What does a positive alpha mean?

The portfolio earned more than CAPM predicts for its level of market risk.

Is alpha the same as excess return?

No. Excess return is usually return minus the risk-free rate or minus a benchmark; alpha adjusts the benchmark for the portfolio's beta.

Which period should the inputs cover?

The same period for all of them, typically one year or an annualized multi-year figure.

Jensen's Alpha Formula and Calculator

Home › Finance Formulas › Jensen's Alpha Formula and Calculator

Jensen's Alpha Calculator

Jensen’s alpha measures how much a portfolio or fund returned above or below what the CAPM says it should have earned given its beta. The benchmark is R_f + β(R_m − R_f), the return you could have got from a mix of the market and risk-free assets with the same market risk. Alpha is the difference between the actual return and that benchmark.

Formula

α = R_p − [R_f + β_p × (R_m − R_f)]

Where

α: Jensen’s alpha: return above what CAPM predicts
R_p: actual portfolio return
R_f: risk-free rate
β_p: portfolio beta
R_m: market return over the same period

Calculator

Portfolio return (Rp) (%)

Risk-free rate (Rf) (%)

Portfolio beta (βp)

Market return (Rm) (%)

Result and step-by-step solution

Jensen’s alpha

2.8%

Positive alpha: the portfolio beat its CAPM benchmark of 11.2%.

CAPM expected return
4% + 1.2 × (10% − 4%) = 11.2%
Subtract from the actual return
α = 14% − 11.2% = 2.8%

How to use the formula

A positive alpha suggests the manager added value through security selection or timing; a negative alpha means investors would have done better with a passive mix of the same risk. Because it is a return, alpha is easy to explain: an alpha of 2% means 2 percentage points a year above the risk-adjusted benchmark.

In the example the portfolio returned 14% with a beta of 1.2, the market returned 10% and the risk-free rate was 4%. CAPM predicts 11.2%, so alpha is 2.8%. For a formal test, alpha is estimated as the intercept of a regression of excess portfolio returns on excess market returns, and you should check that it is statistically different from zero. For ratio-based comparisons see the Treynor and Sharpe ratios.

Frequently asked questions

What is the formula for Jensen’s alpha?: α = R_p − [R_f + β_p × (R_m − R_f)].
What does a positive alpha mean?: The portfolio earned more than CAPM predicts for its level of market risk.
Is alpha the same as excess return?: No. Excess return is usually return minus the risk-free rate or minus a benchmark; alpha adjusts the benchmark for the portfolio’s beta.
Which period should the inputs cover?: The same period for all of them, typically one year or an annualized multi-year figure.

Last reviewed: September 26, 2026. Calculations run in your browser and were checked against numpy-financial, SciPy and published spreadsheet examples.