## Interest Rate Risk and Coupon Rates

We know that bonds with different coupon rates are traded in financial markets. The change in interest rate is mechanically related to the price of the bond. This entails that bonds may have varying interest rate risks based on their coupon rate. In this post, we will demonstrate the relationship between Coupon Rate and Interest Rate Risk.

The literature tells us that there is an inverse relationship. As the periodic coupon payments increase – ceteris paribus- the interest rate risk shoud be lower. What we can observe using a graphical depiction is indeed hard to interpret at all. As a matter of fact, the following graph -derived from the table below to it – virtually says that association is vague. That is a tough job for naked eye.

To recap, Higher the COUPON rate, lower the Interest Rate Risk. This states that price of bonds with higher coupon rates -considering that par and maturity stay the same-, will be affected LESS compared to bonds with lower coupon rates. To observe this association, we better look to the PERCENTAGE CHANGES in the price of Bonds as the interest rate changes. On the following table, we see the percentage changes in the price of the bond as the interest rate increases. So we expect that the price of the bond to drop. Thus, the percentage change in the price of the bonds would be negative.

As you see on the second table, the percentage change in the price of Bond *decreases *(compare % changes on a single row)* *as we see bonds with *higher *coupon rates. The identical change in interest rate **affects **bonds with lower coupon rates **more** than the bonds with higher coupon rates. This proves the initial principle.

“Higher the coupon rate, lower the interest rate risk”.