Question

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 is correct. If market expectations are accurate, what will be the pure yield curve (that is, the yields to maturity on 1- and 2-year zero coupon bonds) next year?

c. If you purchase a 2-year zero-coupon bond now, what is the expected total rate of return over the next year? What if you purchase a 3-year zero-coupon bond?

d. What should be the current price of a 3-year maturity bond with a 12% coupon rate paid annually? If you purchased it at that price, what would your total expected rate of return be over the next year (coupon plus price change)?

Answer #1

1. Present Value of zero coupon bond = PV

Par Value of the bond = FV

Number of Years to maturity = n

Let Yield to Maturity be r

Hence, PV = FV/(1+r)^{n}

=> r = (FV/PV)^{1/n} - 1

For Maturity = 1 year, PV = 953.40, FV = 1000

r = (FV/PV)^{1/n} - 1 = (1000/953.40)^{1/1} - 1
= 0.0489 or 4.89%

For Maturity = 2 year, PV = 898.47, FV = 1000

r = (FV/PV)^{1/n} - 1 = (1000/898.47)^{1/2} - 1
= 0.0550 or 5.50%

For Maturity = 3 year, PV = 847.62, FV = 1000

r = (FV/PV)^{1/n} - 1 = (1000/847.62)^{1/3} - 1
= 0.0567 or 5.67%

For Maturity = 4 year, PV = 792.16, FV = 1000

r = (FV/PV)^{1/n} - 1 = (1000/792.16)^{1/4} - 1
= 0.060 or 6.00%

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. (Do not round
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 maturities and yields of three zero-coupon bonds are as
follows:
Maturity
YTM
1
4%
2
5%
3
6%
Next year, you expect the yields on zero-coupon bonds to be as
follows:
Maturity
YTM
1
5%
2
6%
3
7%
What is the market's expectation of the rate of
return on a 3-year zero-coupon bond over the coming year, assuming
the expectations hypothesis holds? Please express your answer in
percent rounded to the nearest basis point.

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.)...

The yields of four zero-coupon bonds of varying maturities are
as follows:
Maturity YTM
1 6.1%
2 6.2%
3 6.3%
4 6.4%
If you expect the implied term structure to be the same next
year as it is this year, what is the expected return on the 3-year
zero coupon bond over the coming year? Please express your answer
in percent, rounded to the nearest basis point.

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as follows:
Maturity
YTM
1
6.1%
2
6.2%
3
6.3%
4
6.4%
If you expect the implied term structure to be the same next
year as it is this year, what is the expected return on the 1-year
zero-coupon bond over the coming year? Please express your answer
in percent, rounded to the nearest basis point.

The yields of four zero-coupon bonds of varying maturities are
as follows:
Maturity
YTM
1
6.1%
2
6.2%
3
6.3%
4
6.4%
If you expect the implied term structure to be the same next
year as it is this year, what is the expected return on the 1-year
zero-coupon bond over the coming year? Please express your answer
in percent, rounded to the nearest basis point.

The following is a list of prices for zero-coupon bonds with
different maturities and par values of $1,000.
Maturity (Years)
Price maturity 1 year = $ 925.15
Price maturity 2 years = 862.57
Price maturity 3 years = 788.66
Price maturity 4 years = 711.00
According to the expectations theory, what is the expected
forward rate in the third year?

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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Maturity (years)
1
2
3
4
5
YTM
3.25%
3.50%
3.9%
4.25%
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