π― Jensen's Alpha Calculator
Return above what risk predicted.
Jensen's alpha
Estimates for planning only, not financial advice.
Jensen's alpha measures return above what the capital asset pricing model says the risk deserved: portfolio return minus the CAPM expected return. With a 12% portfolio return, 3% risk-free rate, beta of 1.2, and 10% market return, the expected return is 3 + 1.2 x 7 = 11.40%, so alpha is 12 - 11.4 = +0.60%. Positive alpha means skill or luck beyond the risk taken.
How to Use This Calculator
Enter the portfolio's actual return, the risk-free rate, the portfolio beta, and the market return over the same period. The calculator returns alpha and the CAPM expectation behind it.
Enter the portfolio return and the market return for the same period.
Enter the risk-free rate and the portfolio beta.
Read alpha. For consistency of outperformance instead, try our information ratio calculator.
The Jensen's Alpha Formula
The bracketed term is the CAPM expected return: what the portfolio should have earned given its market sensitivity. Subtracting it from the actual return isolates the manager's contribution, positive or negative, after adjusting for risk. A 15% return with a beta of 2 in a 10% market is not skill; it is market exposure doing the work, and alpha exposes that. Persistent positive alpha across cycles is the statistical signature of genuine skill.
Worked Example
Portfolio return 12%, risk-free 3%, beta 1.2, market 10%. Expected return = 3 + 1.2 x (10 - 3) = 11.40%. Alpha = 12 - 11.40 = +0.60%. The manager added 0.6 points beyond the risk taken. Now the trap case: a portfolio returns 14% with beta 1.8 when the market returns 10% and Rf is 3%. Expected = 3 + 1.8 x 7 = 15.6%, so alpha is -1.6%. The 14% headline beat the market but lagged its risk, and the fee was charged anyway.
Reading Alpha Like an Allocator
Three cautions before paying for alpha. First, beta estimates wobble; a mismeasured beta manufactures fake alpha. Second, alpha over short periods is mostly noise; demand five-plus years. Third, survivorship bias flatters every fund database, because dead funds stop reporting. Net-of-fee alpha is the only alpha that matters to you, and most active funds fail to produce it consistently.
My filter: positive net alpha over a full market cycle with a stable process gets a second look; anything else is marketing. And compare fees to the alpha claimed: a 1% fee needs 1% of persistent alpha just to break even against the index. Our investment fees calculator shows what fees compound into over decades.
Estimates for planning only, not financial advice.
Frequently Asked Questions
What is Jensen's alpha?
The excess of a portfolio's return over its CAPM expected return: alpha = Rp - [Rf + beta x (Rm - Rf)]. Positive alpha means the manager beat the risk-adjusted benchmark; negative means they lagged it.
What does a positive alpha mean?
The portfolio earned more than its market risk predicted. It suggests skill, factor exposure the model misses, or luck. One good year proves nothing; persistence across cycles is the test.
What is a good alpha?
Any persistent positive net-of-fee alpha is rare and valuable. Two to three percent annualized over a decade puts a manager in elite company. Most active funds fail to sustain even zero net alpha.
How is alpha different from excess return?
Excess return is raw outperformance versus a benchmark. Alpha adjusts for the risk taken to get there via beta. High-beta portfolios can show excess return with negative alpha.
Why does beta matter so much?
Because it sets the expectation. A beta-2 portfolio should return roughly twice the market risk premium; judging it against the raw market return credits market exposure as skill. Alpha corrects that.
Can alpha be faked?
Yes: mismeasured beta, short measurement windows, survivorship bias, and hidden risks like illiquidity or tail exposure all manufacture fake alpha. Net-of-fee, long-horizon, audited alpha is the standard.
What is the CAPM?
The capital asset pricing model: expected return equals the risk-free rate plus beta times the market risk premium. It is the benchmark Jensen's alpha measures against, and the foundation of modern portfolio theory.
Should I pay for positive alpha?
Only if it is persistent, net of fees, and survives risk adjustment. Compare the fee against the alpha: a 1.5% fee on 1% alpha leaves you poorer than the index. Most investors do better owning the benchmark cheaply.
What is the difference between alpha and beta?
Beta measures sensitivity to the market; alpha measures return beyond what that sensitivity predicts. High beta is a ride, positive alpha is supposed to be skill. You pay fees hoping for the second, but often just get the first.
What are common sources of fake alpha?
Illiquid holdings marked optimistically, selling volatility for premium income, and factor tilts the CAPM ignores, like value or momentum. Each manufactures alpha that evaporates under stress or proper risk adjustment.