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. But is it mandatory to sort the stocks into portfolios as how Fama and French did? Or can I do regression on the three companies separately and analyze it? The final approach will be deciding which between three-factor and five-factor model best describe excess stock returns of the 3 companies.
When you only have three stocks in your data set, trying to form portfolios will not be helpful. Run the analysis on the individual stocks' data as is.
Using portfolios instead of individual assets in estimating and testing asset pricing models makes sense because we expect idiosyncratic (company-specific) patterns in returns to become less pronounced in averages across companies (that is, portfolios). Meanwhile, we expect deterministic patterns to stay about as strong as they were, as long as the companies within a portfolio contain similar deterministic patterns. That is why we do not put just any stocks in a given portfolio but look for ones that have similar deterministic patterns – such as a similar level of systematic risk, similar sensitivity to size or value factors and such.