Your company asks you to manage a short-term guaranteed investment contract. Your job is to create a portfolio that has a 4-year duration.
(a) If you are given the choice of using a 5-year zero coupon bond and a 3-year 8% annual coupon bond with a yield to maturity of 10%, how would you construct your portfolio?
(b) What is the modified duration of that 3-year annual coupon bond in (a)? If the yield to maturity of that 3-year annual coupon bond decreases to 8.045%, how much percentage change in price would you expect to see using modified duration?
(c) Later you are moved to another department inside your company, and now you are maintaining a money market trading desk. In your portfolio, you have a 25-year maturity, 10% coupon, 10% yield bond with a duration of 10 years and a convexity of 135.5. If the interest rate were to fall 125 basis points due to Fed’s policy change, what is your predicted new price for the bond (including convexity)?