Question

1. What is the duration of a 10-year zero-coupon bond with a par value of $1,000?

2. An investor has a 15-year maturity, 8% coupon, 8% yield bond with a duration of 10 years and a convexity of 135.5. If the interest rate were to fall 75 basis points, what is your predicted new price for the bond (including convexity)?

Answer #1

1)

**Duration of a 10 year bond = 10**

As a zero coupon bond pays all it's cash flows at maturity, duration of a zero coupon bond will be equal to maturity.

2)

75 basis point = 0.75% = 0.0075

Modified duration = Macaulay duration / (1 + r)

'Modified duration = 10 / (1 + 0.08)

Modified duration = 9.259259

Percentage change in price = (-Modified duration * change in yield) + [0.5 * Convexity * (change in yield)^2]

Percentage change in price = (-9.259259 * -0.0075) + [0.5 * 135.5 * (-0.0075)^2]

Percentage change in price = 0.069444 * 0.003811

Percentage change in price = 0.000265 or 0.0265%

Assuming face value to be $1000

Since coupon rate of 8% is equal to yield of 8%, current price is equal to face value. Therefore, current price is equal to $1000

Predicted new price = 1000 (1 + 0.000265)

**Predicted new price = $1,000.26**

Suppose that you have a 20-year maturity, 12% coupon, 12% yield
bond with a duration of 11 years and a convexity of 135.5. If the
interest rate were to fall 125 basis points, your predicted new
price for the bond (including convexity) is ________. This bond
sells at par, which means the current price equals its face value,
$1,000.
$1,104.56
$1,113.41
$1,124.22
$1,133.35

A bond has a 25-year maturity, 10% coupon, 10% yields, $1000
face value, a duration of 10 years and a convexity if 135.5.
Calculate the new value of the bond (in $), based on modified
duration and convexity, if interest rates were to fall by 125 basis
points.

You have a 25-year
maturity, 10.2% coupon, 10.2% yield bond with a duration of 10
years and a convexity of 135.7. If the interest rate were to fall
127 basis points, your predicted new price for the bond (including
convexity) is _________.

A bond has a 25-year maturity, 10% coupon, 10% yields, $1000
face value, a duration of 10 years and a convexity if 135.5.
Calculate the new value of the bond (in $), based on modified
duration and convexity, if interest rates were to fall by 125 basis
points.
Please show the working/formulas if done in excel.

You have a 25-year maturity, 10.1% coupon, 10.1% yield bond with
a duration of 10 years and a convexity of 135.6. If the interest
rate were to fall 126 basis points, your predicted new price for
the bond (including convexity) is _________.
a.
$1,114.40
b.
$1,103.64
c.
$1,090.83
d.
$1,125.20

A 25-year semiannual bond has 10% coupon rate and par value
$1,000. The current YTM of the bond is 10%. Its Macaulay duration
is 9.58 years and convexity is 141.03.
(1) What is the bond’s modified duration? (2 points)
(2) What is the percentage price change if interest rate were to
fall 125 basis points considering both duration and convexity? (4
points)
(3) What is the estimated price with 125 basis points decrease
in yield? (4 points)

Coupon
9%
YTM
8%
Maturity
5 Years
Par
1,000
Duration
3.99 years
Convexity
19.76 years
1) Calculate the price of the bond from a 10 basis point
decrease in yield
2) Using duration, estimate the price of the bond for a 10 basis
point decrease in yield

2.8 Calculate the duration of a 6 percent, $1,000 par bond
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2.9 Calculate the convexity of the bond in 2.8.
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before yields changed was $898.49, what is the resulting price
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bond price in the market is $886 per bond, answer the following
questions:
a) What is the yield to maturity? What is the idea of yield to
maturity? Explain the difference between your bond’s yield to
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When the government releases new economic numbers tomorrow, Bill
believes the interest rate on this type of bond will fall 150 basis
points and there will be a parallel shift in the yield curve.
What is the bond’s price to two decimal places?
What is the bond’s value...

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