Effective convexity - putable and callable in rising interest environment

CFA Level II Fixed Income
#1

Hi,

please help to clarify the below statement from p157 in Fixed Income topic (Interest rate risk of bonds with embedded options).

Compared side by side, putable bonds have more upside potential than otherwise identical callable bonds when interest rates decline. In contrast, when interest rates rise, callable bonds have more upside potential than otherwise identical putable bonds.

My logic is that in a rising interest rate environment both callable and putable have positive convexity -> more sensitive to interest rate drops (price still drops but not as much as it would rise for an equal drop in rates) -> when rates rise both callable and putable price drop BUT putable price drop is limited by the put price whereas callable can drop further.

Why would callable have more upside potential? Is it just due to the magnitude of the change in value in call and put?

Callable = straight - call (value decreasing when rates rise)

Putable = straight + put (value increasing when rates rise)

Thanks in advance

K.

#2

Maybe not; it depends on the current level of interest rates.

If the coupon rate on the bonds is, say, 6%, then if current interest rates are at 12% then both the callable and the putable bond will have positive convexity, but if current rates are at 2% then the callable bond will likely have negative convexity while the putable bond has positive convexity.

I suspect that they’re thinking about the latter.

#3

Got it, I suspected could have to do with negative convexity.

Appreciate the explanation!

#4

My pleasure.