Solution Manual for Fundamentals of Investments Valuation and Management 9th Edition by Bradford Jordan, Thomas Miller, Steve Dolvin

SOLUTION

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Fundamentals of Investments Valuation and Management 9th Edition By
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Jordan
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Chapter 1-21 dk




Chapter 1 dk



A Brief History of Risk and Return
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Concept Questions
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1. For both risk and return, increasing order is b, c, a, d. On average, the higher the risk of an
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investment, the higher is its expected return.
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2. Since the price didn’t change, the capital gains yield was zero.
dk dk dk dk dk dk dk dk dk dk d k If the total return was four
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percent, then the dividend yield must be four percent.
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3. It is impossible to lose more than –100 percent of your investment. Therefore, return
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distributions are cut off on the lower tail at –100 percent; if returns were truly normally
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distributed, you could lose much more.
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4. To calculate an arithmetic return, you sum the returns and divide by the number of returns.
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As such, arithmetic returns do not account for the effects of compounding (and, in particular,
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the effect of volatility). Geometric returns do account for the effects of compounding and for
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changes in the base used for each year’s calculation of returns. As an investor, the more
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important return of an asset is the geometric return.
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5. Blume’s formula uses the arithmetic and geometric returns along with the number of
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observations to approximate a holding period return. When predicting a holding period return,
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the arithmetic return will tend to be too high and the geometric return will tend to be too
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low. Blume’s formula adjusts these returns for different holding period expected returns.
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6. T-bill rates were highest in the early eighties since inflation at the time was relatively high.
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As we discuss in our chapter on interest rates, rates on T-bills will almost always be slightly
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higher than the expected rate of inflation.
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7. Risk premiums are about the same regardless of whether we account for inflation. The reason
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is that risk premiums are the difference between two returns, so inflation essentially nets out.
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8. Returns, risk premiums, and volatility would all be lower than we estimated because aftertax
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returns are smaller than pretax returns.
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9. We have seen that T-bills barely kept up with inflation before taxes. After taxes, investors in
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T-bills actually lost ground (assuming anything other than a very low tax rate). Thus, an all
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T-bill strategy will probably lose money in real dollars for a taxable investor.
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,10. It is important not to lose sight of the fact that the results we have discussed cover over 80
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years, well beyond the investing lifetime for most of us. There have been extended periods
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during which small stocks have done terribly. Thus, one reason most investors will choose
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not to pursue a 100 percent stock (particularly small-cap stocks) strategy is that many
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investors have relatively short horizons, and high volatility investments may be very
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inappropriate in such cases. There are other reasons, but we will defer discussion of these to
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later chapters.
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Solutions to Questions and Problems
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NOTE: All end of chapter problems were solved using a spreadsheet. Many problems require
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multiple steps. Due to space and readability constraints, when these intermediate steps are
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included in this solutions manual, rounding may appear to have occurred. However, the final
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answer for each problem is found without rounding during any step in the problem.
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Core Questions
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1. Total dollar return = 100($41 – $37 + $.28) = $428.00
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Whether you choose to sell the stock does not affect the gain or loss for the year; your stock
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is worth what it would bring if you sold it. Whether you choose to do so or not is
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irrelevant (ignoring commissions and taxes).
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2. Capital gains yield = ($41 – $37)/$37 = .1081, or
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10.81% Dividend yield = $.28/$37 = .0076, or .76%
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Total rate of return = 10.81% + .76% = 11.57%
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3. Dollar return = 500($34 – $37 + $.28) = –$1,360
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Capital gains yield = ($34 – $37)/$37 = –.0811, or –
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8.11% Dividend yield = $.28/$37 = .0076, or .76%
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Total rate of return = –8.11% + .76% = –7.35%
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4. a. average return = 6.2%, average risk premium = 2.6%
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b. average return = 3.6%, average risk premium = 0%
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c. average return = 11.9%, average risk premium = 8.3%
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d. average return = 17.5%, average risk premium = 13.9%
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5.Cherry average return = (17% + 11% – 2% + 3% + 14%)/5 =
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8.60% dk


Straw average return = (16% + 18% – 6% + 1% + 22%)/5 = 10.20%
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6. Cherry: RA = 8.60% dk dk dk


Var = 1/4[(.17 – .086)2 + (.11 – .086)2 + (–.02 – .086)2 + (.03 – .086)2 + (.14 – .086)2] = .00623
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Standard deviation = (.00623)1/2 = .0789, or 7.89%
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Straw: RB = 10.20% dk dk dk


Var = 1/4[(.16 – .102)2 + (.18 – .102)2 + (–.06 – .102)2 + (.01 – .102)2 + (.22 – .102)2] = .01452
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Standard deviation = (.01452)1/2 = .1205, or 12.05%
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7. The capital gains yield is ($59 – $65)/$65 = –.0923, or –9.23% (notice the negative sign).
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With a dividend yield of 1.2 percent, the total return is –8.03%.
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, 8. Geometric return = [(1 + .17)(1 + .11)(1 - .02)(1 + .03)(1 + .14)](1/5) – 1 = .0837, or 8.37%
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9. Arithmetic return = (.21 + .12 + .07 –.13 – .04 + .26)/6 = .0817, or 8.17%
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Geometric return = [(1 + .21)(1 + .12)(1 + .07)(1 – .13)(1 – .04)(1 + .26)](1/6) – 1 = .0730, or 7.30%
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Intermediate Questions dk




10. That’s plus or minus one standard deviation, so about two-thirds of the time, or two years
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out of three. In one year out of three, you will be outside this range, implying that you will
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be below it one year out of six and above it one year out of six.
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11. You lose money if you have a negative return. With a 12 percent expected return and a 6
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percent standard deviation, a zero return is two standard deviations below the average. The
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odds of being outside (above or below) two standard deviations are 5 percent; the odds of
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being below are half that, or 2.5 percent. (It’s actually 2.28 percent.) You should expect to
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lose money only 2.5 years out of every 100. It’s a pretty safe investment.
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12. The average return is 5.9 percent, with a standard deviation of 9.8 percent, so Prob(Return <
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–3.9 or Return > 15.7 ) ≈ 1/3, but we are only interested in one tail; Prob(Return < –3.9) ≈
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1/6, which is half of 1/3 .
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95%: 5.9 ± 2σ = 5.9 ± 2(9.8) = –13.7% to 25.5%
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99%: 5.9 ± 3σ = 5.9 ± 3(9.8) = –23.5% to 35.3%
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13. Expected return = 17.5%; σ = 36.3%. Doubling your money is a 100% return, so if the
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return distribution is normal, Z = (100 – 17.5)/36.3 = 2.27 standard deviations; this is in-
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between two and three standard deviations, so the probability is small, somewhere between
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.5% and 2.5% (why?). Referring to the nearest Z table, the actual probability is = 1.152%,
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or about once every 100 years. Tripling your money would be Z = (200 – 17.5)/36.3 = 5.028
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standard deviations; this corresponds to a probability of (much) less than 0.5%, or once every
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200 years. (The actual answer is less than once every 1 million years, so don’t hold your
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breath.)
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14. Year Common stocks dk T-bill return dk Risk premium dk


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).
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b. Average returns: Common stocks = 12.84/5 = .0257, or 2.57%; T-bills = 31.67/5 =
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.0633, or 6.33%;
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Risk premium = –18.83/5 = –.0377, or –3.77%
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c. Common stocks: Var = 1/4[ (–.1469 – .0257)2 + (–.2647 – .0257)2 + (.3723 – .0257)2 +
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(.2393 – .0257)2 + (–.0716 – .0257)2] = .072337
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Standard deviation = (0.072337)1/2 = .2690, or 26.90%
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T-bills: Var = 1/4[(.0729 – .0633)2 + (.0799 – .0633)2 + (.0587 – .0633)2 + (.0507–.0633)2 +
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(.0545 – .0633)2] = .000156 dk dk dk dk