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was working on a project and could use some help. New to the community and looking fwd to being an active part of it.

My question is, let's say we have a vector of securities V, and it trades with some correlation to another vector of securities W. I'm trying to figure out what the best way is to rebucket the risk in V to W equivalents. I tried running a PCA on V and W but am having trouble standardizing the variables. I'm also worried that I might be "overfitting" my dataset a little. Any guidance is appreciated.

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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.

Note that there will in general be some residual "unexplained" risk, i.e. part of the variation in the securities V will not be explained by variation in the securities W.

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