Chapter
8
PORTFOLIO THEORY AND THE
CAPITAL ASSET PRICING MODEL
Brealey, Myers, and Allen
Principles of Corporate Finance
11th Edition
McGraw-Hill/Irwin
Copyright © 2014 by The McGraw-Hill Companies, Inc. All rights reserved.
8-1 HARRY MARKOWITZ AND THE BIRTH OF
PORTFOLIO THEORY
• Combining stocks into portfolios can reduce
standard deviation below simple weightedaverage calculation
• Correlation coefficients make possible
• Various weighted combinations of stocks
that create specific standard deviation
constitute set of efficient portfolios
8-2
FIGURE 8.1 DAILY PRICE CHANGES, IBM
8-3
FIGURE 8.2A STANDARD DEVIATION VERSUS
EXPECTED RETURN
8-4
FIGURE 8.2B STANDARD DEVIATION VERSUS
EXPECTED RETURN
8-5
FIGURE 8.2C STANDARD DEVIATION VERSUS
EXPECTED RETURN
8-6
FIGURE 8.3 EXPECTED RETURN AND STANDARD DEVIATION,
HEINZ, AND EXXON MOBIL
8-7
TABLE 8.1 EXAMPLES OF EFFICIENT PORTFOLIOS
Efficient Portfolios—Percentages
Allocated to Each Stock
Stock
Expected Standard
Return
Deviation
Dow Chemical
16.4%
40.2%
Bank of America
14.3
30.9
10
Ford
15.0
40.4
8
Heinz
6.0
14.6
11
35
IBM
9.1
19.8
18
12
Newmont Mining
8.9
29.2
6
1
Pfizer
8.0
20.8
10
8
Starbucks
10.4
26.2
12
Walmart
6.3
13.8
9
ExxonMobil
10.0
21.9
8
A
B
100
C
6
42
Expected portfolio return
16.4
10.0
6.7
Portfolio standard deviation
40.2
18.4
11.8
8-8
FIGURE 8.4 FOUR EFFICIENT PORTFOLIOS FROM
TEN STOCKS
8-9
8-1 HARRY MARKOWITZ AND THE BIRTH OF
PORTFOLIO THEORY
• Efficient Frontier
• Each half-ellipse represents possible weighted combinations for
two stocks
Expected return (%)
• Composite of all stock sets constitutes efficient frontier
Standard deviation
8-10
FIGURE 8.5 LENDING AND BORROWING
8-11
8-1 HARRY MARKOWITZ AND THE BIRTH OF
PORTFOLIO THEORY
• Example
Correlation Coefficient = .18
Stocks
s
Heinz
14.6
60%
6.0%
ExxonMobil
21.9
40%
10.0%
% of Portfolio
Average Return
• Standard deviation = weighted average = 17.52
• Standard deviation = portfolio = 15.1
• Return = weighted average = portfolio = 7.6%
• Higher return, lower risk through diversification
8-12
8-1 HARRY MARKOWITZ AND THE BIRTH OF
PORTFOLIO THEORY
• Example
Correlation Coefficient = .4
Stocks
s
ABC Corp
28
60%
15%
Big Corp
42
40%
21%
% of Portfolio
Average Return
• Standard deviation = weighted average = 33.6
• Standard deviation = portfolio = 28.1
• Return = weighted average = portfolio = 17.4%
8-13
8-1 HARRY MARKOWITZ AND THE BIRTH OF
PORTFOLIO THEORY
• Example, continued
Correlation Coefficient = .3
• Add new stock to portfolio
Stocks
s
Portfolio
28.1
50%
17.4%
New Corp
30
50%
19%
% of Portfolio
Average Return
• Standard deviation = weighted average = 31.80
• Standard deviation = portfolio = 23.43
• Return = weighted average = portfolio = 18.20%
8-14
8-1 HARRY MARKOWITZ AND THE BIRTH OF
PORTFOLIO THEORY
Return
B
A
Risk
(measured
as s)
8-15
8-1 HARRY MARKOWITZ AND THE BIRTH OF
PORTFOLIO THEORY
Return
B
AB
A
Risk
8-16
8-1 HARRY MARKOWITZ AND THE BIRTH OF
PORTFOLIO THEORY
Return
B
AB
N
A
Risk
8-17
8-1 HARRY MARKOWITZ AND THE BIRTH OF
PORTFOLIO THEORY
Return
B
ABN
AB
N
A
Risk
8-18
8-1 HARRY MARKOWITZ AND THE BIRTH OF
PORTFOLIO THEORY
Goal is to move up
and left—less risk,
more return
Return
B
ABN
AB
N
A
Risk
8-19
8-1 HARRY MARKOWITZ AND THE BIRTH OF
PORTFOLIO THEORY
• Sharpe Ratio
• Ratio of risk premium to standard deviation
Sharpe ratio 
rp  r f
sp
8-20
8-1 HARRY MARKOWITZ AND THE BIRTH OF
PORTFOLIO THEORY
Return
Low Risk
High Risk
High Return
High Return
Low Risk
High Risk
Low Return
Low Return
Risk
8-21
8-1 HARRY MARKOWITZ AND THE BIRTH OF
PORTFOLIO THEORY
Return
Low Risk
High Risk
High Return
High Return
Low Risk
High Risk
Low Return
Low Return
Risk
8-22
8-1 HARRY MARKOWITZ AND THE BIRTH OF
PORTFOLIO THEORY
Return
B
ABN
AB
N
A
Risk
8-23
8-2 THE RELATIONSHIP BETWEEN RISK AND
RETURN
Return
Market return = rm
.
Market portfolio
rf
Risk
8-24
FIGURE 8.6 SECURITY MARKET LINE
Return
Security market line
(SML)
.
r
Market return = m
Market portfolio
rf
1.0
BETA
8-25
8-2 THE RELATIONSHIP BETWEEN RISK AND
RETURN
Return
SML
rf
BETA
1.0
SML Equation: rf + β(rm − rf)
8-26
8-2 THE RELATIONSHIP BETWEEN RISK AND
RETURN
• Capital Asset Pricing Model (CAPM)
r  rf   (rm  rf )
8-27
TABLE 8.2 ESTIMATES OF RETURNS
• Returns estimates in January 2012 based on capital asset pricing
model. Assume 2% for interest rate rf and 7% for expected risk
premium rm − rf.
tock
S
Dow Chemical
Bank of America
Ford
ExxonMobil
Starbucks
IBM
Newmont Mining
Pfizer
Walmart
Heinz
Beta
1.78
Expected Return
14.50
1.54
1.53
0.98
0.95
0.80
0.75
0.66
0.42
0.40
12.80
12.70
8.86
8.68
7.62
7.26
6.63
4.92
4.78
8-28
FIGURE 8.7 SECURITY MARKET LINE EQUILIBRIUM
• In equilibrium, no stock can lie below the security market line
8-29
FIGURE 8.8 CAPITAL ASSET PRICING MODEL
8-30
FIGURE 8.9B BETA VERSUS AVERAGE RETURN
8-31
FIGURE 8.10 RETURN VERSUS BOOK-TO-MARKET
8-32
8-4 ALTERNATIVE THEORIES
• Alternative to CAPM
Return  a  b1 (rfactor1 )  b2 (rfactor2 )  b3 (rfactor3 )  ....  noise
Expected risk premium  r  rf
 b1 (rfactor1  rf )  b2 (rfactor2  rf )  ...
8-33
8-4 ALTERNATIVE THEORIES
• Estimated risk premiums (1978-1990)
Factor
Estimated Risk Premium
Yield spread
(rfactor  rf )
5.10%
Interest rate
Exchange rate
- .61
- .59
Real GNP
Inflation
.49
- .83
Market
6.36
8-34
8-4 ALTERNATIVE THEORIES
• Three-Factor Model
• Identify macroeconomic factors that could affect
stock returns
• Estimate expected risk premium on each factor
( rfactor1 − rf, etc.)
• Measure sensitivity of each stock to factors
( b1, b2, etc.)
8-35
TABLE 8.3 EXPECTED EQUITY RETURNS
8-36