Solution Manual – Fundamentals of Investments: Valuation and
Management, 9th Edition
Wickyaplus stuvia
,SOLUTION MANUAL FOR x x
Fundamentals of Investments Valuation and Management 9th Edition By x x x x x x x x
Jordan
x
Chapter 1-21 x
Chapter 1 x
A Brief History of Risk and Return
x x x x x x
Concept Questions x
1. For both risk and return, increasing order is b, c, a, d. On average, the higher the risk of an
x x x x x x x x x x x x x x x x x x x
investment, the higher is its expected return.
x x x x x x x
2. Since the price didn’t change, the capital gains yield was zero. If the total return was four percent,
x x x x x x x x x x x x x x x x x
then the dividend yield must be four percent.
x x x x x x x x
3. It is impossible to lose more than –100 percent of your investment. Therefore, return distributions
x x x x x x x x x x x x x x
x are cut off on the lower tail at –100 percent; if returns were truly normally distributed, you could
x x x x x x x x x x x x x x x x x
xlose much more. x x
4. To calculate an arithmetic return, you sum the returns and divide by the number of returns. As such,
x x x x x x x x x x x x x x x x x
arithmetic returns do not account for the effects of compounding (and, in particular, the effect of
x x x x x x x x x x x x x x x x
volatility). Geometric returns do account for the effects of compounding and for changes in the
x x x x x x x x x x x x x x x
base used for each year’s calculation of returns. As an investor, the more important return of an
x x x x x x x x x x x x x x x x x
asset is the geometric return.
x x x x x
5. Blume’s formula uses the arithmetic and geometric returns along with the number of observations to
x x x x x x x x x x x x x x
approximate a holding period return. When predicting a holding period return, the arithmetic return
x x x x x x x x x x x x x x
will tend to be too high and the geometric return will tend to be too low. Blume’s formula adjusts
x x x x x x x x x x x x x x x x x x x
these returns for different holding period expected returns.
x x x x x x x x
6. T-bill rates were highest in the early eighties since inflation at the time was relatively high. As we
x x x x x x x x x x x x x x x x x
discuss in our chapter on interest rates, rates on T-bills will almost always be slightly higher than
x x x x x x x x x x x x x x x x x
the expected rate of inflation.
x x x x x
7. Risk premiums are about the same regardless of whether we account for inflation. The reason is that
x x x x x x x x x x x x x x x x
risk premiums are the difference between two returns, so inflation essentially nets out.
x x x x x x x x x x x x x
8. Returns, risk premiums, and volatility would all be lower than we estimated because aftertax returns
x x x x x x x x x x x x x x
are smaller than pretax returns.
x x x x x
9. We have seen that T-bills barely kept up with inflation before taxes. After taxes, investors in T-bills
x x x x x x x x x x x x x x x x
actually lost ground (assuming anything other than a very low tax rate). Thus, an all T-bill strategy
x x x x x x x x x x x x x x x x x
will probably lose money in real dollars for a taxable investor.
x x x x x x x x x x x
Copyright 2021 © McGraw-Hill Education. All rights reserved. No reproduction or distribution without
x x x x x x x x x x x x
the prior written consent of McGraw-Hill Education.
x x x x x x
,10. It is important not to lose sight of the fact that the results we have discussed cover over 80 years,
x x x x x x x x x x x x x x x x x x x
well beyond the investing lifetime for most of us. There have been extended periods during which
x x x x x x x x x x x x x x x x
small stocks have done terribly. Thus, one reason most investors will choose not to pursue a 100
x x x x x x x x x x x x x x x x x
percent stock (particularly small-cap stocks) strategy is that many investors have relatively short
x x x x x x x x x x x x x
horizons, and high volatility investments may be very inappropriate in such cases. There are other
x x x x x x x x x x x x x x x
reasons, but we will defer discussion of these to later chapters.
x x x x x x x x x x x
Solutions to Questions and Problems
x x x x
NOTE: All end of chapter problems were solved using a spreadsheet. Many problems require multiple
x x x x x x x x x x x x x x
steps. Due to space and readability constraints, when these intermediate steps are included in this
x x x x x x x x x x x x x x x
solutions manual, rounding may appear to have occurred. However, the final answer for each problem is
x x x x x x x x x x x x x x x x
found without rounding during any step in the problem.
x x x x x x x x x
Core Questions
x
1. Total dollar return = 100($41 – $37 + $.28) = $428.00
x x x x x x x x x x
Whether you choose to sell the stock does not affect the gain or loss for the year; your stock is
x x x x x x x x x x x x x x x x x x x
worth what it would bring if you sold it. Whether you choose to do so or not is irrelevant (ignoring
x x x x x x x x x x x x x x x x x x x x
commissions and taxes).
x x x
2. Capital gains yield = ($41 – $37)/$37 = .1081, or 10.81%
x x x x x x x x x x
Dividend yield = $.28/$37 = .0076, or .76%
x x x x x x x x
Total rate of return = 10.81% + .76% = 11.57%
x x x x x x x x x
3. Dollar return = 500($34 – $37 + $.28) = –$1,360
x x x x x x x x x
Capital gains yield = ($34 – $37)/$37 = –.0811, or –8.11%
x x x x x x x x x x
Dividend yield = $.28/$37 = .0076, or .76%
x x x x x x x x
Total rate of return = –8.11% + .76% = –7.35%
x x x x x x x x x
4. a. x average return = 6.2%, average risk premium = 2.6% x x x x x x x x
b. average return = 3.6%, average risk premium = 0%x x x x x x x x
c. average return = 11.9%, average risk premium = 8.3%
x x x x x x x x
d. average return = 17.5%, average risk premium = 13.9%
x x x x x x x x
5. Cherry average return = (17% + 11% – 2% + 3% + 14%)/5 = 8.60%
x x x x x x x x x x x x x x
Straw average return = (16% + 18% – 6% + 1% + 22%)/5 = 10.20%
x x x x x x x x x x x x x x
6. Cherry: RA = 8.60% x x x
Var = 1/4[(.17 – .086)2 + (.11 – .086)2 + (–.02 – .086)2 + (.03 – .086)2 + (.14 – .086)2] = .00623
x x x x x x x x x x x x x x x x x x x x x x
Standard deviation = (.00623)1/2 = .0789, or 7.89%
x x x x x x x
Straw: RB = 10.20% x x x
Var = 1/4[(.16 – .102)2 + (.18 – .102)2 + (–.06 – .102)2 + (.01 – .102)2 + (.22 – .102)2] = .01452
x x x x x x x x x x x x x x x x x x x x x x
Standard deviation = (.01452)1/2 = .1205, or 12.05%
x x x x x x x
7. The capital gains yield is ($59 – $65)/$65 = –.0923, or –9.23% (notice the negative sign). With
x x x x x x x x x x x x x x x x
a dividend yield of 1.2 percent, the total return is –8.03%.
x x x x x x x x x x x
Copyright 2021 © McGraw-Hill Education. All rights reserved. No reproduction or distribution without
x x x x x x x x x x x x
the prior written consent of McGraw-Hill Education.
x x x x x x
, 8. Geometric return = [(1 + .17)(1 + .11)(1 - .02)(1 + .03)(1 + .14)](1/5) – 1 = .0837, or 8.37%
x x x x x x x x x x x x x x x x x x x
9. Arithmetic return = (.21 + .12 + .07 –.13 – .04 + .26)/6 = .0817, or 8.17%
x x x x x x x x x x x x x x x x
Geometric return = [(1 + .21)(1 + .12)(1 + .07)(1 – .13)(1 – .04)(1 + .26)](1/6) – 1 = .0730, or 7.30%
x x x x x x x x x x x x x x x x x x x x x
Intermediate Questions x
10. That’s plus or minus one standard deviation, so about two-thirds of the time, or two years out of
x x x x x x x x x x x x x x x x x
three. In one year out of three, you will be outside this range, implying that you will be below it
x x x x x x x x x x x x x x x x x x x x
one year out of six and above it one year out of six.
x x x x x x x x x x x x x
11. You lose money if you have a negative return. With a 12 percent expected return and a 6 percent
x x x x x x x x x x x x x x x x x x
standard deviation, a zero return is two standard deviations below the average. The odds of being
x x x x x x x x x x x x x x x x
outside (above or below) two standard deviations are 5 percent; the odds of being below are half
x x x x x x x x x x x x x x x x x
that, or 2.5 percent. (It’s actually 2.28 percent.) You should expect to lose money only 2.5 years
x x x x x x x x x x x x x x x x x
out of every 100. It’s a pretty safe investment.
x x x x x x x x x
12. The average return is 5.9 percent, with a standard deviation of 9.8 percent, so Prob(Return < –3.9 or
x x x x x x x x x x x x x x x x x
Return > 15.7 ) ≈ 1/3, but we are only interested in one tail; Prob(Return < –3.9) ≈ 1/6, which is
x x x x x x x x x x x x x x x x x x x x x
half of 1/3 .
x x x x
95%: 5.9 ± 2σ = 5.9 ± 2(9.8) = –13.7% to 25.5% x x x x x x x x x x
99%: 5.9 ± 3σ = 5.9 ± 3(9.8) = –23.5% to 35.3% x x x x x x x x x x
13. Expected return = 17.5%; σ = 36.3%. Doubling your money is a 100% return, so if the return
x x x x x x x x x x x x x x x x x
distribution is normal, Z = (100 – 17.5)/36.3 = 2.27 standard deviations; this is in-between two and
x x x x x x x x x x x x x x x x x
three standard deviations, so the probability is small, somewhere between .5% and 2.5% (why?).
x x x x x x x x x x x x x x
Referring to the nearest Z table, the actual probability is = 1.152%, or about once every 100 years.
x x x x x x x x x x x x x x x x x x
Tripling your money would be Z = (200 – 17.5)/36.3 = 5.028 standard deviations; this corresponds
x x x x x x x x x x x x x x x x
to a probability of (much) less than 0.5%, or once every 200 years. (The actual answer is less than
x x x x x x x x x x x x x x x x x x x
once every 1 million years, so don’t hold your breath.)
x x x x x x x x x x
14. Year Common stocks x T-bill return x Risk premium x
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).
x x x x x x x x x x x x
b. Average returns: Common stocks = 12.84/5 = .0257, or 2.57%; T-bills = 31.67/5 = .0633,
x x x x x x x x x x x x x x
or 6.33%;
x x
Risk premium = –18.83/5 = –.0377, or –3.77%
x x x x x x x
c. Common stocks: Var = 1/4[ (–.1469 – .0257)2 + (–.2647 – .0257)2 + (.3723 – .0257)2 +
x x x x x x x x x x x x x x x x
(.2393 – .0257)2 + (–.0716 – .0257)2] = .072337
x x x x x x x x
Standard deviation = (0.072337)1/2 = .2690, or 26.90% x x x x x x x
T-bills: Var = 1/4[(.0729 – .0633)2 + (.0799 – .0633)2 + (.0587 – .0633)2 + (.0507–.0633)2 +
x x x x x x x x x x x x x x x x
(.0545 – .0633)2] = .000156 x x x x
Standard deviation = (.000156)1/2 = .0125, or 1.25% x x x x x x x
Copyright 2021 © McGraw-Hill Education. All rights reserved. No reproduction or distribution without
x x x x x x x x x x x x
the prior written consent of McGraw-Hill Education.
x x x x x x
Management, 9th Edition
Wickyaplus stuvia
,SOLUTION MANUAL FOR x x
Fundamentals of Investments Valuation and Management 9th Edition By x x x x x x x x
Jordan
x
Chapter 1-21 x
Chapter 1 x
A Brief History of Risk and Return
x x x x x x
Concept Questions x
1. For both risk and return, increasing order is b, c, a, d. On average, the higher the risk of an
x x x x x x x x x x x x x x x x x x x
investment, the higher is its expected return.
x x x x x x x
2. Since the price didn’t change, the capital gains yield was zero. If the total return was four percent,
x x x x x x x x x x x x x x x x x
then the dividend yield must be four percent.
x x x x x x x x
3. It is impossible to lose more than –100 percent of your investment. Therefore, return distributions
x x x x x x x x x x x x x x
x are cut off on the lower tail at –100 percent; if returns were truly normally distributed, you could
x x x x x x x x x x x x x x x x x
xlose much more. x x
4. To calculate an arithmetic return, you sum the returns and divide by the number of returns. As such,
x x x x x x x x x x x x x x x x x
arithmetic returns do not account for the effects of compounding (and, in particular, the effect of
x x x x x x x x x x x x x x x x
volatility). Geometric returns do account for the effects of compounding and for changes in the
x x x x x x x x x x x x x x x
base used for each year’s calculation of returns. As an investor, the more important return of an
x x x x x x x x x x x x x x x x x
asset is the geometric return.
x x x x x
5. Blume’s formula uses the arithmetic and geometric returns along with the number of observations to
x x x x x x x x x x x x x x
approximate a holding period return. When predicting a holding period return, the arithmetic return
x x x x x x x x x x x x x x
will tend to be too high and the geometric return will tend to be too low. Blume’s formula adjusts
x x x x x x x x x x x x x x x x x x x
these returns for different holding period expected returns.
x x x x x x x x
6. T-bill rates were highest in the early eighties since inflation at the time was relatively high. As we
x x x x x x x x x x x x x x x x x
discuss in our chapter on interest rates, rates on T-bills will almost always be slightly higher than
x x x x x x x x x x x x x x x x x
the expected rate of inflation.
x x x x x
7. Risk premiums are about the same regardless of whether we account for inflation. The reason is that
x x x x x x x x x x x x x x x x
risk premiums are the difference between two returns, so inflation essentially nets out.
x x x x x x x x x x x x x
8. Returns, risk premiums, and volatility would all be lower than we estimated because aftertax returns
x x x x x x x x x x x x x x
are smaller than pretax returns.
x x x x x
9. We have seen that T-bills barely kept up with inflation before taxes. After taxes, investors in T-bills
x x x x x x x x x x x x x x x x
actually lost ground (assuming anything other than a very low tax rate). Thus, an all T-bill strategy
x x x x x x x x x x x x x x x x x
will probably lose money in real dollars for a taxable investor.
x x x x x x x x x x x
Copyright 2021 © McGraw-Hill Education. All rights reserved. No reproduction or distribution without
x x x x x x x x x x x x
the prior written consent of McGraw-Hill Education.
x x x x x x
,10. It is important not to lose sight of the fact that the results we have discussed cover over 80 years,
x x x x x x x x x x x x x x x x x x x
well beyond the investing lifetime for most of us. There have been extended periods during which
x x x x x x x x x x x x x x x x
small stocks have done terribly. Thus, one reason most investors will choose not to pursue a 100
x x x x x x x x x x x x x x x x x
percent stock (particularly small-cap stocks) strategy is that many investors have relatively short
x x x x x x x x x x x x x
horizons, and high volatility investments may be very inappropriate in such cases. There are other
x x x x x x x x x x x x x x x
reasons, but we will defer discussion of these to later chapters.
x x x x x x x x x x x
Solutions to Questions and Problems
x x x x
NOTE: All end of chapter problems were solved using a spreadsheet. Many problems require multiple
x x x x x x x x x x x x x x
steps. Due to space and readability constraints, when these intermediate steps are included in this
x x x x x x x x x x x x x x x
solutions manual, rounding may appear to have occurred. However, the final answer for each problem is
x x x x x x x x x x x x x x x x
found without rounding during any step in the problem.
x x x x x x x x x
Core Questions
x
1. Total dollar return = 100($41 – $37 + $.28) = $428.00
x x x x x x x x x x
Whether you choose to sell the stock does not affect the gain or loss for the year; your stock is
x x x x x x x x x x x x x x x x x x x
worth what it would bring if you sold it. Whether you choose to do so or not is irrelevant (ignoring
x x x x x x x x x x x x x x x x x x x x
commissions and taxes).
x x x
2. Capital gains yield = ($41 – $37)/$37 = .1081, or 10.81%
x x x x x x x x x x
Dividend yield = $.28/$37 = .0076, or .76%
x x x x x x x x
Total rate of return = 10.81% + .76% = 11.57%
x x x x x x x x x
3. Dollar return = 500($34 – $37 + $.28) = –$1,360
x x x x x x x x x
Capital gains yield = ($34 – $37)/$37 = –.0811, or –8.11%
x x x x x x x x x x
Dividend yield = $.28/$37 = .0076, or .76%
x x x x x x x x
Total rate of return = –8.11% + .76% = –7.35%
x x x x x x x x x
4. a. x average return = 6.2%, average risk premium = 2.6% x x x x x x x x
b. average return = 3.6%, average risk premium = 0%x x x x x x x x
c. average return = 11.9%, average risk premium = 8.3%
x x x x x x x x
d. average return = 17.5%, average risk premium = 13.9%
x x x x x x x x
5. Cherry average return = (17% + 11% – 2% + 3% + 14%)/5 = 8.60%
x x x x x x x x x x x x x x
Straw average return = (16% + 18% – 6% + 1% + 22%)/5 = 10.20%
x x x x x x x x x x x x x x
6. Cherry: RA = 8.60% x x x
Var = 1/4[(.17 – .086)2 + (.11 – .086)2 + (–.02 – .086)2 + (.03 – .086)2 + (.14 – .086)2] = .00623
x x x x x x x x x x x x x x x x x x x x x x
Standard deviation = (.00623)1/2 = .0789, or 7.89%
x x x x x x x
Straw: RB = 10.20% x x x
Var = 1/4[(.16 – .102)2 + (.18 – .102)2 + (–.06 – .102)2 + (.01 – .102)2 + (.22 – .102)2] = .01452
x x x x x x x x x x x x x x x x x x x x x x
Standard deviation = (.01452)1/2 = .1205, or 12.05%
x x x x x x x
7. The capital gains yield is ($59 – $65)/$65 = –.0923, or –9.23% (notice the negative sign). With
x x x x x x x x x x x x x x x x
a dividend yield of 1.2 percent, the total return is –8.03%.
x x x x x x x x x x x
Copyright 2021 © McGraw-Hill Education. All rights reserved. No reproduction or distribution without
x x x x x x x x x x x x
the prior written consent of McGraw-Hill Education.
x x x x x x
, 8. Geometric return = [(1 + .17)(1 + .11)(1 - .02)(1 + .03)(1 + .14)](1/5) – 1 = .0837, or 8.37%
x x x x x x x x x x x x x x x x x x x
9. Arithmetic return = (.21 + .12 + .07 –.13 – .04 + .26)/6 = .0817, or 8.17%
x x x x x x x x x x x x x x x x
Geometric return = [(1 + .21)(1 + .12)(1 + .07)(1 – .13)(1 – .04)(1 + .26)](1/6) – 1 = .0730, or 7.30%
x x x x x x x x x x x x x x x x x x x x x
Intermediate Questions x
10. That’s plus or minus one standard deviation, so about two-thirds of the time, or two years out of
x x x x x x x x x x x x x x x x x
three. In one year out of three, you will be outside this range, implying that you will be below it
x x x x x x x x x x x x x x x x x x x x
one year out of six and above it one year out of six.
x x x x x x x x x x x x x
11. You lose money if you have a negative return. With a 12 percent expected return and a 6 percent
x x x x x x x x x x x x x x x x x x
standard deviation, a zero return is two standard deviations below the average. The odds of being
x x x x x x x x x x x x x x x x
outside (above or below) two standard deviations are 5 percent; the odds of being below are half
x x x x x x x x x x x x x x x x x
that, or 2.5 percent. (It’s actually 2.28 percent.) You should expect to lose money only 2.5 years
x x x x x x x x x x x x x x x x x
out of every 100. It’s a pretty safe investment.
x x x x x x x x x
12. The average return is 5.9 percent, with a standard deviation of 9.8 percent, so Prob(Return < –3.9 or
x x x x x x x x x x x x x x x x x
Return > 15.7 ) ≈ 1/3, but we are only interested in one tail; Prob(Return < –3.9) ≈ 1/6, which is
x x x x x x x x x x x x x x x x x x x x x
half of 1/3 .
x x x x
95%: 5.9 ± 2σ = 5.9 ± 2(9.8) = –13.7% to 25.5% x x x x x x x x x x
99%: 5.9 ± 3σ = 5.9 ± 3(9.8) = –23.5% to 35.3% x x x x x x x x x x
13. Expected return = 17.5%; σ = 36.3%. Doubling your money is a 100% return, so if the return
x x x x x x x x x x x x x x x x x
distribution is normal, Z = (100 – 17.5)/36.3 = 2.27 standard deviations; this is in-between two and
x x x x x x x x x x x x x x x x x
three standard deviations, so the probability is small, somewhere between .5% and 2.5% (why?).
x x x x x x x x x x x x x x
Referring to the nearest Z table, the actual probability is = 1.152%, or about once every 100 years.
x x x x x x x x x x x x x x x x x x
Tripling your money would be Z = (200 – 17.5)/36.3 = 5.028 standard deviations; this corresponds
x x x x x x x x x x x x x x x x
to a probability of (much) less than 0.5%, or once every 200 years. (The actual answer is less than
x x x x x x x x x x x x x x x x x x x
once every 1 million years, so don’t hold your breath.)
x x x x x x x x x x
14. Year Common stocks x T-bill return x Risk premium x
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).
x x x x x x x x x x x x
b. Average returns: Common stocks = 12.84/5 = .0257, or 2.57%; T-bills = 31.67/5 = .0633,
x x x x x x x x x x x x x x
or 6.33%;
x x
Risk premium = –18.83/5 = –.0377, or –3.77%
x x x x x x x
c. Common stocks: Var = 1/4[ (–.1469 – .0257)2 + (–.2647 – .0257)2 + (.3723 – .0257)2 +
x x x x x x x x x x x x x x x x
(.2393 – .0257)2 + (–.0716 – .0257)2] = .072337
x x x x x x x x
Standard deviation = (0.072337)1/2 = .2690, or 26.90% x x x x x x x
T-bills: Var = 1/4[(.0729 – .0633)2 + (.0799 – .0633)2 + (.0587 – .0633)2 + (.0507–.0633)2 +
x x x x x x x x x x x x x x x x
(.0545 – .0633)2] = .000156 x x x x
Standard deviation = (.000156)1/2 = .0125, or 1.25% x x x x x x x
Copyright 2021 © McGraw-Hill Education. All rights reserved. No reproduction or distribution without
x x x x x x x x x x x x
the prior written consent of McGraw-Hill Education.
x x x x x x
