Treynor Ratio Calculator
Last updated: 27 June 2026
Reviewed by Gavin Meiring, Lead research and primary author · Doctoral Candidate (Corporate Governance) · Research and drafting assisted by AI
- The Treynor ratio was introduced by Jack L. Treynor in a 1965 Harvard Business Review article, 'How to Rate Management of Investment Funds' — making it the oldest of the famous risk-adjusted performance ratios.
- Treynor is also widely called the father of the CAPM: his unpublished 1961 paper anticipated the capital asset pricing model before William Sharpe published his version, and both men's work underlies how we measure beta.
- Unlike the Sharpe ratio, which penalises total volatility, the Treynor ratio divides return by beta only — so a fund with lots of diversifiable risk can look great on Treynor while looking ordinary on Sharpe.
Treynor Ratio Calculator
The Treynor ratio calculator measures the risk-adjusted return of an investment relative to its market risk (beta), rather than its total volatility. It is used by institutional investors and portfolio managers evaluating a fund or portfolio that is one component of a larger diversified portfolio. The Treynor ratio is particularly appropriate when the portfolio being assessed is already well-diversified and only systematic (market) risk remains.
How to Use the Treynor Ratio Calculator
- Enter the portfolio's average annual return as a percentage.
- Input the risk-free rate, such as the current yield on short-term government bonds.
- Enter the portfolio's beta: a measure of its sensitivity to market movements.
- The calculator divides the excess return by beta and displays the Treynor ratio.
- Compare the result to other portfolios or to the market's own Treynor ratio to assess relative performance.
The Formula
Treynor Ratio = (Portfolio Return minus Risk-Free Rate) divided by Beta
Where:
Portfolio Return is the mean annual return of the portfolio over the measurement period.
Risk-Free Rate is the return from a risk-free instrument such as UK gilts or US Treasury bills. It represents the minimum return required for bearing any investment risk.
Beta measures the portfolio's sensitivity 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 it amplifies market moves; below 1.0 means it dampens them.
The Treynor ratio is expressed as a return per unit of market risk. A higher ratio is better, meaning the portfolio earns more return for each unit of market risk taken.
Real-World Example
Three funds are being compared. The risk-free rate is 4%.
Fund A: 14% return, beta of 1.2 Treynor Ratio = (14 minus 4) divided by 1.2 = 10 divided by 1.2 = 8.33
Fund B: 12% return, beta of 0.8 Treynor Ratio = (12 minus 4) divided by 0.8 = 8 divided by 0.8 = 10.0
Fund C: 16% return, beta of 1.5 Treynor Ratio = (16 minus 4) divided by 1.5 = 12 divided by 1.5 = 8.0
Ranked by Treynor ratio: Fund B (10.0) is best, Fund A (8.33) is second, Fund C (8.0) is third.
Despite Fund C producing the highest raw return, it takes on the most market risk (beta 1.5). Fund B produces the best return per unit of market risk even with the lowest absolute return. For an investor adding Fund B to an already-diversified portfolio, it offers the best risk-adjusted value.
Treynor Ratio vs Sharpe Ratio
The key difference between the Treynor ratio and the Sharpe ratio lies in how risk is measured.
The Sharpe ratio divides excess return by total volatility (standard deviation), which includes both systematic and unsystematic risk. This is appropriate when evaluating a portfolio as a standalone investment, or when it represents the investor's entire holdings.
The Treynor ratio divides excess return by beta (systematic risk only). This is appropriate when the portfolio is one of many holdings in a larger diversified portfolio. In a diversified portfolio, unsystematic (company-specific) risk has been diversified away, leaving only market risk. The Treynor ratio measures performance relative to the risk that cannot be diversified away.
If you are selecting a single fund to hold in isolation, use the Sharpe ratio. If you are assessing a fund to add to a broadly diversified portfolio, the Treynor ratio is the more relevant metric.
Jensen's alpha is a related concept that measures the portfolio's excess return above what would be expected given its beta, using the Capital Asset Pricing Model (CAPM) as the benchmark.
Frequently Asked Questions
What is a good Treynor ratio? The Treynor ratio is most meaningful relative to the market's own Treynor ratio. The market by definition has a beta of 1.0, so its Treynor ratio equals the equity risk premium (market return minus risk-free rate). In long-run historical data, this has been roughly 4% to 6% in developed markets. A fund with a Treynor ratio above the market's ratio has outperformed on a risk-adjusted basis. There is no single "good" absolute number without this comparison.
Why use beta rather than standard deviation to measure risk? Beta measures only the portion of risk that is correlated with the market and cannot be removed by diversification. Standard deviation includes both diversifiable (company-specific) and non-diversifiable (market) risk. When evaluating a fund that will be held alongside many other funds, only market risk is relevant because the other risks cancel out across the portfolio. Beta captures exactly this relevant risk.
What does a negative Treynor ratio mean? A negative Treynor ratio can occur in two ways: the portfolio return is below the risk-free rate (indicating underperformance), or the portfolio has a negative beta (meaning it moves opposite to the market, like some hedging strategies). A negative ratio from underperformance is a warning signal. A negative ratio from negative beta may indicate a useful portfolio hedge rather than poor management.
Is the Treynor ratio useful for evaluating bond funds? The Treynor ratio is most naturally suited to equity funds, where beta to a broad equity index is a meaningful risk measure. For bond funds, beta to an equity index is less relevant; other measures such as duration, credit spread sensitivity, or the Sharpe ratio are more commonly used. If a bond fund's beta to equities is being used specifically to assess its role in a mixed portfolio, the Treynor ratio can still be applied.
What the choice of risk-free rate does to the ranking
The three funds from the example above are worth running again at a different risk-free rate, because the input the ratio divides by beta is an excess return. A higher risk-free rate takes a fixed amount off each fund's return, and because that amount is then divided by each fund's beta, the three ratios do not all fall by the same distance.
| Fund | Return | Beta | Treynor at rf = 2% | Treynor at rf = 4% | Treynor at rf = 6% |
|---|---|---|---|---|---|
| A | 14% | 1.2 | 10.000 | 8.333 | 6.667 |
| B | 12% | 0.8 | 12.500 | 10.000 | 7.500 |
| C | 16% | 1.5 | 9.333 | 8.000 | 6.667 |
Fund B leads at every rate, so the conclusion in this example holds. The gap between first and last place does not. At a 2% risk-free rate, B sits 3.167 units above C. At 6% the gap is 0.833 units, and A and C finish level at 6.667. A fund with a high beta loses proportionally less when the risk-free rate rises, which is worth remembering before treating a narrow ranking as a decision.
The market itself gives a reference point. The market has a beta of 1.0 by definition, so its Treynor ratio is the equity risk premium: with a market return of 11% and a risk-free rate of 4%, that is 7.0. Fund A and Fund B both beat it. Fund C does not.
Three measures on the same three funds
A worked comparison shows why the three common risk-adjusted measures sometimes agree and sometimes do not.
| Fund | Return | Beta | Volatility | Treynor | Sharpe | Jensen's alpha |
|---|---|---|---|---|---|---|
| A | 14% | 1.2 | 18% | 8.333 | 0.556 | 1.60% |
| B | 12% | 0.8 | 11% | 10.000 | 0.727 | 2.40% |
| C | 16% | 1.5 | 24% | 8.000 | 0.500 | 1.50% |
The risk-free rate is 4% and the market return is 11% throughout. Jensen's alpha uses the Capital Asset Pricing Model, so the expected return for each fund is 4% plus beta times 7%. Fund A should have returned 12.40% and returned 14%, leaving an alpha of 1.60%. Fund B should have returned 9.60% and returned 12%, leaving 2.40%.
All three measures rank Fund B first here, and that is a coincidence of the numbers rather than a rule. Treynor and Sharpe disagree whenever a fund's volatility comes mostly from risk that is not correlated with the market, and Jensen's alpha disagrees with both when a fund holds a large cash balance, because cash reduces beta and drags the return without changing the alpha story.
What beta is measuring, and how the estimate moves
Beta comes from a regression of the fund's excess return on the market's excess return. The slope of that line is the beta. Three choices change the number.
| Choice | Common settings | What changes |
|---|---|---|
| Return interval | Daily, weekly, monthly | Daily data captures short bursts of co-movement, which raises the estimate for a fund that trades actively |
| Window | One year, three years, five years | A window that excludes a market fall will understate beta for a fund that fell with the market |
| Benchmark | Broad domestic index, regional index, global index | A UK equity fund measured against a global index shows a beta well below 1 because the two markets move apart |
Two smaller points belong with the input fields. The calculator rejects a beta of zero, because the ratio divides by it, and a beta of zero is the one case where the measure has no meaning. A negative beta is accepted, and the result then has the opposite sign to the excess return, which is the correct output for a position built to move against the market.
Where the ratio stops being useful
Five limits are worth stating.
- The ratio assumes the Capital Asset Pricing Model describes returns. If a portfolio's risk comes from factors other than the market, such as size or value, beta understates what the investor is carrying.
- It needs a benchmark. A Treynor ratio of 8.333 means nothing on its own. It means something against the market's ratio or against another fund measured over the same period with the same risk-free rate.
- It is silent about total risk. A concentrated fund with a low beta can still lose a third of its value in a bad quarter, and the Treynor ratio will look steady.
- Time period matters. A ratio computed on three good years is a statement about three years.
- It suits equity funds. For a bond fund, beta to an equity index is a weak description of risk, and duration or spread measures do more work.
The ratio takes its name from Jack L. Treynor's article "How to Rate Management of Investment Funds", published in the Harvard Business Review in 1965 (volume 43, number 1, pages 63 to 75). The Sharpe ratio used in the comparison table comes from William F. Sharpe's "Mutual Fund Performance", published in the Journal of Business in 1966 (volume 39, number 1, pages 119 to 138).
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