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2

If you look at changes of the points on the yield curve, then you probably find something stationary - right? Applying PCA on the covariance of these changes makes sense. E.g. you will find out that on PC describes a parallel shift (a change in the yield curve). Look at this question too: What do eigenvalues/eigenvectors of the yield/forward rates ...

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Following @silencer's comment, your formula for variance is wrong. I would suggest that instead of trying to re-invent the wheel, you just use the formula that everyone else uses. So I'd replace your first indented line with $$w^{*}\equiv argmin\left\{ \frac{1}{2}w'\varSigma w-\lambda\left(w'\mathbf{1}-1\right)\right\}$$ which will give you $$... 1 The derivation is correct and given the formula you should get w^{*'} \vec{1} = 1. My guess is that the inversion of the \Omega matrix is numerically badly conditioned. Instead of implementing the formula as it is, have you tried to calculate \vec{1}^{'} \Omega^{-1} and e^{'} \Omega^{-1} only once and rewrite:$$ w^{*\prime} = \frac{1}{2}\left[ ...

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Q #1: I'm not sure if you have the answer quite right. The signs for the loadings are arbitrary, but you cannot take the absolute value. You can multiply by -1. Q #2: It might be helpful to think about what PCA is actually doing. This paper might be helpful: http://arxiv.org/pdf/1404.1100v1.pdf (A Tutorial on Principal Component Analysis by Jonathon ...

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