Principles of Corporate Finance
Brealey and Myers

Sixth Edition
Risk and Return
Slides by
Matthew Will
Irwin/McGraw Hill
Chapter 8
©The McGraw-Hill Companies, Inc., 2000
8- 2
Topics Covered
 Markowitz Portfolio Theory
 Risk and Return Relationship
 Testing the CAPM
 CAPM Alternatives
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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.
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Markowitz Portfolio Theory
Price changes vs. Normal distribution
Microsoft - Daily % change 1986-1997
600
# of Days
(frequency)
500
400
300
200
100
0
-10%
-8%
-6%
-4%
-2%
0%
2%
4%
6%
8%
10%
Daily % Change
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8- 5
Markowitz Portfolio Theory
Price changes vs. Normal distribution
Microsoft - Daily % change 1986-1997
600
# of Days
(frequency)
500
400
300
200
100
0
-10%
-8%
-6%
-4%
-2%
0%
2%
4%
6%
8%
10%
Daily % Change
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8- 6
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
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8- 7
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
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8- 8
Markowitz Portfolio Theory
 Expected Returns and Standard Deviations vary given
different weighted combinations of the stocks.
Expected Return (%)
McDonald’s
45% McDonald’s
Bristol-Myers Squibb
Standard Deviation
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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
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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
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8- 11
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%
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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
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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%
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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
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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?
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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
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Efficient Frontier
Return
B
A
Risk
(measured
as s)
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Efficient Frontier
Return
B
AB
A
Risk
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Efficient Frontier
Return
B
AB
A
N
Risk
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8- 20
Efficient Frontier
Return
B
ABN AB
A
N
Risk
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Efficient Frontier
Goal is to move
up and left.
Return
WHY?
B
ABN AB
A
N
Risk
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Efficient Frontier
Return
Low Risk
High Return
Risk
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Efficient Frontier
Return
Low Risk
High Risk
High Return
High Return
Risk
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Efficient Frontier
Return
Low Risk
High Risk
High Return
High Return
Low Risk
Low Return
Risk
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Efficient Frontier
Return
Low Risk
High Risk
High Return
High Return
Low Risk
High Risk
Low Return
Low Return
Risk
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Efficient Frontier
Return
Low Risk
High Risk
High Return
High Return
Low Risk
High Risk
Low Return
Low Return
Risk
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8- 27
Efficient Frontier
Return
B
ABN
AB
A
N
Risk
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Security Market Line
Return
.
Efficient Portfolio
Risk Free
Return
= rf
Risk
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Security Market Line
Return
Market Return = rm
Efficient Portfolio
Risk Free
Return
.
= rf
Risk
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Security Market Line
Return
Market Return = rm
Efficient Portfolio
Risk Free
Return
.
= rf
Risk
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Security Market Line
Return
Market Return = rm
.
Efficient Portfolio
Risk Free
Return
= rf
1.0
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BETA
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8- 32
Security Market Line
Return
Market Return = rm
Security Market
Line (SML)
Risk Free
Return
= rf
1.0
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BETA
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Security Market Line
Return
SML
rf
1.0
BETA
SML Equation = rf + B ( rm - rf )
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8- 34
Capital Asset Pricing Model
R = r f + B ( r m - rf )
CAPM
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Testing the CAPM
Beta vs. Average Risk Premium
Avg Risk Premium
1931-65
SML
30
20
Investors
10
Market
Portfolio
0
1.0
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Portfolio Beta
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Testing the CAPM
Beta vs. Average Risk Premium
Avg Risk Premium
1966-91
30
20
SML
Investors
10
Market
Portfolio
0
1.0
Irwin/McGraw Hill
Portfolio Beta
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8- 37
Testing the CAPM
Company Size vs. Average Return
Average Return (%)
25
20
15
10
5
Company size
0
Smallest
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Largest
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Testing the CAPM
Book-Market vs. Average Return
Average Return (%)
25
20
15
10
5
Book-Market Ratio
0
Highest
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Lowest
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Consumption Betas vs Market Betas
Stocks
(and other risky assets)
Wealth = market
portfolio
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Consumption Betas vs Market Betas
Stocks
(and other risky assets)
Market risk
makes wealth
uncertain.
Wealth = market
portfolio
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8- 41
Consumption Betas vs Market Betas
Stocks
(and other risky assets)
Market risk
makes wealth
uncertain.
Standard
CAPM
Wealth = market
portfolio
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Consumption Betas vs Market Betas
Stocks
(and other risky assets)
Market risk
makes wealth
uncertain.
Wealth = market
portfolio
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Stocks
(and other risky assets)
Standard
CAPM
Consumption
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Consumption Betas vs Market Betas
Stocks
(and other risky assets)
Stocks
(and other risky assets)
Wealth is uncertain
Market risk
makes wealth
uncertain.
Standard
Wealth
CAPM
Consumption is uncertain
Wealth = market
portfolio
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Consumption
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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
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Consumption
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Arbitrage Pricing Theory
Alternative to CAPM
Expected Risk
Premium = r
- rf
= Bfactor1(rfactor1
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- rf) + Bf2(rf2 - rf) + …
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Arbitrage Pricing Theory
Alternative to CAPM
Expected Risk
Premium = r
- rf
= Bfactor1(rfactor1
Return
Irwin/McGraw Hill
- rf) + Bf2(rf2 - rf) + …
= a + bfactor1(rfactor1)
+ bf2(rf2) + …
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Arbitrage Pricing Theory
Estimated risk premiums for taking on risk factors
(1978-1990)
Factor
Yield spread
Interest rate
Exchange rate
Real GNP
Inflation
Mrket
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Estimated Risk Prem ium
(rfactor  rf )
5.10%
- .61
- .59
.49
- .83
6.36
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