Carry and Roll-Down in Forward-Starting Interest Rate Swaps

Summary

The document distinguishes carry from roll-down for forward-starting interest rate swaps. Before the swap begins, its floating leg has no certain payments over the investor’s holding horizon, so the response describes the position as having no earned carry when that horizon ends before the forward start. Its value can still change as the start date approaches and the forward swap tenor shortens.

The example considers a forward swap held for three months: a six-month-starting five-year swap becomes a three-month-starting five-year swap. Under an unchanged yield curve, the roll P&L is approximated by the difference between the two swap rates multiplied by the later swap’s DV01. This is a simplified illustration rather than a general valuation formula; actual outcomes depend on curve movements and instrument conventions, and the document does not provide numerical rates or a broader treatment of swap cash flows.

Key ideas

• A forward-starting swap may earn no carry over a horizon that ends before its start date.
• As time passes, the forward start moves closer while the swap’s stated tenor remains the same.
• Roll-down P&L can be illustrated as the rate difference across the rolled positions times the later swap’s DV01.
• The example assumes the yield curve remains unchanged.
• Actual results depend on market moves and swap conventions beyond the simplified illustration.

Tags

# Carry and Roll on Interest rate Swap


# Carry and Roll on Interest rate Swap












Only spot starting swaps have a known fixing, F(0,6m). There’s no carry in a forward starting swap as there’s no certain payments (on the float leg).

This is claimed in an excellent research note by Lars Peter Lilleøre in a research note: https://corporate.nordea.com/api/research/attachment/2796

i am having trouble visualizing:

For forward starting swaps, there’s no carry, and roll simply entails reducing the forward period. That is, Swp(6M,5Y) becomes Swp(0d,5Y). Similarly, e.g. Swp(1Y,5Y) becomes Swp(6M,5Y).

This is on page 3.

I will appreciate it if someone can either explain or point me to something basic on this.

## Answer by user68819 (score 1)

https://quant.stackexchange.com/a/79747

A fwd starting swap only has roll down as there is no income earnt if your horizon is less than the fwd start. If I receive 6m5y with a horizon of 3m, in 3m time my 6m5y is 3m5y and under the assumption of an unchanged yield curve my roll pnl will be (6m5y-3m5y) × dv01(3m5y)

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.