Asset Pricing Models
Chapter 9
Charles P. Jones, Investments: Analysis and Management,
Ninth Edition, John Wiley & Sons
Prepared by
G.D. Koppenhaver, Iowa State University
20-1
Capital Asset Pricing Model
Focus on the equilibrium relationship
between the risk and expected return on
risky assets
 Builds on Markowitz portfolio theory
 Each investor is assumed to diversify his
or her portfolio according to the Markowitz
model

20-2
CAPM Assumptions

All investors:
– Use the same
information to
generate an efficient
frontier
– Have the same oneperiod time horizon
– Can borrow or lend
money at the risk-free
rate of return
No transaction costs,
no personal income
taxes, no inflation
 No single investor can
affect the price of a
stock
 Capital markets are in
equilibrium

20-3
Borrowing and Lending Possibilities

Risk free assets
– Certain-to-be-earned expected return and a
variance of return of zero
– No correlation with risky assets
– Usually proxied by a Treasury security
 Amount to be received at maturity is free of default
risk, known with certainty

Adding a risk-free asset extends and
changes the efficient frontier
20-4
Risk-Free Lending
Riskless assets can
be combined with any
L
B portfolio in the
efficient set AB

T
E(R)
Z
X
RF
A
– Z implies lending

Set of portfolios on
line RF to T
dominates all
portfolios below it
Risk
20-5
Impact of Risk-Free Lending

If wRF placed in a risk-free asset
– Expected portfolio return
E(R p )  w RF RF  ( 1-w RF )E(R X )
– Risk of the portfolio
σ p  ( 1-w RF )σ X
 Expected return and risk of the portfolio
with lending is a weighted average
20-6
Borrowing Possibilities
Investor no longer restricted to own wealth
 Interest paid on borrowed money

– Higher returns sought to cover expense
– Assume borrowing at RF

Risk will increase as the amount of
borrowing increases
– Financial leverage
20-7
The New Efficient Set
Risk-free investing and borrowing creates
a new set of expected return-risk
possibilities
 Addition of risk-free asset results in

– A change in the efficient set from an arc to a
straight line tangent to the feasible set without
the riskless asset
– Chosen portfolio depends on investor’s riskreturn preferences
20-8
Portfolio Choice
The more conservative the investor the
more is placed in risk-free lending and the
less borrowing
 The more aggressive the investor the less
is placed in risk-free lending and the more
borrowing

– Most aggressive investors would use leverage
to invest more in portfolio T
20-9
Capital Market Line
A risk averse investor makes investment
decisions based on Markowitz principles.
 Investors can borrow and lend freely at the RFR.
 Each investor should construct an optimal
portfolio that matches his or her preferred risk
return combinations.
 All investors can construct an efficient portfolio
by combining an efficient portfolio M, with a risk
free asset.

20-10
CML
Depicts the equilibrium conditions that
prevail in the market for efficient portfolio
consisting of the optimal portfolio of risky
assets and the risk free asset.
 All combinations of the risk free asset and
the risky portfolio M are on CML, and, in
equilibrium, all investors will end up with a
portfolio somewhere on CML based on
their risk tolerance.

20-11
Capital Market Line
L

M
E(RM)

x
RF


y
M

Line from RF to L is
capital market line
(CML)
x = risk premium
=E(RM) - RF
y =risk =M
Slope =x/y
=[E(RM) - RF]/M
y-intercept = RF
Risk
20-12
Capital Market Line
Slope of the CML is the market price of
risk for efficient portfolios, or the
equilibrium price of risk in the market
 Relationship between risk and expected
return for portfolio P (Equation for CML):

E(RM )  RF
E(Rp )  RF 
σp
σM
20-13
Important points about the CML
Only efficient portfolios consisting of the risk free
asset and portfolio M lie on the CML.
 The CML must always be upward sloping
because the price of risk must always be
positive. (risk & return relationship)
 On a historical basis, for some particular time
period, the CML can be downward sloping.
(RF>RM)
 The CML can be used to determine the optimal
expected returns associated with different
portfolio risk levels. CML indicates the required
return for each portfolio risk level.

20-14
Market Portfolio

Most important implication of the CAPM
– All investors hold the same optimal portfolio of
risky assets
– The optimal portfolio is at the highest point of
tangency between RF and the efficient frontier
– The portfolio of all risky assets is the optimal
risky portfolio
 Called the market portfolio
20-15
Characteristics of the
Market Portfolio

All risky assets must be in portfolio, so it is
completely diversified
– Includes only systematic risk
All securities included in proportion to their
market value
 Unobservable but proxied by S&P 500
 Contains worldwide assets

– Financial and real assets
20-16
The Separation Theorem
Investors use their preferences
(reflected in an indifference curve) to
determine their optimal portfolio
 Separation Theorem:

– The investment decision, which risky
portfolio to hold, is separate from the
financing decision
– Allocation between risk-free asset and
risky portfolio separate from choice of risky
portfolio, T
20-17
Separation Theorem

All investors
– Invest in the same portfolio
– Attain any point on the straight line RF-T-L by
by either borrowing or lending at the rate RF,
depending on their preferences

Risky portfolios are not tailored to each
individual’s taste
20-18
Security Market Line
CML Equation only applies to markets in
equilibrium and efficient portfolios
 The Security Market Line depicts the
tradeoff between risk and expected return
for individual securities
 Under CAPM, all investors hold the market
portfolio

– How does an individual security contribute to
the risk of the market portfolio?
20-19
Security Market Line
A security’s contribution to the risk of the
market portfolio is based on beta
 Equation for expected return for an
individual stock

E(Ri )  RF  βi E(RM )  RF 
20-20
Security Market Line
SML
E(R)
A
kM
B
kRF
C
Beta = 1.0 implies as
risky as market
 Securities A and B
are more risky than
the market

– Beta >1.0
Security C is less
1.0 1.5 2.0 risky than the market

0
0.5
BetaM
– Beta <1.0
20-21
Security Market Line

Beta measures systematic risk
– Measures relative risk compared to the
market portfolio of all stocks
– Volatility different than market

All securities should lie on the SML
– The expected return on the security should be
only that return needed to compensate for
systematic risk
20-22
CAPM’s Expected
Return-Beta Relationship

Required rate of return on an asset (ki) is
composed of
– risk-free rate (RF)
– risk premium (i [ E(RM) - RF ])
 Market risk premium adjusted for specific security
ki = RF +i [ E(RM) - RF ]
– The greater the systematic risk, the greater
the required return
20-23
Estimating the SML
Treasury Bill rate used to estimate RF
 Expected market return unobservable

– Estimated using past market returns and
taking an expected value

Estimating individual security betas difficult
– Only company-specific factor in CAPM
– Requires asset-specific forecast
20-24
Estimating Beta

Market model
– Relates the return on each stock to the return
on the market, assuming a linear relationship
Ri =i +i RM +ei

Characteristic line
– Line fit to total returns for a security relative to
total returns for the market index
20-25
How Accurate Are Beta Estimates?

Betas change with a company’s situation
– Not stationary over time

Estimating a future beta
– May differ from the historical beta

RM represents the total of all marketable
assets in the economy
– Approximated with a stock market index
– Approximates return on all common stocks
20-26
How Accurate Are Beta Estimates?
No one correct number of observations
and time periods for calculating beta
 The regression calculations of the true 
and  from the characteristic line are
subject to estimation error
 Portfolio betas more reliable than
individual security betas

20-27
Arbitrage Pricing Theory

Based on the Law of One Price
– Two otherwise identical assets cannot sell at
different prices
– Equilibrium prices adjust to eliminate all
arbitrage opportunities

Unlike CAPM, APT does not assume
– single-period investment horizon, absence of
personal taxes, riskless borrowing or lending,
mean-variance decisions
20-28
Factors
APT assumes returns generated by a
factor model
 Factor Characteristics

– Each risk must have a pervasive influence on
stock returns
– Risk factors must influence expected return
and have nonzero prices
– Risk factors must be unpredictable to the
market
20-29
APT Model
Most important are the deviations of the
factors from their expected values
 The expected return-risk relationship for
the APT can be described as:

E(Ri) =RF +bi1 (risk premium for factor 1)
+bi2 (risk premium for factor 2) +… +bin
(risk premium for factor n)
20-30
Problems with APT

Factors are not well specified ex ante
– To implement the APT model, need the
factors that account for the differences among
security returns
 CAPM identifies market portfolio as single factor

Neither CAPM or APT has been proven
superior
– Both rely on unobservable expectations
20-31