Question

A bond with a yield to maturity of 3% and a coupon rate of 3% has 3 years remaining until maturity. Calculate the duration and the modified duration for this bond assuming annual interest payments and a par value of $1,000. Why is the duration of this bond higher than the 3-year 10% coupon bond yielding 10% we looked at in the notes that had a duration of 2.7 years? If the required market yield on this bond increases to 4%, what approximate per- cent change in the bond price would you have based on the modified duration?

Answer #1

As yield to maturity is equal to coupon rate, price is equal to par=1000

Macaulay Duration or Duration=(1*3%*1000/1.03+2*3%*1000/1.03^2+3*3%*1000/1.03^3+3*1000/1.03^3)/1000=2.9135

Modified Duration=Macaulay Duration/(1+yield)=2.9135/1.03=2.8286

Duration decreases with increase in coupon rate and increase in yield to maturity

% change=-Modified Duration*change in yields=-2.8286*(4%-3%)=-2.8286%

A bond has a coupon rate of 6 percent, with payments
semi-annually. It matures in 2.5 years and has a yield to maturity
of 7 percent (15 points). a. Use the “long method” to determine the
duration and modified duration of this bond? b. If the yield to
maturity increases to 9 percent, what is the approximate percent
change in price based on the modified duration calculated in ‘a?’
c. What is the actual percentage change in price if the...

Bond B has a $1,000 par value and a 7% coupon rate, three years
remaining to maturity, and a 9% yield to maturity. The duration of
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(excel) Consider a 8% coupon bond
making annual coupon payments with 4 years until maturity
and a yield to maturity of 10%.
What is the modified duration of this bond?
If the market yield increases by 75 basis points, what is the
actual percentage change in the bond’s
price? [Actual, not approximation]
Given that this bond’s convexity is 14.13, what price would you
predict using the duration-with-convexity
approximation for this bond at this new yield?
What is the percentage error?

Assume a bond with a $1,000 par value and an 8 percent coupon
rate, two years remaining to maturity, and a 10 percent yield to
maturity. The modified duration of this bond is_________.

Calculate the requested measures for the bond with the following
information.
Coupon rate
4%
Yield to maturity
3%
Maturity (years)
2
Face value
$100
a. Macaulay duration
b. Modified duration
c. Price value of a basis point (DV01)
d. The approximate bond price estimated using modified duration
if the yield increases by 35
basis points

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A bond with a coupon rate of 9 percent sells at a yield to
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(Do not round intermediate calculations. Round your answers to 3
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time to maturity and YTM stands for yield to maturity. N.B: You
need to show how you have calculated duration. A single value will
not suffice.
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A bond with a coupon of 11.5% and 10 years remaining until
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work!

Find the duration of a 4% coupon bond making annual coupon
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Duration 4% YTM:
6% YTM:

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