Question

Problem 1. (a) The current term structure is defined by st = 0.06 + 0.01t for t = 1, 2, 3. Calculate the at-par yield rate for three-year bond. (b) You are given a $1000 three-year bond with annual 6% coupons redeemable at par. The annual spot rates are the same as in part (a). (i) Determine whether it is a premium or a discount bond using the at-par yield rate in part (a). (ii) Calculate the amount of premium or discount.

Answer 1

s1= 0.06+0.01*1 = 0.07

s2= 0.06+0.01*2 = 0.08

s3= 0.06+0.01*3=0.09

The par yield is the same as the coupon rate for which the bond price equals its par value

So, if the coupon rate is C% and the par value of the bond is $100, annual coupon =$C

C/1.07+C/1.08^2+C/1.09^3+100/1.09^3= 100

=> 3.08694726*C = 22.78165199

=> C = 7.37999

So, the par-yield is 7.38%

b) i) As the bond's coupon rate is 6% which is lower than the par-yield of 7.38%, the bond should be trading at a discount i.e. it is a discount bond.

c) Price of $1000 three-year bond with annual 6% coupons redeemable at par.

P = 60/1.07+60/1.08^2+60/1.09^3+1000/1.09^3 = $926.03

Amount of discount = $1000-$926.03 = $73.97

The bond is trading at a discount of $73.97