Carry and slide for Swaps

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).