1. What is Macaulay Duration?

Macaulay Duration is a measure of the weighted average time until a bond's cash flows are received. It's expressed in years and helps investors understand a bond's interest rate risk and price volatility.

2. How Does the Calculator Work?

The calculator uses the Macaulay Duration formula:

Where:

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

Explanation: The formula calculates the weighted average time until cash flows are received, with weights being the present value of each cash flow as a proportion of the bond's price.

3. Importance of Macaulay Duration

Details: Macaulay Duration is crucial for bond portfolio management, immunization strategies, and measuring interest rate risk. Higher duration indicates greater price sensitivity to interest rate changes.

4. Using the Calculator

Tips: Enter cash flows as comma-separated values (e.g., "50,50,50,1050" for a 4-year bond with 5% coupon), yield as decimal (e.g., 0.05 for 5%), and current bond price in dollars.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between Macaulay and Modified Duration?
A: Modified Duration = Macaulay Duration / (1 + y), and measures the percentage price change for a 1% change in yield.

Q2: How does coupon rate affect duration?
A: Higher coupon rates generally result in shorter durations because more cash flows are received earlier.

Q3: What does a higher duration indicate?
A: Higher duration means greater price sensitivity to interest rate changes and higher interest rate risk.

Q4: Can duration be longer than maturity?
A: No, Macaulay Duration is always less than or equal to the bond's time to maturity.

Q5: How is duration used in portfolio management?
A: Duration matching helps immunize portfolios against interest rate risk by aligning asset and liability durations.