Convexity and coupon

XXu · May 13, 2020, 2:26am

There are two statements about convexity and coupon. Can someone explain them?

For a given yield and maturity, the lower the coupon, the greater the convexity of a bond.
For a given yield and modified duration, the lower the coupon, the smaller the convexity.

S2000magician · May 13, 2020, 4:05am

What sort of explanation are you looking to get?

XXu · May 13, 2020, 4:35am

Why with same modified duration, bond with lower coupon will has smaller convexity?

S2000magician · May 13, 2020, 4:49am

Convexity increases with maturity, all else equal.

MGreg99 · May 14, 2020, 2:53am

I’m not sure if I understand your question. Lower coupon and longer maturity bonds have higher modified durations, which make them more sensitive to interest rate movements (price risk)