1. What is Effective Duration?

Effective Duration measures a bond's sensitivity to changes in interest rates, accounting for the fact that expected cash flows may change when yields change (unlike modified duration which assumes cash flows don't change).

2. How Does the Calculator Work?

The calculator uses the Effective Duration formula:

Where:

• \( P_{\text{down}} \) — Price if yield increases by Δy
• \( P_{\text{up}} \) — Price if yield decreases by Δy
• \( P \) — Current price of the bond
• \( \Delta y \) — Change in yield (in decimal form)

Explanation: The formula calculates the percentage change in price for a given change in yield, using a symmetric yield change up and down.

3. Importance of Effective Duration

Details: Effective duration is crucial for bonds with embedded options (like callable or putable bonds) where cash flows may change with interest rates. It helps investors understand interest rate risk.

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: How is effective duration different from modified duration?
A: Modified duration assumes cash flows don't change with yield, while effective duration accounts for possible cash flow changes (important for bonds with options).

Q2: What's a typical effective duration range?
A: Duration varies by bond type: short-term bonds might have 1-3 years, while long-term bonds could have 10+ years duration.

Q3: When should I use effective duration?
A: Always use for bonds with embedded options, and for any bond when you want the most accurate measure of interest rate sensitivity.

Q4: What Δy value should I use?
A: Typically 0.01 (100 basis points) is used, but you can use any small change that makes sense for your analysis.

Q5: Can effective duration be negative?
A: Yes, for certain instruments like some mortgage-backed securities where price may increase when yields rise.