Bond Convexity Calculator
Measure non-linear interest rate risk and bond price sensitivity
Calculate Bond Convexity
Bond Characteristics
Par value or principal amount
Annual interest rate
Payment frequency per year
Time until bond matures
Yield Parameters
Current market yield
Yield change for sensitivity analysis
Quick Presets
Bond Convexity Results
Convexity Analysis
Example: Bond Alpha Convexity Analysis
Bond Alpha Characteristics
Face Value: $1,000
Annual Coupon Rate: 5%
Coupon Frequency: Annual (1x per year)
Years to Maturity: 10 years
Yield to Maturity: 8%
Yield Differential: 1%
Step-by-Step Convexity Calculation
Step 1 - Coupon per Period: $1,000 × 5% ÷ 1 = $50
Step 2 - Bond Price @ 8% YTM: $798.70
Step 3 - Upward Price @ 7% YTM: $859.53
Step 4 - Downward Price @ 9% YTM: $743.29
Step 5 - Convexity Formula:
($859.53 + $743.29 - 2×$798.70) / ($798.70 × 0.01²)
= ($1,602.82 - $1,597.40) / ($798.70 × 0.0001)
= $5.42 / $0.07987 = 67.95
Result: Bond convexity of 67.95 indicates moderate sensitivity
Convexity Levels
Very High
Extreme sensitivity
Long-term zero-coupon bonds
High
High sensitivity
Long-term bonds
Moderate
Balanced sensitivity
Medium-term bonds
Low
Low sensitivity
Short-term bonds
Factors Affecting Convexity
Time to Maturity: Longer maturity increases convexity
Coupon Rate: Lower coupons increase convexity
Current Yield: Lower yields increase convexity
Embedded Options: Can create negative convexity
Understanding Bond Convexity
What is Bond Convexity?
Bond convexity measures the non-linear relationship between bond prices and interest rate changes. While duration captures the linear effect, convexity accounts for the curvature in the price-yield relationship, providing a more accurate assessment of interest rate risk.
Why is Convexity Important?
- •More accurate price sensitivity measurement
- •Better risk management for bond portfolios
- •Improved hedging strategy development
- •Enhanced understanding of embedded options
Convexity Formula
Convexity = (BP↑ + BP↓ - 2×BP) / (BP × YD²)
Where:
BP↑ = Bond price when yield decreases
BP↓ = Bond price when yield increases
BP = Current bond price
YD = Yield differential (change)
Convexity vs Duration
Duration measures linear price sensitivity, while convexity captures the non-linear effects. Together, they provide a comprehensive view of how bond prices respond to interest rate changes.
Note: Higher convexity is generally favorable as it provides upside protection when rates fall while limiting downside when rates rise.