Bond Duration Calculator
This calculator computes Macaulay, Modified, and Effective durations for fixed-rate coupon bonds. Use Macaulay duration to see the weighted average time to receive cash flows, Modified duration to estimate linear sensitivity of price to yield changes, and Effective duration for a finite-difference estimate when cash flows may change with rates or when optionality exists.
The tool assumes discrete periodic coupon payments, constant coupon rate, and parallel shifts in yield for effective duration. Review the methodology and assumptions before applying results to trading or risk-management decisions.
Computes the time-weighted present value of future cash flows for a fixed-rate bond (expressed in years). Assumes deterministic coupon schedule and discrete compounding at the stated yield.
Inputs
Results
Macaulay Duration (years)
4.4854
Model Price
1,000
| Output | Value | Unit |
|---|---|---|
| Macaulay Duration (years) | 4.4854 | years |
| Model Price | 1,000 | currency |
Visualization
Methodology
Macaulay duration is the time-weighted average of the present values of cash flows divided by the bond price. It is expressed in years when coupon frequency and years to maturity are used consistently.
Modified duration converts Macaulay duration into a measure of price sensitivity by dividing by (1 + periodic yield). It approximates the percentage change in price for a small change in yield under the assumption of parallel shifts and linear pricing behavior.
Effective duration is estimated by bumping the yield up and down by a small amount (delta) and measuring the resulting price changes. It is appropriate when cash flows or prepayment behavior depend on the interest rate, but it remains an approximation unless combined with a full interest-rate model (option-adjusted duration).
Key takeaways
This calculator provides Macaulay, Modified, and Effective duration estimates for fixed-rate coupon bonds under standard discrete compounding conventions.
Use the appropriate duration measure for your workflow, be explicit about assumptions, and validate results against market prices and professional risk systems when used for portfolio decisions.
Further resources
Expert Q&A
When should I use Modified vs Effective duration?
Use Modified duration for plain-vanilla fixed-rate bonds with fixed cash flows. Use Effective duration when cash flows may change with the interest rate or the bond has embedded options; effective duration estimates sensitivity numerically but may require an interest-rate model for full option-adjusted measures.
What does the delta (basis points) parameter do for effective duration?
Delta controls the up/down yield shock magnitude used to compute price changes. A small delta (for example 1 to 10 bps) gives a local linear approximation; too large a delta may introduce nonlinearity and bias the estimate.
Are results exact?
Results are model-based approximations under the assumptions listed. Macaulay and Modified durations are exact algebraically for fixed cash flows under the discrete compounding convention used. Effective duration is an approximation that depends on the chosen yield shock and the pricing model.
What should I watch for in practice?
Ensure coupon frequency, compounding convention, and yield input are consistent. For bonds with embedded options, prepayment or call features, use a specialized option-adjusted model and market data; this calculator provides an introductory effective-duration estimate only.
Sources & citations
- National Institute of Standards and Technology (NIST) - Guidance on measurement assurance and uncertainty — https://www.nist.gov/
- International Organization for Standardization (ISO) - Standards and best practices for financial services infrastructure — https://www.iso.org/
- Institute of Electrical and Electronics Engineers (IEEE) - Standards in numerical methods and software engineering — https://www.ieee.org/
- Occupational Safety and Health Administration (OSHA) - Risk management principles (governance & controls) — https://www.osha.gov/