1. What is Bond Convexity?

Convexity measures the curvature in the relationship between bond prices and yields. It shows how a bond's duration changes with interest rates and provides a more complete picture of interest rate risk than duration alone.

2. How Does the Calculator Work?

The calculator uses the convexity formula:

Where:

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

Explanation: The formula accounts for the timing and size of all cash flows, discounted appropriately by the yield.

3. Importance of Convexity

Details: Bonds with higher convexity have less price volatility when interest rates change. Convexity is particularly important for bonds with embedded options and for portfolio immunization strategies.

4. Using the Calculator

Tips: Enter cash flows and corresponding time periods as comma-separated values. Ensure yield is in decimal form (e.g., 0.05 for 5%). All values must be positive.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between duration and convexity?
A: Duration measures linear price sensitivity to yield changes, while convexity measures the curvature (non-linearity) of this relationship.

Q2: What are typical convexity values?
A: For plain vanilla bonds, convexity is typically positive and ranges from 0-100 yr², depending on maturity and coupon.

Q3: Why is convexity important for bond investors?
A: Higher convexity bonds will gain more when yields fall and lose less when yields rise, all else being equal.

Q4: How does coupon rate affect convexity?
A: Lower coupon bonds generally have higher convexity than higher coupon bonds with the same maturity.

Q5: Can convexity be negative?
A: Yes, callable bonds can have negative convexity at certain yield levels when the call option becomes likely to be exercised.