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