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
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.
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.
