Question

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 |
3.603.60% |
4.204.20% |
4.404.40% |
4.804.80% |
5.205.20% |

Consider a four-year, default-free security with annual coupon payments and a face value of

$ 1 comma 000$1,000

that is issued at par. What is the coupon rate of this bond?

Answer #1

Given yield on zero coupon default free bond

Maturity yield

1 year 3.60%

2 year 4.20%

3 year 4.40%

4 year 4.80%

So for a coupon bond, that has a face value of $1000 and sells on par, its price = $1000

let coupon payment be C

then, Price = C/(1+r1) + C/(1+r2)^2 + C/(1+r3)^3 + C/(1+r4)^4 + 1000/(1+r4)^4

So, 1000 = C/1.036 + C/1.042^2 + C/1.044^3 + C/1.048^4 + 1000/1.048^4

1000 = 0.9653C + 0.9210C + 0.8788C + 0.8290C + 829.0

So, 171 = 3.5941C or, C = 171/3.5941

C = $47.58

or coupon rate = 47.58/1000 = 4.76%

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%
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1
2
3
Zero-coupon YTM
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A. 4.73%
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Maturity
1 year
2 years
3 years
4 years
5 years
Zero-Coupon Yields
3.003.00%
3.503.50%
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Security
Yield
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AAA Corporate1
2.991%
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3.614%
B Corporate
4.379%
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Maturity (years)
1
2
3
4
5
Price (per $100 face value)
$96.95
$92.52
$88.00
$83.13
$78.10
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c. Is the yield curve upward sloping, downward sloping, or
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Note:
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value) of a one-year, zero-coupon corporate bond with a AAA
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Q19)
The following table summarizes the yields to maturity on
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Security
Yield (%)
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3.13
AAA corporate
3.22
BBB corporate
4.28
B corporate
4.96
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value) of a one-year, zero-coupon corporate bond with a AAA
rating?
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d. How does the credit spread change with the...

The following table summarizes prices of various default-free
zero-coupon bonds (expressed as a percentage of the face
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Maturity (years)
1
2
3
4
5
Price (per $100 face value)
$96.09
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$82.23
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c. Is the yield curve upward sloping, downward sloping, or
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Maturity (years)
1
2
3
4
5
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$95.26
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c. Is the yield curve upward sloping or downward sloping or
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