Round your answers to two decimal points, and don’t round intermediate calculations.
Problem 1.
Suppose that you have decided to fund a three–year liability with a portfolio consisting of positions in a two– interest rate level is 10%.
- a) Compute the price of both bonds.
- b) Since our liability is a three–year liability, we want to immunize our portfolio by duration matching. Set up the portfolio, describing how many dollars you have to invest into each bond.
- c) Immediately after you make your initial purchases, rates fall to 8%. If you do not rebalance your portfolio, what is your realized yield after three years?
- d) What is the duration of the portfolio after the drop in interest rates without rebalancing?
- e) How would you have to rebalance your portfolio?
Problem 2.
A 30–year maturity bond has an 8.5% coupon rate, paid annually. It sells today for $871.17. A 20–year maturity bond has an 8.0% coupon rate, also paid annually. It sells today for $894.50. A bond market analyst forecasts that in five years, 25–year maturity bonds will sell at yields to maturity of 9.5% and 15–year maturity bonds will sell at yields of 9.0%. Because the yield curve is upward sloping, the analyst believes that coupons will be invested in short–term securities at a rate of 7%.
- a) Calculate the annualized expected rate of return of the 30–year bond over the 5–year period.
- b) Calculate the annualized expected rate of return of the 20–year bond over the 5–year period.
Problem 3.
Consider a 7.4% coupon bond with face value of $1,000, making annual coupon payments, that has three years until maturity.
- a) Find the duration of the bond if the yield to maturity is 7.4%.
- b) Repeat your calculation, but instead consider a bond paying semiannually instead of annually.
Problem 4.
A five–year bond with a yield of 11% pays an 8% coupon at the end of each year.
- a) What is the bond’s price?
- b) What is the bond’s duration?
- c) Use the duration to calculate the effect on the bond’s price of a 0.2% decrease in its yield.
- d) Recalculate the bond’s price on the basis of a 10.8% per annum yield, and compare.
