4. Asset Pricing Models:
CAPM & APT
Chapter 9-11
McGraw-Hill/Irwin
Copyright © 2005 by The McGraw-Hill Companies, Inc. All rights reserved.
Capital Asset Pricing Model (CAPM)
It is the 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.
9-2
Assumptions
Individual investors are price takers.
Single-period investment horizon.
Investments are limited to traded
financial assets.
No taxes and transaction costs.
9-3
Assumptions (cont’d)
Information is costless and available to
all investors.
Investors are rational mean-variance
optimizers.
There are homogeneous expectations.
9-4
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.
9-5
Resulting Equilibrium Conditions (cont’d)
Risk premium on the 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.
9-6
Capital Market Line
E(r)
E(rM)
M
CML
rf
m

9-7
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
M
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
Security Market Line
E(r)
SML
E(rM)
rf
bM = 1.0
b
9-10
SML Relationships
b = [COV(ri,rm)] / m2
Slope SML = E(rm) - rf
= market risk premium
SML = rf + b[E(rm) - rf]
Betam = [Cov (ri,rm)] / m2
= m2 / m2 = 1
9-11
Sample Calculations for SML
E(rm) - rf = .08 rf = .03
bx = 1.25
E(rx) = .03 + 1.25(.08) = .13 or 13%
by = .6
e(ry) = .03 + .6(.08) = .078 or 7.8%
9-12
Graph of Sample Calculations
E(r)
SML
Rx=13%
.08
Rm=11%
Ry=7.8%
3%
b
.6
by
1.0
1.25
bx
9-13
Disequilibrium Example
E(r)
SML
15%
Rm=11%
rf=3%
b
1.0
1.25
9-14
Disequilibrium Example (cont.)
Suppose a security with a b 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.
9-15
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.
9-16
Black’s Zero Beta Model Formulation

E (ri )  E (rQ )  E (rP )  E (rQ )

Cov(ri , rP )  Cov(rP , rQ )
 P2  Cov(rP , rQ )
9-17
Efficient Portfolios and Zero Companions
E(r)
Q
P
E[rz (Q)]
E[rz (P)]
Z(Q)
Z(P)

9-18
Zero Beta Market Model

E (ri )  E (rZ ( M ) )  E (rM )  E (rZ ( M ) )

Cov(ri , rM )
 M2
CAPM with E(rz (m)) replacing rf
9-19
CAPM & Liquidity
Liquidity
Illiquidity Premium
Research supports a premium for
illiquidity.
Amihud and Mendelson
9-20
CAPM with a Liquidity Premium


E (ri )  rf  b i E (ri )  rf  f (ci )
f (ci) = liquidity premium for security i
f (ci) increases at a decreasing rate
9-21
Liquidity and Average Returns
Average monthly return(%)
Bid-ask spread (%)
9-22
Arbitrage Pricing Theory
Arbitrage - arises if an investor can construct
a zero investment portfolio with a sure profit.
Since no investment is required, an investor
can create large positions to secure large
levels of profit.
In efficient markets, profitable arbitrage
opportunities will quickly disappear.
9-23
APT & Well-Diversified Portfolios
rP = E (rP) + bPF + eP
F = some factor
For a well-diversified portfolio:
eP approaches zero
Similar to CAPM
9-24
Portfolios and Individual Security
E(r)%
E(r)%
F
F
Portfolio
Individual Security
9-25
Disequilibrium Example
E(r)%
10
7
6
A
D
C
Risk Free 4
.5
1.0
Beta for F
9-26
Disequilibrium Example
Short Portfolio C
Use funds to construct an equivalent
risk higher return Portfolio D.
D is comprised of A & Risk-Free Asset
Arbitrage profit of 1%
9-27
»APT with Market Index Portfolio
E(r)%
M
[E(rM) - rf]
Market Risk Premium
Risk Free
1.0
Beta (Market Index)
9-28
APT and CAPM Compared
APT applies to well diversified portfolios and
not necessarily to individual stocks.
With APT it is possible for some individual
stocks to be mispriced - not lie on the SML.
APT is more general in that it gets to an
expected return and beta relationship without
the assumption of the market portfolio.
APT can be extended to multifactor models.
9-29