Chapter 9
Capital Asset Pricing
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Capital Asset Pricing Model (CAPM)
• Equilibrium model that underlies all modern
financial theory
• Derived using principles of diversification with
simplified assumptions
• Markowitz, Sharpe, Lintner and Mossin are
researchers credited with its development
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Assumptions
•
•
•
•
•
•
•
Individual investors are price takers
Single-period investment horizon
Investments are limited to traded financial assets
No taxes, and transaction costs
Information is costless and available to all investors
Investors are rational mean-variance optimizers
Homogeneous expectations
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Resulting Equilibrium Conditions
• All investors will hold the same portfolio for risky assets –
market portfolio
• Market portfolio contains all securities and the proportion
of each security is its market value as a percentage of total
market value
• Risk premium on the market depends on the average risk
aversion of all market participants
• Risk premium on an individual security is a function of its
covariance with the market
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Capital Market Line
E(r)
E(rM)
CML
M
rf
McGraw-Hill/Irwin
sm
s
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Slope and Market Risk Premium
M
rf
E(rM) - rf
=
=
=
Market portfolio
Risk free rate
Market risk premium
E(rM) - rf
=
Market price of risk
=
Slope of the CAPM
sM
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Components of Risk
• Market or systematic risk: risk related to the
macro economic factor or market index
• Unsystematic or firm specific risk: risk not
related to the macro factor or market index
• Total risk = Systematic + Unsystematic
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Single Index Model
r  r   a   r  r  e
i
f
Risk Prem
a
i
i
i
m
f
i
Market Risk Prem
or Index Risk Prem
= the stock’s expected return if the
market’s excess return is zero (rm - rf) = 0
ßi(rm - rf) = the component of return due to
movements in the market index
ei = firm specific component, not due to market
movements
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Risk Premium Format
Let: Ri = (ri - rf)
Rm = (rm - rf)
Risk premium
format
Ri = ai + ßi(Rm) + ei
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Estimating the Index Model
Excess Returns (i)
. ..
. ..
.
.
.
.
.
. . ..
.. . .
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Security
.
.
.
.
.
.
Characteristic
. . .
Line
.
. .. . .
.
. . . Excess returns
. . . . on market index
.
.
.
.
.
.
.
.
Ri = a i + ßiRm + ei
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Expected Return and Risk on Individual
Securities
• The risk premium on individual securities is
a function of the individual security’s
contribution to the risk of the market
portfolio
• Individual security’s risk premium is a
function of the covariance of returns with
the assets that make up the market
portfolio
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Examining Percentage of Variance
Total Risk = Systematic Risk + Unsystematic Risk
Systematic Risk/Total Risk = r2
ßi2 s m2 / s2 = r2
i2 sm2 / i2 sm2 + s2(ei) = r2
This is useful information since it tells us how
well B explains the security’s returns. Will be
between 0 and 100%.
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Security Market Line
E(r)
SML
E(rM)
rf
ß M = 1.0
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ß
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SML Relationships
 = [COV(ri,rm)] / sm2
Slope SML =
E(rm) - rf
= market risk premium
SML = rf + [E(rm) - rf]
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Sample Calculations for SML
E(rm) - rf = .08
rf = .03
x = 1.25
E(rx) = .03 + 1.25(.08) = .13 or 13%
y = .6
e(ry) = .03 + .6(.08) = .078 or 7.8%
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Graph of Sample Calculations
E(r)
SML
Rx=13%
Rm=11%
Ry=7.8%
3%
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.08
.6 1.0 1.25
ßy ßm ßx
ß
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Disequilibrium Example
E(r)
SML
15%
Rm=11%
rf=3%
1.0 1.25
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ß
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Disequilibrium Example
• Suppose a security with a  of 1.25 is offering
expected return of 15%
• According to SML, it should be 13%
• Underpriced: offering too high of a rate of
return for its level of risk
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Stock A has an estimated rate of return of
12% and a beta of 1.2. The market
expected rate of return is 12% and the
risk-free rate is 2%. The alpha of the
stock is __________.
A) 0%
B) -2%
C) 2%
D) -4%
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You invest $8,000 in stock A with a beta of 1.4
and $12,000 in security B with a beta of 0.8.
The beta of this formed portfolio is
__________.
A) 1.10
B) 1.20
C) 1.04
D) 2.20
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Which of the following is(are) correct according
to the CAPM:
A) There is a linear and positive relationship
between a stock's beta and its required return.
B) The expected return of a stock will be
doubled if its beta increases from 1 to 2.
C) There is a linear and positive relationship
between a portfolio's standard deviation and
its required return.
D) All of the above are correct.
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Which one of the following stocks is relatively
more risky when held in a well-diversified
portfolio?
StockStandard Deviation
Beta
ABC
35%
1.2
XYZ
30%
1.6
A) ABC because its beta is lower.
B) XYZ because its beta is higher.
C) ABC because its standard deviation is
higher.
D) XYZ because its standard deviation is
lower.
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The expected market rate of return is 14%
while the risk-free rate expected return is 4%.
If you expect stock A with a beta of 1.2 to
offer a rate of return of 20%, then you should
__________.
A) buy stock A because it is overpriced
B) buy stock A because it is underpriced
C) sell short stock A because it is overpriced
D) sell short stock A because it is underpriced
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The slope of the Security Market Line is
____________.
A) the beta
B) the risk-free rate of return
C) the market return
D) the market risk premium
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The expected return on the market is 12%.
The expected return on a stock with a beta of
1.5 is 17%. What is the risk-free rate of return
according to the CAPM?
A) 2%
B) 6%
C) 8%
D) 5%
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According to the CAPM, a stock with a high
standard deviation must have a beta
________ that of a stock with a low standard
deviation.
A) higher than
B) lower than
C) the same as
D) There is not sufficient information to
determine.
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The expected risk-free rate of return is 4%.
The expected return on a stock with a beta of
1.2 is 16%. What is the expected return on the
market according to the CAPM?
A) 12%
B) 14%
C) 18%
D) 15%
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According to the systematic risk
principle, which one of the following
risks is rewarded?
A) Unsystematic risk.
B) Total risk.
C) Systematic risk.
D) Industry risk.
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