.pdf)
8. [Sharpe or Treynor Ratio: Which is Best for Risk-Adjusted Returns?, Investopedia](https://www.investopedia.com/ask/answers/010815/what-difference-between-sharpe-ratio-and-traynor-ratio.asp)
9. [Sharpe vs Treynor: Strategies for evaluating stock portfolio performance on the Indonesian Stock Exchange](https://ejurnal.undana.ac.id/index.php/JEM/article/view/26171)
10. [How Do Performance Metrics Correlate? Might Fund Managers Cherry-Pick?, CFA Institute (2023)](https://rpc.cfainstitute.org/blogs/enterprising-investor/2023/how-do-performance-metrics-correlate-might-fund-managers-cherry-pick)
11. [2011 Ibbotson Risk Premia Over Time Report](https://psc.ky.gov/pscecf/2012-00222/rateintervention%40ag.ky.gov/10252012032043/Ibbotsoin_2011_Risk_Premia_Over_Time_Report_%2820110207135556%29.pdf)
12. [Historical Returns on Stocks, Bonds and Bills: 1928-2022, Aswath Damodaran, NYU Stern](https://pages.stern.nyu.edu/~adamodar/New_Home_Page/datafile/histret.html)
13. [TreynorRatio, PerformanceAnalytics R package documentation](https://timelyportfolio.github.io/PerformanceAnalytics/reference/TreynorRatio.html)
14. [An Analytical Confidence Interval for the Treynor Index, Journal of Business Finance & Accounting (2000)](https://ideas.repec.org/a/bla/jbfnac/v27y2000i1-2p127-154.html)

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*Topic: Encyclopedia › Society and history › Economics and business › Finance › Finance theory and quantitative methods › Portfolio theory and risk management › Portfolio performance measures*

*Initially written Oct 10, 2026 · Edited: Oct 11, 2026; Oct 15, 2026; Oct 25, 2026*

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License: Edgepedia Community License 1.0, https://www.edgepedia.org/edgepedia/license