You are managing the portfolio for a university foundation that provides funding for research and scholarships. Your fund wants to provide $10 million of research and scholarships every year forever (e.g., in perpetuity) and that the discount rate associated with this investment is 5%. For simplicity, suppose you have the option of investing in a 30-year zero coupon bond and a 5-year coupon bond with a duration equal to 4 years.

Part 1. What is the duration of your liabilities (e.g., the perpetual research and scholarship obligation)? (Macauly Duration of Perpetuity)

Part 2. What is the duration of the zero-coupon bond?

Part 3. What percentage of your portfolio should be invested in the 30-year, zero-coupon bond if you want to immunize your portfolio from interest rate risk?