Modified duration

Definition

Modified duration measures the sensitivity of a bond's price to changes in interest rates, reflecting how much the price of a bond will change with a 1% change in yield. It is an essential concept in understanding interest rate risk for fixed-income securities and helps investors gauge the potential impact of interest rate movements on their bond investments.

5 Must Know Facts For Your Next Test

1. Modified duration is calculated by dividing Macaulay duration by (1 + yield), providing a more accurate measure of interest rate sensitivity.
2. A higher modified duration indicates greater sensitivity to interest rate changes, meaning the bond's price will fluctuate more with shifts in yield.
3. Investors use modified duration to manage interest rate risk in their portfolios, adjusting their bond holdings based on expected interest rate movements.
4. For bonds with embedded options, such as callable bonds, modified duration may not fully capture interest rate risk due to the potential exercise of those options.
5. Modified duration is generally expressed in years, making it easier to compare across different bonds and understand their relative risks.

Review Questions

• How does modified duration help investors assess the risk associated with bond investments?
  • Modified duration assists investors in understanding how much the price of a bond is likely to change when interest rates fluctuate. By quantifying the sensitivity of a bond's price to interest rate changes, investors can make informed decisions about which bonds to hold or sell based on their expectations for future interest rates. This helps them manage their overall portfolio risk and aligns their investments with their financial goals.
• Compare and contrast modified duration and Macaulay duration in terms of their applications for bond valuation and risk assessment.
  • While both modified duration and Macaulay duration measure bond sensitivity to interest rates, they serve different purposes. Macaulay duration focuses on the weighted average time until cash flows are received, which helps assess how long it takes for an investor to recover their investment. In contrast, modified duration directly relates to price sensitivity by adjusting Macaulay duration for changes in yield. This makes modified duration more applicable for assessing interest rate risk in a practical sense.
• Evaluate the implications of using modified duration for managing an investment portfolio that includes bonds with embedded options, like callable bonds.
  • Using modified duration for managing portfolios that include callable bonds can be challenging due to the uncertainty introduced by embedded options. Callable bonds may be redeemed early if interest rates decline, which can alter expected cash flows and impact price sensitivity. As a result, modified duration might understate the interest rate risk associated with these bonds since it doesn't account for the likelihood of option exercise. Investors must consider both modified duration and other measures like convexity to better navigate the complexities of managing such investments.

Related terms

Macaulay duration: Macaulay duration is the weighted average time until a bond's cash flows are received, used to measure interest rate sensitivity.

Interest rate risk: Interest rate risk is the potential for investment losses due to fluctuations in interest rates, particularly impacting bonds and fixed-income securities.

Convexity: Convexity measures the curvature in the relationship between bond prices and yields, providing insights into how price changes accelerate or decelerate with interest rate changes.