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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?

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There are three sources of carry for bond futures -

  1. 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.
  2. Implied financing rate, for which you need the term repo rate for the CTD.
  3. 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.

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Carry and roll-down are two conceptually different measures which are often used interchangeably but they should not.

If you are just interested in the carry, then in your case 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. The 1-day forward yield should be calculated by using the future implied repo rate.

In this post I discuss what carry and roll are, and look 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/

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