### CFA Practice Question

A 5.25% coupon Treasury security with one year left to maturity is selling for 101.75, and a two-year 5.45% coupon Treasury security is selling at a discount of 0.40% from par. Assume annual discounting. The forward rate for the second year is ______.
A. 5.45%
B. 5.73%
C. 8.07%
Explanation: The first year spot rate is computed first from the 1-year bond. It is then substituted in the 2-year bond valuation equation for solving the forward rate for the second year.

Year 1 spot rate based on the 1-year bond: FV = 105.25; N = 1; PV = -101.75; CPT I/Y = 3.44%

2-year bond valuation equation: 99.60 = 5.45/(1.0344) + 105.45/[(1.0344)(1 + f)] => f = 105.45 / [(99.60 - 5.45/1.0344) x 1.0344] - 1 = 0.0807, or 8.07%

User Comment
octavianus 100 principal + 5.285 coupon/(1 + spot) = 101.75
Should we assume annual coupons, even though normally we use semi-annual if the problem does not make mention?
steved333 Question says to assume annual
steved333 sum of discounted cfs. First coupon discounted at first year. Second year coupon and fv discounted not at rate^2 b/c the second year's rate is different from the first. So it's discounted by the first year's times the second year's rate. Use algebra to solve for the second year's rate.
StanleyMo good questions.
scotty21 Glad I know how to solve this now, but still dont think I could get this in 1.5 mins!
aravinda Does anyone know why the FV for 1st year should be 105.25?
cwa4 It's including the coupon payment of \$5.25 you would receive at maturity.
boddunah good question: expect a question like on the exam.
jpducros DON'T do the following mistake I made : discounting the second cash Flow of the 2 year Bond at (1+X)^2....otherwise you'll find that B is correct.
mindi B is the spot rate for year 2, so in order to get the forward rate = [(1+ .0573)^2]/(1+.0344) -1 = .0807

technically bond valuations should be done CF1/ (1+spot rate1) + CF2/ (1+spot rate2)^2 + ...
Insipidity Thank you mindi!
NickNT I've got the spot for the second bond equal 5.67% - am I wrong?
Lambo83 NickNT I got the same 5.67% for the second bond. I used that in the formula Mindiised and got 7.9% as the forward rate. Mindi I'm curious why you used 5.73% instead. Thanks
Znanje35 jebi ga
chenyr05 how to get the spot rate for year 2 at 5.73%? I got 5.67%, which seems not correct.