I am wondering if there is a considered floor to the percentage variation the 1st principal component must explain in general for PCA - ie. any lower and it is not worth doing PCA at all? Is the floor near 75%, 80% or should the 1st 3 explain a minimum of 90% or what?
As a follow on, if I have 10 X variables (index & sector returns) and only 6 are highly correlated (I take a correlation above 0.8 to be highly correlated - or is that too high?) should I just do PCA on those 6, then combine the 1st two principal components with the 4 remaining original variables and use that as my X for regression?
What I was doing was doing PCA on all 10 variables, taking the 1st 2 or 3 principal components, regressing those on Y (which is a single stock's return) then taking those PC's betas and matrix multiplying them by the eigenvectors to back out sensitivities to the original 10 factors but I am left with the situation of not knowing if all 10 factors are significant (all I know is that the 1st 2 PCs are significant)