Your inputs

Portfolio return (Ri)

Market return (Rm)

Risk-free rate (Rf)

Beta (β)

Results

Jensen's alpha (α)+3.4%outperformed its risk-adjusted benchmark

Expected return (CAPM)11.6%Rf + β × (Rm − Rf)

Market risk premium+8%

Return from beta+9.6%

Excess over market+5%not risk-adjusted

With β = 1.2, CAPM says the portfolio should have earned 11.6%. It actually earned 15%, so +3.4% is attributed to skill (or luck) rather than market exposure.

Return decomposition

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How to calculate Jensen's alpha

α = R_p − [R_f + β × (R_m − R_f)]

Worked example

Portfolio return 15%, risk-free rate 2%, market return 10%, β = 1.2.
Expected return = 2% + 1.2 × (10% − 2%) = 11.6%.
α = 15% − 11.6% = +3.4%.

How to interpret Jensen's alpha

Positive alpha means the portfolio earned more than its market exposure justified; negative alpha means it earned less. A high-beta portfolio that beat the market may still have negative alpha if the extra return was only compensation for the extra risk. Estimate beta with the beta calculator.

Limitations and common mistakes

Use returns, risk-free rate and market return over the same period.
Alpha over a single year is mostly noise; look for persistence over many periods.

Risk Metrics

Beta Calculator

Measure how sensitive an asset or portfolio is to market moves from two return series.

Asset vs index returns → β, correlation, R²

Risk-Adjusted Ratios

Treynor Ratio Calculator

Excess return per unit of market risk (beta) for diversified portfolios.

12% · Rf 2% · β 1.2 → 0.0833

Risk-Adjusted Ratios

Sharpe Ratio Calculator

Measure excess return per unit of volatility from annual figures or a series of returns.

12% return · 2% Rf · 8% σ → 1.25

Alpha calculator FAQ

What is a good alpha?

Any consistently positive alpha after fees is rare and valuable. Most active funds have negative alpha after costs.

Is alpha the same as excess return over the market?

No. Excess return over the market ignores beta. Alpha adjusts for the market risk taken.