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Alpha and t-statistic

Excess return over the market, and whether it is statistically real.

Source data: AMFI daily NAV (38,000+ schemes, 37M+ rows since April 2006) + Nifty benchmark indices · Last updated: 2026-07-02
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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

From the regression: fund_return = α_daily + β × benchmark_return

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?

t = Beta / SE(Beta)
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

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