Macaulay Duration and Coupon rate

Hi all,

I cannot get the intuition here. Hope you guys can clear the doubts.

When Coupon rate increases, doesn’t the Macaulay Duration is longer since the numerator is larger than the denominator. Larger CR divided interest rate will have a larger number. Larger number divide by the PV will have the larger Macaulay.

and my understanding is the shorter the Macaulay, the faster you get your money back.

Hope any kind soul can help me. S2000magician I know you do… :slight_smile:

Start by treating the bond as a zero coupon instrument: 100% of the weight will be on that final payment at time n when calculating the Macauley duration. As you pay a non-zero coupon, some of the weight will be shifted away from time n to the shorter time periods. The higher the coupon rate, the more weight is shifted down from time n to the shorter time periods.

I wrote an article on duration that covers this well:

Full disclosure: as of 4/25 I’ve installed the subscription software on my website, so there’s a charge for viewing the articles.

All analogies are incorrect, but some are useful. Here’s one that might be:

Think of Macauley Duration as a measure of when “on average” a bondholder receives the cash flows from the bond. If you have (for example) a 10-year maturity zero-coupon bond, the “Average” cash flow occurs at time 10.

Another 10-year bond with a 5% coupon would result in the “average” cash flow occuring sooner.

Actually, it’s the weighted-average maturity of the bond, with the weights being the % of the present value of the bond represented by the PV of each individual cash flow. But essentially, it’s the “Average” time to receive cash flows.