Question

Establish the maximum Macaulay duration of an option-free fixed-rate bond with 3 years remaining until maturity? Carefully explain your answer.

Answer 1

We see that Macauly duration decreases if there are cash flows before maturity as it will take lesser time to recover the price paid. Hence, the larger the cash flows the lower the macaulay duration is. Similarly, the lower the cash flows the higher the Macaulay duration is. Therefore, the maximum Macaulay duration occurs when there are no cash flows before maturity i.e., it is a zero coupon bond. And as there are no cash flows prior to maturity, the Macauly duration will be equal to maturity i.e., 3 years. Hence, maximum Macaulay duration of an option-free fixed-rate bond with 3 years remaining until maturity, is 3 years.