Modified Duration
Measures the percentage price sensitivity of a bond to changes in its yield to maturity, adjusting the time-based Macaulay duration for the bond's yield environment.
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Core idea
Overview
While Macaulay Duration measures the weighted average time to receive cash flows, Modified Duration linearizes the relationship between price and yield. It is mathematically defined as the negative percentage change in price for a unit change in yield. By dividing the Macaulay duration by one plus the periodic yield, it provides a precise estimation of how much a bond's price will move given a specific fluctuation in interest rates.
When to use: Use this when calculating the interest rate risk of a bond portfolio or predicting price movements in response to market yield shifts.
Why it matters: It allows portfolio managers to hedge against interest rate volatility and assess the relative risk of different fixed-income securities.
Symbols
Variables
D_M = Modified Duration, D_Macaulay = Macaulay Duration, YTM = Yield to Maturity, k = Compounding periods per year
One free problem
Practice Problem
Calculate the Modified Duration of a bond with a Macaulay Duration of 8.0 years, a YTM of 6%, and annual coupon payments.
Solve for:
Hint: Divide 8.0 by (1 + 0.06/1).
The full worked solution stays in the interactive walkthrough.
Where it shows up
Real-World Context
If a bond has a Modified Duration of 5.0 and interest rates rise by 1%, the bond price is expected to decrease by approximately 5%.
Study smarter
Tips
- Always ensure the YTM is expressed as an annual rate and k matches the compounding frequency.
- Remember that Modified Duration is only an approximation for small yield changes due to the convexity effect.
- Note that Modified Duration is always negative for standard bonds, indicating an inverse relationship between price and yield.
Avoid these traps
Common Mistakes
- Failing to divide the annual YTM by the number of coupon periods per year (k).
- Confusing Macaulay Duration with Modified Duration.
- Assuming the relationship remains linear for large interest rate shocks.
Common questions
Frequently Asked Questions
Use this when calculating the interest rate risk of a bond portfolio or predicting price movements in response to market yield shifts.
It allows portfolio managers to hedge against interest rate volatility and assess the relative risk of different fixed-income securities.
Failing to divide the annual YTM by the number of coupon periods per year (k). Confusing Macaulay Duration with Modified Duration. Assuming the relationship remains linear for large interest rate shocks.
If a bond has a Modified Duration of 5.0 and interest rates rise by 1%, the bond price is expected to decrease by approximately 5%.
Always ensure the YTM is expressed as an annual rate and k matches the compounding frequency. Remember that Modified Duration is only an approximation for small yield changes due to the convexity effect. Note that Modified Duration is always negative for standard bonds, indicating an inverse relationship between price and yield.