Solution Manual for Fundamentals of Investments Valuation
FM FM FM FM FM FM F
and Management, 10th Edition by Bradford Jordan and Th
M FM FM FM FM FM FM FM FM
omas Miller and Steve Dolvin
FM FM FM FM
1
,Solution Manual for Fundamentals of Investments Valuation
FM FM FM FM FM FM F
and Management, 10th Edition by Bradford Jordan and Th
M FM FM FM FM FM FM FM FM
omas Miller and Steve Dolvin FM FM FM FM
Chapter 1-21 FM
Chapter 1 FM
A Brief History of Risk and Return
FM FM FM FM FM FM
Concept Questions FM
1. For both risk and return, increasing order is b, c, a, d. On average, the higher the risk of an
FM FM FM FM FM FM FM FM FM FM FM FM FM FM FM FM FM FM FM F
investment, the higher is its expected return.
M FM FM FM FM FM FM
2. Since the price didn’t change, the capital gains yield was zero. If the total return was four pe
FM FM FM FM FM FM FM FM FM FM FM FM FM FM FM FM FM
rcent, then the dividend yield must be four percent.
FM FM FM FM FM FM FM FM
3. It is impossible to lose more than –
FM FM FM FM FM FM FM
100 percent of your investment. Therefore, return distributions are cut off on the lower tail at
FM FM FM FM FM FM FM FM FM FM FM FM FM FM FM F
M–100 percent; if returns were truly normally distributed, you could lose much more.
FM FM FM FM FM FM FM FM FM FM FM FM
4. To calculate an arithmetic return, you sum the returns and divide by the number of returns.
FM FM FM FM FM FM FM FM FM FM FM FM FM FM FM F
MAs such, arithmetic returns do not account for the effects of compounding (and, in particula
FM FM FM FM FM FM FM FM FM FM FM FM FM FM
r, the effect of volatility). Geometric returns do account for the effects of compounding and
FM FM FM FM FM FM FM FM FM FM FM FM FM FM F
Mfor changes in the base used for each year’s calculation of returns. As an investor, the mor
FM FM FM FM FM FM FM FM FM FM FM FM FM FM FM FM
e important return of an asset is the geometric return.
FM FM FM FM FM FM FM FM FM
5. Blume’s formula uses the arithmetic and geometric returns along with the number of observa
FM FM FM FM FM FM FM FM FM FM FM FM FM
tions to approximate a holding period return. When predicting a holding period return, the a
FM FM FM FM FM FM FM FM FM FM FM FM FM FM
rithmetic return will tend to be too high and the geometric return will tend to be too low. Bl
FM FM FM FM FM FM FM FM FM FM FM FM FM FM FM FM FM FM
ume’s formula adjusts these returns for different holding period expected returns.
FM FM FM FM FM FM FM FM FM FM
6. T-
bill rates were highest in the early eighties since inflation at the time was relatively high. A
FM FM FM FM FM FM FM FM FM FM FM FM FM FM FM FM
s we discuss in our chapter on interest rates, rates on T-
FM FM FM FM FM FM FM FM FM FM FM
bills will almost always be slightly higher than the expected rate of inflation.
FM FM FM FM FM FM FM FM FM FM FM FM
7. Risk premiums are about the same regardless of whether we account for inflation. The reaso
FM FM FM FM FM FM FM FM FM FM FM FM FM FM
n is that risk premiums are the difference between two returns, so inflation essentially nets
FM FM FM FM FM FM FM FM FM FM FM FM FM FM FM
out.
8. Returns, risk premiums, and volatility would all be lower than we estimated because aftertax
FM FM FM FM FM FM FM FM FM FM FM FM FM
returns are smaller than pretax returns.
FM FM FM FM FM FM
2
,Solution Manual for Fundamentals of Investments Valuation
FM FM FM FM FM FM F
and Management, 10th Edition by Bradford Jordan and Th
M FM FM FM FM FM FM FM FM
omas Miller and Steve Dolvin FM FM FM FM
9. We have seen that T-
FM FM FM FM
bills barely kept up with inflation before taxes. After taxes, investors in T-
FM FM FM FM FM FM FM FM FM FM FM FM
bills actually lost ground (assuming anything other than a very low tax rate). Thus, an all T-
FM FM FM FM FM FM FM FM FM FM FM FM FM FM FM FM
bill strategy will probably lose money in real dollars for a taxable investor.
FM FM FM FM FM FM FM FM FM FM FM FM
10. It is important not to lose sight of the fact that the results we have discussed cover over 80
FM FM FM FM FM FM FM FM FM FM FM FM FM FM FM FM FM FM
years, well beyond the investing lifetime for most of us. There have been extended periods
FM FM FM FM FM FM FM FM FM FM FM FM FM FM FM F
during which small stocks have done terribly. Thus, one reason most investors will choose
M FM FM FM FM FM FM FM FM FM FM FM FM FM FM
not to pursue a 100 percent stock (particularly small-
FM FM FM FM FM FM FM FM
cap stocks) strategy is that many investors have relatively short horizons, and high volatility i
FM FM FM FM FM FM FM FM FM FM FM FM FM FM
nvestments may be very inappropriate in such cases. There are other reasons, but we will d
FM FM FM FM FM FM FM FM FM FM FM FM FM FM FM
efer discussion of these to later chapters.
FM FM FM FM FM FM
11.
Solutions to Questions and Problems
FM FM FM FM
NOTE: All end of chapter problems were solved using a spreadsheet. Many problems require multip
FM FM FM FM FM FM FM FM FM FM FM FM FM FM
le steps. Due to space and readability constraints, when these intermediate steps are included in
FM FM FM FM FM FM FM FM FM FM FM FM FM FM FM
this solutions manual, rounding may appear to have occurred. However, the final answer for eac
FM FM FM FM FM FM FM FM FM FM FM FM FM FM
h problem is found without rounding during any step in the problem.
FM FM FM FM FM FM FM FM FM FM FM
Core Questions
FM
1. Total dollar return = 100($41 – $37 + $.28) = $428.00
FM FM FM FM FM FM FM FM FM FM
Whether you choose to sell the stock does not affect the gain or loss for the year; your sto
FM FM FM FM FM FM FM FM FM FM FM FM FM FM FM FM FM FM
ck is worth what it would bring if you sold it. Whether you choose to do so or not is irre
FM FM FM FM FM FM FM FM FM FM FM FM FM FM FM FM FM FM FM FM
levant (ignoring commissions and taxes).
FM FM FM FM
2. Capital gains yield FM FM FM FM $41 – $37 FM FM FM F M / $37
FM FM FM .1081, or 10.81% Dividend yield
FM FM FM FM F M FM $.28/$37 F
.0076, or .76%
FM FM FM
Total rate of return FM FM FM FM 10.81%
FM F M FM .76% F M FM 11.57%
3. Dollar return = 500($34 – $37 + $.28) = –$1,360
FM FM FM FM FM FM FM FM FM
Capital gains yield $34 – $37 /$37
F M – F M F M F M F M F M F M F M
.0811, or –8.11% Dividend yield
F M F M$.28/$37 FM FM F M FM F M
.0076, or .76% Total rate of return = – 8.11% + .76% = –
F M FM FM FM FM FM FM FM FM FM FM FM FM FM
7.35%
4.
a. average FMreturn FM = FM 6.0%, average risk premium = 2.7%
FM FM FM FM FM
b. average FMreturn FM = FM 3.3%, average risk premium = 0%
FM FM FM FM FM
c. average FMreturn FM = FM 12.3%, average risk premium = 9.0%
FM FM FM FM FM
d. average FMreturn FM = FM 16.3%, average risk premium = 13.0%
FM FM FM FM FM
3
, Solution Manual for Fundamentals of Investments Valuation
FM FM FM FM FM FM F
and Management, 10th Edition by Bradford Jordan and Th
M FM FM FM FM FM FM FM FM
omas Miller and Steve Dolvin
FM FM FM FM
5. Cherry average return 17%
FM FM FM FM F M F M 11% – 2% FM FM FM F M 3% FM F M 14% /5 FM
8.60% Straw average return
FM FM FM FM FM
16% F M F M 18% – 6% FM FM FM FM 1% FM FM 22% /5 FM FM 10.20%
6. Cherry: RA FM FM FM 8.60%
2 2 2 2
Var FM F M 1/ 4 FM .17 – .086
FM FM
FM FM
F M .11 – .086
FM FM
FM FM
F M –.02 – .086 FM FM
FM FM
F M .03 – .086FM FM
FM FM
F M .14 – .086
FM FM
2
FM FM
F M FM .00623
1/2
Standard deviation FM FM FM .00623 FM FM
FM .0789, or 7.89% FM FM
Straw: RB FM FM FM 10.20%
Var 1/ 4 F M F M FM .16 – .102FM FM FM
FM 2F M
F M FM .18 – .102FM FM
2F M
F M FM –.06 – .102 FM FM
2F M
F M .01 – .102
FM FM FM
2F M
F M
.22 – .102 2
FM FM FM
FM
F M
.01452 FM
1/2
Standard deviation FM FM FM .01452 FM
FM FM
FM .1205, or 12.05%FM FM
7. The capital gains yield is
FM FM FM FM F M $59 – $65 /$65FM FM F M F M –.0923, or – FM FM
9.23% (notice the negative sign). With a dividend yield of 1.2 percent, the total return is –
FM FM FM FM FM FM FM FM FM FM FM FM FM FM FM FM
8.03%.
8. Geometric return FM FM FM 1 FM FM .17 FM FM 1 FM FM .11 FM FM 1 FM FM .02 FM FM 1 FM FM .03 FM FM 1FM FM .14 FM
FM(1/5)F M
–1FM
FM.0837,
or 8.37% FM
9. Arithmetic return FM FM FM .21 FM FM .12 FM FM .07 –.13 – .04
FM FM FM FM FM . FM FM FM .0817, or 8.17%
FM FM
(1/6)
Geometric return FM FM 1 FM FM .21 FM FM 1 FM FM .12 FM FM 1 FM FM .07 FM FM 1 – .13
FM FM 1 – .04
FM FM FM FM 1FM FM .26
–
F 1 M F M
.0730, or 7.30% FM FM
4
FM FM FM FM FM FM F
and Management, 10th Edition by Bradford Jordan and Th
M FM FM FM FM FM FM FM FM
omas Miller and Steve Dolvin
FM FM FM FM
1
,Solution Manual for Fundamentals of Investments Valuation
FM FM FM FM FM FM F
and Management, 10th Edition by Bradford Jordan and Th
M FM FM FM FM FM FM FM FM
omas Miller and Steve Dolvin FM FM FM FM
Chapter 1-21 FM
Chapter 1 FM
A Brief History of Risk and Return
FM FM FM FM FM FM
Concept Questions FM
1. For both risk and return, increasing order is b, c, a, d. On average, the higher the risk of an
FM FM FM FM FM FM FM FM FM FM FM FM FM FM FM FM FM FM FM F
investment, the higher is its expected return.
M FM FM FM FM FM FM
2. Since the price didn’t change, the capital gains yield was zero. If the total return was four pe
FM FM FM FM FM FM FM FM FM FM FM FM FM FM FM FM FM
rcent, then the dividend yield must be four percent.
FM FM FM FM FM FM FM FM
3. It is impossible to lose more than –
FM FM FM FM FM FM FM
100 percent of your investment. Therefore, return distributions are cut off on the lower tail at
FM FM FM FM FM FM FM FM FM FM FM FM FM FM FM F
M–100 percent; if returns were truly normally distributed, you could lose much more.
FM FM FM FM FM FM FM FM FM FM FM FM
4. To calculate an arithmetic return, you sum the returns and divide by the number of returns.
FM FM FM FM FM FM FM FM FM FM FM FM FM FM FM F
MAs such, arithmetic returns do not account for the effects of compounding (and, in particula
FM FM FM FM FM FM FM FM FM FM FM FM FM FM
r, the effect of volatility). Geometric returns do account for the effects of compounding and
FM FM FM FM FM FM FM FM FM FM FM FM FM FM F
Mfor changes in the base used for each year’s calculation of returns. As an investor, the mor
FM FM FM FM FM FM FM FM FM FM FM FM FM FM FM FM
e important return of an asset is the geometric return.
FM FM FM FM FM FM FM FM FM
5. Blume’s formula uses the arithmetic and geometric returns along with the number of observa
FM FM FM FM FM FM FM FM FM FM FM FM FM
tions to approximate a holding period return. When predicting a holding period return, the a
FM FM FM FM FM FM FM FM FM FM FM FM FM FM
rithmetic return will tend to be too high and the geometric return will tend to be too low. Bl
FM FM FM FM FM FM FM FM FM FM FM FM FM FM FM FM FM FM
ume’s formula adjusts these returns for different holding period expected returns.
FM FM FM FM FM FM FM FM FM FM
6. T-
bill rates were highest in the early eighties since inflation at the time was relatively high. A
FM FM FM FM FM FM FM FM FM FM FM FM FM FM FM FM
s we discuss in our chapter on interest rates, rates on T-
FM FM FM FM FM FM FM FM FM FM FM
bills will almost always be slightly higher than the expected rate of inflation.
FM FM FM FM FM FM FM FM FM FM FM FM
7. Risk premiums are about the same regardless of whether we account for inflation. The reaso
FM FM FM FM FM FM FM FM FM FM FM FM FM FM
n is that risk premiums are the difference between two returns, so inflation essentially nets
FM FM FM FM FM FM FM FM FM FM FM FM FM FM FM
out.
8. Returns, risk premiums, and volatility would all be lower than we estimated because aftertax
FM FM FM FM FM FM FM FM FM FM FM FM FM
returns are smaller than pretax returns.
FM FM FM FM FM FM
2
,Solution Manual for Fundamentals of Investments Valuation
FM FM FM FM FM FM F
and Management, 10th Edition by Bradford Jordan and Th
M FM FM FM FM FM FM FM FM
omas Miller and Steve Dolvin FM FM FM FM
9. We have seen that T-
FM FM FM FM
bills barely kept up with inflation before taxes. After taxes, investors in T-
FM FM FM FM FM FM FM FM FM FM FM FM
bills actually lost ground (assuming anything other than a very low tax rate). Thus, an all T-
FM FM FM FM FM FM FM FM FM FM FM FM FM FM FM FM
bill strategy will probably lose money in real dollars for a taxable investor.
FM FM FM FM FM FM FM FM FM FM FM FM
10. It is important not to lose sight of the fact that the results we have discussed cover over 80
FM FM FM FM FM FM FM FM FM FM FM FM FM FM FM FM FM FM
years, well beyond the investing lifetime for most of us. There have been extended periods
FM FM FM FM FM FM FM FM FM FM FM FM FM FM FM F
during which small stocks have done terribly. Thus, one reason most investors will choose
M FM FM FM FM FM FM FM FM FM FM FM FM FM FM
not to pursue a 100 percent stock (particularly small-
FM FM FM FM FM FM FM FM
cap stocks) strategy is that many investors have relatively short horizons, and high volatility i
FM FM FM FM FM FM FM FM FM FM FM FM FM FM
nvestments may be very inappropriate in such cases. There are other reasons, but we will d
FM FM FM FM FM FM FM FM FM FM FM FM FM FM FM
efer discussion of these to later chapters.
FM FM FM FM FM FM
11.
Solutions to Questions and Problems
FM FM FM FM
NOTE: All end of chapter problems were solved using a spreadsheet. Many problems require multip
FM FM FM FM FM FM FM FM FM FM FM FM FM FM
le steps. Due to space and readability constraints, when these intermediate steps are included in
FM FM FM FM FM FM FM FM FM FM FM FM FM FM FM
this solutions manual, rounding may appear to have occurred. However, the final answer for eac
FM FM FM FM FM FM FM FM FM FM FM FM FM FM
h problem is found without rounding during any step in the problem.
FM FM FM FM FM FM FM FM FM FM FM
Core Questions
FM
1. Total dollar return = 100($41 – $37 + $.28) = $428.00
FM FM FM FM FM FM FM FM FM FM
Whether you choose to sell the stock does not affect the gain or loss for the year; your sto
FM FM FM FM FM FM FM FM FM FM FM FM FM FM FM FM FM FM
ck is worth what it would bring if you sold it. Whether you choose to do so or not is irre
FM FM FM FM FM FM FM FM FM FM FM FM FM FM FM FM FM FM FM FM
levant (ignoring commissions and taxes).
FM FM FM FM
2. Capital gains yield FM FM FM FM $41 – $37 FM FM FM F M / $37
FM FM FM .1081, or 10.81% Dividend yield
FM FM FM FM F M FM $.28/$37 F
.0076, or .76%
FM FM FM
Total rate of return FM FM FM FM 10.81%
FM F M FM .76% F M FM 11.57%
3. Dollar return = 500($34 – $37 + $.28) = –$1,360
FM FM FM FM FM FM FM FM FM
Capital gains yield $34 – $37 /$37
F M – F M F M F M F M F M F M F M
.0811, or –8.11% Dividend yield
F M F M$.28/$37 FM FM F M FM F M
.0076, or .76% Total rate of return = – 8.11% + .76% = –
F M FM FM FM FM FM FM FM FM FM FM FM FM FM
7.35%
4.
a. average FMreturn FM = FM 6.0%, average risk premium = 2.7%
FM FM FM FM FM
b. average FMreturn FM = FM 3.3%, average risk premium = 0%
FM FM FM FM FM
c. average FMreturn FM = FM 12.3%, average risk premium = 9.0%
FM FM FM FM FM
d. average FMreturn FM = FM 16.3%, average risk premium = 13.0%
FM FM FM FM FM
3
, Solution Manual for Fundamentals of Investments Valuation
FM FM FM FM FM FM F
and Management, 10th Edition by Bradford Jordan and Th
M FM FM FM FM FM FM FM FM
omas Miller and Steve Dolvin
FM FM FM FM
5. Cherry average return 17%
FM FM FM FM F M F M 11% – 2% FM FM FM F M 3% FM F M 14% /5 FM
8.60% Straw average return
FM FM FM FM FM
16% F M F M 18% – 6% FM FM FM FM 1% FM FM 22% /5 FM FM 10.20%
6. Cherry: RA FM FM FM 8.60%
2 2 2 2
Var FM F M 1/ 4 FM .17 – .086
FM FM
FM FM
F M .11 – .086
FM FM
FM FM
F M –.02 – .086 FM FM
FM FM
F M .03 – .086FM FM
FM FM
F M .14 – .086
FM FM
2
FM FM
F M FM .00623
1/2
Standard deviation FM FM FM .00623 FM FM
FM .0789, or 7.89% FM FM
Straw: RB FM FM FM 10.20%
Var 1/ 4 F M F M FM .16 – .102FM FM FM
FM 2F M
F M FM .18 – .102FM FM
2F M
F M FM –.06 – .102 FM FM
2F M
F M .01 – .102
FM FM FM
2F M
F M
.22 – .102 2
FM FM FM
FM
F M
.01452 FM
1/2
Standard deviation FM FM FM .01452 FM
FM FM
FM .1205, or 12.05%FM FM
7. The capital gains yield is
FM FM FM FM F M $59 – $65 /$65FM FM F M F M –.0923, or – FM FM
9.23% (notice the negative sign). With a dividend yield of 1.2 percent, the total return is –
FM FM FM FM FM FM FM FM FM FM FM FM FM FM FM FM
8.03%.
8. Geometric return FM FM FM 1 FM FM .17 FM FM 1 FM FM .11 FM FM 1 FM FM .02 FM FM 1 FM FM .03 FM FM 1FM FM .14 FM
FM(1/5)F M
–1FM
FM.0837,
or 8.37% FM
9. Arithmetic return FM FM FM .21 FM FM .12 FM FM .07 –.13 – .04
FM FM FM FM FM . FM FM FM .0817, or 8.17%
FM FM
(1/6)
Geometric return FM FM 1 FM FM .21 FM FM 1 FM FM .12 FM FM 1 FM FM .07 FM FM 1 – .13
FM FM 1 – .04
FM FM FM FM 1FM FM .26
–
F 1 M F M
.0730, or 7.30% FM FM
4