Suppose that you are responsible for managing a $100 million bond portfolio at a large pension fund. Because the pension fund has obligations to retirees in 2028, you want your portfolio to have a duration of 10 years. Suppose that you can only use 2-year and 12-year Zeros to immunize your portfolio. Assume that new 2-year Zeros and 12-year Zeros are issued only in 2018, 2020, etc. (i.e., even years). Assume that interest rates are the same for all these securities.
(a) In 2018, how much of your $100 million do you need to invest in each of the two bonds to immunize your portfolio from interest rate risk?
(b) Suppose that one year has passed (i.e., it’s 2019) and your portfolio now has a target duration of 9 years. What are the portfolio weights on the 2-year and 12-year Zeros (issued in 2018) required to immunize your portfolio? (Hint: consider what happens to the maturity of the Zeros in your portfolio as time passes.) If the yield curve has been flat and constant, do you need to rebalance your portfolio in 2019?