# 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?

• First off all, are you regressing on prices or on returns? Have you made plots? – Bob Jansen Apr 26 '15 at 9:16
• Are you testing for the main regression model assumptions? if not, you could get biased results. So, I suggest to edit the question specifying the methodology you're using in you analysis. – Quantopik Apr 26 '15 at 13:23