The third leg of the risk-adjusted trilogy
Three classic ratios divide the same numerator — return above the risk-free rate — by three different definitions of risk. TheSharpe ratiodivides by total volatility, charging the portfolio for every wiggle. TheSortino ratiodivides by downside deviation only, forgiving the upside. The Treynor ratio, proposed by Jack Treynor in his 1965 Harvard Business Review article “How to Rate Management of Investment Funds,” divides by beta — the portfolio’s sensitivity to the market. The logic: for an investor who is already diversified, a fund’s company-specific ups and downs wash out against everything else they own. The only risk the fund truly adds is its market exposure, so that is the only risk its return should be graded on.
The Treynor ratio formula
Treynor = ( Rp − Rf ) / βp
Treynormarket = ( Rm − Rf ) / 1 = Rm − Rf
where Rp is the portfolio return,Rf the risk-free rate, andβp the portfolio’s beta versus the market. Because the market’s beta is 1 by definition, its own Treynor ratio collapses to the equity risk premium Rm − Rf — the bar any portfolio must clear to have earned its market risk. The ratio is undefined at β = 0, and a negative beta flips its sign, so hedges need separate interpretation.
Worked example
A fund returned 12.00% in a year when Treasury bills paid 4.00% and the market returned 10.00%. The fund runs hot, with a beta of 1.20. Was the extra return worth the extra market risk?
| Step | Amount |
|---|---|
| Portfolio return (Rp)the fund’s annual return over the measurement period | 12.00% |
| − Risk-free rate (Rf)the Treasury-bill yield over the same period | 4.00% |
| = Excess returnthe reward for taking any risk at all — the numerator | 8.00% |
| ÷ Portfolio beta (β)this portfolio moves about 1.2× as much as the market | 1.20 |
| The market’s own Treynor ratio(Rm − Rf) ÷ 1 = 10.00% − 4.00%, since the market’s beta is exactly 1 | 6.00 |
| = Treynor ratio of 6.67 — the portfolio beats the market6.67pp of excess return per unit of beta vs 6.00pp for the index | 6.67 |
Computed with this calculator's default settings — open the tool above and you'll see the same numbers, then swap in your own fund's figures.
Why grade on beta at all
A fund with a beta of 1.2 is, mechanically, a leveraged bet on the market: in a year the index gains 10%, it “should” gain about 12% before any skill enters the picture. Judging it on raw return therefore rewards nothing but the leverage. The Treynor ratio strips that out by asking how much excess return arrived per unit of beta — the slope of the line from the risk-free rate through the portfolio in expected-return-versus-beta space. That is the same space the capital asset pricing model lives in: theCAPM calculatorcomputes the return a given beta is supposed to deliver, and a portfolio whose Treynor ratio beats the market’s is precisely one sitting above that security market line. In practice the ratio is most at home in manager evaluation — comparing sleeves, funds, or sub-portfolios that all hang off the same diversified core against the same benchmark.
Frequently asked questions
What is the Treynor ratio?
The Treynor ratio measures how much return an investment earned above the risk-free rate for each unit of market risk it carried. It is defined as (Rp − Rf) ÷ β, where Rp is the portfolio return, Rf the risk-free rate, and β the portfolio’s beta versus the market. Jack Treynor proposed it in 1965 as a way to rate fund managers on the risk that actually matters to a diversified investor — systematic risk — rather than on total volatility. A higher ratio means more reward per unit of market exposure.
Treynor ratio vs Sharpe ratio — when does each apply?
Both divide excess return by risk; they differ in the denominator. Sharpe uses total volatility (standard deviation), so it charges the portfolio for every source of risk, including company-specific swings. Treynor uses beta, charging only for market risk. Use Sharpe when the portfolio is essentially all of an investor’s wealth, because then total volatility is what the investor feels. Use Treynor when the portfolio is one sleeve of a broadly diversified whole — there, idiosyncratic risk is diversified away by the other holdings, and market risk is the only risk the sleeve truly adds.
What beta should I use?
Use the beta of the portfolio measured against the benchmark you are comparing it to, over the same period as the returns. Fund fact sheets and data providers typically publish beta estimated by regressing the fund’s returns on the index’s returns, often using 36 or 60 months of data. Consistency matters more than precision: if the market return in the comparison is the S&P 500, the beta must be an S&P 500 beta. Mixing a beta computed against one index with returns from another quietly breaks the ratio.
What is a good Treynor ratio?
There is no universal threshold — the number is only meaningful relative to the market’s own Treynor ratio or to peers measured against the same benchmark over the same period. Because the market’s beta is exactly 1, its Treynor ratio is simply Rm − Rf; a portfolio that clears that bar earned more excess return per unit of market risk than the index it is exposed to. Unlike the Sharpe ratio, the Treynor ratio’s units (percentage points per unit of beta) depend on the period and benchmark, so cross-context comparisons of the raw number mean little.
What does a negative beta do to the Treynor ratio?
It flips the sign and breaks the ranking logic. A negative-beta asset — gold in some regimes, a short position, a tail hedge — moves against the market, so dividing a positive excess return by a negative beta produces a negative Treynor ratio even though the asset made money. That does not mean the asset is bad; it means the ratio was built for assets whose risk is positive market exposure. Judge negative-beta holdings by what they do to the risk and return of the whole portfolio, not by their standalone Treynor ratio.
Disclaimer: This calculator is foreducation and illustration only. The Treynor ratio is a backward-looking statistic built from an estimated beta and a chosen benchmark; different periods, benchmarks, or beta estimates give different answers, and past performance does not predict future results. Nothing here is investment, tax, or trading advice.