A bond has a modified duration of 6 and a convexity of 62.5. What happens to the bond's price if interest rates rise 25 basis points?
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A. B. C. D.Explanation
†P/P = (-)(MD)(†i) + (C)†P/P = (-)(6)(+.0025) + (62.5)=- .015 + .00039 = - .01461
To determine the change in the bond's price due to a 25 basis points (0.25%) increase in interest rates, we need to consider both the bond's modified duration and convexity.
Modified duration measures the percentage change in the bond's price for a 1% change in interest rates. In this case, the bond has a modified duration of 6, which means that for every 1% change in interest rates, the bond's price will change by approximately 6%.
To calculate the approximate percentage change in price due to a 0.25% (25 basis points) increase in interest rates, we can multiply the modified duration by the change in interest rates:
Approximate percentage change in price = Modified duration * Change in interest rates = 6 * 0.25% = 1.5%
So, based on the modified duration alone, we can conclude that the bond's price will decrease by approximately 1.5%.
However, convexity comes into play to provide a more accurate estimate. Convexity measures the curvature of the relationship between bond prices and interest rates. It helps refine the approximation provided by modified duration.
Convexity is typically expressed in terms of a value per basis point squared. In this case, the bond has a convexity of 62.5, which means that for a 1% change in interest rates, the bond's price will change by approximately 62.5 basis points squared.
To calculate the additional change in price due to convexity, we can use the following formula:
Additional percentage change in price due to convexity = 0.5 * Convexity * (Change in interest rates)^2
Plugging in the values:
Additional percentage change in price due to convexity = 0.5 * 62.5 * (0.25%)^2 ≈ 0.5 * 62.5 * (0.0025)^2 ≈ 0.5 * 62.5 * 0.00000625 ≈ 0.0001953125
So, the additional change in price due to convexity is approximately 0.01953% (0.0001953125).
Adding the approximate change in price due to modified duration and convexity, we get:
Total approximate percentage change in price = Approximate percentage change in price (due to modified duration) + Additional percentage change in price (due to convexity) = 1.5% + 0.01953% ≈ 1.52%
Therefore, the bond's price is expected to decrease by approximately 1.52% if interest rates rise by 25 basis points. Based on the provided answer choices, the correct answer would be B. It goes down 1.46%.