Explain the concept of duration and convexity.
Learn from Mathematical Finance
Understanding Interest Rate Risk: Duration and Convexity
In the world of fixed-income investments, particularly bonds, interest rate changes significantly impact their prices. Two key concepts, duration and convexity, help investors gauge the sensitivity of a bond's price to these fluctuations.
Duration: A Measure of Price Sensitivity
* Definition: Duration is a weighted average of the time it takes to receive all of a bond's cash flows (coupon payments and principal repayment). It essentially reflects the bond's effective maturity from an interest rate risk perspective.
* Interpretation: A higher duration indicates a greater sensitivity to interest rate changes. When interest rates rise, bond prices generally fall. Conversely, when interest rates decline, bond prices tend to increase. A bond with a duration of 5 years will experience a larger price change (either a decrease or increase) compared to a bond with a duration of 2 years, given the same interest rate movement.
* Limitation: Duration assumes a linear relationship between interest rates and bond prices. However, this relationship is not perfectly linear, especially for larger interest rate changes.
Convexity: Beyond Duration's Linearity
* Definition: Convexity measures the curvature in the relationship between a bond's price and its yield. It essentially reflects how the duration of a bond itself changes as interest rates fluctuate.
* Explanation: Duration provides a good estimate for price changes with small interest rate movements. However, with larger changes, the actual price change may differ. Convexity accounts for this discrepancy.
* Positive Convexity: If a bond has positive convexity, its duration increases as interest rates fall (and vice versa). This means the price increase due to a decline in interest rates will be greater than what duration alone would predict.
* Negative Convexity: Conversely, a bond with negative convexity experiences a decrease in duration as interest rates rise (and vice versa). This translates to a smaller price decline compared to what duration would suggest.
* Importance: Considering convexity provides a more nuanced understanding of how a bond's price will react to significant interest rate movements.
By understanding both duration and convexity, investors can make informed decisions about their fixed-income portfolios and manage their exposure to interest rate risk.
Additional Notes:
* Bond characteristics such as coupon rate, maturity, and call provisions influence both duration and convexity.
* Duration and convexity are also used to assess the interest rate risk of a portfolio of bonds.