Question

the possible answers are 6.6%, 8.5%, 7.6%, 5.9%, 8.1%

23. You are given the following spot rates: Term 1 Spot Rate 5.00% 2 3 6.80% The annual effective yield of a 3-year par bond with annual coupons is 6.75%. Calculate s2.

Answer 1

3-Year Par Bond is one which sells at its par value (basically bond price equals its par value) In such a bond, the bond's yield (annual effective yield to maturity) equals its annual coupon rate. Hence, coupon rate of bond under consideration is 6.75 %.

Par Value = $ 1000 (assumed)

Hence, Bond Price = $ 1000

Annual Coupon = 0.0675 x 1000 = $ 67.5

Spot Rates: Year 1 = 5%, Year 2 = s2% and Year 3 = 6.8%

Therefore, 1000 = 67.5 / (1.05) + 67.5 / (1+s2)^(2)+ 67.5 / (1.068)^(3) + 1000 / (1.068)^(3)

1000 = 64.2857 + 67.5/(1+s2)^(2) + 876.303

67.5 / (1+s2)^(2) = 59.4116

(1+s2)^(2) = (67.5/59.4116) = 1.13614

s2 = [(1.13614)^(1/2)] - 1 = 0.0659 or 6.59 %