# Does PCA for yield curve has any tangible value?

I am aware of an abundant literature on Principal Component Analysis (PCA) application for yield curves. All of these papers to me look merely a statistics-oriented results. Most of the papers argue that by "decoding" yield curve by applying PCA, we are able to explain yield curve movements. And the result of application are just 3 PCs, i.e., level, slope and curvature, which do not have any economic interpretation (to the best of my knowledge some authors try to give some economic interpretation, but those do not appear convincing to me).

Question What is the applied use of PCA for yield curve? Is there any real-life example of this?

• It makes a user more comfortable with pricing derivatives assuming 1 factor models - as most curve moments are parallel. Apr 19 at 21:58
• Most of the papers argue that its use is explaining curve movements though.
– Sane
Apr 22 at 8:20
• there are not tradeoffs in it's use and one can use it anywhere one feels it is useful. Ultimately wherever you want to know the joint distribution of rates is where PCA will be useful. Apr 22 at 9:24

My view on this is summarised in my book "Pricing and Trading Interest Rate Derivatives". In it I give a chapter on PCA calculation and demonstrate calculations and applications. But my overall frank assessment as publicised is that I am not a fan of using PCA.

That is not to say it doesn't have merit, I just have the opinion that there are better methods, which supersede it, for various different reasons.

A couple of examples:

Using PCA for risk management?: No thanks, I prefer using VaR related tools under an assumed multivariate normal distribution. The distribution uses exactly the same covariance matrix from which the PCA is calculated but you can do much more (analytically) with VaR analysis which is more relatable to the actual instruments you can trade in a market. You can never, practically trade a PC in isolation so its property of independence to another PC (which is basically one of the main proponents of the theory) is made moot.

Using PCA to generate simulated market movements: No thanks, since the PCA is generated from a covariance matrix, which is a symmetric positive definitive matrix, just use the Cholesky decomposition and a series of normal random variables instead. Easier to do mathematically with the same result.

I should add that I really tried to get into PCA a number of times over the years and try to find a way for it to really work for me. And I tried hard! But couldn't.

One thing I probably would use it for though is if I wanted to create a smooth (denoised) correlation matrix. The poor man's approach sees one selecting the first few PCs and reconstituting a correlation matrix from those. But possibly, if I looked hard enough at research there might be a better way of doing that than using PCA as well. My ignorance in this problem here probably lends PCA a hand.

• What I feel from your answer, you are also skeptical (don't see much value) about usefulness of PCA application in the context of yield curves, right?
– Sane
Apr 22 at 8:13
• It's better than nothing. Would I cultivate a field with horse and plough? Absolutely. Would I if I had access to a tractor and a cultivator? No.
– Attack68
Apr 22 at 15:36
• I see, thank you! But how would you describe uses of PCA in the framework of yield curve?
– Sane
Apr 22 at 17:03
• I work with yield curves every day. I know about PCA and how to apply it. I never use PCA. Surely, that is telling enough for you, along with my answer, as to my opinion on the use of PCA for yield curves?
– Attack68
Apr 22 at 17:58