Treynor Ratio Calculator

Measure risk-adjusted return per unit of market risk. Enter the portfolio's annualized return, a risk-free rate, and its beta to compute the Treynor Ratio, the excess return, and the equivalent Jensen's alpha.

Quick Facts

Formula
Treynor Ratio = (Rp - Rf) / Beta
Rp is portfolio return, Rf is the risk-free rate, and Beta is the portfolio's sensitivity to market moves.
Developed by
Jack Treynor, one of the originators of CAPM
It measures reward per unit of systematic risk, not total risk.

Your Results

Calculated
Treynor Ratio
-
Excess return per unit of beta
Excess return
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Portfolio return minus risk-free rate
Jensen's alpha
-
Return above what CAPM predicts
CAPM expected return
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Rf + Beta × (market return - Rf)

Ready

Enter portfolio return, risk-free rate, beta, and benchmark return, then press Calculate.

How the Treynor Ratio Calculator works

The Treynor Ratio, developed by Jack Treynor, measures how much excess return a portfolio earned for each unit of market (systematic) risk it took on, where risk is measured by beta rather than total volatility. It answers a narrower question than the Sharpe Ratio: not "how much return per unit of total risk," but "how much return per unit of exposure to the overall market."

The formula

For a portfolio return Rp, a risk-free rate Rf, and a portfolio beta β, the Treynor Ratio is:

Treynor Ratio = (Rp − Rf) / β

The numerator, Rp − Rf, is the excess return: the return earned above a risk-free benchmark such as a short-term Treasury bill. Dividing by beta expresses that excess return per unit of market risk instead of as a raw percentage, which makes portfolios with different market exposure comparable on the same footing.

Worked example

Take a portfolio that returned 12% over the period, a risk-free rate of 4%, and a portfolio beta of 1.2. The excess return is 12% − 4% = 8%, and the Treynor Ratio is 8% / 1.2 ≈ 6.67. A second portfolio with the same 8% excess return but a beta of 0.8 would score 8% / 0.8 = 10.0 — a higher Treynor Ratio, because it earned the same excess return while carrying less market risk.

Treynor Ratio versus CAPM alpha

This calculator also reports the Capital Asset Pricing Model (CAPM) expected return, Rf + β × (market return − Rf), and Jensen's alpha, the portfolio's actual return minus that CAPM expectation. Alpha is a companion figure: it shows return earned above what CAPM predicted for that level of beta, in percentage-point terms rather than as a per-unit-of-risk ratio.

What moves the ratio most

  • Beta: because beta sits in the denominator, a low or near-zero beta amplifies the ratio dramatically — even a small excess return can produce a very large or unstable Treynor Ratio when beta is close to zero.
  • Excess return: a higher portfolio return relative to the risk-free rate directly raises the ratio, holding beta constant.
  • Sign of beta: a negative beta (a portfolio that tends to move opposite the market) flips the sign of the ratio, so a negative Treynor Ratio can mean either underperformance or a negative-beta portfolio with positive excess return — always check beta's sign before interpreting the number.

Limits of the Treynor Ratio

Treynor assumes the portfolio is well-diversified enough that beta captures most of its relevant risk. For a concentrated or undiversified portfolio, unsystematic (stock-specific) risk can be substantial but invisible to this ratio — the Sharpe Ratio, which divides by standard deviation instead of beta, is usually the better tool in that case. The ratio also depends on the accuracy of the beta estimate used, which itself is sensitive to the time period and benchmark chosen. This calculator performs the arithmetic only; it is not personalized investment advice.

Frequently Asked Questions

How is the Treynor Ratio calculated?
The Treynor Ratio equals (Portfolio Return − Risk-Free Rate) divided by Portfolio Beta. The numerator is the excess return earned above a risk-free benchmark such as a Treasury bill, and beta measures the portfolio's sensitivity to overall market movements. The result shows excess return earned per unit of systematic (market) risk taken.
How is the Treynor Ratio different from the Sharpe Ratio?
The Sharpe Ratio divides excess return by standard deviation, which captures total risk (systematic plus unsystematic). The Treynor Ratio divides excess return by beta, which captures only systematic (market) risk. Treynor is most meaningful for a well-diversified portfolio where unsystematic risk has largely been diversified away; Sharpe is more appropriate for a single asset or a concentrated, undiversified portfolio.
What counts as a good Treynor Ratio?
There is no universal cutoff - the ratio is only meaningful compared against a benchmark or another portfolio's Treynor Ratio calculated the same way over the same period. A higher Treynor Ratio means more excess return was earned per unit of market risk. A negative ratio means the portfolio underperformed the risk-free rate on a beta-adjusted basis.
What happens if beta is negative or zero?
A beta near zero makes the ratio extremely sensitive to small changes in beta and can produce misleadingly large values, so the calculator requires a nonzero beta. A negative beta means the portfolio tends to move opposite the market; dividing by a negative number flips the sign of the ratio, so interpret negative-beta results with particular care.

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