Calculating the price change in a bond caused by a 1 percent decline in interest rates using only the modified duration equation will always result in an answer that is:
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A. B. C. D.C
To answer this question, let's first understand the concept of modified duration and its relationship with interest rates and bond prices.
Modified duration is a measure of the sensitivity of a bond's price to changes in interest rates. It indicates the percentage change in the bond's price for a 1 percent change in interest rates. Mathematically, modified duration can be calculated using the following equation:
Modified Duration = Macaulay Duration / (1 + Yield to Maturity / Number of Coupon Payments per Year)
Now, let's consider the scenario presented in the question: a 1 percent decline in interest rates. Since interest rates and bond prices have an inverse relationship, when interest rates decline, bond prices generally increase.
When we calculate the price change using only the modified duration equation, we are assuming a parallel shift in the yield curve, meaning that the yields of all maturities change by the same amount. This assumption is not always accurate because in reality, yield curves can shift in a non-parallel manner. However, for the purposes of this question, we'll assume a parallel shift.
If interest rates decline by 1 percent, the yield to maturity in the modified duration equation would decrease by 1 percent. Since the modified duration equation calculates the percentage change in bond prices for a 1 percent change in interest rates, we would expect the bond price to increase by an amount equal to the modified duration.
Now, considering the answer choices:
A. If the price change calculated using only the modified duration equation is "too high," it means the bond price is expected to increase by more than the modified duration implies. This would only be the case if the bond exhibits a convexity effect, which captures the nonlinear relationship between bond prices and interest rates. However, since the question asks for the price change calculated using only the modified duration equation, we can conclude that the answer cannot be "too high."
B. If the price change calculated using only the modified duration equation is "just right," it means the bond price is expected to increase by an amount equal to the modified duration. This would be the case if the bond has a linear relationship between price and interest rates, which is the assumption made when using modified duration.
C. If the price change calculated using only the modified duration equation is "too low," it means the bond price is expected to increase by less than the modified duration implies. This would be the case if the bond exhibits negative convexity, meaning that the price increases by a smaller amount than expected due to the presence of call features or prepayment options. However, since the question asks for the price change calculated using only the modified duration equation, we can conclude that the answer cannot be "too low."
D. If the price change calculated using only the modified duration equation is "insignificant," it means the bond price is expected to increase by a very small amount, close to zero. This would occur if the bond has a very short duration or if the change in interest rates is very small. However, the question states a 1 percent decline in interest rates, which is not considered insignificant. Therefore, the answer cannot be "insignificant."
Based on the explanations above, the correct answer is B. The price change in a bond caused by a 1 percent decline in interest rates using only the modified duration equation will be "just right," meaning the bond price is expected to increase by an amount equal to the modified duration.