# Why is the formula for the 5y5y inflation swap forward on bloomberg 2*USSWIT10 Curncy-USSWIT5 Curncy

If USSWIT10 Curncy is the expected average inflation for ten years and the USSWIT5 Curncy is the expected average inflation for five years, I don't know why that formula would tell me what the expected 5 year inflation rate would be 5 years from now. Shouldn't there be some sort of compounding taken into account?

I almost feel like you should have to take ((1+USSWIT10)^10 - (1+USSWIT5)^5)/5. Something like that.

• You can also look at this answer for a calculation of the exact value and the simplification Bloomberg uses. Commented Jun 17, 2022 at 20:44

## 1 Answer

The standard method is 2*USSWIT10 - USSWIT5 which as you say, has no compounding. The compounded version that you attempted should be (1+USSWIT10)^2/((1+USSWIT5). If you experiment with actual market values you will find the two are very similar. The higher inflation rates get, the more potential difference there could be. I assume that the non compounded method has been used for simplicity but you are right, the compounded would be more correct since the USSWIT values are zero coupon swaps by definition.

• I see. Sorry to be dense and basic, but why are you raising to the second power? I just figured 10 since USSWIT10 is an annual number and you want to take that ten years out... Commented Apr 12, 2022 at 1:55
• Well it’s really the fifth root of ((1+usswit10)^10/(1+usswit5)^5)). The fifth root just annualizes it. And I forgot to say -1 at the end.
– dm63
Commented Apr 12, 2022 at 3:15