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:

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

Question #1:

• A) On the day it is issued, what is the Coupon Yield?
• 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 spreadsheet tab. (Do the full calculation, I will not accept an answer from a duration calculator or the duration functions in Excel.)

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?

Question #4

The Insurance Company Explores YTM Sensitivity

The Insurance company undertakes a review of all its holdings and wants to know what the price risk is associated with its bonds. It stress tests them by estimating what the effect of a 20 basis point (0.2%) increase in YTM maturity would be.

• Key formula: P/P = -D*y

Summary: the bond now has 7 years to maturity, a coupon of $50, a par value of $1,000 and is trading with at YTM of 3%. Its Macaulay Duration is 6.14 years

• A) Calculate the modified duration
• B) Using the modified duration, estimate in percentage terms how much the price would drop if the YTM rose from 3% to 3.2%.
• C) Convert the percentage estimate in (B) to a dollar estimate.
• D) Calculate accurately using either a spreadsheet or the bond function keys on your calculator what the actual dollar price change would be if the YTM rose from 3% to 3.2%.
• E) How far off (in dollars and cents, not percentages) is the modified duration estimate from the properly calculated change?

Question #5:

Financial Disaster!

2 years go by.

MCOs Treasurer was last seen with 2 suitcases of cash and a plane ticket for the Cayman Islands. The company is in serious financial trouble. Moodys drops the rating from AA to B (Junk). The insurance company sells the bond to a hedge fund with 5 years left to maturity for a YTM of 14%.

Summary: the bond has 5 years to maturity, a coupon of $50, a par value of $1000 and is trading with at YTM of 14%.

• A) What price did the insurance company receive for the bond?
• B) The hedge fund analyst believes that the bond will pay its remaining 5 coupon payments, but thinks the company will then go bankrupt and that it will pay just $500 of returned principal at maturity (not the full $1,000 par). Given what the fund paid for the bond, what YTM/overall return is the hedge fund really expecting to receive?