Treynor Ratio Calculator
Use this Treynor Ratio Calculator to divide the entered strategy’s per-period excess return by its historical beta to one selected benchmark. The page exposes the aligned observations, sample covariance, benchmark variance and every cross-product contribution, so the result can be checked without treating it as a performance grade or forecast.
Enter aligned strategy and benchmark returns
Use signed equal-frequency percentage returns in matching oldest-to-newest order, plus one risk-free return in the same per-period units.
Use the same frequency and percentage-point units as both return series.
Enter percentage numbers without percent signs. Separate with spaces, commas, semicolons or new lines. Maximum 500.
Enter exactly one benchmark return for every strategy return, in the same order and per-period percentage units.
Entered reward-to-beta arithmetic
Entered Benchmark-Adjusted Performance 1.0.0.
| Index | Strategy | Benchmark | Strategy deviation | Benchmark deviation | Cross-product |
|---|
How Treynor Ratio is calculated
Portfolio excess = Strategy mean − Risk-free return
Treynor Ratio = Portfolio excess ÷ Beta
The strategy and benchmark means are calculated from aligned observations. Version 1.0.0 uses N-minus-one sample covariance and benchmark variance; their shared denominator cancels in beta but remains visible in the audit.
The result is a signed per-period percentage-point return per unit of historical beta. A zero beta is rejected. A negative beta is shown arithmetically without being ranked or labelled good or bad.
Worked example from the audited fixture
The audited 30-period example has a strategy mean of 0.110000%, benchmark mean of 0.043333%, risk-free return of 0.020000% and historical beta of 1.639845.
- Portfolio excess return = 0.110000% − 0.020000% = 0.090000 percentage points.
- Treynor Ratio = 0.090000 ÷ 1.639845 = 0.054883 percentage points of entered excess return per unit of historical beta.
Reproduce it: select “Load audited example” above. The calculator loads the same 30 aligned observations used by the independent fixture.
How to interpret the result
- The signed output answers one narrow question: how much entered excess return corresponds to one unit of beta against the selected benchmark over this sample.
- A larger value is not automatically better across different benchmarks, frequencies or windows. Those choices can materially change both excess return and beta.
- The ratio contains no confidence interval or significance test. It is historical arithmetic, not evidence that the relationship will persist.
Assumptions and limits
- Enter 3 to 500 strategy returns and the same number of aligned benchmark returns.
- Returns and the risk-free input must share one frequency and percentage-point convention.
- A constant benchmark or zero beta makes the selected ratio undefined and is rejected.
- Beta depends on the entered window and benchmark and does not measure idiosyncratic or total strategy risk.
- No annualized ratio, diversification claim, skill label, forecast, signal or recommendation is produced.
Treynor vs Jensen’s alpha vs M² vs Information Ratio
These measures are not interchangeable. Choose the one whose denominator and question match the evidence you intend to inspect, then keep the benchmark, frequency, window and return treatment consistent.
| Measure | Reference or denominator | What the output expresses | Main boundary |
|---|---|---|---|
| Treynor Ratio | Historical beta | Excess return per unit of benchmark beta | Ignores total and idiosyncratic volatility. |
| Jensen’s alpha | Single-factor CAPM expectation | Per-period residual return | Sensitive to benchmark, beta and factor-model choice. |
| M² performance | Benchmark sample volatility | Volatility-matched return and active difference | Assumes hypothetical costless scaling. |
| Information Ratio | Tracking error | Active return per unit of active-return variability | Answers a different benchmark-relative consistency question. |
Frequently asked questions
- Enter 3 to 500 aligned strategy and benchmark percentage returns plus one risk-free return in the same per-period units.
- N-minus-one sample covariance between strategy and benchmark returns is divided by N-minus-one sample benchmark variance.
- It is the entered strategy mean return minus the entered per-period risk-free return.
- Portfolio excess return is divided by historical beta, producing percentage-point return per unit of beta.
- The ratio is undefined, so version 1.0.0 rejects the calculation instead of displaying infinity.
- The signed arithmetic result is shown without being ranked or labelled good or bad; interpretation requires care.
- Treynor uses historical benchmark beta as its denominator; Sharpe uses total sample standard deviation.
- No. It describes the entered sample and selected benchmark only and creates no skill, persistence, forecast, signal or recommendation.
Sources and methodology
- CFA Institute — Treynor and Jensen — Official reward-to-beta definition, covariance-over-variance beta and interpretation cautions.
- NIST/SEMATECH — Standard Deviation — N-minus-one sample-moment convention used by version 1.0.0.
Compare reward-to-risk conventions
Compare the trading records behind your sample
Keep one broker account, benchmark, return convention, fee treatment and sampling rule across the entered observations before comparing arithmetic.
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