Getting to Grips with Bond Convexity Calculation
Bond convexity is a complex and advanced bond concept to help investors understand and visualize the changes in yield of a bond. Bonds are debt instruments issued by municipalities or private corporations in order to raise capital for specific projects. When a city wants to build a new bridge, the government will issue a municipal bond. Should a corporation wish to buy a competing company, the board of directors will approve a bond issuance to raise capital for that purpose.
A bond is an investment instrument providing the investor with a pre-determined rate of return and duration. Usually investors will find both short term (3 years or less) and longer term (up to 20 years) bonds with a fixed interest rate. However, it is not uncommon for bonds to be sold from investor to investor during the term of a bond. And because current market interest rates are flexible and change frequently, bond convexity calculation is required to help address the changes in price of a bond on the secondary market.
What Is Bond Convexity?
Bond convexity is a helpful calculation tool to compare two or more different bonds, their current rate of return, and their market risk. Fluctuations in market interest rates have a tremendous impact on bond convexity. A bond with a coupon rate, or a pre-determined schedule of dividend payments, can sell for a higher or lower price depending on the current market interest rate. A bond with a higher coupon rate selling in a market with lower interest will attract a higher price from another investor. Conversely, a lower coupon rate in a market of higher interest rates will provide a reduced yield, and thus, will sell for a lower price. Generally, the higher the coupon rate is, the lower the convexity the bond will be. Zero coupon bonds with only one interest payment at maturity have the highest convexity.
How is Bond Convexity Calculated?
Consider a matrix where the x-axis is price, while the y-axis is yield. Considering all factors remained the same, you would predict that a straight diagonal line represents a convexity tangent. A higher price results in a corresponding lower yield.
However, market conditions are not always the same. Consider that the bond convexity tangent is a bowl shape (convex). The higher the convexity, the deeper the bowl will be. Therefore, the actual bond price changes within the yellow area of the illustration below based on current market interest rates and the duration of the bond.
For example, you are in the market to purchase either Bond I or Bond II. Both have the same interest rate and duration. Bond I is has a higher credibility rating from Moody’s, while Bond II is a zero coupon bond. A higher rating means there is less risk for Bond I, thus it has a smaller convexity. Bond II has a higher convexity since it provides a set yield at maturity, thus it is more susceptible to market fluctuations. By comparing the bond convexities, you can determine as an investor which risk you would rather take with your purchase.
Bond convexity is not for the faint of heart. It is a complex calculation which can be found using online calculators or pre-programmed Excel functions. However, with bond convexity aids, you have the tools needed to determine the right bond for your investment needs.
Popularity: 98% [?]