# tenor basis swap spreads and compounding

Let's say I have a 3mv6m tenor basis swap that is quoted at a spread of x bp (and it is a spread on the 3m leg while the 6m leg is the flat leg). Nowadays, I think the convention in most currencies is to compound the 3m rate so that there is a single payment only at the 6m schedule. For this case I have 2 questions related to the spread and handling of the compounding:

1) is the spread of x bp quoted as a 3m compounded spread (like it was before when there was no compounding) or a 6m compounded spread (to be directly added to a 3m rate compounded to 6m)?

2) assuming the x bp spread is a normal 3m spread: is the implied 3m cashflow (incl. spread cashflow) compounded with the 3m rate flat (i.e. no compounding with spread included)?

Anybody trading tenor basis swaps here?

TIA for any feedback.

This would be specified in the ISDA or term sheet. There are four alternative methods:

No compounding: Meaning neither the rate nor the spread get compounded.

Compounding: Meaning both the spread and the libor rate get compounded.

Spread exclusive compounding:Meaning the libor get compounded but the spread does not. This was not covered by ISDA 2006 but was quite widespread.

Flat compounding: Slightly more involved, but in your example of 3mV6m, would mean that the first 3m of the quarterly leg gets compounded at the interest rate (excluding spread) but then the amount of first sub period would include spread. So you can see it’s half way between the two extremes.

The calculations are detailed in the below excel file:

https://www.isda.org/a/aKiDE/compounding-worked-examples.xls

Convention for most currencies is flat compounding. This includes the most liquid G4 basis swaps:

• EUR 3m vs 6m, 3m vs 12m, 1m vs 3m
• USD 1m vs 3m, 3m vs 6m
• GBP 3m vs 6m, 1m vs 3m
• JPY 3m vs 6m, 1m vs 6m, 1m vs 3m

Typically the spread is quoted in terms of the leg with the shorter tenor.

Two notable exceptions are EONIA v 3m and the (relatively new) SOFR v FF basis swaps. Here we exclude the spread rather than use flat compounding.

• in GBP between 2002 and 2015 I never saw a single compounded basis swap. Q payments were made every quarter (without being compounded to the next quarter), and S payments were made half year. Of course another approach is to book 3m +some spread or 6m -some other spread. This was distinctly different to the way USD basis trades were booked, in my historic experience, which were genuinely compounded. SONIA-3M were always booked as 3M minus some spread. – Attack68 May 30 at 12:49