Chapter 7
Bodie
Kane Marcus Perrakis
Ryan
INVESTMENTS, Fourth Canadian Edition
The Capital
Asset Pricing
Model
Slide 7-1
Copyright © McGraw-Hill Ryerson Limited, 2003
Bodie
Kane Marcus Perrakis
Ryan
INVESTMENTS, Fourth Canadian Edition
Chapter Summary
 Objective: To present the basic version
of the model and its applicability.
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Slide 7-2
Assumptions
Resulting Equilibrium Conditions
The Security Market Line (SML)
Black’s Zero Beta Model
CAPM and Liquidity
Copyright © McGraw-Hill Ryerson Limited, 2003
Bodie
Kane Marcus Perrakis
Ryan
INVESTMENTS, Fourth Canadian Edition
Demand for Stocks and
Equilibrium Prices
 Imagine a world where all investors face
the same opportunity set
 Each investor computes his/her optimal
(tangency) portfolio – as in Chapter 6
 The demand of this investor for a
particular firm’s shares comes from this
tangency portfolio
Slide 7-3
Copyright © McGraw-Hill Ryerson Limited, 2003
Bodie
Kane Marcus Perrakis
Ryan
INVESTMENTS, Fourth Canadian Edition
Demand for Stocks and
Equilibrium Prices (cont’d)
 As the price of the shares falls, the
demand for the shares increases
 The supply of shares is vertical, fixed
and independent of the share price
 The CAPM shows the conditions that
prevail when supply and demand are
equal for all firms in investor’s
opportunity set
Slide 7-4
Copyright © McGraw-Hill Ryerson Limited, 2003
Bodie
Kane Marcus Perrakis
Ryan
INVESTMENTS, Fourth Canadian Edition
Summary Reminder
 Objective: To present the basic version
of the model and its applicability.





Slide 7-5
Assumptions
Resulting Equilibrium Conditions
The Security Market Line (SML)
Black’s Zero Beta Model
CAPM and Liquidity
Copyright © McGraw-Hill Ryerson Limited, 2003
Bodie
Kane Marcus Perrakis
Ryan
INVESTMENTS, Fourth Canadian Edition
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
Slide 7-6
Copyright © McGraw-Hill Ryerson Limited, 2003
Bodie
Kane Marcus Perrakis
Ryan
INVESTMENTS, Fourth Canadian Edition
Assumptions
 Individual investors are price takers
 Single-period investment horizon
 Investments are limited to traded
financial assets
 No taxes, and transaction costs
Slide 7-7
Copyright © McGraw-Hill Ryerson Limited, 2003
Bodie
Kane Marcus Perrakis
Ryan
INVESTMENTS, Fourth Canadian Edition
Assumptions (cont’d)
 Information is costless and available to
all investors
 Investors are rational mean-variance
optimizers
 There are homogeneous expectations
Slide 7-8
Copyright © McGraw-Hill Ryerson Limited, 2003
Bodie
Kane Marcus Perrakis
Ryan
INVESTMENTS, Fourth Canadian Edition
Summary Reminder
 Objective: To present the basic version of
the model and its applicability.





Slide 7-9
Assumptions
Resulting Equilibrium Conditions
The Security Market Line (SML)
Black’s Zero Beta Model
CAPM and Liquidity
Copyright © McGraw-Hill Ryerson Limited, 2003
Bodie
Kane Marcus Perrakis
Ryan
INVESTMENTS, Fourth Canadian Edition
Resulting Equilibrium
Conditions
 All investors will hold the same portfolio
of 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
 The market portfolio is on the efficient
frontier and, moreover, it is the tangency
portfolio
Slide 7-10
Copyright © McGraw-Hill Ryerson Limited, 2003
Bodie
Kane Marcus Perrakis
Ryan
INVESTMENTS, Fourth Canadian Edition
Resulting Equilibrium
Conditions (cont’d)
 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
Slide 7-11
Copyright © McGraw-Hill Ryerson Limited, 2003
Bodie
Kane Marcus Perrakis
Ryan
INVESTMENTS, Fourth Canadian Edition
Capital Market Line
E(r)
CML
E(rM)
M
rf
m
Slide 7-12

Copyright © McGraw-Hill Ryerson Limited, 2003
Bodie
Kane Marcus Perrakis
Ryan
INVESTMENTS, Fourth Canadian Edition
Slope and Market Risk
Premium
M
rf
E(rM) - rf
=
=
=
E(rM)  rf
=
M
Slide 7-13
The market portfolio
Risk free rate
Market risk premium
Slope of the CML
Copyright © McGraw-Hill Ryerson Limited, 2003
Bodie
Kane Marcus Perrakis
Ryan
INVESTMENTS, Fourth Canadian Edition
Summary Reminder
 Objective: To present the basic version
of the model and its applicability.





Slide 7-14
Assumptions
Resulting Equilibrium Conditions
The Security Market Line (SML)
Black’s Zero Beta Model
CAPM and Liquidity
Copyright © McGraw-Hill Ryerson Limited, 2003
Bodie
Kane Marcus Perrakis
Ryan
INVESTMENTS, Fourth Canadian Edition
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
Slide 7-15
Copyright © McGraw-Hill Ryerson Limited, 2003
Bodie
Kane Marcus Perrakis
Ryan
INVESTMENTS, Fourth Canadian Edition
Security Market Line
E(r)
SML
E(rM)
rf
ß
Slide 7-16
M
= 1.0
ß
Copyright © McGraw-Hill Ryerson Limited, 2003
Bodie
Kane Marcus Perrakis
Ryan
INVESTMENTS, Fourth Canadian Edition
SML Relationships
 = Cov(ri,rm) / m2
Slope SML = E(rm) - rf
= market risk premium
E(r)SML = rf + [E(rm) - rf ]
BetaM = Cov (rM,rM) / M2
= M2 / M2 = 1
Slide 7-17
Copyright © McGraw-Hill Ryerson Limited, 2003
Bodie
Kane Marcus Perrakis
Ryan
INVESTMENTS, Fourth Canadian Edition
Sample Calculations for
SML
E(rm) - rf = .08
rf = .03
a) x = 1.25
E(rx) = .03 + 1.25(.08) = .13 or 13%
b) y = .6
E(ry) = .03 + .6(.08) = .078 or 7.8%
Slide 7-18
Copyright © McGraw-Hill Ryerson Limited, 2003
Bodie
Kane Marcus Perrakis
Ryan
INVESTMENTS, Fourth Canadian Edition
Graph of Sample
Calculations
E(r)
SML
Rx=13%
.08
Rm=11%
Ry=7.8%
3%
.6
ß
Slide 7-19
1.0
1.25
ß
ß
y
m
x
ß
Copyright © McGraw-Hill Ryerson Limited, 2003
Bodie
Kane Marcus Perrakis
Ryan
INVESTMENTS, Fourth Canadian Edition
Disequilibrium Example
E(r)
SML
15%
Rm=11%
rf=3%
1.0 1.25
Slide 7-20
ß
Copyright © McGraw-Hill Ryerson Limited, 2003
Bodie
Kane Marcus Perrakis
Ryan
INVESTMENTS, Fourth Canadian Edition
Disequilibrium Example
 Suppose a security with a  of 1.25 is
offering expected return of 15%
 According to SML, it should be 13%
 Under-priced: offering too high of a rate
of return for its level of risk
Slide 7-21
Copyright © McGraw-Hill Ryerson Limited, 2003
Bodie
Kane Marcus Perrakis
Ryan
INVESTMENTS, Fourth Canadian Edition
Summary Reminder
 Objective: To present the basic version
of the model and its applicability.





Slide 7-22
Assumptions
Resulting Equilibrium Conditions
The Security Market Line (SML)
Black’s Zero Beta Model
CAPM and Liquidity
Copyright © McGraw-Hill Ryerson Limited, 2003
Bodie
Kane Marcus Perrakis
Ryan
INVESTMENTS, Fourth Canadian Edition
Black’s Zero Beta Model
 Absence of a risk-free asset
 Combinations of portfolios on the
efficient frontier are efficient
 All frontier portfolios have companion
portfolios that are uncorrelated
 Returns on individual assets can be
expressed as linear combinations of
efficient portfolios
Slide 7-23
Copyright © McGraw-Hill Ryerson Limited, 2003
Bodie
Kane Marcus Perrakis
Ryan
INVESTMENTS, Fourth Canadian Edition
Black’s Zero Beta Model
Formulation
E(ri )  E(rQ )  E(rP )  E(rQ )
Slide 7-24
Cov(ri , rP )  Cov(rP , rQ )
P2  Cov(rP , rQ )
Copyright © McGraw-Hill Ryerson Limited, 2003
Bodie
Kane Marcus Perrakis
Ryan
INVESTMENTS, Fourth Canadian Edition
Efficient Portfolios and
Zero Companions
E(r)
Q
P
E[rz (Q)]
E[rz (P)]
Z(Q)
Z(P)

Slide 7-25
Copyright © McGraw-Hill Ryerson Limited, 2003
Bodie
Kane Marcus Perrakis
Ryan
INVESTMENTS, Fourth Canadian Edition
Zero Beta Market Model
Cov(ri , rM )
E(ri )  E(rZ(M) )  E(rM )  E(rZ(M) )
M2
CAPM with E(rz (M)) replacing rf
Slide 7-26
Copyright © McGraw-Hill Ryerson Limited, 2003
Bodie
Kane Marcus Perrakis
Ryan
INVESTMENTS, Fourth Canadian Edition
Summary Reminder
 Objective: To present the basic version
of the model and its applicability.





Slide 7-27
Assumptions
Resulting Equilibrium Conditions
The Security Market Line (SML)
Black’s Zero Beta Model
CAPM and Liquidity
Copyright © McGraw-Hill Ryerson Limited, 2003
Bodie
Kane Marcus Perrakis
Ryan
INVESTMENTS, Fourth Canadian Edition
CAPM & Liquidity
 Liquidity – cost or ease with which an
asset can be sold
 Illiquidity Premium
 Research supports a premium for
illiquidity

Slide 7-28
Amihud and Mendelson
Copyright © McGraw-Hill Ryerson Limited, 2003
Bodie
Kane Marcus Perrakis
Ryan
INVESTMENTS, Fourth Canadian Edition
CAPM with a Liquidity
Premium
E(ri )  rf  i E(ri )  rf   f(ci )
f (ci) = liquidity premium for security i
f (ci) increases at a decreasing rate
Slide 7-29
Copyright © McGraw-Hill Ryerson Limited, 2003
Bodie
Kane Marcus Perrakis
Ryan
INVESTMENTS, Fourth Canadian Edition
Illiquidity and Average
Returns
Average monthly return (%)
Bid-ask spread (%)
Slide 7-30
Copyright © McGraw-Hill Ryerson Limited, 2003