Problem 1: Consider three Treasury bonds each of which has a 10 percent semiannual coupon and trades at par.
a. Calculate the duration for a bond that has a maturity of four years, three years, and two years.
b. What conclusions can you reach about the relationship between duration and the time to maturity? Plot the relationship.
Problem 2: A six-year, $10,000 CD pays 6 percent interest annually and has a 6 percent yield to maturity. What is the duration of the CD? What would be the duration if interest were paid semiannually? What is the relationship of duration to the relative frequency of interest payments?
Problem 3: Maximum Pension Fund is attempting to manage one of the bond portfolios under its management. The fund has identified three bonds that have five year maturities and trade at a yield to maturity of 9 percent. The bonds differ only in that the coupons are 7 percent, 9 percent, and 11 percent.
a. What is the duration for each bond?
b. What is the relationship between duration and the amount of coupon interest that is paid? Plot the relationship.
Problem 4: An insurance company is analyzing three bonds and is using duration as the measure of interest rate risk. All three bonds trade at a yield to maturity of 10 percent, have $10,000 par values, and have five years to maturity. The bonds differ only in the amount of annual coupon interest they pay: 8, 10, and 12 percent.
a. What is the duration for each five-year bond?
b. What is the relationship between duration and the amount of coupon interest that is paid?
Problem 5: Suppose you purchase a six-year, 8 percent coupon bond (paid annually) that is priced to yield 9 percent. The face value of the bond is $1,000.
a. Show that the duration of this bond is equal to five years.b. Show that if interest rates rise to 10 percent within the next year and your investment horizon is five years from today, you will still earn a 9 percent yield on your investment.
c. Show that a 9 percent yield also will be earned if interest rates fall next year to 8 percent.