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Risk and Return

1.

Principles of
Corporate
Finance
Chapter 8
Risk and Return
Seventh Edition
Richard A. Brealey
Stewart C. Myers
Slides by
Matthew Will
McGraw Hill/Irwin
Copyright © 2003 by The McGraw-Hill Companies, Inc. All rights reserved

2. Topics Covered

8- 2
Topics Covered
Markowitz Portfolio Theory
Risk and Return Relationship
Testing the CAPM
CAPM Alternatives
McGraw Hill/Irwin
Copyright © 2003 by The McGraw-Hill Companies, Inc. All rights reserved

3. Markowitz Portfolio Theory

8- 3
Markowitz Portfolio Theory
Combining stocks into portfolios can reduce
standard deviation, below the level obtained
from a simple weighted average calculation.
Correlation coefficients make this possible.
The various weighted combinations of stocks
that create this standard deviations constitute
the set of efficient portfolios.
McGraw Hill/Irwin
Copyright © 2003 by The McGraw-Hill Companies, Inc. All rights reserved

4. Markowitz Portfolio Theory

8- 4
Markowitz Portfolio Theory
Price changes vs. Normal distribution
Microsoft - Daily % change 1990-2001
Proportion of Days
0.14
0.12
0.1
0.08
0.06
0.04
0.02
0
-9 -8 -7 -6
-5 -4 -3 -2 -1
0
1
2
3
4
5
6
7
8
9
Daily % Change
McGraw Hill/Irwin
Copyright © 2003 by The McGraw-Hill Companies, Inc. All rights reserved

5. Markowitz Portfolio Theory

8- 5
Markowitz Portfolio Theory
Standard Deviation VS. Expected Return
Investment A
20
18
% probability
16
14
12
10
8
6
4
2
0
-50
0
50
% return
McGraw Hill/Irwin
Copyright © 2003 by The McGraw-Hill Companies, Inc. All rights reserved

6. Markowitz Portfolio Theory

8- 6
Markowitz Portfolio Theory
Standard Deviation VS. Expected Return
Investment B
20
18
% probability
16
14
12
10
8
6
4
2
0
-50
0
50
% return
McGraw Hill/Irwin
Copyright © 2003 by The McGraw-Hill Companies, Inc. All rights reserved

7. Markowitz Portfolio Theory

8- 7
Markowitz Portfolio Theory
Standard Deviation VS. Expected Return
Investment C
20
18
% probability
16
14
12
10
8
6
4
2
0
-50
0
50
% return
McGraw Hill/Irwin
Copyright © 2003 by The McGraw-Hill Companies, Inc. All rights reserved

8. Markowitz Portfolio Theory

8- 8
Markowitz Portfolio Theory
Standard Deviation VS. Expected Return
Investment D
20
18
% probability
16
14
12
10
8
6
4
2
0
-50
0
50
% return
McGraw Hill/Irwin
Copyright © 2003 by The McGraw-Hill Companies, Inc. All rights reserved

9. Markowitz Portfolio Theory

8- 9
Markowitz Portfolio Theory
Expected Returns and Standard Deviations vary given
different weighted combinations of the stocks
Expected Return (%)
Reebok
35% in Reebok
Coca Cola
Standard Deviation
McGraw Hill/Irwin
Copyright © 2003 by The McGraw-Hill Companies, Inc. All rights reserved

10. Efficient Frontier

8- 10
Efficient Frontier
•Each half egg shell represents the possible weighted combinations for two
stocks.
•The composite of all stock sets constitutes the efficient frontier
Expected Return (%)
Standard Deviation
McGraw Hill/Irwin
Copyright © 2003 by The McGraw-Hill Companies, Inc. All rights reserved

11. Efficient Frontier

8- 11
Efficient Frontier
•Lending or Borrowing at the risk free rate (rf) allows us to exist outside the
efficient frontier.
Expected Return (%)
T
rf
S
Standard Deviation
McGraw Hill/Irwin
Copyright © 2003 by The McGraw-Hill Companies, Inc. All rights reserved

12. Efficient Frontier

8- 12
Efficient Frontier
Example
Stocks
ABC Corp
Big Corp
s
28
42
Correlation Coefficient = .4
% of Portfolio
Avg Return
60%
15%
40%
21%
Standard Deviation = weighted avg = 33.6
Standard Deviation = Portfolio = 28.1
Return = weighted avg = Portfolio = 17.4%
McGraw Hill/Irwin
Copyright © 2003 by The McGraw-Hill Companies, Inc. All rights reserved

13. Efficient Frontier

8- 13
Efficient Frontier
Example
Stocks
ABC Corp
Big Corp
s
28
42
Correlation Coefficient = .4
% of Portfolio
Avg Return
60%
15%
40%
21%
Standard Deviation = weighted avg = 33.6
Standard Deviation = Portfolio = 28.1
Return = weighted avg = Portfolio = 17.4%
Let’s Add stock New Corp to the portfolio
McGraw Hill/Irwin
Copyright © 2003 by The McGraw-Hill Companies, Inc. All rights reserved

14. Efficient Frontier

8- 14
Efficient Frontier
Example
Stocks
Portfolio
New Corp
s
28.1
30
Correlation Coefficient = .3
% of Portfolio
Avg Return
50%
17.4%
50%
19%
NEW Standard Deviation = weighted avg = 31.80
NEW Standard Deviation = Portfolio = 23.43
NEW Return = weighted avg = Portfolio = 18.20%
McGraw Hill/Irwin
Copyright © 2003 by The McGraw-Hill Companies, Inc. All rights reserved

15. Efficient Frontier

8- 15
Efficient Frontier
Example
Stocks
Portfolio
New Corp
s
28.1
30
Correlation Coefficient = .3
% of Portfolio
Avg Return
50%
17.4%
50%
19%
NEW Standard Deviation = weighted avg = 31.80
NEW Standard Deviation = Portfolio = 23.43
NEW Return = weighted avg = Portfolio = 18.20%
NOTE: Higher return & Lower risk
How did we do that?
DIVERSIFICATION
McGraw Hill/Irwin
Copyright © 2003 by The McGraw-Hill Companies, Inc. All rights reserved

16. Efficient Frontier

17. Efficient Frontier

18. Efficient Frontier

19. Efficient Frontier

20. Efficient Frontier

21. Efficient Frontier

8- 21
Efficient Frontier
Return
Low Risk
High Risk
High Return
High Return
Low Risk
High Risk
Low Return
Low Return
Risk
McGraw Hill/Irwin
Copyright © 2003 by The McGraw-Hill Companies, Inc. All rights reserved

22. Efficient Frontier

8- 22
Efficient Frontier
Return
Low Risk
High Risk
High Return
High Return
Low Risk
High Risk
Low Return
Low Return
Risk
McGraw Hill/Irwin
Copyright © 2003 by The McGraw-Hill Companies, Inc. All rights reserved

23. Efficient Frontier

24. Security Market Line

25. Security Market Line

26. Security Market Line

27. Security Market Line

28. Capital Asset Pricing Model

29. Testing the CAPM

8- 29
Testing the CAPM
Beta vs. Average Risk Premium
Avg Risk Premium
1931-65
SML
30
20
Investors
10
Market
Portfolio
0
1.0
McGraw Hill/Irwin
Portfolio Beta
Copyright © 2003 by The McGraw-Hill Companies, Inc. All rights reserved

30. Testing the CAPM

8- 30
Testing the CAPM
Beta vs. Average Risk Premium
Avg Risk Premium
1966-91
30
20
SML
Investors
10
Market
Portfolio
0
1.0
McGraw Hill/Irwin
Portfolio Beta
Copyright © 2003 by The McGraw-Hill Companies, Inc. All rights reserved

31. Testing the CAPM

8- 31
Testing the CAPM
Return vs. Book-to-Market
Dollars
25
20
High-minus low book-tomarket
15
10
5
Low minus big
1998
1993
1988
1983
1978
1973
1968
1963
1958
1953
1948
1943
1938
1933
1928
0
http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data_library.html
McGraw Hill/Irwin
Copyright © 2003 by The McGraw-Hill Companies, Inc. All rights reserved

32. Consumption Betas vs Market Betas

8- 32
Consumption Betas vs Market Betas
Stocks
(and other risky assets)
Stocks
(and other risky assets)
Wealth is uncertain
Market risk
makes wealth
uncertain.
Standard
Consumption
Wealth
CAPM
CAPM
Consumption is uncertain
Wealth = market
portfolio
McGraw Hill/Irwin
Consumption
Copyright © 2003 by The McGraw-Hill Companies, Inc. All rights reserved

33. Arbitrage Pricing Theory

8- 33
Arbitrage Pricing Theory
Alternative to CAPM
Expected Risk
Premium = r
- rf
= Bfactor1(rfactor1
Return
McGraw Hill/Irwin
- rf) + Bf2(rf2 - rf) + …
= a + bfactor1(rfactor1)
+ bf2(rf2) + …
Copyright © 2003 by The McGraw-Hill Companies, Inc. All rights reserved

34. Arbitrage Pricing Theory

8- 34
Arbitrage Pricing Theory
Estimated risk premiums for taking on risk factors
(1978-1990)
Factor
Estimated Risk Premium
Yield spread
(rfactor rf )
5.10%
Interest rate
- .61
Exchange rate
- .59
Real GNP
.49
Inflation
- .83
Mrket
6.36
McGraw Hill/Irwin
Copyright © 2003 by The McGraw-Hill Companies, Inc. All rights reserved

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