Chapter 11
Return and Risk: The Capital Asset Pricing
Model (CAPM)
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Ch11
Return and Risk: The Capital Asset Pricing Model (CAPM)
Ch12
An Alternative View of Risk and Return: The Arbitrage
Pricing Theory
Ch13
Risk, Cost of Capital, and Valuation
Ch14
Efficient Capital Markets and Behavioral Challenges
Ch15
Long-Term Financing: An Introduction
Ch16
Capital Structure: Basic Concepts
Ch17
Capital Structure: Limits to the Use of Debt
Ch18
Valuation and Capital Budgeting for the Levered Firm
Ch19
Dividends and Other Payouts
Ch20
Raising Capital
Ch21
Leasing
Ch26
Short-Term Finance and Planning
11-1
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Know how to calculate expected returns
Know how to calculate covariances, correlations, and
betas
Understand the impact of diversification
Understand the systematic risk principle
Understand the security market line
Understand the risk-return tradeoff
Be able to use the Capital Asset Pricing Model
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11-2
11.1 Individual Securities
11.2 Expected Return, Variance, and Covariance
11.3 The Return and Risk for Portfolios
11.4 The Efficient Set for Two Assets
11.5 The Efficient Set for Many Assets
11.6 Diversification
11.7 Riskless Borrowing and Lending
11.8 Market Equilibrium
11.9 Relationship between Risk and Expected Return
(CAPM)
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11-3

The characteristics of individual securities that are of
interest are the:
◦ Expected Return
◦ Variance and Standard Deviation
◦ Covariance and Correlation (to another security or index)
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11-4
Consider the following two risky asset world. There
is a 1/3 chance of each state of the economy, and
the only assets are a stock fund and a bond fund.
Scenario
Recession
Normal
Boom
Rate of Return
Probability Stock Fund Bond Fund
33.3%
-7%
17%
33.3%
12%
7%
33.3%
28%
-3%
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11-5
Scenario
Recession
Normal
Boom
Expected return
Variance
Standard Deviation
Stock Fund
Rate of
Squared
Return Deviation
-7%
0.0324
12%
0.0001
28%
0.0289
11.00%
0.0205
14.3%
Bond
Rate of
Return
17%
7%
-3%
7.00%
0.0067
8.2%
Fund
Squared
Deviation
0.0100
0.0000
0.0100
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11-6
Scenario
Recession
Normal
Boom
Expected return
Variance
Standard Deviation
Stock Fund
Rate of
Squared
Return Deviation
-7%
0.0324
12%
0.0001
28%
0.0289
11.00%
0.0205
14.3%
Bond Fund
Rate of
Squared
Return Deviation
17%
0.0100
7%
0.0000
-3%
0.0100
7.00%
0.0067
8.2%
E(rS )  1 3  (7%)  1 3  (12%)  1 3  (28%)
E(rS )  11%
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11-7
Scenario
Recession
Normal
Boom
Expected return
Variance
Standard Deviation
Stock Fund
Rate of
Squared
Return Deviation
-7%
0.0324
12%
0.0001
28%
0.0289
11.00%
0.0205
14.3%
Bond Fund
Rate of
Squared
Return Deviation
17%
0.0100
7%
0.0000
-3%
0.0100
7.00%
0.0067
8.2%
(7% 11%)  .0324
2
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11-8
Scenario
Recession
Normal
Boom
Expected return
Variance
Standard Deviation
Stock Fund
Rate of
Squared
Return Deviation
-7%
0.0324
12%
0.0001
28%
0.0289
11.00%
0.0205
14.3%
Bond Fund
Rate of
Squared
Return Deviation
17%
0.0100
7%
0.0000
-3%
0.0100
7.00%
0.0067
8.2%
1
.0205  (.0324  .0001 .0289)
3
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11-9
Scenario
Recession
Normal
Boom
Expected return
Variance
Standard Deviation
Stock Fund
Rate of
Squared
Return Deviation
-7%
0.0324
12%
0.0001
28%
0.0289
11.00%
0.0205
14.3%
Bond Fund
Rate of
Squared
Return Deviation
17%
0.0100
7%
0.0000
-3%
0.0100
7.00%
0.0067
8.2%
14.3%  0.0205
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11-10
Scenario
Recession
Normal
Boom
Sum
Covariance
Stock
Bond
Deviation Deviation
-18%
10%
1%
0%
17%
-10%
Product
-0.0180
0.0000
-0.0170
Weighted
-0.0060
0.0000
-0.0057
-0.0117
-0.0117
“Deviation” compares return in each state to the expected return.
“Weighted” takes the product of the deviations multiplied by the
probability of that state.
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11-11

Cov(a,b)
 a b
.0117

 0.998
(.143)(.082)
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11-12
Scenario
Recession
Normal
Boom
Expected return
Variance
Standard Deviation
Stock Fund
Rate of
Squared
Return Deviation
-7%
0.0324
12%
0.0001
28%
0.0289
11.00%
0.0205
14.3%
Bond Fund
Rate of
Squared
Return Deviation
17%
0.0100
7%
0.0000
-3%
0.0100
7.00%
0.0067
8.2%
Note that stocks have a higher expected return than bonds
and higher risk. Let us turn now to the risk-return tradeoff
of a portfolio that is 50% invested in bonds and 50%
invested in stocks.
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11-13
Rate of Return
Stock fund Bond fund Portfolio
-7%
17%
5.0%
12%
7%
9.5%
28%
-3%
12.5%
Scenario
Recession
Normal
Boom
Expected return
Variance
Standard Deviation
11.00%
0.0205
14.31%
7.00%
0.0067
8.16%
squared deviation
0.0016
0.0000
0.0012
9.0%
0.0010
3.08%
The rate of return on the portfolio is a weighted average of
the returns on the stocks and bonds in the portfolio:
rP  wB rB  wS rS
5 %  50 %  (  7 %)  50 %  (17 %)
11-14
Rate of Return
Stock fund Bond fund Portfolio
-7%
17%
5.0%
12%
7%
9.5%
28%
-3%
12.5%
Scenario
Recession
Normal
Boom
Expected return
Variance
Standard Deviation
11.00%
0.0205
14.31%
7.00%
0.0067
8.16%
squared deviation
0.0016
0.0000
0.0012
9.0%
0.0010
3.08%
The expected rate of return on the portfolio is a weighted
average of the expected returns on the securities in the
portfolio.
E(rP )  wB E(rB )  wS E(rS )
9%  50%  (11%)  50%  (7%)
11-15
Rate of Return
Stock fund Bond fund Portfolio
-7%
17%
5.0%
12%
7%
9.5%
28%
-3%
12.5%
Scenario
Recession
Normal
Boom
Expected return
Variance
Standard Deviation
11.00%
0.0205
14.31%
7.00%
0.0067
8.16%
squared deviation
0.0016
0.0000
0.0012
9.0%
0.0010
3.08%
The variance of the rate of return on the two risky assets
portfolio is
?  (wB?B )  (w S?S )  2(w B?B )(wS?S )?BS
2
P
2
2
where BS is the correlation coefficient between the returns
on the stock and bond funds.

11-16
Scenario
Recession
Normal
Boom
Expected return
Variance
Standard Deviation
Rate of Return
Stock fund Bond fund Portfolio
-7%
17%
5.0%
12%
7%
9.5%
28%
-3%
12.5%
11.00%
0.0205
14.31%
7.00%
0.0067
8.16%
squared deviation
0.0016
0.0000
0.0012
9.0%
0.0010
3.08%
Observe the decrease in risk that diversification offers.
An equally weighted portfolio (50% in stocks and 50%
in bonds) has less risk than either stocks or bonds held
in isolation. This is not always the case.
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11-17
% in stocks
Risk
Return
0%
5%
10%
15%
20%
25%
30%
35%
40%
45%
50.00%
55%
60%
65%
70%
75%
80%
85%
90%
95%
100%
8.2%
7.0%
5.9%
4.8%
3.7%
2.6%
1.4%
0.4%
0.9%
2.0%
3.08%
4.2%
5.3%
6.4%
7.6%
8.7%
9.8%
10.9%
12.1%
13.2%
14.3%
7.0%
7.2%
7.4%
7.6%
7.8%
8.0%
8.2%
8.4%
8.6%
8.8%
9.00%
9.2%
9.4%
9.6%
9.8%
10.0%
10.2%
10.4%
10.6%
10.8%
11.0%
100%
stocks
100%
bonds
We can consider other
portfolio weights besides
50% in stocks and 50% in
bonds.
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11-18
% in stocks
Risk
Return
0%
5%
10%
15%
20%
25%
30%
35%
40%
45%
50%
55%
60%
65%
70%
75%
80%
85%
90%
95%
100%
8.2%
7.0%
5.9%
4.8%
3.7%
2.6%
1.4%
0.4%
0.9%
2.0%
3.1%
4.2%
5.3%
6.4%
7.6%
8.7%
9.8%
10.9%
12.1%
13.2%
14.3%
7.0%
7.2%
7.4%
7.6%
7.8%
8.0%
8.2%
8.4%
8.6%
8.8%
9.0%
9.2%
9.4%
9.6%
9.8%
10.0%
10.2%
10.4%
10.6%
10.8%
11.0%
100%
stocks
100%
bonds
Note that some portfolios are
“better” than others. They have
higher returns for the same level of
risk or less.
11-19
retur
n
100%
stocks
 = -1.0
100%
bonds



 = 1.0
 = 0.2
Relationship depends on correlation coefficient
-1.0 <  < +1.0
If = +1.0, no risk reduction is possible
If = –1.0, complete risk reduction is possible
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11-20
return
Individual
Assets
P
Consider a world with many risky assets; we can still identify
the opportunity set of risk-return combinations of various
portfolios.
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11-21
return
minimum
variance
portfolio
Individual Assets
P
The section of the opportunity set above the minimum
variance portfolio is the efficient frontier.
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11-22
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Diversification can substantially reduce the variability
of returns without an equivalent reduction in expected
returns.
This reduction in risk arises because worse than
expected returns from one asset are offset by better
than expected returns from another.
However, there is a minimum level of risk that cannot
be diversified away, and that is the systematic
portion.
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11-25

In a large portfolio the variance terms are
effectively diversified away, but the covariance
terms are not.
Diversifiable Risk;
Nonsystematic Risk;
Firm Specific Risk;
Unique Risk
Portfolio risk
Nondiversifiable risk;
Systematic Risk;
Market Risk
n
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11-26

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A systematic risk is any risk that affects a large number of
assets, each to a greater or lesser degree.
An unsystematic risk is a risk that specifically affects a single
asset or small group of assets.
Unsystematic risk can be diversified away.
Examples of systematic risk include uncertainty about general
economic conditions, such as GNP, interest rates or inflation.
On the other hand, announcements specific to a single
company are examples of unsystematic risk.
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11-27

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Total risk = systematic risk + unsystematic risk
The standard deviation of returns is a measure of total
risk.
For well-diversified portfolios, unsystematic risk is
very small.
Consequently, the total risk for a diversified portfolio
is essentially equivalent to the systematic risk.
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11-28
return
100%
stocks
rf
100%
bonds

In addition to stocks and bonds, consider a world that also
has risk-free securities like T-bills.
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11-29
return
100%
stocks
Balanced
fund
rf
100%
bonds

Now investors can allocate their money across the Tbills and a balanced mutual fund.
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11-30
return
rf
P
With a risk-free asset available and the efficient frontier
identified, we choose the capital allocation line with the
steepest slope.
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11-31
return
M
rf
P
With the capital allocation line identified, all investors choose a point
along the line—some combination of the risk-free asset and the market
portfolio M. In a world with homogeneous expectations, M is the same
for all investors.
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11-32
return
100%
stocks
Balanced
fund
rf
100%
bonds

Where the investor chooses along the Capital Market Line depends
on her risk tolerance. The big point is that all investors have the
same CML.
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11-33
11-34
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
Researchers have shown that the best measure of the
risk of a security in a large portfolio is the beta (b) of
the security.
Beta measures the responsiveness of a security to
movements in the market portfolio (i.e., systematic
risk).
Cov(Ri,RM )
bi 
2
 (RM )
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11-35

Cov(Ri,RM )
 (Ri )
bi 

2
 (RM )
 (RM )
Clearly, your estimate of beta will depend
upon your choice of a proxy for the market
portfolio.
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11-37

This formula is called the Capital Asset Pricing
Model (CAPM):
Ri  RF  bi  (RM  RF )
Expected
return on
a security
RiskBeta of the
Market risk
=
+
×
free rate
security
premium
•
Assume bi = 0, then the expected return is RF.
• Assume bi = 1, then R i  R M
11-39
Expected return

Ri  RF  bi  (RM  RF )
RM
RF
1.0
b
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11-40
Expected
return


13.5%
3%
1.5
b
bi 1.5 RF  3% R M 10%
R i  3 %  1 .5  (10 %  3 %)  13 .5 %
11-41
11-42
Suppose the return on the market is expected
to be 14%, a stock has a beta of 1.2, and the
T-bill rate is 6%. What is the expected return
on the stock?
11-43
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How do you compute the expected return and
standard deviation for an individual asset? For a
portfolio?
What is the difference between systematic and
unsystematic risk?
What type of risk is relevant for determining the
expected return?
Consider an asset with a beta of 1.2, a risk-free rate of
5%, and a market return of 13%.
◦ What is the expected return on the asset?
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11-44