# bond convexity and coupon rate

Generally, the higher the coupon rate, the less sensitive to interest rate changes, and the higher the convexity of the bond, so a 5% bond is more sensitive to interest rate changes than a 10% bond.

The investopedia says the higher coupon rate, the lower the convexity of the bond. Isn’t that wrong?

IMO, higher coupon rate means lower duration so the convexity should be lower as well.

bond with higher convexity less affected by interest rate changes than bond with lower convexity.

high coupon bond less affected by interest rate changes than low coupon bond.

So high coupon bond will have higher convexity.

Then Investopedia is wrong.

Think 1% bond - ir changes 50bps - think of its pv relative to pv of 10% bond and the same change

lower coupon - higher sensitivity to ir change - so higher convexity (price underestimated using duration)

I am not expert for fixed income but what I learnt from CFAI:

Convexity is second order change whereas duration is first order change at bonds. Like delta and gamma at options. Thus, it is logical that both same IR movements cause same reaction on bond prices. Maybe I missed something and might not be correct.

At the risk of sounding like the voice of sanity, why not simply compute the convexity of a couple of bonds yourself? It’s not as if it’s all that difficult; you learned the formula at Level I.

this is what happens when you have answered the same question a 1,361 times…

Or 1,362 times.

A: If two bonds offer the same duration and yield but one exhibits greater convexity, changes in interest rates will affect each bond differently. A bond with greater convexity is less affected by interest rates than a bond with less convexity. B: Bond’s convexity refers to the relationship between its yield and its price. A high convexity bond is more sensitive to changes in interest rates and should see larger fluctuations in price when interest rates move.

A or B, which one is the correct answer?

Draw a bond with a high convexity, draw one that is linear. On the rate decrease, Greater return convexity > Less. On rate increase, greater convexity losses less compared to one that has less convexity.

Thank you. Both The sentences are copied from investopedia. We can’t​ trust investopedia.