Negative Convexity

A property of certain bonds where price appreciation is limited when rates fall, and price depreciation accelerates when rates rise.

Negative convexity is a characteristic of certain fixed-income securities where the relationship between price and interest rates is non-linear in an unfavorable way. In a standard bond, which exhibits positive convexity, price increases accelerate as interest rates fall, and price declines slow down as rates rise. In contrast, a negatively convex bond experiences capped or slowing price appreciation as rates decline, while its price losses accelerate as interest rates rise. This phenomenon is most commonly observed in callable bonds and mortgage-backed securities (MBS). It occurs because these instruments contain embedded options. When interest rates fall, homeowners refinance their mortgages and issuers call back high-coupon bonds to reissue debt at lower rates. This prepayment activity forces the investor to receive their principal back early and reinvest it at lower prevailing rates, a dynamic known as prepayment risk. Conversely, when rates rise, borrowers hold onto their low-rate loans longer, extending the bond's life and locking the investor into a depreciating asset, which is known as extension risk. For retail investors, understanding negative convexity is crucial for managing risk in fixed-income portfolios. Because of this asymmetric risk profile, where the investor faces limited upside and accelerated downside, negatively convex assets must typically offer a yield premium—or a higher spread over risk-free government bonds—to compensate investors for taking on the embedded option risk.

An investor purchases a callable bond at par ($1,000) with a 6% coupon when market rates are at 6%. If market interest rates drop sharply to 3%, a standard non-callable bond's price might rise to $1,200 due to its positive convexity. However, because the issuer has the right to call the bond at $1,050, the market price of this callable bond will not rise much past $1,050. The investor's potential capital gain is capped at $50 ($1,050 - $1,000) rather than the $200 gain a standard bond would have achieved.