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Chapter 12

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CHAPTER12
SOME LESSONS FROM CAPITAL
MARKET HISTORY
Learning Objectives
LO1 How to calculate the return on investment.
LO2 The historical returns on various important types of investments.
LO3 The historical risks on various important types of investments.
LO4 The implications of market efficiency.
Answers to Concepts Review and Critical Thinking Questions
1. (LO4) They all wish they had! Since they didn’t, it must have been the case that the stellar performance
was not foreseeable, at least not by most.
2. (LO4) As in the previous question, it’s easy to see after the fact that the investment was terrible, but it
probably wasn’t so easy ahead of time.
3. (LO2, 3) No, stocks are riskier. Some investors are highly risk averse, and the extra possible return
doesn’t attract them relative to the extra risk.
4. (LO4) On average, the only return that is earned is the required return—investors buy assets with
returns in excess of the required return (positive NPV), bidding up the price and thus causing the return
to fall to the required return (zero NPV); investors sell assets with returns less than the required return
(negative NPV), driving the price lower and thus the causing the return to rise to the required return
(zero NPV).
5. (LO4) The market is not weak form efficient.
6. (LO4) Yes, historical information is also public information; weak form efficiency is a subset of semi-
strong form efficiency.
7. (LO4) Ignoring trading costs, on average, such investors merely earn what the market offers; the trades
all have zero NPV. If trading costs exist, then these investors lose by the amount of the costs.
8. (LO4) Unlike gambling, the stock market is a positive sum game; everybody can win. Also, speculators
provide liquidity to markets and thus help to promote efficiency.
9. (LO4) The EMH only says, within the bounds of increasingly strong assumptions about the information
processing of investors, that assets are fairly priced. An implication of this is that, on average, the
typical market participant cannot earn excessive profits from a particular trading strategy. However,
that does not mean that a few particular investors cannot outperform the market over a particular
investment horizon. Certain investors who do well for a period of time get a lot of attention from the
financial press, but the scores of investors who do not do well over the same period of time generally
get considerably less attention from the financial press.
S12-1 10. (LO4)
a. If the market is not weak form efficient, then this information could be acted on and a profit
earned from following the price trend. Under 2, 3, and 4, this information is fully impounded in
the current price and no abnormal profit opportunity exists.
b. Under 2, if the market is not semi-strong form efficient, then this information could be used to
buy the stock “cheap” before the rest of the market discovers the financial statement anomaly.
Since 2 is stronger than 1, both imply that a profit opportunity exists; under 3 and 4, this
information is fully impounded in the current price and no profit opportunity exists.
c. Under 3, if the market is not strong form efficient, then this information could be used as a
profitable trading strategy, by noting the buying activity of the insiders as a signal that the stock is
underpriced or that good news is imminent. Since 1 and 2 are weaker than 3, all three imply that a
profit opportunity exists. Under 4, this information does not signal any profit opportunity for
traders; any pertinent information the manager-insiders may have is fully reflected in the current
share price.
Solutions to Questions and Problems
NOTE: All end of chapter problems were solved using a spreadsheet. Many problems require multiple steps.
Due to space and readability constraints, when these intermediate steps are included in this solutions
manual, rounding may appear to have occurred. However, the final answer for each problem is found
without rounding during any step in the problem.
Basic
1. (LO1) The return of any asset is the increase in price, plus any dividends or cash flows, all divided by
the initial price. The return of this stock is:
R = [($102 – 91) + 2.40] / $91 = .1472 or 14.73%
2. (LO1) The dividend yield is the dividend divided by price at the beginning of the period price, so:
Dividend yield = $2.40 / $91 = .0263 or 2.637%
And the capital gains yield is the increase in price divided by the initial price, so:
Capital gains yield = ($102 – 91) / $91= .1209 or 12.09%
3. (LO1) Using the equation for total return, we find:
R = [($83 – 91) + 2.40] / $91 = –.0615 or –6.15%
And the dividend yield and capital gains yield are:
Dividend yield = $2.40 / $91 = .02637 or 2.637%
Capital gains yield = ($83 – 91) / $91 = –.08791 or –8.791%
Here’s a question for you: Can the dividend yield ever be negative? No, that would mean you were
paying the company for the privilege of owning the stock.
S12-2 4. (LO1) The total dollar return is the increase in price plus the coupon payment, so:
Total dollar return = $1070 – 1040 + 70 = $100
The total percentage return of the bond is:
R = [($1070 – 1040) + 70] / $1040 = .09615 or 9.615%
Notice here that we could have simply used the total dollar return of $100 in the numerator of this
equation.
Using the Fisher equation, the real return was:
(1 + R) = (1 + r)(1 + h)
r = (1.09615 / 1.04) – 1 = .0539 or 5.4%
5. (LO2) The nominal return is the stated return, which is 10.45 percent from Table 12.4. Using the Fisher
equation, the real return was:
(1 + R) = (1 + r)(1 + h)
r = (1.1045)/(1.0395) – 1 = .0625 or 6.25%
6. (LO2) The nominal return is the stated return, which is 8.74 percent from Table 12.4. Using the Fisher
equation, the real return was:
(1 + R) = (1 + r)(1 + h)
r = (1.0874)/(1.0395) – 1 = .04607 or 4.608%
7. (LO1) The average return is the sum of the returns, divided by the number of returns. The average return for
each stock was:
N .08 .21.17 .16 .09
X xi N 7.80%
i1 5
N .16 .38.14 .22 .26
Y yi N 14.40%
i1 5
Remembering back to “sadistics,” we calculate the variance of each stock as:
N
X2 xi x2 N 1
i1
2 1 .08.078 .21.078 2 .17 .078 .16 .078 2 .09 .078 2 .02067
X 51
2 1 .16 .144 2 .38.144 2 .14 .144 2 .22 .144 2 .26 .144 2 .05048
Y 51
The standard deviation is the square root of the variance, so the standard deviation of each stock is:
X= (.002067)/= .1437 or 14.37%
Y= (.05048)/= .22467 or 22.467%
S12-3 8. (LO2, 3)
Year Large co. stock return T-bill return Risk premium
1970 – 3.57% 6.89% 10.46%
1971 8.01 3.86 4.15
1972 27.37 3.43 23.94
1973 0.27 4.78 –4.51
1974 –25.93 7.68 –33.61
1975 18.48 7.05 11.43
24.63 33.69 –9.06
a. Large company stocks: average return = 24.63 / 6 = 4.105%
T-bills: average return = 33.69 / 6 = 5.615%
b. Large company stocks:
2 2 2 2
variance = 1/5[(–.0357 – .04105) + (.0801 – .04105) + (.2737 – .04105) + (.0027 – .04105) +
(–.2593 – .04105) + (.1848 – .04105) ] = 0.034777
1/2
standard deviation = (0.034777) = 0.186486 = 18.65%
T-bills:
variance = 1/5[(.0689 – .05615) + (.0386–.05615) + (.0343–.05615) + (.0478–.05615) + 2
2 2
(.0768 – . 05615) + (.0705 – . 056151/2 = 0.00033001
standard deviation = (0.00033001) = 0.018166 = 1.82%
c. Average observed risk premium = –9.06 / 6 = –1.51%
2 2 2
variance = 1/5[(–21046 + .0151) + (.0425 + .0151) + (.23942+ .0151) +
(–.0451 + .0151) + (–.3361 + .0151) + (.1143 + .0151) ] = 0.03933388
standard deviation = (0.03933388) 1/2= 0.1983277 = 19.83%
d. Before the fact, for most assets the risk premium will be positive; investors demand compen-
sation over and above the risk-free return to invest their money in the risky asset. After the fact,
the observed risk premium can be negative if the asset’s nominal return is unexpectedly low, the
risk-free return is unexpectedly high, or if some combination of these two events occurs.
9. (LO1)
a. To find the average return, we sum all the returns and divide by the number of returns, so:
Average return = (.07 –.12 +.11 +.38 +.14)/5 = .116 or 11.6%
b. Using the equation to calculate variance, we find:
2 2 2 2
Variance = 1/4[(.07 – .116) + (–.12 – .116) + (.11 – .116) + (.38 – .116) +
(.14 – .116) ]
Variance = 0.03203
So, the standard deviation is:
Standard deviation = (0.03203) 1/2= 0.1789 or 17.89%
S12-4 10. (LO1)
a. To calculate the average real return, we can use the average nominal return of the asset, and the
average inflation rate in the Fisher equation. Doing so, we find:
(1 + R) = (1 + r)(1 + h)
r = (1.116/1.035) – 1 = .0783 or 7.83%
b. The average risk premium is simply

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