Bond Convexity Calculator
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While Modified Duration estimates how much a bond’s price changes in response to small interest rate shifts, duration assumes a straight linear relationship. In reality, the price-yield relationship of a bond is curved (convex). For large interest rate fluctuations, relying solely on duration leads to inaccurate price estimates. To capture the curvature of bond price sensitivity, portfolio managers measure Bond Convexity.
Our free Bond Convexity Calculator computes bond convexity, calculates the secondary convexity price adjustment, and models accurate bond price shifts under major interest rate changes.
How to Calculate Bond Convexity & Price Shift
Convexity is the second derivative of a bond’s price with respect to interest rate yields, acting as an adjustment multiplier for Modified Duration.
Combined Duration-Convexity Price Change Formula:
% Price Change ≈ [ - Modified Duration × Δy ] + [ 0.5 × Convexity × (Δy)² ] × 100
- Modified Duration: Linear price sensitivity measure in years.
- Convexity: Second-order non-linear curvature measure.
- Δy: Change in yield-to-maturity (expressed as a decimal, e.g., +1.0% = +0.01).
Step-by-Step Fixed Income Risk Example
Suppose a portfolio manager holds a 10-year corporate bond with a Modified Duration of 7.50 years and a Convexity score of 70.0. Interest rates suddenly rise by 1.00% (Δy = +0.01).
Let’s calculate the linear duration estimate, the convexity adjustment, and the total net price change:
Linear Duration Estimate = -7.50 × (+0.01) = -0.075 (-7.50%)
Convexity Adjustment = 0.5 × 70.0 × (+0.01)² = 35.0 × 0.0001 = +0.0035 (+0.35%)
Combined Net Price Change = -7.50% + 0.35% = -7.15%
| Interest Rate Shift (Δy) | Linear Duration Change | Convexity (+0.5 × C × Δy²) | Actual Net Bond Price Change |
|---|---|---|---|
| Rate Increase (+1.00%) | -7.50% Drop | +0.35% Cushion | -7.15% Actual Loss |
| Rate Decrease (-1.00%) | +7.50% Gain | +0.35% Boost | +7.85% Actual Gain |
Frequently Asked Questions (FAQ)
What is Bond Convexity?
Bond Convexity is a measure of the curvature in the relationship between a bond’s price and market interest rates. It measures how much a bond’s duration changes as yield shifts.
Why is positive convexity desirable for bond investors?
Positive convexity is highly desirable because it works in the investor’s favor in both directions: when rates fall, bond prices rise more than duration predicts; when rates rise, bond prices fall less than duration predicts.
What is negative convexity in callable bonds?
Negative Convexity occurs in callable bonds and mortgage-backed securities (MBS). As interest rates fall, the issuer is likely to call back the bond to refinance at lower rates, capping capital appreciation and causing the price-yield curve to flatten or drop.