Using Yield-Curve PCA to Study On-the-Run Bonds and Repo Rates

Summary

The document considers whether principal component analysis of on-the-run Treasury yields and overnight SOFR can estimate how yield-curve changes relate to repo rates. The proposed setup includes several Treasury maturities alongside SOFR. A move at one maturity could be expressed through the curve's principal components, then mapped to SOFR; assuming repo remains a constant spread over SOFR would provide an implied repo response.

The author questions whether this setup is sound and notes a potential modeling issue: on-the-run yields and SOFR may reflect related discounting information. Fitting a discount curve from many coupon-bearing bond points may effectively recover a SOFR-based curve, making the interpretation of PCA inputs less straightforward. An alternative suggested is to derive the discount curve first and then include SOFR in the analysis. No data, fitted components, or empirical results are provided, and the constant repo spread is an assumption that would need testing; the text is a methodological question rather than a validated estimate.

Key ideas

• PCA can summarize co-movements across Treasury yield maturities and overnight SOFR.
• A maturity-specific yield move can be represented through principal components, but its estimated SOFR association is not automatically causal.
• Inferring repo-rate changes from SOFR changes requires the assumption that the repo spread over SOFR stays constant.
• On-the-run bond yields and SOFR discounting may contain overlapping information, complicating the interpretation of the PCA inputs.
• The proposed alternatives are questions for empirical assessment, not demonstrated findings.

Tags

# Impact of ONTR on repo


# Impact of ONTR on repo












How would one estimate the impact of a change in the yield of the on-the-run (OTR) bonds on the repo rate?

One approach I considered is using PCA. I would run PCA on the OTR yield curve (including the 2-, 3-, 5-, 7-, 10-, 20-, and 30-year OTR points) along with the overnight SOFR rate. By doing this, I could decompose, for example, a 1 basis point move in the 30-year point as a combination of PC1, PC2, and PC3. This would allow me to quantify how much SOFR is affected by a move in the 30-year point. Then, assuming the repo rate is a constant spread over SOFR, I could estimate how much the repo rate is affected by changes in the OTR yield curve.

Does this method seem sound, or are there any other robust approaches I should consider?

Ultimately, the OTR curve is essentially a SOFR curve since all cash flows are discounted using SOFR. When attempting to derive the discount curve from the OTR points, I effectively input an overspecified curve due to the inclusion of all the OTR points (because of the coupon cash flows), resulting in a discount curve that is the SOFR discount curve. Therefore, including the overnight SOFR rate initially seems accurate to me, though I may be overlooking something. Perhaps it would be better to first derive the discount curve from the OTR points, then add the overnight SOFR rate, and perform PCA on this adjusted curve.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.