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Jensen's Alpha Calculator

Find how much a portfolio's actual return beat (or missed) its CAPM-predicted return: α = Rp − [Rf + β(Rm − Rf)].

Jensen's alpha
1%
CAPM-expected return
9%

How it works

Jensen's alpha (Michael Jensen, 1968) measures how much a portfolio's actual return beat or missed what the Capital Asset Pricing Model predicts it should have earned given its systematic risk: α = Rp − [Rf + β(Rm − Rf)]. The bracketed term is exactly this site's own CAPM calculator's expected return — Jensen's alpha is simply the actual return minus that CAPM baseline. A positive alpha means the portfolio outperformed what its beta alone would predict (often attributed to manager skill or a mispriced asset); a negative alpha means it underperformed that baseline.

At beta = 0, the CAPM-expected return collapses to just the risk-free rate, so alpha becomes the portfolio's entire excess return over that rate — the same quantity this site's Sharpe and Treynor ratio calculators use as their numerator, just not yet divided by a risk measure. All four figures here (actual portfolio return, risk-free rate, beta, and actual market return) are inputs you supply for a specific period you're evaluating, not universal constants.

FAQ

How is Jensen's alpha different from the Treynor ratio?

Both start from the same CAPM framework, but they answer different questions. Treynor ratio divides excess return by beta to produce a per-unit-of-risk figure useful for ranking portfolios against each other. Jensen's alpha instead subtracts the full CAPM-expected return from the actual return, producing a single percentage-point figure that directly answers "did this beat what its risk level predicted, and by how much" — it doesn't normalize by risk the way Treynor does.

Can alpha be positive even with a negative beta?

Yes. A negative beta lowers the CAPM-expected return (since the risk-premium term subtracts from the risk-free rate for a hedge-like asset), so even a modest actual return can exceed that lowered baseline and produce a positive alpha. Alpha is always measured relative to what beta alone would predict, not against some fixed benchmark return.

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