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Jensen’s Alpha Calculator

Calculate Jensen’s alpha — a portfolio or fund’s return above what CAPM predicts for its beta — from the portfolio return, risk-free rate, beta and market return.

Portfolio return (annual)

Risk-free rate (annual)

Portfolio beta

Market (benchmark) return (annual)

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How it works

Expected return (CAPM) = Rf + β × (Rm − Rf) · Jensen’s alpha α = Rp − [Rf + β × (Rm − Rf)]

Michael Jensen introduced this measure in 1968 to test whether mutual fund managers added value. CAPM says a portfolio with beta β should earn the risk-free rate plus β times the market risk premium; anything above that is alpha, the return attributable to the manager’s skill (or luck) rather than to market exposure. A positive alpha means the fund beat its risk-adjusted benchmark. Use returns, risk-free rate and market return for the same period, and a beta estimated against the same benchmark.

Worked example

A portfolio returned 12% with a beta of 1.1 while the market returned 10% and the risk-free rate was 4%. CAPM expected 4% + 1.1 × (10% − 4%) = 10.60%, so Jensen’s alpha = 12% − 10.60% = 1.40%. Its Treynor ratio is (12 − 4) ÷ 1.1 = 7.27.

Sources: Jensen (1968) — The Performance of Mutual Funds in the Period 1945–1964, Journal of Finance · Investopedia — Jensen’s Measure (Alpha)

Frequently asked questions

What is a good Jensen’s alpha?

Any consistently positive alpha is good — it means returns beyond what market exposure explains. Most actively managed funds show negative alpha after fees over long periods.

How is Jensen’s alpha different from simple outperformance?

Simple outperformance compares returns directly. Jensen’s alpha first adjusts for beta, so a high-beta fund that beat the market only because markets rose may still have zero or negative alpha.

Where do I find a fund’s beta?

Fund fact sheets and data sites list it, usually measured over 3 or 5 years against the fund’s benchmark. You can also estimate it from monthly returns with the stock beta calculator.

Can alpha be calculated monthly?

Yes — use monthly portfolio, market and risk-free returns. Alpha is often estimated as the intercept of a regression of excess portfolio returns on excess market returns.

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Educational estimate, not investment, trading or tax advice. Brokers, exchanges and data providers use their own conventions, fees and figures — confirm with your broker, the exchange’s documentation or a licensed adviser before acting.