Understanding Effective Duration: Definition, Formula & Examples

Effective duration measures a bond’s sensitivity to changes in interest rates when the bond has embedded options (for example, call or put provisions). It accounts for how expected cash flows may change as yields move, making it the preferred duration metric for securities whose cash flows are not fixed.

Key points

• Applies to bonds with embedded options; reflects changes in expected cash flows as yields change.
• Estimates the approximate percentage change in price for a 1% (100 basis point) parallel shift in yields.
• Typically lower than the bond’s maturity; longer maturities generally imply higher effective duration.
• If exercising an embedded option would never be beneficial, the bond behaves like an option‑free bond and modified duration can approximate effective duration.
• Effective duration is an approximation that is improved by also considering convexity.

Intuition

Embedded options (callable, putable, etc.) introduce uncertainty in future cash flows because the issuer or holder may alter the bond’s cash flows if rates move. Effective duration captures the price impact of yield changes while allowing for these option-driven changes in cash flow patterns.

Example intuition: if interest rates are much higher than a bond’s coupon, calling the bond is unlikely, so the bond behaves like an option‑free bond and cash flows won’t change with yield moves.

Formula and variables

Let:
* P0 = bond price at the current yield (per $100 par)
P(−Δy) = price if yield decreases by Δy
P(+Δy) = price if yield increases by Δy
* Δy = small change in yield (in decimal form; e.g., 10 basis points = 0.001)

Effective duration:
Effective duration = (P(−Δy) − P(+Δy)) / (2 × P0 × Δy)

This uses a central difference to approximate the derivative of price with respect to yield, normalized by price.

Worked example

Assume:
* P0 = $100 (current price)
Δy = 10 basis points = 0.001
P(−Δy) = $101 (price if yield falls by 10 bps)
* P(+Δy) = $99.25 (price if yield rises by 10 bps)

Calculation:
* Numerator = $101 − $99.25 = $1.75
Denominator = 2 × $100 × 0.001 = $0.20
Effective duration = $1.75 / $0.20 = 8.75

Interpretation: an effective duration of 8.75 implies the bond’s price would change by about 8.75% for a 1% (100 bps) parallel shift in yield, holding the option exercise behavior implied by the model.

Limitations and practical notes

• The measure is an approximation and is most accurate for small yield changes.
• Convexity (the curvature of the price–yield relationship) affects accuracy; including effective convexity improves estimates for larger yield moves.
• Effective duration depends on assumptions about future rates and option exercise behavior; different interest‑rate scenarios or valuation models can produce different effective durations.
• Useful in portfolio risk analysis and hedging when comparing interest‑rate sensitivity of mortgage‑backed securities, callable bonds, and other option‑embedded instruments.

Conclusion

Effective duration is the standard tool for quantifying interest‑rate sensitivity of bonds whose cash flows can change with yield movements. Use the central-difference formula with a small Δy to estimate percent price change per 1% yield move, and complement the estimate with convexity and scenario analysis for greater accuracy.