Effective Duration
Effective duration is a measure of a bond's price sensitivity to a parallel shift in the yield curve that accounts for changes in a bond's cash flows when rates change — particularly relevant for bonds with embedded options such as callable bonds, putable bonds, and mortgage-backed securities — making it applicable where modified duration would be inaccurate.
Modified duration assumes that a bond's cash flows remain fixed regardless of changes in interest rates — an assumption that is valid for plain-vanilla Treasury notes and bonds but breaks down for instruments with embedded optionality. Callable bonds, for example, are likely to be called by the issuer when rates fall, shortening the effective maturity and reducing interest rate sensitivity. Mortgage-backed securities prepay faster when rates decline (homeowners refinance), which similarly reduces duration. Effective duration captures this cash flow optionality by computing price sensitivity numerically rather than analytically.
Effective duration is defined as: Effective Duration = (Price when Yields Fall by ΔY - Price when Yields Rise by ΔY) / (2 x Initial Price x ΔY), where prices are computed using an option-adjusted pricing model that fully reflects how cash flows change at each rate scenario. Typically, ΔY is set to 25 or 50 basis points.
For a non-callable Treasury bond, effective duration closely approximates modified duration since the cash flows do not change with rates. For a mortgage-backed security with significant prepayment sensitivity, effective duration can be substantially lower than the scheduled maturity-based Macaulay duration, and it changes dynamically as rates move — a phenomenon called negative convexity. As rates fall and prepayments accelerate, the effective duration of a mortgage shortens rather than lengthening as it would for a plain-vanilla bond.
Effective duration requires an interest rate model to price the bond at the two rate scenarios used in the numerical computation. The choice of model — short-rate models like BDT (Black-Derman-Toy), Hull-White, or more complex HJM-based models — can meaningfully affect the effective duration estimate, particularly for deeply out-of-the-money options.
For portfolio managers at insurance companies, pension funds, and mortgage REITs, effective duration is the correct duration measure to use for interest rate hedging. Using modified duration for a callable bond portfolio or a mortgage portfolio would systematically overstate the rate sensitivity of the assets, leading to over-hedging or incorrect liability matching.