Topics Covered
Average Market Risk Premia (1999-2000)
Measuring Risk
Measuring Risk
Measuring Risk
Measuring Risk
Measuring Risk
Measuring Risk
Measuring Risk
Portfolio Risk
Portfolio Risk
Portfolio Risk
Portfolio Risk
Portfolio Risk
Portfolio Risk
Beta and Unique Risk
Beta and Unique Risk
Beta and Unique Risk
Beta and Unique Risk
306.50K
Category: financefinance

Introduction to Risk, Return, and the Opportunity Cost of Capital

1.

Principles of
Corporate
Finance
Seventh Edition
Richard A. Brealey
Chapter 7
Introduction to Risk, Return,
and the Opportunity Cost of
Capital
Stewart C. Myers
Slides by
Matthew Will
McGraw Hill/Irwin
Copyright © 2003 by The McGraw-Hill Companies, Inc. All rights reserved

2. Topics Covered

7- 2
Topics Covered
75 Years of Capital Market History
Measuring Risk
Portfolio Risk
Beta and Unique Risk
Diversification
McGraw Hill/Irwin
Copyright © 2003 by The McGraw-Hill Companies, Inc. All rights reserved

3.

7- 3
The Value of an Investment of $1 in 1926
1000
6402
S&P
Small Cap
Corp Bonds
Long Bond
T Bill
2587
64.1
Index
48.9
16.6
10
1
0.1
1925
1940
Source: Ibbotson Associates
McGraw Hill/Irwin
1955
1970
1985
2000
Year End
Copyright © 2003 by The McGraw-Hill Companies, Inc. All rights reserved

4.

7- 4
The Value of an Investment of $1 in 1926
Index
1000
S&P
Small Cap
Corp Bonds
Long Bond
T Bill
Real returns
660
267
6.6
10
5.0
1
0.1
1925
1.7
1940
Source: Ibbotson Associates
McGraw Hill/Irwin
1955
1970
1985
2000
Year End
Copyright © 2003 by The McGraw-Hill Companies, Inc. All rights reserved

5.

7- 5
Rates of Return 1926-2000
40
20
0
95
90
85
80
75
70
65
60
55
50
45
40
35
26
-60
Common Stocks
Long T-Bonds
T-Bills
20
-40
00
-20
30
Percentage Return
60
Year
Source: Ibbotson Associates
McGraw Hill/Irwin
Copyright © 2003 by The McGraw-Hill Companies, Inc. All rights reserved

6. Average Market Risk Premia (1999-2000)

7- 6
Average Market Risk Premia (1999-2000)
Risk premium, %
It
Jap
Fra
Ger
9.9 10 11
9.9
8.5
Aus
8
Swe
USA
Neth
Ire
UK
Spa
Swi
7.1 7.5
6 6.1 6.1 6.5 6.7
Can
5.1
Bel
4.3
Den
11
10
9
8
7
6
5
4
3
2
1
0
Country
McGraw Hill/Irwin
Copyright © 2003 by The McGraw-Hill Companies, Inc. All rights reserved

7. Measuring Risk

7- 7
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.
McGraw Hill/Irwin
Copyright © 2003 by The McGraw-Hill Companies, Inc. All rights reserved

8. Measuring Risk

7- 8
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 =
McGraw Hill/Irwin
450 = 21.2%
Copyright © 2003 by The McGraw-Hill Companies, Inc. All rights reserved

9. Measuring Risk

7- 9
Measuring Risk
Histogram of Annual Stock Market Returns
# of Years
2
Return %
50 to 60
40 to 50
30 to 40
20 to 30
10 to 20
0 to 10
-30 to -20
McGraw Hill/Irwin
3
-10 to 0
1
13 12 13
11
4
-20 to -10
1
2
-40 to -30
13
-50 to -40
13
12
11
10
9
8
7
6
5
4
3
2
1
0
Copyright © 2003 by The McGraw-Hill Companies, Inc. All rights reserved

10. Measuring Risk

7- 10
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.”
McGraw Hill/Irwin
Copyright © 2003 by The McGraw-Hill Companies, Inc. All rights reserved

11. Measuring Risk

7- 11
Measuring Risk
Portfolio rate
of return
(
(
=
+
McGraw Hill/Irwin
)(
)(
fraction of portfolio
in first asset
fraction of portfolio
in second asset
x
x
rate of return
on first asset
rate of return
)
)
on second asset
Copyright © 2003 by The McGraw-Hill Companies, Inc. All rights reserved

12. Measuring Risk

7- 12
Portfolio standard deviation
Measuring Risk
0
5
10
15
Number of Securities
McGraw Hill/Irwin
Copyright © 2003 by The McGraw-Hill Companies, Inc. All rights reserved

13. Measuring Risk

7- 13
Portfolio standard deviation
Measuring Risk
Unique
risk
Market risk
0
5
10
15
Number of Securities
McGraw Hill/Irwin
Copyright © 2003 by The McGraw-Hill Companies, Inc. All rights reserved

14. Portfolio Risk

7- 14
Portfolio Risk
The variance of a two stock portfolio is the sum of these
four boxes
Stock 1
Stock 1
Stock 2
McGraw Hill/Irwin
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
Copyright © 2003 by The McGraw-Hill Companies, Inc. All rights reserved

15. Portfolio Risk

7- 15
Portfolio Risk
Example
Suppose you invest 65% of your portfolio in CocaCola 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.
McGraw Hill/Irwin
Copyright © 2003 by The McGraw-Hill Companies, Inc. All rights reserved

16. Portfolio Risk

7- 16
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.
Coca - Cola
Coca - Cola
Reebok
McGraw Hill/Irwin
x 12 σ12 (.65) 2 (31.5) 2
x 1 x 2 ρ12 σ1σ 2 .65 .35
1 31.5 58.5
Reebok
x 1 x 2 ρ12 σ1σ 2 .65 .35
1 31.5 58.5
x 22 σ 22 (.35) 2 (58.5) 2
Copyright © 2003 by The McGraw-Hill Companies, Inc. All rights reserved

17. Portfolio Risk

7- 17
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.
Portfolio Valriance [(.65) 2 x(31.5) 2 ]
[(.35) 2 x(58.5) 2 ]
2(.65x.35x 1x31.5x58. 5) 1,006.1
Standard Deviation 1,006.1 31.7 %
McGraw Hill/Irwin
Copyright © 2003 by The McGraw-Hill Companies, Inc. All rights reserved

18. Portfolio Risk

7- 18
Portfolio Risk
Expected Portfolio Return (x 1 r1 ) ( x 2 r2 )
Portfolio Variance x12σ 12 x 22σ 22 2( x1x 2ρ 12σ 1σ 2 )
McGraw Hill/Irwin
Copyright © 2003 by The McGraw-Hill Companies, Inc. All rights reserved

19. Portfolio Risk

7- 19
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
McGraw Hill/Irwin
Copyright © 2003 by The McGraw-Hill Companies, Inc. All rights reserved

20. Beta and Unique Risk

7- 20
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
by The McGraw-Hill Companies, Inc Copyright © 2003 by The McGraw-Hill Companies, Inc. All rights reserved
McGraw1996
Hill/Irwin

21. Beta and Unique Risk

7- 21
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.
McGraw Hill/Irwin
Copyright © 2003 by The McGraw-Hill Companies, Inc. All rights reserved

22. Beta and Unique Risk

7- 22
Beta and Unique Risk
im
Bi 2
m
McGraw Hill/Irwin
Copyright © 2003 by The McGraw-Hill Companies, Inc. All rights reserved

23. Beta and Unique Risk

7- 23
Beta and Unique Risk
im
Bi 2
m
Covariance with the
market
Variance of the market
McGraw Hill/Irwin
Copyright © 2003 by The McGraw-Hill Companies, Inc. All rights reserved
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