Jensen's Alpha Calculator
Jensen's alpha answers a simple question: did this portfolio beat what the market would have paid you for taking the same amount of market risk? It does this by comparing the portfolio's actual return against the return predicted by the capital asset pricing model for its beta. A positive alpha is evidence of value added beyond passive market exposure, while a negative alpha shows the portfolio lagged its risk-adjusted benchmark. This calculator takes the portfolio return, the risk-free rate, the portfolio beta, and the market return, all for the same period, and returns Jensen's alpha along with the CAPM expected return and the market risk premium.
Jensen's alpha formula
Market risk premium = Rm - Rf
CAPM expected return = Rf + beta * (Rm - Rf)
Jensen's alpha = Rp - CAPM expected return
Rp is the portfolio return, Rf the risk-free rate, Rm the market return, and beta the portfolio's sensitivity to the market. Alpha is the gap between actual and CAPM-predicted return.
How to interpret alpha
- Positive alpha: the portfolio beat its risk-adjusted benchmark over the period.
- Zero alpha: the portfolio earned exactly what CAPM predicted for its beta.
- Negative alpha: the portfolio lagged the return its market risk should have produced.
- Use returns net of fees for a fair view of manager skill.
- Judge alpha across several periods; one period can reflect luck or a regime shift.
Jensen's alpha: frequently asked questions
What is Jensen's alpha?
Jensen's alpha measures how much a portfolio's actual return beat (or fell short of) the return predicted by the capital asset pricing model (CAPM) for its level of market risk. A positive alpha means the manager added value beyond what the beta-adjusted market exposure would justify; a negative alpha means underperformance.
How is Jensen's alpha calculated?
Alpha equals the portfolio return minus the CAPM expected return, where CAPM expected return is the risk-free rate plus beta times the market risk premium (market return minus risk-free rate). In symbols: alpha = Rp minus [Rf + beta times (Rm minus Rf)].
What is a good Jensen's alpha?
Any positive alpha indicates the portfolio outperformed its risk-adjusted benchmark over the period. Larger positive values are better, but alpha should be judged over multiple periods and net of fees, since a single period can be driven by luck rather than skill.
What inputs do I need?
You need the portfolio's realized return, the risk-free rate (often a short-term Treasury yield), the portfolio's beta relative to the market, and the market or benchmark return over the same period. All are entered as percentages for the same time horizon.
How does alpha differ from beta?
Beta measures a portfolio's sensitivity to market movements (its systematic risk). Alpha measures the excess return after accounting for that beta exposure. Beta tells you how much market risk you took; alpha tells you whether you were rewarded for skill beyond that risk.
Official sources
- U.S. Securities and Exchange Commission, Investor.gov: Investing glossary.
- Board of Governors of the Federal Reserve System: Selected interest rates (risk-free rate reference).
Reviewed by the CalculatorHub team, edited by James Graham, 17 June 2026. See our methodology.