— Stock Market
Alpha Calculator
Calculate Jensen’s alpha: the return earned above what CAPM predicts for the risk taken. Enter actual return, risk-free rate, beta, and market return — or expected return directly — to see whether a stock, fund, or portfolio outperformed its benchmark.
Alpha (Jensen’s)
2.6%
- Expected return (CAPM)
- 11.4%
Try: 14% actual, β 1.2, 10% market, Underperformer: 8% actual, With a benchmark & Fama-French, Compare three funds
— How the alpha is built
| Component | Return |
|---|---|
| Risk-free rate (Rf) | 3% |
| Beta × market premium | 8.4% |
| Expected return | 11.4% |
| Actual return | 14% |
| Alpha | 2.6% |
— Alpha by fund
Download— How it works
Jensen’s alpha = actual return − expected return, where the CAPM expected return = Rf + β(Rm − Rf). Simple alpha = actual − benchmark return. Multi-factor (Fama-French) alpha also subtracts the size and value factor contributions.
Skill, not just risk
Beating the market isn’t impressive on its own — you can do it by simply taking more risk. Alpha strips that out. It asks: given how much market risk this portfolio took (its beta), what return should it have earned? CAPM answers with Rf + β(Rm − Rf). Alpha is whatever the portfolio earned above that. A fund up 14% sounds great, but if its beta of 1.2 in a 10% market meant it “should” have returned 11.4%, the real achievement — the alpha — is 2.6%. That 2.6% is the part attributable to skill, selection or luck, not market exposure.
Worked example — 14% actual return, beta 1.2, 10% market, 3% risk-free: Expected = 3% + 1.2 × (10% − 3%) = 11.4%. Alpha = 14% − 11.4% = +2.6% — genuine outperformance over the risk-adjusted bar.
Simple alpha, and why beta matters
A cruder measure — “simple alpha” — just subtracts a benchmark’s return from the portfolio’s, ignoring risk entirely. It’s easy and intuitive, but it flatters high-risk funds: beating the index by 3% means little if you took 50% more risk to do it. Jensen’s alpha is the honest version because it adjusts for beta. The calculator shows both, so you can see how much of an apparent edge survives once risk is accounted for. A high simple alpha paired with a low Jensen’s alpha is the signature of a fund that’s just dialled up the risk.
Multi-factor alpha and its limits
Modern research shows much of what looked like alpha was really exposure to known factors — small-cap and value stocks have historically earned premiums. The Fama-French model controls for these: it subtracts the size and value contributions too, leaving the alpha that isn’t explained by style. A manager with a big positive Jensen’s alpha but a near-zero multi-factor alpha wasn’t skilled — just tilted toward small, cheap stocks. Two cautions: alpha is only as reliable as the inputs, and a low R² (the portfolio barely tracking the market) makes both alpha and beta shaky. Persistent positive alpha is rare and hard to repeat. Not investment advice.
— Reader questions
How do I calculate alpha?
Subtract the CAPM expected return from the actual return: alpha = actual − [Rf + β(Rm − Rf)]. For a 14% return with beta 1.2, a 10% market and 3% risk-free, expected is 11.4%, so alpha is +2.6%.
What does a positive alpha mean?
The investment outperformed what its risk (beta) and the market predicted — the return attributable to skill or selection rather than just market exposure. A negative alpha means it underperformed that risk-adjusted expectation.
What is the difference between Jensen’s alpha and simple alpha?
Simple alpha is just the portfolio return minus a benchmark, ignoring risk. Jensen’s alpha subtracts the CAPM expected return, so it adjusts for how much market risk the portfolio took — a fairer measure that doesn’t reward simply taking more risk.
What is multi-factor (Fama-French) alpha?
Alpha measured after also controlling for the size and value factors, not just the market. It reveals whether a manager’s edge is genuine skill or merely a tilt toward small-cap or value stocks, which have historically earned premiums of their own.
Why does R² matter for alpha?
R² shows how much of the portfolio’s movement the market explains. When it’s low, the beta — and the CAPM expected return built on it — is unreliable, which makes the resulting alpha shaky too. Trust alpha most when R² is high.