Implied Forward Rate?

CFA Level I
#1

Could someone help me understand how this is calculated?

Assume the yields to maturity on four-year and five-year zero-coupon bonds are 4.67% and 5.35%, respectively, stated on a semiannual bond basis. The “4y1y” implied forward rate is?

A- 8.114%

B- 8.092%

C- 4.046%

#2

I wrote an article on this: http://financialexamhelp123.com/calculating-forward-rates-from-spot-rates/

Without doing any calculations, I suspect that the answer is B.

#3

The YTM of the zeros are the respective spot rates for 4 and 5 years:

SR4=4.67% SR5=5.35% You are looking for the 1 year forward rate 4 years from now (1FR4) which is the rate between the spot rate for year 4 and year 5. (Draw a timeline if this is not clear!)

Note that the yields are stated on a semmiannual basis. You need to divide them by 2 and instead of taking annual periods you need to take semiannual periods:

(1+0.0467/2)^8* (1+1FR4/2)^2 = (1+0.0535/2)^10 (1+1FR4/2)^2 = 1.082563958 1FR4 = 0.0809266 = 8.093% (Answer B)

An approximate shortcut is the “banana method” (which is the way I assume magician calculated it):

5* 5.35% - 4*4.67% = 8.07% (Answer B is the most closest)

Regards, Oscar

#4

I didn’t calculate it at all (or even approximate it) before stating my conclusion.

I based it on the fact that they had one answer ( C ) which was a half-year rate (for those who forgot to double it to get an annual rate); I figured that the correct answer was twice that rate, which was answer B.

#5

Wish I’d have known about the ‘banana method’ when taking L1. Pretty slick.

#6

I’d never heard it called the banana method before today, but it’s a pretty good approximation, and easy to do. I discuss it in the article I cited above.