Positive vs Negative Convexity

[Only5mia]

Hi, we know that a callable bond has negative convexity, and the way we usually describe it is by saying that when rates fall, a callable bond’s price increases less than a straight bond. What about when the rates rise, does a callable bond price still decrease at a slower rate? I’d think so.
I feel that whenever we talk about callable bonds and negative convexity, we associates them with rates falling; whereas when talking about puttable bonds and positive convexity, we associate them with rates rising. Is there a reason for doing that? Or we can describe them in either rates rising or falling?

 

[Yayyywork]

A callable bond only has negative convexity at specific times (at rates below that of which the bond will likely be called) if rates are rising the bond has positive convexity

 

[Only5mia]

Does what you said above apply to putable bonds as well?

 

[S2000magician]

Putable bonds don’t have negative convexity.
They have extra positive convexity as yields rise.

 

[sameerjpatel]

Also, just so ya know, the negative convexity hitting the callable bond curve only applies post-call date. If rates are low and the firm can’t call yet to “refinance,” the price is not yet capped. Pre-call date, I believe the option decreases positive convexity. Still a smiley face, just less smiley. Post-call, that smiley face turns frowny face as market rates fall.

 

[Only5mia]

So bascially putable bonds always have positive convexity, whereas callable bonds have negative convexity post-call date, but positive convexity pre-call date??