Treynor Ratio Calculator

Measure excess return per unit of market beta rather than per unit of total volatility.

The Treynor ratio takes what a portfolio earned above the risk-free rate and divides it by beta, so this Treynor ratio calculator reports a beta-adjusted return: percentage points of excess return per unit of market exposure. It is the Sharpe ratio with one substitution made in the denominator, and that substitution carries an argument with it rather than merely a different number.

Formula: treynor = (portfolio return - risk-free rate) / beta

Your figures

Portfolio return

What the portfolio returned over the period you are measuring.

Risk-free rate

Over the same period as the returns beside it, from whatever you treat as risk-free — a deposit rate, a short bill yield, or zero to measure the raw return. Annual returns need an annual rate.

Beta

Beta against whatever benchmark the market exposure is measured to, from the beta calculator or your own estimate. It is the denominator here, so a beta near zero is refused rather than answered.

Results

Treynor ratio

6.15

percentage points of excess return per unit of beta

Excess return over the risk-free ratePortfolio return less the rate entered. This is the numerator, and it is the same numerator the Sharpe ratio uses.: +8.000%
Beta usedThe denominator: market exposure alone, where the Sharpe ratio would put total volatility. That substitution is the whole of the difference between the two.: 1.300

What this means

The portfolio earned +8.000% over the risk-free rate, and it carried 1.300 of the benchmark's risk to do it, so each unit of that exposure returned 6.154 percentage points. Swapping the Sharpe ratio's total volatility for beta alone is an argument as much as a formula: volatility that can be diversified away is, on this view, not something anyone should expect to be paid for, and only the part that moves with the market is. For one position inside a diversified account that is the fairer denominator. For an account whose entire value sits in three positions it is not, because the wobble Treynor discards is very real to whoever owns it. The figure is in percentage points per unit of beta, which only compares across portfolios measured over the same period against the same benchmark. Two Treynor ratios from different years answer two different questions.

Comparable only against other Treynor ratios over the same period and the same benchmark. The units are percentage points of excess return per unit of beta, and both halves of that depend on which record and which benchmark produced them.
A beta within 0.01 of zero is refused rather than divided by. A market-neutral book has no market exposure to earn a premium on, so the question does not apply to it — the Sharpe ratio does.
Beta is an input, so everything on this page inherits its accuracy. A beta estimated from twelve monthly returns carries real uncertainty, and quoting a result to two decimals from it is false precision — which is why the beta calculator reports R² beside the slope.
Every figure entered has to cover the same period. An annual return beside a monthly risk-free rate produces a number, and that number means nothing.
The ratio assumes the rest of the portfolio is diversified enough that only market exposure is worth pricing. Where that is not true, the risk being ignored is the concentrated part, which is usually the part that matters most.
Nothing here is fetched. The returns, the benchmark, the rate and the beta are all as entered, so the same arithmetic works on a backtest, a factsheet and a live account. The risk-free rate a field opens with is a round illustration, not a current market rate.
This describes a record that has already happened. It summarises the figures entered and says nothing about the ones that follow them, and no particular level of it carries a meaning beyond the arithmetic that produced it.

The link reopens this calculator with the same numbers. Nothing you enter is sent to a server.

Continue with these figures

About the Treynor Ratio calculation

The argument is that volatility a holding brings which can be diversified away is not something anyone should expect to be paid for. Only the part that moves with the market survives being combined with everything else, so only that part deserves to sit under the division. Sharpe disagrees by construction: it puts total volatility there and prices every wobble the account experienced, diversifiable or not.

Three figures produce the ratio here — the portfolio's return, the risk-free rate over the same period, and the beta the market exposure is measured at. The beta is an input rather than an assumption, because it depends entirely on which benchmark you are measuring against, and this page does not choose one for you. Factsheets often call the result the Treynor measure, and Treynor's own name for it was the reward-to-volatility ratio; the arithmetic is the same under all three labels.

Treynor Ratio formula

excess return = portfolio return − risk-free rate

treynor = excess return ÷ beta

for contrast, the same numerator over a different denominator:
sharpe  = excess return ÷ standard deviation of the returns

portfolio return: What the account returned over the period measured, as a percentage, on whatever basis you are using.
risk-free rate: The rate over that same period from whatever you treat as carrying no market exposure. Enter zero to divide the raw return by beta instead.
excess return: The numerator: return beyond the rate available without taking market risk. It is identical to the Sharpe ratio's numerator.
beta: The denominator: sensitivity to the benchmark, measured over the same record. Systematic exposure alone, with everything else discarded.

The Treynor ratio formula is short, and all of its content sits in the denominator: putting beta underneath rather than total volatility is a statement about whose risk is being priced. For one position sitting inside a well-diversified account, the position's own idiosyncratic movement will largely be cancelled by everything else held, and what remains is the part that moves with the market — so beta is the fairer denominator and Sharpe over-penalises the holding for a risk the portfolio never actually bore.

The reverse case is just as real. For an account whose entire value sits in three positions, the variation the benchmark does not explain is not theoretical at all; it is most of what the owner will experience. Treynor discards exactly that risk by construction, so on a concentrated book it flatters, and the figure it discards is the one that matters most to whoever owns it.

The units are percentage points of excess return per unit of beta, which is not a percentage and has no natural scale. That makes the ratio comparable only across portfolios measured over the same period and against the same benchmark, and useless as a standalone score. Two Treynor ratios from different years, or from the same year against different indices, answer two different questions and cannot be ranked against each other.

The denominator needs care at both ends. Near zero the ratio stops describing anything: at a beta of 0.005 a two-point excess return scores 400, and a revision to beta far smaller than its own standard error moves that to 200 or 800, so anything inside 0.01 either side of zero is refused rather than answered with a large number that will be misread as a large result. Below zero the arithmetic is sound but the ranking inverts, because a negative beta is expected to move against the market and the premium it should be paid is negative too.

Treynor Ratio: a worked example

A portfolio that returned 12% over the year at a beta of 1.3, with a 4% risk-free rate over the same year, set beside a second book that made the same 12% at a beta of 0.8.

Excess return12 − 4 = 8.00%
Beta used1.3
Treynor ratio8.00 ÷ 1.3 = 6.15
Second book, same excess return8.00 ÷ 0.8 = 10.00
Difference in market exposure1.3 ÷ 0.8 = 1.63 times as much beta for the same 8 points

6.15 percentage points of excess return per unit of beta. The two books returned exactly the same 12% and are separated only by what they carried to get it: the second earned 10.00 per unit, because it produced the same eight points of excess return on roughly three fifths of the market exposure. Whether that ordering survives depends on the denominator you accept — if the lower-beta book got there through concentrated positions the benchmark does not explain, the Sharpe ratio would rank them the other way round.

How to use the Treynor Ratio calculator

Enter the portfolio return for the period you are measuring, then the risk-free rate covering exactly that same period rather than an annual headline figure.
Take the beta from the beta calculator or your own estimate, measured against the benchmark you consider the relevant market for this account.
Compare the result only with other Treynor ratios computed over the same period against the same benchmark. The figure has no meaning against a fixed scale.
Calculate the Sharpe ratio on the same record as well. Where the two rank a set of portfolios differently, the difference is entirely the diversifiable risk Treynor ignores, and that gap is the finding.
If the beta is close to zero, use the Sharpe ratio instead. A market-neutral book has no market exposure to earn a premium on, so the question this ratio asks does not apply to it.

Limitations of the Treynor Ratio calculator

Every calculation makes assumptions. These are the ones that matter here.

The ratio is not a percentage and has no natural scale, so a figure of 6.15 is meaningless without knowing the period, the benchmark and the frequency the beta was measured on.
It prices systematic risk only. Every unit of concentration, leverage-driven blow-up risk or single-name exposure that the benchmark does not explain is invisible to the denominator, however large it was in the account.
The denominator is an estimate with its own standard error, and dividing by a small estimate magnifies that error. A beta of 0.2 carrying a standard error of 0.1 produces a ratio that could plausibly be half or double the figure shown.
A negative beta produces a negative ratio for a positive excess return, which sorts below a portfolio that lost money. The calculator flags this rather than taking an absolute value, because the inversion is real and hiding it would be worse.
A single period gives a single number with no measure of reliability. A ratio computed over one good year is dominated by that year, and nothing in the arithmetic distinguishes a repeatable process from a fortunate one.
Both figures must cover the same period. Subtracting an annual risk-free rate from a monthly return produces a large negative numerator and a ratio that looks like a catastrophe.
The whole measure assumes the rest of the holdings are diversified enough that only market exposure is worth pricing. Where that assumption fails, the risk being discarded is precisely the concentrated part.

Frequently asked questions about Treynor Ratio

How is the Treynor ratio different from the Sharpe ratio?

The numerator is identical — excess return over the risk-free rate — and only the denominator changes. Sharpe divides by the total standard deviation of the returns, pricing every source of variation; Treynor divides by beta, pricing only the part that moved with the benchmark. When the two rank portfolios differently, the gap is exactly the diversifiable risk Sharpe counts and Treynor does not.

What is a good Treynor ratio?

There is no level that is good in isolation, because the units depend on the period, the frequency and the benchmark that produced them. The ratio is a comparison instrument: it says something when two portfolios measured the same way over the same window are placed side by side, and nothing at all as a standalone score.

Why does the calculator refuse a beta near zero?

Because the denominator becomes smaller than the uncertainty in its own estimate. At a beta of 0.005, an excess return of two points scores 400; move that beta to 0.01 and the same record scores 200. Both figures sit far inside the standard error of any real beta estimate, so refusing is more honest than reporting a number that carries no information.

Can the Treynor ratio be negative?

In two ways, and they mean opposite things. A portfolio that failed to beat the risk-free rate has a negative numerator and a genuinely negative ratio. A portfolio with a negative beta that did beat the risk-free rate also produces a negative figure, and there the sign is an artefact of the denominator rather than a poor result, which is why the calculator flags the case separately.

Should I annualise the ratio?

The ratio inherits whatever period the inputs cover, and this page does not scale it. If you want an annual figure, annualise the return and the risk-free rate before entering them and leave beta alone — beta is a slope between two series and does not scale with time the way a return or a volatility does.

Which denominator is the right one for my account?

It depends on what the account is part of rather than on which measure is superior. If the holding sits inside a larger diversified portfolio, its idiosyncratic movement will largely be cancelled by everything else and beta is the exposure that survives. If the account is the whole of someone's capital, the risk beta leaves out is the risk they will actually live through.

Last reviewed 29 August 2026. See our methodology and editorial policy.

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