CHAPTER 10
SOME LESSONS FROM CAPITAL MARKET HISTORY
CHAPTER 10 QUIZ
CHAPTER ORGANIZATION
When determining how much to pay for a given security, investors consider the uncertainty of its cash flows. The result
is that discount rates are positively related to risk; higher discount rates decrease market values.
10.1

Returns
Dollar Returns – The return on an investment comes in either or both of two general forms; the income
component, and the capital gain or capital loss, which reflects the change in the value of the asset. For a
common stock, return takes two forms: dividends and capital gains.
Total dollar return = Dividend income + Capital gain (or loss)

Percentage Returns – It is usually more useful to think of percentage returns because the result does not depend
on the dollar amount invested.
Total percentage return = [Dividend income + Capital gain (or loss)] / Initial investment
For a common stock, the total return is comprised of the dividend yield plus the percentage capital gain (or
capital loss) yield.
Total Return 
D t 1 Pt 1  Pt (D t 1  Pt 1  Pt )


,
Pt
Pt
Pt
where Pt is the price of the stock at the beginning of the year, Dt+1 is the dividend paid during the year, and Pt+1
D
P P
is the price at the end of the year. Therefore, t 1 is the stock’s dividend yield and t 1 t is the capital gain
Pt
Pt
(or loss) yield on the stock.
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Suppose a stock had an initial price of $78 per share, paid a dividend of $1.25 per share during the year, and had an
ending share price of $87. Compute the percentage total return.
Total Percentage Return 
$1.25 $87  $78 ($1.25  $87 - $78) $10.25



 .1314  13.14%
$78
$78
$78
$78
What was the dividend yield? The capital gains yield?
Dividend yield 
Capital gains yield 
D t 1 $1.25

 .01603  1.60%
Pt
$78
Pt 1  Pt ($87  $78) $9


 .11538  11.54%
Pt
$78
$78
Total return = 13.14% = 1.60% + 11.54%
10.2
The Historical Record
The following are the basis for the nominal pretax rates of return reported by Ibbotson and Sinquefield and
presented in the figures throughout the chapter.
1. Large-company stocks – S&P 500 index, which contains 500 of the largest companies in terms of total
market value in the U.S.
2. Small-company stocks – Smallest 20% of stocks listed on the New York Stock Exchange based on
market value of outstanding stock.
3. Long-term corporate bonds – High quality corporate bonds with 20 years to maturity.
4. Long-term government bonds – Portfolio of U.S. government bonds with 20 years to maturity.
5. U.S. Treasury bills – Portfolio of T-bills with a three-month maturity.
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 A First Look – Historical evidence indicates a positive relationship between return and risk.
 A Closer Look – The variability of historical returns is positively related to the magnitude of the returns.
10.3 Average Returns: The First Lesson
 Calculating Average Returns – The average (or mean) rate of return is simply the arithmetic average, total
returns divided by the number of observations. The average return is the best guess of what returns will be in any
given year in the future.
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Security returns are examples of random variables – categories of numbers for which, in any particular instance, more
things can happen than will happen – and the things that can happen have an associated probability of occurrence.
Random variables are typically characterized by their probability distributions (i.e., a graph, a table, or function that
relates the potential values of the random variable to its associated probabilities) along with measures of its central
tendency and dispersion (the deviation from that central tendency). The normal distribution is a common probability
distribution; mean, median, and mode measure central tendency, while variance and standard deviation are common
measures of dispersion.
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 Average Returns: The Historical Record – Historical average annual returns have been the lowest for U.S.
Treasury Bills, and highest for small-firm common stocks.
 Risk Premiums – We refer to the T-bill rate as the risk-free rate of return, since they have short maturities and
the U.S. government can always raise taxes in order to meet its debts. From 1926 to 2008, the average return on
T-bills was 3.8% per year. During the same period, large U.S. company common stocks had an average annual
return of 11.7%. The difference of 7.9% is the excess return or risk premium for investing in the risky asset
(stocks).
 The First Lesson - Risky investments earn a risk premium; there is a reward for bearing risk.
10.4

The Variability of Returns: The Second Lesson
Frequency Distributions and Variability – Frequency distributions are often used to describe the changes in a
variable. The variability of those changes is indicated by the range of the distribution, often measured by its
variance or standard deviation.
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Frequency distribution of returns on common stocks: 1926-2006

The Historical Variance and Standard Deviation – The greater the deviations from the average (or mean) return,
the more variable the rate of return and the greater the level of risk. If we are looking at historical returns, the
variance is calculated as shown below:
[(R 1  R) 2  (R 2  R) 2  ...  (R T  R) 2 ]
Var(R)  σ 
(T  1)
2
Var(R) 
.027 .027

 .009
(4  1)
3
The standard deviation is the square root of the variance:
SD(R)  σ 2  σ  .009  .094868  9.487%
Note: The square root of a number can be found by raising that number to the power of → .5
SD(R)  .009  (.009).5  .094868  9.487%
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Calculating the Variance and Standard Deviation
Suppose the Supertech Company and the Hyperdrive Company have experienced the following returns in the last four
years:
What are the average returns? The variances? The standard deviations? Which investment was more volatile?
To calculate the average returns, we add up the returns and divide by 4. The results are:
To calculate the variance for Supertech, we can summarize the relevant calculations as follows:
Since there are four years of returns, we calculate the variances by dividing .2675 by (4 − 1) = 3:
For practice, verify that you get the same answer as we do for Hyperdrive.
Year
2005
2006
2007
2008
(1)
(2)
(3)
(4)
Actual Average Deviation Squared
Return Return
(1) – (2) Deviation
.05
.09
-.12
.20
.055
.055
.055
.055
Totals
Notice that the standard deviation for Supertech, 29.87 percent, is a little more than twice Hyperdrive's 13.27 percent;
Supertech was thus the more volatile investment.
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
The Historical Record – The variability of returns is positively related to the size of historical returns.

Normal Distribution – For many random events, the normal distribution (or bell curve) is useful for deriving the
probability that the value of a variable falls within a certain range. Historical returns on securities have
probability distributions that are approximately normal. The normal distribution is completely described by its
mean and variance. Since 1926, annual returns on large company stocks have averaged about 11.7% with a
standard deviation of about 20.6%. An observation on a normally distributed random variable has a 68%
chance of being within plus or minus one standard deviation from the mean, a 95% chance of being within plus
or minus two standard deviations, and a 99% chance of being within plus or minus three standard deviations of
the mean.
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
The Second Lesson – The greater the potential reward, the greater is the risk.

Using Capital Market History - Based upon the historical risk premium for large company common stocks, an
investment of “average risk” should return about 7.9% above the T-bill rate. Not all risky investments have the
same risk as large company common stocks; it is necessary to develop an appropriate measure of risk and to
quantify the risk-return relationship.
10.5
More on Average Returns

Arithmetic Versus Geometric Average – The arithmetic average return answers the question “What was your
return in an average year over a particular time period?” The geometric average return answers the question
“What was your average compound return per year over a particular time period?”

Calculating Geometric Average Returns
The geometric average return over T periods is calculated as shown:
Geometric average return  [(1  R1 ) x (1  R 2 ) x ... x (1  R T )]1/T  1
A stock has had returns of 36 percent, 19 percent, 27 percent, −7 percent, 6 percent, and 13 percent over the last six
years. What are the arithmetic and geometric returns for the stock?
Arithmetic return 
(36  19  27  7  6  13) 94

 15.6666  15.67%
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6
Geometric return  [(1.36)(1. 19)(1.27)(0.93)(1.06)(1.13)]1/6  1
Geometric return  (2.289585404)1/6  1  .1480  14.80%
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
Arithmetic Average Return or Geometric Average Return?
If you are using averages calculated over a long period to forecast returns over a shorter period, the arithmetic
average should be used. If you are forecasting for very long periods, you should use the geometric average.
10.6
Capital Market Efficiency - An efficient capital market is a market in which current market prices fully reflect
available information. In such a market, it is not possible to devise trading rules that consistently “beat the
market” after taking risk into account.

Price Behavior in an Efficient Market - U.S. financial markets have low trading costs and numerous buyers and
sellers, all of whom have ready access to information. In such a market, transactions have, on average, a zero
NPV, that is, assets are worth exactly what they cost. This is the basis for the idea that financial markets are
efficient.

The Efficient Markets Hypothesis – The EMH asserts that U.S. capital markets are efficient with respect to
information. This implies that a strategy based on current or historical information is unlikely to produce
abnormal profits, and that the adjustment of prices to new information is virtually instantaneous. Implications of
market efficiency are: (1) investors buying stocks and bonds should expect to earn a rate of return that is
commensurate with the level of risk they undertake, and (2) firms issuing securities will receive a price equal to
the present value of the securities’ expected cash flows, discounted at the required rate of return.

Some Common Misconceptions about the EMH - Market efficiency does NOT imply that it doesn’t make a
difference how you invest, since the risk/return trade-off still applies, but rather that you can’t expect to
consistently earn excess returns using costless trading strategies. Stock price fluctuations are evidence that the
market is efficient since new information is constantly arriving – prices that don’t change are evidence of
inefficiency. The EMH doesn’t say prices are random. Rather, the influence of previously unknown information
causes randomness in price changes. As a result, price changes can’t be predicted before they happen.

The Forms of Market Efficiency
o Strong form efficiency – All information, both public and private is already incorporated in the price.
Empirical evidence indicates that this form of efficiency does NOT hold.
o Semistrong form efficiency – All public information is already incorporated in the price. It says that you
cannot consistently earn excess returns using available information to do fundamental analysis.
Evidence is mixed, but suggests that it holds for widely-held firms.
o Weak form efficiency – All market information, including prices and volume, is included in the price. It
says that you cannot consistently earn excess returns by looking for patterns in past price and volume
information, such as is done by technical analysts. Evidence suggests that markets are weak form
efficient based on the trading rules that we have been able to test.
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Ethics Note
Insider trading is illegal, but the determination of what constitutes insider trading is difficult. Rule 10B-5 of
the Securities Exchange Act of 1934 states: “It shall be unlawful for any person, directly or indirectly, by
use of any means or instrumentality of interstate commerce, or of the mails, or of any facility on a national
securities exchange, (1) to employ any device, scheme, or artifice to defraud, (2) to make any untrue
statement of a material fact or omit to state a material fact necessary in order to make the statements made,
in light of the circumstances under which they were made, not misleading, (3) to engage in any act, practice,
or course of business which operates or would operate as a fraud or deceit upon any person, in connection
with the purchase or sale of any security.”
Additionally, several court cases have sought to more clearly define insider trading. For insider trading to
exist, there must be a fiduciary relationship between the parties. Actions of the inside trader do not have to
meet the legal requirements of fraud; they merely have to have the appearance of acting as a fraud or deceit.
Accidental discovery does not constitute a fiduciary relationship.
The court decided in Chiarella v. United States that an employee of a printing firm, who was requested to
proofread proxies that contained unannounced tender offers (and unnamed targets) was not guilty of insider
trading because the employee determined the identity of the target through his own expertise. However, a
member of a company’s board of directors, who has knowledge of the company’s future prospects, may not
individually trade on this information prior to public disclosure. The details of the case may be found in
SEC v. Texas Gulf Sulfur, 401 F.2d 833 (2d Cir. 1968).
Despite the passage of increasingly severe penalties for insider trading (see the Insider Trading Sanctions
Act of 1984 and the Insider Trading and Securities Fraud Enforcement Act of 1988), the evidence suggests
that the practice persists in one form or another. One of the more recent cases deals with Martha Stewart,
who recently completed a five-month prison sentence for obstruction of justice for allegedly lying to
investigators during the investigation into violations of insider trading laws. The investigation stems from a
sale of 4000 shares of Imclone stock a day before it announced that the FDA rejected the company’s
application for a proposed cancer drug. Stewart and Imclone’s then-CEO, Samuel Waksal were friends and
shared the same stock broker. Waksal pleaded guilty to insider trading, and was sentenced to seven years in
prison and was fined $4.3million.
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