USE THE INFORMATION BELOW FOR THE FOLLOWING PROBLEM(S)
Consider two bonds: both pay annual interest. Bond Y 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 X has a coupon of 7 percent per year, maturity of 10 years, yield to maturity of 4 percent per year, and a face value of $1000.
-Refer to Exhibit 13.13. Assume that your investment horizon is five years and your portfolio consists only of Bond Y and Bond X. Indicate the proportions invested in each bond, so that the portfolio is immunized.
A) 50 percent in Bond Y and 50 percent in Bond X
B) 76 percent in Bond Y and 24 percent in Bond X
C) 36 percent in Bond Y and 64 percent in Bond X
D) 100 percent in Bond X
E) 100 percent in Bond Y

Question

Quizplus · Accepted Answer

To immunize the portfolio, the Macaulay duration of the portfolio should be equal to the investment horizon of 5 years. Bond Y has a Macaulay duration of 4.38 years and Bond X has a Macaulay duration of 7.51 years. By investing 76 percent in Bond Y and 24 percent in Bond X, the weighted average Macaulay duration of the portfolio would be equal to 5 years, thus immunizing the portfolio.