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