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.作者: yodacaia 时间: 2011-7-11 19:18
c is doable, i am doing an example to show you how, and mainly to practice myself作者: zephyranalyst 时间: 2011-7-11 19:18
I think a. You need all maturities along the curve or forwards thereof if I remember right作者: jacksparrow 时间: 2011-7-11 19:18
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作者: benbenxiong 时间: 2011-7-11 19:18
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作者: sameeragarwal 时间: 2011-7-11 19:18
noel
btw where did this questions come from, i dont think this is in the Level II LOS ?作者: kkn006 时间: 2011-7-11 19:18
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
