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Negative Convexity


Negative convexity refers to the shape of the price-yield curve for certain fixed-income securities, specifically, when the price appreciation of the security is less than the price depreciation for an equal change in yield. This typically occurs in mortgage-backed securities and callable bonds, where prepayment or call options limit the potential price gains. Investors holding securities with negative convexity may face higher interest rate risk and price volatility.


Negative Convexity can be broken down phonetically as follows:Negative: /ˈneɡətɪv/Convexity:/kənˈvɛksɪti/

Key Takeaways

  1. Negative convexity occurs when a bond or financial instrument’s price decreases more rapidly due to an increase in interest rates as compared to the rate at which it increases with declining yields.
  2. Bonds with negative convexity, such as callable bonds or mortgage-backed securities (MBS), typically offer higher yields to compensate for the increased reinvestment risk and uncertainty in their cash flows and duration.
  3. In a fixed income portfolio, managing negative convexity is crucial to successful risk management. Investors may need to diversify their holdings or utilize derivative strategies to hedge or offset the potential impact of changes in interest rates.


Negative convexity is an important concept in business and finance because it has significant implications for investors, portfolio managers, and bond issuers. It refers to a bond or debt security’s price sensitivity to changes in interest rates, which can ultimately affect the potential earnings and risks associated with bond investments. When a bond exhibits negative convexity, its duration decreases as interest rates rise, making it more susceptible to price declines in response to increasing rates. Consequently, this may lead to reduced potential returns and a higher risk profile for investors, particularly in a rising interest rate environment. Additionally, negative convexity can lead to active portfolio management strategies to mitigate risk, such as using derivatives and restructuring portfolios, ultimately adding to the complexity and costs for both investors and financial professionals. Understanding negative convexity allows investors to make more informed decisions and better manage their fixed-income investments in the context of a dynamic market environment.


Negative convexity is a notable concept in finance, particularly in the bond market, as it plays a vital role in determining the risk associated with bond investments. It primarily refers to the relationship between a bond’s yield and its duration or price sensitivity. A bond with negative convexity exhibits a decreased price as the yield rises and an increased price when its yield falls. This inverse relationship between a bond’s price and interest rate changes may significantly affect a bondholder’s potential returns and risk exposure. Considering the purpose and application of negative convexity, it helps investors and fund managers in making informed decisions regarding their bond portfolios. Bonds with negative convexity, like mortgage-backed securities (MBS) and callable bonds, often come with prepayment or call risk. This risk arises when bond issuers have the right to redeem bonds before their maturity date, usually during low-interest environments. As a result, investors tend to reinvest the proceeds at lower rates, which directly impacts their overall returns. By analyzing negative convexity, market participants can more accurately assess the potential payoff and risks involved in holding such securities, thus enabling them to optimize their portfolios according to the desired goal – whether it is capital preservation, income generation, or balanced growth.


Negative convexity is a characteristic of certain types of fixed income investments where the price appreciation experienced when interest rates fall is smaller than the price depreciation experienced when interest rates rise. This results in an additional layer of risk for investors holding these types of securities. Here are three real-world examples of financial instruments with negative convexity: 1. Callable Bonds: A callable bond is a type of bond that allows the issuer to repurchase the bond and return the principal to the investor before the bond’s maturity date. When interest rates decline, the issuer can call the bond, forcing the investor to reinvest the returned principal at lower interest rates. In this situation, the price appreciation of the bond is limited by the call feature, while the potential price depreciation when interest rates rise remains significant, leading to negative convexity. 2. Mortgage-Backed Securities (MBS): Mortgage-backed securities are a type of investment where investors purchase pools of mortgages repackaged as a single security. Homeowners, however, have the option to prepay their mortgages (i.e., refinance) when mortgage rates fall. As a result, the securities’ investors receive their principal payments early, forcing them to reinvest at lower interest rates. The price appreciation when interest rates decline is limited by the prepayment option, while the price depreciation when interest rates rise remains significant, resulting in negative convexity. 3. Collateralized Mortgage Obligations (CMOs): CMOs are a type of mortgage-backed security that segregate the mortgage pools into different tranches, each with different risk profiles and cash flow characteristics. Some tranches in a CMO may exhibit negative convexity due to their exposure to prepayment risk, as homeowners have the option to prepay their mortgages when interest rates fall. Just like with MBS, the price appreciation when interest rates decline is limited by the prepayment option, while the price depreciation when interest rates rise remains significant for specific tranches, leading to negative convexity in those cases.

Frequently Asked Questions(FAQ)

What is Negative Convexity?
Negative Convexity is a characteristic of some fixed-income securities, where the bond’s price sensitivity to interest rate changes is negatively curved. In simpler terms, when interest rates rise, the bond’s duration shortens, and when interest rates fall, the bond’s duration lengthens. This feature leads to unfavorable price movements for investors.
Which types of securities typically exhibit Negative Convexity?
Securities such as callable bonds, mortgage-backed securities (MBS), and some asset-backed securities (ABS) often exhibit Negative Convexity. These securities can be called or pre-paid, leading to changes in cash flows in response to interest rate fluctuations.
How does Negative Convexity impact a bond’s performance?
A bond with Negative Convexity tends to perform poorly when interest rates change, as it leads to an undesirable price behavior. When interest rates fall, the bond may experience less price appreciation compared to other bonds with similar characteristics. Conversely, when interest rates rise, these bonds may see greater price depreciation.
How does Negative Convexity differ from Positive Convexity?
Positive Convexity is a characteristic where a bond gains price sensitivity when interest rates fall, and loses price sensitivity when interest rates rise. This feature is more desirable for bond investors, as it leads to favorable price movements. In contrast, Negative Convexity works in the opposite way, with bonds losing price sensitivity when rates fall and gaining sensitivity when rates rise, leading to unfavorable price performance.
How can I manage the risks of Negative Convexity?
To manage the risks of Negative Convexity, investors can diversify their fixed income portfolio by investing in a mix of securities with different convexity profiles. This can reduce the overall impact of interest rate changes on the portfolio’s performance. Investors can also consider other factors like yield, credit quality, and maturity to create a balanced fixed income strategy.
Is it possible for a bond to switch from Negative Convexity to Positive Convexation during its lifetime?
Yes, it is possible for a bond to switch from Negative Convexity to Positive Convexity during its life. Such a change might occur due to alterations in interest rates, changes in cash flow schedules, or other factors related to the bond’s structure. However, it’s essential for investors to monitor and manage their portfolios actively.

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