Reading 44, EOC 3

[CAR1082]

I’m trying to understand how C is the correct answer to this problem.
The problem deals with a partially completed binomial interest rate tree (see below).
Current Year 1 Year 2 Year 3 Year 4
1.25% 1.8229% 1.8280% 2.6241% 4.2009%
1.4925% Node 2-2 Node 3-2 3.4394%
1.2254% 1.7590% 2.8159%
Node 3-4 2.8159%
Node 4-5
The CFAI text says the correct answer is C, which states that “Node 2-2 approximates the implied one-year foreard rate one year from now.” I thought Node 2-2 would approximate the implied one year forward rate TWO years from now - not one.
It looks to me like Blue Box problem 4 on page 293 treats the middle node at time 2 as the one-year forward rate two years from now.
Can anyone help me with what I’m missing here?
Thanks in advance.

 

[cpk123]

1 year from now - you are at year 1.
and 2,2 is 1 year beyond that…
so it is the 1 year forward rate 1 year from now. that is the right answer.

 

[Harrogath]

I agree with cpk123. However, CAR1082 has a point, the example 4 of chapter 44 calculates the year-2 forward rate as F(2,1) which is the one-year forward rate 2 years from now. This deserves more discussion. Anybody knows the secret?

 

[CAR1082]

Thanks to both cpk123 and Harrogath for your comments. After I read cpk123’s comment last night, I, like you, Harrogath, agreed with his/her conclusion.
I do still *think* there’s an inconsistency with BB 4. I’ll be interested to see if anyone else can shed some light on whether there’s a distinction or not.
Thanks again to you both.