Bond Modified Duration Calculator
Modified duration tells you exactly how much a bond's price changes when interest rates move 1%. A duration of 6.23 means a 1% rate rise drops the price about 6.23% — and a 1% rate fall lifts it the same. Enter your bond's yield to maturity (YTM), years to maturity, and coupon frequency below to get the result instantly. The formula used is the closed-form at-par Macaulay Duration, the standard approach taught by the CFA Institute.
Bond modified duration measures how much a bond's price changes for a 1% move in yield. A 10-year bond with 10% YTM (semi-annual coupons) has a modified duration of about 6.23 — meaning a 1% rate rise drops the price roughly 6.23%. Formula: Modified Duration = Macaulay Duration ÷ (1 + YTM/m), where m is coupon payments per year.
When to use this calculator
- Compare interest-rate risk between two bonds (e.g. 5-year vs 10-year Treasuries)
- Estimate the dollar loss if the Fed raises rates by 1%
- Construct a bond ladder matched to your investment horizon
- Calculate hedge ratios using bond futures or interest-rate swaps
- Immunize a fixed-income portfolio against rate movements
- CFA exam practice: Macaulay and modified duration problems
10-Year US Treasury at 10% YTM
- YTM = 10% annual, semi-annual coupons (m = 2)
- Per-period yield r = 10% / 2 = 5%
- Total periods N = 10 × 2 = 20
- Macaulay Duration = [(1.05/0.05) × (1 − 1/1.05²⁰)] / 2 = 6.54 years
- Modified Duration = 6.54 / 1.05 = 6.23
How it works
2 min readWhat Is Modified Duration?
Modified duration (MD) is the standard measure of a bond's price sensitivity to interest rates. An MD of 6.23 means: for every 1 percentage-point move in yield, the bond price changes approximately 6.23% in the opposite direction. It is used by portfolio managers, treasurers, and the CFA Institute as the primary fixed-income risk metric.
The Formula
This calculator uses the closed-form Macaulay Duration for an at-par bond (coupon rate = YTM), which is the industry-standard formula:
Macaulay Duration = [(1+r)/r × (1 − 1/(1+r)^N)] / m
Modified Duration = Macaulay Duration / (1 + r)
Price Change ≈ −Modified Duration × ΔrateWhere: r = YTM/m (per-period yield), N = years × m (total periods), m = coupon payments per year.
Worked example: 10% YTM, 10 years, semi-annual (m=2):
Modified Duration Reference Table
| Bond type | YTM | Maturity | Coupon freq | Modified Duration |
|---|---|---|---|---|
| Short T-bill | 5% | 0.5 yr | 2 | ~0.49 |
| 2-year Treasury | 5% | 2 yr | 2 | ~1.89 |
| 5-year Treasury | 5% | 5 yr | 2 | ~4.38 |
| 10-year Treasury | 5% | 10 yr | 2 | ~7.99 |
| 10-year Treasury | 10% | 10 yr | 2 | 6.23 |
| 30-year Treasury | 5% | 30 yr | 2 | ~15.37 |
| Zero-coupon 10yr | 5% | 10 yr | 1 | ~9.52 |
| Zero-coupon 30yr | 5% | 30 yr | 1 | ~28.57 |
How Duration Varies
When Modified Duration Is Not Enough
Disclaimer
Results are for reference and education. For actual portfolio decisions, verify with live market data and consult a registered financial advisor.
Frequently asked questions
What is bond modified duration?
Modified duration is a number that tells you how much a bond's price will change (in percent) when interest rates move by 1%. A modified duration of 6.23 means a 1% rate rise drops the price roughly 6.23%, and a 1% rate fall raises it 6.23%.
What is the modified duration formula?
Modified Duration = Macaulay Duration / (1 + YTM/m), where m is the number of coupon payments per year. For an at-par bond with semi-annual coupons: Mac Duration = [(1+r)/r × (1 − 1/(1+r)^N)] / m, where r = YTM/m and N = years × m.
What is a typical modified duration for a 10-year bond?
At 5% YTM with semi-annual coupons, a 10-year bond has a modified duration of about 8. At 10% YTM it is about 6.23. Lower YTM → higher duration. Zero-coupon bonds at 5% over 10 years have duration close to 9.5.
What is the difference between Macaulay duration and modified duration?
Macaulay duration is the weighted average time (in years) to receive the bond's cash flows. Modified duration adjusts it by dividing by (1 + YTM/m), turning it into an interest-rate sensitivity metric — how much the price changes per 1% rate move. Modified duration is what practitioners actually use.
Why do longer bonds have higher modified duration?
Longer bonds have more of their cash flow far in the future. Future flows are discounted more heavily, making their present value more sensitive to any change in the discount rate (YTM). A 30-year bond has far more rate sensitivity than a 2-year bond.
Why do zero-coupon bonds have the highest modified duration?
Zero-coupon bonds pay nothing until maturity — all cash is at the final date. There are no interim coupon payments to reduce the weighted-average time to receive cash. This makes the price extremely sensitive to rate changes. A 10-year zero-coupon bond at 5% has MD ≈ 9.5, versus ~8 for a coupon bond.
How do I use modified duration to estimate my bond's dollar loss?
Dollar loss ≈ Modified Duration × Rate Change × Bond Value. Example: MD = 6.23, rate rises 1%, bond value = $100,000 → loss ≈ 6.23% × $100,000 = $6,230. This is a first-order linear approximation; actual loss is slightly less due to convexity.
What is portfolio immunization and how does duration help?
Immunization means setting your bond portfolio's duration equal to your investment horizon. When you do this, price risk (bond falls when rates rise) and reinvestment risk (coupons reinvested at lower rates when rates fall) offset each other, locking in a target return regardless of rate movements.
Does coupon frequency affect modified duration?
Yes. More frequent coupon payments (quarterly vs annual) return cash sooner, reducing the weighted-average time to receive flows and therefore lowering duration. Semi-annual coupons (standard for US Treasuries) give slightly lower duration than annual coupons at the same YTM.
When should I use convexity alongside modified duration?
For rate moves larger than 1–2 percentage points, modified duration alone underestimates bond gains (when rates fall) and overestimates losses (when rates rise). Convexity corrects this: ΔPrice ≈ −MD × Δy + ½ × Convexity × (Δy)². For small moves, modified duration alone is sufficient.