# bond equivalent basis?

An investor has a I-year, 10% semiannual coupon bond with a price of \$975. lfthe 6-month Treasury bill (T-bill) has a holding period yield of6%, what is the I-year theoretical spot rate on a bond-equivalent basis? A. 6.4%. B. 8.7%. C.9.9%. D. 12.8%.

I would say A: 975 = (50/1.06) + 1050(1+X)^2 Solve for X and you get 6.38%.

you’d have to double that so you get 12.8

Also, bond is selling at discount, so BEY must be higher than coupon rate., so easily eliminate the top 3 and pick D.

pepp Wrote: ------------------------------------------------------- > you’d have to double that > > so you get 12.8 Dang, I think you’re right! I love how they throw in the HPY as opposed to the normal yield! yeah, for the first minute i just didn’t know how to solve this problem, then i was like, there gotta be an easy way. i thought and dind’t even bother doing any computation. just said, hey its giving 6% for half a year, gotta atleast double that to go for full year. but gotta be more than 6% cuz of compounding issues…the only answer choice luckily is 12.8 lol. NOW I REALLY HOPE I AM NOT WRONG cuz i dont know how else to do or think about such problems.

pepp Wrote: ------------------------------------------------------- > Also, bond is selling at discount, so BEY must be > higher than coupon rate., so easily eliminate the > top 3 and pick D. ok for the guess option but can you show it rationnaly (by calculations in case there are many rate higher than coupon rate)

from my understanding, what sox did is fine, but other rationality is simply to convert an HPY to BEY, however if cash flows are known, its easily to just compute BEY based on above calculation.

975 = (50/1.06) + 1050(1+X)^2 Solve for X and you get 6.38% and now multiply by 2 = 12.8%

soxboy I agree with you (I did the same but had error in my discount factor so i didn’t get the right anwser) and after the formula of BEY makes me complicate thing a little bit more… but when we need to use BEY then? (I mean the formula)