Effective Duration Calculator

Enter a bond's current price and its prices after yields shift up and down to compute effective duration, effective convexity, and the estimated price change for a given rate move.

Quick Facts

Duration formula
D = (V- − V+) / (2 × V0 × Δy)
V- and V+ are re-priced values after yields fall/rise by Δy; V0 is the current price.
Convexity formula
C = (V+ + V- − 2V0) / (V0 × Δy²)
Corrects the duration estimate for the curvature of the price-yield relationship.
Why "effective"
Uses re-priced bond values
Unlike modified duration, effective duration captures cash-flow changes in bonds with embedded options (callable, putable, mortgage-backed).

Your Results

Calculated
Effective duration
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% price change per 1% yield move
Effective convexity
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Curvature adjustment to duration
Estimated price change
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For the rate move entered above
Estimated price
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Current price adjusted by the estimate

Ready

Enter the current price and the prices at shifted yields, then press Calculate.

How the Effective Duration Calculator works

Effective duration measures how much a bond's price is expected to move for a given change in interest rates. Instead of deriving the sensitivity analytically from the bond's coupon and maturity (the way modified duration does), effective duration is built from three actual — or model-generated — prices: the bond's current price, its price if yields fell by a small amount, and its price if yields rose by that same amount. That makes it the standard tool for bonds whose cash flows can change as rates move, such as callable bonds, putable bonds, and mortgage-backed securities.

The formula

For a current price V0, a price V- after yields fall by Δy, and a price V+ after yields rise by the same Δy (expressed as a decimal, e.g. 0.50% = 0.005), effective duration is:

D = (V- − V+) / (2 × V0 × Δy)

Because bond prices actually curve rather than move in a straight line as yields change, a second term — effective convexity — corrects the duration estimate for larger rate moves:

C = (V+ + V- − 2 × V0) / (V0 × Δy²)

Combining both terms gives a more accurate estimate of the percentage price change for a target yield shift Δytarget:

%ΔP ≈ −D × Δytarget + 0.5 × C × Δytarget²

Worked example

Suppose a bond currently prices at $1,000 (V0). Re-pricing it with yields down 0.50% gives $1,035 (V-), and re-pricing with yields up 0.50% gives $967 (V+). With Δy = 0.005: D = (1,035 − 967) / (2 × 1,000 × 0.005) = 68 / 10 = 6.80 years. Effective convexity works out to C = (967 + 1,035 − 2,000) / (1,000 × 0.005²) = 2 / 0.000025 = 80.0. For a 100 basis point (1%) rise in rates, the duration-plus-convexity estimate is %ΔP ≈ −6.80 × 0.01 + 0.5 × 80 × 0.01² = −0.068 + 0.004 = −6.4%, versus a duration-only estimate of −6.8% — the convexity term softens the loss slightly, as it typically does for a straightforward, option-free bond.

Reading the result

  • Effective duration is the approximate percentage price change for a 1 percentage point (100 bp) change in yield. A duration of 6.80 means roughly a 6.8% price move (in the opposite direction) per 1% yield change, for small moves.
  • Effective convexity is positive for most option-free bonds, meaning price gains from falling yields slightly exceed price losses from an equal rise in yields — a favorable curvature. Convexity can turn negative for callable bonds and many mortgage-backed securities, since the issuer's or borrower's option caps the price upside.
  • Bigger Δy shocks amplify convexity's role. For small rate moves, duration alone is usually enough; for larger moves, the convexity term matters more.

Effective vs. modified duration

Modified duration is calculated analytically from a bond's yield, coupon, and maturity, and it implicitly assumes the bond's cash flows never change no matter how rates move. That assumption holds for plain fixed-rate, option-free bonds, where effective and modified duration are typically very close. It breaks down for bonds with embedded options: a callable bond's issuer may redeem it early if rates fall, and a mortgage-backed security's prepayment speed changes with rates. Effective duration sidesteps the problem by using actual re-priced values — from a pricing model that accounts for those options — at shifted yields, so it reflects the real cash-flow behavior rather than an assumption that it stays fixed.

Frequently Asked Questions

How is effective duration calculated?
Effective duration uses three bond prices: the current price (V0), the price if yields fall by a small amount (V-), and the price if yields rise by that same amount (V+). The formula is D = (V- − V+) / (2 × V0 × Δy), where Δy is the yield change expressed as a decimal. It measures the percentage price change per 1 percentage point (100 basis point) change in yield.
Why use effective duration instead of modified duration?
Modified duration assumes a bond's cash flows never change as rates move, which works for plain fixed-rate bonds but fails for bonds with embedded options (callable, putable, or mortgage-backed securities) whose cash flows shift with rates. Effective duration instead uses actual re-priced values from a pricing model at shifted yields, so it captures those cash-flow changes automatically.
What is effective convexity and why does it matter?
Effective convexity, C = (V+ + V- − 2 × V0) / (V0 × Δy²), measures the curvature of the price-yield relationship that duration alone misses. Duration alone is a straight-line (linear) approximation; adding convexity corrects that estimate for larger yield moves, since bond prices actually curve rather than move in a straight line.
What does a higher effective duration mean?
A higher effective duration means the bond's price is more sensitive to interest rate changes. A bond with an effective duration of 8 years will move roughly twice as much in price for a given rate change as a bond with a duration of 4 years, all else equal. Longer-maturity bonds and lower-coupon bonds generally have higher effective duration.

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