Carry and Roll-Down: back to the basics

Interest Rate Traders and salespeople talk about carry and roll-down all the time. It is useful to remember what they are talking about.

1. Upfront Carry:
1. For a 10-year receive fixed swap, the 1 year carry is the net present value of a 10-year swap less the net present value of a 9-year swap starting 1 year from now.
2. Upfront roll-down:
1. For a 10-year receive fixed swap, the 1 year roll-down is the net present value of a 10-year swap and less net present value of a 9-year swap today.
2. Typical documentation will have carry and roll-down for various swap lengths: 1M, 2M, 3M and so on. So a 1 year carry can be provided as 0.45 $ per 100 $ of notional or some other dollar convention.
3. Running Carry:
1. the Upfront Carry divided by the PV01 of the forward starting 9-year swap.
4. Running roll-down:
1. the Upfront roll-down divided by the 9-year swap starting today.
5. Actual Vol-adjusted Running Carry & Running Roll-down:
1. 1Y Running Carry divided by the actual volatility of the 1Y rate over the past 1 year.

How to Read the Quotes:

6. Notional Neutral Switch:
1. Typically quoted as where one receives fixed for the shorter rate and pays fixed for the longer rate.
2. If the expected carry and roll-down is 180bps on a 5s/30s – one should read this as follows. For an investor, who receives fixed on a 5 year swap 1mn notional and pays fixed on a 30 year swap 1mn notional -- expected profit is 180,000.
7. Duration Neutral Switch:
1. Typically quoted where one receives a short dated swap, and pays a long dated swap.
2. The notionals can vary here – such that the durations cancel out.
8. Butterfly:
1. Quoted as 2bps on a 3s/4s/15s. Read this as expected roll-down and carry as pay fixed on the 3yr and the 15yr, and receive the 4yr fixed rate.