CHAPTER 9
The Capital Asset
Pricing Model
Investments, 8th edition
Bodie, Kane and Marcus
Slides by Susan Hine
McGraw-Hill/Irwin
Copyright © 2009 by The McGraw-Hill Companies, Inc. All rights reserved.
Capital Asset Pricing Model (CAPM)
• It gives a precise prediction of the relationship
that should be observed between the risk of an
asset and its expected return.
• Beneftis:
– Provides benchmark rate of return for evaluating possible
investments
– Helps to make an educated guess as to the expected return
on assets that have not yet been traded in the marketplace
• It is the equilibrium model
• Derived using principles of diversification with
simplified assumptions
• Markowitz, Sharpe, Lintner and Mossin
9-2
Assumptions
• Individual investors are price takers: they act
as though security prices are unaffected by
their own trades (their wealth is small
compared to the total wealth of all investors)
• Single-period investment horizon: myopicshort-sighted behavior (ignores everything
that might happen after the end of the single
period horizon)
• Investments are limited to traded financial
assets: (traded financial assets –bonds and
stocks) and risk-free borrowing or lending)
9-3
Assumptions Continued
• No taxes and transaction costs
• Information is costless and available to all
investors
• Investors are rational mean-variance
optimizers: all investors use Markowitz
Portfolio Selection Model (minimum-variance
frontier, efficient frontier, CAL, optimal risky
portfolio and optimal complete portfolio)
• There are homogeneous expectations: all
investors analyze securities in the same way
and share the same economic view
9-4
Resulting Equilibrium Conditions
• All investors will hold the same portfolio for
risky assets – market portfolio
• Market portfolio contains all securities (all
traded assets) and the proportion of each
security is its market value as a percentage
of total market value
• Market portfolio:
– on the efficient frontier
– The tangency portfolio to the optimal CAL
9-5
Figure 9.1 The Efficient Frontier and the
Capital Market Line
9-6
Resulting Equilibrium Conditions
Continued
• 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
9-7
Market Risk Premium
•The risk premium on the market portfolio will
be proportional to its risk and the degree of risk
aversion of the investor:
E (rM )  rf  A M2
where 
2
M
X 0.01
is the variance of the market portolio and
A is the average degree of risk aversion across investors
9-8
Return and Risk For Individual Securities
• The risk premium on individual securities is a
function of the individual security’s
contribution to the risk of the market portfolio
• An individual security’s risk premium is a
function of the covariance of returns with the
assets that make up the market portfolio
9-9
Using GE Text Example
• Covariance of GE return with the market
portfolio:
n

 n
Cov(rGE , rM )  Cov  rGE ,  wk rk    wk Cov (rk , rGE )
k 1

 k 1
• Therefore, the reward-to-risk ratio for
investments in GE would be:
GE's contribution to risk premium wGE  E (rGE )  rf  E (rGE )  rf


GE's contribution to variance
wGE Cov(rGE , rM ) Cov(rGE , rM )
9-10
Using GE Text Example Continued
• Reward-to-risk ratio for investment in
market portfolio:
Market risk premium E (rM )  rf

Market variance
 M2
• Reward-to-risk ratios of GE and the market
Basic
portfolio:
Principle: all
E (rGE )  rf
E (rM ( rf )
Cov (rGE , rM )


2
M
• And the risk premium for GE:
E (rGE )  rf 
Cov (rGE , rM )

2
M
 E (rM )  rf 
investments
should offer
the same
reward-to-risk
raito.
Otherwise
investors will
rearrange
their
portfolios.
9-11
Expected Return-Beta Relationship
• CAPM holds for the overall portfolio because:
E (rP )   wk E (rk ) and
k
 P   wk  k
k
• This also holds for the market portfolio:
E (rM )  rf   M  E (rM )  rf 
9-12
Figure 9.2 The Security Market Line
9-13
Figure 9.3 The SML and a PositiveAlpha Stock
Alpha: the
difference
between the
fair and the
actual
expected rates
of return
9-14
The CAPM and Reality
• Is the condition of zero alphas for all stocks
as implied by the CAPM met
– Not perfect but one of the best available
• Is the CAPM testable
– Proxies must be used for the market
portfolio
• CAPM is still considered the best available
description of security pricing and is widely
accepted
9-15
Extensions of the CAPM
• Zero-Beta Model
– Helps to explain positive alphas on low
beta stocks and negative alphas on high
beta stocks
• Consideration of labor income and nontraded assets
• Merton’s Multiperiod Model and hedge
portfolios
– Incorporation of the effects of changes in
the real rate of interest and inflation
9-16
Extensions of the CAPM Continued
• A consumption-based CAPM
– Models by Rubinstein, Lucas, and Breeden
• Investor must allocate current wealth between
today’s consumption and investment for the future
9-17
Liquidity and the CAPM
• Liquidity
• Illiquidity Premium
• Research supports a premium for illiquidity.
– Amihud and Mendelson
– Acharya and Pedersen
9-18
Figure 9.5 The Relationship Between
Illiquidity and Average Returns
9-19
Three Elements of Liquidity
• Sensitivity of security’s illiquidity to market
illiquidity:  L1  Cov(Ci , CM )
Var ( RM  CM )
• Sensitivity of stock’s return to market
illiquidity:   Cov( R , C )
i
L2
M
Var ( RM  CM )
• Sensitivity of the security illiquidity to the
market rate of return:
 L3 
Cov (Ci , RM )
Var ( RM  CM )
9-20