Wendy Jones, CFA, is reviewing a current bond holding. The bond's duration is 10 and its convexity is 200. Jones believes that interest rates will fall by 100 basis points. Calculate the bond's percentage price change based on a 100 basis point decline.
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A. B. C.C
To calculate the bond's percentage price change based on a 100 basis point decline in interest rates, we need to use the concept of duration and convexity.
Duration measures the sensitivity of a bond's price to changes in interest rates. It represents the weighted average time it takes to receive the bond's cash flows, considering both coupon payments and the bond's final principal payment.
Convexity measures the curvature of the relationship between bond prices and interest rates. It helps refine the estimation of the bond's price change when there are larger or nonlinear changes in interest rates.
The formula to calculate the approximate percentage price change using duration and convexity is:
Percentage price change ≈ - Duration * ΔYield + 0.5 * Convexity * (ΔYield)^2
Where:
Let's calculate the percentage price change:
Percentage price change ≈ - 10 * (-0.01) + 0.5 * 200 * (-0.01)^2 Percentage price change ≈ 0.10 + 0.001 Percentage price change ≈ 0.101
The approximate percentage price change is 0.101, or 10.1%.
However, the question asks for the percentage price change based on a 100 basis point decline. Since a 100 basis point decline corresponds to a -1% change in yield, we need to multiply the result by 100:
Percentage price change = 0.101 * 100 Percentage price change = 10.1%
Therefore, the bond's percentage price change based on a 100 basis point decline is 10.1%.
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