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CHAPTER
9
Capital Market Theory:
An Overview
McGraw-Hill/Irwin
Corporate Finance, 7/e
© 2005 The McGraw-Hill Companies, Inc. All Rights Reserved.
Chapter Outline
9.1
9.2
9.3
9.4
9.5
9.6
Returns
Holding-Period Returns
Return Statistics
Average Stock Returns and Risk-Free Returns
Risk Statistics
Summary and Conclusions
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9-2
9.1 Returns
Dollar Returns
the sum of the cash received
and the change in value of the
asset, in dollars.
Time
0
Initial
investment
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Dividends
Ending
market value
1
•Percentage Returns
–the sum of the cash received and the
change in value of the asset divided by
the original investment.
© 2005 The McGraw-Hill Companies, Inc. All Rights Reserved.
9.1 Returns
Dollar Return = Dividend + Change in Market Value
dollar return
percentage return =
beginning market value
dividend + change in market value
=
beginning market value
= dividend yield + capital gains yield
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9.1 Returns: Example
Suppose you bought 100 shares of Wal-Mart (WMT) one
year ago today at $25. Over the last year, you received
$20 in dividends (= 20 cents per share × 100 shares). At
the end of the year, the stock sells for $30. How did you
do?
Quite well. You invested $25 × 100 = $2,500. At the end
of the year, you have stock worth $3,000 and cash
dividends of $20. Your dollar gain was $520 = $20 +
($3,000 – $2,500).
$520
Your percentage gain for the year is 20.8% =
$2,500
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9.1 Returns: Example
Dollar Return:
$20
$520 gain
$3,000
Time
0
-$2,500
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1
Percentage Return:
$520
20.8% =
$2,500
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9-6
9.2 Holding-Period Returns
The holding period return is the return that
an investor would get when holding an
investment over a period of n years, when
the return during year i is given as ri:
holding period return =
= (1 + r1 )  (1 + r2 )   (1 + rn )  1
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Holding Period Return: Example
Suppose your investment provides the following
returns over a four-year period:
Year Return
1
10%
2
-5%
3
20%
4
15%
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Your holding period return =
= (1 + r1 )  (1 + r2 )  (1 + r3 )  (1 + r4 )  1
= (1.10)  (.95)  (1.20)  (1.15)  1
= .4421 = 44.21%
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9-8
Holding Period Return: Example
An investor who held this investment would have
actually realized an annual return of 9.58%:
Year Return
1
10%
2
-5%
3
20%
4
15%
Geometric average return =
(1 + rg ) 4 = (1 + r1 )  (1 + r2 )  (1 + r3 )  (1 + r4 )
rg = 4 (1.10)  (.95)  (1.20)  (1.15)  1
= .095844 = 9.58%
So, our investor made 9.58% on his money for four
years, realizing a holding period return of 44.21%
1.4421 = (1.095844) 4
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9-9
Holding Period Return: Example
Note that the geometric average is not the same
thing as the arithmetic average:
Year Return
1
10%
2
-5%
3
20%
4
15%
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r1 + r2 + r3 + r4
Arithmetic average return =
4
10%  5% + 20% + 15%
=
= 10%
4
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9-10
Holding Period Returns
A famous set of studies dealing with the rates of returns
on common stocks, bonds, and Treasury bills was
conducted by Roger Ibbotson and Rex Sinquefield.
They present year-by-year historical rates of return
starting in 1926 for the following five important types of
financial instruments in the United States:
Large-Company Common Stocks
Small-company Common Stocks
Long-Term Corporate Bonds
Long-Term U.S. Government Bonds
U.S. Treasury Bills
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The Future Value of an Investment
of $1 in 1925
$1,775.34
1000
$59.70
$17.48
10
Common Stocks
Long T-Bonds
T-Bills
0.1
1930
1940
1950
1960
1970
1980
1990
2000
Source: © Stocks, Bonds, Bills, and Inflation 2003 Yearbook™, Ibbotson Associates, Inc., Chicago (annually updates work by
Roger G. Ibbotson and Rex A. Sinquefield). All rights reserved.
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9-12
9.3 Return Statistics
The history of capital market returns can be summarized
by describing the
average return
( R1 +  + RT )
R=
T
the standard deviation of those returns
( R1  R) 2 + ( R2  R) 2 +  ( RT  R) 2
SD = VAR =
T 1
the frequency distribution of the returns.
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Historical Returns, 1926-2002
Series
Average
Annual Return
Standard
Deviation
Large Company Stocks
12.2%
20.5%
Small Company Stocks
16.9
33.2
Long-Term Corporate Bonds
6.2
8.7
Long-Term Government Bonds
5.8
9.4
U.S. Treasury Bills
3.8
3.2
Inflation
3.1
4.4
Distribution
– 90%
0%
+ 90%
Source: © Stocks, Bonds, Bills, and Inflation 2003 Yearbook™, Ibbotson Associates, Inc., Chicago
(annually updates work by Roger G. Ibbotson and Rex A. Sinquefield). All rights reserved.
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9.4 Average Stock Returns
and Risk-Free Returns
The Risk Premium is the additional return (over and
above the risk-free rate) resulting from bearing risk.
One of the most significant observations of stock market
data is this long-run excess of stock return over the riskfree return.
The average excess return from large company common stocks
for the period 1926 through 1999 was 8.4% = 12.2% – 3.8%
The average excess return from small company common stocks
for the period 1926 through 1999 was 13.2% = 16.9% – 3.8%
The average excess return from long-term corporate bonds for
the period 1926 through 1999 was 2.4% = 6.2% – 3.8%
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Risk Premia
Suppose that The Wall Street Journal announced that the
current rate for on-year Treasury bills is 5%.
What is the expected return on the market of smallcompany stocks?
Recall that the average excess return from small
company common stocks for the period 1926 through
1999 was 13.2%
Given a risk-free rate of 5%, we have an expected return
on the market of small-company stocks of 18.2% =
13.2% + 5%
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The Risk-Return Tradeoff
18%
Small-Company Stocks
Annual Return Average
16%
14%
Large-Company Stocks
12%
10%
8%
6%
T-Bonds
4%
T-Bills
2%
0%
5%
10%
15%
20%
25%
30%
Annual Return Standard Deviation
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9-17
Rates of Return 1926-2002
60
40
20
0
-20
Common Stocks
Long T-Bonds
T-Bills
-40
-60 26
30
35
40
45
50
55
60
65
70
75
80
85
90
95 2000
Source: © Stocks, Bonds, Bills, and Inflation 2000 Yearbook™, Ibbotson Associates, Inc., Chicago (annually updates work by
Roger G. Ibbotson and Rex A. Sinquefield). All rights reserved.
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Risk Premiums
Rate of return on T-bills is essentially risk-free.
Investing in stocks is risky, but there are
compensations.
The difference between the return on T-bills and
stocks is the risk premium for investing in stocks.
An old saying on Wall Street is “You can either
sleep well or eat well.”
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Stock Market Volatility
The volatility of stocks is not constant from year to year.
60
50
40
30
20
10
19
26
19
35
19
40
19
45
19
50
19
55
19
60
19
65
19
70
19
75
19
80
19
85
19
90
19
95
19
98
0
Source: © Stocks, Bonds, Bills, and Inflation 2000 Yearbook™, Ibbotson Associates, Inc., Chicago (annually updates work by
Roger G. Ibbotson and Rex A. Sinquefield). All rights reserved.
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9.5 Risk Statistics
There is no universally agreed-upon definition of
risk.
The measures of risk that we discuss are variance
and standard deviation.
The standard deviation is the standard statistical
measure of the spread of a sample, and it will be the
measure we use most of this time.
Its interpretation is facilitated by a discussion of the
normal distribution.
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Normal Distribution
A large enough sample drawn from a normal
distribution looks like a bell-shaped curve.
Probability
The probability that a yearly
return will fall within 20.1
percent of the mean of 13.3
percent will be
approximately 2/3.
– 3s
– 49.3%
– 2s
– 28.8%
– 1s
– 8.3%
0
12.2%
68.26%
+ 1s
32.7%
+ 2s
53.2%
+ 3s
73.7%
Return on
large company common
stocks
95.44%
99.74%
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Normal Distribution
The 20.1-percent standard deviation we
found for stock returns from 1926 through
1999 can now be interpreted in the
following way: if stock returns are
approximately normally distributed, the
probability that a yearly return will fall
within 20.1 percent of the mean of 13.3
percent will be approximately 2/3.
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Normal Distribution
S&P 500 Return Frequencies
16
16
Normal
approximation
Mean = 12.8%
Std. Dev. = 20.4%
14
12
12
11
10
9
8
6
5
4
2
1
1
2
2
1
0
0
0
-58% -48% -38% -28% -18%
-8%
2%
12%
22%
32%
42%
52%
62%
Annual returns
Source: © Stocks, Bonds, Bills, and Inflation 2002 Yearbook™, Ibbotson Associates, Inc., Chicago
(annually updates work by Roger G. Ibbotson and Rex A. Sinquefield). All rights reserved.
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Return frequency
12
9-24
9.6 Summary and Conclusions
This chapter presents returns for four asset
classes:
Large Company Stocks
Small Company Stocks
Long-Term Government Bonds
Treasury Bills
Stocks have outperformed bonds over most of
the twentieth century, although stocks have also
exhibited more risk.
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9.6 Summary and Conclusions
The stocks of small companies have
outperformed the stocks of small
companies over most of the twentieth
century, again with more risk.
The statistical measures in this chapter are
necessary building blocks for the material
of the next three chapters.
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