9-0
Chapter Nine
Capital Market
Corporate Finance
Ross Westerfield Jaffe
Theory: An Overview


9
Sixth Edition
Prepared by
Gady Jacoby
University of Manitoba
and
Sebouh Aintablian
American University of
Beirut
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9-1
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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9.1 Returns
• Dollar Returns
– the sum of the cash received and
the change in value of the asset, in
dollars.
Dividends
Ending
market value
Time
0
Initial
investment
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•Percentage Returns
– the sum of the cash received and the
change in value of the asset divided by
the original investment.
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9-3
9.1 Returns
Dollar Return = Dividend + Change in Market Value
dollar return
percentage return 
beginning market val ue
dividend  change in market val ue

beginning market val ue
 dividend yield  capital gains yield
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9.1 Returns: Example
• Suppose you bought 100 shares of BCE 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 Returns
– $520 gain
$20
$3,000
Time
0
-$2,500
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•Percentage Returns
20.8% 
$520
$2,500
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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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Holding Period Return: Example
• An investor who held this investment would have
actually realized an annual return of 9.58%:
Year Return Geometric average return 
1
10% (1  r ) 4  (1  r )  (1  r )  (1  r )  (1  r )
g
1
2
3
4
2
-5%
4 (1.10)  (.95)  (1.20)  (1.15)  1
r

g
3
20%
4
15%  .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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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%
r1  r2  r3  r4
Arithmetic average return 
4
10%  5%  20%  15%

 10%
4
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Holding Period Returns
• A famous set of studies dealing with the rates of returns on
common stocks, bonds, and Treasury bills in the U.S. was
conducted by Roger Ibbotson and Rex Sinquefield.
• James Hatch and Robert White examined Canadian returns.
• The text presents year-by-year historical rates of return
starting in 1948 for the following five important types of
financial instruments:
– Large-Company Canadian Common Stocks
– Large-Company U.S. Common Stocks
– Small-Company Canadian Common Stocks
– Long-Term Canadian Bonds
– Canadian Treasury Bills
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The Future Value of an Investment of $1 in 1948
1000
$1  (1  r1948)  (1  r1949 )   (1  r2000)  $383.82
$41.09
$21.48
10
Common Stocks
Long Bonds
T-Bills
0.1
1948
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1958
1968
1978
1988
1998
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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, 1948-2000
Investment
Canadian common stocks
Average
Annual Return
13.09%
Standard
Deviation
Distribution
16.48%
Long Bonds
7.78
10.49
Treasury Bills
6.20
4.11
Inflation
4.23
3.48
– 60%
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0%
+ 60%
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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 and bond
market data is this long-run excess of security return over
the risk-free return.
– The average excess return from Canadian largecompany common stocks for the period 1948 through
2000 was
6.89% = 13.09% – 6.20%
– The average excess return from Canadian long-term
bonds for the period 1948 through 2000 was
1.58% = 7.78% – 6.20%
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Risk Premia
• Suppose that The National Post announced that the current
rate for one-year Treasury bills is 5%.
• What is the expected return on the market of Canadian largecompany stocks?
• Recall that the average excess return from Canadian largecompany common stocks for the period 1948 through 2000
was 6.89%
• Given a risk-free rate of 5%, we have an expected return on
the market of Canadian large-company common stocks of
11.89% = 6.89% + 5%
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The Risk-Return Tradeoff
18%
Annual Return Average
16%
14%
Large-Company Stocks
12%
10%
8%
6%
Long Bonds
4%
T-Bills
2%
0%
5%
10%
15%
20%
25%
Annual Return Standard Deviation
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Rates of Return 1948-2000
Common Stocks
Long Bonds
T-Bills
60
50
40
30
20
10
0
-10
-20
-30
1945
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1955
1965
1975
1985
1995
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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 Bay Street is “You can either sleep
well or eat well.”
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U.S. Stock Market Volatility
The volatility of stocks is not constant from year to year.
60
50
40
30
20
10
98
19
95
19
90
19
85
19
80
19
75
19
70
19
65
19
60
19
55
19
50
19
45
19
40
19
35
19
19
26
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
68%
95%
> 99%
–3
–2
– 36.35% – 19.87%
–1
– 3.39%
0
13.09%
+1
29.57%
+2
46.05%
+3
62.53%
Return on
large company
common
stocks
The probability that a yearly return will fall within 16.48-percent of the mean of
13.09-percent will be approximately 2/3.
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Normal Distribution
• The 16.48-percent standard deviation we found for stock
returns from 1948 through 2000 can now be interpreted in
the following way: if stock returns are approximately
normally distributed, the probability that a yearly return will
fall within 16.48-percent of the mean of 13.09-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%
12
12
12
11
10
9
8
6
5
Return frequency
14
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 2000 Yearbook™, Ibbotson Associates, Inc., Chicago (annually updates work by
Roger G. Ibbotson and Rex A. Sinquefield). All rights reserved.
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9.6 Summary and Conclusions
• This chapter presents returns for five asset classes:
– Canadian Large-Company Common Stocks
– U.S. Large-Company Common Stocks
– Canadian Small-Company Common Stocks
– Canadian Long-Term Bonds
– Canadian Treasury Bills
• Stocks have outperformed bonds over most of the twentieth
century, although stocks have also exhibited more risk.
• The statistical measures in this chapter are necessary
building blocks for the material of the next three chapters.
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