Solution Manual for Fundamentals of Investments Valuation nn nn nn nn nn nn
and Management, 10th Edition by Bradford Jordan and
nn nn nn nn nn nn nn nn
Thomas Miller and Steve Dolvin
nn nn nn nn nn
SOLUTION MANUAL FOR n n nn
Fundamentals of Investments Valuation and Management, 10th Edition Jordan nn nn nn nn nn nn nn nn
Chapter 1-21 nn
Chapter 1 nn
A Brief History of Risk and Return
nn nn nn nn nn nn
Concept Questions nn
1. For both risk and return, increasing order is b, c, a, d. On average, the higher the risk of an
nn nn nn nn nn nn nn nn nn nn nn nn nn nn nn nn nn nn nn
investment, the higher is its expected return.
nn nn nn nn nn nn nn
2. Since the price didn’t change, the capital gains yield was zero. If the total return was four percent,
nn nn nn nn nn nn nn nn nn nn nn nn nn nn nn nn nn
then the dividend yield must be four percent.
nn nn nn nn nn nn nn nn
3. It is impossible to lose more than –100 percent of your investment. Therefore, return distributions
nn nn nn nn nn nn nn nn nn nn nn nn nn nn
are cut off on the lower tail at –100 percent; if returns were truly normally distributed, you could lose
nn nn nn nn nn nn nn nn nn nn nn nn nn nn nn nn nn nn nn
much more.
nn nn
4. To calculate an arithmetic return, you sum the returns and divide by the number of returns. As
nn nn nn nn nn nn nn nn nn nn nn nn nn nn nn nn
such, arithmetic returns do not account for the effects of compounding (and, in particular, the
nn nn nn nn nn nn nn nn nn nn nn nn nn nn nn
effect of volatility). Geometric returns do account for the effects of compounding and for changes
nn nn nn nn nn nn nn nn nn nn nn nn nn nn nn
in the base used for each year’s calculation of returns. As an investor, the more important return of
nn nn nn nn nn nn nn nn nn nn nn nn nn nn nn nn nn nn
an asset is the geometric return.
nn nn nn nn nn nn
5. Blume’s formula uses the arithmetic and geometric returns along with the number of observations
nn nn nn nn nn nn nn nn nn nn nn nn nn
to approximate a holding period return. When predicting a holding period return, the arithmetic
nn nn nn nn nn nn nn nn nn nn nn nn nn nn
return will tend to be too high and the geometric return will tend to be too low. Blume’s formula
nn nn nn nn nn nn nn nn nn nn nn nn nn nn nn nn nn nn nn
adjusts these returns for different holding period expected returns.
nn nn nn nn nn nn nn nn nn
6. T-bill rates were highest in the early eighties since inflation at the time was relatively high. As we
nn nn nn nn nn nn nn nn nn nn nn nn nn nn nn nn nn
discuss in our chapter on interest rates, rates on T-bills will almost always be slightly higher than
nn nn nn nn nn nn nn nn nn nn nn nn nn nn nn nn nn
the expected rate of inflation.
nn nn nn nn nn
7. Risk premiums are about the same regardless of whether we account for inflation. The reason is
nn nn nn nn nn nn nn nn nn nn nn nn nn nn nn
,Solution Manual for Fundamentals of Investments Valuation
nn nn nn nn nn nn
and Management, 10th Edition by Bradford Jordan and
nn nn nn nn nn nn nn nn
Thomas Miller and Steve Dolvin
nn nn nn nn nn
that risk premiums are the difference between two returns, so inflation essentially nets out.
nn nn nn nn nn nn nn nn nn nn nn nn nn nn
8. Returns, risk premiums, and volatility would all be lower than we estimated because aftertax
nn nn nn nn nn nn nn nn nn nn nn nn nn
returns are smaller than pretax returns.
nn nn nn nn nn nn
1
,Solution Manual for Fundamentals of Investments Valuation nn nn nn nn nn nn
and Management, 10th Edition by Bradford Jordan and
nn nn nn nn nn nn nn nn
Thomas Miller and Steve Dolvin
nn nn nn nn nn
9. We have seen that T-bills barely kept up with inflation before taxes. After taxes, investors in T-
nn nn nn nn nn nn nn nn nn nn nn nn nn nn nn nn
bills actually lost ground (assuming anything other than a very low tax rate). Thus, an all T-bill
nn nn nn nn nn nn nn nn nn nn nn nn nn nn nn nn
strategy will probably lose money in real dollars for a taxable investor.
nn nn nn nn nn nn nn nn nn nn nn nn
10. It is important not to lose sight of the fact that the results we have discussed cover over 80 years,
nn nn nn nn nn nn nn nn nn nn nn nn nn nn nn nn nn nn nn
well beyond the investing lifetime for most of us. There have been extended periods during which
nn nn nn nn nn nn nn nn nn nn nn nn nn nn nn nn
small stocks have done terribly. Thus, one reason most investors will choose not to pursue a 100
nn nn nn nn nn nn nn nn nn nn nn nn nn nn nn nn nn
percent stock (particularly small-cap stocks) strategy is that many investors have relatively short
nn nn nn nn nn nn nn nn nn nn nn nn nn
horizons, and high volatility investments may be very inappropriate in such cases. There are other
nn nn nn nn nn nn nn nn nn nn nn nn nn nn nn
reasons, but we will defer discussion of these to later chapters.
nn nn nn nn nn nn nn nn nn nn nn
11.
Solutions to Questions and Problems
nn nn nn nn
NOTE: All end of chapter problems were solved using a spreadsheet. Many problems require multiple steps.
nn nn nn nn nn nn nn nn nn nn nn nn nn nn nn
Due to space and readability constraints, when these intermediate steps are included in this solutions
nn nn nn nn nn nn nn nn nn nn nn nn nn nn nn
manual, rounding may appear to have occurred. However, the final answer for each problem is found
nn nn nn nn nn nn nn nn nn nn nn nn nn nn nn nn
without rounding during any step in the problem.
nn nn nn nn nn nn nn nn
Core Questions
nn
1. Total dollar return = 100($41 – $37 + $.28) = $428.00
nn nn nn nn nn nn nn nn nn nn
Whether you choose to sell the stock does not affect the gain or loss for the year; your stock is
nn nn nn nn nn nn nn nn nn nn nn nn nn nn nn nn nn nn nn
worth what it would bring if you sold it. Whether you choose to do so or not is irrelevant
nn nn nn nn nn nn nn nn nn nn nn nn nn nn nn nn nn nn nn
(ignoring commissions and taxes).
nn nn nn nn
2. Capital gains yield nn nn nn nn $41 – $37 nn nn n n n / $37nn nn .1081, or 10.81% Dividend yield
nn nn nn nn nn n n nn $.28/$37 n n .0076, or
nn nn
.76%
nn
Total rate of return nn nn nn n n 10.81%
n n n nn .76% n n nn 11.57%
3. Dollar return = 500($34 – $37 + $.28) = –$1,360
nn nn nn nn nn nn nn nn nn
Capital gains yield $34 – $37 /$37 n n –.0811, n n n n n n n n n n n n n n
or –8.11% Dividend yield
n n n n $.28/$37 .0076, or .76% nn nn n n nn n n n n nn nn
nn Total rate of return = – 8.11% + .76% = –7.35%
nn nn nn nn nn nn nn nn nn nn
4.
a. average nn return = 6.0%, average risk premium = 2.7%
nn nn nn nn nn nn nn
b. average nn return = 3.3%, average risk premium = 0%
nn nn nn nn nn nn nn
c. average nn return = 12.3%, average risk premium = 9.0%
nn nn nn nn nn nn nn
d. average nn return = 16.3%, average risk premium = 13.0%
nn nn nn nn nn nn nn
2
, Solution Manual for Fundamentals of Investments Valuation nn nn nn nn nn nn
and Management, 10th Edition by Bradford Jordan and
nn nn nn nn nn nn nn nn
Thomas Miller and Steve Dolvin
nn nn nn nn nn
5. Cherry average return nn nn n n nn 17% n n n n 11% – 2% nn nn n n n n 3% n n n n 14% /5 nn nn 8.60% Straw average nn nn
return
nn
16% n n n n 18% – 6% nn nn nn nn 1% nn nn 22% /5 nn nn 10.20%
6. Cherry: RA nn nn n n 8.60%
2 2 2 2 2
Var nn 1/ 4
n n nn .17 – .086 nn nn
n nn
n n .11 – .086 nn nn
n nn
n n –.02 – .086 nn nn
nn nn
n n .03 – .086 nn nn
nn nn
n n .14 – .086 nn nn
nn nn
n n nn .006
1/2
Standard deviation nn nn nn .00623 nn nn
nn .0789, or 7.89% nn nn
Straw: RB nn nn nn 10.20%
2
Var n n n n 1/ 4 nn .16 – .102 nn nn n
nn nn
n n .18 – .102
n nn nn
2
nn n n –.06 – .102
n nn nn
2
nn n n .01 – .102
n nn nn
2
nn n n .22 – .102
n nn nn
2
.01452
1/2
Standard deviation nn .01452 .1205, or 12.05% nn nn
7. The capital gains yield is
nn nn nn nn $59 – $65 /$65 nn nn n n –.0923, or –9.23% (notice the negative sign). With
nn nn nn nn nn nn nn
nn a dividend yield of 1.2 percent, the total return is –8.03%.
nn nn nn nn nn nn nn nn nn nn
8. Geometric return nn 1 .17 1 .11 1 .02 1 .03 1 .14 (1/5) n n
– 1 .0837,
nn
or 8.37% nn
9. Arithmetic return nn .21 .12 .07 –.13 – .04 .
nn nn nn nn .0817, or 8.17% nn nn
(1/6)
Geometric return nn 1 .21 1 .12 1 .07 1 – .13
nn nn 1 – .04
nn nn 1 .26 –
n 1 n
.0730, or 7.30% nn nn
Intermediate Questions nn
10. That’s plus or minus one standard deviation, so about two-thirds of the time, or two years out of three.
nn nn nn nn nn nn nn nn nn nn nn nn nn nn nn nn nn nn
In one year out of three, you will be outside this range, implying that you will be below it one year
nn nn nn nn nn nn nn nn nn nn nn nn nn nn nn nn nn nn nn nn nn
out of six and above it one year out of six.
nn nn nn nn nn nn nn nn nn nn nn
and Management, 10th Edition by Bradford Jordan and
nn nn nn nn nn nn nn nn
Thomas Miller and Steve Dolvin
nn nn nn nn nn
SOLUTION MANUAL FOR n n nn
Fundamentals of Investments Valuation and Management, 10th Edition Jordan nn nn nn nn nn nn nn nn
Chapter 1-21 nn
Chapter 1 nn
A Brief History of Risk and Return
nn nn nn nn nn nn
Concept Questions nn
1. For both risk and return, increasing order is b, c, a, d. On average, the higher the risk of an
nn nn nn nn nn nn nn nn nn nn nn nn nn nn nn nn nn nn nn
investment, the higher is its expected return.
nn nn nn nn nn nn nn
2. Since the price didn’t change, the capital gains yield was zero. If the total return was four percent,
nn nn nn nn nn nn nn nn nn nn nn nn nn nn nn nn nn
then the dividend yield must be four percent.
nn nn nn nn nn nn nn nn
3. It is impossible to lose more than –100 percent of your investment. Therefore, return distributions
nn nn nn nn nn nn nn nn nn nn nn nn nn nn
are cut off on the lower tail at –100 percent; if returns were truly normally distributed, you could lose
nn nn nn nn nn nn nn nn nn nn nn nn nn nn nn nn nn nn nn
much more.
nn nn
4. To calculate an arithmetic return, you sum the returns and divide by the number of returns. As
nn nn nn nn nn nn nn nn nn nn nn nn nn nn nn nn
such, arithmetic returns do not account for the effects of compounding (and, in particular, the
nn nn nn nn nn nn nn nn nn nn nn nn nn nn nn
effect of volatility). Geometric returns do account for the effects of compounding and for changes
nn nn nn nn nn nn nn nn nn nn nn nn nn nn nn
in the base used for each year’s calculation of returns. As an investor, the more important return of
nn nn nn nn nn nn nn nn nn nn nn nn nn nn nn nn nn nn
an asset is the geometric return.
nn nn nn nn nn nn
5. Blume’s formula uses the arithmetic and geometric returns along with the number of observations
nn nn nn nn nn nn nn nn nn nn nn nn nn
to approximate a holding period return. When predicting a holding period return, the arithmetic
nn nn nn nn nn nn nn nn nn nn nn nn nn nn
return will tend to be too high and the geometric return will tend to be too low. Blume’s formula
nn nn nn nn nn nn nn nn nn nn nn nn nn nn nn nn nn nn nn
adjusts these returns for different holding period expected returns.
nn nn nn nn nn nn nn nn nn
6. T-bill rates were highest in the early eighties since inflation at the time was relatively high. As we
nn nn nn nn nn nn nn nn nn nn nn nn nn nn nn nn nn
discuss in our chapter on interest rates, rates on T-bills will almost always be slightly higher than
nn nn nn nn nn nn nn nn nn nn nn nn nn nn nn nn nn
the expected rate of inflation.
nn nn nn nn nn
7. Risk premiums are about the same regardless of whether we account for inflation. The reason is
nn nn nn nn nn nn nn nn nn nn nn nn nn nn nn
,Solution Manual for Fundamentals of Investments Valuation
nn nn nn nn nn nn
and Management, 10th Edition by Bradford Jordan and
nn nn nn nn nn nn nn nn
Thomas Miller and Steve Dolvin
nn nn nn nn nn
that risk premiums are the difference between two returns, so inflation essentially nets out.
nn nn nn nn nn nn nn nn nn nn nn nn nn nn
8. Returns, risk premiums, and volatility would all be lower than we estimated because aftertax
nn nn nn nn nn nn nn nn nn nn nn nn nn
returns are smaller than pretax returns.
nn nn nn nn nn nn
1
,Solution Manual for Fundamentals of Investments Valuation nn nn nn nn nn nn
and Management, 10th Edition by Bradford Jordan and
nn nn nn nn nn nn nn nn
Thomas Miller and Steve Dolvin
nn nn nn nn nn
9. We have seen that T-bills barely kept up with inflation before taxes. After taxes, investors in T-
nn nn nn nn nn nn nn nn nn nn nn nn nn nn nn nn
bills actually lost ground (assuming anything other than a very low tax rate). Thus, an all T-bill
nn nn nn nn nn nn nn nn nn nn nn nn nn nn nn nn
strategy will probably lose money in real dollars for a taxable investor.
nn nn nn nn nn nn nn nn nn nn nn nn
10. It is important not to lose sight of the fact that the results we have discussed cover over 80 years,
nn nn nn nn nn nn nn nn nn nn nn nn nn nn nn nn nn nn nn
well beyond the investing lifetime for most of us. There have been extended periods during which
nn nn nn nn nn nn nn nn nn nn nn nn nn nn nn nn
small stocks have done terribly. Thus, one reason most investors will choose not to pursue a 100
nn nn nn nn nn nn nn nn nn nn nn nn nn nn nn nn nn
percent stock (particularly small-cap stocks) strategy is that many investors have relatively short
nn nn nn nn nn nn nn nn nn nn nn nn nn
horizons, and high volatility investments may be very inappropriate in such cases. There are other
nn nn nn nn nn nn nn nn nn nn nn nn nn nn nn
reasons, but we will defer discussion of these to later chapters.
nn nn nn nn nn nn nn nn nn nn nn
11.
Solutions to Questions and Problems
nn nn nn nn
NOTE: All end of chapter problems were solved using a spreadsheet. Many problems require multiple steps.
nn nn nn nn nn nn nn nn nn nn nn nn nn nn nn
Due to space and readability constraints, when these intermediate steps are included in this solutions
nn nn nn nn nn nn nn nn nn nn nn nn nn nn nn
manual, rounding may appear to have occurred. However, the final answer for each problem is found
nn nn nn nn nn nn nn nn nn nn nn nn nn nn nn nn
without rounding during any step in the problem.
nn nn nn nn nn nn nn nn
Core Questions
nn
1. Total dollar return = 100($41 – $37 + $.28) = $428.00
nn nn nn nn nn nn nn nn nn nn
Whether you choose to sell the stock does not affect the gain or loss for the year; your stock is
nn nn nn nn nn nn nn nn nn nn nn nn nn nn nn nn nn nn nn
worth what it would bring if you sold it. Whether you choose to do so or not is irrelevant
nn nn nn nn nn nn nn nn nn nn nn nn nn nn nn nn nn nn nn
(ignoring commissions and taxes).
nn nn nn nn
2. Capital gains yield nn nn nn nn $41 – $37 nn nn n n n / $37nn nn .1081, or 10.81% Dividend yield
nn nn nn nn nn n n nn $.28/$37 n n .0076, or
nn nn
.76%
nn
Total rate of return nn nn nn n n 10.81%
n n n nn .76% n n nn 11.57%
3. Dollar return = 500($34 – $37 + $.28) = –$1,360
nn nn nn nn nn nn nn nn nn
Capital gains yield $34 – $37 /$37 n n –.0811, n n n n n n n n n n n n n n
or –8.11% Dividend yield
n n n n $.28/$37 .0076, or .76% nn nn n n nn n n n n nn nn
nn Total rate of return = – 8.11% + .76% = –7.35%
nn nn nn nn nn nn nn nn nn nn
4.
a. average nn return = 6.0%, average risk premium = 2.7%
nn nn nn nn nn nn nn
b. average nn return = 3.3%, average risk premium = 0%
nn nn nn nn nn nn nn
c. average nn return = 12.3%, average risk premium = 9.0%
nn nn nn nn nn nn nn
d. average nn return = 16.3%, average risk premium = 13.0%
nn nn nn nn nn nn nn
2
, Solution Manual for Fundamentals of Investments Valuation nn nn nn nn nn nn
and Management, 10th Edition by Bradford Jordan and
nn nn nn nn nn nn nn nn
Thomas Miller and Steve Dolvin
nn nn nn nn nn
5. Cherry average return nn nn n n nn 17% n n n n 11% – 2% nn nn n n n n 3% n n n n 14% /5 nn nn 8.60% Straw average nn nn
return
nn
16% n n n n 18% – 6% nn nn nn nn 1% nn nn 22% /5 nn nn 10.20%
6. Cherry: RA nn nn n n 8.60%
2 2 2 2 2
Var nn 1/ 4
n n nn .17 – .086 nn nn
n nn
n n .11 – .086 nn nn
n nn
n n –.02 – .086 nn nn
nn nn
n n .03 – .086 nn nn
nn nn
n n .14 – .086 nn nn
nn nn
n n nn .006
1/2
Standard deviation nn nn nn .00623 nn nn
nn .0789, or 7.89% nn nn
Straw: RB nn nn nn 10.20%
2
Var n n n n 1/ 4 nn .16 – .102 nn nn n
nn nn
n n .18 – .102
n nn nn
2
nn n n –.06 – .102
n nn nn
2
nn n n .01 – .102
n nn nn
2
nn n n .22 – .102
n nn nn
2
.01452
1/2
Standard deviation nn .01452 .1205, or 12.05% nn nn
7. The capital gains yield is
nn nn nn nn $59 – $65 /$65 nn nn n n –.0923, or –9.23% (notice the negative sign). With
nn nn nn nn nn nn nn
nn a dividend yield of 1.2 percent, the total return is –8.03%.
nn nn nn nn nn nn nn nn nn nn
8. Geometric return nn 1 .17 1 .11 1 .02 1 .03 1 .14 (1/5) n n
– 1 .0837,
nn
or 8.37% nn
9. Arithmetic return nn .21 .12 .07 –.13 – .04 .
nn nn nn nn .0817, or 8.17% nn nn
(1/6)
Geometric return nn 1 .21 1 .12 1 .07 1 – .13
nn nn 1 – .04
nn nn 1 .26 –
n 1 n
.0730, or 7.30% nn nn
Intermediate Questions nn
10. That’s plus or minus one standard deviation, so about two-thirds of the time, or two years out of three.
nn nn nn nn nn nn nn nn nn nn nn nn nn nn nn nn nn nn
In one year out of three, you will be outside this range, implying that you will be below it one year
nn nn nn nn nn nn nn nn nn nn nn nn nn nn nn nn nn nn nn nn nn
out of six and above it one year out of six.
nn nn nn nn nn nn nn nn nn nn nn
