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Bond Roll-Down Return Versus Pull-to-Par

Article Quant Q&A · Author: B R O
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Summary

The document asks whether a premium bond necessarily has negative roll-down return, as several cited explanations claim. It distinguishes that claim from pull-to-par: on an upward-sloping yield curve, a bond that ages into a lower-yield maturity point may gain value from the curve’s shape, while a premium bond may lose value as it approaches face value.

The question proposes that these effects can offset one another, and that a sufficiently steep curve could make the combined price change positive even for a premium bond. It offers no answer or supporting calculation, so the distinction remains unresolved in the text. The discussion is a useful prompt to separate curve roll-down from pull-to-par when analyzing bond returns; actual effects depend on the yield curve and the bond’s characteristics, which the document does not specify.

Key ideas

  • The document questions whether premium status alone determines the sign of roll-down return.
  • It distinguishes a possible gain from moving along an upward-sloping yield curve from pull-to-par.
  • A premium bond may experience a negative pull-to-par effect while benefiting from positive curve roll-down.
  • The document poses the possibility that a steep curve could outweigh pull-to-par but does not establish it.

Tags

Fixed incomeCarryStatistics
Full text
# True or false: roll-down return is negative when a bond is trading at a premium


# True or false: roll-down return is negative when a bond is trading at a premium












These three sources all say that the bond roll-down effect is negative if the bond is trading at a premium:

- https://www.investopedia.com/terms/r/rolldownreturn.asp

- https://corporatefinanceinstitute.com/resources/fixed-income/rolling-down-the-yield-curve/

- https://www.wallstreetoasis.com/resources/skills/finance/rolling-down-the-yield-curve

It seems to me this is mixing up roll-down and pull-to-par. As long as the yield curve is not inverted (i.e. is upward sloping to the right), then as time passes, the yield of the bond decreases. Doesn't that mean that roll-down (isolated from the pull-to-par effect) has a positive effect on bond price, regardless of whether the bond is at a premium or discount?

If a premium bond's price is declining over time with no change to the yield curve, couldn't that simply mean that the pull-to-par effect (negative) is stronger than the roll-down effect (positive)?

And, if the yield curve is steep enough, couldn't that make the roll-down stronger than pull-to-par, meaning that a premium bond's price could increase?

Or, since all three sources above agree, maybe I'm just missing something important. What is it?

Quote from the first source above:

> Roll-down return works in two ways. The direction depends on whether the bond is trading at a premium or at a discount to its face value.

> If the bond is trading at a discount, the roll-down effect will be positive. This means the roll-down will pull the price up towards par. If the bond is trading at a premium the opposite will occur. The roll-down return will be negative and pull the price of the bond down back to par.

Thanks. This is my first question in this community.

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.