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Effective Duration

Duration measure that accounts for embedded options (call/put features).

Effective duration measures interest rate sensitivity for bonds with embedded options (callable, putable, mortgage-backed securities). Modified duration assumes cash flows are fixed, but callable bonds have uncertain cash flows — if rates fall, the issuer may call the bond. Effective duration captures this by calculating duration using option-adjusted cash flows. Calculation: Shock yields up/down by small amount (e.g., ±25bp), reprice bond with option model, measure price sensitivity. Example: A 10-year callable bond might have modified duration of 7, but effective duration of 4 if it's likely to be called in 5 years. When to use: Always use effective duration for MBS, callables, putables. Use modified duration only for option-free bonds.

Formula
Eff Dur=Py−Δy−Py+Δy2×P0×Δy\text{Eff Dur} = \frac{P_{y-\Delta y} - P_{y+\Delta y}}{2 \times P_0 \times \Delta y}