Given the following Treasury data, what is the 1-year spot rate? Maturity YTM Coupon Price 6 months 1.0% 1.0% 100 1 year 1.5% 1.5% 100 18 months 2.5% 2.5% 100 A) 1.13%. B) 1.50%. C) 1.51%.
use the bootstrapping method given in CFA notes for calculation of “Yield calucllation” chapter
Is the answer C?
100 = (1.5%/2) /(1+ 1%/2) + (100+(1.5%/2))/ (1 + 1 yr spot rate/2) ^2 --> solve for spot rate ~1.5%
SJZ answer is C. NeeraJDBA, this is about spot rates and forward rates, not boot strapping
The way I guessed ‘C’ was I saw the yields averaging out to something pretty much bigger than 1.5% This subject is one of my weakest though, so my conclusion could totally be wrong.
elcfa, what formula are you using? where did you get 100?
As NeerajDBA said, bootstrapping is the standard calculation of doing this. 100 = price of the bond which is sold at par so price 1 yr bond = 1 coupon discount at 6 month spot + last payment discount at 1 yr spot. 6 month spot calculated by price 6 month bond = (1 coupon + par) discount at 6 month spot --> .5% for 6 month I was wrong in using BEY (standard in practice) instead of EAY (theoretically correct) in calculating. Normally, it is not much a difference. THe right one is 100 = (1.5%/2) /(1+ 1%/2) + (100+(1.5%/2))/ (1 + 1 yr spot rate) --> solve for spot rate ~1.51%
omg, i’ve just been looking at the wrong topic!! too much studying. thanks everyone
To me, SJZ’s answer is the easiest way to answer this question. Most won’t remember the bootstrapping formula or just choose not to learn it. It won’t be exactly the same rate as the 1yr but will be very close.