Treynor Ratio Explained: Beta, Benchmarks and Its Limits

A Treynor ratio is one division: the return earned above the risk-free rate, divided by beta. Everything that decides whether the answer means anything sits inside that beta, and beta is not a property of the account being measured. It is the slope of a regression against a benchmark somebody chose.

Change the benchmark and the number changes. Measure it over too few observations, or against an index the account barely tracks, and the denominator is closer to noise than to a figure. This page is about the denominator.

What the Treynor Ratio Measures

The numerator is the return of the portfolio minus the risk-free rate over the same window. The denominator is beta, the sensitivity of that portfolio to a benchmark. The quotient is excess return per unit of market exposure.

That last phrase is the whole difference from the Sharpe ratio, which divides by the total standard deviation of returns. Treynor keeps only the part of the variability that moves with the benchmark and discards the rest, on the assumption that the rest has already been diversified away elsewhere in the portfolio.

The risk-free rate is a real rate, not a placeholder. On 12 August 2026 the three-month Treasury bill yielded 3.87 per cent and the five-year note 4.38 per cent, so the choice of horizon alone moves the numerator by half a percentage point before beta is touched.

Beta Is the Denominator and It Needs a Benchmark

Beta is not a number an account owns. It is the slope coefficient of a least-squares regression of the excess returns of the portfolio on the excess returns of a benchmark, and the benchmark is an input to the calculation rather than a property of the thing being measured.

Regress the same portfolio on a broad domestic index and then on a global one, and two different betas come out. Neither is wrong. They answer different questions, and the Treynor ratio built on each answers a different question too.

So a Treynor ratio quoted on its own is a quotient with an unstated denominator. Comparing two of them computed against different indices is not a comparison at all, and nothing in the printed figure reveals that the two were measured against different things.

Any statistic measured against something chosen rather than given carries the same weakness, which is why a currency correlation figure means nothing without its window and its reference pair attached.

When the Beta Is Not Reliable Enough to Divide By

R-squared is the fraction of the variance of the portfolio that the regression explains. It is usually printed beside beta and usually ignored, and it is the figure that decides whether the beta underneath a Treynor ratio can support a division at all.

The link is arithmetic rather than a rule of thumb. For a simple regression, the standard error of the slope divided by the slope itself equals the square root of one minus R-squared, over R-squared times the quantity n minus two, where n is the number of observations. Both inputs already sit on the same report page as the beta.

At an R-squared of 0.30 the denominator lies anywhere between 0.49 and 1.51, so a Treynor ratio printed as 0.06 is somewhere between 0.04 and 0.12. That is a threefold range, and no decimal place in the printed figure discloses it.

At 0.10 the interval crosses zero. The sign of the denominator is not established, so the ratio has no established sign either, and the two decimal places it is quoted to are decoration.

Treynor and Sharpe Answer Different Questions

Both divide the same numerator. The denominators differ, and with them the question each one answers.

Sharpe divides by the standard deviation of the returns of the account, all of the variability whatever caused it. Treynor divides by beta and keeps only the part that moves with the benchmark. The two coincide when the portfolio is perfectly correlated with that benchmark, and separate as the correlation falls.

They are therefore tools for different decisions. Sharpe asks whether a holding earned its own variability. Treynor asks what a holding adds to a portfolio in which the specific risk has already been diversified away by everything else in it.

Neither reports how far the account actually fell along the way, which is the separate question maximum drawdown answers.

The Negative Beta Problem

Beta can be negative. A portfolio that tends to rise when the benchmark falls produces a negative slope, and the Treynor ratio divides by it.

Two cases then invert. A portfolio that beat the risk-free rate while running against the benchmark gives a positive numerator over a negative denominator, so the ratio prints negative, the same sign a losing portfolio prints. One that fell short of the risk-free rate while running against the benchmark gives a negative over a negative, so the ratio prints positive.

Ranking a set of portfolios by the figure therefore orders any such pair backwards. Reading the number as a score requires knowing the sign of every beta in the set first, which is not information the ratio itself carries.

Beta near zero is the same failure at its limit. The quotient runs away towards infinity for an arbitrarily small change in a slope that the previous section has already shown to be an interval rather than a point.

How Many Observations the Number Needs

The observation count sits in the same arithmetic as R-squared, and it moves the answer as hard. Cut the window from thirty-six monthly observations to twelve and the relative standard error of the beta nearly doubles: at an R-squared of 0.70 it moves from 11.2 per cent to 20.7 per cent.

That is the denominator only. How long a return record has to run before the excess return in the numerator can be separated from luck is a different question with its own arithmetic, and it is worked through on the Sharpe ratio page rather than repeated here.

The two conditions compound rather than trade off. A short window together with a low R-squared can leave a beta whose interval spans zero, and a ratio built on that denominator should not be quoted at all.

Whether It Applies to a Trading Account at All

The ratio was built for portfolios measured against an index. A retail forex or CFD account has no such index. No published benchmark exists that a discretionary currency account is expected to track, so there is nothing to regress against and no beta to divide by.

Choosing an index anyway does not repair it. Regressed against an equity benchmark, a currency account usually returns a low R-squared, and the table above already says what that produces: a wide interval presented as a number.

Platform reporting matches that. The MetaTrader 5 strategy tester report lists a Sharpe ratio and carries no Treynor field. Its only correlation statistic, LR Correlation, measures the balance curve against its own linear regression line, which describes the smoothness of that curve rather than any relationship to a market.

The tester also sets the risk-free rate to zero, so even the Sharpe numerator it prints is not the one the definition asks for. What a single account can measure without any benchmark is the distribution of its own outcomes, which is what expectancy per trade reports.

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