Why Constant-Maturity Par Yields Improve Treasury PCA
Summary
The document considers whether principal component analysis of US Treasury rates should use cash yields or Treasury futures. It recommends constant-maturity par yields, which keep the maturity of each series stable as bonds and futures delivery baskets change. This helps prevent changes in the underlying instrument from appearing as changes in the yield curve. Par yields also avoid coupon effects that can bias comparisons over time, particularly when coupons change and the curve slopes upward.
For a comparison related to the two-year, ten-year, and bond futures, the answer suggests using par yields at maturities that approximate the contracts’ current cheapest-to-deliver bonds. This is presented as more robust than constructing rolling yield series from the futures. A second answer notes that cash bonds support yield and relative-value analysis, while futures can add a technical view, and suggests combining them depending on the trading strategy. The document provides reasoning and an illustrative tenor choice, but no empirical PCA results or performance comparison; suitable inputs may depend on the strategy and data available.
Key ideas
- Constant-maturity yields avoid breaks caused by changing bonds or futures delivery instruments.
- Par yields reduce distortions from coupon changes when comparing rates over time.
- Par-yield tenors can be selected to approximate the maturities of futures contracts’ current cheapest-to-deliver bonds.
- Cash bonds and futures can provide complementary yield-based and technical signals.
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Full text
# Principal components in treasuries: spot vs futures # Principal components in treasuries: spot vs futures I'm looking to use first few principal components of the US treasury yields for trading, and have choice of using either the data for treasuries themselves, or for the corresponding futures contracts. Would the results be similar, or there are reasons to use one particular instrument? ## Answer by Helin (score 7, accepted) https://quant.stackexchange.com/a/31604 It is preferable to use constant maturity yields (ideally par yields) for running PCA analyses. Using constant maturity par yields has several advantages: - By definition, the yields are of constant maturity, so your results won't be distorted by "rolls." When you use either rolling futures yields or on-the-run bond yields, there could be many breaks in the series as the CTD/on-the-run bond changes over time. Rolling futures are particularly bad. The US contract, for example, can trade like a 15-year note or 25-year bond depending on the interest rate environment. - Par yields are immune from coupon effect. If coupon rates gradually increase over time, the associate yield series would be biased downward if the yield curve is upward sloping (high coupon bonds trade at lower yields, all else equal). This makes it difficult to tell whether bonds are really richening, or perhaps we're just seeing a downtrend because of changing bond coupons. Of course, par rates don't suffer from this problem. As an example, let's say you're interested in looking at how TY (10-year contract) is trading relative to TU (2-year contract) and US (bond contract). You can potentially run a PCA analysis using 1.75y/6.75y/20y par yields (tenors approximate the maturities of current CTDs for the respective futures). The result will be much more robust than if you used rolling TU/TY/US yields. ## Answer by rrg (score 4) https://quant.stackexchange.com/a/31595 This is an interesting exercise and would be compelled to see the results of your data gathering. The principal purpose of treasury note (cash bond) analysis is for yields and the cross-asset class relative valuation where both provide signals. Alternatively, futures provide a technical analysis picture supplementary to yield dynamics. Personally I would attempt to combine both, although it depends on your strategies.
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