![]() ![]() ![]() Copy these into excel and plot f1, f2 and f3 against yields and you’ll see why f1 appears almost parallel (upward shift of about 44 bp), explains 95.22%, factor f2 is a slope change and so on. see how Factor 1 (f1) is pretty much the same value for all y1 … y9, that’s how you interpret this as a parallel shift. We solved this very problem in a class I took last term. It’s also common to use SAS, S-Plus and so on. It is pretty safe to assume that the first factor represents parallel shifts, but make sure you don’t have any negative factor loadings just to be sure. mean what I just said - check the factor loadings. But beware, because funky things can happen with the data, so don’t assume that factor 2, 3, etc. Usually if you have > 3 factors, the next ones represent higher scale harmonics on the yield curve. If you have N points on the curve, you will have potentially N factors come out of your PCA analysis. After that, the butterfly or bulging of the curve is the most common event, so it’s assumed (though you can check by looking at the factor loadings) that this would be factor three. After this, the curve most likely steepens and/or flattens, so the second factor probably explains this. So the idea is that a parallel shift in the yield curve should affect all maturities more or less the same way, so probably it explains the most variability in yields, and therefore the first factor will most likely represent parallel shifts. The third does the same thing after taking out all variability that’s explained by the first two factors, and so on. The second factor then finds the common factor that explains the largest amount of the remaining variability (after taking out the contributions of the first). In other words, the first component represents a kind of “common factor” explaining changes in all variables simultaneously. The Principal Components basically sort out the directions of changes in descending order of maximum variance. ![]()
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