1. What is Bond Convexity?

Convexity measures the curvature in the relationship between bond prices and yields. It provides a more complete picture of interest rate risk than duration alone, especially for larger yield changes.

2. How Does the Calculator Work?

The calculator uses the convexity formula:

Where:

• \( t \) — Time period (unitless)
• \( y \) — Yield to maturity (decimal)
• \( CF_t \) — Cash flow at period t (USD)
• \( \text{Price} \) — Current bond price (USD)

Explanation: The formula accounts for the timing and size of all cash flows relative to the bond's price and yield.

3. Importance of Convexity

Details: Higher convexity means less price sensitivity to interest rate changes. Bonds with greater convexity perform better when yields change significantly.

4. Using the Calculator

Tips: Enter yield as decimal (e.g., 0.05 for 5%), bond price in USD, and cash flows as "period:amount" pairs. All values must be positive.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between duration and convexity?
A: Duration measures first-order price sensitivity to yield changes, while convexity measures the second-order (curvature) effect.

Q2: What are typical convexity values?
A: Convexity is typically positive for plain vanilla bonds, ranging from 0-200 for most bonds, but can be higher for certain securities.

Q3: Why is convexity important for bond investors?
A: It helps predict price changes more accurately, especially for large yield movements, and helps in immunization strategies.

Q4: How does coupon affect convexity?
A: Lower coupon bonds generally have higher convexity, all else being equal.

Q5: Can convexity be negative?
A: Yes, for some mortgage-backed securities or callable bonds, convexity can be negative.