Question 2 (17 marks)

a. An investor buys a 4% annual coupon bond with five years to maturity. The bond has a yield-to-maturity of 9%. The par value is $1,000.

i. Calculate the duration and modified duration of the bond. (5 marks)

ii. If the yield decreases to 8.5%, what is the new bond price using the duration concept? (3 marks)

b. Queenie is managing a pension fund with obligations to make payments of $6 million, $10 million, and $15 million at the end of the next three years, respectively. The market interest rate is 6% per annum.

i. Determine the duration of the funds obligation. (4 marks)

ii. Suppose Queenie plans to fully fund the obligation using both 6-month zero coupon bonds and perpetuities. Determine how much of each of these bonds (in market value) Queenie will hold in the portfolio. (5 marks)