Alpha
Jensen's alpha: α = R_p − [R_f + β(R_m − R_f)], where R_p is portfolio return, R_f the risk-free rate, R_m the market return, and β the portfolio's exposure to the market factor. Generalizes to multi-factor models — Fama-French, Carhart, AQR-style — where alpha is residual excess return after subtracting all priced-factor exposures.
Definition
Alpha
Jensen's alpha: α = R_p − [R_f + β(R_m − R_f)], where R_p is portfolio return, R_f the risk-free rate, R_m the market return, and β the portfolio's exposure to the market factor. Generalizes to multi-factor models — Fama-French, Carhart, AQR-style — where alpha is residual excess return after subtracting all priced-factor exposures.
Why it matters
Returns without context are meaningless. A 20% strategy in a 25% market is negative alpha at beta 1; the same 20% with beta 0.3 is roughly 13% alpha. Allocators pay for alpha and refuse to pay for beta. Most strategies marketed as alpha are mostly disguised beta.
How it works
Run a regression of strategy excess returns on benchmark excess returns. The intercept is alpha; the slope is beta. Multi-factor: regress on (market, size, value, momentum) or your chosen factor set. Significance test the intercept — if its t-stat is below 2, the alpha is statistically indistinguishable from zero on that sample.
Example
Long-only equity strategy, 3 years, monthly
Strategy annualized return
14%
Market annualized return
11%
Risk-free rate
3%
Estimated β
0.95
Expected return at β=0.95
3 + 0.95 × (11 − 3) = 10.6%
Alpha
14 − 10.6 = 3.4%
Headline 14% looks great vs 11% market. Once beta is netted out, the alpha is 3.4% — still positive, but only a third of the apparent edge.
Key Takeaways
Alpha without a defined factor model is rhetoric, not measurement.
Most strategies that claim alpha collapse to near-zero once a 4-factor model is applied.
Statistical significance of alpha matters more than the point estimate on short samples.
Related Terms
FAQ
Questions people ask next
The short answers readers usually want after the first pass.
Sources & References
- The Performance of Mutual Funds in the Period 1945-1964 — Journal of Finance (Jensen, 1968)
Related Content
Keep the topic connected
Beta
Beta as factor sensitivity: what it measures, why a beta of 1 doesn't mean 'tracks the market', and the rolling-vs-static distinction that catches most people.
Sharpe Ratio
Sharpe ratio defined, when it lies (skew, fat tails, autocorrelation), and how to read a Sharpe number you didn't compute yourself.