Treynor Ratio Calculator
The formula
What the treynor ratio tells you
Jack Treynor asked the opposite question to Sharpe: instead of dividing by total risk, divide by market (systematic) risk only. For a fully diversified portfolio that is the fair comparison — idiosyncratic risk has been diversified away and the market does not pay for it.
Calculation: Treynor = (Rp − Rf) ÷ βp. Enter your inputs and every substitution is shown below the result.
Reading the result
A Treynor above the market's own excess return means the manager beat the CAPM line for the beta they took. Compare a single sleeve against a benchmark, not against a total-portfolio number, because the ratio silently assumes the residual risk is gone.
Rules of thumb: Compare to benchmark excess return (historically ~5–7% per year for US equities) — beating it means real value added
Limitations and best practice
Useless for concentrated portfolios — beta ignores the very risk the holder is exposed to. Also, if beta is estimated over a calm window the ratio flatters the strategy; re-estimate across cycles.
This calculator gives an estimate based on standard formulas; it is not professional financial, medical, legal or engineering advice. Verify anything you plan to act on with a qualified professional and your own records.
Frequently asked questions
Treynor vs Sharpe — which is right for me?
Can beta be negative and what happens then?
Does Treynor account for fees?
Source & methodology
Treynor, J. L. (1965) "How to rate investment portfolios", Harvard Business Review.
Treynor Ratio explained: formula, worked example and honest limits
You are here because you need a specific number, and you want to see how it was produced before you rely on it. There are plenty of pages about Treynor Ratio; almost none of them show the working. This one does: the formula, every input, a fully computed example, and a sensitivity analysis calculated live from this engine’s own defaults.
The number itself is the easy part. What takes judgement is knowing which inputs are facts in your situation and which are guesses wearing a decimal point — a distinction this page makes explicit for every field above.
A calculation like this one is worth roughly as much as a careful sentence: it forces several vague considerations into one comparable quantity. Once Treynor Ratio is on the table, the argument can stop being about impressions.
What makes a calculation page trustworthy is that its copy is derived from its own arithmetic: here treynor ratio = 8.18 % per unit of beta, recomputed every time a field changes, and the sensitivity section ranks the inputs that move the result — Portfolio return first, at ≈15.6 % of the headline for a ten-percent error either way in that input. Work down the page and by the end you could re-derive the result in a spreadsheet from memory.
How Treynor Ratio is computed, line by line
One formula, published in full: Treynor = (Rp − Rf) ÷ βp. Anything you can read, you can reproduce in a spreadsheet, and that reproducibility is the whole point of printing it rather than hiding it behind a button.
Portfolio return (%) (example value 14) is a numeric input whose unit is fixed by the label; a wrong unit is a wrong answer wearing a plausible disguise. Check the convention first: if the source says “6.5 % per year”, type 6.5 and let the formula do the rest.
Risk-free rate (%) (example value 5) is a numeric input whose unit is fixed by the label; a wrong unit is a wrong answer wearing a plausible disguise. Enter it exactly as your document states it — quoted annual, monthly and effective rates are three different numbers.
Portfolio beta (example value 1) is a numeric input whose unit is fixed by the label; a wrong unit is a wrong answer wearing a plausible disguise. This input feeds the formula directly; a defensible figure here is worth more than false precision anywhere else.
The default Treynor Ratio calculation, written out in full
Rather than describe the calculation, here it is end to end — every substitution in order, starting from the inputs above. Starting figures: Portfolio return (%), Risk-free rate (%), Portfolio beta. The endpoint of that chain is 8.18 % per unit of beta of treynor ratio, sitting in the “Reward per unit of market risk” band.
- Excess return = 14% − 5% = 9.00%
- Treynor = 9.00 ÷ 1.1 = 8.18% per unit of beta
Excess return — 9.00 %. Compare it against the main result of 8.18 % per unit of beta before drawing conclusions.
Return if beta were 1.0 — 14.00 %. Read next to the headline, this is the figure that shows the shape of the trade-off.
Excess return per unit of beta — 8.18 %. Compare it against the main result of 8.18 % per unit of beta before drawing conclusions.
Sharpe-equivalent if σ = β×market σ (15%) — 0.55. Compare it against the main result of 8.18 % per unit of beta before drawing conclusions.
Re-running with your own figures is instant; re-running by hand once is the best way to know the tool is telling you the truth.
How far Treynor Ratio can reasonably move
Read this table as the practical error bar on the headline figure. It answers the question people actually have after seeing a single number: how wrong could this be if the main input is off by ten or twenty percent?
| Portfolio return setting | Treynor ratio |
|---|---|
| 80 % of the example value | 5.64 % per unit of beta |
| 90 % of the example value | 6.91 % per unit of beta |
| example inputs | 8.18 % per unit of beta |
| 110 % of the example value | 9.45 % per unit of beta |
| 120 % of the example value | 10.73 % per unit of beta |
That spread — 5.64 % per unit of beta at the low end, 10.73 % per unit of beta at the high — is what a careful read of Treynor Ratio looks like: a band you can state out loud, with the reason for each edge. Reproduce it in the form above by editing Portfolio return alone; the substitution steps will follow your figures exactly.
Sensitivity: which inputs change Treynor Ratio the most
Generic advice says “it depends on your inputs”; this section says exactly how much. Each field was perturbed by ±10 % in isolation and the treynor ratio recomputed, so the ranking below is measured rather than asserted. For Treynor Ratio the ranking is measured rather than guessed, and it belongs to these defaults: shift the starting point and the order can shift with it.
- Nudge Portfolio return by ±10 % and Treynor Ratio lands between 6.91 % per unit of beta and 9.45 % per unit of beta (sensitivity ≈15.6 %)
- Nudge Portfolio beta by ±10 % and Treynor Ratio lands between 7.44 % per unit of beta and 9.09 % per unit of beta (sensitivity ≈11.1 %)
- Risk-free rate +10 % → Treynor Ratio = 7.73 % per unit of beta · −10 % → 8.64 % per unit of beta (the treynor ratio shifts ≈5.6 %)
Portfolio return is the dominant lever here: ten percent either way moves the result by about 15.6 %, from 6.91 % per unit of beta to 9.45 % per unit of beta. That is where a careless figure does the most damage, so check it against a source, and treat Portfolio beta as the second priority (≈11.1 % per ten percent). The remaining fields can sit at safe defaults without materially changing the answer — knowing which is which is what separates a careful calculation from an anxious one.
Reading the result: bands, zones and thresholds
The value above only becomes useful the moment you know what it is being measured against. The verdict attached to the default calculation — “Reward per unit of market risk” — is one band on a ladder your own figure may sit somewhere else on. How much of that band is luck? On Portfolio return alone ten percent either way covers 6.91 % per unit of beta to 9.45 % per unit of beta. The practical reading rules: ask what would have to change to move you one band. If the answer is “a small, plausible input difference”, the band itself is not the finding — the uncertainty is.
In Investing & Markets, Treynor Ratio is one instrument in an orchestra: on its own it is a number, next to Excess return and Return if beta were 1.0 it becomes a diagnosis. The tools linked above exist so the headline never has to carry that weight alone.
Common mistakes with Treynor Ratio (and the fix)
Useless for concentrated portfolios — beta ignores the very risk the holder is exposed to. Also, if beta is estimated over a calm window the ratio flatters the strategy; re-estimate across cycles. This calculator gives an estimate based on standard formulas; it is not professional financial, medical, legal or engineering advice. Verify anything you plan to act on with a qualified professional and your own records.
Comparing a Treynor Ratio computed here with a figure from another source that uses different conventions. Same name, different denominator — the disagreement is usually in the definitions, not the data.
One mistake is specific to this engine: assuming every input matters equally. The computation above shows Portfolio return dominating — a careful figure there beats false precision everywhere else.
A final trap is presentation: reporting Treynor Ratio to more decimal places than the inputs support. The tool prints what the arithmetic gives; you should quote only what your least precise field justifies.
Six things to confirm before acting on Treynor Ratio
- Compare the result with one independent method or published benchmark.
- Note the date and the inputs beside the number so the figure can be audited later.
- Put Portfolio return under a magnifier; the sensitivity table above is the reason why.
- Re-run the calculation with a ±10 % stress on the two most sensitive inputs.
- State, in one sentence, which convention each rate, unit or period in the form is using.
- Confirm the answer against one independent method or published benchmark for Treynor Ratio.
A routine for decision-grade Treynor Ratio
Using a calculator well sounds trivial, but the difference between a decision-grade figure and a throwaway one lives entirely in the routine. The routine for Treynor Ratio takes a minute to learn and applies to every input above.
Step 1 — gather before you type. Treynor Ratio depends on portfolio return (%), risk-free rate (%), portfolio beta. Collect them from a source document — a statement, a report, an invoice, a log — rather than from memory, because recalled inputs are the single largest cause of wrong results. If the verdict changes with a ten-percent nudge, report the nudge alongside the number.
Step 2 — baseline before exploration. Get one defensible Treynor ratio on screen before you start nudging numbers. Without a baseline, every variation looks interesting and none of them means anything. Re-running a number costs seconds; retracting a decision costs considerably more.
Step 3 — measure what deserves measuring. The ranked levers above tell you where a careful figure pays off. Everything else can stay approximate, which is a licence to stop hunting for data you do not need. Estimates improve most when the worst case is written down in ink.
Step 4 — run the scenario trio. Expected, pessimistic, optimistic. The gap between pessimistic and expected is the number to plan against; the optimistic result is useful only as a ceiling. If a result feels obviously right, that is the moment to check the inputs hardest.
Step 5 — save the story with the figure. A number without its inputs and its date is unusable within a quarter. Record 8.18 % per unit of beta, the assumptions behind it, and today’s date; your future self will be auditing a stranger’s arithmetic. Write the assumptions in the same file as the result, and future arguments take minutes instead of meetings.
Who actually uses Treynor Ratio — and when
Investing & Markets arguments end at arithmetic or they do not end. Treynor Ratio is the arithmetic: 8.18 % per unit of beta on the example inputs, reproducible by anyone who types the same numbers. Rounding early is the quietest way to introduce a permanent error.
The companion outputs — Excess return and Return if beta were 1.0 — exist for the second stage of that screen: the headline sizes the prize, while the companions describe the trade-off you are accepting to get it. Write the figure down before moving on; memory flatters whichever number you saw last.
Re-running this page costs nothing and catches the slow drifts that never announce themselves. In Investing & Markets the expensive mistakes are rarely sudden; they are small changes in Portfolio return (%) that nobody recalculated for a year. If the answer changes your behaviour, it deserves a second run with different assumptions.
Quick answers: what searchers ask about Treynor Ratio
What affects Treynor Ratio the most?
Measured on this engine, Portfolio return is the dominant lever: moving it ±10 % shifts the treynor ratio across 6.91 % per unit of beta to 9.45 % per unit of beta — about 15.6 % of the headline, with Portfolio beta next at ≈11.1 %. The ranked list in the sensitivity section is computed live, not asserted from a template.
Which matters more: portfolio beta or portfolio return?
Portfolio return, by a factor of about 1.4. Concretely: ten percent on Portfolio return is worth ≈15.6 % of Treynor Ratio, the same nudge on Portfolio beta only ≈11.1 %. That ranking is re-computed for each page from that page’s own defaults.
What is a typical Treynor Ratio?
On the worked example above Treynor Ratio comes out at 8.18 % per unit of beta. Treat that as one point on a distribution rather than a norm: the bands, the companion outputs and the sensitivity ranking tell you how wide the plausible range really is.
How do I calculate Treynor Ratio by hand?
Three steps: write the formula (Treynor = (Rp − Rf) ÷ βp), insert your values, and simplify. The worked example section shows exactly that chain for the default inputs; replicating it once on paper teaches you more about Treynor Ratio than any number of calculator runs.
What happens to Treynor Ratio if portfolio return changes by 10 %?
The engine was re-run with that field moved by ten percent while everything else stayed fixed: the treynor ratio goes across 6.91 % per unit of beta to 9.45 % per unit of beta, a swing of roughly 15.6 % around the 8.18 % per unit of beta baseline. That ratio is the practical definition of how much this input matters.
Is the Treynor Ratio result of 8.18 % per unit of beta good or bad?
The tool answers “what”, not “whether”: 8.18 % per unit of beta carries the verdict “Reward per unit of market risk” for the default case, which is a starting interpretation rather than a verdict on your situation. Re-run with your own figures and compare the bands.
Can Treynor Ratio be negative or empty?
Yes, and that is informative rather than broken: a negative Treynor Ratio usually means the inputs encode an outflow or a shortfall, and the verdict band above labels exactly that situation instead of hiding it.
Can I predict future returns with Treynor Ratio?
No tool predicts; Treynor Ratio computes implications. Use it to ask "if these inputs hold, what follows" — then stress the assumptions.
Treynor vs Sharpe — which is right for me?
Sharpe for total portfolios you actually hold; Treynor for diversified sleeves judged against a market index.
Can beta be negative and what happens then?
A negative beta (some hedged funds) makes a positive excess return produce a negative Treynor — the ratio stops being interpretable; fall back to Sharpe.
Is my data private on this page?
Yes — computation happens locally in your browser, with no account, no tracking of your inputs and nothing sent to a server. The printed formula is the whole story of what happens to your figures.
What the labels on this page mean
- Excess return
- 9.00 % on the example inputs — a companion figure printed beside the headline of Treynor Ratio so that no result is read in isolation.
- Return if beta were 1.0
- 14.00 % for the Treynor Ratio worked case; it sits next to the main result because it carries context the headline leaves out.
- Excess return per unit of beta
- 8.18 % for the Treynor Ratio worked case; it sits next to the main result because it carries context the headline leaves out.
- Treynor ratio
- The primary output of this tool: 8.18 % per unit of beta for the default inputs, computed exactly from Treynor = (Rp − Rf) ÷ βp.
- Worked example
- Every substitution in order, from the example inputs to 8.18 % per unit of beta — the audit trail for the headline figure.
- Verdict band
- The interpretation attached to a result (“Reward per unit of market risk” on these inputs), which turns a bare number into a position on a scale.
- Sensitivity (±10 %)
- How far the Treynor Ratio moves when a single input is nudged ten percent either way; the ranked list on this page is computed live from this engine.
The provenance of this Treynor Ratio calculation
The model is published arithmetic implemented exactly as written: Treynor = (Rp − Rf) ÷ βp. Source of record: Treynor, J. L. (1965) "How to rate investment portfolios", Harvard Business Review. Specialist software layers extra coefficients on top of the same algebra; none are hidden here, and that transparency is what makes a disagreement traceable to a specific input instead of a black box.
Nothing here replaces a qualified professional, and nothing here is approximate either — the arithmetic is exact, and the honesty is in the inputs you supply. The promise to the reader is narrow and testable: same inputs, same output, no silent rounding, and no figure presented without the formula that produced it.
After the number: what to do with it
Save the number together with its inputs and today’s date; a Treynor Ratio figure without context is unusable the moment an input changes.
This page was written for people who need one trustworthy number before their next decision, and the promise is that nothing above required trust. Bookmark the tool, re-run it whenever an input moves by more than a few percent, and keep the date with the number.