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The Capital Asset Pricing Model
Chapter 9
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 is a centerpiece of
modern financial theory.
It gives us a precise prediction of the relationship
between risk and return.
Gives us a benchmark to make comparisons
Gives us a way to evaluate non traded assets
such as investment projects (use in Capital
Budgeting)
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. (What would happen if
this were not true?)
9-5
Capital Market Line
E(r)
E(rM)
The CML is the CAL between the risk
free asset and the Market Portfolio
M
CML
rf
m

9-6
Derivation of the CAPM
9-7
Recall the optimal choice equation
y 
*
E (rp )  rf
0.01A
2
p
Given that on balance, for every $1 borrower
there must be $1 lent, we can plug y=1 into
this equation and compute the market risk
premium – it depends on variance of the
market portfolio, and overall average risk
aversion
9-8
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. i.e. the beta
9-9
Mutual Fund Theorem
The passive investment strategy is
efficient
Another way of stating the “separation
theorem” of last chapter
Portfolio selection has two components
First the technological to create a mutual
fund of the market portfolio (index fund)
Second to optimize to an individual, based
on risk tolerance, how much of the risk free
each person should hold
9-10
Slope and Market Risk Premium
M
rf
E(rM) - rf
=
=
=
Market portfolio
Risk free rate
Market risk premium
E(rM) - rf
=
Market reward to variability
M
=
Slope of the CAPM
9-11
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 (i.e. the beta).
An individual security’s risk premium is a
function of the covariance of returns with the
assets that make up the market portfolio.
i 
cov( ri , rM )

2
M
 i ,M
i
M
9-12
Security Market Line (Graph of CAPM)
E (ri )  ( E (rM )  rf )  i  rf
E(r)
SML
E(rM)
rf
M = 1.0

9-13
SML Relationships
 = [COV(ri,rm)] / m2
Slope SML = E(rm) - rf
= market risk premium
SML = rf + [E(rm) - rf]
Betam = [Cov (rm,rm)] / m2
= m2 / m2 = 1
9-14
Sample Calculations for SML
E(rm) - rf = .08 (market risk premium)
rf = .03
x = 1.25
E(rx) = 0.03 + 1.25(0.08) = .13 or 13%
y = .6
E(ry) = 0.03 + 0.6(0.08) = .078 or 7.8%
These show, the expected return is a
function of beta
9-15
Graph of Sample Calculations
E(r)
SML
Rx=13%
.08
Rm=11%
Ry=7.8%
3%

.6
y
1.0
1.25
x
9-16
Disequilibrium Example
Suppose a security with a  of 1.25 is
offering expected return of 15%.
According to SML, it should be 13%.
This security has an alpha of 2%
Under-priced: offering too high of a rate
of return for its level of risk.
The price must rise, so that the
expected return falls to 13% to regain
equilibrium
9-17
Disequilibrium Example (illustrate alpha)
E(r)
“alpha” is the vertical distance from a
point to the line
SML
15%
Rm=11%
rf=3%

1.0
1.25
9-18
Adjustments to CAPM
Black’s zero beta version if there is no
risk free
Adjustments to consider liquidity
(require a reward for bearing illiquidity)
Market to Book ratio’s seem to have
empirical value (No theoretical basis)
9-19
9-20
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.
9-21
Black’s Zero Beta Model Formulation

E (ri )  E (rQ )  E (rP )  E (rQ )

Cov(ri , rP )  Cov(rP , rQ )
 P2  Cov(rP , rQ )
9-22
Efficient Portfolios and Zero Companions
E(r)
Q
P
E[rz (Q)]
E[rz (P)]
Z(Q)
Z(P)

9-23
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
9-24
CAPM & Liquidity
Liquidity
Illiquidity Premium
Research supports a premium for
illiquidity.
Amihud and Mendelson
9-25
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
9-26
Liquidity and Average Returns
Average monthly return(%)
Bid-ask spread (%)
9-27