Convexity is apparent in the relationship between bond prices and bond yields. It is the curvature in the relationship between bond prices and interest rates, which reflects the rate at which the duration of a bond changes as interest rates change. Duration measures a bond’s sensitivity to changes in interest rates and represents the expected percentage change in the price of a bond for a 1% change in interest rates.
Key Takeaways
- Convexity measures a portfolio’s exposure to market risk.
- It represents the curvature in the relationship between bond prices and bond yields.
- Convexity shows how the duration of a bond changes as interest rates change.
- Negative convexity occurs when a bond’s duration increases as yields increase.
- Positive convexity happens when a bond’s duration rises and yields fall.
Understanding Convexity
Convexity demonstrates how the duration of a bond changes as the interest rates change. Portfolio managers use convexity as a risk-management tool to measure and manage the portfolio’s exposure to interest rate risk.
As interest rates fall, bond prices rise, and conversely, rising market interest rates lead to falling bond prices. The bond yield is the earnings or returns an investor can expect to make by buying and holding that particular security. The bond price depends on several characteristics, including the market interest rate, and can change regularly.
If market rates rise, new bond issues must have higher rates to satisfy investor demand for lending money. The price of bonds returning less than that rate will fall, as bondholders seek bonds with higher yields. Eventually, the price of these bonds with lower coupon rates will drop to a level where the rate of return is equal to the prevailing market interest rates.
Bond Duration
Bond duration measures the change in a bond’s price when interest rates fluctuate. If the duration of a bond is high, it indicates that the bond’s price will move to a greater degree in the opposite direction of interest rates. If rates rise by 1%, a bond or bond fund with a 5-year average duration would likely lose approximately 5% of its value. Conversely, when this figure is low, the debt instrument shows less movement to the change in interest rates.
The higher a bond’s duration, the larger the change in its price and the greater its interest rate risk. Investors anticipating rising interest rates should consider bonds with a lower duration.
Bond duration should not be confused with its term to maturity. Though both decline as the maturity date approaches, the latter measures the time during which the bondholder will receive coupon payments until the principal is paid.
As a general rule, if rates rise by 1%, bond prices fall by 1% for each year of maturity.
Convexity and Risk
Convexity builds on the concept of duration by measuring the sensitivity of the duration of a bond as yields change. Convexity is a better measure of interest rate risk where duration assumes a linear relationship between interest rates and bond prices, while convexity produces a slope.
Convexity is especially useful for assessing the impact on bond prices during large fluctuations in interest rates. Increased convexity indicates higher systemic risk to the portfolio, as fixed-income instruments become less attractive with rising rates. Conversely, decreased convexity indicates lower exposure to market interest rates, making the bond portfolio more hedged. Higher coupon rates usually correlate with lower convexity, reducing market risk.
Example of Convexity
A bond issuer, XYZ Corporation, offers two bonds: Bond A and Bond B. Both have a face value of $100,000 and a coupon rate of 5%. Bond A matures in 5 years, while Bond B matures in 10 years.
Using duration, Bond A has a duration of 4 years, while Bond B has a duration of 5.5 years. This means for every 1% change in interest rates, Bond A’s price changes by 4%, while Bond B’s price changes by 5.5%. If interest rates increase by 2%, Bond A drops by 8%, and Bond B by 11%. However, Bond B’s higher convexity buffers against such changes, resulting in smaller-than-expected price fluctuations.
Negative and Positive Convexity
Negative convexity occurs when a bond’s duration increases as yields increase, causing the bond price to decline more rapidly with rising yields.
Positive convexity happens when a bond’s duration rises as yields fall, leading to accelerated bond price increases.
Under normal market conditions, bonds with higher coupon rates typically have lower convexity, presenting less risk as market interest rates need a significant uplift to rival their yield.
Conclusion
Understanding convexity is crucial for managing bond investments as it measures how bond prices react to interest rate changes. By mastering this concept, investors can strategically manage their bond portfolios, optimizing returns and minimizing risks amid fluctuating market conditions.
Related Terms: interest rates, bond yield, bond duration, market risk, systemic risk, coupon rate, negative convexity, positive convexity.
