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The return that you cannot explain by just being levered to the market.
Jensen's alpha is the return a portfolio earned above what its beta-adjusted exposure to the market would have predicted. It isolates skill from leverage. A portfolio that returned 15% with a beta of 1.5 in a year the market did 10% has alpha of zero — all the excess came from extra market exposure, not skill.
α = Rp − [Rf + β·(Rm − Rf)]α = Rp − [Rf + β·(Rm − Rf)]Subtract the CAPM-predicted return (what your beta should have earned) from your actual return. What is left is alpha — the part you cannot explain by beta exposure to the market.
Alpha is the cleanest measure of stock-picking or allocation skill. Long-term positive alpha is exceptionally rare and the gold standard for evaluating active managers. Studies of mutual funds consistently show fewer than 10% have statistically significant positive alpha after fees over multi-decade periods.
The catch: a small-cap manager can show positive alpha against the S&P 500 simply by tilting to small-caps, since the S&P 500 underweights them. The Fama-French 3 and 5-factor models exist specifically to strip out these style tilts so the residual alpha is actually skill, not style.
Portfolio returned 13%. T-bills paid 4.5%. Beta was 1.2. S&P 500 returned 10%.
CAPM prediction: 4.5% + 1.2 · (10% − 4.5%) = 4.5% + 6.6% = 11.1%
Alpha = 13% − 11.1% = +1.9%
You earned 1.9 percentage points more than your beta exposure should have produced. That is the part attributable to skill (or luck — see PSR for the statistical test).
Statistically meaningful long-run alpha is rare. Industry guidelines:
| Alpha (annualized, after fees) | Verdict |
|---|---|
| < 0 | Underperformed the market on a risk-adjusted basis. Closet indexer or worse. |
| 0 – 1% | Statistically indistinguishable from luck for most sample sizes. |
| 1 – 3% | Solid active manager — top quartile over 10+ years. |
| 3 – 5% | Exceptional — top decile, very rare sustained. |
| > 5% | Either Renaissance Medallion territory or overfitting/short sample. |
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Open the Portfolio Alpha Calculator →Beta · R-Squared · Treynor Ratio · Information Ratio · Fama-French 3/5-factor
Active return is Rp − Rb. Alpha is Rp − CAPM_predicted_return. Alpha adjusts for the leverage (beta) you took, active return does not.
At least 5 years of monthly returns; ideally 10+. Alpha is statistically noisy at short windows. Use PSR for a formal test.
Residual alpha after Fama-French 3 or 5 factor adjustment (market, size, value, profitability, investment). Most "alpha" from CAPM is actually exposure to size or value factors.
Yes — Jensen's alpha against S&P 500 by default, with optional Fama-French 5-factor decomposition.
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