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Effective Duration Formula:
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Effective duration is a measure of a bond's price 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 are fixed).
The calculator uses the effective duration formula:
Where:
Explanation: The formula measures the percentage change in price for a given change in yield. The negative sign indicates the inverse relationship between price and yield.
Details: Duration is crucial for bond portfolio management, interest rate risk assessment, and immunization strategies. It helps investors understand how much bond prices might fluctuate with changing interest rates.
Tips: Enter the original bond price in USD, the change in price in USD, and the change in yield as a decimal (e.g., 0.01 for 1%). All values must be valid (price > 0, ΔYield ≠ 0).
Q1: What's the difference between modified and effective duration?
A: Modified duration assumes fixed cash flows, while effective duration accounts for possible changes in cash flows when yields change (important for bonds with embedded options).
Q2: What are typical duration values?
A: Short-term bonds might have durations of 1-3 years, intermediate-term 4-7 years, and long-term bonds 8+ years. Zero-coupon bonds have durations equal to their maturity.
Q3: Why is duration negative in the formula?
A: The negative sign reflects the inverse relationship between bond prices and yields - when yields rise, prices fall, and vice versa.
Q4: Can duration be greater than maturity?
A: For regular bonds, no. But for some mortgage-backed securities with negative convexity, effective duration can exceed stated maturity in certain conditions.
Q5: How does coupon rate affect duration?
A: Higher coupon bonds generally have lower duration because more of their total return comes from earlier coupon payments.