Effective Duration
Effective Duration
Empirical duration computed from a parallel yield shift: the average price response per unit yield change, derived from a full bond repricing rather than analytical differentiation. The right duration measure for bonds with embedded options.
When to use: Use whenever a bond's cash flows depend on yield (callable, puttable, MBS) so that analytical modified duration is invalid. Effective duration takes the actual repriced values from a model and computes a robust empirical sensitivity.
Formula
Variables
| Symbol | Name | Description | Unit |
|---|---|---|---|
| EffDur | Effective Duration | Empirical duration computed from a parallel yield shift, in years | years |
| PriceDown | Price at Lower Yield | Bond price after the yield falls by ΔY | $ |
| PriceUp | Price at Higher Yield | Bond price after the yield rises by ΔY | $ |
| P | Bond Price | Market price of the bond per face value unit | $ |
| DeltaY | Yield Change | Change in yield as a decimal (e.g. 0.0050 for 50 bps) | % |
Real-Life Examples
Example 1: Callable Bond, 50bp Shocks
Callable bond priced at $1,043.76. Repricing at +50bp gives $1,022.19; at −50bp gives $1,062.43. Δy = 0.005.
Given
Step-by-Step
For these inputs, Effective Duration is 3.855292 years under the stated payment, compounding and accounting assumptions.
Frequently Asked Questions
Conventionally 25-50 bps. Too small: numerical noise dominates. Too large: convexity bias affects the central-difference estimate. 25 bps is common for typical bonds; 10-15 bps for high-convexity instruments like long-dated zeros.
Because the call option caps the price upside on rate rallies. P_minus rises less than the option-free analog would, shrinking the numerator and compressing duration. As rates fall further, the bond becomes more "called away" in expectation, eventually approaching call-date duration.
Computed analogously: C_Eff = (P_minus + P_plus − 2 × P_0) / (P_0 × (Δy)²). Callable bonds often have negative effective convexity in low-rate environments — the price-yield curve bends the wrong way as the call gets close to in-the-money.