I am having problem with FRA i can’t understand very well… this is the problem
Period Year Spot Rate
1 0.5 0,80% 2 1 1,20% 3 1.5 2,42% 4 2.0 3.20%
The mock exam ask about the 6 Month forward rate 18 month from now.
As I understand the answer would be
(1 + 0.8%/2)^1 * (1+FRA)^3 = (1+ 3.20%/2)^4
Why the correct answer in the first 6 month has a rate of (1+ 2.42%/2)^3 ?? I get that the full period is 24 month so (1+3.2%)^4 must be but the other the first 6 month??
Can somebody please explain why in the first 6 month the 3 period is choosen.
You’re mistaken: you’re calculating the 18 -month ( 3 -period) forward rate starting 6 months ( 1 period) from today.
They asked for a 6-month (1-period) forward rate, starting 18 months (3 periods) from today.
You need the spot rate for the start of the forward rate period and the spot rate for the end of the forward rate period. It starts 18 months (3 periods) from today and ends 24 (= 18 + 6) months (4 (= 3 + 1) periods) from today, so you need the 18-month spot rate (2.42%) and the 24-month spot rate (3.20%). The calculation is:
(1 + 2.42% / 2)3(1 + 1f3 / 2)1 = (1 + 3.20% / 2)4
1 + 1f3 / 2 = (1 + 3.20% / 2)4 / (1 + 2.42% / 2)3
= 1.065552 / 1.036741 = 1.02779
1f3 / 2 = 0.02779
1f3 = 5.5581%
By the way: this appears to be a Fixed Income question, not an FRA question.