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

• 8 annual payments of $50,
• Along with the 8^thpayment, MCO promised to return the principal of $1,000.

Question #1:

• A) On the day it is issued, what is the Coupon Yield? 5%
• B) On the day it is issued, what is the Yield-to-Maturity (YTM)?
• C) Calculate the Macaulay duration of the bond. Show your work on the "Duration".

Off to the Insurance Company: Using Duration to Immunize

Question #2:

The bond is bought by an insurance company. One year passes, the bond has made its first coupon payment, so it is effectively a 7 year bond. The interest rate/yield-to-maturity on the bond falls to 3%.

• A) What is the Coupon Yield on the bond?
• B) What is the price of the bond?

Question #3:

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).

• 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 15 years, what would be the correct mix of The Bond relative to the 20-year Zero?
• A) percentage amount of The Bond in the portfolio
• B) 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 10year duration?