AuthorTopic: Current Spot Rate calculation
littleangel
@2007-10-27 15:44:12
Hi everyone!

I just got in trouble on the "Current spot rate". Could anybody help? Thanks a lot!

Here's the question.

The 6-month T-bill yields 6%. The 1-year Treasury yields 6.5%. If a Treasury note with a maturity of 1.5 years and a coupon rate of 8% is currently priced to yield 9%, what's the current spot rate for 1.5 year maturity?

(a) 9.11%
(b) 6.5%
(c) 6%
(d) 7%
achu
@2007-11-16 02:13:04
I think the answer is a) 9.11%. Not 100% sure but here it goes:

The key is you have 3 cash flows given in the last sentence: PV0, \$4 (8% coupon at 6 months), \$4 (coupon at 12 months), \$104 at 18 months (\$4 + 100 principal). I used \$100 bond, but \$1000 bond math is same idea.

Using the PV on calcluator with n=3, PMT=4, FV=100, i= 9/2 = 4.5, PV = 98.63.

Now set PV = CF1/(1+s) + CF2/(1+s)^2 + CF3/(1+s)^3.
98.63 = 4/1.03 + 4/1.0325^2 + 104/(1+s^3)

You get 1.14298 = (1+s)^3 ; hard to solve but by pluggingin you can see that (1+ .0911/2)^3 = about 1.14297.
achu
@2007-11-16 02:16:35
Warning: am not 100% sure.
My choice:a)9.11

Solve last sentence for PV of the bond = 98.63 (n3, i=4.5, PMT=4, FV =100)

Then, 98.63 = 4/(1.03) + 4/(1.0325)^2 + 104/(1+s3)^3
You get 1.14298 = (1+s3)^3
Solve for s3 (semiannual % that is).

Using 9.11/2 , the answer works out, I think.
GeorgeC
@2007-11-20 16:03:36
I've just gone through this and come up with same answer. Having just done all the maths though I've just noticed all the YTMs and the spot rates are rising - hence the spot rate at this maturity (1.5 years) must be above the YTM - the only value from the list that is above the YTM is 9.11% so that's a much easier way to answer the question!!! I'm so gonna do the same thing in the exam lol!!!

### CFA Discussion Topic: Current Spot Rate calculation 