You are the Chief Financial Officer of a pension fund and the duration of your liabilities is 20 years. The present value of your assets is $1,000,000, and is equal to the present value of your liability.

Your task is to invest your assets in a portfolio of 5-year and 30-year zero coupon bonds that will immunize the pension fund against changes in interest rates.

1. (2pt) What fraction of your portfolio will be held in 5-year zero coupon bonds, and what fraction will be held in 30-year zero coupon bonds?
2. (2pt) Suppose the YTM of 5 year zero coupon bonds is equal to 3%, and that their face value is equal to $1,000. How many 5 year zero coupon bonds do you have to buy?