Why Constant-Maturity Treasury Series Avoid On-the-Run Duration Jumps

Summary

The document compares constant-maturity Treasury series with yields on actual, currently issued on-the-run bonds. A constant-maturity series can be constructed from a zero-coupon discount curve, allowing analysis across a longer history than the available set of individual bonds. Its key practical benefit is continuity: the series represents a fixed maturity rather than switching to a newly issued bond when the on-the-run security rolls over.

The answers point out that an actual bond’s duration changes over time, its yield can jump when the on-the-run issue changes, and its observed yield may be affected by liquidity. A chart is described as showing similar duration trends for par bonds and rolling on-the-run Treasuries, but with jumps in the latter. The discussion does not provide the chart’s underlying data or a derivation proving that curve construction itself accounts for modified duration. It offers a brief qualitative explanation of the continuity and liquidity advantages, not a detailed treatment of duration measurement.

Key ideas

• A constant-maturity Treasury series can be built from a zero-coupon curve.
• A fixed-maturity series supports historical analysis beyond the lifetimes of individual bonds.
• On-the-run bond duration changes over time, and rolling to a newly issued bond can create a yield jump.
• Observed yields on actual bonds can reflect liquidity as well as interest-rate changes.
• The document describes similar duration trends but gives no underlying data or formal derivation.

Tags

# Why do constant maturity bonds account for modified duration?


# Why do constant maturity bonds account for modified duration?












One can create a constant maturity treasury (CMT) by building a zero coupon discount curve and generating constant maturity bonds from that curve. This allows one to look further back than is possible with the current 'actual' existing bonds.

I was told that CMT bonds account for modified duration, whereas actual bonds do not. The CMT bond accounts for modified duration precisely because it is created using a zero coupon curve.

Why is this?

## Answer by XYQ (score 1, accepted)

https://quant.stackexchange.com/a/43330

if you use existing on the run bond yield for analysis. There are at least three ptoblems.

- The duration is change slightly every day

- on the run roll cause a yield jump

- actual yield influenced a lot by liquidy

## Answer by Helin (score 1)

https://quant.stackexchange.com/a/43283

I'm just guessing, but they might be talking about the continuity of time series. The chart below shows the modified durations of 10-year par bonds and rolling 10-year on-the-run Treasuries. As you can see, they have the same trends (as expected), but you don't have those jumps (caused by new on-the-run 10-year issues being issued).

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.