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 of 11 percent for $1,060. The bond has 20 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. Enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

Expected rate of return %

b1. 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.) Bond price $

b2. What is the HPY on your investment? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) HPY %

Answer 1

Question - a

For computing YTM we need to find out a discount rate = r , such that the present values of all cashflows from the bond shall be equal to its price = 1060

Try with r = 10%

1000 * 11% = Coupon payment (annual) = 110

Bond Price = C [ 1 - (1+r)^-n ] / r + Terminal value [ 1 + r ]^-n

n = maturity period = 20 years

110[ 1 - (1.10)^-20] / 0.10 + 1000 [ 1.10]^-20

110 * 8.5134 + 1000[0.148644] = 1085.11

Now try with 10.5%

110[ 1 - (1.105)^-20] / 0.10 + 1000 [ 1.105]^-20

110 * 8.2309 + 1000[0.135755] = 1041.15

10 % ........ 1085.11

x % .............1060

10.5% ....... 1041.15

Using the interpolation technique

(X-10) / (10.5 - 10) = (1060 - 1085.11) / (1041.15 - 1085.11)

(X - 10)/ 0.5 = -25.11 / -43.96

x = 0.50 * 0.57 + 10 = 10.29 %...................final answer

Question - b

When YTM reduces by 1%, it will be 9.29%

Bond price = 110[ 1 - (1.0929)^-20] / 0.10 + 1000 [ 1.0929]^-20

110 * 8.9430 + 1000 *0.169196 = 1152.93

Question - c

Holding period Yield = [P1 - P0 + Interest for two years ] / P0 * 100

[ 1152.93 - 1060 + 110 +110 ] / 1060 * 100 = 29.52 %