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