Anyone here pretty familiar with principal components (PCA) or interest rate/credit models might be able to help me out with some questions.
1) Say you have log excess returns for a bunch of stocks and the log risk-free rate of return as a matrix you perform PCA on. Since you choose factors in PCA based on how much variance they explain, does mean that log risk-free returns would normally not be one of the more important factors? If that's the case, what's the normal procedure in practice? Model the risk-free separately?
2b) Let's say you have the above, plus a bunch of bond yields (let's say the changes in government curve + changes in YTMs for a bunch of corporate bonds). I would guess this PCA might pull out factors that might be correlated with the market, two important government yields, and a corporate bond risk factor. There might be some non-linearity when trying to explain corporate bonds returns. But PCA assumes linearity. If I shouldn't include these in PCA, any idea what I should do instead?
3) In Matlab, the coefficients from the pca functions do not sum to 1. This means that the factors you produce might have high correlations with an individual security, but they probably have much higher variance. So for instance, the interest rate factor might be highly correlated with one of the yields, but have quite different variance. Is there any advantage to making the coefficients sum to 1 so that the factors more closely reflect the underlying securities they are highly correlated to? |
发表于 2011-9-30 18:49
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