 # Theoretical Spot Rate Question

An investor has a 1-year, 10% semiannual coupon bond with a price of \$975. If the 6-month Treasury bill (T-Bill) has a holding period yield of 6%, what is the 1 year theoretical spot rate on a bond equivalent basis? A. 6.4% B. 8.7% C. 9.9% D. 12.8%

is the answer the ytm of the 1 year bond, which is 12.75%? so D

975=50/1.03+1050/x^2 x= 1.0645 BEY basis: (x-1)*2*100= 12.9 I would go with D.

Yes D is correct

I’d go with D too.

Do we do a simple TVM here or bootstrapping is needed?

barthezz Wrote: ------------------------------------------------------- > 975=50/1.03+1050/x^2 > > x= 1.0645 > > BEY basis: (x-1)*2*100= 12.9 > > I would go with D. Same answer, but it was a holding period yield - so it should be: 975=50/1.06 + 1050x^-2 x = sqrt(1050/927.83)=sqrt(1.1367)=1.0638 so BEY: x*2-1=12.76%

I decided it was D before I even touched my calculator - assumed they were trying to trick us by giving an answer that’s exactly half of the other one (6.4 is half of 12.8) in case you forgot to double your result for a BEY. After touching my calculator turns out D is correct indeed. Wouldn’t recommend guessing like this though, just in case. I think a simple YTM on the bond gives the same answer, but I believe that’s a fluke?

here is my approach w/o calculation, does it sounds correct to you? 10% Bond trading at \$975, then it’s BEY has be greater than 10%, thus, only D qualify. If you see answer choices similar to this one, i.e. one big one, three smaller ones, use fundamental to rule out bad ones without calculation. Steve

D