Macaulay Duration Formula:
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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.
The calculator uses the formula:
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.
Details: Higher duration means greater price sensitivity to interest rate changes. It's crucial for bond portfolio management and immunization strategies.
Tips: Enter comma-separated cash flows and their corresponding time periods, the yield (as decimal), and the present value. All values must be valid.
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.