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Treynor Ratio Calculator

Find a portfolio's excess return per unit of systematic risk: T = (Rp − Rf) ÷ β, from its return, the risk-free rate, and its beta.

Treynor ratio
5.833
Excess return over the risk-free rate
7%

How it works

The Treynor ratio, developed by Jack Treynor, is T = (Rp − Rf) ÷ β: the excess return a portfolio earned above the risk-free rate, divided by its beta rather than by its total volatility. It's the direct sibling of this site's Sharpe ratio calculator — same excess-return numerator — but where Sharpe divides by standard deviation (all of a portfolio's volatility, diversifiable or not), Treynor divides by beta (only the systematic, market-wide risk that diversification can't remove). That makes it the more relevant measure for a well-diversified portfolio, where idiosyncratic risk has already mostly been diversified away.

Beta can be negative for an asset that tends to move opposite the market, which flips the sign of the ratio even when excess return is positive — that's the formula correctly reflecting that a negative-beta hedge is being judged against a baseline where more systematic risk should, in theory, come with more reward, not less. A beta of exactly zero is rejected here rather than producing an answer, since dividing by zero systematic risk makes the ratio undefined, not infinite in any meaningful sense.

FAQ

How is this different from the Sharpe ratio?

Both divide excess return (portfolio return minus the risk-free rate) by a measure of risk, but they use different risk measures: Sharpe uses the portfolio's total standard deviation, while Treynor uses only its beta (systematic risk relative to the market). For a well-diversified portfolio where unsystematic risk is already minimized, Treynor is generally considered the more informative of the two; for a concentrated or undiversified portfolio, Sharpe captures risk Treynor would ignore.

What counts as a "good" Treynor ratio?

There's no single universal threshold — unlike Sharpe ratio, which has loosely conventional bands, Treynor ratio is mainly used to rank or compare portfolios (or a portfolio against a benchmark) against each other rather than against a fixed scale, since its magnitude depends heavily on the time period and asset class being measured. A positive value means the portfolio beat the risk-free rate per unit of systematic risk taken; the comparison that matters is usually against another portfolio's Treynor ratio for the same period.

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