How is Treynor different from Sharpe?

Treynor uses beta (market risk) in the denominator; Sharpe uses standard deviation (total risk).

What is a good Treynor ratio?

One higher than the market's, which equals the market risk premium Rm − Rf.

Can the Treynor ratio be misleading?

Yes, when beta is close to zero or negative, or when the portfolio is not well diversified.

Treynor Ratio Formula and Calculator

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Treynor Ratio Calculator

The Treynor ratio, also called the reward-to-volatility ratio, measures a portfolio’s excess return over the risk-free rate per unit of systematic risk, as measured by beta. It is built on the same idea as the CAPM: in a well-diversified portfolio, only market risk should be rewarded, so performance should be judged against beta rather than total volatility.

Formula

Treynor ratio = R_p − R_fβ_p

Where

R_p: portfolio return
R_f: risk-free rate
β_p: portfolio beta (systematic risk)

Calculator

Portfolio return (Rp) (%)

Risk-free rate (Rf) (%)

Portfolio beta (βp)

Result and step-by-step solution

Treynor ratio

6.67%

Excess return per unit of market (beta) risk. As a decimal: 0.0667.

Excess return
12% − 4% = 8%
Divide by beta
8%1.2 = 6.6667%

How to use the formula

That makes Treynor the better choice for comparing portfolios that are each part of a larger, diversified holding, for example funds within a pension plan. For a single fund that represents most of an investor’s wealth, total risk matters and the Sharpe ratio is more appropriate.

A portfolio that returned 12% with a beta of 1.2 while the risk-free rate was 4% has a Treynor ratio of 6.67%: it earned 6.67 percentage points of excess return per unit of beta. Compare that with the market’s own Treynor ratio, which is simply the market risk premium because the market’s beta is 1. If the portfolio’s ratio is higher, it beat the market on a risk-adjusted basis, which is the same conclusion as a positive Jensen’s alpha.

Frequently asked questions

What is the Treynor ratio formula?: Treynor ratio = (R_p − R_f) ÷ β_p.
How is Treynor different from Sharpe?: Treynor uses beta (market risk) in the denominator; Sharpe uses standard deviation (total risk).
What is a good Treynor ratio?: One higher than the market’s, which equals the market risk premium R_m − R_f.
Can the Treynor ratio be misleading?: Yes, when beta is close to zero or negative, or when the portfolio is not well diversified.

Last reviewed: September 26, 2026. Calculations run in your browser and were checked against numpy-financial, SciPy and published spreadsheet examples.