Question 3 (17 marks) a. An investor buys a 4.4% annual coupon payment bond with six years to maturity. The bond has a yield-to-maturity of 6%. The par value is $1000. i. Determine the market price of the bond. (2 marks) ii. Calculate the bond's duration and modified duration. (5 marks) iii. If the YTM decreases to 5.5%, what is the predicted dollar change in price using the duration concept? (2 marks) b. A bond portfolio consists of the following three annual coupon payment bonds. The par value is $1000. Bond Maturity Market (years) Value (S) AX 13 2,167,600 BZ 15 2,048,200 CY 24 1,436,250 Price ($) 1,083.8 1,024.1 957.5 Coupon (%) 8.50 7.88 7.50 Yield-to- Maturity (%) 7.47 7.60 7.90 Modified Duration (years) 7.94 8.71 10.72 i. Determine the weight of each bond in the bond portfolio. (3 marks) ii. Calculate the bond portfolio's modified duration. (2 marks) c. Which bond should be the most price volatile? Explain. (3 marks) i. 5-year maturity, 2% coupon. ii. 8-year maturity, 2% coupon. iii. 5-year maturity, 6% coupon. iv. 8-year maturity, 6% coupon