I am currently reading a paper, where I stumbled upon the following table. The statistics in which I am interested are in the red rectangles:
To explain what is happening here: They are doing many multiple regressions, where the dependent variable is a stock return and the independent variables are three Factors. They are doing this for n different stocks, so they carry out the regression n times:
$$R_k = a_0 + \beta_1 Factor1 + \beta_2 Factor2+ \beta_3 Factor3 + \epsilon_i$$
As a next step, they sort these stocks into 5 groups based on $ beta_3 $ and look at the mean return of each group (red rectangle). They also create a "5-1" group, where they subtract groups 5 and 1 from each other.
Now to my question: As you can see in the two red rectancles, both 5-1 groups have a p-value. This really confused me, because I do not know how it is possible to report a p-value on something that is not the outcome of a regression, but rather a subtraction of two outcomes of a regression. Am I aloud to subtract p-values from each other? Because this seems somehow wrong, considering that in this case p-values could even become negative?
Does anyone know how to get p-values in this context or what they could mean in this particular example?
Any help would be highly appreciated, thanks in advance
Paper: Does Volatility of Volatility Risk forecast future stock returns? R.Bu, X.Fu & F.Jawadi, 2018