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What it calculates: Alpha, CAPM Expected Return, Market Risk Premium, Band (0 lagged / 1 in line / 2 outperformed).
Updated 5 June 2026 · Transparent assumptions
CAPM expected 10.4%, the portfolio delivered 12%
The capital asset pricing model sets the expected return as the risk-free rate plus beta times the market excess: 2% + 1.2 × (9% − 2%) = 10.4%. The portfolio returned 12%, so alpha is the 1.6-point difference — return that the risk taken does not explain.
The beta term is what makes this more than a benchmark comparison. A portfolio with a beta of 1.2 should beat a 9% market in a rising year simply by being more sensitive; CAPM prices that in before crediting the manager with anything. Beating the index is not alpha. Beating what your beta entitled you to expect is.
Most active funds produce it after costs
Negative alpha means the portfolio returned less than its risk exposure warranted. It is the majority outcome for active management after fees: the aggregate of all investors must hold the market, so before costs active management is roughly zero-sum, and after costs it is negative-sum. Persistent positive alpha across long periods is rare and difficult to distinguish from luck.
Fees are the mechanism. A manager generating 1.5 points of gross alpha and charging 1.5% delivers zero to the investor. This is the entire empirical case for low-cost index investing, and it is why alpha should always be measured net of what was actually paid.
Change the benchmark and the alpha can disappear
Jensen\u2019s alpha is a residual from a specific model, so it inherits every one of that model\u2019s assumptions. CAPM explains returns with a single market factor. Multi-factor models add size, value, momentum and profitability, and returns that look like alpha under CAPM frequently turn out to be exposure to one of those factors instead.
That is not a technicality. A manager systematically buying small, cheap companies will show CAPM alpha in periods when those characteristics pay, while adding nothing a cheap factor fund could not replicate. Measuring alpha against a model that includes those factors is what separates skill from a tilt.
Very little, statistically
One period\u2019s alpha is a single observation from a noisy distribution. Distinguishing genuine skill from luck requires a long record and, ideally, a statistical test of whether the alpha differs from zero — and academic work consistently finds that even multi-year records rarely clear that bar.
The inputs also carry error. Beta is estimated, the market return depends on the index chosen, and the risk-free rate depends on which instrument and maturity is used. Small changes in any of them move alpha by enough to change its sign, which is a reasonable argument for treating any modest alpha figure as indistinguishable from zero.
Sources & References
Figures on this page are checked against primary, authoritative sources. Links open in a new tab.
Returns are assumptions, not guarantees. Actual results may vary because of market performance, taxes, fees, inflation, and timing. This is an educational projection, not investment advice.
Published the calculator with its formula, worked example, assumptions, limitations and a bespoke guide, and added an automated formula test suite covering it.
Verified the CAPM expected return the alpha is measured against, so a portfolio that returns exactly what its beta entitled it to reports zero alpha rather than a positive number.
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