Convexity - Callable bond

[CFA_10]

I understand, callable bond has negative convexity at lower rates due to probablity of getting called is higher and hence it will underperform Callable bond.
While increasing rate scenario would lead callable bond to outperform non-callable bond as probablity of getting called decreases. Does that mean callable bond has positive convexity (as compared to non callable bond) at higher rates?

 

[AmruthSundarkumar]

At higher rates callable bonds fall lesser than comparable non callables. Generally a higher positive convexity than comparable non callables acc to me.

 

[LTD]

And if rates fall. Would return on putable be the same as non putable? Or any will outperform?

 

[CFA_10]

I think putable should have some positive convexity(as compared to non putable bond) at lower yield and hence out perform - not sure
At higher yield, puttable bond out performs non putable as price cannot drop beyond put strike.
In general, Option bond(callable or putable) would have less price/yield risk as compared to normal bond.

 

[AlmostDoneIII]

And to throw in a curveball… MBS have the same convexity as callable bonds right?
#brain overload

 

[AmruthSundarkumar]

MBS and callables have similar convexity
Putables have a positive convexity always unlike callables.
Callables have a higher yield than non callables whereas putables have a lower yield than non putables.
a callable vs non callable with same coupon and other features but different yields ( callable yield>non callable yield) more convexity for non callable as rates rise. And for a putable given the above assumptions and a lower yield for a putable, higher convexity for putables.
Hope I’m right!