Interpreting Regression Alpha and Beta When a Stock Trails the Market

Summary

This question explores why a stock can have a positive regression intercept even when its total return is below the market’s. The central distinction is between total return and alpha: the intercept estimates the stock’s average return when the market return is zero, while beta measures how much its return tends to move with the market. A positive intercept therefore does not mean the stock beat the market over the observed period. It can arise from the fitted relationship across individual observations, including residual variation.

The example reports a positive but statistically insignificant intercept and a significant market coefficient. These estimates do not establish that the stock generated reliable excess performance. Interpretation also depends on how returns are measured, the regression specification, and the sample. The discussion raises the conceptual issue but provides no underlying data or full regression diagnostics, so it cannot establish why the particular estimate has its sign.

Key ideas

• Regression alpha is the estimated intercept, not the difference between cumulative stock and market returns.
• Beta describes the stock’s estimated sensitivity to market returns.
• A positive intercept can coexist with lower total return over the sample.
• Statistical insignificance means the evidence does not clearly distinguish the intercept from zero.

Tags

# Confused on interpretation of betas/alphas in regression in finance


# Confused on interpretation of betas/alphas in regression in finance












I ran a regression on two stocks. I don't have the data in front of me, but it is a more conceptual question.

Let's say SP500 returned a total 23% return over this time period and MSFT returned 9%. I ran the regression in R:

```
 summary(lm(MSFT~SP500,data=mydata))
```

The coefficients show an intercept of around .003 and coefficient of around 1.5 for the SP500. The beta is statistically significant at around the 99.9% confidence and the intercept is NOT - only around 38% interval.

Now my understanding of 'alpha' or the intercept - is that it is the 'excess return' that could be gained by investing in a strategy. I am confused how alpha could ever be positive if the Y value that you are comparing (MSFT) is less than the X (SP500). Here each 1% change in the Sp500 returned a 1.5% in microsoft, but to actually have a positive alpha - even a minuscule amount and even though its not statistically significant - is hurting my head.

If anyone could just explain the relationship of the intercept in a basic regression like this and practical relationship of the betas I would appreciate it. Would I ever get a positive alpha when MSFT's return is LESS than the SP500 and MSFT=Y, SP500=X?

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