Alpha

Alpha (α) is the part of a portfolio's return that cannot be explained by exposure to a benchmark. In Jensen's 1968 formulation, α is the regression intercept of portfolio excess return on benchmark excess return — what the manager added (or subtracted) above the level explained by the market.

CAPM regression

R_p − R_f = α + β ( R_b − R_f ) + ε

Annualised α > 0 with statistical significance is the textbook definition of skill. Significance matters because α estimates are noisy: a 36-month sample typically gives a standard error wide enough that |t| > 2 (the conventional threshold) is rare.

Why "alpha" is often beta in disguise

• ·Hidden factor tilts: a portfolio biased to small-caps, value or quality stocks will show positive α against the S&P 500 — but the α disappears against the right factor model (Fama-French 3-factor or Carhart 4-factor).
• ·Selection bias: surviving funds report α; the dead funds did not. Survivorship bias inflates aggregate industry α by 1-2% per year.
• ·In-sample mining: α optimised on the same window it is reported in is by definition positive. Out-of-sample, the median active manager underperforms.

How MEDGE Capital uses Alpha

Alpha is reported in the Compare report against the user-selected benchmark, annualised, with a confidence interval. The regression also outputs R² so the user sees how much of the portfolio return is explained by benchmark exposure — a high R² with a low α means the portfolio is mostly the benchmark with extra costs.