Question

The following data shows the current prices of four default free zero coupon bonds. The redemption price in each case is 100Euro.

Maturity from now (in years) 1 2 3 4

Price now 98.12 95.46 92.39 88.72

Calculate the yield to maturity and explain the zero coupon yield curve using your answer from yield calculation

Answer #1

YTM is the rate of return from a bond till its maturity period.

YTM of 1 year Zero coupon bond = [ Maturity after a year / Current price ] - 1

= [100 / 98.12 ] - 1

= 1.0192 - 1

= 0.0192 i.e 1.92%

YTM of 2 year Zero coupon bond = [ Maturity after a year /
Current price ]^{1/2} - 1

= [100 / 95.46 ]^{1/2} - 1

= [1.0476]^{1/2} - 1

= 1.0235 - 1

= 0.0235 i.e 2.35%

YTM of 3 year Zero coupon bond = [ Maturity after a year /
Current price ]^{1/3} - 1

=[100 / 92.39 ]^{1/3} - 1

= [1.0824]^{1/3} - 1

= 1.0267 - 1

= 0.0267 i.e 2.67%

YTM of 4 year Zero coupon bond = [ Maturity after a year /
Current price ]^{1/4} - 1

=[100 / 88.72 ]^{1/4} - 1

= [1.1271]^{1/4} - 1

= 1.0304 - 1

= 0.0304 i.e 3.04%

Yield curve is graph on which Yield is plotted on one axis and time is plotted on another axis.

Year1 - 1.92%

Year2 - 2.35%

Year3 - 2.67%

Year4 - 3.04%

The following table summarizes the prices the default-free zero
coupon bonds (expressed as a percentage of the face value)
Maturity (years) 1 2 3 4 5
Price (Per face value) $ 96.47 $ 92.08 $ 87..41 $ 82.55 $
77.48
a. compute the yield to maturity of each bond
b.Plot the zero-coupon yield curve (for the first five
years)
c. Is the yield curve upward sloping or downward sloping or
flat?
a. Compute the yield to maturity of each bond

The following table summarizes prices of various default-free
zero-coupon bonds (expressed as a percentage of the face
value):
Maturity (years)
1
2
3
4
5
Price (per $100 face value)
$95.2795.27
$90.8890.88
$86.3686.36
$81.6481.64
$76.4576.45
a. Compute the yield to maturity for each
bond.
b. Plot the zero-coupon yield curve (for the
first five years).
c. Is the yield curve upward sloping,
downward sloping, or flat?

The following table summarizes prices of various default-free
zero-coupon bonds (expressed as a percentage of the face
value):
Maturity (years)
1
2
3
4
5
Price (per $100 face value)
$96.09
$91.72
$87.08
$82.23
$77.19
a. Compute the yield to maturity for each bond.
b. Plot the zero-coupon yield curve (for the first five
years).
c. Is the yield curve upward sloping, downward sloping, or
flat?
a. Compute the yield to maturity for each bond.
The yield on the 1-year...

The following table summarizes prices of various default-free
zero-coupon bonds (expressed as a percentage of the face
value):
Maturity (years)
1
2
3
4
5
Price (per $100 face value)
$95.26
$90.77
$86.18
$81.34
$76.09
a. Compute the yield to maturity for each bond.
b. Plot the zero-coupon yield curve (for the first five
years).
c. Is the yield curve upward sloping, downward sloping, or
flat?
a. Compute the yield to maturity for each bond.
The yield on the 1-year...

The following table summarizes prices of various default-free,
zero-coupon bonds (expressed as a percentage of face value):
Maturity (years) 1 2 3 4 5
Price (per $100 face value) $95.51 $91.05 $86.38 $81.65
$76.51
a. Compute the yield to maturity for each bond.
b. Plot the zero-coupon yield curve for the first five
years.
c. Is the yield curve upward sloping, downward sloping, or
flat.

The table below shows market prices for four zero coupon bonds
with four different terms: one, two, three and four years. The
bonds all have a face value of $1,000.
Calculate the yields on the zero coupon bonds and graph the
yield curve. What is the shape of the yield curve?
Zero Coupon Bond Prices
Term (years)
Price ($)
1
952.38
2
924.56
3
915.14
4
923.85
What is the yield on the zero coupon bond with a 1-year term?...

The following table summarizes prices of various default-free
zero-coupon bonds ($100 face value):
Maturity (years)
1
2
3
4
5
Price (per $100 face value)
$96.95
$92.52
$88.00
$83.13
$78.10
a. Compute the yield to maturity for each bond.
b. Plot the zero-coupon yield curve (for the first five
years).
c. Is the yield curve upward sloping, downward sloping, or
flat?
Note:
Assume annual compounding.
a. Compute the yield to maturity for each bond.
The yield on the 1-year bond...

1. The following is a list of
prices for zero-coupon bonds of various maturities. Calculate the
yields to maturity of each bond and the implied sequence of forward
rates.
maturity years: Price of bond
1 943.40
2 898.47
3 847.62
4 792.16
2. [Chapter 15] The current yield curve
for default-free zero-coupon bonds is as follows:
Maturity (Years): YTM%
1 10%
2 11%
3 12%
a. What are the implied
1-year forward rates?
b. Assume that the pure
expectations hypothesis of the term structure...

Assume the zero-coupon yields on default-free securities are
as summarized in the following table:
Maturity
1 year
2 years
3 years
4 years
5 years
Zero-Coupon Yields
6.20%
6.60%
6.80%
7.10%
7.40%
What is the price of a three-year, default-free security with a
face value of $1,000 and an annual coupon rate of 4%? What is the
yield to maturity for this bond?
What is the price of a three-year, default-free security with a
face value of $1,000 and an...

Assume the zero-coupon yields on default-free securities are
as summarized in the following table:
Maturity
1 year
2 years
3 years
4 years
5 years
Zero-Coupon Yields
3.003.00%
3.503.50%
3.803.80%
4.204.20%
4.304.30%
What is the price of a five-year, zero-coupon default-free
security with a face value of $1,000. Round to the nearest
cent.

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