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Sounds like PCA is not the approach you're looking for. If you're looking to transform a risk vector in terms of securities V into a risk vector in terms of securities W, then the basic approach would be to perform a linear regression of V against W. The resulting regression coefficients will form a matrix B which will give a change of basis between V and W. ...


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A couple quick thoughts. Do the PCA on changes or log-changes in your series. That is often how PCA is conducted in fixed-income settings. You're large move in wights corresponds to outlier moves in the blue series. Given the assumptions of a PCA, I would consider whether your dataset has suffered from any breakpoints, regime changes or other rare events ...


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If X contains several highly correlated indexes, the first PCA will be a linear combination of them and its weights will be similar because at the end they represent the same underlying phenomena. When you do a regression with the same variable in Y and X you will have perfect match of that specific regressor by construction. The real problem of colinearity ...



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