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One of the applications of Principal Component Analysis in Finance is to analyse the shape of the yield curve.

But what conclusions can be drawn exactly from performing this exercise? Does it help us to build a better yield curve? How are we able to better manage risk if we do it?

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You can see my remark above for some more words on PCA for the yield curve and an interesting paper. About the question whether it helps us to creat a risk model: PCA on the yield curve changes (!) tells us:

  • what are dominant moves (it turn out it is a pralell-shift, steepening and curvature change)? This gives us a picture and language to think and speak about yield curve changes. Recall those structured products that were sold before 2008 and mabye some still are sold: steepeners and such.
  • this moves are uncorrelated. Thus is makes sense to think of the current yield curve and then of scenarios when uncorrelated changes act on it. You might want to have this invariant element in your model.

These are the main points: uncorrelated shape changes.

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