“The benefits of convexity only occurs for large changes in interest rates. Therefore, it is common to say you should reduce convexity if rates will be stable. But that is NOT the most accurate statement because it fails to quantify the initial yield pickup or premium received versus reduction in return for a large movement in rates. The most accurate way to look at it is that reducing convexity is beneficial if future volatility is less than the consensus volatility estimate”
Can anyone explain what the statement is trying to say?
I’ll think out loud and hope that I am answering this correctly. Key point: I have to remind myself that we must assume that a bond’s price has already accounted for all available information, unless said otherwise - I’ll expand on this at the end.
Thinking back to the basics some, convexity is a second derivative of the change in price, with duration being the first derivative, right? When convexity is increased, you inherently are buying a bond with a reduced yield (i.e. compared to a similar bond, a bond with a higher convexity will have a lower yield, but will be more sensitive to the change in the underlying price).
When rates are stable, convexity does not help you as a straight bond (or a less convex bond) has a higher yield than a bond with higher convexity given that you sacrifice yield for convexity. When rates do not fluctuate, the higher-convex, lower yielding bond underperforms given its lower yield.
Now expanding on the quote above, reducing convexity in a stable rate environment is correct, however the CFAI expects us to explain why, not to just state a fact; i.e. we are supposed to answer questions showing we understand the concept fully.
When answering the question, we must assume the bond is priced correctly and reflects all available information, including expected price change (and convexity). Given this fact, the best answer needs to show the grader that we understand that reducing convexity only works if the future price volatility/change is less than what the market expects, given the market is already pricing in a specific price change and you are now taking a bet against the market.
This is essentially what the answer was getting at. This question was a MC question from Exam 2 in Kaplan Schweser. I missed it also (I just said convexity neutral benefits in a stable rates environment). The thing that irritates me about this question is that my answer is 100% correct. I appreciate Schweser trying to point out a subtlety but I can’t yet think of a single CFA question where an answer was 100% correct and defendable be wrong because they liked another answer better.
I’ve marked this question up to Schweser trying to make a point and nothing else.