For fixed income securities such as Treasuries and corporate bonds, duration is a good, relatively stable measure of their price sensitivity to changes in interest rates because they generally mature at a fixed time.

The majority of municipal bonds, however, can be “called”—or redeemed early by their issuers—typically at the 10-year mark for a bond with a 30-year nominal maturity. The probability of that call option being exercised can change a bond’s duration. Negative convexity is the measure of that change.

Here’s how it can impact bondholders: In a falling rate environment, a callable bond’s duration typically shortens, muting price gains for the investors holding them, because they are more likely to be called. And when rates are rising, as they have been since March 2022, a callable bond’s duration tends to lengthen, amplifying price declines as the prospect of calling the bond becomes less attractive. 

In a scenario where yields of newly issued bonds are significantly lower than a callable bond’s coupon rate, the market effectively prices in a 100% probability that the bond will be called because the issuer will want to refinance the debt at a lower cost. Yields moving a little higher or lower than that probably won’t dampen its chances of being called much, so the impact on duration will likely be modest.

And in a scenario where yields of newly issued bonds are significantly higher than a callable bond’s coupon rate, the market effectively prices in a 0% probability that the bond will be called because the issuer won’t want to refinance the debt at a higher cost. Yields moving a little higher or lower than that will probably still result in the call option not being exercised, so here too the impact on duration will likely be modest.

“Where you see the biggest impact from negative convexity is when yields move close to a bond’s coupon rate,” Khang said. “When it’s not clear whether the bond will be called or not, that’s when you see the bond’s duration—and price—change the quickest.”

The figure below illustrates this point for a hypothetical 30-year callable bond with a coupon of 5% under different yield assumptions. 

Following the global financial crisis, callable 5% municipal bonds still dominated the market. These bonds often traded at a premium―or a price above par―given that the coupon was higher than prevailing yields and the likelihood they would be called.

The prolonged low-rate environment, however, led investors to consider lower-coupon bonds to enhance returns. Issuance ramped up for bonds with coupons of 4%, 3%, and even 2%, diversifying what’s referred to as the “coupon stack” available to investors. 

The evolution of the coupon stack brought with it the latent risk of negative convexity, which manifested itself only when the Federal Reserve embarked on an aggressive rate-hiking cycle last year to combat inflation.

Sharply higher rates and steep declines in bond prices made 2022 a bad year for bonds in general.

For callable munis, negative convexity emerged as a significant factor in this underperformance. And it affected a broader swath of the muni market than it might have previously, given the proliferation of lower-coupon callable bonds. Whereas only 13% of the muni bond universe was subject to material negative convexity in 2015 by our estimates, that figure surged to 41% at the end of 2022. 

“Greater diversity in the coupon stack has significantly changed the game for active managers,” said Vanguard municipal analyst Justin Ferrera. “In this higher-yield environment where callable munis no longer all rise and fall together, we can potentially capture performance through managing convexity risk, which simply wasn’t a factor seven or eight years ago.”

Of course, an awareness of the diversified coupon stack and its potential usefulness for navigating negative convexity in the muni market is just the beginning. Implementing any of these ideas in a real-world portfolio management setting requires carefully weighing many additional considerations—the availability of the desired bonds, the pricing of discount versus premium callables, and the capacity for managing active convexity positions as interest rates evolve.

“Negative convexity coming back into play has given us an opportunity to maximize return characteristics for shareholders going forward,” said Nathan Will, head of municipal credit research. “This is something that wasn’t prevalent during the last couple of years given the low interest rate environment.” 

• Active Fixed Income Perspectives Q3 2023: Cruising altitude (article, issued July 2023)
• What the rapid rise in rates could mean for investors (article, issued June 2023)
• A look back and forward at active bonds (article, issued May 2023)