# Spot rate

An investor has a 1 year 10% semi annual coupon bond with price of \$975. If the 6-month T-bill has holding period yield of 6% what is the 1-year theoritical spot rate on a BEY basis? a. 6.4% b. 8.7% c. 9.9% d. 12.8% I’m a bit lost how to even approach this question. Any help?

i was literally about to post that very question…

50/(1.06)+1050/(1+X^2)=975…once you have soved for X, multiply by 2 to get the bond equivalent yield.

I got D.

50/(1.06) + 1050/(1+x)^2 = 975 x = 6.38% This is a 6 month rate, so the 1 year rate should be 12.8% So I say D

Answer is A if you plug in A, you get 975. Basically A is the BEY and D is converted in annual yield.

I also got D. I just used the TVM function to solve I/Y and multiplied it by 2 (totally ignoring that 6month T-bill though).

Or calc. I/y for the bond and multiply x 2.

So I was right the first time. At least it’s not the real thing lol

A?? N=20 PV= -937 FV=1000 PMT= 30 ( .03*1000) CPT, I/Y=3.17 BEY= 3.17*2= 6.34

Audrey- Is that a new question?

D) !!!

This should be: \$975 = \$50/1.03 + \$1050/(1+r/2)^2 Solve for r… \$105/(1+r/2)^2 = \$926.46 r=12.92%, close to D.

Dreary Wrote: ------------------------------------------------------- > This should be: > \$975 = \$50/1.03 + \$1050/(1+r/2)^2 > Solve for r… > > \$105/(1+r/2)^2 = \$926.46 > r=12.92%, close to D. dreary, 6% is the 6 month spot rate and 50 should be discounted by 1.06

Dreary Wrote: ------------------------------------------------------- > This should be: > \$975 = \$50/1.03 + \$1050/(1+r/2)^2 > Solve for r… > > \$105/(1+r/2)^2 = \$926.46 > r=12.92%, close to D. Dreary… the HPY for the 6mo treasury is 6% which means the spot rate is 6%, your first term needs to be \$50/1.06 in this case you were ok, but if the yield curve was steeper and other answers closer you would have been in trouble.

Why divide by 6%? This is the annual rate for the 6-month CD, not your holding period. You If you buy a 6-month CD at 6%, you don’t get 6%, you only get 1/2 of that.Ami I missing something here?

oh I see, the problem says so!! Phew.

This bond’s yield (YTM) is only slightly different from the spot rate (12.74% versus 12.76%), which is interesting. Bonus question, why do you suppose it is so?