introduction to risk, return, and the opportunity cost of capital principles of corporate finance...
TRANSCRIPT
Introduction to Risk, Return, and the Opportunity Cost of Capital
Principles of Corporate FinanceBrealey and Myers Sixth Edition
Slides by
Matthew Will Chapter 7
©The McGraw-Hill Companies, Inc., 2000Irwin/McGraw Hill
©The McGraw-Hill Companies, Inc., 2000Irwin/McGraw Hill
7- 2
Topics Covered
72 Years of Capital Market History Measuring Risk Portfolio Risk Beta and Unique Risk Diversification
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7- 3
The Value of an Investment of $1 in 1926
Source: Ibbotson Associates
0.1
10
1000
1925 1933 1941 1949 1957 1965 1973 1981 1989 1997
S&P
Small Cap
Corp Bonds
Long Bond
T Bill
Inde
x
Year End
1
5520
1828
55.38
39.07
14.25
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7- 4
0.1
10
1000
1925 1933 1941 1949 1957 1965 1973 1981 1989 1997
S&P
Small Cap
Corp Bonds
Long Bond
T Bill
The Value of an Investment of $1 in 1926
Source: Ibbotson Associates
Inde
x
Year End
1
613
203
6.15
4.34
1.58
Real returns
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7- 5
Rates of Return 1926-1997
Source: Ibbotson Associates
-60
-40
-20
0
20
40
60
26 30 35 40 45 50 55 60 65 70 75 80 85 90 95
Common Stocks
Long T-Bonds
T-Bills
Year
Per
cent
age
Ret
urn
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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 RiskCoin 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 = 450 = 21.2%
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Measuring Risk
1 1 24
12 1113
1013
3 20123456789
10111213
-50
to -
40
-40
to -
30
-30
to -
20
-20
to -
10
-10
to 0
0 to
10
10 t
o 20
20 t
o 30
30 t
o 40
40 t
o 50
50 t
o 60
Return %
# of Years
Histogram of Annual Stock Market ReturnsHistogram of Annual Stock Market Returns
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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
of return=
fraction of portfolio
in first assetx
rate of return
on first asset
+fraction of portfolio
in second assetx
rate of return
on second asset
((
(())
))
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7- 11
Measuring Risk
0
5 10 15
Number of Securities
Po
rtfo
lio s
tan
da
rd d
ev
iati
on
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7- 12
Measuring Risk
0
5 10 15
Number of Securities
Po
rtfo
lio s
tan
da
rd d
ev
iati
on
Market risk
Uniquerisk
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Portfolio Risk
22
22
211221
1221
211221
122121
21
σxσσρxx
σxx2Stock
σσρxx
σxxσx1Stock
2Stock 1Stock
The variance of a two stock portfolio is the sum of these four boxes:
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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
2222
22
211221
2112212221
21
)8.20()45(.σx8.201.171
45.55.σσρxxsMcDonald'
8.201.171
45.55.σσρxx)1.17()55(.σxMyers-Bristol
sMcDonald'Myers-Bristol
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- 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.
% 18.7 352.1 DeviationStandard
352.108)1x17.1x20.2(.55x.45x
]x(20.8)[(.45)
]x(17.1)[(.55) Valriance Portfolio22
22
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Portfolio Risk
)rx()r(x Return PortfolioExpected 2211
)σσρxx(2σxσxVariance Portfolio 21122122
22
21
21
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Portfolio Risk
The shaded boxes contain variance terms; the remainder contain covariance terms.
1
2
3
4
5
6
N
1 2 3 4 5 6 N
STOCK
STOCKTo calculate portfolio variance add up the boxes
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Beta and Unique Risk
beta
Expected
return
Expectedmarketreturn
10%10%- +
-10%+10%
stock
Copyright 1996 by The McGraw-Hill Companies, Inc
-10%
1. Total risk = diversifiable risk + market risk2. Market risk is measured by beta, the sensitivity to market changes.
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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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Beta and Unique Risk
2m
imiB
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Beta and Unique Risk
2m
imiB
Covariance with the market
Variance of the market