How Jensen's alpha works
"We beat the market" is not the same claim as "we showed skill". A fund with a beta of 1.3 is supposed to beat the market in a good year — it holds amplified market risk, and CAPM already credits that return to the risk, not the manager. Michael Jensen's insight, in a 1968 Journal of Finance paper (vol. 23, no. 2), was to make CAPM the measuring stick: compute the return a portfolio's beta required, and call only the surplus "alpha". A positive alpha is return that market exposure cannot explain; zero means the portfolio earned exactly its risk-adjusted keep; negative means investors were paid less than the risk they carried.
The formula
α = Rp − [Rf + β(Rm − Rf)]
where Rp is the portfolio's realized return,Rf the risk-free rate, β the portfolio's beta versus the market benchmark, andRm the benchmark's return over the same period. The bracketed term is the CAPM expected return — the benchmark alpha is measured against. All returns must cover the same period, and beta must be estimated against the same benchmark asRm.
Worked example
Take the calculator's default case: a portfolio with a beta of 1.1 returns 14% in a year when the market gains 11% and T-bills yield 4%. Build the CAPM benchmark, then subtract:
| Step | Amount |
|---|---|
| Market risk premiumRm − Rf = 11% − 4% | 7% |
| Risk-adjusted premiumβ × premium = 1.1 × 7% | 7.699999999999999% |
| CAPM expected returnRf + β(Rm − Rf) = 4% + 7.699999999999999% | 11.7% |
| Actual portfolio returnwhat the portfolio really earned over the period | 14% |
| = Jensen's alpha — the portfolio outperformedRp − CAPM expected = 14% − 11.7% | +2.3% |
Computed with this calculator's default settings — open the tool above and you'll see the same numbers, then swap in your own portfolio's figures.
What Jensen actually found
Jensen built the measure to answer a pointed question: do mutual fund managers, as a group, earn their fees? Applying it to 115 funds over 1945–1964, he found the average fund posted a negative alpha after expenses — roughly −1% per year — and that not a single fund showed convincing evidence of skill once market risk was credited. That result has been replicated across decades and markets, and the mechanism is mostly arithmetic: active fees subtract from the numerator every year while the CAPM benchmark pays nothing. It is the founding empirical result behind index investing — we walk through the modern evidence inwhy most active funds lose.
Alpha is one member of a family of risk-adjusted measures. Build the benchmark itself with theCAPM calculator, rank portfolios by excess return per unit of beta with theTreynor ratio calculator, or use total volatility instead of beta with theSharpe ratio calculator.
Frequently asked questions
What is Jensen's alpha?
Jensen's alpha is the return a portfolio earned above or below what the Capital Asset Pricing Model says its market risk deserved. CAPM sets the benchmark: the risk-free rate plus beta times the market risk premium. Alpha is the actual return minus that benchmark. Michael Jensen introduced it in a 1968 Journal of Finance paper to test whether mutual fund managers had genuine selection skill. A positive alpha means the portfolio delivered more than its market exposure alone explains; a negative alpha means it delivered less. It is the number people mean by "alpha" in the phrase "generating alpha".
What is the difference between alpha and excess return?
Excess return usually means the return above the risk-free rate — a 14% portfolio return with T-bills at 4% has a 10% excess return. Alpha is stricter: it subtracts the return CAPM attributes to market risk, not just the risk-free rate. A fund with a beta of 1.5 in a year the market gained 20% should post big excess returns simply by holding levered market exposure; that is not skill. Alpha only counts what is left after crediting beta. A fund can have a large positive excess return and a negative alpha at the same time.
Can alpha persist over time?
Rarely, and that is one of the most robust findings in finance. Jensen's 1968 study of 115 mutual funds found the average fund had negative alpha after fees, and decades of follow-up work — including the persistence studies behind S&P's SPIVA scorecards — show that funds with positive alpha in one period mostly fail to repeat it. Some persistence appears at the negative end: consistently high fees produce consistently negative alpha. A single period of positive alpha is weak evidence of skill; persistent alpha across many periods is the rare and meaningful signal.
What beta and market return should I use?
Use a beta measured against the same benchmark you enter as the market return, over the same horizon as the returns. For a US large-cap portfolio the S&P 500 is the standard proxy; a small-cap or international fund needs a matching index, or the alpha will partly reflect benchmark mismatch rather than skill. Betas are published on most fund and stock quote pages, typically estimated from three or five years of monthly returns. The risk-free rate is conventionally a Treasury bill yield covering the same period. Consistency across the three inputs matters more than the specific choices.
Does negative alpha prove a manager lacks skill?
No — one period of alpha, positive or negative, is mostly noise. Realized returns are volatile, beta estimates carry error, and a benchmark that does not quite match the strategy can manufacture alpha in either direction. What negative alpha does reliably capture over long horizons is cost: fees and trading expenses subtract directly from the numerator every single year, which is why the average fund's alpha lands below zero by roughly its expense ratio. Treat a negative alpha as a prompt to check fees and benchmark fit before concluding anything about skill.
Disclaimer: This calculator is foreducation and illustration only. Jensen's alpha inherits every assumption of CAPM — a single market factor, a stable beta, and a well-matched benchmark — and a single period's alpha is dominated by noise. Results are a textbook calculation, not a performance audit, and nothing here is investment advice.