Question

A bond has a Macaulay duration of 4.5, a yield to maturity of 5.1 percent, a coupon rate of 6.0 percent, and semiannual interest payments. What is the bond's modified duration? a. 6.11 years b. 6.39 years c. 6.92 years d. 7.06 years

Answer 1

Your options say that modified duration must be greater than the Macaulay duration (4.5 years), which not a possible case. The formula for modified duration is:

where:

• Macaulay duration = 4.5
• YTM = 5.1%
• n (the period of compounding in an year) = 2 (as coupon is paid semi-annually)

Putting the values in the formula:

Modified Duration = 4.5 / (1 + 5.1%/2) = 4.5 / 1.0255 = 4.388 years

Hence, the Modified Duration is 4.388 years (which will always be less than Macaulay duration (4.5 years)).