USE THE INFORMATION BELOW FOR THE FOLLOWING PROBLEM(S)
Consider two bonds: both pay annual interest. Bond C has a coupon of 6 percent per year, maturity of five years, yield to maturity of 6 percent per year, and a face value of $1000. Bond D has a coupon of 8 percent per year, maturity of 15 years, yield to maturity of 6 percent per year, and a face value of $1000.
-Refer to Exhibit 13.12. Assume that your investment horizon is 6 years and your portfolio consists only of Bond C and Bond D. Indicate the proportions invested in each bond so that the portfolio is immunized.
A) 50 percent in Bond C and 50 percent in Bond D
B) 64 percent in Bond C and 36 percent in Bond D
C) 36 percent in Bond C and 64 percent in Bond D
D) 100 percent in Bond D
E) 100 percent in Bond C

Question

Quizplus · Accepted Answer

To immunize a portfolio, the present value of the liabilities and the present value of the portfolio assets must be equal. We don't have information about the liability, so we consider the investment horizon which is 6 years.
PV of Bond C = $60*(1.06)^-1 + $60*(1.06)^-2 + $60*(1.06)^-3 + $60*(1.06)^-4 + $1060*(1.06)^-5 = $1026.18
PV of Bond D = $80*(1.06)^-1 + $80*(1.06)^-2 + $80*(1.06)^-3 + $80*(1.06)^-4 + $80*(1.06)^-5 + $80*(1.06)^-6 + $80*(1.06)^-7 + $80*(1.06)^-8 + $80*(1.06)^-9 + $80*(1.06)^-10 + $1080*(1.06)^-11 + $1080*(1.06)^-12 + $1080*(1.06)^-13 + $1080*(1.06)^-14 + $1080*(1.06)^-15 = $1026.18
So, the portfolio should have 64% of Bond C and 36% of Bond D.