Duration vs Convexity in Bond Portfolios
Understanding Duration and Convexity in Fixed Income
Key Definitions and Differences
Duration is a measure of a bond's sensitivity to changes in interest rates. Specifically, it estimates the percentage change in a bond's price for a 1% (100 basis points) change in yield, assuming a linear relationship. Duration is often used as a first-order approximation for interest rate risk and is expressed in years.
Convexity is a measure of the curvature in the relationship between bond prices and yields. While duration assumes a linear price-yield relationship, convexity accounts for the fact that this relationship is actually curved. Convexity quantifies how much the duration of a bond changes as yields change, providing a second-order adjustment to the price change estimate.
| Metric | Definition | Sensitivity Captured | Mathematical Order |
|---|---|---|---|
| Duration | First derivative of price with respect to yield | Linear (first-order) | 1st |
| Convexity | Second derivative of price with respect to yield | Curvature (second-order) | 2nd |
Which Matters More in a Rapid Interest Rate Rise?
In the context of a rapid interest rate rise, duration provides the primary estimate of price sensitivity. However, because large rate moves cause the price-yield relationship to become increasingly non-linear, convexity becomes more important. Duration alone will underestimate the price decline for large rate increases, while convexity adjusts for this underestimation.
For small rate changes, duration is typically sufficient. For large or rapid rate changes, convexity's impact grows, and ignoring it can lead to significant misestimation of risk. Bonds with higher convexity will experience less price decline (or more price appreciation) than those with lower convexity, all else equal, during large rate moves.
Practical Implications for Portfolio Management
In a scenario of rapid interest rate increases, relying solely on duration can lead to underestimating downside risk, especially for long-duration or high-convexity bonds. Portfolio managers typically monitor both metrics, but convexity becomes a critical risk management tool when rate volatility is high or moves are abrupt.
In summary, duration is the primary measure for small, incremental rate changes, but convexity becomes increasingly important for large, rapid rate moves, as it captures the non-linear effects on bond prices.
If you would like a worked example with numbers or a table comparing the price impact for different bonds under a specific rate shock, I can provide that as well.