It Is Now Time 0

Essay

It is now time 0.You are a bond portfolio manager using a barbell strategy to immunize.Your portfolio will consist of two bonds: bond A,which is a $100 par zero coupon bond maturing in five years; bond B,which is a $100 par zero-coupon bond maturing in ten years.You are trying to immunize a $1 million liability that is due in six years.The yield curve is flat at 10%,so you need a present value of $1 million/(1.10)⁶ = $564,474.
a. Of the $564,474, how much will you put in bond A and how much will you put in bond B? How many of the A and B bonds will you buy?
b. One minute after you set up the portfolio, the yield curve shifts up to 15% (staying flat). How much is your portfolio worth?
c. After the shift in part b, is your liability immunized? If not, what should you do to immunize it? Be specific, and give numbers if you can.
d. Now assume that the shift in part b never happened. You leave the firm and nobody bothers to look at the portfolio again until the end of year 4. Interest rates are still at 10%; there have been no further changes. At the end of year 4, a new bond portfolio manager takes over, goes through the files, and finds the records of the portfolio. What, if anything, will she have to do to keep the liability immunized? Be specific, and give numbers if you can.