A 30-year maturity bond making annual coupon payments with a coupon rate of 14.5% has duration of 11.32 years and convexity of 185.2. The bond currently sells at a yield to maturity of 8%.
a. Find the exact price of the bond if its yield to maturity falls to 7%. (Do not round intermediate calculations. Round your answer to 2 decimal places.)
Price of the bond $ _________
b. Assume that you need to make a quick approximation using the duration rule (instead of the exact calculation in part a above). What price would be predicted by the duration rule? (Do not round intermediate calculations. Round your answer to 2 decimal places.)
Predicted price $ _________
c. Assume that you need to make a quick approximation using the duration-with-convexity rule (instead of the exact calculation in part a above). What price would be predicted by the duration-with-convexity rule? (Do not round intermediate calculations. Round your answer to 2 decimal places.)
Predicted price $ _________
d-1. What is the percent error for each rule? [Hint: percent error is the deviation from the exact price, divided by the exact price. It indicates the extent to which the approximated price differs from the exact price. A smaller percent error indicates more precise approximation.] (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 7% ________% ________%
e-1. Find the exact price of the bond if it's yield to maturity rises to 9%. (Do not round intermediate calculations. Round your answer to 2 decimal places.)
Price of the bond $ _________
e-2. What price would be predicted by the duration rule? (Do not round intermediate calculations. Round your answer to 2 decimal places.)
Predicted price $ _________
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.)
Predicted price $ _________
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 9% ________% ________%
A 30-year maturity bond making annual coupon payments with a coupon rate of 14.5% has duration of 11.32 years and convexity of 185.2. The bond currently sells at a yield to maturity of 8%.
a. Find the exact price of the bond if its yield to maturity falls to 7%. (Do not round intermediate calculations. Round your answer to 2 decimal places.)
Price of the bond $ _________
b. Assume that you need to make a quick approximation using the duration rule (instead of the exact calculation in part a above). What price would be predicted by the duration rule? (Do not round intermediate calculations. Round your answer to 2 decimal places.)
Predicted price $ _________
c. Assume that you need to make a quick approximation using the duration-with-convexity rule (instead of the exact calculation in part a above). What price would be predicted by the duration-with-convexity rule? (Do not round intermediate calculations. Round your answer to 2 decimal places.)
Predicted price $ _________
d-1. What is the percent error for each rule? [Hint: percent error is the deviation from the exact price, divided by the exact price. It indicates the extent to which the approximated price differs from the exact price. A smaller percent error indicates more precise approximation.] (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 |
| 7% | ________% | ________% |
e-1. Find the exact price of the bond if it's yield to maturity rises to 9%. (Do not round intermediate calculations. Round your answer to 2 decimal places.)
Price of the bond $ _________
e-2. What price would be predicted by the duration rule? (Do not round intermediate calculations. Round your answer to 2 decimal places.)
Predicted price $ _________
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.)
Predicted price $ _________
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 |
| 9% | ________% | ________% |
Related questions
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.)
| Price of the bond | $ |
b. What price would be predicted by the duration rule? (Do not round intermediate calculations. Round your answer to 2 decimal places.)
| Predicted price | $ |
c. What price would be predicted by the duration-with-convexity rule? (Do not round intermediate calculations. Round your answer to 2 decimal places.)
| Predicted price | $ |
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.)
| Price of the bond | $ |
e-2. What price would be predicted by the duration rule? (Do not round intermediate calculations. Round your answer to 2 decimal places.)
| Predicted price | $ |
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.)
| Predicted price | $ |
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) â (d)?
Yes OR No
| A 12-year maturity zero-coupon bond selling at a yield to maturity of 7% (effective annual yield) has convexity of 151.5 and modified duration of 11.06 years. A 30-year maturity 7% coupon bond making annual coupon payments also selling at a yield to maturity of 7% has nearly identical durationâ11.04 yearsâbut considerably higher convexity of 234.6. |
| a. | Suppose the yield to maturity on both bonds increases to 8%. What will be the actual percentage capital loss/gain on each bond? What percentage capital loss/gain would be predicted by the duration-with-convexity rule? (Input all amounts as positive values. Do not round intermediate calculations. Round your answers to 2 decimal places. Omit the "%" sign in your response.) | |
| Zero Coupon Bond | Coupon Bond | |
| Actual : gain/loss | % | % |
| Predicted : loss/gain | % | % |
| b. | Suppose the yield to maturity on both bonds decreases to 6%. What will be the actual percentage capital loss/gain on each bond? What percentage capital loss/gain would be predicted by the duration-with-convexity rule? (Input all amounts as positive values. Do not round intermediate calculations. Round your answers to 2 decimal places. Omit the "%" sign in your response.) | |
| Zero Coupon Bond | Coupon Bond | |
| Actual : loss/gain | % | % |
| Predicted : loss/gain | % | % |
