You want to hedge the interest rate risk in $100 billion of pension liabilities by buying $100 billion worth of bonds. Suppose these liabilities have a duration of 15 years.

In pension immunization, you would generally have to compute the duration of bonds before you can use them to hedge. Suppose (for liquidity reasons) you want to use the most recently issued (so-called on-the-run) 10- and 30-year bonds to hedge the duration risk of your pension. The on-the-run 10-year bond has a coupon rate of 2.875% and yield of (2.973%). The on-the-run 30-year bond has a coupon rate of 3.125% and a yield of 3.118%.

1. What is the duration of each bond?
2. How much of each bond would you purchase to construct a $100 billion portfolio with the same duration as a 15 year pension?