Effective Duration Calculator - Bond Price Sensitivity
Use this Effective Duration Calculator to estimate bond duration, percent price impact, dollar impact, and scenario price from shocked prices.
Effective Duration Calculator
Results
What Is Effective Duration Calculator?
Effective Duration Calculator estimates a bond's interest-rate sensitivity from its current price and two prices generated from equal upward and downward yield shocks. Use it when a broker screen, portfolio system, spreadsheet, or model gives you shocked prices and you want a quick duration estimate before reviewing a bond sale, fund fact sheet, or rate scenario.
- • Bond risk review: Estimate how much a bond or fixed-income sleeve might move for a rate scenario, using the same price basis throughout.
- • Callable bond modeling: Use model prices that already reflect call assumptions, then let the calculator translate those prices into a duration measure.
- • Portfolio stress check: Enter total market value instead of a per-100 bond price to estimate a rough dollar impact for a holding.
- • Peer comparison: Compare duration estimates across bonds after repricing each one with the same yield shock size.
Effective duration is most useful when cash flows may change as rates move, or when you trust a pricing model more than a simple cash-flow duration formula. It does not choose the shocked prices for you. The quality of the result depends on whether the up-rate and down-rate prices come from the same data source, settlement convention, curve, and option assumptions.
Treat the output as a sensitivity estimate, not a recommendation to buy or sell. If you still need a base price before creating shocked prices, the linked bond price workflow can help you build the starting point from coupon, yield, maturity, and face value.
When you need the starting price before creating shocked values, the Bond Price Calculator supports coupon, yield, maturity, and face-value pricing work.
How Effective Duration Calculator Works
The calculator uses the standard central-difference duration formula. Prices from equal yield shocks estimate the local slope of the bond's price-yield curve.
- P_down: Bond price when the benchmark yield or curve falls by the selected shock.
- P_up: Bond price when the same benchmark yield or curve rises by the selected shock.
- P_0: Current bond price, clean price, dirty price, or portfolio market value.
- Δy: One-sided yield shock as a decimal. A 100 bp shock is 0.01.
Basis points are converted by dividing by 10,000, so 50 bps becomes 0.005 and 125 bps becomes 0.0125. The scenario yield change may be positive or negative. A positive scenario means yields rise, and the duration-only price estimate usually falls.
The price value per basis point output scales the same duration estimate down to a one bp move. It is helpful when you need a small-move dollar sensitivity, but it still inherits the assumptions used to create the shocked prices.
100 bp price-shock example
Current price is 100.00, price if yield falls is 104.40, price if yield rises is 96.00, and the one-sided shock is 100 bps.
Effective duration = (104.40 - 96.00) / (2 x 100.00 x 0.01) = 4.20 years.
For a 100 bp yield rise, estimated percent price impact is -4.20%, or -$4.20 on a 100.00 price.
The direction is negative because bond prices generally move opposite the yield change. A 100 bp yield decline would produce a positive estimate of about 4.20% before separate convexity review.
According to Investor.gov, one basis point equals one one-hundredth of a percentage point, so 100 basis points equals 1 percentage point.
According to CFA Institute, duration measures a bond's price sensitivity to yield changes, and duration-based price estimates assume a linear price-yield relationship even though the actual relationship is nonlinear.
If your rate scenario is stated as a percent move instead of bps, the Basis Point Calculator helps keep the shock input in the right scale.
Key Concepts Explained
These concepts help you decide whether the duration output is meaningful for the bond, fund, or portfolio value you entered.
Effective duration
A sensitivity measure built from modeled price changes. It is often used when cash flows may vary with rates, such as callable bonds or mortgage-backed securities.
Yield shock
The equal upward and downward rate move used to generate P_up and P_down. A smaller shock is more local; a larger shock can reveal model behavior but may reduce precision.
Price basis
All three prices must be on the same basis. Mixing clean and dirty prices, or per-100 price and total market value, can distort the duration estimate.
Convexity
The curvature in the price-yield relationship. Effective duration captures the first-order move; convexity can matter when rate changes are large.
Effective duration differs from modified duration because it does not require fixed cash flows. Modified duration starts from yield-to-maturity and the timing of expected cash flows. Effective duration starts from repriced values, so it can reflect option behavior if the pricing model already includes that behavior.
A duration number stated in years can still be read as a percent sensitivity shortcut. A duration near 4 means a one percentage-point yield rise points to roughly a 4% price decline, before convexity and credit-spread effects.
For larger yield moves where curvature matters, the Bond Convexity Calculator adds the second-order price-risk view that duration alone leaves out.
How to Use This Calculator
Use one consistent valuation source, then enter the prices and yield assumptions in the same scale.
- 1 Enter current price: Use current clean price, dirty price, or total market value. Keep that same price basis for the shocked prices.
- 2 Enter the down-rate price: Add the price produced when the benchmark yield or curve falls by the selected one-sided shock.
- 3 Enter the up-rate price: Add the price produced when the same benchmark yield or curve rises by the same one-sided shock.
- 4 Set the repricing shock: Enter the shock in basis points. Common modeling shocks include 25, 50, and 100 bps.
- 5 Set the scenario move: Enter the rate move you want to estimate. Use a negative number for a yield decline.
- 6 Review direction and size: Check effective duration, percent impact, dollar impact, and the estimated scenario price together.
If your portfolio value is $250,000, the down-rate value is $262,500, the up-rate value is $238,750, and the shock is 100 bps, the effective duration is 4.75 years. A 150 bp yield rise estimates a -7.13% move, or about -$17,812.50.
After estimating price sensitivity, the Bond Yield Calculator can connect the bond's price and coupon assumptions back to an annual yield view.
Benefits of Using This Calculator
The calculator turns model prices into a compact risk view that is easier to compare across bonds.
- • Rate scenario planning: Translate a forecasted yield move into an estimated percent and dollar price impact before adjusting a fixed-income allocation.
- • Model sanity check: Spot unusual shocked-price behavior, such as a very low or negative duration, before relying on a spreadsheet or vendor model.
- • Portfolio scaling: Use market value inputs to move from per-bond sensitivity to a rough holding-level dollar estimate.
- • Consistent bond comparison: Use the same shock size for several bonds, then compare duration and price value per basis point side by side.
- • Risk discussion support: Show how duration connects to potential mark-to-market movement without burying the result in cash-flow tables.
The Effective Duration Calculator is especially helpful when you already have pricing outputs from a broker, analytics platform, or internal model but need a quick sensitivity summary. It also helps separate rate risk from other bond risks, such as credit, liquidity, inflation, and call risk.
For a broader bond review, pair this estimate with yield, coupon income, maturity, credit quality, and convexity. Duration is a useful first pass, but it should not be the only number in a fixed-income decision.
For a broader fixed-income review that includes coupon payments and maturity value, the Bond Calculator gives a wider bond cash-flow context.
Factors That Affect Your Results
Effective duration changes when the bond, market assumptions, or pricing model changes.
Maturity and coupon
Longer maturities generally increase duration, while higher coupons tend to reduce it because more cash flow arrives earlier.
Yield level
Duration can change as yields move. A duration calculated at one market yield may not describe a very different yield environment.
Embedded options
Callable, putable, and mortgage-backed bonds may have cash flows that change when rates change, making model quality central to the estimate.
Shock size
A small shock gives a local sensitivity. A large shock may expose nonlinear behavior but can make a simple duration-only estimate less reliable.
Spread and curve movement
The formula assumes the shocked prices reflect the rate or curve move you care about. Credit spread changes can create a different price path.
- • Duration estimates only the first-order price move. For larger rate changes, convexity can materially change the result.
- • The calculator does not price the bond itself; it depends on your current, up-rate, and down-rate prices.
- • A low duration does not mean a bond is low risk because credit, liquidity, call, inflation, and reinvestment risks may still matter.
If a bond has meaningful option exposure, ask whether the shocked prices came from an option-adjusted model. If they did not, the effective duration output may look precise while missing the behavior you intended to measure.
Use the estimated scenario price as a conversation starter for risk review. For trading, accounting, or suitability decisions, confirm inputs against your official analytics source and offering documents.
According to FINRA, a bond with duration of 10 would be expected to decline by about 10 percent if interest rates rose by 1 percentage point, before considering other risks.
Frequently Asked Questions
Q: How do I calculate effective duration?
A: Use prices from equal upward and downward yield shocks: effective duration equals price if yield falls minus price if yield rises, divided by two times current price times the decimal yield shock. Keep all prices on the same clean, dirty, or market-value basis.
Q: What price inputs do I need?
A: You need the current bond price, the price after yields fall by the selected shock, and the price after yields rise by the same shock. Those shocked prices usually come from a pricing model, broker analytics screen, or fixed-income spreadsheet.
Q: Is effective duration the same as modified duration?
A: No. Modified duration is tied to yield-to-maturity and fixed cash-flow assumptions. Effective duration is based on repriced values, so it can reflect changing cash flows when the pricing model includes options such as calls or prepayments.
Q: What yield shock should I use?
A: Use a shock that matches your pricing source and purpose. A 100 bp shock is common for a broad stress view, while 25 or 50 bps can be better for a local sensitivity check. Use the same shock across bonds you compare.
Q: Can this estimate my bond's price change?
A: Yes, for a rough duration-only estimate. Enter the scenario yield change in basis points, and the calculator reports percent impact, dollar impact, and estimated price. Larger moves may need convexity or full repricing.
Q: Does effective duration work for callable bonds?
A: It can, if the shocked prices come from a model that reflects call behavior. The calculator does not model the option itself. It only translates your supplied up-rate and down-rate prices into a sensitivity measure.