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I've been tasked with researching trading strategies relating PCA to trading fixed income futures instruments. Apparently PCA is frequently used in this area. I'm just looking for some references for obtaining a basic idea of what a strategy might look like. I'm not looking for a winning strategy -- just an outline of how PCA might be useful in generating trading signals. I understand the mathematics behind PCA and have used it in other areas, but its applications to finance are new to me.

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One of the best pieces ever written on this topic is Salomon's "Principles of Principal Components," which is readily available on the Internet. I won't go into the details, since this paper is ridiculously comprehensive, but the fundamental idea is straightforward -- if you run a PCA based on yields, the first three components capture most of the variances, with the three factors roughly interpreted as the level, slope, and curvature of the curve.

The most widely used application for PCA is butterfly trading (e.g., you may buy the TY contract against FV and WN; or you may buy EDZ6 against EDZ5 and EDZ4). PCA allows you t compute the "risk weights" needed so that the structures are neutral to the first two principal components. This allows you to focus on trading the curvature of the yield curve, without taking on level/slope risks.

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  • $\begingroup$ Followup question: I've read and heard this claim that the first three factors correspond to level, slope, and curvature. Is this a mathematical fact, or an empirical observation? I find it hard to see why that should be the case mathematically, although it doesn't seem too farfetched. $\endgroup$ – c12345 Jan 6 '15 at 20:46
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    $\begingroup$ It's an empirical observation, but very much a result of how yield curve is traded & behaves. If do decompose bond portfolio returns over long horizons, you'll almost always find that the duration (i.e., yield level) pretty much is the single most important factor; it is also what people talk about the most ("10-year yield did BLAH today"). Slope is definitely the next thing that's on people's mind ("The yield curve bull flattened/bear steepened/etc. today). Curvature is almost never mentioned in the press, and is indeed a much smaller factor in driving daily yield curves movements. $\endgroup$ – Helin Jan 6 '15 at 21:22

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