Question

An 8%, 30-year corporate bond was recently being priced to yield 10%. The Macaulay duration for the bond is 10.20 years. Given this information, what is the bond's modified duration?

a) 8.05
b) 11.22
c) 9.44
d) 9.27

Answer 1

The modified duration is calculated by dividing the Macaulay duration of 10.20 years by 1 plus the yield to maturity of 10%, which results in a modified duration of 9.27 years for the bond. The correct answer is d) 9.27

Step-by-step explanation:

The question asks for the modified duration of a corporate bond given its Macaulay duration and difference in yield. The modified duration is a measure that helps us determine the sensitivity of a bond's price to interest rate changes. It's calculated using the Macaulay duration and the current yield to maturity (YTM) of the bond. Since the Macaulay duration for the bond is 10.20 years and it's being priced to yield 10%, we can calculate the modified duration as follows:

Modified Duration = Macaulay Duration / (1 + (YTM / number of coupon periods per year))

Assuming the bond pays interest annually, we would calculate the modified duration like this:

Modified Duration = 10.20 / (1 + (0.10 / 1))

Modified Duration = 10.20 / 1.10 = 9.27

The correct answer is d) 9.27.