Solution Manualfor Fundamentalsof Investments Valuation an X X X X X X X
d Management, 10th Edition by Bradford Jordan and
X X X X X X X
ThomasMiller and SteveDolvin X X X X
SOLUTION MANUAL FOR X X
Fundamentals of Investments Valuation and Management, 10th Edition Jordan X X X X X X X X
Chapter 1-21 X
Chapter 1 X
A Brief History of Risk and Return
X X X X X X
Concept Questions X
1. For both risk and return, increasing order is b, c, a, d. On average, the higher the risk of an investment, the hi
X X X X X X X X X X X X X X X X X X X X X X
gher is its expected return.X X X X
2. Since the price didn’t change, the capital gains yield was zero. If the total return was four percent, then the di
X X X X X X X X X X X X X X X X X X X X
vidend yield must be four percent. X X X X X
3. It is impossible to lose more than –
X X X X X X X
100 percent of your investment. Therefore, return distributions are cut off on the lower tail at –
X X X X X X X X X X X X X X X X
100 percent; if returns were truly normally distributed, you could lose much more.
X X X X X X X X X X X X
4. To calculate an arithmetic return, you sum the returns and divide by the number of returns. As such, arithm
X X X X X X X X X X X X X X X X X X
etic returns do not account for the effects of compounding (and, in particular, the effect of volatility). Geo
X X X X X X X X X X X X X X X X X
metric returns do account for the effects of compounding and for changes in the base used for each year’s c
X X X X X X X X X X X X X X X X X X X
alculation of returns. As an investor, the more important return of an asset is the geometric return.
X X X X X X X X X X X X X X X X
5. Blume’s formula uses the arithmetic and geometric returns along with the number of observations to appr
X X X X X X X X X X X X X X X
oximate a holding period return. When predicting a holding period return, the arithmetic return will tend to
X X X X X X X X X X X X X X X X
be too high and the geometric return will tend to be too low. Blume’s formula adjusts these returns for differ
X X X X X X X X X X X X X X X X X X X X
ent holding period expected returns.
X X X X
6. T-
bill rates were highest in the early eighties since inflation at the time was relatively high. As we discuss in o
X X X X X X X X X X X X X X X X X X X X
ur chapter on interest rates, rates on T-
X X X X X X X
bills will almost always be slightly higher than the expected rate of inflation.
X X X X X X X X X X X X
7. Risk premiums are about the same regardless of whether we account for inflation. The reason is that risk pr
X X X X X X X X X X X X X X X X X X
emiums are the difference between two returns, so inflation essentially nets out.
X X X X X X X X X X X
8. Returns, risk premiums, and volatility would all be lower than we estimated because aftertax returns are s
X X X X X X X X X X X X X X X X
maller than pretax returns. X X X
1
,Solution Manualfor Fundamentalsof Investments Valuation an X X X X X X X
d Management, 10th Edition by Bradford Jordan and
X X X X X X X
ThomasMiller and SteveDolvin X X X X
9. We have seen that T-bills barely kept up with inflation before taxes. After taxes, investors in T-
X X X X X X X X X X X X X X X X
bills actually lost ground (assuming anything other than a very low tax rate). Thus, an all T-
X X X X X X X X X X X X X X X X
bill strategy will probably lose money in real dollars for a taxable investor.
X X X X X X X X X X X X
10. It is important not to lose sight of the fact that the results we have discussed cover over 80 years, well beyon
X X X X X X X X X X X X X X X X X X X X X
d the investing lifetime for most of us. There have been extended periods during which small stocks have d
X X X X X X X X X X X X X X X X X X
one terribly. Thus, one reason most investors will choose not to pursue a 100 percent stock (particularly sm
X X X X X X X X X X X X X X X X X
all-
cap stocks) strategy is that many investors have relatively short horizons, and high volatility investments m
X X X X X X X X X X X X X X X
ay be very inappropriate in such cases. There are other reasons, but we will defer discussion of these to late
X X X X X X X X X X X X X X X X X X X
r chapters. X
11.
Solutions to Questions and Problems X X X X
NOTE: All end of chapter problems were solved using a spreadsheet. Many problems require multiple steps. Due t
X X X X X X X X X X X X X X X X X
o space and readability constraints, when these intermediate steps are included in this solutions manual, roundi
X X X X X X X X X X X X X X X
ng may appear to have occurred. However, the final answer for each problem is found without rounding during
X X X X X X X X X X X X X X X X X X
any step in the problem.
X X X X
Core Questions
X
1. Total dollar return = 100($41 – $37 + $.28) = $428.00
X X X X X X X X X X
Whether you choose to sell the stock does not affect the gain or loss for the year; your stock is worth what it
X X X X X X X X X X X X X X X X X X X X X X
would bring if you sold it. Whether you choose to do so or not is irrelevant (ignoring commissions and tax
X X X X X X X X X X X X X X X X X X X X
es).
2. Capital gains yield X X X X X $41 – $37 / $37 .1081, or 10.81% Dividend yield $.28/$37 .0076, or .76%
X X X X X X X X X X X X X X X X X
Total rate of return 10.81% .76% 11.57%
X X X X X X X X X
3. Dollar return = 500($34 – $37 + $.28) = –$1,360
X X X X X X X X X
Capital gains yield $34 – $37 /$37 –.0811, or –8.11%
X X X X X X X X X X X X X X X
Dividend yield $.28/$37 .0076, or .76% Total rate of return = – X X X X X X X X X
X 8.11% + .76% = –7.35% X X X X
4.
a. average return = 6.0%, average risk premium = 2.7% X X X X X X X X
b. average return = 3.3%, average risk premium = 0% X X X X X X X X
c. average return = 12.3%, average risk premium = 9.0% X X X X X X X X
d. average return = 16.3%, average risk premium = 13.0%X X X X X X X X
2
,Solution Manualfor Fundamentalsof Investments Valuation an X X X X X X X
d Management, 10th Edition by Bradford Jordan and
X X X X X X X
ThomasMiller and SteveDolvin X X X X
5. Cherry average return X X 17% 11% – 2% X X 3% 14% /5 X X 8.60% Straw average return
X X X X
16% 18% – 6% X X 1% 22% /5 X X 10.20%
6. Cherry: RA X 8.60%
Var 1/ 4 X .17 – .086 X X X X
2
.11 – .086 X X X X
2
–.02 – .086 X X X X
2
.03 – .086
X X X X
2
.14 – .086
X X X X
2
.0062
1/2
Standard deviation X .00623 X X .0789, or 7.89% X X
Straw: RB X 10.20%
Var 1/ 4 X .16 – .102 X X
2
.18 – .102 X X X X
2
–.06 – .102 X X X X
2
.01 – .102 X X X X
2
.22 – .102 X X X X
2
.01452 X
1/2
Standard deviation X .01452 X X .1205, or 12.05% X X
7. The capital gains yield is
X X X X $59 – $65 /$65 X X X –.0923, or – X X
9.23% (notice the negative sign). With a dividend yield of 1.2 percent, the total return is –8.03%.
X X X X X X X X X X X X X X X X
8. Geometric return X 1 .17 1 .11 1 .02 1 .03 1 .14 (1/5) X
–1 X .0837,
or 8.37%
X
9. Arithmetic return X .21 .12 .07 –.13 – .04 X X X . X X X .0817, or 8.17% X X
(1/6)
Geometric return X 1 .21 1 .12 1 .07 1 – .13
X X 1 – .04
X X 1 .26 – 1
X X
.0730, or 7.30% X X
Intermediate Questions X
10. That’s plus or minus one standard deviation, so about two-
X X X X X X X X X
thirds of the time, or two years out of three. In one year out of three, you will be outside this range, implying that
X X X X X X X X X X X X X X X X X X X X X X X X
you will be below it one year out of six and above it one year out of six.
X X X X X X X X X X X X X X X X X
3
, Solution Manualfor Fundamentalsof Investments Valuation an X X X X X X X
d Management, 10th Edition by Bradford Jordan and
X X X X X X X
ThomasMiller and SteveDolvin X X X X
11. You lose money if you have a negative return. With a 12 percent expected return and a 6 percent standard deviat
X X X X X X X X X X X X X X X X X X X X
ion, a zero return is two standard deviations below the average. The odds of being outside (above or below) two
X X X X X X X X X X X X X X X X X X X X
standard deviations are 5 percent; the odds of being below are half that, or 2.5 percent. (It’s actually 2.28 percen
X X X X X X X X X X X X X X X X X X X
t.) You should expect to lose money only 2.5 years out of every 100. It’s a pretty safe investment.
X X X X X X X X X X X X X X X X X X
12. The average return is 6.0 percent, with a standard deviation of 9.8 percent, so Prob(Return < –
X X X X X X X X X X X X X X X X
3.8 or Return 15.8 )
X X X X 1/3, but we are only interested in one tail; Prob
X X X X X X X X X
Return –3.9 1/ 6 X
, which is half of 1/3 (or about 16%) .
X X X X X X X X X
95%: 6.0 ± 2σ = 6.0 ± 2(9.8) = –13.6% to 25.6%
X X X X X X X X X X X
99%: 6.0 ± 3σ = 6.0 ± 3(9.8) = –23.4% to 35.4%
X X X X X X X X X X X
13. Expected return = 16.4%; σ = 31.2%. Doubling your money is a 100% return, so if the return distribution
X X X X X X X X X X X X X X X X X X
is normal, Z 100 – 16..2 2.68 standard deviations; this is in-
X X X X X X X X X X X X X X
between two and three standard deviations, so the probability is small, somewhere between .5% and 2.5% (wh
X X X X X X X X X X X X X X X X
y?). Referring to the nearest Z table, the actual probability is = 0.369%, or less than every 100 years. Tripling yo
X X X X X X X X X X X X X X X X X X X X
ur money would be Z
X X X X
200 – X
16..2 5.88 standard deviations; this corresponds to a probability of (much) less than 0.01%. (The actual a
X X X X X X X X X X X X X X X X X X X
nswer is less than once every 1 million years, so don’t hold your breath.)
X X X X X X X X X X X X X
14.
Year Common stocks T-bill return Risk premium X X X
1973 –14.69% 7.29% –21.98%
1974 –26.47% 7.99% –34.46%
1975 37.23% 5.87% 31.36%
1796 23.93% 5.07% 18.86%
1977 –7.16% 5.45% –12.61%
sum 12.84% 31.67% –18.83%
a. Annual risk premium = Common stock return – T-bill return (see table above).
X X X X X X X X X X X X
b. Average returns: Common stocks X X X 12.84/5 .0257, or 2.57%; T-bills X X X 31.67/5
.0633 , or 6.33% Risk premium X X X X X –18.83/5 –.0377, or –3.77% X X
c. Common stocks: Var X X 1/ 4[ X –.1469 – .0257 X X X X
2
–.2647 – .0257 X X X X
2
.3723 – .0257 X X
2
.2393 X – .0257 X X X
2
–.0716 – .0257 X X X X
2 X
] .072337
1/2
Standard deviation X 0.072337 X X .2690, or 26.90% X X
T-bills: Var X 1/ 4 X .0729 – .0633 X X X X
2
.0799 – .0633 X X X X
2
.0587 – .0633 X X X X
2
.0507 –.0633 X
.0545 – .0633 X X
4
d Management, 10th Edition by Bradford Jordan and
X X X X X X X
ThomasMiller and SteveDolvin X X X X
SOLUTION MANUAL FOR X X
Fundamentals of Investments Valuation and Management, 10th Edition Jordan X X X X X X X X
Chapter 1-21 X
Chapter 1 X
A Brief History of Risk and Return
X X X X X X
Concept Questions X
1. For both risk and return, increasing order is b, c, a, d. On average, the higher the risk of an investment, the hi
X X X X X X X X X X X X X X X X X X X X X X
gher is its expected return.X X X X
2. Since the price didn’t change, the capital gains yield was zero. If the total return was four percent, then the di
X X X X X X X X X X X X X X X X X X X X
vidend yield must be four percent. X X X X X
3. It is impossible to lose more than –
X X X X X X X
100 percent of your investment. Therefore, return distributions are cut off on the lower tail at –
X X X X X X X X X X X X X X X X
100 percent; if returns were truly normally distributed, you could lose much more.
X X X X X X X X X X X X
4. To calculate an arithmetic return, you sum the returns and divide by the number of returns. As such, arithm
X X X X X X X X X X X X X X X X X X
etic returns do not account for the effects of compounding (and, in particular, the effect of volatility). Geo
X X X X X X X X X X X X X X X X X
metric returns do account for the effects of compounding and for changes in the base used for each year’s c
X X X X X X X X X X X X X X X X X X X
alculation of returns. As an investor, the more important return of an asset is the geometric return.
X X X X X X X X X X X X X X X X
5. Blume’s formula uses the arithmetic and geometric returns along with the number of observations to appr
X X X X X X X X X X X X X X X
oximate a holding period return. When predicting a holding period return, the arithmetic return will tend to
X X X X X X X X X X X X X X X X
be too high and the geometric return will tend to be too low. Blume’s formula adjusts these returns for differ
X X X X X X X X X X X X X X X X X X X X
ent holding period expected returns.
X X X X
6. T-
bill rates were highest in the early eighties since inflation at the time was relatively high. As we discuss in o
X X X X X X X X X X X X X X X X X X X X
ur chapter on interest rates, rates on T-
X X X X X X X
bills will almost always be slightly higher than the expected rate of inflation.
X X X X X X X X X X X X
7. Risk premiums are about the same regardless of whether we account for inflation. The reason is that risk pr
X X X X X X X X X X X X X X X X X X
emiums are the difference between two returns, so inflation essentially nets out.
X X X X X X X X X X X
8. Returns, risk premiums, and volatility would all be lower than we estimated because aftertax returns are s
X X X X X X X X X X X X X X X X
maller than pretax returns. X X X
1
,Solution Manualfor Fundamentalsof Investments Valuation an X X X X X X X
d Management, 10th Edition by Bradford Jordan and
X X X X X X X
ThomasMiller and SteveDolvin X X X X
9. We have seen that T-bills barely kept up with inflation before taxes. After taxes, investors in T-
X X X X X X X X X X X X X X X X
bills actually lost ground (assuming anything other than a very low tax rate). Thus, an all T-
X X X X X X X X X X X X X X X X
bill strategy will probably lose money in real dollars for a taxable investor.
X X X X X X X X X X X X
10. It is important not to lose sight of the fact that the results we have discussed cover over 80 years, well beyon
X X X X X X X X X X X X X X X X X X X X X
d the investing lifetime for most of us. There have been extended periods during which small stocks have d
X X X X X X X X X X X X X X X X X X
one terribly. Thus, one reason most investors will choose not to pursue a 100 percent stock (particularly sm
X X X X X X X X X X X X X X X X X
all-
cap stocks) strategy is that many investors have relatively short horizons, and high volatility investments m
X X X X X X X X X X X X X X X
ay be very inappropriate in such cases. There are other reasons, but we will defer discussion of these to late
X X X X X X X X X X X X X X X X X X X
r chapters. X
11.
Solutions to Questions and Problems X X X X
NOTE: All end of chapter problems were solved using a spreadsheet. Many problems require multiple steps. Due t
X X X X X X X X X X X X X X X X X
o space and readability constraints, when these intermediate steps are included in this solutions manual, roundi
X X X X X X X X X X X X X X X
ng may appear to have occurred. However, the final answer for each problem is found without rounding during
X X X X X X X X X X X X X X X X X X
any step in the problem.
X X X X
Core Questions
X
1. Total dollar return = 100($41 – $37 + $.28) = $428.00
X X X X X X X X X X
Whether you choose to sell the stock does not affect the gain or loss for the year; your stock is worth what it
X X X X X X X X X X X X X X X X X X X X X X
would bring if you sold it. Whether you choose to do so or not is irrelevant (ignoring commissions and tax
X X X X X X X X X X X X X X X X X X X X
es).
2. Capital gains yield X X X X X $41 – $37 / $37 .1081, or 10.81% Dividend yield $.28/$37 .0076, or .76%
X X X X X X X X X X X X X X X X X
Total rate of return 10.81% .76% 11.57%
X X X X X X X X X
3. Dollar return = 500($34 – $37 + $.28) = –$1,360
X X X X X X X X X
Capital gains yield $34 – $37 /$37 –.0811, or –8.11%
X X X X X X X X X X X X X X X
Dividend yield $.28/$37 .0076, or .76% Total rate of return = – X X X X X X X X X
X 8.11% + .76% = –7.35% X X X X
4.
a. average return = 6.0%, average risk premium = 2.7% X X X X X X X X
b. average return = 3.3%, average risk premium = 0% X X X X X X X X
c. average return = 12.3%, average risk premium = 9.0% X X X X X X X X
d. average return = 16.3%, average risk premium = 13.0%X X X X X X X X
2
,Solution Manualfor Fundamentalsof Investments Valuation an X X X X X X X
d Management, 10th Edition by Bradford Jordan and
X X X X X X X
ThomasMiller and SteveDolvin X X X X
5. Cherry average return X X 17% 11% – 2% X X 3% 14% /5 X X 8.60% Straw average return
X X X X
16% 18% – 6% X X 1% 22% /5 X X 10.20%
6. Cherry: RA X 8.60%
Var 1/ 4 X .17 – .086 X X X X
2
.11 – .086 X X X X
2
–.02 – .086 X X X X
2
.03 – .086
X X X X
2
.14 – .086
X X X X
2
.0062
1/2
Standard deviation X .00623 X X .0789, or 7.89% X X
Straw: RB X 10.20%
Var 1/ 4 X .16 – .102 X X
2
.18 – .102 X X X X
2
–.06 – .102 X X X X
2
.01 – .102 X X X X
2
.22 – .102 X X X X
2
.01452 X
1/2
Standard deviation X .01452 X X .1205, or 12.05% X X
7. The capital gains yield is
X X X X $59 – $65 /$65 X X X –.0923, or – X X
9.23% (notice the negative sign). With a dividend yield of 1.2 percent, the total return is –8.03%.
X X X X X X X X X X X X X X X X
8. Geometric return X 1 .17 1 .11 1 .02 1 .03 1 .14 (1/5) X
–1 X .0837,
or 8.37%
X
9. Arithmetic return X .21 .12 .07 –.13 – .04 X X X . X X X .0817, or 8.17% X X
(1/6)
Geometric return X 1 .21 1 .12 1 .07 1 – .13
X X 1 – .04
X X 1 .26 – 1
X X
.0730, or 7.30% X X
Intermediate Questions X
10. That’s plus or minus one standard deviation, so about two-
X X X X X X X X X
thirds of the time, or two years out of three. In one year out of three, you will be outside this range, implying that
X X X X X X X X X X X X X X X X X X X X X X X X
you will be below it one year out of six and above it one year out of six.
X X X X X X X X X X X X X X X X X
3
, Solution Manualfor Fundamentalsof Investments Valuation an X X X X X X X
d Management, 10th Edition by Bradford Jordan and
X X X X X X X
ThomasMiller and SteveDolvin X X X X
11. You lose money if you have a negative return. With a 12 percent expected return and a 6 percent standard deviat
X X X X X X X X X X X X X X X X X X X X
ion, a zero return is two standard deviations below the average. The odds of being outside (above or below) two
X X X X X X X X X X X X X X X X X X X X
standard deviations are 5 percent; the odds of being below are half that, or 2.5 percent. (It’s actually 2.28 percen
X X X X X X X X X X X X X X X X X X X
t.) You should expect to lose money only 2.5 years out of every 100. It’s a pretty safe investment.
X X X X X X X X X X X X X X X X X X
12. The average return is 6.0 percent, with a standard deviation of 9.8 percent, so Prob(Return < –
X X X X X X X X X X X X X X X X
3.8 or Return 15.8 )
X X X X 1/3, but we are only interested in one tail; Prob
X X X X X X X X X
Return –3.9 1/ 6 X
, which is half of 1/3 (or about 16%) .
X X X X X X X X X
95%: 6.0 ± 2σ = 6.0 ± 2(9.8) = –13.6% to 25.6%
X X X X X X X X X X X
99%: 6.0 ± 3σ = 6.0 ± 3(9.8) = –23.4% to 35.4%
X X X X X X X X X X X
13. Expected return = 16.4%; σ = 31.2%. Doubling your money is a 100% return, so if the return distribution
X X X X X X X X X X X X X X X X X X
is normal, Z 100 – 16..2 2.68 standard deviations; this is in-
X X X X X X X X X X X X X X
between two and three standard deviations, so the probability is small, somewhere between .5% and 2.5% (wh
X X X X X X X X X X X X X X X X
y?). Referring to the nearest Z table, the actual probability is = 0.369%, or less than every 100 years. Tripling yo
X X X X X X X X X X X X X X X X X X X X
ur money would be Z
X X X X
200 – X
16..2 5.88 standard deviations; this corresponds to a probability of (much) less than 0.01%. (The actual a
X X X X X X X X X X X X X X X X X X X
nswer is less than once every 1 million years, so don’t hold your breath.)
X X X X X X X X X X X X X
14.
Year Common stocks T-bill return Risk premium X X X
1973 –14.69% 7.29% –21.98%
1974 –26.47% 7.99% –34.46%
1975 37.23% 5.87% 31.36%
1796 23.93% 5.07% 18.86%
1977 –7.16% 5.45% –12.61%
sum 12.84% 31.67% –18.83%
a. Annual risk premium = Common stock return – T-bill return (see table above).
X X X X X X X X X X X X
b. Average returns: Common stocks X X X 12.84/5 .0257, or 2.57%; T-bills X X X 31.67/5
.0633 , or 6.33% Risk premium X X X X X –18.83/5 –.0377, or –3.77% X X
c. Common stocks: Var X X 1/ 4[ X –.1469 – .0257 X X X X
2
–.2647 – .0257 X X X X
2
.3723 – .0257 X X
2
.2393 X – .0257 X X X
2
–.0716 – .0257 X X X X
2 X
] .072337
1/2
Standard deviation X 0.072337 X X .2690, or 26.90% X X
T-bills: Var X 1/ 4 X .0729 – .0633 X X X X
2
.0799 – .0633 X X X X
2
.0587 – .0633 X X X X
2
.0507 –.0633 X
.0545 – .0633 X X
4
