BC_MBA_student

1 - Depends what you're trying to do with the result of the PCA. If you're trying to cluster your securities based on their exposures to the difference PCAs, then you don't need to worry about the risk-free rate at all. If it's important, it will come out as one of the dominant Eigenvectors.

2 - If the linearity in the PCA is troubling you, then use ICA ( independent component analysis). that's not a function in Matlab, you'll have to program it, but it's pretty easy to program ( a day maybe max). ICA does not minimize variance, but rather looks at maximizing independence using Kurtosis as a measure of independence.

3 - There is no value in having the coefficients sum to 1 ( assuming the PCA is not your end point as I said earlier) and that you're using it as a way to cluster your universe.

I'm not sure what you're doing but this whole PCA thing been beaten to death sine the mid-80s, so unless you have access to some new data, don't waste too much time on it.