The Life of a Bond

Birth:

Once upon a time, the treasurer of Mighty Corporation (MCO) decided to issue a bond (hereafter: The bond) The bond would have a 8-year life and promised that the holder of the bond would receive:

• Investors would pay $1000 to obtain the bond. In the future, they are promised to receive:
  • 8 annual payments of $25,
  • Along with the 8^th payment, MCO promised to return the principal of $1,000.

Question #3:

The bond now has a Macaulay duration of 6.53 years. The insurance company wants to use The Bond as part of a portfolio designed to immunize an obligation that it foresees will come due in 10 years. (Hint: Example 11.2 in the book is very useful here, I am posting a PDF of this page on Laulima under: Resources/Syllabus and Reference Materials/Misc./Section11 2).

• To create a bond portfolio with an overall duration of 10 years, the insurance company decides to buy zero coupon bonds with a maturity of 20 years (and with a YTM of 7%) to combine with The Bond . To bring the combination of The Bond plus The Zero to a combined portfolio duration of 10 years, what would be the correct mix of The Bond relative to the 20-year Zero? Use the following steps
  • A) calculate the percentage amount of The Bond in the portfolio
  • B) calculate the percentage amount of The Zero in the portfolio
  • C) Can you suggest a simpler investment that would give the insurance company a bond investment with a 10-year duration?