Coupon Bond Returns: Carry, Roll-Down, Mark-to-Market, and Pull-to-Par

Summary

The question asks how to separate the approximate return of a coupon-bearing bond into yield income, roll-down, duration-driven price change, and pull-to-par effects. The response gives a compact decomposition: return is associated with yield minus repo over the accrual period, roll-down multiplied by the bond’s DV01 at the end of the term, and mark-to-market change multiplied by that DV01. It then splits yield minus repo into yield minus coupon and coupon minus repo, describing these as pull-to-par and cash-flow carry, respectively.

This provides a practical outline for organizing bond return attribution, but not the requested mathematical derivation. It does not define the precise roll-down or mark-to-market inputs, specify conventions, or explain how the terms behave under curve shifts and coupon dates. The expression should therefore be treated as a high-level decomposition that needs a consistent pricing framework and sign conventions before implementation or comparison across bonds.

Key ideas

• Bond return attribution can include carry, roll-down, and mark-to-market components.
• The response expresses roll-down and mark-to-market contributions using end-of-period DV01.
• Yield minus repo is split into yield minus coupon and coupon minus repo.
• The proposed pull-to-par and cash-flow carry labels are a concise outline, not a full derivation.

Tags

# Decomposing Returns of Coupon Bonds: Yield, Roll-Down, Duration, and Pull-to-Par Effects


# Decomposing Returns of Coupon Bonds: Yield, Roll-Down, Duration, and Pull-to-Par Effects












I'm currently exploring how to decompose the return of a coupon-bearing bond into meaningful components such as yield return, roll-down return, duration return, and ideally, pull-to-par effect.

For zero-coupon bonds, the decomposition was already posted here.

I’m looking to extend this decomposition to coupon-bearing bonds. The approximate return over one period is given by (as derived here): $$ R \approx y−\frac{P_{n−1}(y)}{P_n(y)}D_{n−1}(y)\Delta y $$ I'm trying to expand the second term to isolate and identify the roll-down return, the duration return and the pull-to-par effect, which is naturally embedded in coupon-paying instruments as they approach maturity.

Is there a decomposition that clearly separates these effects for a coupon bond along with a mathematical derivation from the defined R?

## Answer by user68819 (score 1)

https://quant.stackexchange.com/a/83845

Return = (yield - repo)× price × accrual + roll down × dv01 at term + mtm × dv01 at term.

Yield minus repo can be broken into yield minus coupon + coupon-repo. First is the pull 2 par, second is cash flow carry.

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.