Effective Duration

Bonds & Fixed Income
Updated Apr 2026 • Has calculator

A numerical duration measure that uses actual price changes from parallel yield shifts, suitable for bonds with embedded options.

What is Effective Duration?

Effective duration estimates interest rate sensitivity using actual market prices observed at a small yield shift up and down, rather than discounting cash flows analytically. This makes it applicable to bonds with embedded options — callable bonds, putable bonds, mortgage-backed securities — whose cash flows change when yields move. By contrast, Macaulay and modified duration assume fixed cash flows and therefore missprice optionality. Effective duration is computed as (P− − P+) / (2 × P0 × ΔY), where P− and P+ are prices at yields below and above the base yield by ΔY. The result is in years, interpreted identically to modified duration.

Formula

EffDur = (P− − P+) / (2 × P0 × ΔY)

Worked Example

Worked example — Hypothetical Callable Corporate Bond

Secondary market pricing at 100 bps yield shift

Step 1  Current price P0: $1,000 | Yield shift ΔY: 1% (100 bps)
Step 2  Price at YTM − 1%: $1,041 | Price at YTM + 1%: $961
Step 3  EffDur = ($1,041 − $961) / (2 × $1,000 × 0.01)
Step 4  EffDur = $80 / $20 = 4.00 years
Step 5  → Bond price changes ~4% for every 100-bps parallel yield move

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

Calculate Effective Duration

Bond price when yield is shifted down by ΔY

Bond price when yield is shifted up by ΔY

Bond price at the base yield

Size of yield shift in percent (e.g. 1 for 100 bps)

Effective Duration

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Not investment advice.

How to Interpret Effective Duration

< 2
< 2 yrs: Very low — money market instruments or short callable bonds
2 – 5
2–5 yrs: Moderate — intermediate-term or callable near the call date
5 – 10
5–10 yrs: High sensitivity — long-term or non-callable bond territory
> 10
> 10 yrs: Very high — long-duration bond; significant interest rate exposure

📚 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 — Effective Duration