Question

The YTM on a bond is the interest rate you earn on your investment if interest rates don’t change. If you actually sell the bond before it matures, your realized return is known as the holding period yield (HPY).

a.	Suppose that today you buy a bond with an annual coupon rate of 8 percent for $1,030. The bond has 17 years to maturity. What rate of return do you expect to earn on your investment? Assume a par value of $1,000. (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)
b-1.	Two years from now, the YTM on your bond has declined by 1 percent, and you decide to sell. What price will your bond sell for? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)
b-2.	What is the HPY on your investment? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

Answer 1

(1)Rate of return we expect to earn on investment(YTM)
= [Interest + (Selling value-Purchase price/n)] / (Selling value+ Purchase price/2)
=[(1000*8%) + (1030-1000/17)] / (1030+1000/2)
=(80 + 1.76)/1015
= 8.06%

(2) Selling price of bond
= [Interest + (Selling value-Purchase price/n)] / (Selling value+ Purchase price/2)
=[(1000*8%) + (1030-1000/17)] / (1030+1000/2)
=(80 + 1.76)/1015
= 8.06%
Note: Given that YTM reduced by 1% then YTM =7.06%(8.06-1) and Maturity period reduced by 2years so n=15(1-2)
7.06% = [80+(s.p-1000)/15]/(s.p+1000)/2
0.0706*(s.p+1000)/2 = 80+(s.p-1000)/15
0.0353*(s.p+1000) =(1200+s.p-1000)/15
0.5295(s.p+1000)=1200+s.p-1000
0.5295s.p+529.5=200+s.p
s.p-0.5295s.p =529.5
0.4705s.p=529.5
s.p =1125.4

(3) HPY = (80*2+1125.4-1030)1030
HPY for 2 years =0.24796 or 24.78%
HPY for Annual Investment = 12.39% (24.78%/2)