A newly issued bond paying a semiannual coupon has the following characteristics:

Coupon Yield to Maturity Maturity Macaulay’s Duration 8% 8% 15 years 10 years

a. Calculate modified duration using the information above.

b. Explain why modified duration is a better measure than maturity when calculating the bond’s sensitivity to changes in interest rates.

c. Identify the direction of change in modified duration if:
i. The coupon of the bond were 4%, not 8%.
ii. The maturity of the bond were 7 years, not 15 years.

d. Define convexity and explain how modified duration and convexity are used to approximate the bond’s percentage change in price, given a change in interest rates. P-963