Question

A 30-year maturity bond making annual coupon payments with a coupon rate of 16.0% has duration of 10.55 years and convexity of 161.7. 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? The duration rule provides more accurate approximations to the actual change in price. 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) – (d)? Yes No

Answer 1

Coupon Rate = 16%

Duration = 10.55

Current Yield = 9%

Convexity = 161.7

Therefore calcuate the Current Price of bond using Financial Calculator.

Input parameters:

N = 30 , I/Y = 9 , PMT =16, FV =100, Calculate PV

PV = 171.9

Now wjhen the Yield changes to 8, Price of bond using the same parameters except the I/Y = 8

PV = 190

b. Price when predicted through duration rule

Percentage change in price of bond = - Duration * change in Yield in percent

= -10.55 * (-1) = 10.55%

Therefore the price of bond after is

0.1055 = Final Price - 171.9 / 171.9

Final Price = 190.03

c. Price using duration + convexity rule:

percentage change in price = {- Duration * yield change + Convexity * (Yield Change)^2} * 100

= {-10.55 * .01 + 161.7 * (0.01)^2} *100

= 12.16%

New Price = 171.9 * (1.1216) = 192.80