# FRA

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.

Thanks a lot!!

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JPEREZAR wrote:
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.

Thanks a lot!!

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.

Simplify the complicated side; don't complify the simplicated side.

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You are totally right!! i think i should have taken a rest…. thanks for the answer!

You’re welcome.

By the way: notice that we have superscripts and subscripts now.  It makes the formulae easier to read.

Simplify the complicated side; don't complify the simplicated side.

Financial Exam Help 123: The place to get help for the CFA® exams
http://financialexamhelp123.com/