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>.

(1…057492)^2/(1.052498)=1.0625 Hence answer is 6.25%

bring it back old school level 1 styles

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