Skelton

Eco 4368

Homework 9

  1. Assume a pension plan is obligated to make disbursements of $1 million, $2 million and $1 million at the end of the next three years, respectively.
  1. If the interest rate is 10% annually, what is the duration of the plan’s obligations (don’t forget that the bond’s price is the present value of the expected cash flows)?
  2. If the plan wants to fully fund and immunize its position using only one-year zero coupon bonds and perpetuities, how much of its portfolio should be allocated to each bond type?
  1. A nine-year bond has a yield of 10% and duration of 7.194 years. If the bond’s yield changes by 50 basis points, what is the percent change in the bond’s price?
  1. You purchase a fixed income asset with a duration of five years and interest rate of 8%. If interest rates decline 10 basis points, how much do you expect the price of the asset to rise (in percent)?
  1. Assume that you have to make a $10,000 payment at the end of the each of the next two years and that bonds currently yield 8%.
  1. What is the present value and duration of your obligation?
  2. What maturity zero-coupon bond would immunize your obligation?
  3. Suppose you buy a zero-coupon bond with value and duration equal to your obligation. What happens to your net position (the difference between the value of the bond and your payment obligation) if rates immediately increase to 9%? What if they fell to 7% instead?
  1. You are managing a $1 million portfolio. Assume that your target duration is 10 years and you want to immunize your portfolio using 5 year, zero-coupon bonds and perpetuities. Interest rates on both instruments are 5%.
  1. How much of each bond will you hold in your portfolio?
  2. How will these fractions change next year (assuming no change in interest rates)?
  1. You manage a pension fund that provides lifetime annuities to workers and determine that the payouts will resemble level perpetuities of $1 million a year. The interest rate is 10%. You plan to fully fund the obligation using 5-year and 20-year zero-coupon bonds.

A)How much market value of each of the zero-coupon bonds will be necessary to fund the plan if you want to immunize the portfolio?

B)What will the face value of the two zero-coupon bonds be?

  1. A 30-year maturity bond making annual coupon payments at a coupon rate of 12% has a duration of 11.54 years and convexity of 192.4. The bond currently sells at a yield to maturity of 8%. Use a financial calculator to find the price of the bond if the yield to maturity falls to 7% or rises to 9%. What prices for the bond at each of the new yields would be predicted by the duration rule and the duration-with-convexity rule? What is the percent error for each rule? What does this tell us about the accuracy of the two rules?
  1. A 12.75-year maturity zero-coupon bond selling at a yield to maturity of 8% has convexity of 150.3 and modified duration of 11.81 years. A 30-year maturity 6% coupon bond making annual coupon payments also sells at a yield to maturity of 8% and a similar modified duration of 11.79 years but considerably higher convexity of 231.2. Assume both bonds have a face value of $1,000.

A)Suppose the yield to maturity on both bonds increases to 9%. What will be the actual percentage capital loss on each bond? What percentage capital loss would be predicted by the duration-with-convexity rule?

B)Repeat part A but assume the yield to maturity decreases to 7%.

C)Compare the performance of the two bonds in the two scenarios. Based on their comparative performance, explain the attraction of convexity.

D)Given your answer to part C, do you think it would be possible for two bonds with equal duration but different convexity to be priced at the same yield to maturity if the yields on the bonds increased or decreased by equal amounts (as in this example? Would anyone be willing to buy the lower convexity bond?

  1. The ability to immunize a bond portfolio can be very desirable.

A)Discuss the components of interest rate risk. In other words, explain the two risks faced by bondholders when interest rates fluctuate.

B)Define immunization and discuss why a bond manager would immunize their portfolio.

C)True/False/Uncertain: A maturity-matching strategy is just as effective at minimizing exposure to interest rate risk as a duration-matching strategy.