1. Advanced Bond Concepts: Introduction
  2. Advanced Bond Concepts: Bond Type Specifics
  3. Advanced Bond Concepts: Bond Pricing
  4. Advanced Bond Concepts: Yield and Bond Pricing
  5. Advanced Bond Concepts: Term Structure of Interest Rates
  6. Advanced Bond Concepts: Duration
  7. Advanced Bond Concepts: Convexity
  8. Advanced Bond Concepts: Formula Cheat Sheet
  9. Advanced Bond Concepts: Conclusion

Duration is a linear measure, meaning it assumes that for a certain percentage of change in interest rates, an equal percentage change in price will occur. As interest rates change, however, a bond’s price is unlikely to change linearly, and instead would change over some curved, or “convex” function of interest rates.

How Convexity Works

The graph that shows the relationship between bond price and yield will be convex. A bond’s convexity measures the curvature of its price/yield relationship. The degree of convexity shows how much a bond’s yield changes in response to a change in price.

When used together, duration and convexity offer a better approximation of the percentage of price change resulting from a particular change in a bond’s yield than using duration alone. In addition to improving this estimate, convexity can also be used to compare bonds with the same duration.

If two bonds offer the same duration and yield but one exhibits greater convexity, changes in interest rates will affect each bond in a different manner. A bond with greater convexity is less affected by interest rates than a bond with less convexity. In addition, bonds with greater convexity will have a higher price than bonds with lower convexity, regardless of what’s happening with interest rates.

Some convexity points to remember:

  • The graph of the price-yield relationship for plain vanilla bonds shows positive convexity. The price-yield curve increases as yield decreases, and vice versa. And as market yields decrease, the duration increases, and vice versa.
  • The higher the coupon rate, the lower a bond’s convexity. Zero-coupon bonds have the highest convexity.
  • Callable bonds will show negative convexity at certain price-yield combinations. Negative convexity means that as market yields decrease, duration decreases as well.

Advanced Bond Concepts: Formula Cheat Sheet
Related Articles
  1. Investing

    Immunization Inoculates Against Interest Rate Risk

    Big-money investors can hedge against bond portfolio losses caused by rate fluctuations.
  2. Investing

    Use Duration And Convexity To Measure Bond Risk

    Find out how this measure can help fixed-income investors manage their portfolios.
  3. Investing

    Treasuries Rout May Deepen on Mortgage Hedging

    Fed rate hikes may spur mortage bond owners to sell Treasuries to reduce their exposure to rising rates
  4. Investing

    Why Investors Should Use Duration to Compare Bonds

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

    The Basics Of Bond Duration

    Duration tells investors the length of time it will take a bond's cash flows to repay the investor the price he or she paid for the bond. A bond's duration is stated as a number of years and ...
  6. Investing

    Find The Right Bond At The Right Time

    Find out which bonds you should be investing in and when you should be buying them.
Frequently Asked Questions
  1. What is the difference between secured and unsecured debts?

    The differences between secured and unsecured debt, and how banks buffer risks associated with each type of loan through ...
  2. How Many Times has Warren Buffett Been Married?

    Warren Buffett has been married twice in his life, but the circumstances surrounding the marriages were unconventional.
  3. What's the smallest number of shares of stock that I can buy?

    Many people would say the smallest number of shares an investor can purchase is one, but the real answer is not as straightforward. ...
  4. What is an economic moat?

    An economic moat refers to a company's ability to maintain competitive advantages to protect its long-term profits and market ...
Trading Center