1
,SOLUTION MANUAL FOR dt dt
Fundamentals of Investments Valuation and Management, 10th Edition Jordan dt dt dt dt dt dt dt dt
Chapter 1-21 dt
Chapter 1 dt
A Brief History of Risk and Return
dt dt dt dt dt dt
Concept Questions dt
1. For both risk and return, increasing order is b, c, a, d. On average, the higher the risk of an investment, the
dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt
higher is its expected return.
dt dt dt dt dt
2. Since the price didn’t change, the capital gains yield was zero. If the total return was four percent, then th
dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt
e dividend yield must be four percent.
dt dt dt dt dt dt
3. It is impossible to lose more than –
dt dt dt dt dt dt dt
100 percent of your investment. Therefore, return distributions are cut off on the lower tail at –
dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt
100 percent; if returns were truly normally distributed, you could lose much more.
dt dt dt dt dt dt dt dt dt dt dt dt
4. To calculate an arithmetic return, you sum the returns and divide by the number of returns. As such, ari
dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt
thmetic returns do not account for the effects of compounding (and, in particular, the effect of volatility
dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt
). Geometric returns do account for the effects of compounding and for changes in the base used for eac
dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt
h year’s calculation of returns. As an investor, the more important return of an asset is the geometric ret
dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt
urn.
5. Blume’s formula uses the arithmetic and geometric returns along with the number of observations to a
dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt
pproximate a holding period return. When predicting a holding period return, the arithmetic return will
dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt
tend to be too high and the geometric return will tend to be too low. Blume’s formula adjusts these returns
dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt
for different holding period expected returns.
dt dt dt dt dt
6. T-
bill rates were highest in the early eighties since inflation at the time was relatively high. As we discuss
dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt d
in our chapter on interest rates, rates on T-
t dt dt dt dt dt dt dt dt
bills will almost always be slightly higher than the expected rate of inflation.
dt dt dt dt dt dt dt dt dt dt dt dt
7. Risk premiums are about the same regardless of whether we account for inflation. The reason is that ris
dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt
k premiums are the difference between two returns, so inflation essentially nets out.
dt dt dt dt dt dt dt dt dt dt dt dt
8. Returns, risk premiums, and volatility would all be lower than we estimated because aftertax returns ar
dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt
e smaller than pretax returns.
dt dt dt dt
2
,9. We have seen that T-bills barely kept up with inflation before taxes. After taxes, investors in T-
dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt
bills actually lost ground (assuming anything other than a very low tax rate). Thus, an all T-
dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt
bill strategy will probably lose money in real dollars for a taxable investor.
dt dt dt dt dt dt dt dt dt dt dt dt
10. It is important not to lose sight of the fact that the results we have discussed cover over 80 years, well b
dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt
eyond the investing lifetime for most of us. There have been extended periods during which small stoc
dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt
ks have done terribly. Thus, one reason most investors will choose not to pursue a 100 percent stock (p
dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt
articularly small- dt
cap stocks) strategy is that many investors have relatively short horizons, and high volatility investments
dt dt dt dt dt dt dt dt dt dt dt dt dt dt
may be very inappropriate in such cases. There are other reasons, but we will defer discussion of these
dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt
to later chapters. dt dt
11.
Solutions to Questions and Problems dt dt dt dt
NOTE: All end of chapter problems were solved using a spreadsheet. Many problems require multiple steps. Du
dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt
e to space and readability constraints, when these intermediate steps are included in this solutions manual,
dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt
rounding may appear to have occurred. However, the final answer for each problem is found without round
dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt
ing during any step in the problem.
dt dt dt dt dt dt
Core Questions
dt
1. Total dollar return = 100($41 – $37 + $.28) = $428.00
dt dt dt dt dt dt dt dt dt dt
Whether you choose to sell the stock does not affect the gain or loss for the year; your stock is worth w
dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt
hat it would bring if you sold it. Whether you choose to do so or not is irrelevant (ignoring commission
dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt
s and taxes).
dt dt
2. Capital gains yield dt dt d t d t d t $41 – $37 dt dt d t d t / $37dt d t d t .1081, or 10.81% Dividend yield dt dt dt dt d t d t $.28/$37 d t d t .0076, or .76%
dt dt
Total rate of return dt dt dt d t d t 10.81% d t d t .76% d t d t 11.57%
3. Dollar return = 500($34 – $37 + $.28) = –$1,360
dt dt dt dt dt dt dt dt dt
Capital gains yield $34 – $37 /$37 –.0811, or –8.11%
d t d t d t d t d t d t d t d t d t d t d t d t d t d t d t
Dividend yield $.28/$37 .0076, or .76% Total rate of return = –
dt dt dt dt dt dt dt dt dt
dt 8.11% + .76% = –7.35% dt dt dt dt
4.
a. average return = 6.0%, average risk premium = 2.7% dt dt dt dt dt dt dt dt
b. average return = 3.3%, average risk premium = 0% dt dt dt dt dt dt dt dt
c. average return = 12.3%, average risk premium = 9.0% dt dt dt dt dt dt dt dt
d. average return = 16.3%, average risk premium = 13.0% dt dt dt dt dt dt dt dt
3
, 5. Cherry average return dt dt 17% 11% – 2% dt dt 3% 14% /5 d t d t 8.60% Straw average return dt dt dt dt
16% 18% – 6% dt dt 1% 22% d t d t /5 10.20%
6. Cherry: RA dt 8.60%
Var 1/ 4 dt .17 – .086 dt dt d t d t
2
.11 – .086 dt dt d t d t
2
–.02 – .086 dt dt d t d t
2
.03 – .086 dt dt d t d t
2
.14 – .086
dt dt d t d t
2
.0062
1/2
Standard deviation dt .00623 d t d t .0789, or 7.89% dt dt
Straw: RB dt 10.20%
Var 1/ 4 dt .16 – .102 dt dt
2
.18 – .102 dt dt d t d t
2
–.06 – .102 dt dt d t d t
2
.01 – .102 dt dt d t d t
2
.22 – .102 dt dt d t d t
2
.01452 dt
1/2
Standard deviation dt .01452 d t d t .1205, or 12.05% dt dt
7. The capital gains yield is
dt dt dt dt $59 – $65 /$65 dt dt d t –.0923, or – dt dt
9.23% (notice the negative sign). With a dividend yield of 1.2 percent, the total return is –8.03%.
dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt
8. Geometric return dt 1 .17 1 .11 1 .02 1 .03 1 .14 (1/5)d t
– 1 .0837,
dt
or 8.37%
dt
9. Arithmetic return dt .21 .12 .07 –.13 – .04
dt dt dt .26 d t d t /6
dt .0817, or 8.17% dt dt
(1/6)
Geometric return dt 1 .21 1 .12 1 .07 1 – .13
dt dt 1 – .04
dt dt 1 .26 – 1
d t
.0730, or 7.30% dt dt
Intermediate Questions dt
10. That’s plus or minus one standard deviation, so about two-
dt dt dt dt dt dt dt dt dt
thirds of the time, or two years out of three. In one year out of three, you will be outside this range, implying
dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt
that you will be below it one year out of six and above it one year out of six.
dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt
4
,SOLUTION MANUAL FOR dt dt
Fundamentals of Investments Valuation and Management, 10th Edition Jordan dt dt dt dt dt dt dt dt
Chapter 1-21 dt
Chapter 1 dt
A Brief History of Risk and Return
dt dt dt dt dt dt
Concept Questions dt
1. For both risk and return, increasing order is b, c, a, d. On average, the higher the risk of an investment, the
dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt
higher is its expected return.
dt dt dt dt dt
2. Since the price didn’t change, the capital gains yield was zero. If the total return was four percent, then th
dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt
e dividend yield must be four percent.
dt dt dt dt dt dt
3. It is impossible to lose more than –
dt dt dt dt dt dt dt
100 percent of your investment. Therefore, return distributions are cut off on the lower tail at –
dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt
100 percent; if returns were truly normally distributed, you could lose much more.
dt dt dt dt dt dt dt dt dt dt dt dt
4. To calculate an arithmetic return, you sum the returns and divide by the number of returns. As such, ari
dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt
thmetic returns do not account for the effects of compounding (and, in particular, the effect of volatility
dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt
). Geometric returns do account for the effects of compounding and for changes in the base used for eac
dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt
h year’s calculation of returns. As an investor, the more important return of an asset is the geometric ret
dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt
urn.
5. Blume’s formula uses the arithmetic and geometric returns along with the number of observations to a
dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt
pproximate a holding period return. When predicting a holding period return, the arithmetic return will
dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt
tend to be too high and the geometric return will tend to be too low. Blume’s formula adjusts these returns
dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt
for different holding period expected returns.
dt dt dt dt dt
6. T-
bill rates were highest in the early eighties since inflation at the time was relatively high. As we discuss
dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt d
in our chapter on interest rates, rates on T-
t dt dt dt dt dt dt dt dt
bills will almost always be slightly higher than the expected rate of inflation.
dt dt dt dt dt dt dt dt dt dt dt dt
7. Risk premiums are about the same regardless of whether we account for inflation. The reason is that ris
dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt
k premiums are the difference between two returns, so inflation essentially nets out.
dt dt dt dt dt dt dt dt dt dt dt dt
8. Returns, risk premiums, and volatility would all be lower than we estimated because aftertax returns ar
dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt
e smaller than pretax returns.
dt dt dt dt
2
,9. We have seen that T-bills barely kept up with inflation before taxes. After taxes, investors in T-
dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt
bills actually lost ground (assuming anything other than a very low tax rate). Thus, an all T-
dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt
bill strategy will probably lose money in real dollars for a taxable investor.
dt dt dt dt dt dt dt dt dt dt dt dt
10. It is important not to lose sight of the fact that the results we have discussed cover over 80 years, well b
dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt
eyond the investing lifetime for most of us. There have been extended periods during which small stoc
dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt
ks have done terribly. Thus, one reason most investors will choose not to pursue a 100 percent stock (p
dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt
articularly small- dt
cap stocks) strategy is that many investors have relatively short horizons, and high volatility investments
dt dt dt dt dt dt dt dt dt dt dt dt dt dt
may be very inappropriate in such cases. There are other reasons, but we will defer discussion of these
dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt
to later chapters. dt dt
11.
Solutions to Questions and Problems dt dt dt dt
NOTE: All end of chapter problems were solved using a spreadsheet. Many problems require multiple steps. Du
dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt
e to space and readability constraints, when these intermediate steps are included in this solutions manual,
dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt
rounding may appear to have occurred. However, the final answer for each problem is found without round
dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt
ing during any step in the problem.
dt dt dt dt dt dt
Core Questions
dt
1. Total dollar return = 100($41 – $37 + $.28) = $428.00
dt dt dt dt dt dt dt dt dt dt
Whether you choose to sell the stock does not affect the gain or loss for the year; your stock is worth w
dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt
hat it would bring if you sold it. Whether you choose to do so or not is irrelevant (ignoring commission
dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt
s and taxes).
dt dt
2. Capital gains yield dt dt d t d t d t $41 – $37 dt dt d t d t / $37dt d t d t .1081, or 10.81% Dividend yield dt dt dt dt d t d t $.28/$37 d t d t .0076, or .76%
dt dt
Total rate of return dt dt dt d t d t 10.81% d t d t .76% d t d t 11.57%
3. Dollar return = 500($34 – $37 + $.28) = –$1,360
dt dt dt dt dt dt dt dt dt
Capital gains yield $34 – $37 /$37 –.0811, or –8.11%
d t d t d t d t d t d t d t d t d t d t d t d t d t d t d t
Dividend yield $.28/$37 .0076, or .76% Total rate of return = –
dt dt dt dt dt dt dt dt dt
dt 8.11% + .76% = –7.35% dt dt dt dt
4.
a. average return = 6.0%, average risk premium = 2.7% dt dt dt dt dt dt dt dt
b. average return = 3.3%, average risk premium = 0% dt dt dt dt dt dt dt dt
c. average return = 12.3%, average risk premium = 9.0% dt dt dt dt dt dt dt dt
d. average return = 16.3%, average risk premium = 13.0% dt dt dt dt dt dt dt dt
3
, 5. Cherry average return dt dt 17% 11% – 2% dt dt 3% 14% /5 d t d t 8.60% Straw average return dt dt dt dt
16% 18% – 6% dt dt 1% 22% d t d t /5 10.20%
6. Cherry: RA dt 8.60%
Var 1/ 4 dt .17 – .086 dt dt d t d t
2
.11 – .086 dt dt d t d t
2
–.02 – .086 dt dt d t d t
2
.03 – .086 dt dt d t d t
2
.14 – .086
dt dt d t d t
2
.0062
1/2
Standard deviation dt .00623 d t d t .0789, or 7.89% dt dt
Straw: RB dt 10.20%
Var 1/ 4 dt .16 – .102 dt dt
2
.18 – .102 dt dt d t d t
2
–.06 – .102 dt dt d t d t
2
.01 – .102 dt dt d t d t
2
.22 – .102 dt dt d t d t
2
.01452 dt
1/2
Standard deviation dt .01452 d t d t .1205, or 12.05% dt dt
7. The capital gains yield is
dt dt dt dt $59 – $65 /$65 dt dt d t –.0923, or – dt dt
9.23% (notice the negative sign). With a dividend yield of 1.2 percent, the total return is –8.03%.
dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt
8. Geometric return dt 1 .17 1 .11 1 .02 1 .03 1 .14 (1/5)d t
– 1 .0837,
dt
or 8.37%
dt
9. Arithmetic return dt .21 .12 .07 –.13 – .04
dt dt dt .26 d t d t /6
dt .0817, or 8.17% dt dt
(1/6)
Geometric return dt 1 .21 1 .12 1 .07 1 – .13
dt dt 1 – .04
dt dt 1 .26 – 1
d t
.0730, or 7.30% dt dt
Intermediate Questions dt
10. That’s plus or minus one standard deviation, so about two-
dt dt dt dt dt dt dt dt dt
thirds of the time, or two years out of three. In one year out of three, you will be outside this range, implying
dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt
that you will be below it one year out of six and above it one year out of six.
dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt
4
