Question

A 30-year maturity bond making annual coupon payments with a coupon rate of 8% has duration of 11.37 years and convexity of 187.81. 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 answers to 2 decimal places.)

b. What price would be predicted by the duration rule? (Do not round intermediate calculations. Round your answers to 2 decimal places.)

c. What price would be predicted by the duration-with-convexity rule? (Do not round intermediate calculations. Round your answers to 2 decimal places.)

d-1. What is the percent error for each rule? (Negative answers should be indicated by a minus sign. Do not round intermediate calculations. Round your answers to 2 decimal places.)

d-2. What do you conclude about the accuracy of the two rules?

• The duration-with-convexity rule provides more accurate approximations to the true change in price.

• The duration rule provides more accurate approximations to the true change in price.

e-1. Find the price of the bond if its yield to maturity increases to 10%. (Do not round intermediate calculations. Round your answers to 2 decimal places.)

e-2. What price would be predicted by the duration rule? (Do not round intermediate calculations. Round your answers to 2 decimal places.)

e-3. What price would be predicted by the duration-with-convexity rule? (Do not round intermediate calculations. Round your answers to 2 decimal places.)

e-4. What is the percent error for each rule? (Negative answers should be indicated by a minus sign. Do not round intermediate calculations. Round your answers to 2 decimal places.)

e-5. Are your conclusions about the accuracy of the two rules consistent with parts (a) – (d)?

• Yes

• No

Answer 1

(a) Coupon Rate = 8%, Yield to Maturity = 8 %, Duration = 11.37 years and Convexity = 187.81, Tenure = 30 years

As the bond's coupon rate equals its yield to maturity, then the bond should sell at its par value. Assuming a Par Value of $ 1000, the bond should have a price of $ 1000.

(b) Original YTM = 9 %

Annual Coupon = 0.08 x 1000 = 80

Actual Bond Price = 80 x (1/0.09) x [1-{1/(1.09)^(30)}] + 1000 / (1.09)^(30) = $ 897.263

Duration = D = 11.37 and % Change in Yield = 1 %

% Change in Price = - D x % Change in Yield = - 11.37 x (-0.01) = 0.1137 or 11.37 %

Therefore, New Bond Price = 1.1137 x 897.263 = $ 999.282 ~ $ 999.28

(c) Convexity = 187.81 , Duration = 11.37 years, % Change in YTM = 1 % and Original Bond Price = $ 897.263

Therefore, % Change in Bond Price = - Duration x % Change in YTM + (1/2) x (Convexity) x (% Change in Yield)^(2) = - 11.37 x (-0.01) + 1/2 x 187.81 x (-0.01)^(2) = 0.12309 or 12.309 %

New Bond Price = 1.12309 x 897.263 = $ 1007.71

(d1) Duration Rule % Error = (1000 - 999.282) / 1000 = 0.00072 or 0.072 %

Convexity + Duration Rule % Error = (1000 - 1007.71) / 1000 = - 0.0077 or - 0.77 %

(d2) The duration rule gives a more accurate prediction of the price change as the % error for the duration rule is lower as compared to the convexity + duration rule

NOTE: Please raise separate queries for solutions to the remaining unrelated questions, as one query is restricted to the solution of only one complete question with up to four sub-parts.