Assume 3 month interest rate is 1.02% and 9 month is 1.05%.
What is FRA fixed rate?
You divide the 9 month rate by the 3 month rate, but to annualize the rate, do you multiply the number by 2 or 4?
The loan is for 6 months (9-3=6), so you would multiply by 12/6 = 2.
Always draw the timeline, you won’t get confused this way.
6 month loan in 3 months…
Take both rates and de-annualize, then divide both, and re-annualize…
1.05(270/360) = 0.787
1.03(90/360) = 0.2575
1.00787/1/002575 = 1.005281 - = .5281
.5281(360/180) = 1.0562%
Let’s say 1 month passes and you want to value the gain/loss. You were paying the fixed rate.
Let’s assume the new 6 month rate after 1 month is 1.08%
So you lose 1.08 - 1.0562 = X%
You need to take the Present Value of X%. What month rate do you use to PV X%?
Should be the 8 month rate if 1 has passed