Understanding Effective Duration: Definition, Formula & Examples
By Markets & Investing DeskUpdated Nov 10, 2026
Definition
Effective duration measures how much a bond's price should change when interest rates move, while letting cash flows shift as embedded options like calls, puts or prepayments come into play.
Key takeaways
- An effective duration of 6 implies a price move of about 6% opposite to a 1 percentage point yield change.
- The formula is (P1 minus P2) divided by (2 times P0 times the yield change, in decimal form).
- Callable bonds see effective duration drop as falling rates make a call more likely, capping price gains.
- Interest-only mortgage strips can have negative effective duration because prepayments erase future interest.
Effective duration is a measure of how much a bond’s price is expected to change for a given change in interest rates, calculated in a way that allows the bond’s cash flows to change as rates move. That makes it the standard duration measure for bonds with embedded options, such as callable bonds, putable bonds and mortgage-backed securities, whose payments depend on where rates go. It is also called option-adjusted duration. An effective duration of 6 means the bond’s price should move about 6% in the opposite direction for a 1 percentage point (100 basis point) change in yield.
How Effective Duration Works
An embedded option makes a bond’s cash flows uncertain. A callable bond may be redeemed early if rates fall, because the issuer can refinance more cheaply. A putable bond may be handed back to the issuer if rates rise, because the holder can reinvest at a higher yield. Mortgage-backed securities pay down faster when falling rates trigger refinancing.
Measures built on yield to maturity treat the promised cash flows as fixed. Effective duration does not: it shifts the benchmark yield curve up and down by a small amount, reprices the bond at each curve with a valuation model that lets the option be exercised when it makes economic sense, and measures how far the price moved.
When exercising the option offers no benefit, the bond behaves like an option-free bond. For example, an issuer gains nothing by calling a 6% callable bond when market rates are 10%, so the call is effectively irrelevant and the bond’s effective duration is close to its modified duration.
Effective Duration Formula
The formula uses four inputs:
- P0: the bond’s current price (often per $100 of par value)
- P1: the bond’s price if yields fall by Δy
- P2: the bond’s price if yields rise by Δy
- Δy: the yield change used to compute P1 and P2, in decimal form (10 basis points = 0.001)
Effective duration = (P1 − P2) / (2 × P0 × Δy)
Example of Effective Duration
Hypothetical example. A bond trades at $100 per $100 of par and yields 6%. Using a 10 basis point shift:
- Yield falls to 5.9%: modeled price is $101.00 (P1)
- Yield rises to 6.1%: modeled price is $99.25 (P2)
Effective duration = ($101.00 − $99.25) / (2 × $100 × 0.001) = $1.75 / $0.20 = 8.75
The approximate price change for any small yield move is:
%ΔP ≈ −Effective duration × Δy
For a 1% rise in yield, the estimate is −8.75 × 0.01 = −8.75%, or a price near $91.25. For a 0.50% decline, it is a gain of about 4.375%.
Because the price-yield relationship is curved, the estimate becomes less accurate as the yield change gets larger. Adding effective convexity improves it:
- Effective convexity = (P1 + P2 − 2 × P0) / (P0 × Δy²)
- %ΔP ≈ (−Effective duration × Δy) + (½ × Effective convexity × Δy²)
Callable, Putable and Mortgage-Backed Bonds
Options change duration in predictable directions:
- Callable bonds. As rates fall and a call becomes more likely, the expected life of the bond shortens and its effective duration drops. Price gains are capped near the call price. This is negative convexity.
- Putable bonds. As rates rise and the put becomes valuable, the expected life shortens, so effective duration falls and price losses are cushioned.
- Mortgage-backed securities. Prepayments speed up when rates fall and slow down when rates rise, which shortens duration in rallies and extends it in selloffs.
Because a callable bond responds differently to rate increases than to decreases, analysts sometimes compute one-sided durations, measuring the price change for an up-shift and a down-shift separately instead of averaging them.
Effective duration is not always positive. Interest-only mortgage strips can have negative effective duration: when rates fall, faster prepayments wipe out future interest payments, so the security’s price can drop even as yields decline.
Effective Duration vs. Modified Duration
| Modified duration | Effective duration | |
|---|---|---|
| Rate input | The bond’s own yield to maturity | Shift in the benchmark yield curve |
| Cash flows | Assumed fixed | Allowed to change with rates |
| Best suited to | Option-free bonds | Bonds with embedded options, and portfolios |
Approximate modified duration uses the same formula, but P1 and P2 come from changing the bond’s yield to maturity with fixed cash flows. For a callable bond whose call is likely, effective duration is shorter because modified duration assumes the bond runs to maturity even when the issuer would probably redeem it sooner.
Macaulay duration is a different concept: a weighted-average time to receive cash flows, expressed in years. Effective duration is a price-sensitivity measure, expressed as a percentage price change per 1% move in rates.
How Effective Duration Is Used
Effective duration applies to any fixed-income security or portfolio and is the measure of choice for callable corporate bonds, municipal bonds and securitized debt. Bond funds and bond ETFs often report it for the whole portfolio, typically as a market-value-weighted average of the holdings’ durations, so investors can compare interest rate risk across funds holding very different securities. Portfolio managers use it to match asset sensitivity to liabilities, size hedges and position for expected rate moves.
Limitations
- Model dependence. P1 and P2 come from a valuation model. Assumptions about rate volatility, prepayment speeds or call behavior change the answer, so two sources can report different effective durations for the same bond.
- Parallel shifts only. The standard calculation moves the whole curve by the same amount. Real curves steepen, flatten and twist, which key rate durations address.
- Choice of Δy. Very small shifts amplify rounding in modeled prices, and large shifts blur the curvature.
- Rates, not spreads. Effective duration measures sensitivity to benchmark rates. Sensitivity to changes in a bond’s credit spread is a separate measure, spread duration.
The Bottom Line
Investors comparing bond funds or holding callable bonds, municipal bonds or mortgage-backed securities get a more realistic read on rate risk from effective duration than from modified duration. The figure depends on model assumptions and parallel curve shifts, so different sources may disagree. For larger rate moves, pairing it with effective convexity gives a better price estimate.
