Modified Duration
Quick Definition
A measure of a bond's price sensitivity to interest rate changes, expressed as the approximate percentage price change for a 1% change in yield.
Key Takeaways
- Measures approximate percentage price change per 1% yield change
- Calculated as Macaulay duration / (1 + yield/n)
- Higher modified duration means greater interest rate sensitivity
- A linear approximation — convexity corrects for larger rate changes
What Is Modified Duration?
Modified duration adjusts Macaulay duration to directly estimate how much a bond's price will change when interest rates move. It is calculated by dividing Macaulay duration by (1 + yield/number of compounding periods). For example, a bond with a modified duration of 5 would be expected to lose approximately 5% of its value if interest rates rise by 1 percentage point. Modified duration is a linear approximation, so it becomes less accurate for larger rate changes — this is where convexity provides a correction. Portfolio managers use modified duration to manage interest rate risk, matching the duration of their assets to their liabilities or adjusting duration based on their interest rate outlook.
Modified Duration Example
- 1A bond with modified duration of 7 would drop approximately 7% in price if yields rise from 4% to 5%
- 2Portfolio managers might shorten modified duration from 6 to 3 years if they expect rates to rise
Related Terms
Duration
A measure of a bond's price sensitivity to interest rate changes, expressed in years, indicating how much the price will move for a 1% change in rates.
Duration Risk
The risk that changes in interest rates will cause significant fluctuations in bond prices, with longer-duration bonds facing greater price volatility.
Convexity
A measure of the curvature in the relationship between bond prices and yields, indicating how duration changes as interest rates move.
Yield to Maturity (YTM)
The total annualized return an investor earns if a bond is held until maturity, accounting for coupon payments, purchase price, and par value at redemption.
Bond
A fixed-income debt security where investors loan money to an issuer in exchange for regular interest payments and return of principal at maturity.
Treasury Bond (T-Bond)
A long-term U.S. government debt security with a maturity of 20 or 30 years, paying semiannual coupon interest.
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