Bond duration measures a bond's price sensitivity to interest rate changes. Macaulay duration is the weighted average time to receive cash flows; modified duration translates that into an estimated percentage price change per 1% yield move. This calculator computes both and shows the dollar impact on your position.
Bond Parameters
Duration Results
Price Sensitivity (per $1,000 face)
Duration is an approximation. Actual price changes for large yield moves are affected by convexity. This tool uses the standard linear approximation: ΔPrice ≈ −Modified Duration × ΔYield × Price.
How to Calculate Bond Duration
Bond duration is the primary measure of interest rate risk for fixed income investors. Understanding it helps you manage portfolio sensitivity to rate changes and compare bonds with different maturities and coupons.
Step 1: Enter Bond Parameters
Enter the face value (typically $1,000 for US bonds), annual coupon rate, current yield to maturity (YTM), years to maturity, and coupon payment frequency. Most US Treasury and corporate bonds pay semi-annual coupons.
Step 2: Understand Macaulay Duration
The Macaulay duration represents the weighted average time (in years) to receive all the bond's cash flows, with each cash flow weighted by its present value relative to the bond's total price. It is calculated as the sum of (time × present value of cash flow) divided by the bond price. For a 10-year bond with a 5% coupon and 6% YTM, Macaulay duration might be around 7.5 years.
Step 3: Use Modified Duration for Risk Management
Modified Duration = Macaulay Duration / (1 + YTM / periods per year). This converts duration into a direct price sensitivity measure. A bond with modified duration of 7.0 will change in price by approximately 7% for each 1% change in yield. If rates rise by 0.25%, the bond loses about 1.75% in price.
Using Duration in Portfolio Management
If you believe interest rates will rise, you want to shorten portfolio duration (buy shorter-term bonds or floating-rate instruments). If you believe rates will fall, lengthening duration amplifies price gains. Duration matching — aligning your portfolio duration to your investment horizon — is a core strategy for immunizing a portfolio against interest rate moves.
FAQ
Is this bond duration calculator free?
Yes, completely free with no signup required. All calculations run in your browser.
What is Macaulay duration?
Macaulay duration is the weighted average time (in years) it takes to receive all of a bond's cash flows (coupons and principal), where each cash flow is weighted by its present value as a proportion of the bond's total price. A Macaulay duration of 5 years means the average wait for cash flows — accounting for time value of money — is 5 years.
What is modified duration?
Modified duration = Macaulay Duration / (1 + YTM/periods per year). It measures the percentage price change of a bond for a 1% (100 basis point) change in yield. A modified duration of 4.5 means a 1% yield increase causes approximately a 4.5% price decrease. Modified duration is used to manage interest rate risk in bond portfolios.
How does duration affect bond price?
Price change ≈ -Modified Duration × Change in Yield. Higher duration = greater price sensitivity to interest rate changes. Long-term bonds have higher duration than short-term bonds. Zero-coupon bonds have duration equal to their maturity. Coupon-paying bonds have duration less than maturity because early coupon payments reduce the average wait for cash flows.
What is the difference between duration and maturity?
Maturity is simply when the bond matures (e.g., 10 years). Duration is always less than or equal to maturity (except for zero-coupon bonds where they are equal). A 10-year bond paying a 5% coupon might have a Macaulay duration of only 7.5 years because early coupon payments shorten the weighted average time to receive all cash flows.