# Alpha and t-statistic

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

Source data: AMFI daily NAV (17,900+ schemes) + Nifty benchmark indices. Last updated: 2026-07-02. Interactive tool: https://mfpro.tigzig.com

## 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





- **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:

- [Beta and R-Squared](/mfpro/beta-and-r-squared)

- [Sharpe Ratio](/mfpro/sharpe-ratio)

- [Sortino Ratio](/mfpro/sortino-ratio)

- [Tracking Error and Information Ratio](/mfpro/tracking-error-information-ratio)

- [Capture Ratios (Upside and Downside)](/mfpro/capture-ratio)

- [Win Rate](/mfpro/win-rate)

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Source: https://www.tigzig.com/mfpro/alpha-and-t-stat