Chapter 15
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180.367
Subject
Finance
Date
Jan 9, 2024
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58
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1.
Award: 10.00
points
Problems? Adjust credit for all students.
Under the expectations hypothesis, if the yield curve is upward-sloping, the market must expect an increase in short-term interest rates.
True
Explanation:
True. Under the expectations hypothesis alone, there are no risk premia built into bond prices. The only reason for long-term yields to exceed short-term yields is an expectation of higher short-term rates in the future.
Worksheet
Difficulty: 1 Basic
Source: Investments (Bodie, 13e, ISBN 1266836322) > Chapter 15: The Term Structure of Interest Rates > Chapter 15 Problems - Algorithmic & Static
References
2.
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points
Problems? Adjust credit for all students.
Under the liquidity preference theory, if inflation is expected to be falling over the next few years, long-term interest rates will be higher than short-term rates.
Uncertain
Explanation:
Uncertain. Expectations of lower inflation will usually lead to lower nominal interest rates. Nevertheless, if the liquidity premium is sufficiently great, long-term yields may exceed short-term yields despite
expectations of falling
short rates.
Worksheet
Difficulty: 1 Basic
Source: Investments (Bodie, 13e, ISBN 1266836322) > Chapter 15: The Term Structure of Interest Rates > Chapter 15 Problems - Algorithmic & Static
References
3.
Award: 10.00
points
Problems? Adjust credit for all students.
If the liquidity preference hypothesis is true, what shape should the term structure curve have in a period where interest rates are expected to be constant?
Upward sloping
Explanation:
The liquidity theory holds that investors demand a premium to compensate them for interest rate exposure and the premium increases with maturity. Add this premium to a flat curve and the result is an upward sloping yield
curve.
Worksheet
Difficulty: 1 Basic
Source: Investments (Bodie, 13e, ISBN 1266836322) > Chapter 15: The Term Structure of Interest Rates > Chapter 15 Problems - Algorithmic & Static
References
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4.
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Problems? Adjust credit for all students.
Which of the following is true
according to the pure expectations theory? Forward rates
exclusively represent expected future short rates.
Explanation:
The pure expectations theory, also referred to as the unbiased expectations theory, purports that forward rates are solely a function of expected future spot rates. Under the pure expectations theory, a yield curve that is upward
(downward) sloping, means that short-term rates are expected to rise (fall). A flat yield curve implies that the market expects short-term rates to remain constant.
Worksheet
Difficulty: 1 Basic
Source: Investments (Bodie, 13e, ISBN 1266836322) > Chapter 15: The Term Structure of Interest Rates > Chapter 15 Problems - Algorithmic & Static
References
5.
Award: 10.00
points
Problems? Adjust credit for all students.
Assuming the pure expectations theory is correct, an upward-sloping yield curve implies
interest rates are expected to increase in the future.
Explanation:
The yield curve slopes upward because short-term rates are lower than long-term rates. Since market rates are determined by supply and demand, it follows that investors (demand side) expect rates to be higher in the future
than in the near-term.
Worksheet
Difficulty: 2 Intermediate
Source: Investments (Bodie, 13e, ISBN 1266836322) > Chapter 15: The Term Structure of Interest Rates > Chapter 15 Problems - Algorithmic & Static
References
6.
Award: 10.00
points
Problems? Adjust credit for all students.
The following is a list of prices for zero-coupon bonds of various maturities.
Maturity (years)
Price of Bond
1
$ 943.40
2
898.47
3
847.62
4
792.16
Required:
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. Assume annual coupon payments.
b. Calculate the forward rate for (i) the second year; (ii) the third year; (iii) the fourth year. Assume annual coupon payments.
Required A
Required B
Complete this question by entering your answers in the tabs below.
Calculate the yield to maturity for a bond with a maturity of (i) one year; (ii) two years; (iii) three years; (iv) four
years. Assume annual coupon payments.
Note: Do not round intermediate calculations. Round your answers to 2 decimal places.
Required A
Required B
$
$
$
$
Maturity (Years)
Price of Bond
YTM
1
943.40
6.00
%
2
898.47
5.50
%
3
847.62
5.67
%
4
792.16
6.00
%
Explanation:
a. Zero-coupon bond YTM
b. Forward rate
(
1.0550
2
÷ 1.0600) − 1 = 5%
(
1.0567
3
÷ 1.0550
2
) − 1 = 6%
(
1.0600
4
÷ 1.0567
3
) − 1 = 7%
Worksheet
Difficulty: 2 Intermediate
Source: Investments (Bodie, 13e, ISBN 1266836322) > Chapter 15: The Term Structure of Interest Rates > Chapter 15 Problems - Algorithmic & Static
References
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6.
Award: 10.00
points
Problems? Adjust credit for all students.
The following is a list of prices for zero-coupon bonds of various maturities.
Maturity (years)
Price of Bond
1
$ 943.40
2
898.47
3
847.62
4
792.16
Required:
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. Assume annual coupon payments.
b. Calculate the forward rate for (i) the second year; (ii) the third year; (iii) the fourth year. Assume annual coupon payments.
Required A
Required B
Complete this question by entering your answers in the tabs below.
Calculate the forward rate for (i) the second year; (ii) the third year; (iii) the fourth year. Assume annual coupon payments.
Note: Do not round intermediate calculations. Round your answers to the nearest whole percent.
Required A
Required B
$
$
$
Maturity (Years)
Price of Bond
Forward Rate
2
898.47
5
%
3
847.62
6
%
4
792.16
7
%
Explanation:
a. Zero-coupon bond YTM
b. Forward rate
(
1.0550
2
÷ 1.0600) − 1 = 5%
(
1.0567
3
÷ 1.0550
2
) − 1 = 6%
(
1.0600
4
÷ 1.0567
3
) − 1 = 7%
Worksheet
Difficulty: 2 Intermediate
Source: Investments (Bodie, 13e, ISBN 1266836322) > Chapter 15: The Term Structure of Interest Rates > Chapter 15 Problems - Algorithmic & Static
References
7.
Award: 10.00
points
Problems? Adjust credit for all students.
Required:
a. Assuming that the expectations hypothesis is valid, compute the expected price of the four-year zero coupon bond shown below at the end of (i) the first year; (ii) the second year; (iii) the third year; (iv) the fourth year.
b. What is the rate of return of the bond in years 1, 2, 3, and 4? Conclude that the expected return equals the forward rate for each year.
Required A
Required B
Complete this question by entering your answers in the tabs below.
Assuming that the expectations hypothesis is valid, compute the expected price of the four-year zero coupon bond shown
below at the end of (i) the first year; (ii) the second year; (iii) the third year; (iv) the fourth year.
Note: Do not round intermediate calculations. Round your answers to 2 decimal places.
Required A
Required B
$
$
$
$
$
$
$
$
Beginning
of Year
Price of Bond
Expected Price
1
943.40
792.16
2
898.47
839.69
3
847.62
881.68
4
792.16
934.58
Explanation:
a & b.
The expected price path of the 4-year zero coupon bond is shown below. (Note that we discount the face value by the appropriate sequence of forward rates implied by this year’s yield curve.)
Zero-coupon bond YTM
Forward rate
(
1.055
2
÷ 1.06) − 1 = 5%
(
1.0567
3
÷ 1.055
2
) − 1 = 6%
(
1.06
4
÷ 1.0567
3
) − 1 = 7%
Beginning of
Year
a. Expected Price
b. Expected Rate of Return
1
$792.16
($839.69 ÷ $792.16) − 1 = 6.00%
2
($1,000 ÷ 1.05 × 1.06 × 1.07) = $839.69
($881.68 ÷ $839.69) − 1 = 5.00%
3
($1,000 ÷ 1.06 × 1.07) = $881.68
($934.58 ÷ $881.68) − 1 = 6.00%
4
($1,000 ÷ 1.07) = $934.58
($1,000.00 ÷ $934.58) − 1 = 7.00%
Worksheet
Difficulty: 2 Intermediate
Source: Investments (Bodie, 13e, ISBN 1266836322) > Chapter 15: The Term Structure of Interest Rates > Chapter 15 Problems - Algorithmic & Static
References
7.
Award: 10.00
points
Problems? Adjust credit for all students.
Required:
a. Assuming that the expectations hypothesis is valid, compute the expected price of the four-year zero coupon bond shown below at the end of (i) the first year; (ii) the second year; (iii) the third year; (iv) the fourth year.
b. What is the rate of return of the bond in years 1, 2, 3, and 4? Conclude that the expected return equals the forward rate for each year.
Required A
Required B
Complete this question by entering your answers in the tabs below.
What is the rate of return of the bond in years 1, 2, 3, and 4? Conclude that the expected return equals the forward rate for
each year.
Note: Do not round intermediate calculations. Round your answers to 2 decimal places.
Required A
Required B
Beginning
of Year
Expected Rate of Return
1
6.00
%
2
5.00
%
3
6.00
%
4
7.00
%
Explanation:
a & b.
The expected price path of the 4-year zero coupon bond is shown below. (Note that we discount the face value by the appropriate sequence of forward rates implied by this year’s yield curve.)
Zero-coupon bond YTM
Forward rate
(
1.055
2
÷ 1.06) − 1 = 5%
(
1.0567
3
÷ 1.055
2
) − 1 = 6%
(
1.06
4
÷ 1.0567
3
) − 1 = 7%
Beginning of
Year
a. Expected Price
b. Expected Rate of Return
1
$792.16
($839.69 ÷ $792.16) − 1 = 6.00%
2
($1,000 ÷ 1.05 × 1.06 × 1.07) = $839.69
($881.68 ÷ $839.69) − 1 = 5.00%
3
($1,000 ÷ 1.06 × 1.07) = $881.68
($934.58 ÷ $881.68) − 1 = 6.00%
4
($1,000 ÷ 1.07) = $934.58
($1,000.00 ÷ $934.58) − 1 = 7.00%
Worksheet
Difficulty: 2 Intermediate
Source: Investments (Bodie, 13e, ISBN 1266836322) > Chapter 15: The Term Structure of Interest Rates > Chapter 15 Problems - Algorithmic & Static
References
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8.
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points
Problems? Adjust credit for all students.
Consider the following $1,000 par value zero-coupon bonds:
Bond
Years to Maturity
YTM(%)
A
1
5%
B
2
6
C
3
6.5
D
4
7
Required:
According to the expectations hypothesis, what is the market’s expectation of the yield curve one year from now? Specifically, what are the expected values of next year’s yields on bonds with maturities of (a) one year? (b) two
years? (c) three years?
Note: Do not round intermediate calculations. Round your answers to 2 decimal places.
Bond
Years to Maturity
YTM (%)
B
1
7.01
%
C
2
7.26
%
D
3
7.67
%
Explanation:
Bond B YTM = [1 + E
(
r
2
)]
1/1
− 1 = 7.01%
Bond C YTM = [(1 + E
(
r
2
)) × (1 + E
(
r
3
))]
1/2
− 1 = (1.0701 ×
1.0751)
1/2
= 7.26%
Bond D YTM = [(1 + E
(
r
2
)) × (1 + E
(
r
3
)) × (1 + E
(
r
4
))]
1/3
− 1 = (1.0701 × 1.0751 × 1.0851)
1/3
= 7.67%
In one year, the market’s expectation of the yield curve is:
Bond
Years to Maturity
YTM(%)
B
1
7.01%
C
2
7.26%
D
3
7.67%
Worksheet
Difficulty: 2 Intermediate
Source: Investments (Bodie, 13e, ISBN 1266836322) > Chapter 15: The Term Structure of Interest Rates > Chapter 15 Problems - Algorithmic & Static
References
9.
Award: 10.00
points
Problems? Adjust credit for all students.
The term structure for zero-coupon bonds is currently:
Maturity (Years)
YTM (%)
1
4%
2
5
3
6
Next year at this time, you
expect it to be:
Maturity (Years)
YTM (%)
1
5%
2
6
3
7
Required:
a. What do you
expect the rate of return to be over the coming year on a 3-year zero-coupon bond?
b. Under the expectations theory, what yields to maturity does the market expect to observe on 1- and 2-year zeros at the end of the year?
c. Is the market's expectation of the return on the 3-year bond greater or less than yours?
Required A
Required B
Complete this question by entering your answers in the tabs below.
What do you
expect the rate of return to be over the coming year on a 3-year zero-coupon bond?
Required A
Required B
Required C
Rate of return
6
%
Explanation:
a. A 3-year zero coupon bond with face value $100 will sell today at a yield of 6% and a price of:
$100 ÷ 1.06
3
= $83.96
Next year, the bond will have a two-year maturity, and therefore a yield of 6% (from next year's forecasted yield curve). The price will be $89.00, resulting in a holding period return of 6%.
b. The forward rates based on today’s yield curve are as follows:
Year
Forward Rate
2
(1.05
2
÷ 1.04) − 1 = 6.01%
3
(1.06
3
÷ 1.05
2
) − 1 = 8.03%
Using the forward rates, the forecast for the yield curve next
year is:
Maturity
YTM
1
6.01%
2
(1.0601 × 1.0803)
1/2
− 1 = 7.02%
The market forecast is for a higher YTM on 2-year bonds than your forecast. Thus, the market predicts a lower price and higher rate of return.
Worksheet
Difficulty: 2 Intermediate
Source: Investments (Bodie, 13e, ISBN 1266836322) > Chapter 15: The Term Structure of Interest Rates > Chapter 15 Problems - Algorithmic & Static
References
9.
Award: 10.00
points
Problems? Adjust credit for all students.
The term structure for zero-coupon bonds is currently:
Maturity (Years)
YTM (%)
1
4%
2
5
3
6
Next year at this time, you
expect it to be:
Maturity (Years)
YTM (%)
1
5%
2
6
3
7
Required:
a. What do you
expect the rate of return to be over the coming year on a 3-year zero-coupon bond?
b. Under the expectations theory, what yields to maturity does the market expect to observe on 1- and 2-year zeros at the end of the year?
c. Is the market's expectation of the return on the 3-year bond greater or less than yours?
Required A
Required C
Complete this question by entering your answers in the tabs below.
Under the expectations theory, what yields to maturity does the market
expect to observe on 1- and 2-year zeros at the end
of the year?
Note: Round your answers to 2 decimal places.
Required A
Required B
Required C
Maturity
YTM
1
6.01
%
2
7.02
%
Explanation:
a. A 3-year zero coupon bond with face value $100 will sell today at a yield of 6% and a price of:
$100 ÷ 1.06
3
= $83.96
Next year, the bond will have a two-year maturity, and therefore a yield of 6% (from next year's forecasted yield curve). The price will be $89.00, resulting in a holding period return of 6%.
b. The forward rates based on today’s yield curve are as follows:
Year
Forward Rate
2
(1.05
2
÷ 1.04) − 1 = 6.01%
3
(1.06
3
÷ 1.05
2
) − 1 = 8.03%
Using the forward rates, the forecast for the yield curve next
year is:
Maturity
YTM
1
6.01%
2
(1.0601 × 1.0803)
1/2
− 1 = 7.02%
The market forecast is for a higher YTM on 2-year bonds than your forecast. Thus, the market predicts a lower price and higher rate of return.
Worksheet
Difficulty: 2 Intermediate
Source: Investments (Bodie, 13e, ISBN 1266836322) > Chapter 15: The Term Structure of Interest Rates > Chapter 15 Problems - Algorithmic & Static
References
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9.
Award: 10.00
points
Problems? Adjust credit for all students.
The term structure for zero-coupon bonds is currently:
Maturity (Years)
YTM (%)
1
4%
2
5
3
6
Next year at this time, you
expect it to be:
Maturity (Years)
YTM (%)
1
5%
2
6
3
7
Required:
a. What do you
expect the rate of return to be over the coming year on a 3-year zero-coupon bond?
b. Under the expectations theory, what yields to maturity does the market expect to observe on 1- and 2-year zeros at the end of the year?
c. Is the market's expectation of the return on the 3-year bond greater or less than yours?
Required B
Required C
Complete this question by entering your answers in the tabs below.
Is the market's expectation of the return on the 3-year bond greater or less than yours?
Required A
Required B
Required C
Is the market's expectation of the return on the 3-year bond greater or less than yours?
Greater
Explanation:
a. A 3-year zero coupon bond with face value $100 will sell today at a yield of 6% and a price of:
$100 ÷ 1.06
3
= $83.96
Next year, the bond will have a two-year maturity, and therefore a yield of 6% (from next year's forecasted yield curve). The price will be $89.00, resulting in a holding period return of 6%.
b. The forward rates based on today’s yield curve are as follows:
Year
Forward Rate
2
(1.05
2
÷ 1.04) − 1 = 6.01%
3
(1.06
3
÷ 1.05
2
) − 1 = 8.03%
Using the forward rates, the forecast for the yield curve next
year is:
Maturity
YTM
1
6.01%
2
(1.0601 × 1.0803)
1/2
− 1 = 7.02%
The market forecast is for a higher YTM on 2-year bonds than your forecast. Thus, the market predicts a lower price and higher rate of return.
Worksheet
Difficulty: 2 Intermediate
Source: Investments (Bodie, 13e, ISBN 1266836322) > Chapter 15: The Term Structure of Interest Rates > Chapter 15 Problems - Algorithmic & Static
References
10.
Award: 10.00
points
Problems? Adjust credit for all students.
The yield to maturity on 1-year zero-coupon bonds is currently 7%; the YTM on 2-year zeros is 8%. The Treasury plans to issue a 2-year maturity coupon
bond, paying coupons once per year with a coupon rate of 9%. The face
value of the bond is $100.
Required:
a. At what price will the bond sell?
Note: Do not round intermediate calculations. Round your answer to 2 decimal places.
b. What will the yield to maturity on the bond be?
Note: Do not round intermediate calculations. Round your answer to 3 decimal places.
c. If the expectations theory of the yield curve is correct, what is the market expectation of the price for which the bond will sell next year?
Note: Do not round intermediate calculations. Round your answer to 2 decimal places.
d. Recalculate your answer to part (c) if you believe in the liquidity preference theory and you believe that the liquidity premium is 1%.
Note: Do not round intermediate calculations. Round your answer to 2 decimal places.
$
$
$
a. Price
101.86
b. Yield to maturity
7.958
%
c. Price
99.99
d. Price
100.92
Explanation:
a. P
= ($9 ÷ 1.07) + ($109 ÷ 1.08
2
) = $101.86
b. The yield to maturity is the solution for y
in the following equation:
($9 ÷ (1 + y
)) + $109 ÷ (1 + y
)
2
= $101.86
[Using a financial calculator, enter n
= 2; FV = 100; PMT = 9; PV = −101.86; Compute I/Y
] → YTM = 7.958%
c. The forward rate for next year, derived from the zero-coupon yield curve, is the solution for f
2
in the following equation:
1 + f
2
=
(1.08)
2
÷
1.07
= 1.0901
f
2
= 0.0901 = 9.01%.
Therefore, using an expected rate for next year of r
2
= 9.01%
, we find that the forecast bond price is $99.99:
P = $109 ÷ 1.0901 = $99.99
d. If the liquidity premium is 1% then the forecast interest rate is:
E
(
r
2
) = f
2
− liquidity premium = 9.01% − 1.00% = 8.01%
The forecast of the bond price is:
$109 ÷ 1.0801 = $100.92
Worksheet
Difficulty: 2 Intermediate
Source: Investments (Bodie, 13e, ISBN 1266836322) > Chapter 15: The Term Structure of Interest Rates > Chapter 15 Problems - Algorithmic & Static
References
11.
Award: 10.00
points
Problems? Adjust credit for all students.
Below is a list of prices for zero-coupon bonds of various maturities.
Maturity (Years)
Price of $1,000 Par Bond
(Zero-Coupon)
1
$ 943.40
2
873.52
3
816.37
Required:
a. An 8.5% coupon $1,000 par bond pays an annual coupon and will mature in three years. What should the yield to maturity on the bond be?
b. If at the end of the first year the yield curve flattens out at 8%, what will be the 1-year holding-period return on the coupon bond?
Required A
Required B
Complete this question by entering your answers in the tabs below.
An 8.5% coupon $1,000 par bond pays an annual coupon and will mature in three years. What should the yield to maturity on
the bond be?
Note: Round your answer to 2 decimal places.
Required A
Required B
Yield to maturity
6.97
%
Explanation:
a. The current bond price is:
($85 × 0.94340) + ($85 × 0.87352) + ($1,085 × 0.81637) = $1,040.20
This price implies a yield to maturity of 6.97%, as shown by the following:
[$85 × Annuity factor (6.97%, 3)] + [$1,000 × PV factor (6.97%, 3)] = $1,040.17
b. If one year from now y = 8%, then the bond price will be:
[$85 × Annuity factor (8%, 2)] + [$1,000 × PV factor (8%, 2)] = $1,008.92
The holding period rate of return is:
[$85 + ($1,008.92 − $1,040.20)] ÷ $1,040.20 = 0.0516 = 5.16%
Worksheet
Difficulty: 2 Intermediate
Source: Investments (Bodie, 13e, ISBN 1266836322) > Chapter 15: The Term Structure of Interest Rates > Chapter 15 Problems - Algorithmic & Static
References
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11.
Award: 10.00
points
Problems? Adjust credit for all students.
Below is a list of prices for zero-coupon bonds of various maturities.
Maturity (Years)
Price of $1,000 Par Bond
(Zero-Coupon)
1
$ 943.40
2
873.52
3
816.37
Required:
a. An 8.5% coupon $1,000 par bond pays an annual coupon and will mature in three years. What should the yield to maturity on the bond be?
b. If at the end of the first year the yield curve flattens out at 8%, what will be the 1-year holding-period return on the coupon bond?
Required A
Required B
Complete this question by entering your answers in the tabs below.
If at the end of the first year the yield curve flattens out at 8%, what will be the 1-year holding-period return on the coupon
bond?
Note: Round your answer to 2 decimal places.
Required A
Required B
Holding-period return
5.16
%
Explanation:
a. The current bond price is:
($85 × 0.94340) + ($85 × 0.87352) + ($1,085 × 0.81637) = $1,040.20
This price implies a yield to maturity of 6.97%, as shown by the following:
[$85 × Annuity factor (6.97%, 3)] + [$1,000 × PV factor (6.97%, 3)] = $1,040.17
b. If one year from now y = 8%, then the bond price will be:
[$85 × Annuity factor (8%, 2)] + [$1,000 × PV factor (8%, 2)] = $1,008.92
The holding period rate of return is:
[$85 + ($1,008.92 − $1,040.20)] ÷ $1,040.20 = 0.0516 = 5.16%
Worksheet
Difficulty: 2 Intermediate
Source: Investments (Bodie, 13e, ISBN 1266836322) > Chapter 15: The Term Structure of Interest Rates > Chapter 15 Problems - Algorithmic & Static
References
12.
Award: 10.00
points
Problems? Adjust credit for all students.
Prices of zero-coupon bonds reveal the following pattern of forward rates:
Year
Forward Rate
1
5%
2
7
3
8
In addition to the zero-coupon bond, investors also may purchase a 3-year bond making annual payments of $60 with par value $1,000.
Required:
a. What is the price of the coupon bond?
Note: Do not round intermediate calculations. Round your answer to 2 decimal places.
b. What is the yield to maturity of the coupon bond?
Note: Do not round intermediate calculations. Round your answer to 2 decimal places.
c. Under the expectations hypothesis, what is the expected realized compound yield of the coupon bond?
Note: Do not round intermediate calculations. Round your answer to 2 decimal places.
d. If you forecast that the yield curve in 1 year will be flat at 7%, what is your forecast for the expected rate of return on the coupon bond for the 1-year holding period?
Note: Do not round intermediate calculations. Round your answer to 2 decimal places.
$
a. Price
984.14
b. Yield to maturity
6.60
%
c. Realized compound yield
6.66
%
d. Holding period return
5.88
%
Explanation:
Year
Forward Rate
PV of $1 received at period end
1
5%
$1 ÷ 1.05 = $0.9524
2
7%
$1 ÷ (1.05 × 1.07) = $0.8901
3
8%
$1 ÷ (1.05 × 1.07 × 1.08) = $0.8241
a. Price = ($60 × 0.9524) + ($60 × 0.8901) + ($1,060 × 0.8241) = $984.14
b. To find the yield to maturity, solve for y
in the following equation:
$984.14 = [$60 × Annuity factor (
y
, 3)] + [$1,000 × PV factor (
y
, 3)]
This can be solved using a financial calculator to show that y
= 6.60%
PV = −$984.14; N = 3; FV = $1,000; PMT = $60. Solve for I = 6.60%.
c. Period
Payment Received at End of
Period:
Will Grow by a Factor
of:
To a Future Value of:
1
$ 60.00
1.07 × 1.08
$ 69.34
2
60.00
1.08
64.80
3
1,060.00
1,060.00
$ 1,194.14
$984.14 × (1 + y
realized
)
3
= $1,194.14
Alternatively, PV = −$984.14; N = 3; FV = $1,194.14; PMT = $0. Solve for I = 6.66%.
d. Next year, the price of the bond will be:
[$60 × Annuity factor (7%, 2)] + [$1,000 × PV factor (7%, 2)] = $981.92
Therefore, there will be a capital loss equal to: $981.92 − $984.14 = − $2.18
The holding period return is: $60 + (−$2.18) ÷ $984.14 = 0.05875 = 5.88%
Worksheet
Difficulty: 2 Intermediate
Source: Investments (Bodie, 13e, ISBN 1266836322) > Chapter 15: The Term Structure of Interest Rates > Chapter 15 Problems - Algorithmic & Static
References
13.
Award: 10.00
points
Problems? Adjust credit for all students.
You observe the following term structure:
Effective Annual YTM
1-year zero-coupon bond
6.1%
2-year zero-coupon bond
6.2
3-year zero-coupon bond
6.3
4-year zero-coupon bond
6.4
Required:
a. If you believe that the term structure next year will be the same as today’s, calculate the return on (i) the 1-year zero and (ii) the 4-year zero.
b. Which bond provides a greater expected 1-year return?
Required A
Required B
Complete this question by entering your answers in the tabs below.
If you believe that the term structure next year will be the same as today’s, calculate the return on (i) the 1-year zero and (ii)
the 4-year zero.
Note: Do not round intermediate calculations. Round your answers to 1 decimal place.
Required A
Required B
One year return on 1-year bond
6.1
%
One year return on 4-year bond
6.7
%
Explanation:
a. The return on the one-year zero-coupon bond will be 6.10%. The price of the 4-year zero today is:
$1,000 ÷ 1.064
4
= $780.25
Next year, if the yield curve is unchanged, today’s 4-year zero coupon bond will have a 3-year maturity, a YTM of 6.3%, and therefore the price will be:
$1,000 ÷ 1.063
3
= $832.53
The resulting one-year rate of return will be: 6.70%
b. In this case, the longer-term bond is expected to provide the higher return because its YTM is expected to decline during the holding period.
Worksheet
Difficulty: 2 Intermediate
Source: Investments (Bodie, 13e, ISBN 1266836322) > Chapter 15: The Term Structure of Interest Rates > Chapter 15 Problems - Algorithmic & Static
References
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13.
Award: 10.00
points
Problems? Adjust credit for all students.
You observe the following term structure:
Effective Annual YTM
1-year zero-coupon bond
6.1%
2-year zero-coupon bond
6.2
3-year zero-coupon bond
6.3
4-year zero-coupon bond
6.4
Required:
a. If you believe that the term structure next year will be the same as today’s, calculate the return on (i) the 1-year zero and (ii) the 4-year zero.
b. Which bond provides a greater expected 1-year return?
Required A
Required B
Complete this question by entering your answers in the tabs below.
Which bond provides a greater expected 1-year return?
Required A
Required B
Which bond provides a greater expected 1-year return?
4-year zero-coupon bond
Explanation:
a. The return on the one-year zero-coupon bond will be 6.10%. The price of the 4-year zero today is:
$1,000 ÷ 1.064
4
= $780.25
Next year, if the yield curve is unchanged, today’s 4-year zero coupon bond will have a 3-year maturity, a YTM of 6.3%, and therefore the price will be:
$1,000 ÷ 1.063
3
= $832.53
The resulting one-year rate of return will be: 6.70%
b. In this case, the longer-term bond is expected to provide the higher return because its YTM is expected to decline during the holding period.
Worksheet
Difficulty: 2 Intermediate
Source: Investments (Bodie, 13e, ISBN 1266836322) > Chapter 15: The Term Structure of Interest Rates > Chapter 15 Problems - Algorithmic & Static
References
14.
Award: 10.00
points
Problems? Adjust credit for all students.
The yield to maturity (YTM) on 1-year zero-coupon bonds is 5%, and the YTM on 2-year zeros is 6%. The yield to maturity on 2-year-maturity coupon bonds with coupon rates of 12% (paid annually) is 5.8%.
Required:
a. What arbitrage opportunity is available for an investment banking firm?
b. What is the profit on the activity?
Required A
Required B
Complete this question by entering your answers in the tabs below.
What arbitrage opportunity is available for an investment banking firm?
Required A
Required B
$
$
The arbitrage strategy is to buy zeros with face values of
120
and
1,120
, and respective maturities of one year and two years.
Explanation:
a. The price of the coupon bond, based on its yield to maturity, is:
[$120 × Annuity factor (5.8%, 2)] + [$1,000 × PV factor (5.8%, 2)] = $1,113.99
If the coupons were stripped and sold separately as zeros, then, based on the yield to maturity of zeros with maturities of one and two years, respectively, the coupon payments could be sold separately for:
($120 ÷ 1.05) + ($1,120 ÷ 1.06
2
) = $1,111.08
The arbitrage strategy is to buy zeros with face values of $120 and $1,120, and respective maturities of one year and two years, and simultaneously sell the coupon bond. b. The profit equals $1,113.99 – $1,111.08 = $2.91 on each bond.
Worksheet
Difficulty: 2 Intermediate
Source: Investments (Bodie, 13e, ISBN 1266836322) > Chapter 15: The Term Structure of Interest Rates > Chapter 15 Problems - Algorithmic & Static
References
14.
Award: 10.00
points
Problems? Adjust credit for all students.
The yield to maturity (YTM) on 1-year zero-coupon bonds is 5%, and the YTM on 2-year zeros is 6%. The yield to maturity on 2-year-maturity coupon bonds with coupon rates of 12% (paid annually) is 5.8%.
Required:
a. What arbitrage opportunity is available for an investment banking firm?
b. What is the profit on the activity?
Required A
Required B
Complete this question by entering your answers in the tabs below.
What is the profit on the activity?
Note: Do not round intermediate calculations. Round your answer to 2 decimal places.
Required A
Required B
$
Profit
2.91
each bond
Explanation:
a. The price of the coupon bond, based on its yield to maturity, is:
[$120 × Annuity factor (5.8%, 2)] + [$1,000 × PV factor (5.8%, 2)] = $1,113.99
If the coupons were stripped and sold separately as zeros, then, based on the yield to maturity of zeros with maturities of one and two years, respectively, the coupon payments could be sold separately for:
($120 ÷ 1.05) + ($1,120 ÷ 1.06
2
) = $1,111.08
The arbitrage strategy is to buy zeros with face values of $120 and $1,120, and respective maturities of one year and two years, and simultaneously sell the coupon bond. b. The profit equals $1,113.99 – $1,111.08 = $2.91 on each bond.
Worksheet
Difficulty: 2 Intermediate
Source: Investments (Bodie, 13e, ISBN 1266836322) > Chapter 15: The Term Structure of Interest Rates > Chapter 15 Problems - Algorithmic & Static
References
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15.
Award: 10.00
points
Problems? Adjust credit for all students.
Suppose that a 1-year zero-coupon bond with face value $100 currently sells at $94.34, while a 2-year zero sells at $84.99. You are considering the purchase of a 2-year-maturity bond making annual coupon payments. The face
value of the bond is $100, and the coupon rate is 12% per year.
Required:
a. What is the yield to maturity of the 2-year zero?
b. What is the yield to maturity of the 2-year coupon bond?
c. What is the forward rate for the second year?
d. If the expectations hypothesis is accepted, what are (1) the expected price of the coupon bond at the end of the first year and (2) the expected holding-period return on the coupon bond over the first year?
e. Will the expected rate of return be higher or lower if you accept the liquidity preference hypothesis?
Required A
Required B
Complete this question by entering your answers in the tabs below.
What is the yield to maturity of the 2-year zero?
Note: Do not round intermediate calculations. Round your answer to 3 decimal places.
Required A
Required B
Required C
Required D
Required E
Yield to Maturity
2-year zero
8.472
%
Explanation:
a. The one-year zero-coupon bond has a yield to maturity of 6%, as shown below:
$94.34 = $100 ÷ (1 + y
1
) y
1
= 0.06000 = 6.000%
The yield on the two-year zero is 8.472%, as shown below:
$84.99 = $100 ÷ (1 + y
2
)
2
y
2
= 0.08472 = 8.472%
b. The price of the coupon bond is: $12 ÷ 1.06 + $112 ÷ (1.08472)
2
= $106.51
Therefore: yield to maturity for the coupon bond = 8.333%
[On a financial calculator, enter: n = 2; PV = −106.51; FV = 100; PMT = 12]
c. f
2
= (1 + y
2
)
2
÷ (1 + y
1
) − 1 = (1.08472)
2
÷ 1.06 − 1 = 0.1100 = 11.00%
d. Expected price = $112 ÷ 1.11 = $100.90
(Note that next year, the coupon bond will have one payment left.)
Expected holding period return
= $12 + ($100.90 − $106.51) ÷ $106.51 = 0.6000 = 6.00%
This holding period return is the same as the return on the one-year zero.
e. If there is a liquidity premium, then: E
(
r
2
) < f
2
E
(Price) = $112 ÷ (1 + E
(
r
2
)) > $100.90
E(HPR) > 6%
Worksheet
Difficulty: 2 Intermediate
Source: Investments (Bodie, 13e, ISBN 1266836322) > Chapter 15: The Term Structure of Interest Rates > Chapter 15 Problems - Algorithmic & Static
References
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15.
Award: 10.00
points
Problems? Adjust credit for all students.
Suppose that a 1-year zero-coupon bond with face value $100 currently sells at $94.34, while a 2-year zero sells at $84.99. You are considering the purchase of a 2-year-maturity bond making annual coupon payments. The face
value of the bond is $100, and the coupon rate is 12% per year.
Required:
a. What is the yield to maturity of the 2-year zero?
b. What is the yield to maturity of the 2-year coupon bond?
c. What is the forward rate for the second year?
d. If the expectations hypothesis is accepted, what are (1) the expected price of the coupon bond at the end of the first year and (2) the expected holding-period return on the coupon bond over the first year?
e. Will the expected rate of return be higher or lower if you accept the liquidity preference hypothesis?
Required A
Required C
Complete this question by entering your answers in the tabs below.
What is the yield to maturity of the 2-year coupon bond?
Note: Do not round intermediate calculations. Round your answer to 3 decimal places.
Required A
Required B
Required C
Required D
Required E
Yield to Maturity
2-year coupon bond
8.333
%
Explanation:
a. The one-year zero-coupon bond has a yield to maturity of 6%, as shown below:
$94.34 = $100 ÷ (1 + y
1
) y
1
= 0.06000 = 6.000%
The yield on the two-year zero is 8.472%, as shown below:
$84.99 = $100 ÷ (1 + y
2
)
2
y
2
= 0.08472 = 8.472%
b. The price of the coupon bond is: $12 ÷ 1.06 + $112 ÷ (1.08472)
2
= $106.51
Therefore: yield to maturity for the coupon bond = 8.333%
[On a financial calculator, enter: n = 2; PV = −106.51; FV = 100; PMT = 12]
c. f
2
= (1 + y
2
)
2
÷ (1 + y
1
) − 1 = (1.08472)
2
÷ 1.06 − 1 = 0.1100 = 11.00%
d. Expected price = $112 ÷ 1.11 = $100.90
(Note that next year, the coupon bond will have one payment left.)
Expected holding period return
= $12 + ($100.90 − $106.51) ÷ $106.51 = 0.6000 = 6.00%
This holding period return is the same as the return on the one-year zero.
e. If there is a liquidity premium, then: E
(
r
2
) < f
2
E
(Price) = $112 ÷ (1 + E
(
r
2
)) > $100.90
E(HPR) > 6%
Worksheet
Difficulty: 2 Intermediate
Source: Investments (Bodie, 13e, ISBN 1266836322) > Chapter 15: The Term Structure of Interest Rates > Chapter 15 Problems - Algorithmic & Static
References
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15.
Award: 10.00
points
Problems? Adjust credit for all students.
Suppose that a 1-year zero-coupon bond with face value $100 currently sells at $94.34, while a 2-year zero sells at $84.99. You are considering the purchase of a 2-year-maturity bond making annual coupon payments. The face
value of the bond is $100, and the coupon rate is 12% per year.
Required:
a. What is the yield to maturity of the 2-year zero?
b. What is the yield to maturity of the 2-year coupon bond?
c. What is the forward rate for the second year?
d. If the expectations hypothesis is accepted, what are (1) the expected price of the coupon bond at the end of the first year and (2) the expected holding-period return on the coupon bond over the first year?
e. Will the expected rate of return be higher or lower if you accept the liquidity preference hypothesis?
Required B
Required D
Complete this question by entering your answers in the tabs below.
What is the forward rate for the second year?
Note: Do not round intermediate calculations. Round your final answer to 2 decimal places.
Required A
Required B
Required C
Required D
Required E
Forward rate
11.00
%
Explanation:
a. The one-year zero-coupon bond has a yield to maturity of 6%, as shown below:
$94.34 = $100 ÷ (1 + y
1
) y
1
= 0.06000 = 6.000%
The yield on the two-year zero is 8.472%, as shown below:
$84.99 = $100 ÷ (1 + y
2
)
2
y
2
= 0.08472 = 8.472%
b. The price of the coupon bond is: $12 ÷ 1.06 + $112 ÷ (1.08472)
2
= $106.51
Therefore: yield to maturity for the coupon bond = 8.333%
[On a financial calculator, enter: n = 2; PV = −106.51; FV = 100; PMT = 12]
c. f
2
= (1 + y
2
)
2
÷ (1 + y
1
) − 1 = (1.08472)
2
÷ 1.06 − 1 = 0.1100 = 11.00%
d. Expected price = $112 ÷ 1.11 = $100.90
(Note that next year, the coupon bond will have one payment left.)
Expected holding period return
= $12 + ($100.90 − $106.51) ÷ $106.51 = 0.6000 = 6.00%
This holding period return is the same as the return on the one-year zero.
e. If there is a liquidity premium, then: E
(
r
2
) < f
2
E
(Price) = $112 ÷ (1 + E
(
r
2
)) > $100.90
E(HPR) > 6%
Worksheet
Difficulty: 2 Intermediate
Source: Investments (Bodie, 13e, ISBN 1266836322) > Chapter 15: The Term Structure of Interest Rates > Chapter 15 Problems - Algorithmic & Static
References
Your preview ends here
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15.
Award: 10.00
points
Problems? Adjust credit for all students.
Suppose that a 1-year zero-coupon bond with face value $100 currently sells at $94.34, while a 2-year zero sells at $84.99. You are considering the purchase of a 2-year-maturity bond making annual coupon payments. The face
value of the bond is $100, and the coupon rate is 12% per year.
Required:
a. What is the yield to maturity of the 2-year zero?
b. What is the yield to maturity of the 2-year coupon bond?
c. What is the forward rate for the second year?
d. If the expectations hypothesis is accepted, what are (1) the expected price of the coupon bond at the end of the first year and (2) the expected holding-period return on the coupon bond over the first year?
e. Will the expected rate of return be higher or lower if you accept the liquidity preference hypothesis?
Required C
Required E
Complete this question by entering your answers in the tabs below.
If the expectations hypothesis is accepted, what are (1) the expected price of the coupon bond at the end of the first year and
(2) the expected holding-period return on the coupon bond over the first year?
Note: Do not round intermediate calculations. Round your answers to 2 decimal places.
Required A
Required B
Required C
Required D
Required E
Expected price
100.90
Holding-period return
6.00
%
Explanation:
a. The one-year zero-coupon bond has a yield to maturity of 6%, as shown below:
$94.34 = $100 ÷ (1 + y
1
) y
1
= 0.06000 = 6.000%
The yield on the two-year zero is 8.472%, as shown below:
$84.99 = $100 ÷ (1 + y
2
)
2
y
2
= 0.08472 = 8.472%
b. The price of the coupon bond is: $12 ÷ 1.06 + $112 ÷ (1.08472)
2
= $106.51
Therefore: yield to maturity for the coupon bond = 8.333%
[On a financial calculator, enter: n = 2; PV = −106.51; FV = 100; PMT = 12]
c. f
2
= (1 + y
2
)
2
÷ (1 + y
1
) − 1 = (1.08472)
2
÷ 1.06 − 1 = 0.1100 = 11.00%
d. Expected price = $112 ÷ 1.11 = $100.90
(Note that next year, the coupon bond will have one payment left.)
Expected holding period return
= $12 + ($100.90 − $106.51) ÷ $106.51 = 0.6000 = 6.00%
This holding period return is the same as the return on the one-year zero.
e. If there is a liquidity premium, then: E
(
r
2
) < f
2
E
(Price) = $112 ÷ (1 + E
(
r
2
)) > $100.90
E(HPR) > 6%
Worksheet
Difficulty: 2 Intermediate
Source: Investments (Bodie, 13e, ISBN 1266836322) > Chapter 15: The Term Structure of Interest Rates > Chapter 15 Problems - Algorithmic & Static
References
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15.
Award: 10.00
points
Problems? Adjust credit for all students.
Suppose that a 1-year zero-coupon bond with face value $100 currently sells at $94.34, while a 2-year zero sells at $84.99. You are considering the purchase of a 2-year-maturity bond making annual coupon payments. The face
value of the bond is $100, and the coupon rate is 12% per year.
Required:
a. What is the yield to maturity of the 2-year zero?
b. What is the yield to maturity of the 2-year coupon bond?
c. What is the forward rate for the second year?
d. If the expectations hypothesis is accepted, what are (1) the expected price of the coupon bond at the end of the first year and (2) the expected holding-period return on the coupon bond over the first year?
e. Will the expected rate of return be higher or lower if you accept the liquidity preference hypothesis?
Required D
Required E
Complete this question by entering your answers in the tabs below.
Will the expected rate of return be higher or lower if you accept the liquidity preference hypothesis?
Required A
Required B
Required C
Required D
Required E
Will the expected rate of return be higher or lower if you accept the liquidity preference hypothesis?
Higher
Explanation:
a. The one-year zero-coupon bond has a yield to maturity of 6%, as shown below:
$94.34 = $100 ÷ (1 + y
1
) y
1
= 0.06000 = 6.000%
The yield on the two-year zero is 8.472%, as shown below:
$84.99 = $100 ÷ (1 + y
2
)
2
y
2
= 0.08472 = 8.472%
b. The price of the coupon bond is: $12 ÷ 1.06 + $112 ÷ (1.08472)
2
= $106.51
Therefore: yield to maturity for the coupon bond = 8.333%
[On a financial calculator, enter: n = 2; PV = −106.51; FV = 100; PMT = 12]
c. f
2
= (1 + y
2
)
2
÷ (1 + y
1
) − 1 = (1.08472)
2
÷ 1.06 − 1 = 0.1100 = 11.00%
d. Expected price = $112 ÷ 1.11 = $100.90
(Note that next year, the coupon bond will have one payment left.)
Expected holding period return
= $12 + ($100.90 − $106.51) ÷ $106.51 = 0.6000 = 6.00%
This holding period return is the same as the return on the one-year zero.
e. If there is a liquidity premium, then: E
(
r
2
) < f
2
E
(Price) = $112 ÷ (1 + E
(
r
2
)) > $100.90
E(HPR) > 6%
Worksheet
Difficulty: 2 Intermediate
Source: Investments (Bodie, 13e, ISBN 1266836322) > Chapter 15: The Term Structure of Interest Rates > Chapter 15 Problems - Algorithmic & Static
References
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16.
Award: 10.00
points
Problems? Adjust credit for all students.
The current yield curve for default-free zero-coupon bonds is as follows:
Maturity (Years)
YTM (%)
1
10%
2
11
3
12
Required:
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 yield to maturity on 1-year zero-coupon bonds next year?
c. Assume that the pure expectations hypothesis of the term structure is correct. If market expectations are accurate, what will be the yield to maturity on 2-year zero-coupon bonds next year?
d. If you purchase a 2-year zero-coupon bond now, what is the expected total rate of return over the next year? (
Hint:
Compute the current and expected future prices.) Ignore taxes.
e. What is the expected total rate of return over the next year on a 3-year zero-coupon bond?
f. What should be the current price of a 3-year maturity bond with a 12% coupon rate paid annually?
g. If you purchased the coupon bond at the price you computed in part (
f
), what would your total expected rate of return be over the next year (coupon plus price change)? Ignore taxes.
Required A
Required B
Complete this question by entering your answers in the tabs below.
What are the implied 1-year forward rates?
Note: Do not round intermediate calculations. Round your answers to 2 decimal places.
Required A
Required B
Required C
Required D
Required E
Required F
Required G
Maturity
Forward Rate
2 years
12.01
%
3 years
14.03
%
Explanation:
a.
We obtain forward rates from the following table:
Maturity
YTM
Forward Rate
Price
(for
parts c
,
d
)
1 year
10%
10.00%
$ 1,000
÷ 1.10 =
$
909.09
2 years
11%
(1.11
2
÷ 1.10) − 1 = 12.01%
$1,000
÷ 1.11
2
=
$811.62
3 years
12%
(1.12
3
÷ 1.11
2
) − 1 = 14.03%
$1,000
÷ 1.12
3
=
$711.78
b., c.
We obtain next year’s prices and yields by discounting each zero’s face value at the forward rates for next year that we derived in part (
a
):
Maturity
Price
YTM
1 year
$ 1,000 ÷ 1.1201
= $ 892.78
12.01%
2 years
$1,000 ÷ (1.1201
× 1.1403) =
$782.93
13.02%
Note that this year’s upward sloping yield curve implies, according to the expectations hypothesis, a shift upward in next year’s curve.
d.
Next year, the 2-year zero will be a 1-year zero, and will therefore sell at a price of: $1,000 ÷ 1.1201 = $892.78
Expected total rate of return:
2-year bond: ($892.78 ÷ $811.62) − 1 = 1.1000 − 1 = 10%
e.
The current 3-year zero will be a 2-year zero and will sell for: $782.93
3-year bond: ($782.93 ÷ $711.78) − 1 = 1.1000 − 1 = 10%
f.
The current price of the bond should equal the value of each payment times the present value of $1 to be received at the “maturity” of that payment. The present value schedule can be taken directly from the prices of zero-
coupon bonds calculated above.
Current price = ($120 × 0.90909) + ($120 × 0.81162) + ($1,120 × 0.71178)
= $109.0908 + $97.3944 + $797.1936 = $1,003.68
g.
The expected prices of zeros one year from now can be used to calculate the expected bond value at that time:
Expected price 1 year from now = ($120 × 0.89278) + ($1,120 × 0.78293)
= $107.1336 + $876.8816 = $984.02
Total expected rate of return =
$120 + ($984.02 − $1,003.68) ÷ 1,003.68 = 0.1000 = 10%
Worksheet
Difficulty: 3 Challenge
Source: Investments (Bodie, 13e, ISBN 1266836322) > Chapter 15: The Term Structure of Interest Rates > Chapter 15 Problems - Algorithmic & Static
References
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16.
Award: 10.00
points
Problems? Adjust credit for all students.
The current yield curve for default-free zero-coupon bonds is as follows:
Maturity (Years)
YTM (%)
1
10%
2
11
3
12
Required:
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 yield to maturity on 1-year zero-coupon bonds next year?
c. Assume that the pure expectations hypothesis of the term structure is correct. If market expectations are accurate, what will be the yield to maturity on 2-year zero-coupon bonds next year?
d. If you purchase a 2-year zero-coupon bond now, what is the expected total rate of return over the next year? (
Hint:
Compute the current and expected future prices.) Ignore taxes.
e. What is the expected total rate of return over the next year on a 3-year zero-coupon bond?
f. What should be the current price of a 3-year maturity bond with a 12% coupon rate paid annually?
g. If you purchased the coupon bond at the price you computed in part (
f
), what would your total expected rate of return be over the next year (coupon plus price change)? Ignore taxes.
Required A
Required C
Complete this question by entering your answers in the tabs below.
Assume that the pure expectations hypothesis of the term structure is correct. If market expectations are accurate, what will
be the yield to maturity on 1-year zero-coupon bonds next year?
Required A
Required B
Required C
Required D
Required E
Required F
Required G
Assume that the pure expectations hypothesis of the term structure is correct. If market expectations are accurate, what will be the yield to maturity on 1-year zero-coupon bonds next year?
Shift upward.
Explanation:
a.
We obtain forward rates from the following table:
Maturity
YTM
Forward Rate
Price
(for
parts c
,
d
)
1 year
10%
10.00%
$ 1,000
÷ 1.10 =
$
909.09
2 years
11%
(1.11
2
÷ 1.10) − 1 = 12.01%
$1,000
÷ 1.11
2
=
$811.62
3 years
12%
(1.12
3
÷ 1.11
2
) − 1 = 14.03%
$1,000
÷ 1.12
3
=
$711.78
b., c.
We obtain next year’s prices and yields by discounting each zero’s face value at the forward rates for next year that we derived in part (
a
):
Maturity
Price
YTM
1 year
$ 1,000 ÷ 1.1201
= $ 892.78
12.01%
2 years
$1,000 ÷ (1.1201
× 1.1403) =
$782.93
13.02%
Note that this year’s upward sloping yield curve implies, according to the expectations hypothesis, a shift upward in next year’s curve.
d.
Next year, the 2-year zero will be a 1-year zero, and will therefore sell at a price of: $1,000 ÷ 1.1201 = $892.78
Expected total rate of return:
2-year bond: ($892.78 ÷ $811.62) − 1 = 1.1000 − 1 = 10%
e.
The current 3-year zero will be a 2-year zero and will sell for: $782.93
3-year bond: ($782.93 ÷ $711.78) − 1 = 1.1000 − 1 = 10%
f.
The current price of the bond should equal the value of each payment times the present value of $1 to be received at the “maturity” of that payment. The present value schedule can be taken directly from the prices of zero-
coupon bonds calculated above.
Current price = ($120 × 0.90909) + ($120 × 0.81162) + ($1,120 × 0.71178)
= $109.0908 + $97.3944 + $797.1936 = $1,003.68
g.
The expected prices of zeros one year from now can be used to calculate the expected bond value at that time:
Expected price 1 year from now = ($120 × 0.89278) + ($1,120 × 0.78293)
= $107.1336 + $876.8816 = $984.02
Total expected rate of return =
$120 + ($984.02 − $1,003.68) ÷ 1,003.68 = 0.1000 = 10%
Worksheet
Difficulty: 3 Challenge
Source: Investments (Bodie, 13e, ISBN 1266836322) > Chapter 15: The Term Structure of Interest Rates > Chapter 15 Problems - Algorithmic & Static
References
Your preview ends here
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- Access to all documents
- Unlimited textbook solutions
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16.
Award: 10.00
points
Problems? Adjust credit for all students.
The current yield curve for default-free zero-coupon bonds is as follows:
Maturity (Years)
YTM (%)
1
10%
2
11
3
12
Required:
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 yield to maturity on 1-year zero-coupon bonds next year?
c. Assume that the pure expectations hypothesis of the term structure is correct. If market expectations are accurate, what will be the yield to maturity on 2-year zero-coupon bonds next year?
d. If you purchase a 2-year zero-coupon bond now, what is the expected total rate of return over the next year? (
Hint:
Compute the current and expected future prices.) Ignore taxes.
e. What is the expected total rate of return over the next year on a 3-year zero-coupon bond?
f. What should be the current price of a 3-year maturity bond with a 12% coupon rate paid annually?
g. If you purchased the coupon bond at the price you computed in part (
f
), what would your total expected rate of return be over the next year (coupon plus price change)? Ignore taxes.
Required B
Required D
Complete this question by entering your answers in the tabs below.
Assume that the pure expectations hypothesis of the term structure is correct. If market expectations are accurate, what will
be the yield to maturity on 2-year zero-coupon bonds next year?
Required A
Required B
Required C
Required D
Required E
Required F
Required G
Assume that the pure expectations hypothesis of the term structure is correct. If market expectations are accurate, what will be the yield to maturity on 2-year zero-coupon bonds next year?
Shift upward.
Explanation:
a.
We obtain forward rates from the following table:
Maturity
YTM
Forward Rate
Price
(for
parts c
,
d
)
1 year
10%
10.00%
$ 1,000
÷ 1.10 =
$
909.09
2 years
11%
(1.11
2
÷ 1.10) − 1 = 12.01%
$1,000
÷ 1.11
2
=
$811.62
3 years
12%
(1.12
3
÷ 1.11
2
) − 1 = 14.03%
$1,000
÷ 1.12
3
=
$711.78
b., c.
We obtain next year’s prices and yields by discounting each zero’s face value at the forward rates for next year that we derived in part (
a
):
Maturity
Price
YTM
1 year
$ 1,000 ÷ 1.1201
= $ 892.78
12.01%
2 years
$1,000 ÷ (1.1201
× 1.1403) =
$782.93
13.02%
Note that this year’s upward sloping yield curve implies, according to the expectations hypothesis, a shift upward in next year’s curve.
d.
Next year, the 2-year zero will be a 1-year zero, and will therefore sell at a price of: $1,000 ÷ 1.1201 = $892.78
Expected total rate of return:
2-year bond: ($892.78 ÷ $811.62) − 1 = 1.1000 − 1 = 10%
e.
The current 3-year zero will be a 2-year zero and will sell for: $782.93
3-year bond: ($782.93 ÷ $711.78) − 1 = 1.1000 − 1 = 10%
f.
The current price of the bond should equal the value of each payment times the present value of $1 to be received at the “maturity” of that payment. The present value schedule can be taken directly from the prices of zero-
coupon bonds calculated above.
Current price = ($120 × 0.90909) + ($120 × 0.81162) + ($1,120 × 0.71178)
= $109.0908 + $97.3944 + $797.1936 = $1,003.68
g.
The expected prices of zeros one year from now can be used to calculate the expected bond value at that time:
Expected price 1 year from now = ($120 × 0.89278) + ($1,120 × 0.78293)
= $107.1336 + $876.8816 = $984.02
Total expected rate of return =
$120 + ($984.02 − $1,003.68) ÷ 1,003.68 = 0.1000 = 10%
Worksheet
Difficulty: 3 Challenge
Source: Investments (Bodie, 13e, ISBN 1266836322) > Chapter 15: The Term Structure of Interest Rates > Chapter 15 Problems - Algorithmic & Static
References
Your preview ends here
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- Access to all documents
- Unlimited textbook solutions
- 24/7 expert homework help
16.
Award: 10.00
points
Problems? Adjust credit for all students.
The current yield curve for default-free zero-coupon bonds is as follows:
Maturity (Years)
YTM (%)
1
10%
2
11
3
12
Required:
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 yield to maturity on 1-year zero-coupon bonds next year?
c. Assume that the pure expectations hypothesis of the term structure is correct. If market expectations are accurate, what will be the yield to maturity on 2-year zero-coupon bonds next year?
d. If you purchase a 2-year zero-coupon bond now, what is the expected total rate of return over the next year? (
Hint:
Compute the current and expected future prices.) Ignore taxes.
e. What is the expected total rate of return over the next year on a 3-year zero-coupon bond?
f. What should be the current price of a 3-year maturity bond with a 12% coupon rate paid annually?
g. If you purchased the coupon bond at the price you computed in part (
f
), what would your total expected rate of return be over the next year (coupon plus price change)? Ignore taxes.
Required C
Required E
Complete this question by entering your answers in the tabs below.
If you purchase a 2-year zero-coupon bond now, what is the expected total rate of return over the next year? (
Hint:
Compute
the current and expected future prices.) Ignore taxes.
Note: Do not round intermediate calculations. Round your answer to the nearest whole percent.
Required A
Required B
Required C
Required D
Required E
Required F
Required G
Expected total rate of return (2-year bond)
10
%
Explanation:
a.
We obtain forward rates from the following table:
Maturity
YTM
Forward Rate
Price
(for
parts c
,
d
)
1 year
10%
10.00%
$ 1,000
÷ 1.10 =
$
909.09
2 years
11%
(1.11
2
÷ 1.10) − 1 = 12.01%
$1,000
÷ 1.11
2
=
$811.62
3 years
12%
(1.12
3
÷ 1.11
2
) − 1 = 14.03%
$1,000
÷ 1.12
3
=
$711.78
b., c.
We obtain next year’s prices and yields by discounting each zero’s face value at the forward rates for next year that we derived in part (
a
):
Maturity
Price
YTM
1 year
$ 1,000 ÷ 1.1201
= $ 892.78
12.01%
2 years
$1,000 ÷ (1.1201
× 1.1403) =
$782.93
13.02%
Note that this year’s upward sloping yield curve implies, according to the expectations hypothesis, a shift upward in next year’s curve.
d.
Next year, the 2-year zero will be a 1-year zero, and will therefore sell at a price of: $1,000 ÷ 1.1201 = $892.78
Expected total rate of return:
2-year bond: ($892.78 ÷ $811.62) − 1 = 1.1000 − 1 = 10%
e.
The current 3-year zero will be a 2-year zero and will sell for: $782.93
3-year bond: ($782.93 ÷ $711.78) − 1 = 1.1000 − 1 = 10%
f.
The current price of the bond should equal the value of each payment times the present value of $1 to be received at the “maturity” of that payment. The present value schedule can be taken directly from the prices of zero-
coupon bonds calculated above.
Current price = ($120 × 0.90909) + ($120 × 0.81162) + ($1,120 × 0.71178)
= $109.0908 + $97.3944 + $797.1936 = $1,003.68
g.
The expected prices of zeros one year from now can be used to calculate the expected bond value at that time:
Expected price 1 year from now = ($120 × 0.89278) + ($1,120 × 0.78293)
= $107.1336 + $876.8816 = $984.02
Total expected rate of return =
$120 + ($984.02 − $1,003.68) ÷ 1,003.68 = 0.1000 = 10%
Worksheet
Difficulty: 3 Challenge
Source: Investments (Bodie, 13e, ISBN 1266836322) > Chapter 15: The Term Structure of Interest Rates > Chapter 15 Problems - Algorithmic & Static
References
Your preview ends here
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- Access to all documents
- Unlimited textbook solutions
- 24/7 expert homework help
16.
Award: 10.00
points
Problems? Adjust credit for all students.
The current yield curve for default-free zero-coupon bonds is as follows:
Maturity (Years)
YTM (%)
1
10%
2
11
3
12
Required:
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 yield to maturity on 1-year zero-coupon bonds next year?
c. Assume that the pure expectations hypothesis of the term structure is correct. If market expectations are accurate, what will be the yield to maturity on 2-year zero-coupon bonds next year?
d. If you purchase a 2-year zero-coupon bond now, what is the expected total rate of return over the next year? (
Hint:
Compute the current and expected future prices.) Ignore taxes.
e. What is the expected total rate of return over the next year on a 3-year zero-coupon bond?
f. What should be the current price of a 3-year maturity bond with a 12% coupon rate paid annually?
g. If you purchased the coupon bond at the price you computed in part (
f
), what would your total expected rate of return be over the next year (coupon plus price change)? Ignore taxes.
Required D
Required F
Complete this question by entering your answers in the tabs below.
What is the expected total rate of return over the next year on a 3-year zero-coupon bond?
Note: Do not round intermediate calculations. Round your answer to the nearest whole percent.
Required A
Required B
Required C
Required D
Required E
Required F
Required G
Expected total rate of return (3-year bond)
10
%
Explanation:
a.
We obtain forward rates from the following table:
Maturity
YTM
Forward Rate
Price
(for
parts c
,
d
)
1 year
10%
10.00%
$ 1,000
÷ 1.10 =
$
909.09
2 years
11%
(1.11
2
÷ 1.10) − 1 = 12.01%
$1,000
÷ 1.11
2
=
$811.62
3 years
12%
(1.12
3
÷ 1.11
2
) − 1 = 14.03%
$1,000
÷ 1.12
3
=
$711.78
b., c.
We obtain next year’s prices and yields by discounting each zero’s face value at the forward rates for next year that we derived in part (
a
):
Maturity
Price
YTM
1 year
$ 1,000 ÷ 1.1201
= $ 892.78
12.01%
2 years
$1,000 ÷ (1.1201
× 1.1403) =
$782.93
13.02%
Note that this year’s upward sloping yield curve implies, according to the expectations hypothesis, a shift upward in next year’s curve.
d.
Next year, the 2-year zero will be a 1-year zero, and will therefore sell at a price of: $1,000 ÷ 1.1201 = $892.78
Expected total rate of return:
2-year bond: ($892.78 ÷ $811.62) − 1 = 1.1000 − 1 = 10%
e.
The current 3-year zero will be a 2-year zero and will sell for: $782.93
3-year bond: ($782.93 ÷ $711.78) − 1 = 1.1000 − 1 = 10%
f.
The current price of the bond should equal the value of each payment times the present value of $1 to be received at the “maturity” of that payment. The present value schedule can be taken directly from the prices of zero-
coupon bonds calculated above.
Current price = ($120 × 0.90909) + ($120 × 0.81162) + ($1,120 × 0.71178)
= $109.0908 + $97.3944 + $797.1936 = $1,003.68
g.
The expected prices of zeros one year from now can be used to calculate the expected bond value at that time:
Expected price 1 year from now = ($120 × 0.89278) + ($1,120 × 0.78293)
= $107.1336 + $876.8816 = $984.02
Total expected rate of return =
$120 + ($984.02 − $1,003.68) ÷ 1,003.68 = 0.1000 = 10%
Worksheet
Difficulty: 3 Challenge
Source: Investments (Bodie, 13e, ISBN 1266836322) > Chapter 15: The Term Structure of Interest Rates > Chapter 15 Problems - Algorithmic & Static
References
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
- Access to all documents
- Unlimited textbook solutions
- 24/7 expert homework help
16.
Award: 10.00
points
Problems? Adjust credit for all students.
The current yield curve for default-free zero-coupon bonds is as follows:
Maturity (Years)
YTM (%)
1
10%
2
11
3
12
Required:
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 yield to maturity on 1-year zero-coupon bonds next year?
c. Assume that the pure expectations hypothesis of the term structure is correct. If market expectations are accurate, what will be the yield to maturity on 2-year zero-coupon bonds next year?
d. If you purchase a 2-year zero-coupon bond now, what is the expected total rate of return over the next year? (
Hint:
Compute the current and expected future prices.) Ignore taxes.
e. What is the expected total rate of return over the next year on a 3-year zero-coupon bond?
f. What should be the current price of a 3-year maturity bond with a 12% coupon rate paid annually?
g. If you purchased the coupon bond at the price you computed in part (
f
), what would your total expected rate of return be over the next year (coupon plus price change)? Ignore taxes.
Required E
Required G
Complete this question by entering your answers in the tabs below.
What should be the current price of a 3-year maturity bond with a 12% coupon rate paid annually?
Note: Do not round intermediate calculations. Round your answer to 2 decimal places.
Required A
Required B
Required C
Required D
Required E
Required F
Required G
$
Current price
1,003.68
Explanation:
a.
We obtain forward rates from the following table:
Maturity
YTM
Forward Rate
Price
(for
parts c
,
d
)
1 year
10%
10.00%
$ 1,000
÷ 1.10 =
$
909.09
2 years
11%
(1.11
2
÷ 1.10) − 1 = 12.01%
$1,000
÷ 1.11
2
=
$811.62
3 years
12%
(1.12
3
÷ 1.11
2
) − 1 = 14.03%
$1,000
÷ 1.12
3
=
$711.78
b., c.
We obtain next year’s prices and yields by discounting each zero’s face value at the forward rates for next year that we derived in part (
a
):
Maturity
Price
YTM
1 year
$ 1,000 ÷ 1.1201
= $ 892.78
12.01%
2 years
$1,000 ÷ (1.1201
× 1.1403) =
$782.93
13.02%
Note that this year’s upward sloping yield curve implies, according to the expectations hypothesis, a shift upward in next year’s curve.
d.
Next year, the 2-year zero will be a 1-year zero, and will therefore sell at a price of: $1,000 ÷ 1.1201 = $892.78
Expected total rate of return:
2-year bond: ($892.78 ÷ $811.62) − 1 = 1.1000 − 1 = 10%
e.
The current 3-year zero will be a 2-year zero and will sell for: $782.93
3-year bond: ($782.93 ÷ $711.78) − 1 = 1.1000 − 1 = 10%
f.
The current price of the bond should equal the value of each payment times the present value of $1 to be received at the “maturity” of that payment. The present value schedule can be taken directly from the prices of zero-
coupon bonds calculated above.
Current price = ($120 × 0.90909) + ($120 × 0.81162) + ($1,120 × 0.71178)
= $109.0908 + $97.3944 + $797.1936 = $1,003.68
g.
The expected prices of zeros one year from now can be used to calculate the expected bond value at that time:
Expected price 1 year from now = ($120 × 0.89278) + ($1,120 × 0.78293)
= $107.1336 + $876.8816 = $984.02
Total expected rate of return =
$120 + ($984.02 − $1,003.68) ÷ 1,003.68 = 0.1000 = 10%
Worksheet
Difficulty: 3 Challenge
Source: Investments (Bodie, 13e, ISBN 1266836322) > Chapter 15: The Term Structure of Interest Rates > Chapter 15 Problems - Algorithmic & Static
References
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
- Access to all documents
- Unlimited textbook solutions
- 24/7 expert homework help
16.
Award: 10.00
points
Problems? Adjust credit for all students.
The current yield curve for default-free zero-coupon bonds is as follows:
Maturity (Years)
YTM (%)
1
10%
2
11
3
12
Required:
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 yield to maturity on 1-year zero-coupon bonds next year?
c. Assume that the pure expectations hypothesis of the term structure is correct. If market expectations are accurate, what will be the yield to maturity on 2-year zero-coupon bonds next year?
d. If you purchase a 2-year zero-coupon bond now, what is the expected total rate of return over the next year? (
Hint:
Compute the current and expected future prices.) Ignore taxes.
e. What is the expected total rate of return over the next year on a 3-year zero-coupon bond?
f. What should be the current price of a 3-year maturity bond with a 12% coupon rate paid annually?
g. If you purchased the coupon bond at the price you computed in part (
f
), what would your total expected rate of return be over the next year (coupon plus price change)? Ignore taxes.
Required F
Required G
Complete this question by entering your answers in the tabs below.
If you purchased the coupon bond at the price you computed in part (
f
), what would your total expected rate of return be
over the next year (coupon plus price change)? Ignore taxes.
Note: Do not round intermediate calculations. Round your answer to the nearest whole percent.
Required A
Required B
Required C
Required D
Required E
Required F
Required G
Total expected rate of return
10
%
Explanation:
a.
We obtain forward rates from the following table:
Maturity
YTM
Forward Rate
Price
(for
parts c
,
d
)
1 year
10%
10.00%
$ 1,000
÷ 1.10 =
$
909.09
2 years
11%
(1.11
2
÷ 1.10) − 1 = 12.01%
$1,000
÷ 1.11
2
=
$811.62
3 years
12%
(1.12
3
÷ 1.11
2
) − 1 = 14.03%
$1,000
÷ 1.12
3
=
$711.78
b., c.
We obtain next year’s prices and yields by discounting each zero’s face value at the forward rates for next year that we derived in part (
a
):
Maturity
Price
YTM
1 year
$ 1,000 ÷ 1.1201
= $ 892.78
12.01%
2 years
$1,000 ÷ (1.1201
× 1.1403) =
$782.93
13.02%
Note that this year’s upward sloping yield curve implies, according to the expectations hypothesis, a shift upward in next year’s curve.
d.
Next year, the 2-year zero will be a 1-year zero, and will therefore sell at a price of: $1,000 ÷ 1.1201 = $892.78
Expected total rate of return:
2-year bond: ($892.78 ÷ $811.62) − 1 = 1.1000 − 1 = 10%
e.
The current 3-year zero will be a 2-year zero and will sell for: $782.93
3-year bond: ($782.93 ÷ $711.78) − 1 = 1.1000 − 1 = 10%
f.
The current price of the bond should equal the value of each payment times the present value of $1 to be received at the “maturity” of that payment. The present value schedule can be taken directly from the prices of zero-
coupon bonds calculated above.
Current price = ($120 × 0.90909) + ($120 × 0.81162) + ($1,120 × 0.71178)
= $109.0908 + $97.3944 + $797.1936 = $1,003.68
g.
The expected prices of zeros one year from now can be used to calculate the expected bond value at that time:
Expected price 1 year from now = ($120 × 0.89278) + ($1,120 × 0.78293)
= $107.1336 + $876.8816 = $984.02
Total expected rate of return =
$120 + ($984.02 − $1,003.68) ÷ 1,003.68 = 0.1000 = 10%
Worksheet
Difficulty: 3 Challenge
Source: Investments (Bodie, 13e, ISBN 1266836322) > Chapter 15: The Term Structure of Interest Rates > Chapter 15 Problems - Algorithmic & Static
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17.
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Problems? Adjust credit for all students.
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
$ 925.93
2
853.39
3
782.92
4
715.00
5
650.00
Required:
a. Calculate the forward rate of interest for each year.
b. How could you construct a 1-year forward loan beginning in year 3?
c. How could you construct a 1-year forward loan beginning in year 4?
Required A
Required B
Complete this question by entering your answers in the tabs below.
Calculate the forward rate of interest for each year.
Note: Round your answers to 2 decimal places.
Required A
Required B
Required C
Maturity (years)
Forward Rate
2
8.50
%
3
9.00
%
4
9.50
%
5
10.00
%
Explanation:
a. Maturity (years)
Price
YTM
Forward Rate
1
$ 925.93
8.00%
2
853.39
8.25
8.50
3
782.92
8.50
9.00
4
715.00
8.75
9.50
5
650.00
9.00
10.00
Calculated from: f
i,j
= 1 + s
j
j
1 + s
i
i
1
j-i
- 1
b. For each 3-year zero issued today, use the proceeds to buy:
$782.92 ÷ $715.00 = 1.095 four-year zeros
Your cash flows are thus as follows:
Time
Cash Flow
0
$ 0
3
−$ 1,000
The 3-year zero issued at time 0 matures;
the issuer pays out $1,000 face value
4
+$ 1,095
The 4-year zeros purchased at time 0
mature; receive face value
This is a synthetic one-year loan originating at time 3. The rate on the synthetic loan is 0.095 = 9.5%, precisely the forward rate for year 4.
c. For each 4-year zero issued today, use the proceeds to buy:
$715.00 ÷ $650.00 = 1.100 five-year zeros
Your cash flows are thus as follows:
Time
Cash Flow
0
$ 0
4
−$ 1,000
The 4-year zero issued at time 0 matures;
the issuer pays out $1,000 face value
5
+$ 1,100
The 5-year zeros purchased at time 0
mature; receive face value
This is a synthetic one-year loan originating at time 4. The rate on the synthetic loan is 0.100 = 10.0%, precisely the forward rate for year 5.
Worksheet
Difficulty: 3 Challenge
Source: Investments (Bodie, 13e, ISBN 1266836322) > Chapter 15: The Term Structure of Interest Rates > Chapter 15 Problems - Algorithmic & Static
[
(
)
(
)
]
(
)
References
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17.
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Problems? Adjust credit for all students.
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
$ 925.93
2
853.39
3
782.92
4
715.00
5
650.00
Required:
a. Calculate the forward rate of interest for each year.
b. How could you construct a 1-year forward loan beginning in year 3?
c. How could you construct a 1-year forward loan beginning in year 4?
Required A
Required C
Complete this question by entering your answers in the tabs below.
How could you construct a 1-year forward loan beginning in year 3?
Note: Round your Rate of synthetic loan answer to 1 decimal place.
Required A
Required B
Required C
$
Face value
1,095
Rate of synthetic loan
9.5
%
Explanation:
a. Maturity (years)
Price
YTM
Forward Rate
1
$ 925.93
8.00%
2
853.39
8.25
8.50
3
782.92
8.50
9.00
4
715.00
8.75
9.50
5
650.00
9.00
10.00
b. For each 3-year zero issued today, use the proceeds to buy:
$782.92 ÷ $715.00 = 1.095 four-year zeros
Your cash flows are thus as follows:
Time
Cash Flow
0
$ 0
3
−$ 1,000
The 3-year zero issued at time 0 matures;
the issuer pays out $1,000 face value
4
+$ 1,095
The 4-year zeros purchased at time 0
mature; receive face value
This is a synthetic one-year loan originating at time 3. The rate on the synthetic loan is 0.095 = 9.5%, precisely the forward rate for year 4.
c. For each 4-year zero issued today, use the proceeds to buy:
$715.00 ÷ $650.00 = 1.100 five-year zeros
Your cash flows are thus as follows:
Time
Cash Flow
0
$ 0
4
−$ 1,000
The 4-year zero issued at time 0 matures;
the issuer pays out $1,000 face value
5
+$ 1,100
The 5-year zeros purchased at time 0
mature; receive face value
This is a synthetic one-year loan originating at time 4. The rate on the synthetic loan is 0.100 = 10.0%, precisely the forward rate for year 5.
Worksheet
Difficulty: 3 Challenge
Source: Investments (Bodie, 13e, ISBN 1266836322) > Chapter 15: The Term Structure of Interest Rates > Chapter 15 Problems - Algorithmic & Static
References
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17.
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Problems? Adjust credit for all students.
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
$ 925.93
2
853.39
3
782.92
4
715.00
5
650.00
Required:
a. Calculate the forward rate of interest for each year.
b. How could you construct a 1-year forward loan beginning in year 3?
c. How could you construct a 1-year forward loan beginning in year 4?
Required B
Required C
Complete this question by entering your answers in the tabs below.
How could you construct a 1-year forward loan beginning in year 4?
Required A
Required B
Required C
$
Face value
1,100
Rate of synthetic loan
10
%
Explanation:
a. Maturity (years)
Price
YTM
Forward Rate
1
$ 925.93
8.00%
2
853.39
8.25
8.50
3
782.92
8.50
9.00
4
715.00
8.75
9.50
5
650.00
9.00
10.00
b. For each 3-year zero issued today, use the proceeds to buy:
$782.92 ÷ $715.00 = 1.095 four-year zeros
Your cash flows are thus as follows:
Time
Cash Flow
0
$ 0
3
−$ 1,000
The 3-year zero issued at time 0 matures;
the issuer pays out $1,000 face value
4
+$ 1,095
The 4-year zeros purchased at time 0
mature; receive face value
This is a synthetic one-year loan originating at time 3. The rate on the synthetic loan is 0.095 = 9.5%, precisely the forward rate for year 4.
c. For each 4-year zero issued today, use the proceeds to buy:
$715.00 ÷ $650.00 = 1.100 five-year zeros
Your cash flows are thus as follows:
Time
Cash Flow
0
$ 0
4
−$ 1,000
The 4-year zero issued at time 0 matures;
the issuer pays out $1,000 face value
5
+$ 1,100
The 5-year zeros purchased at time 0
mature; receive face value
This is a synthetic one-year loan originating at time 4. The rate on the synthetic loan is 0.100 = 10.0%, precisely the forward rate for year 5.
Worksheet
Difficulty: 3 Challenge
Source: Investments (Bodie, 13e, ISBN 1266836322) > Chapter 15: The Term Structure of Interest Rates > Chapter 15 Problems - Algorithmic & Static
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The prices of zero-coupon bonds with various maturities are given in the following table.
Suppose that you want to construct a 2-
year
maturity forward loan commencing in 3 years. The face value of each bond is $1,000.
Maturity (Years)
Price
1
$ 925.93
2
853.39
3
782.92
4
715.00
5
650.00
Required:
a.
Suppose that you buy today
one 3-year maturity zero-coupon bond with face value $1,000. How many 5-year maturity zeros would you have to sell to make your initial cash flow equal to zero (specifically, what must be the
total face value of those 5-year zeros)?
b.
What are the cash flows on this strategy in each year?
c.
What is the effective 2-year interest rate on the effective 3-year-ahead forward loan?
d. & e.
Confirm that the effective 2-year forward interest rate equals (1 + f
4
) ×(1 + f
5
)−1
. You therefore can interpret the 2-year loan rate as a 2-year forward rate for the last two years. Alternatively, show that the effective
2-year forward rate equals
(1 + y
5
)
5
÷ (1 + y
3
)
3
− 1
Required A C D and E
Required B
Complete this question by entering your answers in the tabs below.
a.
Suppose that you buy today
one 3-year maturity zero-coupon bond with face value $1,000. How many 5-year maturity
zeros would you have to sell to make your initial cash flow equal to zero (specifically, what must be the total face value of
those 5-year zeros)?
Note: Round your answer to 4 decimal places.
c.
What is the effective 2-year interest rate on the effective 3-year-ahead forward loan?
Note: Round your answer to 2 decimal places.
d&e.
Confirm that the effective 2-year forward interest rate equals (1 + f
4
) ×(1 + f
5
)−1. You therefore can interpret the 2-
year loan rate as a 2-year forward rate for the last two years. Alternatively, show that the effective 2-year forward rate equals
Note: Round your answer to 2 decimal places.
Required A C
D and E
Required B
Show less
a.
5-year maturity zeros
1.2045
c.
2-year interest rate
20.45
%
d&e.
2-year loan rate
20.46
%
Explanation:
a. For each three-year zero you buy today, issue:
$782.92 ÷ $650.00 = 1.2045 five-year zeros
The time-0 cash flow equals zero.
b. Your cash flows are thus as follows:
Time
Cash Flow
0
$ 0
3
+$ 1,000.00
The 3-year zero purchased at time 0
matures; receive $1,000 face value
5
−$ 1,204.50
The 5-year zeros issued at time 0 mature;
issuer pays face value
This is a synthetic two-year loan originating at time 3.
c. The effective two-year interest rate on the forward loan is:
$1,204.50 ÷ $1,000 − 1 = 0.2045 = 20.45%
d. The one-year forward rates for years 4 and 5 are 9.5% and 10%, respectively.
Notice that:
1.095 × 1.10 = 1.2045 =
1 + (two-year forward rate on the 3-year ahead forward loan)
The 5-year YTM is 9.0%. The 3-year YTM is 8.5%. Therefore, another way to derive the 2-year forward rate for a loan starting at time 3 is:
[Note: slight discrepancies here from rounding errors in YTM calculations]
Worksheet
Difficulty: 3 Challenge
Source: Investments (Bodie, 13e, ISBN 1266836322) > Chapter 15: The Term Structure of Interest Rates > Chapter 15 Problems - Algorithmic & Static
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18.
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points
Problems? Adjust credit for all students.
The prices of zero-coupon bonds with various maturities are given in the following table.
Suppose that you want to construct a 2-
year
maturity forward loan commencing in 3 years. The face value of each bond is $1,000.
Maturity (Years)
Price
1
$ 925.93
2
853.39
3
782.92
4
715.00
5
650.00
Required:
a.
Suppose that you buy today
one 3-year maturity zero-coupon bond with face value $1,000. How many 5-year maturity zeros would you have to sell to make your initial cash flow equal to zero (specifically, what must be the
total face value of those 5-year zeros)?
b.
What are the cash flows on this strategy in each year?
c.
What is the effective 2-year interest rate on the effective 3-year-ahead forward loan?
d. & e.
Confirm that the effective 2-year forward interest rate equals (1 + f
4
) ×(1 + f
5
)−1
. You therefore can interpret the 2-year loan rate as a 2-year forward rate for the last two years. Alternatively, show that the effective
2-year forward rate equals
(1 + y
5
)
5
÷ (1 + y
3
)
3
− 1
Required A C D and E
Required B
Complete this question by entering your answers in the tabs below.
b.
What are the cash flows on this strategy in each year?
Note: Negative value should be indicated by a minus sign. Leave cell blank if there is no effect. Round your answers to 2
decimal places.
Required A C
D and E
Required B
$
$
$
Time
Cash Flow
0
0
3
1,000.00
5
(1,204.50)
Explanation:
a. For each three-year zero you buy today, issue:
$782.92 ÷ $650.00 = 1.2045 five-year zeros
The time-0 cash flow equals zero.
b. Your cash flows are thus as follows:
Time
Cash Flow
0
$ 0
3
+$ 1,000.00
The 3-year zero purchased at time 0
matures; receive $1,000 face value
5
−$ 1,204.50
The 5-year zeros issued at time 0 mature;
issuer pays face value
This is a synthetic two-year loan originating at time 3.
c. The effective two-year interest rate on the forward loan is:
$1,204.50 ÷ $1,000 − 1 = 0.2045 = 20.45%
d. The one-year forward rates for years 4 and 5 are 9.5% and 10%, respectively.
Notice that:
1.095 × 1.10 = 1.2045 =
1 + (two-year forward rate on the 3-year ahead forward loan)
The 5-year YTM is 9.0%. The 3-year YTM is 8.5%. Therefore, another way to derive the 2-year forward rate for a loan starting at time 3 is:
[Note: slight discrepancies here from rounding errors in YTM calculations]
Worksheet
Difficulty: 3 Challenge
Source: Investments (Bodie, 13e, ISBN 1266836322) > Chapter 15: The Term Structure of Interest Rates > Chapter 15 Problems - Algorithmic & Static
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1.
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Structure of interest rates is:
the relationship between the rates of interest on all securities.
the relationship between the interest rate on a security and its time to maturity.
the relationship between the yield on a bond and its default rate.
All of the options are correct.
None of the options are correct.
The term structure of interest rates is the relationship between two variables, years and yield to maturity (holding all else constant).
References
Multiple Choice
Difficulty: 1 Basic
Treasury STRIPS are:
securities issued by the Treasury with very long maturities.
extremely risky securities.
created by selling each coupon or principal payment from a whole Treasury bond as a separate cash flow.
created by pooling mortgage payments made to the Treasury.
None of the options are correct.
Treasury STRIPS are created by selling each coupon or principal payment from a whole Treasury bond as a separate cash flow.
References
Multiple Choice
Difficulty: 1 Basic
The value of a Treasury bond should:
be equal to the sum of the value of STRIPS created from it.
be less than the sum of the value of STRIPS created from it.
be greater than the sum of the value of STRIPS created from it.
All of the options are correct.
None of the options are correct.
The value of a Treasury bond should be equal to the sum of the value of STRIPS created from it.
References
Multiple Choice
Difficulty: 1 Basic
If the value of a Treasury bond was higher than the value of the sum of its parts (STRIPPED cash flows), you could:
profit by buying the stripped cash flows and reconstituting the bond.
not profit by buying the stripped cash flows and reconstituting the bond.
profit by buying the bond and creating STRIPS.
not profit by buying the stripped cash flows and reconstituting the bond and profit by buying the bond and creating STRIPS.
None of the options are correct.
Only buying STRIPS and reconstituting the bond would be profitable.
References
Multiple Choice
Difficulty: 2 Intermediate
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If the value of a Treasury bond was lower than the value of the sum of its parts (STRIPPED cash flows), you could:
profit by buying the stripped cash flows and reconstituting the bond.
not by buying the bond and creating STRIPS.
profit by buying the bond and creating STRIPS.
profit by buying the stripped cash flows and reconstituting the bond and profit by buying the bond and creating STRIPS.
None of the options are correct.
Buying and stripping the bond would be profitable. So you could profit by buying the stripped cash flows and reconstituting the bond and profit by buying the bond and creating STRIPS.
References
Multiple Choice
Difficulty: 2 Intermediate
If the value of a Treasury bond was lower than the value of the sum of its parts (STRIPPED cash flows),
arbitrage would probably occur.
arbitrage would probably not occur.
the FED would adjust interest rates.
All of the options are correct.
None of the options are correct.
If the value of a Treasury bond was lower than the value of the sum of its parts (STRIPPED cash flows) arbitrage would probably occur.
References
Multiple Choice
Difficulty: 2 Intermediate
If the value of a Treasury bond was higher than the value of the sum of its parts (STRIPPED cash flows),
arbitrage would probably occur.
arbitrage would probably not occur.
the FED would adjust interest rates.
All of the options are correct.
None of the options are correct.
If the value of a Treasury bond was higher than the value of the sum of its parts (STRIPPED cash flows) arbitrage would probably occur.
References
Multiple Choice
Difficulty: 2 Intermediate
Bond stripping and bond reconstitution offer opportunities for __________, which can occur if the __________ is violated.
arbitrage; law of one price
arbitrage; restrictive covenants
huge losses; law of one price
huge losses; restrictive covenants
None of the options are correct.
Bond stripping and bond reconstitution offer opportunities for arbitrage, which can occur if the law of one price is violated.
References
Multiple Choice
Difficulty: 2 Intermediate
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__________ can occur if __________.
Arbitrage; the law of one price is not violated
Arbitrage; the law of one price is mandated
Low-risk economic profit; the law of one price is not violated
High-risk economic profit; the law of one price is violated
Arbitrage and low-risk economic profit; the law of one price is violated
Arbitrage (also known as riskless economic profit) can occur if the law of one price is violated.
References
Multiple Choice
Difficulty: 2 Intermediate
The yield curve shows at any point in time:
the relationship between the yield on a bond and the duration of the bond.
the relationship between the coupon rate on a bond and time to maturity of the bond.
the relationship between yield on a bond and the time to maturity on the bond.
All of the options are correct.
None of the options are correct.
The yield curve shows the relationship between yield on a bond and the time to maturity on the bond.
References
Multiple Choice
Difficulty: 1 Basic
An inverted yield curve implies that:
long-term interest rates are lower than short-term interest rates.
long-term interest rates are higher than short-term interest rates.
long-term interest rates are the same as short-term interest rates.
intermediate-term interest rates are higher than either short- or long-term interest rates.
None of the options are correct.
The inverted, or downward sloping, yield curve is one in which short-term rates are higher than long-term rates. The inverted yield curve has been observed frequently, although not as frequently as the upward sloping, or normal,
yield curve.
References
Multiple Choice
Difficulty: 1 Basic
An upward sloping yield curve is a(n) __________ yield curve.
normal
humped
inverted
flat
None of the options are correct.
The upward sloping yield curve is referred to as the normal yield curve, probably because, historically, the upward sloping yield curve is the shape that has been observed most frequently.
References
Multiple Choice
Difficulty: 1 Basic
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According to the expectations hypothesis, an upward-sloping yield curve implies that:
interest rates are expected to remain stable in the future.
interest rates are expected to decline in the future.
interest rates are expected to increase in the future.
interest rates are expected to decline first, then increase.
interest rates are expected to increase first, then decrease.
An upward sloping yield curve is based on the expectation that short-term interest rates will increase.
References
Multiple Choice
Difficulty: 1 Basic
Which of the following are possible explanations for the term structure of interest rates?
The expectations theory, only
The liquidity preference theory, only
Modern portfolio theory, only
The expectations theory and the liquidity preference theory
None of the options are correct.
The expectations theory and the liquidity preference theory are theories that have been proposed to explain the term structure.
References
Multiple Choice
Difficulty: 1 Basic
The expectations theory of the term structure of interest rates states that:
forward rates are determined by investors' expectations of future interest rates.
forward rates exceed the expected future interest rates.
yields on long- and short-maturity bonds are determined by the supply and demand for the securities.
All of the options are correct.
None of the options are correct.
The forward rate equals the market consensus expectation of future short interest rates.
References
Multiple Choice
Difficulty: 1 Basic
Suppose that all investors expect that interest rates for the 4 years will be as follows:
Year
Forward Interest Rate
0
4%
(today)
1
5%
2
6%
3
7%
What is the price of a 3-year zero-coupon bond with a par value of $1,000?
$896.83
$863.92
$772.18
$765.55
None of the options are correct.
$1,000 ÷ (1.04 × 1.05 × 1.06) = $863.92
References
Multiple Choice
Difficulty: 2 Intermediate
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Suppose that all investors expect that interest rates for the 4 years will be as follows:
Year
Forward Interest Rate
0
4%
(today)
1
5%
2
6%
3
7%
If you have just purchased a 4-year zero-coupon bond, what would be the expected rate of return on your investment in the first year if the implied forward rates stay the same? (Par value of the bond = $1,000)
4%
5%
6%
7%
None of the options are correct.
The forward interest rate given for the first year of the investment is given as 4% (see table above).
References
Multiple Choice
Difficulty: 2 Intermediate
Suppose that all investors expect that interest rates for the 4 years will be as follows:
Year
Forward Interest Rate
0
4%
(today)
1
5%
2
6%
3
7%
What is the price of a 2-year maturity bond with a 10% coupon rate paid annually? (Par value = $1,000)
Note: Do not round your intermediate calculations.
$1,092
$1,054
$986
$1,103
None of the options are correct.
[1.04 × 1.05]
½
−
1 = 4.5%
n
= 2, I
/ Y
= 4.5, PV
= ?, PMT
= 100, FV
= 1000 →
PV
= $1,103.
References
Multiple Choice
Difficulty: 2 Intermediate
Suppose that all investors expect that interest rates for the 4 years will be as follows:
Year
Forward Interest Rate
0
4%
(today)
1
5%
2
6%
3
7%
What is the yield to maturity of a 3-year zero-coupon bond?
9.00%
7.00%
5.00%
4.00%
None of the options are correct.
[1.04 × 1.05 × 1.06]
⅓
−
1 = 5%
References
Multiple Choice
Difficulty: 2 Intermediate
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The following is a list of prices for zero-coupon bonds with different maturities and par values of $1,000.
Maturity (Years)
Price
1
$ 943.40
2
881.68
3
808.88
4
742.09
According to the expectations theory, what is the expected forward rate in the third year?
7.00%
7.33%
9.00%
11.19%
None of the options are correct.
($881.68 ÷ $808.88) −
1 = 9%
References
Multiple Choice
Difficulty: 2 Intermediate
The following is a list of prices for zero-coupon bonds with different maturities and par values of $1,000.
Maturity (Years)
Price
1
$ 943.40
2
881.68
3
808.88
4
742.09
What is the yield to maturity on a 3-year zero-coupon bond?
6.37%
9.00%
7.33%
10.00%
None of the options are correct.
($1,000 ÷ $808.81)
⅓
−
1 = 7.33%
References
Multiple Choice
Difficulty: 2 Intermediate
The following is a list of prices for zero-coupon bonds with different maturities and par values of $1,000.
Maturity (Years)
Price
1
$ 943.40
2
881.68
3
808.88
4
742.09
What is the price of a 4-year maturity bond with a 12% coupon rate paid annually?
Note: Do not round your intermediate calculations.
$742.09
$1,222.09
$1,000.00
$1,141.84
None of the options are correct.
($1,000 ÷ $742.09)
¼
−
1 = 7.74%
n
= 4, I
/ Y
= 7.74, PV
= ?, PMT
= 120, FV
= 1,000 →
PV
= $1,141.84
References
Multiple Choice
Difficulty: 3 Challenge
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An upward-sloping yield curve:
may be an indication that interest rates are expected to increase, only.
may incorporate a liquidity premium, only.
may reflect the confounding of the liquidity premium with interest rate expectations.
implies an impending recession.
None of the options are correct.
One of the problems of the most commonly used explanation of term structure, the expectations hypothesis, is that it is difficult to separate out the liquidity premium from interest rate expectations.
References
Multiple Choice
Difficulty: 1 Basic
The "break-even" interest rate for year n
that equates the return on an n
-period zero-coupon bond to that of an n
−
1 period zero-coupon bond rolled over into a one-year bond in year n
is defined as:
the forward rate.
the short rate.
the yield to maturity.
the discount rate.
None of the options are correct.
The forward rate for year n
, fn, is the "break-even" interest rate for year n
that equates the return on an n
-period zero-coupon bond to that of an n
−
1 period zero-coupon bond rolled over into a one-year bond in year n
.
References
Multiple Choice
Difficulty: 1 Basic
When computing yield to maturity, the implicit reinvestment assumption is that the interest payments are reinvested at the:
coupon rate.
current yield.
yield to maturity at the time of the investment.
prevailing yield to maturity at the time interest payments are received.
the average yield to maturity throughout the investment period.
In order to earn the yield to maturity quoted at the time of the investment, coupons must be reinvested at that rate.
References
Multiple Choice
Difficulty: 2 Intermediate
Par Value
$ 1,000
Time to Maturity
20
Years
Coupon
10%
(paid annually)
Current price
$ 850
Yield to Maturity
12%
Given the bond described, if interest were paid semi-annually (rather than annually), and the bond continued to be priced at $850, the resulting effective annual yield to maturity would be:
less than 12%.
more than 12%.
12%.
Cannot be determined.
None of the options are correct.
FV
= 1000, PV
= 850, PMT
= 50, n
= 40, i
= 5.9964 (semi-annual); (1.059964)
2
−
1 = 12.35%.
References
Multiple Choice
Difficulty: 2 Intermediate
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Forward rates __________ future short rates because __________.
are equal to; they are both extracted from yields to maturity
are equal to; they are perfect forecasts
differ from; they are imperfect forecasts
differ from; forward rates are estimated from dealer quotes while future short rates are extracted from yields to maturity
are equal to; although they are estimated from different sources, they both are used by traders to make purchase decisions
Forward rates are the estimates of future short rates extracted from yields to maturity, but they are not perfect forecasts because the future cannot be predicted with certainty; therefore they will usually differ.
References
Multiple Choice
Difficulty: 1 Basic
The pure yield curve can be estimated:
by using zero-coupon Treasuries, only.
by using stripped Treasuries if each coupon is treated as a separate "zero," only.
by using corporate bonds with different risk ratings, only.
by estimating liquidity premiums for different maturities, only.
by using zero-coupon Treasuries and by using stripped Treasuries if each coupon is treated as a separate "zero."
The pure yield curve is calculated using stripped or zero-coupon Treasuries.
References
Multiple Choice
Difficulty: 2 Intermediate
The on the run yield curve is:
a plot of yield as a function of maturity for zero-coupon bonds.
a plot of yield as a function of maturity for recently-issued coupon bonds trading at or near par.
a plot of yield as a function of maturity for corporate bonds with different risk ratings.
a plot of liquidity premiums for different maturities.
None of the options are correct.
The on the run yield curve is a plot of yield as a function of maturity for recently issued coupon bonds trading at or near par.
References
Multiple Choice
Difficulty: 2 Intermediate
The yield curve:
is a graphical depiction of term structure of interest rates, only.
is usually depicted for U.S. Treasuries to hold risk constant across maturities and yields, only.
is usually depicted for corporate bonds of different ratings, only.
is a graphical depiction of term structure of interest rates and is usually depicted for U.S. Treasuries in order to hold risk constant across maturities and yields.
is a graphical depiction of term structure of interest rates and is usually depicted for corporate bonds of different ratings.
The yield curve (yields versus maturities, all else equal) is depicted for U.S. Treasuries more frequently than for corporate bonds, as the risk is constant across maturities for Treasuries.
References
Multiple Choice
Difficulty: 1 Basic
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Consider the following 1-year forward rates:
Year
1-Year Forward Rate
1
4.5%
2
5.2%
3
5.9%
4
6.3%
5
6.8%
6
7.0%
What should the purchase price of a 2-year zero-coupon bond be if it is purchased at the beginning of year 2 and has face value of $1,000?
$897.61
$888.33
$883.32
$893.36
$871.80
$1,000 ÷ (1.052 × 1.059) = $897.61
References
Multiple Choice
Difficulty: 3 Challenge
Consider the following 1-year forward rates:
Year
1-Year Forward Rate
1
4.5%
2
5.2%
3
5.9%
4
6.3%
5
6.8%
6
7.0%
What would the yield to maturity be on a four-year zero-coupon bond purchased today?
7.80%
6.30%
5.47%
4.25%
None of the options are correct.
[1.045 × 1.052 × 1.059 × 1.063]
¼
− 1 = 5.47%
References
Multiple Choice
Difficulty: 2 Intermediate
Year
1-Year Forward Rate
1
4.5%
2
5.2%
3
5.9%
4
6.3%
5
6.8%
6
7.0%
Calculate the price at the beginning of year 1 of a 10% annual coupon bond with face value $1,000 and 5 years to maturity.
Note: Do not round your intermediate calculations.
$1,195
$1,181
$1,175
$1,162
$1,151
[1.045 × 1.052 × 1.059 × 1.063 × 1.068]
− 1 = 5.74% n
= 5, I
/ Y
= 5.74, P
/ Y
= 1, PV
= ?, PMT
= 100, FV
= 1000 →
PV = $1,181
References
Multiple Choice
Difficulty: 3 Challenge
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Given the yield on a 3-year zero-coupon bond is 8.2% and forward rates of 6.3% in year 1 and 7.1% in year 2, what must be the forward rate in year 3?
11.84%
11.27%
10.95%
10.87%
None of the options are correct.
f
3
= 1.082
3
÷ (1.063 × 1.071) − 1 = 11.27%
References
Multiple Choice
Difficulty: 2 Intermediate
An inverted yield curve is one:
with a hump in the middle.
constructed by using convertible bonds.
that is relatively flat.
that plots the inverse relationship between bond prices and bond yields.
that slopes downward.
An inverted yield curve occurs when short-term rates are higher than long-term rates.
References
Multiple Choice
Difficulty: 1 Basic
Investors can use publicly available financial data to determine which of the following?
1. The shape of the yield curve
2. Expected future short-term rates (if liquidity premiums are ignored)
3. The direction the Dow indexes are heading
4. The actions to be taken by the Federal Reserve
1 and 2
1 and 3
1, 2, and 3
1, 3, and 4
1, 2, 3, and 4
Only the shape of the yield curve and future inferred rates can be determined. The movement of the Dow Indexes and Federal Reserve policy are influenced by term structure but are determined by many other variables also.
References
Multiple Choice
Difficulty: 2 Intermediate
Which of the following combinations will result in a sharply-increasing yield curve?
Increasing future expected short rates and increasing liquidity premiums
Decreasing future expected short rates and increasing liquidity premiums
Increasing future expected short rates and decreasing liquidity premiums
Increasing future expected short rates and constant liquidity premiums
Constant future expected short rates and increasing liquidity premiums
Both of the forces will act to increase the slope of the yield curve.
References
Multiple Choice
Difficulty: 2 Intermediate
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The yield curve is a component of:
the Dow Jones Industrial Average.
the consumer price index.
the index of leading economic indicators.
the producer price index.
the inflation index.
Since the yield curve is often used to forecast the business cycle, it is used as one of the leading economic indicators.
References
Multiple Choice
Difficulty: 1 Basic
The most recently issued Treasury securities are called:
on the run.
off the run.
on the market.
off the market.
None of the options are correct.
The most recently issued Treasury securities are called on the run.
References
Multiple Choice
Difficulty: 1 Basic
Suppose that all investors expect that interest rates for the 4 years will be as follows:
Year
Forward Interest Rate
0
(today) 3%
1
4%
2
5%
3
6%
What is the price of 3-year zero-coupon bond with a par value of $1,000?
$889.08
$816.58
$772.18
$765.55
None of the options are correct.
$1,000 ÷ (1.03 × 1.04 × 1.05) = $889.08
References
Multiple Choice
Difficulty: 2 Intermediate
Suppose that all investors expect that interest rates for the 4 years will be as follows:
Year
Forward Interest Rate
0
(today) 3%
1
4%
2
5%
3
6%
If you have just purchased a 4-year zero-coupon bond, what would be the expected rate of return on your investment in the first year if the implied forward rates stay the same? (Par value of the bond = $1,000.)
5%
3%
9%
10%
None of the options are correct.
The forward interest rate given for the first year of the investment is given as 3% (see table above).
References
Multiple Choice
Difficulty: 2 Intermediate
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Suppose that all investors expect that interest rates for the 4 years will be as follows:
Year
Forward Interest Rate
0
(today) 3%
1
4%
2
5%
3
6%
What is the price of a 2-year maturity bond with a 5% coupon rate paid annually? (Par value = $1,000.)
Note: Do not round your intermediate calculations.
$1,092.97
$1,054.24
$1,028.52
$1,073.34
None of the options are correct.
[1.03 × 1.04]
½
− 1 = 3.50% n
= 2, I
/ Y
= 3.5, P
/ Y
= 1, PV
= ?, PMT
= 50, FV
= 1,000 →
PV
= $1,028.52
References
Multiple Choice
Difficulty: 2 Intermediate
Suppose that all investors expect that interest rates for the 4 years will be as follows:
Year
Forward Interest Rate
0
(today) 3%
1
4%
2
5%
3
6%
What is the yield to maturity of a 3-year zero-coupon bond?
7.00%
9.00%
6.99%
4.00%
None of the options are correct.
[1.03 × 1.04 × 1.05]
⅓
− 1 = 4%
References
Multiple Choice
Difficulty: 2 Intermediate
The following is a list of prices for zero-coupon bonds with different maturities and par values of $1,000.
Maturity (Years)
Price
1
$ 925.15
2
862.57
3
788.66
4
711.00
According to the expectations theory, what is the expected forward rate in the third year?
7.23%
9.37%
9.00%
10.9%
None of the options are correct.
($862.57 ÷ $788.66)
1/1
− 1 = 9.37%
References
Multiple Choice
Difficulty: 2 Intermediate
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The following is a list of prices for zero-coupon bonds with different maturities and par values of $1,000.
Maturity (Years)
Price
1
$ 925.15
2
862.57
3
788.66
4
711.00
What is the yield to maturity on a 3-year zero-coupon bond?
6.37%
9.00%
7.33%
8.24%
None of the options are correct.
($1,000 ÷ $788.66)
⅓
− 1 = 8.24%
References
Multiple Choice
Difficulty: 2 Intermediate
The following is a list of prices for zero-coupon bonds with different maturities and par values of $1,000.
Maturity (Years)
Price
1
$ 925.15
2
862.57
3
788.66
4
711.00
What is the price of a 4-year maturity bond with a 10% coupon rate paid annually?
Note: Do not round your intermediate calculations.
$742.09
$1,222.09
$1,035.68
$1,141.84
None of the options are correct.
($1,000 ÷ $711.00)
¼
− 1 = 8.9%
n
= 4, I
/ Y
= 8.9, P
/ Y
= 1, PV
= ?, PMT
= 100, FV
= 1000 →
PV
= $1,035.68
References
Multiple Choice
Difficulty: 3 Challenge
The following is a list of prices for zero-coupon bonds with different maturities and par values of $1,000.
Maturity (Years)
Price
1
$ 925.15
2
862.57
3
788.66
4
711.00
You have purchased a 4-year maturity bond with a 9% coupon rate paid annually. The bond has a par value of $1,000. What would the price of the bond be one year from now if the implied forward rates stay the same?
Note: Do not round your intermediate calculations.
$995.63
$1,108.88
$1,000.00
$1,042.78
None of the options are correct.
($925.16 ÷ $711.00)
⅓
− 1 = 9.17%
n
= 3, I
/ Y
= 9.17, P
/ Y
= 1, PV
= ?, PMT
= 90, FV
= 1000 →
PV
= $995.63
References
Multiple Choice
Difficulty: 3 Challenge
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Par Value
$ 1,000
Time to Maturity
18
Years
Coupon
9%
(paid annually)
Current price
$ 917.99
Yield to Maturity
12%
Given the bond described above, if interest were paid semi-annually (rather than annually) and the bond continued to be priced at $917.99, the resulting effective annual yield to maturity would be:
less than 10%.
more than 10%.
10%.
Cannot be determined.
None of the options are correct.
FV
= 1,000, PV
= 917.99, PMT
= 45, n
= 36, i
= 4.995325 (semi-annual); (1.04995325)
2
− 1 = 10.24%.
References
Multiple Choice
Difficulty: 2 Intermediate
Year
1-Year Forward Rate
1
5%
2
5.5%
3
6.0%
4
6.5%
5
7.0%
What should the purchase price of a 2-year zero-coupon bond be if it is purchased at the beginning of year 2 and has face value of $1,000?
$877.54
$888.33
$883.32
$894.21
$871.80
$1,000 ÷ (1.055 × 1.06) = $894.21
References
Multiple Choice
Difficulty: 3 Challenge
Year
1-Year Forward Rate
1
5%
2
5.5%
3
6.0%
4
6.5%
5
7.0%
What would the yield to maturity be on a four-year zero-coupon bond purchased today?
5.75%
6.30%
5.65%
5.25%
None of the options are correct.
[1.05 × 1.055 × 1.06 × 1.065]
¼
− 1 = 5.75%
References
Multiple Choice
Difficulty: 2 Intermediate
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Year
1-Year Forward Rate
1
5%
2
5.5%
3
6.0%
4
6.5%
5
7.0%
Calculate the price at the beginning of year 1 of an 8% annual coupon bond with face value $1,000 and 5 years to maturity.
$1,105.47
$1,131.91
$1,084.35
$1,150.01
$719.75
[1.05 × 1.055 × 1.06 × 1.065 × 1.07]
− 1 = 6%
n
= 5, I
/ Y
= 6, P
/ Y
= 1, PV
= ?, PMT
= 80, FV
= 1000 →
PV
= $1,084.35
References
Multiple Choice
Difficulty: 3 Challenge
Given the yield on a 3-year zero-coupon bond is 7% and forward rates of 6% in year 1 and 6.5% in year 2, what must be the forward rate in year 3?
7.2%
8.6%
8.5%
6.9%
None of the options are correct.
f
3
= (1.07)
3
÷ (1.06 × 1.065) − 1 = 8.5%
References
Multiple Choice
Difficulty: 2 Intermediate
Year
1-Year Forward Rate
1
4.6%
2
4.9%
3
5.2%
4
5.5%
5
6.8%
What should the purchase price of a 1-year zero-coupon bond be if it is purchased today and has face value of $1,000?
$966.37
$912.87
$950.21
$956.02
$945.51
$1,000 ÷ 1.046 = $956.02
References
Multiple Choice
Difficulty: 2 Intermediate
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Year
1-Year Forward Rate
1
4.6%
2
4.9%
3
5.2%
4
5.5%
5
6.8%
What should the purchase price of a 2-year zero-coupon bond be if it is purchased today and has face value of $1,000?
$966.87
$911.37
$950.21
$956.02
$945.51
$1,000 ÷ (1.046 × 1.049) = $911.37
References
Multiple Choice
Difficulty: 2 Intermediate
Year
1-Year Forward Rate
1
4.6%
2
4.9%
3
5.2%
4
5.5%
5
6.8%
What should the purchase price of a 3-year zero-coupon bond be if it is purchased today and has face value of $1,000?
$887.42
$871.12
$879.54
$856.02
$866.32
$1,000 ÷ (1.046 × 1.049 × 1.052) = $866.32
References
Multiple Choice
Difficulty: 2 Intermediate
Year
1-Year Forward Rate
1
4.6%
2
4.9%
3
5.2%
4
5.5%
5
6.8%
What should the purchase price of a 4-year zero-coupon bond be if it is purchased today and has face value of $1,000?
$887.42
$821.15
$879.54
$856.02
$866.32
$1,000 ÷ (1.046 × 1.049 × 1.052 × 1.055) = $821.15
References
Multiple Choice
Difficulty: 2 Intermediate
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Year
1-Year Forward Rate
1
4.6%
2
4.9%
3
5.2%
4
5.5%
5
6.8%
What should the purchase price of a 5-year zero-coupon bond be if it is purchased today and has face value of $1,000?
$768.87
$721.15
$779.54
$756.02
$766.32
$1,000 ÷ (1.046 × 1.049 × 1.052 × 1.055 × 1.068) = $768.87.
References
Multiple Choice
Difficulty: 2 Intermediate
Year
1-Year Forward Rate
1
4.6%
2
4.9%
3
5.2%
4
5.5%
5
6.8%
What is the yield to maturity of a 1-year bond?
4.6%
4.9%
5.2%
5.5%
5.8%
4.6% (given in table).
References
Multiple Choice
Difficulty: 2 Intermediate
Year
1-Year Forward Rate
1
4.6%
2
4.9%
3
5.2%
4
5.5%
5
6.8%
What is the yield to maturity of a 5-year bond?
4.6%
4.9%
5.4%
5.5%
5.8%
[1.046 × 1.049 × 1.052 × 1.055 × 1.068]
− 1 = 5.4%
References
Multiple Choice
Difficulty: 2 Intermediate
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Year
1-Year Forward Rate
1
4.6%
2
4.9%
3
5.2%
4
5.5%
5
6.8%
What is the yield to maturity of a 4-year bond?
4.69%
4.95%
5.01%
5.05%
5.08%
[1.046 × 1.049 × 1.052 × 1.055]
¼
− 1 = 5.05%
References
Multiple Choice
Difficulty: 2 Intermediate
Year
1-Year Forward Rate
1
4.6%
2
4.9%
3
5.2%
4
5.5%
5
6.8%
What is the yield to maturity of a 3-year bond?
4.6%
4.9%
5.2%
5.5%
5.8%
[1.046 × 1.049 × 1.052]
⅓
− 1 = 4.9%
References
Multiple Choice
Difficulty: 2 Intermediate
Year
1-Year Forward Rate
1
4.6%
2
4.9%
3
5.2%
4
5.5%
5
6.8%
What is the yield to maturity of a 2-year bond?
4.5%
4.9%
5.2%
4.7%
5.8%
[1.046 × 1.049]
½
− 1 = 4.7%
References
Multiple Choice
Difficulty: 2 Intermediate
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What theory believes short-term investors dominate the market so that the forward rate will generally exceed the expected short rate?
Liquidity preference theory
Expectations theory
Market segmentation theory
Forward rate theory
Short rate theory
Advocates of the liquidity preference theory of the term structure believe that short-term investors dominate the market so that the forward rate will generally exceed the expected short rate.
References
Multiple Choice
Difficulty: 1 Basic
What theory believes forward rates equals the market consensus of what the future short interest rate will be?
Liquidity preference theory
Expectations theory
Market segmentation theory
Forward rate theory
Short rate theory
A common version states that the forward rate equals the market consensus expectation of the future short interest rate.
References
Multiple Choice
Difficulty: 1 Basic
The graphic representation of the term structure of interest rates is the __________.
forward rate
volatility index
yield curve
expectations table
None of the options are correct.
The yield curve is merely a graph of the yields and maturities found in the term structure.
References
Multiple Choice
Difficulty: 1 Basic
__________ are created from coupon paying treasuries, where the coupon and principal are separated.
Stripped treasuries
Forward rates
A yield curve
Futures contracts
None of the options are correct.
Stripped Treasuries are zero-coupon bonds created by selling each coupon or principal payment from a whole Treasury bond as a separate cash flow.
References
Multiple Choice
Difficulty: 1 Basic
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67.
Award: 10.00 points
The __________ yield curve is created from stripped treasuries.
basic
forward
inverted
pure
None of the options are correct.
The pure yield curve refers to the curve for stripped, or zero-coupon, treasuries.
References
Multiple Choice
Difficulty: 1 Basic
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Related Questions
help me with this practice problem
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What is the shape of the yield curve given the term structure below? What expectations are investors likely to have about future interest rates?
5 yr
7 yr
10 yr
20 yr
1 yr
2 yr
3 yr
Term
4.13
4.93
3.32
3.74
2.38
2.73
1.98
Rate (EAR %)
...
What is the shape of the yield curve given the term structure below? (Select the best choice below.)
A. The yield curve is an inverted yield curve (decreasing).
B. It is hard to tell because we are not given an EAR for every year.
C. The yield curve is a flat yield curve.
D. The yield curve is a normal yield curve (increasing).
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24) What is the shape of the yield curve given in the following term structure? What expectations are investors likely to have about future interest rates?
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4. Given a real rate of interest of 3.2%, an expected inflation premium of 5.1%, and risk premiums for investments A and B of
7.4% and 8.9% respectively, find the following:
a. The risk-free rate of return, r;
b. The required returns for investments A and B
Review Only
Click the icon to see the Worked Solution.
a. The risk-free rate of return is
%. (Round to one decimal place.)
b. The required return for investment A is
%. (Round to one decimal place.)
The required return for investment B is
%. (Round to one decimal place.)
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Suppose that the borrowing rate that your client faces is 8% Assume that the equity market index has an expected return of 12% and
standard deviation of 28%, that ry -
What is the range of risk aversion for which a client will neither borrow nor lend, that is, for which y-1?
Note: Do not round intermediate calculations. Round your answers to 2 decimal places.
y=1 for
SAS
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Which one of the following statements about the term structure of interest rates is true?a. The expectations hypothesis indicates a flat yield curve if anticipated future short-term rates exceed current short-term rates.b. The expectations hypothesis contends that the long-term rate is equal to the anticipated short-term rate.c. The liquidity premium theory indicates that, all else being equal, longer maturities will have lower yields.d. The liquidity preference theory contends that lenders prefer to buy securities at the short end of the yield curve.
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3. Consider the model of Credit Risk and Dilution Costs in Freixas and Rochet 2.5.5 based
on Bolton and Freixas (2000) where firms have to choose between Bond financing, Equity
Issue and Bank debt. Firms live for two periods and in each period will obtain, y, if suc-
cessful and zero if unsuccessful. The probability of success in period 2 is 1 for good firms
and O for bad firms, where each firms knows its own type but lenders cannnot see this type,
where the proportion of good firms in period 2 is v. The probability of success in period 1
is uniformly distributed independently of type over the interval [plow, 1]. This probability is
observable and represents a frim's credit rating. Under bond financing,the firm is liquidated
for value A if unsuccessful in period 1. Under equity issue a share ac 0, 1] of any cash flow
is given to the investors and under bank debt, if the firms defaults in period 1 then bank
will claim all revenues in period 2 at a cost of C for monitoring and…
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D3)
Finance
Suppose Bond A carried a higher yield than comparable Bond B because of investors’ uncertainty about the future of company B. If you were an investment manager who thought the market was overplaying these fears. In particular, if you thought that yields on Bond A would fall by 50 basis points. Which bonds would you buy or sell? Explain in words.
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Please correct answer and don't use hand raiting
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Which of the following statements is CORRECT about the yield curve?
A) The yield curve shows the behaviour of interest rate forecasts. B) When short-term rates are lower than long-term rates, there is a downward-sloping yield curve. C) A downward-sloping yield curve shows that investors demand an additional risk premium for lending money over the long term. D) A downward-sloping yield curve indicates that the market expects a future rise in interest rates.
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What the required return for the market? ? Solve question general Accounting
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4
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A normal yield curve
a.has an upward slope
b.is a sign of a coming recession
c.indicates that the interest rate will decrease in the future
d.All of the above.
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What does WRF = -0.50 mean?
Group of answer choices
The investor can borrow money at the risk-free rate.
The investor can lend money at the current market rate.
The investor can borrow money at the current market rate.
The investor can borrow money at the prime rate of interest.
The investor can lend money at the prime rate of interest.
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If we assume that investor can borrow at risk-free interest rate, then the efficient frontier is
1) AB
2) MV-B
3) Rf-T-A
4) Rf-T-B
5) Rf-T-L
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Q2.a. Consider the following scenario analysis.
Scenario
Probability
Recession
Normal
Boom
0.20
0.60
0.20
iii. Which investment would
Rate of Return
you prefer?
Stocks
-5%
+15
+25<
Bonds
+14%
+84
i. Is it reasonable to assume that Treasury bonds will provide higher returns in
recessions than booms? Explain your argument.<
ii. Calculate the expected rate of return and standard deviation for each
investment?
+4
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Consider the following scenario analysis:
Scenario
Recession
Normal economy
Boom.
Probability
0.20
Stocks
Bonds
0.60
0.20
a. Is it reasonable to assume that Treasury bonds will provide higher returns in recessions than in booms?
b. Calculate the expected rate of return and standard deviation for each investment.
c. Which investment would you prefer?
Expected
Rate of
Return
1.3%
0.8 %
Complete this question by entering your answers in the tabs below.
Required A Required B Required C
Calculate the expected rate of return and standard deviation for each investment.
Note: Do not round intermediate calculations. Enter your answers as a percent rounded to 1 decimal place.
Rate of Return.
Bonds
14%
8%
4%
Standard
Deviation
Stocks
-5%
15%
25%
15.3
Answer is complete but not entirely correct.
%
8.1 %
Dequired A
Required
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What can you tell just by looking at the above yield curve?
Group of answer choices
An expectation of falling interest rates suggests trouble in the economy, a rise in bond prices, and a decline for stocks.
The economy is expected to do well in the short-run.
A correction in bond prices is expected.
Bond prices are expected to decline and so the stock market should do extremely well.
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This is part a) question and it's answer in order to answer part b) question
Question: You hold a consol that pays a coupon C in perpetuity. The current interest rate is i, and the average expectation in the market is that this will remain unchanged. What will be the price of the consol today?
answer : According to the question we need to calculate the current price of the perpetual consol. Perpetual consoles are priced differently because their expected income is spread through an indefinite period. So, perpetual consoles are priced using the current yield.
The current yield is calculated as:- coupon amountMarket price×100coupon amountMarket price×100
After calculating the current yield price is calculated by the above formula where,
i = Current interest rate
y = yield
so, the price of this consol will be
Price = i/y
I please need the solutions for part b)
question b) In the next period however, the interest rate changes unexpectedly to i . What is the new price of the bond? If…
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Related Questions
- help me with this practice problemarrow_forwardWhat is the shape of the yield curve given the term structure below? What expectations are investors likely to have about future interest rates? 5 yr 7 yr 10 yr 20 yr 1 yr 2 yr 3 yr Term 4.13 4.93 3.32 3.74 2.38 2.73 1.98 Rate (EAR %) ... What is the shape of the yield curve given the term structure below? (Select the best choice below.) A. The yield curve is an inverted yield curve (decreasing). B. It is hard to tell because we are not given an EAR for every year. C. The yield curve is a flat yield curve. D. The yield curve is a normal yield curve (increasing).arrow_forward24) What is the shape of the yield curve given in the following term structure? What expectations are investors likely to have about future interest rates?arrow_forward
- 4. Given a real rate of interest of 3.2%, an expected inflation premium of 5.1%, and risk premiums for investments A and B of 7.4% and 8.9% respectively, find the following: a. The risk-free rate of return, r; b. The required returns for investments A and B Review Only Click the icon to see the Worked Solution. a. The risk-free rate of return is %. (Round to one decimal place.) b. The required return for investment A is %. (Round to one decimal place.) The required return for investment B is %. (Round to one decimal place.)arrow_forwardSuppose that the borrowing rate that your client faces is 8% Assume that the equity market index has an expected return of 12% and standard deviation of 28%, that ry - What is the range of risk aversion for which a client will neither borrow nor lend, that is, for which y-1? Note: Do not round intermediate calculations. Round your answers to 2 decimal places. y=1 for SASarrow_forwardWhich one of the following statements about the term structure of interest rates is true?a. The expectations hypothesis indicates a flat yield curve if anticipated future short-term rates exceed current short-term rates.b. The expectations hypothesis contends that the long-term rate is equal to the anticipated short-term rate.c. The liquidity premium theory indicates that, all else being equal, longer maturities will have lower yields.d. The liquidity preference theory contends that lenders prefer to buy securities at the short end of the yield curve.arrow_forward
- 3. Consider the model of Credit Risk and Dilution Costs in Freixas and Rochet 2.5.5 based on Bolton and Freixas (2000) where firms have to choose between Bond financing, Equity Issue and Bank debt. Firms live for two periods and in each period will obtain, y, if suc- cessful and zero if unsuccessful. The probability of success in period 2 is 1 for good firms and O for bad firms, where each firms knows its own type but lenders cannnot see this type, where the proportion of good firms in period 2 is v. The probability of success in period 1 is uniformly distributed independently of type over the interval [plow, 1]. This probability is observable and represents a frim's credit rating. Under bond financing,the firm is liquidated for value A if unsuccessful in period 1. Under equity issue a share ac 0, 1] of any cash flow is given to the investors and under bank debt, if the firms defaults in period 1 then bank will claim all revenues in period 2 at a cost of C for monitoring and…arrow_forwardD3) Finance Suppose Bond A carried a higher yield than comparable Bond B because of investors’ uncertainty about the future of company B. If you were an investment manager who thought the market was overplaying these fears. In particular, if you thought that yields on Bond A would fall by 50 basis points. Which bonds would you buy or sell? Explain in words.arrow_forwardPlease correct answer and don't use hand raitingarrow_forward
- Which of the following statements is CORRECT about the yield curve? A) The yield curve shows the behaviour of interest rate forecasts. B) When short-term rates are lower than long-term rates, there is a downward-sloping yield curve. C) A downward-sloping yield curve shows that investors demand an additional risk premium for lending money over the long term. D) A downward-sloping yield curve indicates that the market expects a future rise in interest rates.arrow_forwardWhat the required return for the market? ? Solve question general Accountingarrow_forward4arrow_forward
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