Why Two-Factor Yield Models Often Suit Bond Futures Basis Analysis
Summary
The document explains why practitioners may use two yield factors, typically level and slope, when analyzing bond futures and deciding which deliverable bond is cheapest to deliver (CTD). A model with more factors could represent more yield-curve movements, but estimating the volatilities and correlations of every bond in a basket reliably is difficult. The answer says principal component analysis (PCA) often captures most yield variation with the first two components, while individual bond richness or cheapness can be modeled separately against a fitted curve or on an asset-swap basis.
The author favors the two-factor approach partly because it is easier to interpret and use to manage or hedge duration and curve exposure. The document gives no independent data or tests to support its variance-capture range, and presents this as personal experience. It also cautions that basis analysis depends on assumptions about implied volatility, newly issued bonds, repo specialness, and central bank activity; these effects may matter more than higher PCA factors. The argument concerns yield-factor models and explicitly distinguishes them from two-factor short-rate models, which the answer says perform poorly for this purpose.
Key ideas
- Two yield factors can offer a practical balance between model complexity and interpretability in bond futures analysis.
- PCA can capture much of bond yield co-movement with the first two components, according to the answer's practitioner experience.
- Bond-specific richness or cheapness can be modeled separately from broad curve movements.
- Implied volatility, new issuance, repo specialness, and central bank activity can materially affect futures basis and CTD analysis.
- The discussion concerns yield-factor models and cautions against conflating them with two-factor short-rate models.
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Full text
# Why is two-factor model so popular for bond futures? # Why is two-factor model so popular for bond futures? Given that which bond in the basket becomes CTD depends massively on idiosyncratic moves among different bonds, should we not be always using N factor model instead of 2 Factor model? By using only 2 Factors we are only capturing Slope and Level changes but ignoring curvature and other higher order movements which should, in theory, be also very important for determining CTD, especially when we have lots of closely contending bonds. By 2 Factor model, I mean modeling yields using first two factors only. ## Answer by Helin (score 5) https://quant.stackexchange.com/a/14770 There's always a balance between model complexity and interpretability. Of course, it'll be great if we can perfectly capture the comovement of all the bonds in the deliverable basket, but that would require the volatilities of all the bond's yields and the correlations amongst all these bonds as well -- it's not easy to come up with reliable assumptions for these... Two-factor models typically depend on PCA to capture the co-movements of bond yields. My personal experience is that this works well enough -- in most environments, the first two principle components would capture 85-99% of the variances already. As to the residual, instead of thinking about "changes in curvature," I'd rather focus on the relative richening/cheapening of individual bonds, either relative to a fitted bond curve or on asset swap basis. This can be easily incorporated into your model. At the end of the day, these models are meant to help with trading decisions, and 2-factor models are very easy to "think through." Personally, when looking at basis, I'd either take the duration/curve risks or hedge them out. This can be done very easily within a 2-factor framework. Finally, there are so many intricacies involved when modeling bond futures/basis: - Are you using the correct implied volatility? - How do you model bonds that haven't even been auctioned yet? How rich should these issues be trading relative to current on-the-runs? - Will the CTD and near-CTDs trade special in the repo market? - Is the fed active and thus will repo rates increase/decrease substantially? All of these factors can easily dominate the 3rd or 4th PCA factors... P.S. I'm assuming you're not using one of those 2-factor short-rate models, right? Those don't work very well..
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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.