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Principles of Corporate Finance
Seventh Edition
Richard A. Brealey
Stewart C. Myers
Slides by
Matthew Will
Chapter 7
McGraw Hill/Irwin Copyright © 2003 by The McGraw-Hill Companies, Inc. All rights reserved
Introduction to Risk, Return, and the Opportunity Cost of
Capital
7- 2
McGraw Hill/Irwin Copyright © 2003 by The McGraw-Hill Companies, Inc. All rights reserved
Topics Covered
75 Years of Capital Market History Measuring Risk Portfolio Risk Beta and Unique Risk Diversification
7- 3
McGraw Hill/Irwin Copyright © 2003 by The McGraw-Hill Companies, Inc. All rights reserved
The Value of an Investment of $1 in 1926
Source: Ibbotson Associates
0.1
10
1000
1925 1940 1955 1970 1985 2000
S&PSmall CapCorp BondsLong BondT Bill
Inde
x
Year End
1
6402
2587
64.1
48.9
16.6
7- 4
McGraw Hill/Irwin Copyright © 2003 by The McGraw-Hill Companies, Inc. All rights reserved
0.1
10
1000
1925 1940 1955 1970 1985 2000
S&PSmall CapCorp BondsLong BondT Bill
Source: Ibbotson Associates
Inde
x
Year End
1
660
267
6.6
5.0
1.7
Real returns
The Value of an Investment of $1 in 1926
7- 5
McGraw Hill/Irwin Copyright © 2003 by The McGraw-Hill Companies, Inc. All rights reserved
Rates of Return 1926-2000
Source: Ibbotson Associates
-60
-40
-20
0
20
40
60
Common Stocks
Long T-Bonds
T-Bills
Year
Per
cent
age
Ret
urn
7- 6
McGraw Hill/Irwin Copyright © 2003 by The McGraw-Hill Companies, Inc. All rights reserved
Average Market Risk Premia (1999-2000)
4.35.1 6 6.1 6.1 6.5 6.7 7.1 7.5 8
8.5 9.9 9.9 10 11
0123456789
1011
Den Bel
Can Sw
i
Spa UK Ire
Net
h
US
A
Sw
e
Aus
Ger
Fra
Jap It
Risk premium, %
Country
7- 7
McGraw Hill/Irwin Copyright © 2003 by The McGraw-Hill Companies, Inc. All rights reserved
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.
7- 8
McGraw Hill/Irwin Copyright © 2003 by The McGraw-Hill Companies, Inc. All rights reserved
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 = 450 = 21.2%
7- 9
McGraw Hill/Irwin Copyright © 2003 by The McGraw-Hill Companies, Inc. All rights reserved
Measuring Risk
1 1 24
1311
13 12 13
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
7- 10
McGraw Hill/Irwin Copyright © 2003 by The McGraw-Hill Companies, Inc. All rights reserved
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.”
7- 11
McGraw Hill/Irwin Copyright © 2003 by The McGraw-Hill Companies, Inc. All rights reserved
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
((
((
))
))
7- 12
McGraw Hill/Irwin Copyright © 2003 by The McGraw-Hill Companies, Inc. All rights reserved
Measuring Risk
0
5 10 15
Number of Securities
Po
rtfo
lio s
tan
da
rd d
ev
iati
on
7- 13
McGraw Hill/Irwin Copyright © 2003 by The McGraw-Hill Companies, Inc. All rights reserved
Measuring Risk
0
5 10 15
Number of Securities
Po
rtfo
lio s
tan
da
rd d
ev
iati
on
Market risk
Uniquerisk
7- 14
McGraw Hill/Irwin Copyright © 2003 by The McGraw-Hill Companies, Inc. All rights reserved
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
7- 15
McGraw Hill/Irwin Copyright © 2003 by The McGraw-Hill Companies, Inc. All rights reserved
Portfolio Risk
Example
Suppose you invest 65% of your portfolio in Coca-Cola and 35% in Reebok. The expected dollar return on your CC is 10% x 65% = 6.5% and on Reebok it is 20% x 35% = 7.0%. The expected return on your portfolio is 6.5 + 7.0 = 13.50%. Assume a correlation coefficient of 1.
7- 16
McGraw Hill/Irwin Copyright © 2003 by The McGraw-Hill Companies, Inc. All rights reserved
Portfolio Risk
2222
22
211221
2112212221
21
)5.58()35(.σx5.585.311
35.65.σσρxxReebok
5.585.311
35.65.σσρxx)5.31()65(.σxCola-Coca
ReebokCola-Coca
Example
Suppose you invest 65% of your portfolio in Coca-Cola and 35% in Reebok. The expected dollar return on your CC is 10% x 65% = 6.5% and on Reebok it is 20% x 35% = 7.0%. The expected return on your portfolio is 6.5 + 7.0 = 13.50%. Assume a correlation coefficient of 1.
7- 17
McGraw Hill/Irwin Copyright © 2003 by The McGraw-Hill Companies, Inc. All rights reserved
Portfolio Risk
Example
Suppose you invest 65% of your portfolio in Coca-Cola and 35% in Reebok. The expected dollar return on your CC is 10% x 65% = 6.5% and on Reebok it is 20% x 35% = 7.0%. The expected return on your portfolio is 6.5 + 7.0 = 13.50%. Assume a correlation coefficient of 1.
% 31.7 1,006.1 Deviation Standard
1.006,15)1x31.5x58.2(.65x.35x
]x(58.5)[(.35)
]x(31.5)[(.65) Valriance Portfolio22
22
7- 18
McGraw Hill/Irwin Copyright © 2003 by The McGraw-Hill Companies, Inc. All rights reserved
Portfolio Risk
)rx()r(x Return PortfolioExpected 2211
)σσρxx(2σxσxVariance Portfolio 21122122
22
21
21
7- 19
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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
7- 20
McGraw Hill/Irwin Copyright © 2003 by The McGraw-Hill Companies, Inc. All rights reserved
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
7- 21
McGraw Hill/Irwin Copyright © 2003 by The McGraw-Hill Companies, Inc. All rights reserved
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.
7- 22
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Beta and Unique Risk
2m
imiB
7- 23
McGraw Hill/Irwin Copyright © 2003 by The McGraw-Hill Companies, Inc. All rights reserved
Beta and Unique Risk
2m
imiB
Covariance with the market
Variance of the market
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