Problem 1. Suppose a two-year bond with annual 10% coupon rate is trading at par. The bondsface value is $1,000.
(a) What is the Macaulays duration?
(b) What is the modi?ed duration?
(c) What is the DV01?
Problem 2. You work for a pension fund that has an obligation that must be paid in 10 years.Currently this obligation, which has a present value of $200 million, is exactly funded (i.e., themarket value of the fund's assets equals the present value of its obligation; net equity is exactlyzero). Te duration of the fund's assets is currently 8. The yield-to-maturity on zero coupon bondsof all maturities is currently 6%.
(a) Using the duration information, what would be the approximate change in the equity ofthe fund if interest rates decrease to 5% at all maturities?
(b) Your boss tells you that she would like you to shift all of the fund's assets into a combinationof 5-year and 20-year zero-coupon bonds. How would you structure your investment to immunizethe fund against interest rate risk? That is, how much should you invest in the 5-year zero, andhow much in the 20-year zero?
Problem 3. Suppose you own $1,000 worth of two-year zero coupon bonds.
(a) what position would you need to take in 20-year zero coupon bonds to get duration neutral?
(b) Suppose you took the position in 20-year from part (a). Using the duration approximation,what would be the approximate change in the value of your portfolio if the yield curve steepened1%
• I.e., what happens if the 20-year rate increases 100 basis points more than the 2-year rate?• Assume the yield curve started ?at at 5.26% (i.e., y=1/19).