What is effective duration and when must I use it instead of modified duration?

Question

AcadiFi · Accepted Answer

Modified duration assumes cash flows are fixed and known: P = Σ CFt / (1+y)^t, and the derivative is closed-form. But for bonds with embedded options — callables, putables, MBS with prepayment — cash flows depend on yield. A drop in rates accelerates calls and prepayments, shortening effective life; a rise slows them, extending life. The closed-form derivative misses this feedback. **Effective duration (empirical)**: numerically perturb the yield curve and re-price using a full option-adjusted model: Effective Duration = [P(-Δy) − P(+Δy)] / [2 × P₀ × Δy] You parallel-shift the entire yield curve by ±Δy (typically 25-50 bps), re-run the pricing model (which re-evaluates the call/prepayment option using trees or Monte Carlo), and measure the resulting price change. This captures the option's behavior. **Example**: A 10% callable bond at par with 5 years to call. Closed-form modified duration (assuming held to maturity) might be 7.5. But at current yields of 4%, the bond will almost certainly be called in 5 years — effective duration is closer to 4. Using MD would massively overstate interest-rate risk. **When effective > modified**: - Putable bonds when rates rising (put becomes ITM, shortening cash flows) - MBS when rates rising (prepayment slows, extending life) **When effective < modified**: - Callable bonds when rates falling (call becomes ITM) - MBS when rates falling (prepayment accelerates) **Practical use**: Always use effective duration for any bond with optionality. Dealers and OMS systems compute it via binomial trees (for interest-rate models) or Monte Carlo (for path-dependent MBS). CFA exam will test both formulas and the contexts where each applies — the trigger word is 'embedded option' or 'prepayment'. ```mermaid flowchart TD A{Bond Has
Embedded Option?} A -->|No| B[Use Modified
Duration] A -->|Yes| C[Use Effective
Duration] C --> D[Shift Yield
Curve Parallel] D --> E[Re-price With
Option Model] E --> F[Compute Numerical
Derivative] ```

What is effective duration and when must I use it instead of modified duration?

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