Components of Carry and Roll-Down in Bond Futures
Summary
The document distinguishes several effects relevant to the daily economics of a bond futures position. Underlying carry and yield roll-down can be estimated from the cheapest-to-deliver bond, including its coupon accrual. Financing is another component and requires the CTD’s term repo rate or the futures-implied repo rate when estimating a one-day forward yield. The answers also identify embedded short options in a long futures position, including switch, end-of-month, and wild-card options.
The replies differ in terminology: one describes these as sources of futures carry, while another emphasizes that a futures contract itself receives no income and distinguishes carry from roll-down. They agree that CTD behavior is central, subject to the simplifying assumption that the CTD remains unchanged. The option effects are often smaller than underlying and financing effects, but the answers caution they can matter. The discussion offers conceptual guidance rather than a complete calculation recipe for all contract conventions or CTD switches.
Key ideas
- Underlying coupon accrual and yield roll-down can be assessed using the cheapest-to-deliver bond.
- Financing effects depend on repo rates, including the futures-implied repo rate for a forward-yield calculation.
- A long bond futures position embeds options whose theta may contribute to its economics.
- Carry and roll-down are distinct concepts, and the answers use the term carry differently.
- Calculations that assume a fixed CTD may miss effects when delivery economics change.
Tags
Full text
# How to calculate the daily carry on a bond future? # How to calculate the daily carry on a bond future? I have been calculating daily carry on a normal bond as the difference in yields from one day to the next (roll down basically), interpolating the yield on one day, and interpolating it for the previous business day. My question is, how do we calculate this for a bond future? Is it sufficient to take the Cheapest To Deliver (CTD) and do the same calculation as above? ## Answer by Chris Taylor (score 5) https://quant.stackexchange.com/a/32995 There are three sources of carry for bond futures - - Carry on the underlying (coupon accrual and yield roll-down) for which you just compute the carry on the cheapest-to-deliver as you suggest. - Implied financing rate, for which you need the term repo rate for the CTD. - Theta on the various short options inherent in a long futures position (switch option, end-of-month option, wild-card option) Of these, the first two are generally the dominant effects, but you can't always ignore the third. There have certainly been periods in the past where the yield pick-up on a long futures position compared to a position in the CTD has been worth 50-100 basis points annually. If you want to go into more detail, I suggest that you take a look at one of the many questions on treasury futures on this site, e.g. here or here or here, or the book The Treasury Bond Basis which is probably the best reference on the subject. ## Answer by Riccardo (score 1) https://quant.stackexchange.com/a/37788 Carry and roll-down are two conceptually different measures. From the question it is not clear which one you are attempting to calculate. If you are indeed just interested in the carry [as per the subject], then it is the yield difference between the 1-day forward yield and the spot yield of the CTD, as the forward is priced to be arbitrage-free. Note that the 1-day forward yield should be calculated using as repo rate the future implied repo rate. [we make the simplifying assumption that the CTD is set in stone] This post discusses what carry and roll are, and looks at the bond future's asset swap as well: http://swapsball.net/how-to-calculate-carry-and-roll-down-for-a-bond-futures-asset-swap/ ## Answer by user68819 (score 1) https://quant.stackexchange.com/a/77388 Carry is a concept which manifests due to income received. By definition a futures contract has no carry..as there is no income received. A spot starting coupon bond however will have carry, roughly the difference between the coupon and repo rate rec'd. The future will roll at a similar rate to the ctd.
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