I was always under the impression that, ceteris paribus, higher the coupon rate, higher the convexity of the bond.

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But Investopedia says the following:

"zero-coupon bonds have the highest degree of convexity".

Isn't that wrong?

Please correct me if I am missing something here.


1 Answer 1


The chart you posted does not give a correct visual representaion of convexity . Convexity is not $\frac{\partial^2 P}{\partial y^2}$ but $\frac{1}{P}\frac{\partial^2 P}{\partial y^2}$. So you have to normalize for P. The 4 curves you plot have very different P.

When the curves are redrawn normalized so they go through the same point $(y_0,P_0)$ you will see that smaller coupons have bigger convexity. And zero coupons the biggest of all.

Put differently: convexity is measured "per dollar invested" not "per bond".


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