Bond Duration — Smart Financial Analysis
Calculate Macaulay duration, modified duration, convexity, and price sensitivity for fixed-income bonds. Essential for portfolio immunization and interest rate risk management.
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Bond duration measures sensitivity to interest rate changes. Macaulay duration measures the weighted-average time to receive cash flows (in years). Macaulay Duration = Σ(t × PV_CF) / Bond Price, where t is the period and PV_CF is the present value of each cash flow. Duration is the primary measure of interest rate risk.
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Why: Bond duration measures sensitivity to interest rate changes. It tells you how much a bond's price will change when yields move. Macaulay duration is the weighted average ti...
How: Enter Face Value ($), Coupon Rate (%), Yield to Maturity (%) to get instant results. Try the preset examples to see how different scenarios affect the outcome, then adjust to match your situation.
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Bond Parameters
Duration by Maturity
Price Sensitivity to Yield Changes
Duration Comparison by Bond Type
Cash Flow Timeline
For educational purposes only — not financial advice. Consult a qualified advisor before making decisions.
💡 Money Facts
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Bond Duration — The Most Important Risk Metric
Bond duration measures sensitivity to interest rate changes. Macaulay Duration = weighted average time to receive cash flows. Modified Duration ≈ Macaulay / (1 + y/n). A bond with modified duration of 8 loses ~8% when rates rise 1%. The 2022 bond crash: 30yr Treasuries with duration 18.5 lost ~33% as rates rose from 1.5% to 3.5%. Duration is the MOST important risk metric for bond investors. Zero coupon bonds have duration equal to maturity — maximum rate sensitivity.
Key Takeaways
- Macaulay duration = weighted average time to receive cash flows
- Modified duration = Macaulay / (1 + YTM/n) — direct price sensitivity
- 1% rate increase → bond price falls by roughly Modified Duration %
- Longer maturity + lower coupon = higher duration = more interest rate risk
Macaulay vs Modified Duration
Macaulay duration measures the weighted-average time to receive cash flows. Modified duration adjusts for yield level and directly estimates percentage price change for a 1% yield shift. Modified = Macaulay / (1 + YTM/n). Modified is more useful for risk management and hedging.
Duration Formula
Macaulay Duration = Σ(t × PV_CF) / Bond Price. Modified Duration = Macaulay / (1 + YTM/n). Price change ≈ -Modified Duration × Δy for small yield changes. For large moves, add the convexity adjustment.
Duration and Interest Rate Risk
Duration is the primary measure of interest rate risk. A bond with modified duration of 7 loses approximately 7% when rates rise 1%. The relationship is inverse: higher rates → lower bond prices. The 2022 bond crash demonstrated this — long-duration bonds suffered massive losses.
Duration of Zero Coupon Bond
Zero coupon bonds have duration equal to maturity. All cash flow arrives at maturity — no coupons to reduce the weighted-average time. A 30yr zero has duration 30 years — maximum interest rate sensitivity.
Portfolio Duration
Portfolio duration = weighted average of individual bond durations. Example: 60% in bonds with duration 5yr + 40% in bonds with duration 12yr → portfolio duration = 0.6×5 + 0.4×12 = 7.8 years. Match portfolio duration to your investment horizon for immunization.
Sources
- CFA Institute — Fixed income and duration methodology
- Bloomberg — Bond market data and duration analytics
- PIMCO — Duration and interest rate risk
- Fabozzi — Bond valuation and duration
⚠️ Disclaimer: This calculator provides theoretical bond duration and price sensitivity estimates based on standard fixed-income models. Actual bond prices may differ due to credit risk, liquidity, embedded options, and market conditions. Not financial advice — consult a financial professional before making investment decisions.
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