I have run a PCA on some returns to get a set of factors. All is good except that the first PC seems to be the short of the market, it has a correlation of -0.9 with the S&P500 but all the loadings are negative (except one which is very small and basically +0).
I am confused as to why the PC is negative and all the loadings are negative, I assume it is ok to switch BOTH signs also?