I understand that convexity is generally a good thing (when expecting volatility in r, buy convexity, when expect low volatility in r, sell convexity). Convexity dampens the impact of higher rates on price, and has a stronger impact on the price for lower rates. It’s also a requirement in multiple-liability immunization using duration-matching where the asset convexity must be >= that of liabilities.
The only time convexity is presented as a buzz-kill is for single liabilities, where cashflows should be more concentrated than dispersed (i.e. lower convexity). The CFAI text refers to this as structural risk facing non-parallel shifts and twists.
What if we have a flattening twist, or a down-ward non-parallel shift, for single-liability immunization? Wouldn’t convexity be a good thing? What’s raising this question in my head is that later in the fixed income readings, the curriculum talks about barbell portfolios with higher convexity being better for flattening twists than bulleted portfolios.
I’ve got a similar question- why does a barbell do better if rate volatility is expected, exactly? wouldn’t it’s long end exposure be hurt badly if rates went way up ont he back end?
Similarly- convexity confused me as well- why is convexity better when rates aren’t going to change? Doesn’t higher convexity imply taking on a slightly lower yield?
Sorry mph but I disagree. The book shows an example of a non-parallel shift on page 128 (short rates rise, long rates unchanged) where barbell portfolios outperform bullet portfolios. Since barbell portfolios have greater dispersion and greater convexity, this goes against what you said.
I’ve studied this enough that I think I can answer your questions (I had the same questions a few days ago)
For your first question, remember that with convexity, the downward impact of higher rates on prices is lower while the upward impact of lower rates on prices is higher than a portfolio with less convexity. This is why during volatility (rates could go up or down), convexity and barbell portfolios would outperform less convex and bulleted portfolios.
For your second question, convexity actually doesn’t help you when you expect rates aren’t going to change. So to increase your yield, you would sell convexity. That requires a premium generating activity, such as writing a call option, or buying a MBS. Writing a call is the same as buying a callable bond (remember the price of a callable bond = price of straight bond - price of embedded call option).
My response wasn’t complete I guess. I buy convexity for parallel shifts, and I have more specific strategies depending on the level, slope and curvature changes. For example, a steepening yield (which is also considered a change in yield), you would want a bullet structure rather than a barbell structure… And the bullet has less convexity than the barbell.
I guess the point of my comment is whether convexity is “good enough.” Though yes, I definitely agree convexity is always a good thing (provided I don’t expect rates to remain stable).
Although to be fair, there are folks that are willing to take massive negative carry for lots of positive convexity if they want to take a view on vol. So “good enough” isn’t super precise.
