Formula, in Risk & Portfolio Construction

Treynor Ratio Formula

The Treynor ratio divides a portfolio's excess return over the risk-free rate by its beta. It measures reward per unit of systematic (market) risk rather than total risk, which makes it the right comparison metric for portfolios that are part of a larger, well-diversified holding where only undiversifiable risk matters.

3 variables. Published May 26, 2026. By AI Fin Hub Research.

Formula

Treynor = (R_p - R_f) / beta_p

Variables

R_p

Portfolio return

The portfolio's realized return over the measurement period, typically stated on an annualized basis.

R_f

Risk-free rate

Return on a near-riskless asset, such as a Treasury bill, over the same horizon. Subtracting it gives the excess return that beta is asked to justify.

beta_p

Portfolio beta

Sensitivity of portfolio returns to the market, the slope of portfolio returns regressed on market returns. Using beta instead of standard deviation is the defining feature: only systematic risk enters the denominator.

Step by step

1

Determine the portfolio's annualized return and the risk-free rate over the same period.

Portfolio returns 12% for the year while the risk-free rate is 3%.
2

Compute the excess return as portfolio return minus the risk-free rate.

12% - 3% = 9% excess return.
3

Estimate the portfolio beta by regressing portfolio excess returns on market excess returns.

The regression slope gives a beta of 1.2.
4

Divide the excess return by beta.

9% / 1.2 = 7.5%.

Worked example

Comparing two funds with different market exposure

Fund A return / beta

12% / 1.2

Fund B return / beta

9% / 0.7

Risk-free rate

Fund A: (0.12 - 0.03) / 1.2 = 0.09 / 1.2 = 0.075. Fund B: (0.09 - 0.03) / 0.7 = 0.06 / 0.7 = 0.0857.

Treynor of 0.075 for Fund A versus 0.0857 for Fund B. Although Fund A posted the higher raw return, Fund B delivered more excess return per unit of systematic risk, so a diversified investor adding either to a broad portfolio should prefer Fund B on this measure.

Common variations

Sharpe ratio: uses total standard deviation in the denominator instead of beta, so it is the right measure for a standalone, undiversified portfolio.

Treynor-Black appraisal ratio: a related construct that scores active positions by alpha over residual risk for optimal active weighting.

Information ratio: replaces the risk-free rate with a benchmark and beta with tracking error.

Run the numbers next

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Sources

How to Rate Management of Investment Funds , Jack L. Treynor, Harvard Business Review (1965)
Capital Asset Prices: A Theory of Market Equilibrium under Conditions of Risk , William F. Sharpe, Journal of Finance (1964)

Keep the topic connected

Formula Beta Formula
The beta formula: covariance of asset and market returns over market variance. The CAPM regression slope measuring systematic risk, with an example.
Formula CAPM Formula
The CAPM formula: expected return equals the risk-free rate plus beta times the market risk premium. The basis for pricing systematic risk.
Formula Jensen's Alpha Formula
Jensen's alpha formula: realized return minus the CAPM-expected return given beta. The excess return a manager earns beyond market risk.
Formula Sharpe Ratio Formula
The Sharpe ratio formula: excess return over the risk-free rate divided by return volatility, then annualized. Every variable defined, with a worked example.