Jensen's Alpha Calculator — Risk-Adjusted Portfolio Performance
Jensen's alpha tells you whether a portfolio manager added value above what the Capital Asset Pricing Model (CAPM) predicts given the portfolio's systematic risk (beta). Enter the portfolio return, the risk-free rate, the portfolio's beta, and the market return to compute alpha.
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Portfolio outperformed the CAPM expectation — positive alpha.
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Market risk premium
Rm − Rf = 10 − 4.5 = 5.5 - 2
Beta-adjusted premium
β × (Rm − Rf) = 1.2 × 5.5 = 6.6 - 3
CAPM expected return
Rf + β(Rm − Rf) = 4.5 + 6.6 = 11.1 - 4
Jensen's Alpha
Rp − CAPM = 12 − 11.1 = 0.900Positive means the portfolio beat its risk-adjusted CAPM expectation.
How does this calculator work?
Jensen's alpha = Rp − [Rf + β(Rm − Rf)]. It measures how much a portfolio returns above the CAPM expectation for its level of market risk (beta). Enter actual portfolio return, risk-free rate, beta, and market return to see whether the manager added value on a risk-adjusted basis.
Formula
How this is calculated
Jensen's alpha, introduced by Michael Jensen in 1968, extends the Capital Asset Pricing Model to evaluate portfolio performance. CAPM says that a rational investor should expect a return of Rf + β × (Rm − Rf), where Rf is the risk-free rate, Rm is the market return, and β captures how much systematic (non-diversifiable) market risk the portfolio holds. If β = 1 the portfolio moves one-for-one with the market; if β = 1.5 it amplifies market swings by 50%.
Alpha is the residual: the actual portfolio return Rp minus the CAPM expectation. A positive alpha means the manager generated returns above what the risk taken justifies — skill (or luck). A negative alpha means the risk-adjusted performance was worse than simply buying an index fund. Alpha of zero means the manager matched the CAPM benchmark exactly.
The calculator also shows the Treynor ratio — (Rp − Rf) / β — a related measure that expresses excess return per unit of systematic risk. All inputs are percentage returns; typical values for the risk-free rate are the 3-month T-bill or 10-year bond yield; the market return is usually the broad index (S&P 500, MSCI World, etc.) for the same period as the portfolio return.
Frequently asked questions
Any positive alpha is technically above the risk-adjusted expectation. In practice, passive index funds deliver an alpha near zero by definition. Active managers who consistently deliver alpha above 1–2% annualised are outperforming — but most research shows that after fees, the majority of active funds produce negative alpha over long horizons.
The Sharpe ratio divides excess return by total volatility (standard deviation), penalising both systematic and unsystematic risk. Jensen's alpha uses CAPM and only accounts for systematic risk (beta). For well-diversified portfolios the two metrics are closely related; for concentrated portfolios they can diverge significantly.
Beta is typically estimated from a linear regression of the portfolio's returns against the market's returns over a historical window (commonly 36–60 months). Many financial data providers (Bloomberg, Morningstar, Yahoo Finance) publish rolling betas for funds and individual stocks. If you don't have one, a beta of 1.0 reduces alpha to simply Rp − Rm.
TG we-Calculate Editorial Team. (2026). Jensen's Alpha Calculator — Risk-Adjusted Portfolio Performance [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/jensen-alpha-calculator
TG we-Calculate Editorial Team. "Jensen's Alpha Calculator — Risk-Adjusted Portfolio Performance." TG we-Calculate. 2026. https://we-calculate.com/calculator/jensen-alpha-calculator.
TG we-Calculate Editorial Team, "Jensen's Alpha Calculator — Risk-Adjusted Portfolio Performance," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/jensen-alpha-calculator
@misc{wecalculate_jensen_alpha_calculator, title = {Jensen's Alpha Calculator — Risk-Adjusted Portfolio Performance}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/jensen-alpha-calculator}}, year = {2026}, note = {TG we-Calculate} }
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