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Bond Duration Formula:
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Bond duration is a measure of the sensitivity of a bond's price to changes in interest rates. It represents the weighted average time it takes to receive all cash flows from a bond, with weights being the present value of each cash flow relative to the bond's price.
The calculator uses the Macaulay duration formula:
Where:
Explanation: The formula calculates the weighted average time until cash flows are received, where weights are the proportion of each cash flow's present value to the total bond price.
Details: Duration is crucial for bond portfolio management as it helps measure interest rate risk. Higher duration indicates greater sensitivity to interest rate changes. It's used for immunization strategies and asset-liability matching.
Tips: Enter cash flows as comma-separated values (e.g., "50,50,50,1050" for a 4-year bond with $50 annual coupon and $1000 face value). Enter the current bond price in USD. All values must be positive numbers.
Q1: What's the difference between Macaulay and modified duration?
A: Macaulay duration is the weighted average time to cash flows, while modified duration measures price sensitivity to yield changes (Macaulay duration / (1 + yield/periods)).
Q2: How does coupon rate affect duration?
A: Higher coupon bonds have shorter durations because more cash flows are received earlier. Zero-coupon bonds have durations equal to their maturity.
Q3: What is a good duration for a bond portfolio?
A: It depends on interest rate expectations and risk tolerance. Shorter durations are less sensitive to rate changes but typically offer lower yields.
Q4: How does yield affect duration?
A: Higher yields generally result in shorter durations because later cash flows are discounted more heavily.
Q5: Can duration be negative?
A: For standard bonds, duration is always positive. Some complex instruments like interest-only strips can have negative duration.