Question

Suppose you're a financial analyst who has been asked to provide some general information about duratio of information: n as well as duration analysis of several bonds. You've determined the following two pieces Bond A has a Macaulay duration of 6.5 years and a yield to maturity Bond B has a Macaulay duration of 5.8 years and a yield to maturity of 10.1.

a) Which of the two has a higher modifed duration? Show your work and explain how you arrived at

b). You're also analyzing a U.S. Treasury STRIPS with a maturity of 6 years and a current value of $456 your answer What's the Macaulay duration (also known as effective duration) of this STRIPS? Show your work and how you arrived at your answer.

Answer 1

Note- In the question, you have missed adding the YTM of bond A. We will use the YTM for bond B for this, but if there is a separate value, you are requested to change it in the formula for bond A.

a. The modified duration is given as = Macaulay duration/(1+YTM). Hence, the modified duration of bond A will be = 6.5/(1+0.101) = 5.9037

Similarly, for bond B, the modified duration will be = 5.8/1.101 = 5.2679. Hence, bond A has higher modified duration (Note that the answer can change if the YTM of A is different than B).

b. Treasury Strips are zero-coupon bonds. Hence, their duration is sames as their maturity = 6 years. (Zero coupon bonds have duration equal to their maturity).