Duration & Convexity Calculator
Measure bond price sensitivity to interest rate changes with precision.
Why Duration & Convexity Matter
Duration and convexity are key metrics for measuring how bond prices change with interest rates. They help investors manage interest rate risk in fixed-income portfolios.
How to Use This Calculator
Enter the bond’s face value, coupon rate, yield to maturity, and maturity period. The tool calculates:
- Macaulay Duration: Weighted average time to receive cash flows
- Modified Duration: Price sensitivity to yield changes (in %)
- Convexity: Curvature correction for large rate changes
The Formulas
Macaulay Duration = Σ [t × CFₜ / (1 + y/m)ᵗ] / PriceModified Duration = Macaulay / (1 + y/m)Convexity = Σ [t(t+1) × CFₜ / (1 + y/m)ᵗ⁺²] / (Price × (1 + y/m)²)Where:
- CFₜ = Cash flow at time t
- y = Yield to maturity
- m = Compounding frequency per year
- t = Time period (in years)
Real-World Applications
- Portfolio Risk Management: Match duration to investment horizon
- Interest Rate Hedging: Use duration to hedge against rate changes
- Bond Comparison: Choose bonds with lower sensitivity if rates are rising
- Immunization: Balance duration and convexity to protect portfolio value
Example
A 10-year bond with a 5% coupon and 6% yield has a modified duration of 7.4 years. If rates rise 1%, the price drops ~7.4%. With convexity, the actual drop is slightly less (~7.1%) due to curvature.
Key Insights
- Longer maturity → higher duration
- Higher coupon → lower duration
- Higher yield → lower duration
- Convexity improves accuracy for large rate moves
Free Financial Planning Tools: Budget, Invest & Plan Retirement
Free Financial Planning Tools – Try Now
Explore All Calculators→