# Understanding the Relationship Between Coupon Rates and Duration

Course: Investment Planning
Lesson 9: Fixed Income Securities

## Student Question:

There is a question regarding duration that I continue to struggle with.
Which of the following are true:

1 – Lower coupon bonds are more sensitive to interest rates than high coupon bonds.
2 – There is inverse relationship between bond prices and change in interest rates.
3 – There is a positive relationship between coupon rates and duration.

Can you explain #1 and #3?

Thank You

## Instructor Response:

Hi Angela,

Thank you for your question.  This can become a bit convoluted.

Let’s unpack the word “duration” first.  Duration is nothing more than the length of time required to recover your investment in the bond.  Specifically, it’s the weighted average length of time required to recover your investment in the bond.  As a bond holder, the more cash I receive and the earlier I receive it will result in a lower duration. A high coupon rate bond provides more cash flow than a low coupon rate bond. Accordingly, a high coupon rate bond has a lower duration that a low coupon bond.  For example, if I purchase a zero-coupon bond on its issue date the bond will have a duration of 30 years – no cash flow until the bond matures. If I purchased a bond with a 6% coupon rate, duration would be significantly less than 30 years because I’m receiving semi-annual bond interest until the bond matures.

As we translate this concept into your question, lower coupon bonds have higher duration than higher coupon bonds. Answer choice three is false; a positive relationship would require that duration increases with increases to the coupon rate. The opposite is true. Duration decreases as the coupon rate rises.  There is an inverse relationship between coupon rate and duration. Lower coupon rates increase duration while higher coupon rates decrease duration.

Let me know how completely that addresses your question please.

Onward and Upward,

Bruce