Bootstrap question different, question, discover, cannot, correct

chunty

Assume you have a 6-month and 1 year zero coupon bond. You are trying to bootstrap 2.5 year spot rate and discover that there are NO 1.5 year coupon bonds trading in the market:

a. Bootstrapping cannot be done
b. you can bootstrap if you have 2 different 2.5 year coupon bonds and a 2-year coupn bond
c. you can bootstrap if you have a 2.5 year coupon bond and two different 2-year coupon bonds
d. Both c and d are correct
e. Neither b or c are correct.

yodacaia

c is doable, i am doing an example to show you how, and mainly to practice myself

zephyranalyst

I think a. You need all maturities along the curve or forwards thereof if I remember right

jacksparrow

c is very doable guys, i was gona prepare an example, but my math skills failed me

go get 2.5 spot rate, you need to have the 1.5 and the 2 spot rates

after that i assume it is straight forward for you....

here is how you get the 1.5 and 2 spot rates

you get two bonds of diff coupon that expire in 2 years

price Bond A=
(coupon a)/(1+six month spot rate)+
(coupon a)/(1+ one year spot)+
(coupon a)/(1+ one and half spot rate)+
(coupon a+par a)/(1+ two year spot rate)

price Bond B=
(coupon b)/(1+six month spot rate)+
(coupon b)/(1+ one year spot)+
(coupon b)/(1+ one and half spot rate)+
(coupon b+par b)/(1+ two year spot rate)

in these two equations your online unknowns are the (two year spot rate), and (one and half year spot rate). you rearrange the first equation to where you get

(one and the half year spot rate)= (two and half year spot rate) pluus whatever devided by whatever

ie you write the one and half year spot in term of the two and the half year spot

you plug it into the second equation and now you have one unknown

you solve for this unknown

you plug in the value in the first rearranged equation and get the second unknown

so now you got the 1.5 and the 2 year spots, you use them to get the 2.5 year spot

solving this equation should be easy, unfortunatly i was playing tetris on the ti 84 plus calculator in high school algebra, but any high school kid should be able to do it

benbenxiong

i typed the above from my phone

i forgot to add the exponents when deviding the coupons

online=only

god knows what other typos are in there

but the idea is correct

sameeragarwal

noel

btw where did this questions come from, i dont think this is in the Level II LOS ?

kkn006

seeki, your probably right, i know C will work, but i wasted enough time on it and i am not willing to explore B...

this is not in the CFA level II, I am the king of wasting time on things that are not in Level II, but if i keep doing this i am gona fail

everyday i spend 3 hours or something like this while i should be spending it on the LOS

i am off to bed, hope noel will say where he got this from