Formula, in Risk & Portfolio Construction
Jensen's Alpha Formula
Jensen's alpha is the portfolio's realized return minus the return the Capital Asset Pricing Model says it should have earned given its beta. A positive alpha means the manager delivered more than market exposure alone would justify; a negative alpha means they fell short of fair compensation for the risk taken.
5 variables. Published May 26, 2026. By AI Fin Hub Research.
alpha = R_p - [ R_f + beta_p x (R_m - R_f) ] Variables
R_p
Portfolio return
The realized return of the portfolio over the measurement period.
R_f
Risk-free rate
Return on a near-riskless asset over the same period. It anchors the CAPM expected return.
beta_p
Portfolio beta
Systematic risk of the portfolio relative to the market. It scales the market risk premium to the portfolio's exposure.
R_m
Market return
Return on the broad market benchmark over the period.
R_m - R_f
Market risk premium
Compensation the market paid for bearing systematic risk. Multiplied by beta it gives the portfolio's CAPM-expected risk premium, which alpha measures the result against.
Step by step
- 1
Gather the portfolio return, risk-free rate, market return, and the portfolio beta over the same period.
Portfolio 14%, risk-free 3%, market 10%, beta 1.1.
- 2
Compute the market risk premium as market return minus risk-free rate.
10% - 3% = 7%.
- 3
Scale the risk premium by beta and add the risk-free rate to get the CAPM-expected return.
3% + 1.1 x 7% = 3% + 7.7% = 10.7%.
- 4
Subtract the CAPM-expected return from the realized portfolio return.
14% - 10.7% = 3.3% alpha.
Worked example
Active fund evaluated against the market with CAPM
Portfolio return
14%
Market return
10%
Risk-free rate
3%
Beta
1.1
CAPM-expected return = 0.03 + 1.1 x (0.10 - 0.03) = 0.03 + 1.1 x 0.07 = 0.03 + 0.077 = 0.107 = 10.7%. Jensen's alpha = 0.14 - 0.107 = 0.033 = 3.3%.
Jensen's alpha of +3.3%. The fund returned 14% while CAPM said a beta-1.1 portfolio should have returned only 10.7% in this market, so the manager added 3.3 percentage points beyond fair compensation for systematic risk. Statistical significance still depends on the standard error of the estimated alpha over the sample.
Common variations
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Sources
- The Performance of Mutual Funds in the Period 1945-1964 , Michael C. Jensen, Journal of Finance (1968)
- Capital Asset Prices: A Theory of Market Equilibrium under Conditions of Risk , William F. Sharpe, Journal of Finance (1964)
Keep the topic connected
- 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 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 Treynor Ratio Formula
The Treynor ratio formula: excess return over the risk-free rate divided by beta. Reward per unit of systematic market risk, with a worked example.
- Learn Alpha
Alpha as risk-adjusted excess return: definition, the beta-adjustment math, and why most claimed alpha disappears once you adjust for the right factors.