Separating Bond Index Carry from Roll-Down Return
Summary
The document explains how to think about carry and roll-down when modeling a bond index. It distinguishes carry, the bond’s return effect under an unchanged yield curve, from roll-down, the part of carry associated with moving along the curve as time passes. For an index, it proposes calculating roll-down and carry for each constituent bond, then aggregating each set of returns using the bonds’ index weights.
The answer also cautions that a roll-down estimate depends on the chosen horizon. A one-day estimate cannot necessarily be extended linearly to a year because the yield curve’s shape affects the result over time. It recommends choosing a horizon closer to the expected trade duration, with three months offered as an example. The discussion does not provide a worked numerical example, address index rebalancing or constituent changes, or fully specify how each bond’s carry and roll-down should be calculated; those choices must be defined for the intended model.
Key ideas
- Carry describes the return effect under an unchanged yield curve.
- Roll-down captures the effect of moving along the yield curve as time passes.
- Calculate carry and roll-down for each bond, then aggregate them using index weights.
- The estimated roll-down depends on the selected horizon and the curve’s shape.
- Choose a measurement horizon that reflects the expected duration of the trade.
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Full text
# Bond fund's roll and carry
# Bond fund's roll and carry
This is a question about modelling the returns of a bond index. Understand there's quite a bit about the roll and carry of an individual bond, but what about a bond index.
Roll I would calculate the bond's roll (assuming no change in yields) by multiplying -dur(index) x change in yields(index)T to T-1. Is this financially sound?
Carry How would this be modelled? Should I instead be modelling the annualised geometric valuation loss?
Thanks
## Answer by vanguard2k (score 1)
https://quant.stackexchange.com/a/41590
Carry is most often defined as the effect on the bond if the yield curve does not change.
Roll down is seen as a component of carry that results from changes on the position of the yield curve.
See this reference on the topic.
## Answer by Attack68 (score 0)
https://quant.stackexchange.com/a/40208
Heres a note about roll and carry for bonds Question on pure carry for two bonds.
For a bond index you calculate the roll-downs of each bond in the index in vector, `R` and calculate the carry in each of the bonds in vector, `C`, and you also know the weight of the respective bonds in the index, in vector, `w`. Then the constituent roll and carry respectively is:
$$r = \frac{R^Tw}{||w||}, \quad c = \frac{C^Tw}{||w||}$$
where I included the norm of the weight vector just in case your weights didn't sum to one.
Note that you reference T and T-1 for roll-down. This is a 1-day measure of roll-down, you can define any measure over any time period, and a 1-year metric is not necessarily the same as 365*1-day metric due to the arbitrary shape of the curve. The general advice is use a time measure more akin to your trade duration. I typically use 3-months since my trade turnover is likely to be something along those lines.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.