If a bond has a modified duration of 7 and convexity of 100 and interest rates fall 1 percent, what will happen to the price of the bond?
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A. B. C. D.Explanation
†V = -(7) (.01) + 1/2 (100) (.01)2.
To determine the impact of a 1 percent decrease in interest rates on the price of the bond, we need to consider the bond's modified duration and convexity.
Modified duration measures the sensitivity of a bond's price to changes in interest rates. A higher modified duration indicates a greater sensitivity to interest rate changes. In this case, the bond has a modified duration of 7, which means that for every 1 percent change in interest rates, the bond's price will change by approximately 7 percent in the opposite direction.
Convexity, on the other hand, measures the curvature of the bond's price-yield relationship. It provides a more refined measure of the bond's sensitivity to interest rate changes, particularly for larger changes in interest rates. A positive convexity value indicates that the bond's price-yield relationship is curved upward.
Given that the bond has a convexity of 100, we can infer that the bond has a positive convexity, which means that the bond's price will increase by more than what would be predicted by the modified duration alone when interest rates decrease.
Now, let's analyze the options:
A. Fall 7.5%: This suggests that the bond's price would decrease by 7.5% in response to a 1 percent decrease in interest rates. However, this contradicts the positive convexity of the bond, which implies that the price should increase more than predicted by the modified duration.
B. Rise 6.5%: This option suggests that the bond's price would increase by 6.5% in response to a 1 percent decrease in interest rates. This contradicts the positive convexity and the fact that the modified duration is 7, which indicates a larger price change.
C. Rise 7.5%: This option suggests that the bond's price would increase by 7.5% in response to a 1 percent decrease in interest rates. This aligns with the positive convexity and implies that the bond's price will increase more than predicted by the modified duration.
D. Fall 6.5%: This option suggests that the bond's price would decrease by 6.5% in response to a 1 percent decrease in interest rates. This contradicts the positive convexity and the fact that the modified duration is 7, which indicates a larger price change.
Therefore, the correct answer is C. Rise 7.5%. The bond's price would be expected to increase by approximately 7.5% in response to a 1 percent decrease in interest rates, considering both the modified duration and convexity.