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Macaulay Duration Calculator

Macaulay Duration Formula:

\[ D = \frac{\sum_{i=1}^{n} \left( t_i \times \frac{C_i}{(1 + r)^{t_i}} \right)}{P} \]

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1. What is Macaulay Duration?

Definition: Macaulay duration is the weighted average time until cash flows are received, measured in years.

Purpose: It helps investors understand interest rate risk and the sensitivity of bond prices to changes in interest rates.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ D = \frac{\sum_{i=1}^{n} \left( t_i \times \frac{C_i}{(1 + r)^{t_i}} \right)}{P} \]

Where:

Explanation: Each cash flow is discounted by the yield rate, weighted by its time period, and summed. This sum is divided by the bond's present value.

3. Importance of Macaulay Duration

Details: Higher duration means greater price sensitivity to interest rate changes. It's crucial for bond portfolio management and immunization strategies.

4. Using the Calculator

Tips: Enter comma-separated cash flows and their corresponding time periods, the yield (as decimal), and the present value. All values must be valid.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between Macaulay and modified duration?
A: Modified duration adjusts Macaulay duration to directly estimate price changes when yields change.

Q2: How does coupon rate affect duration?
A: Higher coupons generally mean shorter duration as more cash flows are received earlier.

Q3: What does zero duration mean?
A: Zero duration means the investment is insensitive to interest rate changes (e.g., cash).

Q4: Can duration be longer than maturity?
A: No, duration cannot exceed the bond's maturity, though it can be close for zero-coupon bonds.

Q5: How is duration used in portfolio management?
A: Managers match assets and liabilities durations to immunize against interest rate risk.

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