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

A 30-year maturity bond making annual coupon payments with a
coupon rate of 10.2% has duration of 11.03 years and convexity of
176.83. 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%.
b. What price would be predicted by the duration rule?
c. What price would be predicted by the duration-with-convexity
rule?
d-1. What is the percent error for each rule?
d-2. What...

A 30-year maturity bond making annual coupon payments with a
coupon rate of 7% has duration of 15.16 years and convexity of
315.56. The bond currently sells at a yield to maturity of 5%.
a.
Find the price of the bond if its yield to maturity falls to 4%
or rises to 6%. (Round your answers to 2 decimal places.
Omit the "$" sign in your response.)
Yield to maturity of
4%
$
Yield to maturity of
6%...

Find the duration of a 8% coupon bond making annual
coupon payments if it has three years until maturity and a yield to
maturity of 7.8%. What is the duration if the yield to maturity is
11.8%? (Do not round intermediate calculations. Round your
answers to 4 decimal places.)
YTM
Duration
7.8% YTM
11.8% YTM

Find the duration of a 6% coupon bond making annual coupon
payments if it has three years until maturity and a yield to
maturity of 7.7%. What is the duration if the yield to maturity is
11.7%? (Do not round intermediate calculations. Round your answers
to 4 decimal places.)
YTM Duration 7.7% YTM 11.7% YTM

Find the duration of a 8% coupon bond making annual
coupon payments if it has three years until maturity and a yield to
maturity of 7.8%. What is the duration if the yield to maturity is
11.8%? (Do not round intermediate calculations. Round your
answers to 4 decimal places.)
YTM
Duration
7.8% YTM

Find the duration of a 4% coupon bond making annual coupon
payments if it has 3 years until maturity and has a yield to
maturity of 4%. What is the duration if the yield to maturity is
6%? Note: The face value of the bond is $1,000. (Do not round
intermediate calculations. Round your answers to 3 decimal
places.)
Duration 4% YTM:
6% YTM:

a. Find the duration of a 6% coupon bond making annual coupon
payments if it has three years until maturity and has a yield to
maturity of 6%. Note: The face value of the bond is $1,000. (Do not
round intermediate calculations. Round your answers to 3 decimal
places.) b. What is the duration if the yield to maturity is 10%?
Note: The face value of the bond is $1,000. (Do not round
intermediate calculations. Round your answers to 3...

A 4 year maturity bond making annual coupon payments with a
coupon of 8% has a duration of 3.607 years and a convexity of
16.08. The bond currently sells at a yield of 4%. What is the
actual price of the bond if the YTM immediately increases to 6%?
Round you answer to the nearest penny. Answer:

A 30-year bond making annual payments has a coupon rate of 12%,a
duration of 11.54years, and convexity of 192.4.The bond is
currently selling at a yield to maturity of 8%. Use the
duration-with -convexity approximation to predict the new price of
the bond iftheyield to maturitydeclines from 8% to 7%.Assume a
facevalue of 1000.

a. What is the duration of a two-year bond that pays an annual
coupon of 12 percent and whose current yield to maturity is 13
percent? Use $1,000 as the face value. (Do not round intermediate
calculations. Round your answer to 3 decimal places. (e.g.,
32.161))
b. What is the expected change in the price of the bond if
interest rates are expected to increase by 0.6 percent? (Negative
amount should be indicated by a minus sign. Do not round...

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 8 minutes ago

asked 13 minutes ago

asked 13 minutes ago

asked 30 minutes ago

asked 36 minutes ago

asked 55 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 2 hours ago

asked 2 hours ago

asked 3 hours ago

asked 3 hours ago