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.