Alpha
Quantitative Finance glossary · Probability, Statistics & Linear Algebra
Definition
Excess return over the CAPM benchmark prediction; the regression intercept in R_i - r_f = α_i + β_i(R_m - r_f) + varepsilon_i. Statistically significant positive α is the empirical signature of manager skill, but the Information Ratio IR = α / σ(varepsilon) (alpha per unit of idiosyncratic risk) is the cleaner skill metric because it penalises noisy alpha. Most reported alpha disappears after fees and after controlling for size, value, momentum, and quality factors (Fama-French / Carhart).
Alpha in plain English
Alpha is the part of an investment's return that can't be explained by simply riding the overall market up and down — it's the manager's own value-add, good or bad. Picture two runners: one just gets carried along by a moving walkway (that's the market), while the other actually runs on their own; alpha measures how much faster (or slower) the runner moves beyond what the walkway already gives them. A reliably positive alpha is the fingerprint of real skill, but a smarter check divides alpha by how erratic those extra returns are, since lucky-looking gains that swing wildly aren't proof of anything. The catch: once you subtract fees and account for well-known shortcuts everyone can buy cheaply (like favoring small or cheap stocks), most claimed alpha quietly vanishes.
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