Suppose you are a bond portfolio manager and you need to create a bond portfolio with a duration of 5 years. After reviewing all bonds available, you decide that you will definitely include a coupon bond in your bond portfolio. This bond has a duration of 9 years, 10 years till maturity, and a YTM of 4% . To complete the portfolio, you decide to also buy one of the following two bonds:

1. A 3-year zero that has a YTM of 4%
2. A perpetual bond that has a YTM of 4%

Based on information give above, answer the following two-part questions:

(a) Which of the two bonds should be chosen?

(b) What should be the portfolio weights for the two bonds in your portfolio so that the duration of your portfolio is 5 years?