Question

Suppose that the prices of zero-coupon bonds with various maturities are given in the following table. The face value of each bond is $1,000.

Maturity (Years) | Price | ||

1 | $ | 974.68 | |

2 | 903.39 | ||

3 | 842.92 | ||

4 | 783.00 | ||

5 | 669.92 | ||

**a.** Calculate the forward rate of interest for
each year. **(Round your answers to 2 decimal
places.)**

Maturity (years) | Forward rate |

2 | % |

3 | % |

4 | % |

5 | % |

**b.** How could you construct a 1-year forward
loan beginning in year 3? **(Round your Rate of synthetic
loan answer to 2 decimal places.****)**

Face value | |

Rate if synthetic loan | % |

**c.** How could you construct a 1-year forward
loan beginning in year 4? **(Round your answers to 2 decimal
places.)**

Face value | |

Rate if synthetic loan | % |

Answer #1

**Answer :**

**a)** Forward rate = [ ( current price / future
price ) - 1 ] * 100

Maturity |
Price |
Working |
Forward
rate |

1 | 974.68 | - | - |

2 | 903.39 | ( 974.68 / 903.39 ) - 1 |
7.89% |

3 | 842.92 | ( 903.39 / 842.92 ) - 1 |
7.17% |

4 | 783.00 | ( 842.92 / 783.00 ) - 1 |
7.65% |

5 | 669.92 | ( 783.00 / 669.92 ) - 1 |
16.88% |

**b)** 3 year zero coupon bond issue today, price
at the maturity at year 3 = $ 842.92

Use this to buy bond next year = $ 842.92 / $ 783.00 = 1.07653

Value at the end of year 3 = $ 1000

**Value at the end of year 4 = $ 1000 * 1.0765 = $
1,076.53**

**Rate of synthetic loan = 7.65%**

**c) **4 year zero coupon bond issue
today, price at the maturity at year 4 = $ 783.00

Use this to buy bond next year = $ 783.00 / $ 669.92 = 1.16879

Value at the end of year 4 = $ 1000

**Value at the end of year 5 = $ 1000 * 1.1688 =**
**$ 1,168.80**

**Rate of synthetic loan = 16.88%.**

Suppose that the prices today of zero-coupon bonds with various
maturities are in the following table. The face value of every bond
is $1,000.
Maturity in years
Price
1
925.93
2
853.39
3
782.92
4
715.00
5
650.00
Calculate the one-year forward rate of interest for every
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The following is a list of prices for zero-coupon bonds of
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intermediate calculations. Round your answers to 2 decimal places .
Omit the "%" sign in your response.
Maturity (Years)
Price of Bond
YTM
Forward Rate
1
$980.90
___%
2
$914.97
___%
____%
3
$843.12
___%
____%
4
$771.76
___%
____%

The following is a list of prices for zero-coupon bonds of
various maturities.
a. Calculate the yield to maturity for a bond
with a maturity of (i) one year; (ii) two years; (iii) three years;
(iv) four years. (Do not round intermediate
calculations. Round your answers to two decimal
places.)
Maturity (years)
Price of Bond
1
$
955.90
2
916.47
3
834.12
4
766.39
b. Calculate the forward rate for (i) the
second year; (ii) the third year; (iii) the...

The following is a list of prices for zero-coupon bonds of
various maturities.
a. Calculate the yield to maturity for a bond
with a maturity of (i) one year; (ii) two years; (iii) three years;
(iv) four years. (Do not round intermediate
calculations. Round your answers to two decimal
places.)
b. Calculate the forward rate for (i) the
second year; (ii) the third year; (iii) the fourth year.
(Do not round intermediate calculations.
Round your answers to two decimal places.)...

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...

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...

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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
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c. Is the yield curve upward sloping, downward sloping, or
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The yield on the 1-year...

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Maturity (Years)
Price maturity 1 year = $ 925.15
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Price maturity 4 years = 711.00
According to the expectations theory, what is the expected
forward rate in the third year?

The following table summarizes prices of various default-free
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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
a. Compute the yield to maturity for each bond.
b. Plot the zero-coupon yield curve (for the first five
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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...

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)
$95.2795.27
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$81.6481.64
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c. Is the yield curve upward sloping,
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