Question

A 30-year maturity bond making annual coupon payments with a coupon rate of 15.0% has duration of 9.41 years and convexity of 129.3. The bond currently sells at a yield to maturity of 11%.

a. Find the price of the bond if its yield to maturity falls to 10%. (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
10%	%	%

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 12%. (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
12%	%	%

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

	Yes
	No

Answer 1

a) Assuming bond pays coupon annually and has face value = 100

Using financial calculator or Excel function

[FV=100, N=30, PMT=15, I/Y= 11%, Compute PV] gives PV = 134.77517 (this is price with YTM=11%)

[FV=100, N=30, PMT=15, I/Y= 10%, Compute PV] gives PV = 147.1345723 = 147.13 (with YTM=10%)

b) % change in Price = [-Duration * (Change in Yield)/(1+y)] = -9.41*(-1%)/(1.10) = +0.0941/1.1 = +0.085545455

BondPrice(YTM=10%) = BondPrice(YTM=11%) (1+0.0941) = 134.77517 (1.085545455) =146.3045732 = 146.30

Note: Above we divided Maculay Duration by (1+y) to get modified Duration.

c) % change in Price = [-Duration * (Change in Yield)/(1+y)] + [0.5 * Convexity * (Change in Yield)^2]

= [0.085545455] + [0.5* 129.3 * (-1%)^2]= +0.085545455 +0.006465 = 0.092010455

BondPrice(YTM=10%) = BondPrice(YTM=11%) (1+0.092010455) = 134.77517 (1.092010455) =147.1758947=147.18

d1) Duration Rule Error =(146.3045732-147.13)/147.13 = -0.56%

DurationConvexity Rule Error = (147.1758947-147.13)/147.13 = 0.031%

d2) % error with Duration Convexity rule is less as compared to Duration rule.

Therefore-

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