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Bond Price Percentage Change Formula:
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The bond price percentage change formula estimates how much a bond's price will change given a change in yield to maturity (YTM). It uses the bond's duration and current YTM to approximate price sensitivity to interest rate changes.
The calculator uses the modified duration formula:
Where:
Explanation: The formula shows that bond prices move inversely to yield changes, with the sensitivity determined by duration and scaled by the current yield level.
Details: Understanding price sensitivity helps investors assess interest rate risk, compare bonds, and construct portfolios with desired risk characteristics.
Tips: Enter duration in years, ΔYTM as a decimal (e.g., 0.01 for 1%), and YTM as a decimal. All values must be valid (duration > 0, YTM ≥ 0).
Q1: What's the difference between Macaulay duration and modified duration?
A: Macaulay duration is the weighted average time to receive cash flows. Modified duration (used here) adjusts Macaulay duration by dividing by (1+YTM) to directly measure price sensitivity.
Q2: How accurate is this approximation?
A: It works well for small yield changes. For larger changes, convexity (the curvature of the price-yield relationship) should also be considered.
Q3: Why is there a negative sign in the formula?
A: It reflects the inverse relationship between bond prices and yields - when yields rise, prices fall, and vice versa.
Q4: Does this work for all bond types?
A: It works best for option-free bonds. Bonds with embedded options (like callable bonds) require different duration measures.
Q5: How does coupon rate affect duration?
A: Higher coupon bonds generally have lower duration because more of their value comes from earlier cash flows.