Effective Duration Calculator — Bond Price Sensitivity
Enter bond parameters — face value, coupon rate, YTM, maturity and coupon frequency — and a yield shock in basis points to compute effective duration (price sensitivity), modified duration, Macaulay duration, DV01 and convexity.
%
%
years
Coupon frequency
bps
Years — approximate % price change for a 1% parallel yield shift
- 1
Coupon per period
5% × 1,000 ÷ 2 = 25 - 2
Bond price at current YTM (P₀)
1,000 - 3
Bond price at YTM − Δy (P−)
1,081.7572 - 4
Bond price at YTM + Δy (P+)
925.6126 - 5
Effective Duration
(1,081.7572 − 925.6126) ÷ (2 × 1,000 × 0.01) = 7.8072Approximate % price change for a 1% parallel yield shift.
How does this calculator work?
Effective Duration = (P− − P+) / (2 × P₀ × Δy). Enter face value, coupon, YTM, maturity and a yield shock in basis points. The calculator prices the bond at ±Δy, then computes duration, DV01 and convexity. A duration of 7 means ~7% price change per 1% yield move.
Formula
How this is calculated
Effective duration (ED) measures how sensitive a bond's price is to a parallel shift in the yield curve. It is computed numerically by bumping the yield up and down by a small amount Δy, repricing the bond at each yield, then taking the symmetric difference: ED = (P− − P+) / (2 × P₀ × Δy), where P₀ is the price at the current YTM, P− is the price if the yield falls by Δy, and P+ is the price if the yield rises by Δy. A bond with effective duration 7 will gain approximately 7% in price for each 1% fall in yield (and lose 7% for a 1% rise) — this is a linear approximation that becomes less accurate for large moves.
For a plain vanilla fixed-rate bond with no embedded options, effective duration equals modified duration. Modified duration = Macaulay duration / (1 + y/m), where Macaulay duration is the weighted-average time to receipt of cash flows (in years). DV01 (dollar value of 1 basis point) is the price change in currency units for a 1-bp move in yield: DV01 = P₀ × ED × 0.0001.
Convexity captures the curvature of the price–yield relationship. A bond with positive convexity gains more than the linear approximation predicts when yields fall and loses less when yields rise — this is always beneficial. The convexity approximation here uses (P+ + P− − 2P₀) / (P₀ × Δy²). The price–yield plot below shows the convex shape: higher convexity means more curvature.
Frequently asked questions
For option-free fixed-rate bonds they are numerically equivalent. Effective duration is more general: it is used when the cash flows themselves can change with interest rates — for example, callable bonds (the issuer may refinance if rates fall), putable bonds or mortgage-backed securities. In those cases, modified duration understates the true sensitivity and effective duration is computed by fully repricing the instrument with its option model at each yield.
Common choices are 25, 50 or 100 basis points. Smaller shocks give a more accurate local derivative but may amplify numerical noise for instruments with complex cash-flow models; larger shocks average the sensitivity over a wider range but mix in convexity effects. For plain vanilla bonds, 50–100 bps is standard. The default 100 bps is a classic industry choice for normal market conditions.
DV01 (also called PVBP — Price Value of a Basis Point) is the monetary change in bond price for a 1 basis-point (0.01%) change in yield. It is useful for hedging: if a bond portfolio has a total DV01 of 10,000, a 1-bp rise in rates causes a €/$ 10,000 loss in value. You can offset this by entering a position in a hedging instrument with the same DV01 but opposite sign.
Also known as
TG we-Calculate Editorial Team. (2026). Effective Duration Calculator — Bond Price Sensitivity [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/effective-duration-calculator
TG we-Calculate Editorial Team. "Effective Duration Calculator — Bond Price Sensitivity." TG we-Calculate. 2026. https://we-calculate.com/calculator/effective-duration-calculator.
TG we-Calculate Editorial Team, "Effective Duration Calculator — Bond Price Sensitivity," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/effective-duration-calculator
@misc{wecalculate_effective_duration_calculator, title = {Effective Duration Calculator — Bond Price Sensitivity}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/effective-duration-calculator}}, year = {2026}, note = {TG we-Calculate} }
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