Adding put options to bond portfolio and convexity

From Kaplan:

“Adding put options on either a bond price or a bond futures contract will decrease
the duration of a fixed-income portfolio because the puts will increase in value as yields
rise and bond prices fall. They also lower the convexity of the overall portfolio due to the
floor that the put options place under the portfolio, which causes the portfolio to move in
a straighter line versus yields than the equivalent option-free bond.”

I don’t get the convexity part. Convexity is higher when “bond value increase when rates fall” is higher than “bond value decrease when rates rise”, put option will minimize the second term - “bond value decrease when rates rise”, then how does having put options decrease convexity? Is it because option premium paid decrease profits when interest rate falls or do I miss something?

It’s wrong.

Are you sure? The same pattern is mentioned in other sources too.

Pretty sure.

Which has more convexity: a straight bond or a putable bond?

I think difference is that here they don’t speak about putable bond, rather adding put option to bond portfolio, still I don’t get it.

I realize that. They’re analogous.

So . . . which bond has more convexity: a straight bond or a putable bond.

Putable bond


And a straight bond plus a put option is essentially the same a s a putable bond.