Solution ManualforFundamentalsofInvestmentsValuation v v v v v v
and Management, 10th Edition by Bradford Jordan and
v v v v v v v v
ThomasMillerandSteveDolvin v v v v
SOLUTION MANUAL FOR v v
Fundamentals of Investments Valuation and Management, 10th Edition Jordan v v v v v v v v
Chapter1-21 v
Chapter1 v
A Brief History of Risk and Return
v v v v v v
Concept Questions v
1. For both risk and return, increasing order is b, c, a, d. On average, the higher the risk of an investment, the
v v v v v v v v v v v v v v v v v v v v v
higher is its expected return.
v v v v v
2. Since the price didn’t change, the capital gains yield was zero. If the total return was four percent, then the
v v v v v v v v v v v v v v v v v v v
dividend yield must be four percent.
v v v v v v
3. It is impossible to lose more than –100 percent of your investment. Therefore, return distributions are cut
v v v v v v v v v v v v v v v v
off on thelower tail at –100 percent; if returns weretruly normally distributed, you could lose much more.
v v v v v v v v v v v v v v v v v v v
4. To calculate an arithmetic return, you sum the returns and divide by the number of returns. As such,
v v v v v v v v v v v v v v v v v
arithmetic returns do not account for the effects of compounding (and, in particular, the effect of
v v v v v v v v v v v v v v v v
volatility). Geometric returns do account for the effects of compounding and for changes in the base used
v v v v v v v v v v v v v v v v v
for each year’s calculation of returns. As an investor, the more important return of an asset is the geometric
v v v v v v v v v v v v v v v v v v v
return.
v
5. Blume’s formula uses the arithmetic and geometric returns along with the number of observations to
v v v v v v v v v v v v v v
approximate a holding period return. When predicting a holding period return, the arithmetic return will
v v v v v v v v v v v v v v v
tend to be too high and the geometric return will tend to be too low. Blume’s formula adjusts these returns for
v v v v v v v v v v v v v v v v v v v v v
different holding period expected returns.
v v v v v
6. T-bill rates were highest in the early eighties since inflation at the time was relatively high. As we discuss
v v v v v v v v v v v v v v v v v v
in our chapter on interest rates, rates on T-bills will almost always be slightly higher than the expected rate
v v v v v v v v v v v v v v v v v v v
of inflation.
v v
7. Risk premiums are about the same regardless of whether we account for inflation. The reason is that risk
v v v v v v v v v v v v v v v v v
premiums are the difference between two returns, so inflation essentially nets out.
v v v v v v v v v v v v
8. Returns, risk premiums, and volatility would all be lower than we estimated because aftertax returns are
v v v v v v v v v v v v v v v
smaller than pretax returns.
v v v v
1
,Solution ManualforFundamentalsofInvestmentsValuation v v v v v v
and Management, 10th Edition by Bradford Jordan and
v v v v v v v v
ThomasMillerandSteveDolvin v v v v
9. We have seen that T-bills barely kept up with inflation before taxes. After taxes, investors in T-bills
v v v v v v v v v v v v v v v v
actually lost ground (assuming anything other than a very low tax rate). Thus, an all T-bill strategy will
v v v v v v v v v v v v v v v v v v
probably lose money in real dollars for a taxable investor.
v v v v v v v v v v
10. It is important not to lose sight of the fact that the results we have discussed cover over 80 years, well
v v v v v v v v v v v v v v v v v v v v
beyond the investing lifetime for most of us. There have been extended periods during which small stocks
v v v v v v v v v v v v v v v v v
have done terribly. Thus, one reason most investors will choose not to pursue a 100 percent stock
v v v v v v v v v v v v v v v v v
(particularly small-cap stocks) strategy is that many investors have relatively short horizons, and high
v v v v v v v v v v v v v v
volatility investments may be very inappropriate in such cases. There are other reasons, but we will defer
v v v v v v v v v v v v v v v v v
discussion of these to later chapters.
v v v v v v
11.
Solutions to Questions and Problems
v v v v
NOTE: All end of chapter problems were solvedusinga spreadsheet.Many problems require multiplesteps. Due to
v v v v v v v v v v v v v v v v v
space and readability constraints, when these intermediate steps are included in this solutions manual,
v v v v v v v v v v v v v v
rounding may appear to have occurred. However, the final answer for each problem is found without rounding
v v v v v v v v v v v v v v v v v
during any step in the problem.
v v v v v v
Core Questions
v
1. Total dollar return = 100($41 – $37 + $.28) = $428.00
v v v v v v v v v v
Whether you choose to sell the stock does not affect the gain or loss for the year; your stock is worth what
v v v v v v v v v v v v v v v v v v v v v
it would bring if you sold it. Whether you choose to do so or not is irrelevant (ignoring commissions and
v v v v v v v v v v v v v v v v v v v v
taxes).
v
2. Capital gains yield v v v v v $41 – $37 v v v v / $37 v v v .1081, or 10.81% Dividend yield v v v v v v $.28/$37 v v .0076, or .76% v v
Total rate of return v v v v v 10.81% v v .76% v v 11.57%
3. Dollar return = 500($34 – $37 + $.28) = –$1,360
v v v v v v v v v
Capital gains yield $34 – $37 /$37 –.0811, or –8.11%
v v v v v v v v v v v v v v v
Dividend yield $.28/$37 .0076, or .76% Total rate of return = – v v v v v v v v v
v 8.11% + .76% = –7.35% v v v v
4.
a. average return = 6.0%, average risk premium = 2.7% v v v v v v v v
b. average return = 3.3%, average risk premium = 0% v v v v v v v v
c. average return = 12.3%, average risk premium = 9.0% v v v v v v v v
d. average return = 16.3%, average risk premium = 13.0% v v v v v v v v
2
,Solution ManualforFundamentalsofInvestmentsValuation v v v v v v
and Management, 10th Edition by Bradford Jordan and
v v v v v v v v
ThomasMillerandSteveDolvin v v v v
5. Cherry average return v v 17% 11% – 2% v v 3% 14% /5 v v 8.60% Straw average return v v v v
16% 18% – 6% v v 1% 22% /5 v v 10.20%
6. Cherry: RA v 8.60%
Var 1/ 4 v .17 – .086 v v v v
2
.11 – .086 v v v v
2
–.02 – .086 v v v v
2
.03 – .086
v v v v
2
.14 – .086 v v v v
2
.00623
1/2
Standard deviation v .00623 v v .0789, or 7.89% v v
Straw: RB v 10.20%
Var 1/ 4 v .16 – .102 v v
2
.18 – .102 v v v v
2
–.06 – .102 v v v v
2
.01 – .102 v v v v
2
.22 – .102 v v v v
2
.01452 v
1/2
Standard deviation v .01452 v v .1205, or 12.05% v v
7. The capital gains yield is
v v v v $59 – $65 /$65 v v v –.0923, or –9.23% (notice the negative sign). With a
v v v v v v v v
v dividend yield of 1.2 percent, the total return is –8.03%.
v v v v v v v v v
8. Geometricreturn v 1 .17 1 .11 1 .02 1 .03 1 .14 (1/5) v
–1 v .0837,
or 8.37% v
9. Arithmetic return v .21 .12 .07 –.13 – .04 v v v . v v v .0817, or 8.17% v v
(1/6)
Geometric return v 1 .21 1 .12 1 .07 1 – .13 v v 1 – .04 v v 1 .26 – 1
v v
.0730, or 7.30% v v
Intermediate Questions v
10. That’s plus or minus one standard deviation, so about two-thirds of the time, or two years out of three. In one
v v v v v v v v v v v v v v v v v v v v
year out of three, you will be outside this range, implying that you will be below it one year out of six and above
v v v v v v v v v v v v v v v v v v v v v v v v
it one year out of six.
v v v v v v
3
, Solution ManualforFundamentalsofInvestmentsValuation v v v v v v
and Management, 10th Edition by Bradford Jordan and
v v v v v v v v
ThomasMillerandSteveDolvin v v v v
11. You lose money if you have a negative return. With a 12 percent expected return and a 6 percent standard
v v v v v v v v v v v v v v v v v v v
deviation, a zero return is two standard deviations below the average. The odds of being outside (above or
v v v v v v v v v v v v v v v v v v
below) two standard deviations are 5 percent; the odds of being below are half that, or 2.5 percent. (It’s actually
v v v v v v v v v v v v v v v v v v v v
2.28 percent.) You should expect to lose money only 2.5 years out of every 100. It’s a pretty safe investment.
v v v v v v v v v v v v v v v v v v v v
12. The average return is 6.0 percent, with a standard deviation of 9.8 percent, so Prob(Return < –3.8 or Return 15.8 )
v v v v v v v v v v v v v v v v v v v v
1/3, but we are only interested in one tail; Prob
v v v v v v v v v Return –3.9 1/ 6 v
, which is half of 1/3 (or about 16%) .
v v v v v v v v v
95%: 6.0 ± 2σ = 6.0 ± 2(9.8) = –13.6% to 25.6%
v v v v v v v v v v v
99%: 6.0 ± 3σ = 6.0 ± 3(9.8) = –23.4% to 35.4%
v v v v v v v v v v v
13. Expected return = 16.4%; σ = 31.2%. Doubling your money is a 100% return, so if the return distribution
v v v v v v v v v v v v v v v v v v
is normal, Z 100 – 16..2 2.68 standard deviations; this is in-between two and three standard
v v v v v v v v v v v v v v v v v v
deviations, so the probability is small, somewhere between .5% and 2.5% (why?). Referring to the nearest Z
v v v v v v v v v v v v v v v v v
table, the actual probability is = 0.369%, or less than every 100 years. Tripling your money would be Z
v v v v v v v v v v v v v v v v v v v
200 – 16..2 5.88 standard deviations; this corresponds to a probability of (much) less than 0.01%. (The
v v v v v v v v v v v v v v v v v v
v actual answer is less than once every 1 million years, so don’t hold your breath.)
v v v v v v v v v v v v v v
14.
Year Common stocks T-bill return Risk premium v v v
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).
v v v v v v v v v v v v
b. Average returns: Common stocks 12.84/5 .0257, or 2.57%; T-bills v 31.67/5 v v v v v .0633 ,or 6.33% v v v
v Risk premium v –18.83/5 –.0377, or –3.77% v v
c. Common stocks: Var v v 1/ 4[ v –.1469 – .0257 v v v v
2
–.2647 – .0257 v v v v
2
.3723 – .0257 v v
2
.2393 v – .0257 v v v
2
–.0716 – .0257 v v v v
2 v
] .072337
1/2
Standard deviation v 0.072337 v v .2690, or 26.90% v v
T-bills: Var v 1/ 4 v .0729 – .0633 v v v v
2
.0799 – .0633 v v v v
2
.0587 – .0633 v v v v
2
.0507 –.0633 v
2
.0545 – .0633 v v
4
and Management, 10th Edition by Bradford Jordan and
v v v v v v v v
ThomasMillerandSteveDolvin v v v v
SOLUTION MANUAL FOR v v
Fundamentals of Investments Valuation and Management, 10th Edition Jordan v v v v v v v v
Chapter1-21 v
Chapter1 v
A Brief History of Risk and Return
v v v v v v
Concept Questions v
1. For both risk and return, increasing order is b, c, a, d. On average, the higher the risk of an investment, the
v v v v v v v v v v v v v v v v v v v v v
higher is its expected return.
v v v v v
2. Since the price didn’t change, the capital gains yield was zero. If the total return was four percent, then the
v v v v v v v v v v v v v v v v v v v
dividend yield must be four percent.
v v v v v v
3. It is impossible to lose more than –100 percent of your investment. Therefore, return distributions are cut
v v v v v v v v v v v v v v v v
off on thelower tail at –100 percent; if returns weretruly normally distributed, you could lose much more.
v v v v v v v v v v v v v v v v v v v
4. To calculate an arithmetic return, you sum the returns and divide by the number of returns. As such,
v v v v v v v v v v v v v v v v v
arithmetic returns do not account for the effects of compounding (and, in particular, the effect of
v v v v v v v v v v v v v v v v
volatility). Geometric returns do account for the effects of compounding and for changes in the base used
v v v v v v v v v v v v v v v v v
for each year’s calculation of returns. As an investor, the more important return of an asset is the geometric
v v v v v v v v v v v v v v v v v v v
return.
v
5. Blume’s formula uses the arithmetic and geometric returns along with the number of observations to
v v v v v v v v v v v v v v
approximate a holding period return. When predicting a holding period return, the arithmetic return will
v v v v v v v v v v v v v v v
tend to be too high and the geometric return will tend to be too low. Blume’s formula adjusts these returns for
v v v v v v v v v v v v v v v v v v v v v
different holding period expected returns.
v v v v v
6. T-bill rates were highest in the early eighties since inflation at the time was relatively high. As we discuss
v v v v v v v v v v v v v v v v v v
in our chapter on interest rates, rates on T-bills will almost always be slightly higher than the expected rate
v v v v v v v v v v v v v v v v v v v
of inflation.
v v
7. Risk premiums are about the same regardless of whether we account for inflation. The reason is that risk
v v v v v v v v v v v v v v v v v
premiums are the difference between two returns, so inflation essentially nets out.
v v v v v v v v v v v v
8. Returns, risk premiums, and volatility would all be lower than we estimated because aftertax returns are
v v v v v v v v v v v v v v v
smaller than pretax returns.
v v v v
1
,Solution ManualforFundamentalsofInvestmentsValuation v v v v v v
and Management, 10th Edition by Bradford Jordan and
v v v v v v v v
ThomasMillerandSteveDolvin v v v v
9. We have seen that T-bills barely kept up with inflation before taxes. After taxes, investors in T-bills
v v v v v v v v v v v v v v v v
actually lost ground (assuming anything other than a very low tax rate). Thus, an all T-bill strategy will
v v v v v v v v v v v v v v v v v v
probably lose money in real dollars for a taxable investor.
v v v v v v v v v v
10. It is important not to lose sight of the fact that the results we have discussed cover over 80 years, well
v v v v v v v v v v v v v v v v v v v v
beyond the investing lifetime for most of us. There have been extended periods during which small stocks
v v v v v v v v v v v v v v v v v
have done terribly. Thus, one reason most investors will choose not to pursue a 100 percent stock
v v v v v v v v v v v v v v v v v
(particularly small-cap stocks) strategy is that many investors have relatively short horizons, and high
v v v v v v v v v v v v v v
volatility investments may be very inappropriate in such cases. There are other reasons, but we will defer
v v v v v v v v v v v v v v v v v
discussion of these to later chapters.
v v v v v v
11.
Solutions to Questions and Problems
v v v v
NOTE: All end of chapter problems were solvedusinga spreadsheet.Many problems require multiplesteps. Due to
v v v v v v v v v v v v v v v v v
space and readability constraints, when these intermediate steps are included in this solutions manual,
v v v v v v v v v v v v v v
rounding may appear to have occurred. However, the final answer for each problem is found without rounding
v v v v v v v v v v v v v v v v v
during any step in the problem.
v v v v v v
Core Questions
v
1. Total dollar return = 100($41 – $37 + $.28) = $428.00
v v v v v v v v v v
Whether you choose to sell the stock does not affect the gain or loss for the year; your stock is worth what
v v v v v v v v v v v v v v v v v v v v v
it would bring if you sold it. Whether you choose to do so or not is irrelevant (ignoring commissions and
v v v v v v v v v v v v v v v v v v v v
taxes).
v
2. Capital gains yield v v v v v $41 – $37 v v v v / $37 v v v .1081, or 10.81% Dividend yield v v v v v v $.28/$37 v v .0076, or .76% v v
Total rate of return v v v v v 10.81% v v .76% v v 11.57%
3. Dollar return = 500($34 – $37 + $.28) = –$1,360
v v v v v v v v v
Capital gains yield $34 – $37 /$37 –.0811, or –8.11%
v v v v v v v v v v v v v v v
Dividend yield $.28/$37 .0076, or .76% Total rate of return = – v v v v v v v v v
v 8.11% + .76% = –7.35% v v v v
4.
a. average return = 6.0%, average risk premium = 2.7% v v v v v v v v
b. average return = 3.3%, average risk premium = 0% v v v v v v v v
c. average return = 12.3%, average risk premium = 9.0% v v v v v v v v
d. average return = 16.3%, average risk premium = 13.0% v v v v v v v v
2
,Solution ManualforFundamentalsofInvestmentsValuation v v v v v v
and Management, 10th Edition by Bradford Jordan and
v v v v v v v v
ThomasMillerandSteveDolvin v v v v
5. Cherry average return v v 17% 11% – 2% v v 3% 14% /5 v v 8.60% Straw average return v v v v
16% 18% – 6% v v 1% 22% /5 v v 10.20%
6. Cherry: RA v 8.60%
Var 1/ 4 v .17 – .086 v v v v
2
.11 – .086 v v v v
2
–.02 – .086 v v v v
2
.03 – .086
v v v v
2
.14 – .086 v v v v
2
.00623
1/2
Standard deviation v .00623 v v .0789, or 7.89% v v
Straw: RB v 10.20%
Var 1/ 4 v .16 – .102 v v
2
.18 – .102 v v v v
2
–.06 – .102 v v v v
2
.01 – .102 v v v v
2
.22 – .102 v v v v
2
.01452 v
1/2
Standard deviation v .01452 v v .1205, or 12.05% v v
7. The capital gains yield is
v v v v $59 – $65 /$65 v v v –.0923, or –9.23% (notice the negative sign). With a
v v v v v v v v
v dividend yield of 1.2 percent, the total return is –8.03%.
v v v v v v v v v
8. Geometricreturn v 1 .17 1 .11 1 .02 1 .03 1 .14 (1/5) v
–1 v .0837,
or 8.37% v
9. Arithmetic return v .21 .12 .07 –.13 – .04 v v v . v v v .0817, or 8.17% v v
(1/6)
Geometric return v 1 .21 1 .12 1 .07 1 – .13 v v 1 – .04 v v 1 .26 – 1
v v
.0730, or 7.30% v v
Intermediate Questions v
10. That’s plus or minus one standard deviation, so about two-thirds of the time, or two years out of three. In one
v v v v v v v v v v v v v v v v v v v v
year out of three, you will be outside this range, implying that you will be below it one year out of six and above
v v v v v v v v v v v v v v v v v v v v v v v v
it one year out of six.
v v v v v v
3
, Solution ManualforFundamentalsofInvestmentsValuation v v v v v v
and Management, 10th Edition by Bradford Jordan and
v v v v v v v v
ThomasMillerandSteveDolvin v v v v
11. You lose money if you have a negative return. With a 12 percent expected return and a 6 percent standard
v v v v v v v v v v v v v v v v v v v
deviation, a zero return is two standard deviations below the average. The odds of being outside (above or
v v v v v v v v v v v v v v v v v v
below) two standard deviations are 5 percent; the odds of being below are half that, or 2.5 percent. (It’s actually
v v v v v v v v v v v v v v v v v v v v
2.28 percent.) You should expect to lose money only 2.5 years out of every 100. It’s a pretty safe investment.
v v v v v v v v v v v v v v v v v v v v
12. The average return is 6.0 percent, with a standard deviation of 9.8 percent, so Prob(Return < –3.8 or Return 15.8 )
v v v v v v v v v v v v v v v v v v v v
1/3, but we are only interested in one tail; Prob
v v v v v v v v v Return –3.9 1/ 6 v
, which is half of 1/3 (or about 16%) .
v v v v v v v v v
95%: 6.0 ± 2σ = 6.0 ± 2(9.8) = –13.6% to 25.6%
v v v v v v v v v v v
99%: 6.0 ± 3σ = 6.0 ± 3(9.8) = –23.4% to 35.4%
v v v v v v v v v v v
13. Expected return = 16.4%; σ = 31.2%. Doubling your money is a 100% return, so if the return distribution
v v v v v v v v v v v v v v v v v v
is normal, Z 100 – 16..2 2.68 standard deviations; this is in-between two and three standard
v v v v v v v v v v v v v v v v v v
deviations, so the probability is small, somewhere between .5% and 2.5% (why?). Referring to the nearest Z
v v v v v v v v v v v v v v v v v
table, the actual probability is = 0.369%, or less than every 100 years. Tripling your money would be Z
v v v v v v v v v v v v v v v v v v v
200 – 16..2 5.88 standard deviations; this corresponds to a probability of (much) less than 0.01%. (The
v v v v v v v v v v v v v v v v v v
v actual answer is less than once every 1 million years, so don’t hold your breath.)
v v v v v v v v v v v v v v
14.
Year Common stocks T-bill return Risk premium v v v
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).
v v v v v v v v v v v v
b. Average returns: Common stocks 12.84/5 .0257, or 2.57%; T-bills v 31.67/5 v v v v v .0633 ,or 6.33% v v v
v Risk premium v –18.83/5 –.0377, or –3.77% v v
c. Common stocks: Var v v 1/ 4[ v –.1469 – .0257 v v v v
2
–.2647 – .0257 v v v v
2
.3723 – .0257 v v
2
.2393 v – .0257 v v v
2
–.0716 – .0257 v v v v
2 v
] .072337
1/2
Standard deviation v 0.072337 v v .2690, or 26.90% v v
T-bills: Var v 1/ 4 v .0729 – .0633 v v v v
2
.0799 – .0633 v v v v
2
.0587 – .0633 v v v v
2
.0507 –.0633 v
2
.0545 – .0633 v v
4
