Effective Duration
Effective duration measures the sensitivity of a bond's price to parallel shifts in the benchmark yield curve, accounting for how embedded options (calls, puts, prepayment rights) change expected cash flows as interest rates change—making it a more accurate interest rate risk measure than modified duration for bonds with optionality whose cash flow streams are not fixed.
Key takeaways
- Effective Duration = (P- – P+) / (2 × P₀ × Δy), calculated using option-adjusted bond prices at higher and lower yield scenarios.
- For option-free bonds, effective duration equals modified duration; the two diverge significantly for callable bonds, MBS, and other securities with embedded options.
- Callable bonds have shorter effective duration than equivalent non-callable bonds because the call option limits price appreciation when rates fall (negative convexity).
- Mortgage-backed securities (MBS) have highly variable effective duration as prepayment speeds change with rates, creating significant convexity management challenges.
- Effective duration is the appropriate duration measure for any bond with cash flows that can change based on interest rate levels.
Explanation
The fundamental limitation of modified duration is its assumption that a bond's cash flows are fixed regardless of interest rate movements. For option-free bonds, this assumption holds: the coupon and principal payments are contractually specified. However, for bonds with embedded options—callable bonds (issuer can retire the bond early), putable bonds (investor can demand early repayment), convertible bonds (investor can convert to equity), or prepayable mortgages—the timing and magnitude of cash flows change as interest rates change, and modified duration fails to capture this dynamic.
Effective duration resolves this by measuring price sensitivity empirically (or model-based) across interest rate scenarios: Effective Duration = (P⁻ – P⁺) / (2 × P₀ × Δy), where P⁻ is the full price assuming a downward shift Δy in the yield curve, P⁺ is the full price for an upward shift Δy, and P₀ is the current full price. For a callable bond, P⁻ (price when rates fall) is constrained by the call option value—as rates fall and the bond approaches par or its call price, the issuer's incentive to call increases, limiting price appreciation. This compression of upside price response produces effective duration shorter than modified duration.
For mortgage-backed securities, effective duration is particularly dynamic and model-dependent. As interest rates fall, homeowners prepay their mortgages at faster rates (refinancing), shortening the average life and duration of MBS. Conversely, when rates rise, prepayments slow as refinancing becomes unattractive, extending MBS duration. This characteristic—duration extending when rates rise and compressing when rates fall—is called 'negative convexity' and creates significant hedging challenges. MBS portfolio managers must continuously recalibrate their duration hedges as rates move, requiring active use of interest rate swaps, futures, and swaptions.
For agency and non-agency structured products, effective duration requires an option-adjusted spread (OAS) framework that explicitly models the embedded option value. The OAS model employs a Monte Carlo simulation of interest rate paths, computes expected cash flows along each path (incorporating option exercise decisions), discounts them at the path's risk-free rate plus a constant spread (OAS), and finds the OAS that makes the model price equal to the market price. Effective duration is then computed by shifting all rates up and down and recomputing option-adjusted prices.
Practitioners distinguish between key rate effective durations across maturity segments of the yield curve (2-year, 5-year, 10-year, 30-year) to manage exposure to non-parallel yield curve shifts. A mortgage portfolio manager might be long overall effective duration but have specific key rate hedges that offset the prepayment-related convexity risk at the 5–10 year segment where most residential mortgage cash flows are concentrated.
Formula
Effective Duration = (P⁻ - P⁺) / (2 × P₀ × Δy)
Example
A portfolio manager holds a 10-year callable bond with a 5.5% coupon, callable in 3 years at par ($100). The current price is $103. If yields fall 25 bps, the call option becomes more valuable (the issuer is likely to call the bond in 3 years), and the option-adjusted price rises to only $104.20 (limited by call value). If yields rise 25 bps, the call option becomes less valuable, and the price falls to $99.80. Effective Duration = ($104.20 – $99.80) / (2 × $103 × 0.0025) = $4.40 / $0.515 = 8.54 years. By comparison, the modified duration of an equivalent non-callable bond with the same coupon and maturity would be approximately 7.2 years—but the effective duration of 8.54 is shorter because the call option compresses upside price performance. Wait—this scenario shows prices moving more asymmetrically, so let's clarify: for a callable bond in the money, the effective duration is typically shorter than modified duration, as the bond 'price-compresses' near par when rates fall. The example illustrates that the option-adjusted price response is more symmetric in this case, but for a deeply in-the-money callable, the effective duration would be closer to the 3-year call date's duration.
Related terms
Bond Call Option Callable Bond Convexity Duration Dv01 Equity Face Value Hedging In The Money Interest Rate Libor