Principles of Corporate Finance
Brealey and Myers

Sixth Edition
Introduction to Risk, Return, and the
Opportunity Cost of Capital
Slides by
Matthew Will
Irwin/McGraw Hill
Chapter 7
©The McGraw-Hill Companies, Inc., 2000
7- 2
Topics Covered
 72 Years of Capital Market History
 Measuring Risk
 Portfolio Risk
 Beta and Unique Risk
 Diversification
Irwin/McGraw Hill
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7- 3
The Value of an Investment of $1 in 1926
5520
Index
1000
S&P
Small Cap
Corp Bonds
Long Bond
T Bill
1828
55.38
39.07
14.25
10
1
0.1
1925
1933
1941
Source: Ibbotson Associates
Irwin/McGraw Hill
1949
1957
1965
1973
1981
1989
1997
Year End
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7- 4
The Value of an Investment of $1 in 1926
Index
1000
Real returns
S&P
Small Cap
Corp Bonds
Long Bond
T Bill
613
203
6.15
10
4.34
1
1.58
0.1
1925
1933
1941
Source: Ibbotson Associates
Irwin/McGraw Hill
1949
1957
1965
1973
1981
1989
1997
Year End
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7- 5
Rates of Return 1926-1997
Percentage Return
60
40
20
0
-20
Common Stocks
Long T-Bonds
T-Bills
-40
-60 26
30
35
40
Source: Ibbotson Associates
Irwin/McGraw Hill
45
50
55
60
65
70
75
80
85
90
95
Year
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7- 6
Measuring Risk
Variance - Average value of squared deviations from
mean. A measure of volatility.
Standard Deviation - Average value of squared
deviations from mean. A measure of volatility.
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7- 7
Measuring Risk
Coin Toss Game-calculating variance and standard deviation
(1)
(2)
(3)
Percent Rate of Return Deviation from Mean Squared Deviation
+ 40
+ 30
900
+ 10
0
0
+ 10
0
0
- 20
- 30
900
Variance = average of squared deviations = 1800 / 4 = 450
Standard deviation = square of root variance =
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450 = 21.2%
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7- 8
Measuring Risk
Histogram of Annual Stock Market Returns
# of Years
Irwin/McGraw Hill
2
Return %
50 to 60
40 to 50
30 to 40
20 to 30
10 to 20
0 to 10
-30 to -20
3
-10 to 0
1
4
-20 to -10
1
2
-40 to -30
13
12 11 13
10
-50 to -40
13
12
11
10
9
8
7
6
5
4
3
2
1
0
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7- 9
Measuring Risk
Diversification - Strategy designed to reduce risk by
spreading the portfolio across many investments.
Unique Risk - Risk factors affecting only that firm.
Also called “diversifiable risk.”
Market Risk - Economy-wide sources of risk that
affect the overall stock market. Also called
“systematic risk.”
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7- 10
Measuring Risk
(
(
)(
)(
Portfolio rate
fraction of portfolio
=
x
of return
in first asset
rate of return
on first asset
)
)
fraction of portfolio
rate of return
+
x
in second asset
on second asset
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7- 11
Portfolio standard deviation
Measuring Risk
0
5
10
15
Number of Securities
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7- 12
Portfolio standard deviation
Measuring Risk
Unique
risk
Market risk
0
5
10
15
Number of Securities
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7- 13
Portfolio Risk
The variance of a two stock portfolio is the sum of these
four boxes:
Stock 1
Stock 1
Stock 2
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x 12σ 12
x 1x 2σ 12 
x 1x 2ρ 12σ 1σ 2
Stock 2
x 1x 2σ 12 
x 1x 2ρ 12σ 1σ 2
x 22σ 22
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7- 14
Portfolio Risk
Example
Suppose you invest $55 in Bristol-Myers and $45
in McDonald’s. The expected dollar return on
your BM is .10 x 55 = 5.50 and on McDonald’s it
is .20 x 45 = 9.90. The expected dollar return on
your portfolio is 5.50 + 9300 = 14.50. The
portfolio rate of return is 14.50/100 = .145 or
14.5%. Assume a correlation coefficient of 1.
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7- 15
Portfolio Risk
Example
Suppose you invest $55 in Bristol-Myers and $45 in McDonald’s. The
expected dollar return on your BM is .10 x 55 = 5.50 and on
McDonald’s it is .20 x 45 = 9.90. The expected dollar return on your
portfolio is 5.50 + 9300 = 14.50. The portfolio rate of return is
14.50/100 = .145 or 14.5%. Assume a correlation coefficient of 1.
Bristol - Myers
Bristol - Myers
McDonald' s
Irwin/McGraw Hill
x 12σ 12  (.55) 2  (17.1) 2
x 1x 2ρ 12σ 1σ 2  .55  .45
 1  17.1  20.8
McDonald' s
x 1x 2ρ 12σ 1σ 2  .55  .45
 1  17.1  20.8
x 22σ 22  (.45) 2  ( 20.8) 2
©The McGraw-Hill Companies, Inc., 2000
7- 16
Portfolio Risk
Example
Suppose you invest $55 in Bristol-Myers and $45 in McDonald’s. The
expected dollar return on your BM is .10 x 55 = 5.50 and on
McDonald’s it is .20 x 45 = 9.90. The expected dollar return on your
portfolio is 5.50 + 9300 = 14.50. The portfolio rate of return is
14.50/100 = .145 or 14.5%. Assume a correlation coefficient of 1.
Portfolio Valriance  [(.55) 2 x(17.1) 2 ]
 [(.45) 2 x(20.8) 2 ]
 2(.55x.45x 1x17.1x20. 8)  352.10
Standard Deviation  352.1  18.7 %
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7- 17
Portfolio Risk
Expected Portfolio Return  (x 1 r1 )  ( x 2 r2 )
Portfolio Variance  x12σ 12  x 22σ 22  2( x1x 2ρ 12σ 1σ 2 )
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7- 18
Portfolio Risk
The shaded boxes contain variance terms; the remainder
contain covariance terms.
1
2
3
STOCK
To calculate
portfolio
variance add
up the boxes
4
5
6
N
1
2
3
4
5
6
N
STOCK
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7- 19
Beta and Unique Risk
1. Total risk =
diversifiable risk +
market risk
2. Market risk is
measured by beta,
the sensitivity to
market changes.
Expected
stock
return
beta
+10%
-10%
- 10%
+10%
-10%
Expected
market
return
Copyright 1996 by The McGraw-Hill Companies, Inc
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7- 20
Beta and Unique Risk
Market Portfolio - Portfolio of all assets in the
economy. In practice a broad stock market
index, such as the S&P Composite, is used
to represent the market.
Beta - Sensitivity of a stock’s return to the
return on the market portfolio.
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7- 21
Beta and Unique Risk
 im
Bi  2
m
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7- 22
Beta and Unique Risk
 im
Bi  2
m
Covariance with the
market
Variance of the market
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