one-year implied forward rate one year from now question

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Wallace presents the relationships between spot and forward rates according to the pure expectations theory. Which of the following is closest to the one-year implied forward rate one year from now?
1 year spot rate is 5.2498
2 year spot rate is 5.7492
A) 6.58%.
B) 5.75%.
C) 6.25%.
 
I guess everyone is asleep.
This is the answer:
Your answer: A was incorrect. The correct answer was C) 6.25%.
The 2 year spot rate is 5.7492 meaning the return that should be earned after 2 years would be 5.7492 + 5.7492 = 11.498%. The 1 year spot rate is 5.2498 therefore the 1 year forward rate 1 year from now must be the difference between the 11.498% earned over the 2 year spot rates and the 1 year spot rate. Thus the 1 year forward rate 1 year from now is 11.498 − 5.2498 = 6.2486 or 6.25%.
** I thought we used this formula: Implied Forward Rate1,2 = (1 + y2)2 / (1 + y1) − 1
The answer is the same…
How you y’all compute forward rates?
 
That’s how I would do it too. The way they described it looks weird and will get very complex if you try it for more complex forward rate calculations.
 
OK…will give it a shot although am sleepy now…it 2.34 here.
The formula I have from L1 was:
2 year spot rate ( given) add to 1 and then raise to power 2 = ( equal) the 1 year spot rate (given) X 1 year forward rate
Work the math, find the forward rate.
1.11829/1.0525 - 1= 6.25%
I tried the first option and you do get answer A, because it is compounded, which is what it should be, the interest is compounded, so am curious that they want u to just add together, and the substract the first spot rate….Interesting?????anyone>.
 
Their method is simply a linear approximation. It’ll get you close if there are only a couple of compounding periods.
Remember the linear approximation of the International Fisher Relation? It’s along those lines.
 
Answer: C
1 year spot rate is 5.2498
2 year spot rate is 5.7492
Therefore, 1 year implied forward rate 1 year from now
= 2 x 5.7492 - 5.2498 = 6.25%
just remember, you should be indifferent to be investing say 100$ at these 2 options
Invest it at 5.7492% for 2 years
OR
invest it at 5.2498 first year, and x% second year.
the solution presented, implies that.
 
You can use either:
a) (1 + r1) * (1 + f1) = (1 + r2)^2
which yields f1 = (1 + r2)^2 / (1 + r1) - 1
and so f1 = 6.2510 %
b) f1 = 2*r2 - r1
which yields f1 = 6.2486 %
Formula a) is exact, formula b) is an approximation that will usually be close enough and save you a few calculator punches on the exam.
In fact, if you expand a) :
(1 + r1) * (1 + f1) = (1 + r2)^2
1 + r1 + f1 + r1 * f1 = 1 + 2 * r2 + r2^2
Here comes the approximation: r2^2 and r1 * f1 are small, plus they cancel out to some degree. So we’ll drop those (and also the “1” on each side). Now we have
r1 + f1 = 2 * r2 which leads to
f1 = 2 * r2 - r1
 
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