# Fama-French Regression Output Interpretation (Intercept/Alpha)

I am currently doing a report regarding Fama and French 3 and 5 factors model. I was provided 3 companies with each of its daily stock return from 2015-2020, and the values of all 5 factors during that period (Mkt-RF, SMB, HML, RMW, CMA, RF). I will be using Excel to compute a regression analysis with no sorting portfolios. I got the multiple regression output (5 independent var) already for each company individually. However, for the intercept/alpha values, I got coefficient 0.226 and the p-value 0.210. The p-value indicates here that it is not statistically significant (since its >0.05 sig level). So does it mean that the model is unreliable? How is the correct way to interpret the coefficient and p-value of intercept/alpha according to Fama French?

• What kind of regression did you run? This cannot be a cross-sectional regression, as you only have 3 data points (3 companies) and 5 explanatory variables. If it is a time-series regression, why is it only one? After all, you have three companies, not one. Nov 24, 2023 at 19:47
• Oh sorry, yes it is a time-series regression. I just stated Company A's ouput on the question. The other two companies: Company B (pvalue: 0.407, coefficient:0.0001), Company C (pvalue:0.15, coefficient: 0.0002) Nov 25, 2023 at 5:20

If the model holds, $$\alpha_1=\dots=\alpha_N=0$$ for all the test assets $$i=1,\dots,N$$. (In your case $$N=3$$.) Conversely, if $$\alpha_i\neq 0$$ for at least one asset $$i$$, the model does not hold. Now, you report individual assessments of $$\alpha_1$$, $$\alpha_2$$ and $$\alpha_3$$. Individually, each $$p$$-value is greater than any conventional significance level (1%, 5%, 10%), so it would seem that you do not have solid evidence against the model. However, you want to test the joint hypothesis, not the individual ones. Thus, you want to run the GRS test. Unfortunately, it may be a little tedious to implement in Excel.