how do you calculate jensen’s alpha

Alpha equals the portfolio’s actual return minus its CAPM-expected return, where the expected return is the risk-free rate plus beta times the market return above the risk-free rate. For example, if a portfolio returned 18%, the risk-free rate is 6%, the market returned 12%, and the portfolio’s beta is 1.2, then CAPM expected 6% + 1.2 × (12% − 6%) = 13.2%, so the alpha is 18% − 13.2% = +4.8%. That positive 4.8% is the return the portfolio delivered beyond what its market exposure entitled it to.

is a positive alpha good

Yes — a positive alpha is the goal of active management, because it means the portfolio beat the return its risk alone would have produced, which is what genuine skill looks like. But sustained positive alpha is extremely rare after fees, and much of what looks like alpha is really disguised risk: exposure to factors CAPM does not capture, or leverage, or simply luck over a short period. Real, persistent alpha is so scarce that its scarcity is a large part of the argument for low-cost index investing.

What is Jensen’s alpha and how is it calculated

Beat the market by 18% in a year the market rose 12%, and you look like a genius. But if you did it with a high-beta portfolio that should have risen more anyway, you may have added nothing. Jensen’s alpha strips that away: it is the return you earned beyond what your risk entitled you to — the closest thing to a clean measure of skill.

Actual return minus what CAPM expected

Alpha builds directly on CAPM. The model predicts a required return from the risk-free rate, the portfolio’s beta, and the market’s return. Whatever the portfolio earns above that prediction is alpha; whatever it falls short by is negative alpha. So alpha is not "did you beat the market?" but "did you beat what your level of market risk entitled you to?" — a much harder and more honest bar.

Worked example

An 18% return, decomposed

Beta 1.2, market +12%

Risk-free rateThe baseline6%

CAPM expectedWhat the risk entitled you to6% + 1.2 × (12% − 6%) = 13.2%

Actual returnWhat you got18%

Jensen’s alphaThe genuine excess18% − 13.2% = +4.8%

The lessonThe rest was just betaOnly 4.8% was skill

Of the 18% return, CAPM says 13.2% was simply the reward for carrying a beta of 1.2 in a rising market — the portfolio was owed that. Only the remaining 4.8% is alpha, the part that beat the risk taken. Reporting the 18% alone flatters a manager who mostly just took more market risk; alpha is what isolates the real contribution.

Check yourself

A fund returned 20% when the market rose 15%. Its beta is 1.5, and the risk-free rate is 6%. Did it actually generate positive alpha?

Simple bhasha mein

Jo return market ne udhaar nahi diya

Market 12% badhi, aapne 18% kamaya — genius? Ruko. Beta 1.2 tha, toh CAPM ke hisaab se 6% + 1.2×(12−6) = 13.2% toh aapko milna hi tha. Sirf bacha hua 4.8% asli skill hai — wahi Jensen ka alpha. Bada return sirf zyada market-risk (beta) le ke bhi aa jaata hai; alpha woh hissa hai jo risk se upar kamaya. Aur asli, tikne wala alpha fees ke baad bahut hi kam milta — isiliye index fund ki baat hoti hai.

What to remember

Jensen’s alpha is actual return minus the CAPM-expected return for the portfolio’s beta.
It isolates skill from the return simply owed to market-risk exposure.
Positive alpha is the goal of active management — but it is rare after fees.
Much apparent alpha is hidden factor exposure, leverage or luck, not real edge.
Measure it against the right benchmark, net of fees, over a full cycle.

You reached the endMark it done and keep your streak going.

Up nextModern portfolio theory: the free lunch of diversification Previous: The information ratio: skill against a benchmark

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Common questions

Short, direct answers to what people ask about this topic.

what is jensen’s alpha: Jensen’s alpha is the return a portfolio earned above what the Capital Asset Pricing Model says it should have earned for its level of market risk. CAPM predicts a required return from the risk-free rate, the portfolio’s beta and the market’s return; alpha is the difference between the actual return and that prediction. A positive alpha means the portfolio did better than its risk justified — the signature of genuine skill or an exploited edge — while a negative alpha means it underperformed what its beta alone would have delivered.
how do you calculate jensen’s alpha: Alpha equals the portfolio’s actual return minus its CAPM-expected return, where the expected return is the risk-free rate plus beta times the market return above the risk-free rate. For example, if a portfolio returned 18%, the risk-free rate is 6%, the market returned 12%, and the portfolio’s beta is 1.2, then CAPM expected 6% + 1.2 × (12% − 6%) = 13.2%, so the alpha is 18% − 13.2% = +4.8%. That positive 4.8% is the return the portfolio delivered beyond what its market exposure entitled it to.
is a positive alpha good: Yes — a positive alpha is the goal of active management, because it means the portfolio beat the return its risk alone would have produced, which is what genuine skill looks like. But sustained positive alpha is extremely rare after fees, and much of what looks like alpha is really disguised risk: exposure to factors CAPM does not capture, or leverage, or simply luck over a short period. Real, persistent alpha is so scarce that its scarcity is a large part of the argument for low-cost index investing.

Jensen’s alpha: return the market did not owe you

Actual return minus what CAPM expected

Common questions