Question: A 30-year maturity bond making annual coupon payments with a coupon rate of 16.3% has duration of 10.54 years and convexity of 161.2. The bond currently sells at a yield to maturity of 9%.
a. Find the price of the bond if its yield to maturity falls to 8%. (Do not round intermediate calculations. Round your answer to 2 decimal places.)
b. What price would be predicted by the duration rule? (Do not round intermediate calculations. Round your answer to 2 decimal places.)
c. What price would be predicted by the duration-with-convexity rule? (Do not round intermediate calculations. Round your answer to 2 decimal places.)
d-1. What is the percent error for each rule? (Enter your answer as a positive value. Do not round intermediate calculations. Round "Duration Rule" to 2 decimal places and "Duration-with-Convexity Rule" to 3 decimal places.)
Percent Error
YTM
Duration Rule
Duration-with-Convexity Rule
8%
%
%
d-2. What do you conclude about the accuracy of the two rules? A or B
A. The duration rule provides more accurate approximations to the actual change in price.
B. The duration-with-convexity rule provides more accurate approximations to the actual change in price.
e-1. Find the price of the bond if it's yield to maturity rises to 10%. (Do not round intermediate calculations. Round your answer to 2 decimal places.)
e-2. What price would be predicted by the duration rule? (Do not round intermediate calculations. Round your answer to 2 decimal places.)
e-3. What price would be predicted by the duration-with-convexity rule? (Do not round intermediate calculations. Round your answer to 2 decimal places.)
e-4. What is the percent error for each rule? (Do not round intermediate calculations. Round "Duration Rule" to 2 decimal places and "Duration-with-Convexity Rule" to 3 decimal places.)
Percent Error
YTM
Duration Rule
Duration-with- Convexity Rule
10%
%
%
e-5. Are your conclusions about the accuracy of the two rules consistent with parts (a) - (d)?