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Treynor Ratio Calculator

Measure return per unit of market risk with the Treynor ratio.

How it is calculated

The Treynor ratio measures how much return a portfolio earned above the risk-free rate for each unit of market risk: Treynor = (Rp − Rf) ÷ β. Rp is the portfolio return and Rf the risk-free return, both in percent over the same period, and β is the portfolio's beta against the market. The tool also shows the excess return, Rp − Rf, as a percentage. If you leave the risk-free rate empty it is treated as 0. A beta of exactly 0 gives no result, since the ratio would be undefined. The figure has no fixed scale; it is meant for comparing portfolios over the same period, not for judging one in isolation.

Worked example

A fund returned 12% over the year, the risk-free rate was 3%, and the fund's beta is 1.2. Excess return: 12 − 3 = 9, shown as 9.00%. Divide by beta: 9 ÷ 1.2 = 7.50. Each unit of market risk earned about 7.5 percentage points above the risk-free rate. A second fund with the same 9% excess return but a beta of 0.9 would score 10.00 and look better per unit of risk.

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Common mistakes

  • Entering returns as decimals (0.12) when the tool expects percent (12). The ratio comes out 100 times too small.
  • Leaving out the risk-free rate. The default of 0 inflates the ratio for any period when safe assets paid something.
  • Using a different period for the return and the risk-free rate, such as a monthly return with an annual risk-free rate.
  • Using standard deviation instead of beta. Dividing by total volatility gives the Sharpe ratio, a different measure.
  • Comparing ratios for negative betas or negative excess returns. The sign flips the meaning, and a higher number is not always better.

Sources

About this calculator

This calculator computes the Treynor ratio: (Rp − Rf) / β, the portfolio's return above the risk-free rate divided by its beta — a measure of systematic (market) risk rather than total volatility, unlike the Sharpe ratio which divides by standard deviation.

Portfolio managers and investment analysts use it to compare how efficiently different well-diversified portfolios convert market risk into excess return, since beta assumes unsystematic risk has already been diversified away.

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Comments (1)

  • Editorial team

    Treat the beta input with care, because it comes from a regression against a benchmark and changes with the benchmark you pick. Use the index that actually matches what the portfolio holds. When beta is very small the ratio blows up: an excess return of 9 with a beta of 0.05 gives 180, which says more about the divisor than about skill. Which benchmark and period do you use to estimate beta?

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