Chapter 9
Capital Market Theory
Learning Objectives
• Explain capital market theory and the Capital Asset
Pricing Model (CAPM).
• Discuss the importance and composition of the
market portfolio.
• Describe two important relationships in CAPM as
represented by the capital market line and the
security market line.
• Describe how betas are estimated and how beta is
used.
• Discuss the Arbitrage Pricing Theory as an
alternative to the Capital Asset Pricing Model.
Capital Market Theory
Describes the pricing of capital assets in
financial markets
Capital Asset Pricing Model
• Relates the required rate of return for any
security with the market risk for the security as
measured by beta
• 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,
choosing a location on the efficient frontier that
matches his/her return-risk preferences
CAPM Assumptions
• All investors:
•
 Use the same
•
information to
generate an efficient
frontier (i.e., identical
inputs: E(R), σ, ρ) •
 Have the same one- •
period time horizon
 Can borrow or lend
money at the risk- •
free rate of return
No transaction costs
No personal income
(i.e., indifferent
between dividends and
capital gains) taxes
No inflation
No single investor can
affect the price of a
stock (i.e., price-takers)
Capital markets are in
equilibrium
CAPM Assumptions
• These assumptions appear unrealistic
• The important issue is how well the theory predicts
(describes) reality
• The CAPM is robust since most of its assumptions
can be relaxed without significant effects on the
model
• Not all of the CAPM assumptions are unrealistic:



Some institutional investors are tax-exempt
Significant reduction in transaction costs by using
discount brokers and/or internet
For the one-period horizon of the model, inflation
may be fully (or mostly) anticipated
Market Portfolio
• Most important implication of the CAPM

All investors hold the same optimal portfolio of risky
assets
•


As a result of the assumption that all investors have
the same time horizon and homogenous expectations
regarding the expected returns and risks for any given
risky asset
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
Characteristics of the Market Portfolio (M)
• All risky assets must be in portfolio, so it is
completely diversified

Contains only systematic risk (cannot be eliminated)
• All securities included in proportion to their market
value
• Unobservable, but proxied by S&P/TSX Composite
Index in Canada (or the S&P 500 in the US)
• In theory, should contain all risky assets worldwide,
both financial and real, in their proper proportions
• Is found by determining which efficient portfolio
offers the highest risk premium, given the existence
of a risk-free asset
The Equilibrium Risk-Return trade-off
• The CAPM is an equilibrium model that
encompasses two important relationships:


The capital market line (CML), specifies the
equilibrium relationship between expected
return and total risk for efficient portfolios
The security market line (SML), specifies the
equilibrium relationship between expected
return and systematic risk
Capital Market Line
L
M
E(RM)
x
RF
y
M
Risk
• Line from RF to L is
capital market line (CML)
• x = risk premium
= E(RM) - RF
• y = risk = M
• Slope = x/y = market
price of risk for efficient
portfolios
= [E(RM) - RF]/M
• y-intercept = RF = price
of forgone consumption
Example: Capital Market Line
• (Pg 247) Assume that the expected return on
portfolio M is 13%, with a standard deviation of
25%, and that RF is 7%
• Calculate the slope of the CML
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(R p )  RF 
E(R M )  RF
M
p
Capital Market Line
• The following should be noted about the CML:




Only efficient portfolios consisting of the risk-free
asset and portfolio M lie on the CML
It indicates the optimal expected returns associated
with different portfolio risk levels
It must always be upwards sloping because the
price of risk must always be positive
Although, it must be upward sloping ex ante (before
the fact), it can be, and sometimes is, downward
sloping ex post (after the fact). This merely indicates
that the returns actually realized differed from those
that were expected
Security Market Line
• CML Equation only applies to markets in equilibrium
and efficient portfolios (i.e., cannot be used to
assess the expected return on individual securities
or inefficient portfolios)
• The Security Market Line depicts the tradeoff
between risk and expected return for individual
securities
• Under CAPM, all investors hold the risky portion of
their portfolio in the market portfolio

How does an individual security contribute to the risk
of the market portfolio?
Security Market Line
• The expected return on any risky asset is directly
proportional to its covariance with the market
portfolio
• Equation for expected return for an individual stock
similar to CML Equation
E(R i )  RF 
E(R M )  RF  i,M
M
M
 RF   i E(R M )  RF
Security Market Line
• Beta = 1.0 implies as
risky as market
• Securities A and B are
more risky than the
market
SML
E(R)
A
E(RM)
RF
B

C
• Security C is less risky
than the market

0
0.5
Beta > 1.0
1.0 1.5
BetaM
2.0
Beta < 1.0
Security Market Line
• The SML represents the trade-off between systematic
risk (β) and the expected return for all assets, whether
individual securities, inefficient portfolios, or efficient
portfolios
• Beta measures systematic risk




Measures relative risk compared to the market portfolio of
all stocks
Volatility of security i is different (higher or lower) than
that of the market if β_i > 1 or β_i < 1 and is equal to that
of the market if β_i = 1
β_i = 1 means that for every 1% change in the market’s
return, on average security i’s returns change 1%
β_M = 1 and β_RF = 0
Security Market Line
• β is useful for comparing the relative systematic
risk of different stocks and, in practice, is used by
investors to judge a stock’s riskiness
• βs may vary widely across companies in different
industries and within a give industry (e.g., β for
Barrick Gold Corp. is 0.63 and for Eldorado Gold
Corp. is 1.2)
• All securities should lie on the SML

The expected return on the security should be only
that return needed to compensate for systematic
risk
SML and Asset Values
Er
Underpriced
SML: Er = rf +  (Erm – rf)
Overpriced
rf
β
 expected return > required return according to CAPM
 lie “above” SML
Overpriced
 expected return < required return according to CAPM
 lie “below” SML
Correctly priced  expected return = required return according to CAPM
 lie along SML
Underpriced
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
Example: Expected Return-Beta
Relationship
• (Pg 252) If the β estimate for security i is 1.04,
the RF is 0.0241, and the expected return on the
market is estimated to be 0.10.
• Calculate the required return on security i
Estimating the SML
• To use the SML, an investor needs estimates of the
return on the risk-free asset, the expected return on
the market index, and the β for an individual
security
• Treasury Bill rate used to estimate RF
• Expected return for the market index in not
observable

Estimated using past market returns and taking an
expected value
• Estimating individual security betas is difficult


β is only company-specific factor in CAPM
Requires asset-specific forecast
Estimating Beta
• Market model

Relates the return on each stock to the return on the
market, assuming a linear relationship with an
intercept and slope
Rit =i +i RMt + eit


It is identical to the single-index model except that it
does not make the assumption that the error terms
of the different securities are uncorrelated
The Market Model produces an estimate of return
for any stock
Estimating Beta
• Characteristic line



A regression equation used to estimate β by
regressing stock returns on market returns
Line fitted to total returns for a security relative to
total returns for the market index (Fig 9.6 pg 255)
β is the slope of the characteristic line
How Accurate Are Beta Estimates?
• Betas change with a company’s situation (e.g.,
earnings & cash flows)

Not stationary over time
• Estimating a future beta

May differ from the historical beta
• RMt represents the total of all marketable assets
in the economy

Approximated with a stock market index, which, in
turn, approximates return on all common stocks
How Accurate Are Beta Estimates?
• No one correct number of observations and
time periods for calculating beta. As a result,
estimates of β will vary
• The regression estimates of the true  and 
from the characteristic line are subject to
estimation error
• Portfolio betas more reliable than individual
security betas
• βs for large portfolios are stable (show less
change from period to period) because of the
averaging effect (i.e., errors involved in
estimating βs tend to cancel out)
Test of CAPM
• Previous empirical results indicate that:
Ri =a1 +i a2

The SML appears to be linear (i.e., the trade-ff
between expected return and risk is an upward
sloping straight line

The intercept term, a1, is generally found to be
higher than RF

The slope of the CAPM, a2, is generally found to be
less steep than predicted by the theory (i.e.,
overpredicts returns for low-β stocks and
underpredicts returns for high-β stock)
Test of CAPM
• Fama and French (1992)



Indicate that the CAPM’s sole risk factor, market risk
β, posses no explanatory power in discriminating
among the cross-sectional returns of US stocks
Common market equity (ME) and the ratio of book
equity to market equity (BE/ME) combine to explain
the cross-section of expected returns
Three-factor model (overall market factors, factors
related to firm size, & BE/ME ratio)
Test of CAPM
• Empirical SML is “flatter” than predicted SML
• Fama and French (1992)



Market
Size
Book-to-market ratio
• Roll’s Critique


True market portfolio is unobservable
Tests of CAPM are merely tests of the meanvariance efficiency of the chosen market proxy
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
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
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(Rit) =a0+bi1 (risk premium for factor 1) +bi2
(risk premium for factor 2) +… +bin (risk
premium for factor n)
APT Model
• Reduces to CAPM if there is only one factor
and that factor is market risk
• Roll and Ross (1980) Factors:





Changes in expected inflation
Unanticipated changes in inflation
Unanticipated changes in industrial production
Unanticipated changes in the default risk
premium
Unanticipated changes in the term structure of
interest rates
Problems with APT
• Factors are not well specified ex ante

To implement the APT model, the factors that
account for the differences among security
returns are required
•
CAPM identifies market portfolio as single
factor
• Neither CAPM or APT has been proven
superior

Both rely on unobservable expectations