What is Alpha?
Alpha is the excess return a fund generates beyond what its market exposure (beta) would predict. Positive alpha means the fund manager is adding value through stock selection. Negative alpha means the fund is underperforming its risk level.
How We Compute It
α_daily = the intercept of the regression (REGR_INTERCEPT in DuckDB)
Annualized Alpha = ((1 + α_daily / 100)252 − 1) × 100
The daily intercept is a tiny number (like 0.01%). We compound it over 252 trading days to get the annualized figure. This compounding approach is more accurate than simply multiplying by 252.
t-Statistic for Beta
The t-stat tells you whether beta is statistically significant - i.e., is the fund-to-market relationship real or could it be random noise?
SE(Beta) = √(MSE / SXX)
MSE = (SYY − Beta × SXY) / (n − 2)
|t| ≥ 2 → beta is significant at roughly the 95% confidence level. In the table, we show beta in normal black text when significant, and grey italic when not.
With 250+ daily observations (1 year), beta is almost always significant. It becomes marginal only with very short periods or funds with extremely low R².
Worked Example
Alpha interpretation
Alpha = 3.2%, Beta = 0.95, t-stat = 28.4
After accounting for its 0.95× market exposure, the fund generated 3.2% annual excess return. The t-stat of 28.4 ≫ 2 confirms the beta is highly significant.
Edge Cases
- Alpha doesn't account for fees: Our NAVs are after expenses, so the alpha already reflects the expense ratio. A fund with 0% alpha is keeping pace with the market after fees.
- Annualization method matters: We compound the daily alpha ((1 + α/100)^252 − 1). Some providers multiply daily alpha × 252, which gives a slightly different number. Our compounding approach is mathematically more correct.
Related metrics
More Risk Metrics methodology from the MFPRO analytics tool: