Struggling with one of the CFAI mock’s questions - Under what scenario is the putable’s convexity lower than equivalent option-free?
I was thinking as rates go down, putable and option-free behave similarly, so let’s ignore that. As rates go up, putable doesn’t go down in price as much, since investor can put the bond back. Graphing this in my head, I see the putable bond price curve more than straight, being bounded by its put price. Feels like the convexity would be greater
But the mock says it can be less. Under what scenario?
Less convexity = flatter curve. As rates go up, the profile of the putable bond becomes less convex (rates do not affect the price as much as in an option-free equivalent, and the one-sided upside duration is less than the one-sided downside duration).
What does an investor want protection from? A decline in the price of the bond.
When does a bond’s price decline? When interest rates rise.
The put serves as a floor on the bond’s price. So the curve for a putable bond flattens at higher interest rates relative to straight bonds than can continue falling in price. Flatter curve = less convexity.
So if the Kaplan book says, “Putable bonds exhibit positive convexity throughout.” Do they have it wrong? Or do they just mean something different than what I gather from that statement?.
Putable bonds have positive convexity everywhere, just as straight bonds have.
I’d want to price a putable bond at a dozen or so YTMs and see how the convexity compares to that of a straight bond. At low yields they’ll be quite close to each other, but I suspect that as the yield increases, the putable’s convexity will first move above the straight bond’s, then drop below it.