Many have told me that it is a good idea to look at the third principal component (PC) of yield curve movements, as well as third and fourth PC of G10 currencies. They claim these PCs represent "pricing noise", and thus should mean-revert.

Do you have experience with these strategies? Are there relevant papers I should read?


1 Answer 1


Within the fixed income space, there's a lot of literature on PCA trading.

The first 2-3 principal component factors (PCs) can typically explain 90-99% of the total variances in yield curve movement. It's also nice, because the first PC looks like a change in the overall level of the yield curve, the second PC looks like a slope change, while the third factor corresponds to change in the overall curvature of the yield curve. So if you neutralize the first 2-3 PCs, you can indeed trade on the mean-reverting behavior of the residuals.

PCA is most commonly used for structuring so-called "butterfly trades." In this, you're neutralizing the first two PCs (level and slope) and trade on the third PC (curvature). For example, after running a PCA on 2y, 5y, and 10y yields, you may conclude that 5y yields are too high relative to 2- and 10-year yields (i.e., 5-year bonds are "cheap"). In this case, you'd buy 5-year bonds, while simultaneously shorting 2- and 10-year bonds. PCA comes into play, because for each unit of 5-year bonds, you have to choose appropriate units of 2- and 10-year bonds ("risk weights") so that the the first two principal components are neutralized, allowing you to trade any abnormalities in the third principle component.

The best literature I've come across is Salmon's Principles of Principal Components, which is easily available by Googling. It also includes extensive backtesting results from butterfly trading. Another (not as good but still pretty good) one is Morgan Stanley's "PCA for Interest Rates."

I would point out that trading on PCA mechanically is usually not a great idea. A lot of macro-factors can disrupt "well established" patterns in truly splendid ways. After the financial crisis, 5- and 7-year bonds looked rich based on many statistical methods, PCA included, but they just kept getting richer...

  • $\begingroup$ Thanks for the answer. Is it possible that the speed of mean reversion just went lower for some factors? $\endgroup$ Feb 3, 2016 at 14:59
  • $\begingroup$ @SlowLearner It's not necessarily about mean reversion speed. It's more about what it reverts toward. Being macro-aware when trading flies is not a new concept. Traders always know that these trades work well only when the macro environment is stable. Until 2014, the belly part of the yield curve (5s, 7s) is rich because of QE. No model would've predicted it in 2007. $\endgroup$
    – Helin
    Feb 3, 2016 at 21:19
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    $\begingroup$ Where is this Morgan Stanley paper? I cant find it online $\endgroup$
    – Trajan
    Feb 2, 2018 at 18:10
  • $\begingroup$ @Helin - Do you happen to have PCA for Interest Rates handy? I'd be interested in learning about it. $\endgroup$ Jun 24, 2018 at 16:31

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