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I am trying to understand the differences between carry vs roll-down on a zero-coupon interest rate swap.

Lets say we have a 10 day ZC IRS, meaning we will only swap once on maturity. We are a payer of the swap.

  • Current 10-day spot rate: 3%
  • Current 9-day spot rate: 2.9%
  • Current Overnight rate: 3.2%

What is the carry on this trade? What is the roll-down?

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(This is my opinion; someone is likely to disagee).

I like to think of the carry as the predictable part (e.g. the coupon that accrues daily) and the rolldown as the stochastic part (the curves moved - maybe the forwards realized, maybe not. A good estimate of what it might turn out to be as to reprice for the next day assuming all forwards are realized.

I would therefore view a zero-coupon as having all rolldown and no carry.

You could view the financing cost of the swap as carry.

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Most people would say: carry = the 1day p/l resulting from overnight rate being different from coupon = (3.2- 3.0)* 1day accrual. Roll down = p/l on remaining swap assuming spot rates remain the same = (2.9-3.0) * 9 days accrual.

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