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- Convexity and prepayment risk
- Bonds, particularly longer duration bonds, demonstrate non-linear sensitivity between prices and changes in yields. This change in duration or interest rate sensitivity is most commonly referred to as convexity.
- While traditional non-callable fixed income securities such as US Treasuries demonstrate positive convexity, where the price sensitivity increases and yields fall and vice versa, callable bonds demonstrate negative convexity where price sensitivity to rising yields can increase.
- For fixed income investors who allocate to asset classes with issuer or borrower callability, negative convexity can compound price risks, as duration can extend simultaneously with rising yields, resulting in a larger negative effect on prices and returns.
- Elevated levels of interest rate or credit spread volatility can also amplify price risks around negatively convex bonds, as the empirical or implied risk of a larger move in yields—and corresponding decline in prices—is increased. — Selloffs in both short-term and longer-term bond
- Selloffs in both short-term and longer-term bond yields has resulted in elevated convexity risks around mortgages and other callable bond asset classes, with higher base level yields, elevated rate and spread volatility, and the potential for rates and spreads to become more positively correlated relative to the previous decade.
Introduction
Following historically low interest rates reached during the COVID-19 crisis, upward price pressures forced global central banks to adopt more restrictive monetary policy in an effort to calm inflationary fears. Coordinated monetary policy that both increased short-term funding rates and gradually reduced central bank balance sheet sizes put pressure on the entire US sovereign yield curve, resulting in a historically fast repricing in medium-to-long-term US Treasury yields between 2021 and 2023. The magnitude and pace of these interest rate moves brought to light the significant impact of interest rate duration and convexity that can, in some cases, amplify the sensitivity of bond prices to moves in interest rates.
The move higher in US Treasury yields was a double-edged sword for fixed income investors. Longer duration portfolio holdings in particular experienced significant negative mark-to-market returns; however, this higher interest rate environment has been the first time since the Global Financial Crisis (“GFC”)—and the introduction of Quantitative Easing (“QE”)—that long-duration bond investors have been able to attain any meaningful yield in fixed income, either via reinvestment or through allocation of new capital. Mortgage bonds and other negatively convex fixed income asset classes were particularly problematic as they experienced duration extension that amplified the negative returns as a result of the back up in interest rates.
Going forward, investors may benefit from a more thoughtful approach to managing interest rate and credit spread duration particularly for callable bond holdings. Understanding the potential impact of negative convexity in a more normalized interest rate environment may serve as an important risk management component of fixed income portfolio risk management.
1 / What impacts the bond price?
1.1 Bond price sensitivity
For large segments of the core fixed income market, the relationship between the bond price and its yield is positively convex, meaning that as yields move lower—and bond prices move higher, the rate at which the price increases as a function of the yield declining also increases. This can be demonstrated by looking at the simple formula for pricing a bond (see Figure 1), which calculates the bond price as a function of three main components:
- Time (the tenor or difference between settlement and maturity dates as well as the coupon payment frequency)
- Bond Payments (the current coupon and current price of the bond)
- Discount Rate (the current market yield)
