Loading the player...

What is 'Convexity'

Convexity is a measure of the curvature in the relationship between bond prices and bond yields that demonstrates how the duration of a bond changes as the interest rate changes. Convexity is used as a risk-management tool, which helps measure and manage the amount of market risk to which a portfolio of bonds is exposed.

Graph of bond price and yield; convexity.

BREAKING DOWN 'Convexity'

As interest rates increase, bond yields increase, and consequently, bond prices decrease. Conversely, as interest rates fall, bond yields fall and bond prices rise. In the example figure shown above, Bond A has a higher convexity than Bond B, which indicates that all else being equal, Bond A will always have a higher price than Bond B as interest rates rise or fall.

Convexity and Risk

Convexity is a better measure of interest rate risk, in relation to duration, because the concept of duration assumes that interest rates and bond prices have a linear relationship. Duration can be a good measure of how bond prices may be affected due to small and sudden fluctuations in interest rates. However, the relationship between bond prices and yields is typically more sloped, or convex. Therefore, convexity is a better measure for assessing the impact on bond prices when there are large fluctuations in interest rates.

As convexity increases, the systemic risk to which the portfolio is exposed increases. As convexity decreases, the exposure to market interest rates decreases and the bond portfolio can be considered hedged. In general, the higher the coupon rate, the lower the convexity (or market risk) of a bond. This is because market rates would have to increase greatly to surpass the coupon on the bond, meaning there is less risk to the investor.

Negative and Positive Convexity

If a bond's duration increases as yields increase, the bond is said to have negative convexity. In other words, the shape of the bond is said to be concave. Therefore, if a bond has negative convexity, its price would increase in value as interest rates rise, and the opposite is true. Some examples of bonds that exhibit negative convexity are bonds with a traditional call provision, preferred bonds and most mortgage-backed securities (MBS).

If a bond's duration rises and yields fall, the bond is said to have positive convexity. If a bond has positive convexity, it would typically experience larger price increases if yields fall, in relation to price decreases when yields increase. The typical types of bonds with positive convexity are bonds with make-whole call provisions and non-callable bonds. Under normal market conditions, the higher the coupon rate, the lower a bond's degree of convexity. Consequently, zero-coupon bonds have the highest degree of convexity because they do not offer any coupon payments.

RELATED TERMS
  1. Negative Convexity

    Negative convexity occurs when the shape of a bond's yield curve ...
  2. Convexity Adjustment

    A convexity adjustment is the change required to be made to a ...
  3. Bond

    A bond is a fixed income investment in which an investor loans ...
  4. Above Par

    Above par is a term used to describe the price of a bond when ...
  5. Rate Level Risk

    Rate level risk refers to the fact that the value of an existing ...
  6. Discount Bond

    A discount bond is a bond that is issued for less than its par ...
Related Articles
  1. Investing

    Corporate Bond Basics: Learn to Invest

    Understand the basics of corporate bonds to increase your chances of positive returns.
  2. Investing

    Understanding Interest Rates, Inflation And Bonds

    Get to know the relationships that determine a bond's price and its payout.
  3. Investing

    Corporate Bonds for Retirement Accounts

    Corporate bonds are usually the preferred choice in retirement accounts. Here are some of the benefits of corporate bonds, and strategies for a portfolio.
  4. Investing

    The Basics Of Bonds

    Bonds play an important part in your portfolio as you age; learning about them makes good financial sense.
  5. Investing

    Find the Right Bond at the Right Time

    Learn about the types of bonds you should consider investing in, when you should be buying them and how to compare yields against their time to maturity.
  6. Investing

    Why Investors Should Use Duration to Compare Bonds

    Duration is a helpful metric that determines a bond's sensitivity to interest rates.
  7. Investing

    How Rising Interest Rates Impact Bond Portfolios

    A look at the impact that changing interest rates - rising or falling - have on bonds and what investors need to consider.
  8. Investing

    Six biggest bond risks

    Bonds can be a great tool to generate income, but investors need to be aware of the pitfalls and risks of holding corporate and/or government securities.
  9. Investing

    Corporate Bonds: Advantages and Disadvantages

    Corporate bonds can provide compelling returns, even in low-yield environments. But they are not without risk.
  10. Investing

    4 basic things to know about bonds

    Learn the basic lingo of bonds to unveil familiar market dynamics and open to the door to becoming a competent bond investor.
RELATED FAQS
  1. How can I calculate convexity in Excel?

    Learn how to approximate the effective convexity of a bond using Microsoft Excel using a modified and simpler version of ... Read Answer >>
Hot Definitions
  1. Intrinsic Value

    Intrinsic value is the perceived or calculated value of a company, including tangible and intangible factors, and may differ ...
  2. Current Assets

    Current assets is a balance sheet account that represents the value of all assets that can reasonably expected to be converted ...
  3. Volatility

    Volatility measures how much the price of a security, derivative, or index fluctuates.
  4. Money Market

    The money market is a segment of the financial market in which financial instruments with high liquidity and very short maturities ...
  5. Cost of Debt

    Cost of debt is the effective rate that a company pays on its current debt as part of its capital structure.
  6. Depreciation

    Depreciation is an accounting method of allocating the cost of a tangible asset over its useful life and is used to account ...
Trading Center