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

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.

  • Thanks for that. I meant an annual rebalancing. I'm more questioning the methodology of calculating roll in relation to a bond portfolio. Assuming a bottom up approach is computationally unfeasible, I use the simplifying assumption that the bond portfolio is duration targeted, so when 5year bonds becomes 4year bonds, 4year bonds are sold and proceeds used to buy 5year bonds again to capture that price appreciation ie -D*(change in Treasury yield). Is this assumption sound? But what about carry assuming costs of borrowing are not taken into consideration, is it just the yield? – hauterob Jun 8 at 8:08

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.

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