Modified Duration

Bonds & Fixed Income
Updated Apr 2026 • Has calculator

Estimates the percentage price change of a bond for a 1% change in yield.

What is Modified Duration?

Modified duration adjusts Macaulay duration for the level of yield to produce a direct measure of interest rate sensitivity. A modified duration of 4 means the bond's price will change by approximately 4% for every 1 percentage-point change in yield — rising when yields fall and falling when yields rise. Modified duration is a linear approximation; for large yield changes, convexity must be added for accuracy. Because it depends on both the cash flow timing (Macaulay duration) and the discount rate, modified duration decreases as yields rise and increases as maturity lengthens.

Formula

ModDur = MacaulayDuration / (1 + YTM / freq)

Worked Example

Worked example — Hypothetical 8% Annual Coupon Bond

5-year maturity, YTM = 8%

Step 1  Macaulay duration: 4.3121 years | YTM: 8% | Annual coupons (freq=1)
Step 2  ModDur = 4.3121 / (1 + 0.08/1)
Step 3  ModDur = 4.3121 / 1.08 = 3.9927 ≈ 3.99 years
Step 4  → A 100-bps rise in yield drops the bond price by approximately 3.99%

Source: CFA Institute — Fixed Income Analysis, 3rd ed., Ch. 5 (2023-01-01)

Calculate Modified Duration

Macaulay duration in years (calculated separately)

Annual YTM of the bond

1 = annual, 2 = semi-annual

Modified Duration

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Not investment advice.

How to Interpret Modified Duration

< 2
< 2 yrs: Very low rate sensitivity — short-term notes
2 – 5
2–5 yrs: Moderate — typical intermediate-term bond
5 – 10
5–10 yrs: High sensitivity — long-dated investment-grade bonds
> 10
> 10 yrs: Very high sensitivity — long-duration Treasury or strips

📚 Bond Risk — Complete the path

  1. Macaulay Duration
  2. Modified Duration
  3. Effective Duration
  4. Convexity
  5. Duration Price Approximation
Sources
  1. CFA Institute — Fixed Income Analysis, 3rd ed., Ch. 5
  2. Investopedia — Modified Duration