Jensen Alpha Calculator
Raw return tells you nothing about how much risk was taken to earn it. Jensen's alpha fixes this by comparing a portfolio's actual return with the return the Capital Asset Pricing Model would predict for its beta. The gap, the alpha, is the risk-adjusted excess return often read as a measure of skill. This calculator takes the portfolio return, the risk-free rate, beta, and the market return, computes the CAPM expected return, and reports the alpha and the benchmark return. All rates are your own period figures.
Jensen's alpha formula
CAPM expected return = Rf + beta * (Rm - Rf)
Jensen's alpha = portfolio return - CAPM expected return
Rf is the risk-free rate, Rm is the market return, and beta is the portfolio's systematic risk. Alpha is positive when the portfolio outperforms its CAPM benchmark and negative when it lags.
Interpreting alpha
- Jensen's alpha was introduced by Michael Jensen in a 1968 study of mutual funds.
- Positive alpha suggests return above what the risk level justified.
- A high-beta fund can beat the market in raw terms yet post negative alpha.
- Alpha relies on the CAPM, so it inherits the model's assumptions and limits.
- Measure all inputs over the same period for a valid comparison.
Jensen's alpha: frequently asked questions
What is Jensen's alpha?
Jensen's alpha measures the excess return a portfolio earned over and above what the Capital Asset Pricing Model predicts for its level of systematic risk. A positive alpha means the portfolio beat its risk-adjusted benchmark; a negative alpha means it lagged. It is named after economist Michael Jensen, who introduced it in 1968.
What is the Jensen's alpha formula?
Alpha = portfolio return - [risk-free rate + beta * (market return - risk-free rate)]. The bracketed term is the CAPM expected return for the portfolio's beta. Alpha is the difference between the realised return and that CAPM benchmark.
How is alpha different from simply beating the market?
Beating the market in raw return can come from taking more risk. Alpha adjusts for systematic risk through beta, so it isolates skill or value added beyond what the risk level alone would justify. A high-beta portfolio can beat the market yet still have negative alpha.
What does a positive alpha indicate?
A positive alpha indicates the portfolio delivered more return than its systematic risk warranted under CAPM, often interpreted as manager skill or favourable security selection. A zero alpha means performance was exactly in line with the risk taken, and a negative alpha means underperformance on a risk-adjusted basis.
What inputs do I need?
Enter the portfolio's realised return, the risk-free rate, the portfolio's beta, and the market or benchmark return, all over the same period. Returns and the risk-free rate are percentages. The calculator computes the CAPM expected return and subtracts it from the actual return to give alpha.
Official sources
- U.S. Securities and Exchange Commission: Total return.
- U.S. Securities and Exchange Commission: Stocks and risk.
Reviewed by the CalculatorHub team, edited by James Graham, 16 June 2026. See our methodology.