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Treynor Ratio Calculator

Calculate the Treynor ratio to evaluate risk-adjusted return relative to systematic risk (Beta).

Portfolio inputs

Enter annualized percentages. The Treynor ratio compares excess return to systematic risk (beta).

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Treynor ratio

7.50

Excess return 9.00% over beta 1.20

Excess return (Rp - Rf)

9.00%

Portfolio beta

1.20

How the Treynor ratio is calculated

From portfolio return, risk-free rate, and beta to risk-adjusted performance.

  1. Calculate excess return over the risk-free rate

    Rp−Rf=12.00%−3.00%=9.00%R_p - R_f = 12.00\% - 3.00\% = 9.00\%

    Subtract the 3.00% risk-free rate from the 12.00% portfolio return to get 9.00% excess return.

  2. Divide excess return by portfolio beta

    Treynor Ratio=Rp−Rfβ=9.00%1.20=7.50\text{Treynor Ratio} = \frac{R_p - R_f}{\beta} = \frac{9.00\%}{1.20} = 7.50

    Treynor ratio equals excess return divided by beta (1.20).

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What is the Treynor ratio?

The Treynor ratio measures how much excess return a portfolio earns per unit of systematic risk, represented by beta. Jack Treynor developed the measure to reward managers who deliver strong returns without taking on unnecessary market exposure.

Compare downside-focused performance with the Sortino ratio calculator. For total volatility adjustment, use the Sharpe ratio calculator. Estimate portfolio beta with the portfolio beta calculator.

Treynor ratio formula

Treynor Ratio=Rp−Rfβ\text{Treynor Ratio} = \frac{R_p - R_f}{\beta}

Where RpR_p is portfolio return, RfR_f is the risk-free rate, and β\beta measures sensitivity to the broad market. All return inputs should be annualized percentages in the same units.

Worked example

Suppose a portfolio earns 12%, the risk-free rate is 3%, and beta is 1.2. Excess return equals 12% minus 3%, or 9%. Treynor ratio equals 9% divided by 1.2, which is 7.5. A higher Treynor ratio generally indicates better return per unit of systematic risk.

Treynor vs Sharpe ratio

  • Sharpe uses total standard deviation in the denominator, penalizing all volatility.
  • Treynor uses beta, focusing only on market-related risk that cannot be diversified away.
  • Treynor is most useful when comparing diversified portfolios against the same benchmark.

Frequently asked questions

What risk-free rate should I use?
Common choices include short-term Treasury bill yields or the rate on cash equivalents. Use the same rate when comparing multiple portfolios.
Can beta be negative?
Yes, though it is rare. A negative beta means the portfolio tends to move opposite the market, which produces a negative Treynor ratio when excess return is positive.
Is a Treynor ratio of 7.5 good?
Higher is generally better, but acceptable values depend on asset class and time period. Compare against peers or a benchmark portfolio rather than a fixed threshold.
When should I use Treynor instead of Sharpe?
Use Treynor when portfolios are well diversified and systematic risk is the main concern. Use Sharpe when idiosyncratic volatility matters.
Are results stored on your servers?
No. All math runs in your browser. Nothing is sent to the server.

Resources and references

The formulas and methods in this calculator were checked against these independent sources.