Found the answer, courtesy of Elaine Lin from Morgan Stanley:
Roll-down and carry allow an investor to estimate the PNL of
a swap over a given horizon assuming an unchanged rate
environment. Below, we calculate roll-down and carry
separately for a receiving fixed position on an interest rate
swap.
As with that of a bond (or any financial instrument), the carry
on a swap is the difference between what the investor
receives (a fixed coupon) and what the investor pays (a
floating financing rate) over the investment horizon.
Implicitly, the carry can be “locked in” at the inception of the
swap by paying on the swap (at the same rate) forward to
the horizon date, and the forward price of this swap should
reflect this carry. That is,
Forward Price = Spot Price - Carry
This identity allows us to easily calculate carry as the
difference between the spot price (0 for an ATM swap) of the
swap and the forward price of the swap at the same rate.
Whereas carry can be determined by today’s market prices,
the roll-down of a swap makes an assumption about the
shape of the curve at horizon. At horizon (e.g., 6m), a 5 year
swap will be a 4½ year swap. The roll-down estimates the
value of the swap (at the current 5 year rate) under the
assumption that the yield curve is unchanged from today.
Therefore, the roll-down is the difference between the value
of this shorter-term (or “rolled-down”) swap and the value of
the spot swap (0 for ATM).
So would it only provide utility to mention a rolled-down swap with a "rolled-down" date in relation to a future date which would then be the ATM spot swap? Something like: There is a negative difference in the roll-down between the 4.5 yr YTM swap and the spot rate which is around 3yrs since contract inception which provided it was 5yrs in length?
Sed rerum facere ratione repellendus laudantium quia nobis. A blanditiis at commodi expedita a molestiae. Atque aut dolores et aut laudantium quos. Reprehenderit voluptatibus qui odio harum architecto eaque odit.
Iste quaerat libero quia ea deleniti et fugit. Qui vero unde sequi et. Laborum nisi voluptatem ipsam reprehenderit natus officiis eos. Optio mollitia et iste ut iste. Dolores quo voluptas sed dolorem provident repellat. Esse velit tempora neque iure quaerat ducimus quo consequatur.
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Found the answer, courtesy of Elaine Lin from Morgan Stanley:
Roll-down and carry allow an investor to estimate the PNL of a swap over a given horizon assuming an unchanged rate environment. Below, we calculate roll-down and carry separately for a receiving fixed position on an interest rate swap.
As with that of a bond (or any financial instrument), the carry on a swap is the difference between what the investor receives (a fixed coupon) and what the investor pays (a floating financing rate) over the investment horizon. Implicitly, the carry can be “locked in” at the inception of the swap by paying on the swap (at the same rate) forward to the horizon date, and the forward price of this swap should reflect this carry. That is, Forward Price = Spot Price - Carry
This identity allows us to easily calculate carry as the difference between the spot price (0 for an ATM swap) of the swap and the forward price of the swap at the same rate. Whereas carry can be determined by today’s market prices, the roll-down of a swap makes an assumption about the shape of the curve at horizon. At horizon (e.g., 6m), a 5 year swap will be a 4½ year swap. The roll-down estimates the value of the swap (at the current 5 year rate) under the assumption that the yield curve is unchanged from today. Therefore, the roll-down is the difference between the value of this shorter-term (or “rolled-down”) swap and the value of the spot swap (0 for ATM).
So would it only provide utility to mention a rolled-down swap with a "rolled-down" date in relation to a future date which would then be the ATM spot swap? Something like: There is a negative difference in the roll-down between the 4.5 yr YTM swap and the spot rate which is around 3yrs since contract inception which provided it was 5yrs in length?
Sed rerum facere ratione repellendus laudantium quia nobis. A blanditiis at commodi expedita a molestiae. Atque aut dolores et aut laudantium quos. Reprehenderit voluptatibus qui odio harum architecto eaque odit.
Iste quaerat libero quia ea deleniti et fugit. Qui vero unde sequi et. Laborum nisi voluptatem ipsam reprehenderit natus officiis eos. Optio mollitia et iste ut iste. Dolores quo voluptas sed dolorem provident repellat. Esse velit tempora neque iure quaerat ducimus quo consequatur.
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