Question

If you are trying to immunize a portfolio that is worth $20 million dollars and has a duration of 6 years, which of the following could you do (YOU CAN CHOOSE MORE THAN ONE)

Purchase a zero-coupon bond with a face value of $20 million and a time to maturity of 6 years

Purchase a $20 million worth of zero-coupon bonds with a duration of 6 years

Purchase a coupon-paying bond that has a value of $20 million and a time to maturity of 6 years

Answer 1

Answers are:

Purchase a zero-coupon bond with a face value of $20 million and a time to maturity of 6 years

Purchase a $20 million worth of zero-coupon bonds with a duration of 6 years

Explanation

Immunization is a strategy that matches the durations of assets and liabilities, thereby minimizing the impact of interest rates on the net worth.

For all zero coupon bonds duration is equal to maturity (because there is only one cashflow that happens at maturity). So, in order to immunize a portfolio of $20 mil of duration 6, you need a counter portfolio with duration of 6. So, if you purchase 1 zero coupon bond of $20 mil with 6 years to maturity or a set of zero coupon bonds collectively valued at $20 mil with all having 6 years to maturity - both will work.