I am running a PCA on a set of returns and I would like to cluster the results of the output to group stocks that have similar factor exposures.
However when I run the PCA on the covariance of the returns, the PCA score (values mapped to new plane of PCs) gives me a matrix with dates and the principal components, to cluster on this would cluster on date therefore.
I can cluster on factor coefficients for each stock but then I have found this ignores the variance. For PC1 for instance the variance of loadings is very low compared to PC2 and therefore when clustering using the loadings it simply clusters using mainly PC2 which seem inherently wrong to me?
Or is this still correct and we can assume that because most stocks are loaded in a similar way to the PC1 then the clustering can’t determine much from that PC anyway.
I’m worried that I am missing some of the information from the variance here as PC1 explains 55% of the variance compared with PC2 at 18%!