1. What is Convexity?

Convexity is a measure of the curvature in the relationship between bond prices and bond yields. It shows how the duration of a bond changes as interest rates change, providing a more complete picture of interest rate risk than duration alone.

2. How Does the Calculator Work?

The calculator uses the convexity formula:

Where:

• \( P_{\text{up}} \) — Bond price when yield decreases by Δy (USD)
• \( P_{\text{down}} \) — Bond price when yield increases by Δy (USD)
• \( P \) — Current bond price (USD)
• \( \Delta y \) — Change in yield (decimal)

Explanation: The formula measures the second derivative of the price-yield relationship, showing how much a bond's duration changes as yields change.

3. Importance of Convexity

Details: Bonds with greater convexity will have larger price increases when yields fall than price decreases when yields rise. This makes them more valuable in volatile interest rate environments.

4. Using the Calculator

Tips: Enter all prices in USD and yield change as a decimal (e.g., 0.01 for 1%). All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is a typical convexity value?
A: Convexity values vary by bond type but are typically positive for standard bonds, ranging from 50 to 300 for most bonds.

Q2: How does convexity relate to duration?
A: Duration measures first-order price sensitivity to yield changes, while convexity measures the second-order (curvature) effect.

Q3: Why is convexity important for bond investors?
A: Higher convexity bonds provide better downside protection when rates rise and greater upside potential when rates fall.

Q4: Can convexity be negative?
A: Yes, some mortgage-backed securities and callable bonds can have negative convexity.

Q5: How is convexity used in portfolio management?
A: Portfolio managers use convexity to assess interest rate risk and construct portfolios with desired risk/return characteristics.