

Investment
Analysis & Portfolio Management
(FIN630)
VU
Lesson
# 36
ASSET
PRICING MODEL
Capital
Market Theory:
Capital
market theory is a positive
theory in that it hypothesis
how investors do behave
rather
than, how investors should
behave, as, in the case of
Modem Portfolio
Theory
(MPT).
It is reasonable "to view
capital market" theory; as an
extension of portfolio
theory,
but
it is important to understand that
MPT is not based on the
validity, or lack thereof,
of
capital
market theory.
The
equilibrium model of interest to
many investors is known as
the capital asset
pricing
model,
typically referred to as the
CAPM. It allows us to measure
the relevant risk of
an
individual
security as well as to assess
the relationship between
relevant risk of and
the
returns
expected from investing. The
CAPM is attractive as an equilibrium
model because
of
its simplicity and its
implications. Because of serious
challenges, to the model,
however,
alternatives
have been developed. The
primary alternative to the
CAPM is arbitrage
pricing
theory,
or APT, which allows for
multiple sources of
risk.
Capital
Theory Assumptions:
Capital
market theory involves a set
of predictions concerning equilibrium
expected return
on
risky assets. It typically is
derived by making some
simplifying assumptions in order
to
facilitate
the analysis and help us to
understand the arguments
without fundamentally
changing
the predictions of asset
pricing theory.
Capital
market theory builds on
Markowitz portfolio theory to
diversify his or; her
portfolio,
according
to the Markowitz model,
choosing a location on the
efficient frontier that
matches
his
or her returnrisk references. Because of
the complexity of the real
world, additional
assumptions;
are made to make individual
more alike.
1. All
investors can borrow or lend
money at the riskfree rate of
return.
2. All
investors have identical
probability distributions for
future rates of return;
they
have
homogeneous expectations with
respect to the three inputs
of the portfolio
model
i.e. expected returns, the
variance of returns, and the
correlation matrix.
Therefore,
given a set of security prices and a
riskfree rate, all
investors use the
same
information to generate an efficient
frontier.
3. All
investors have the same
oneperiod time
horizon.
4.
There are no transaction
costs.
5.
There are no personal income
taxesinvestors are indifferent
between capital gains
and
dividends.
6.
There is no inflation.
7.
There are many investors,
and no single investor can affect
the price of a stock
through
his or her buying and
selling decisions. Investors are
price takers and act as
if prices
are unaffected by their own
trades.
8.
Capital markets are in
equilibrium.
These
assumptions appear to be unrealistic and
often disturb investors
encountering capital
market
theory for the first
time. However, the important
issue is how well the
theory
predicts
or describes reality, and not
the realism of its
assumptions. If CMT does a good
job
of
explaining the returns on
risky .assets, it is very
useful, and the assumptions made
in
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Investment
Analysis & Portfolio Management
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VU
deriving
the theory are of less
importance.
Most
of these assumptions can be relaxed
without significant effects on
the CAPM or its
implications
in other words, the CAPM is
robust. Although the results
from such a
relaxation
of the assumptions may be
less clearcut and precise no
significant damage is
done.
Many conclusions of the
basic model still
hold.
Finally,
most investors recognize
that all of the assumptions of CMT
are not unrealistic.
For
example,
some institutional investors
are tax exempt, and brokerage
costs today, as
percentage
of the transaction, are
quite small. Nor is it too
unreasonable to as that for
the,
oneperiod
horizon of the model,
inflation may be fully (or
mostly) anticipated
and,
therefore,
not a major factor.
The
Equilibrium ReturnRisk
Tradeoff:
Given
the previous analysis, we can
now derive some predictions
concerning equilibrium
expected
returns and risk. The CAPM
is an equilibrium model that
encompasses two
important
relationships. The first,
the capital market line
specifies the equilibrium
relationship
between expected return and risk
for efficient portfolios.
The second, the
security
market line specifies the
equilibrium relationship between expected
return and
systematic
risk. It applies to individual securities
as well as portfolios.
The
Capital Market
Line:
We
now know that portfolio M is
die tangency point to a straight
line drawn front RF to
the
efficient
frontier and that this
straight line is the best
obtainable efficient set
line. All
investors
will hold portfolio M as their
optimal risky portfolio, and
all investors will be
somewhere
on this steepest; tradeoff
line between expected return and
risk, because it
represents, those
combinations of riskfree investing /
borrowing and portfolio M that
yield
the
highest return obtainable
for a given level of
risk.
The
straight line usually
referred to as the capital
market line (CML, depicts
the equilibrium
conditions
that prevail in the market
for efficient portfolios
consisting of the
optimal
portfolio
of risky assets and die riskfree
assets. All combinations of the
riskfree asset and
the
risk portfolio M are on the
CML, and, in equilibrium,
all investors will end up
;with
portfolios
somewhere on the CML.
The
Market Portfolio:
Portfolio
M is called the market
portfolio of risky securities. It is
the highest point of
tangency
between RF and the efficient
frontier and is the optimal
risky portfolio. All
investors
would want to be on the
optimal line RFML, and,
unless they invested
100
percent
of their wealth in the
riskfree asset, they would
own portfolio M with some
portion
of
their investable wealth or
they would invest their
own wealth plus borrowed
funds in
portfolio
M. This portfolio is the
optimal portfolio of risky
assets.
Why do
all investors hold identical
risky portfolios? Based on
our assumptions above,
all
investors
use the same Markowitz
analysis on the same set of
securities, have the
same
expected
returns and covariance's and have an
identical time horizon
Therefore, they will,
arrive
at the same optimal risky
portfolio, arid it will be the
market portfolio, designated
M.
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Investment
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The
Separation Theorem:
We
have established that each
investor will hold combinations of
the riskfree asset
(either
lending
or borrowing) and the tangency
portfolio from the efficient
frontier, which is
the
market
portfolio. Because we are
assuming homogeneous expectations, in
equilibrium all
investors
will determine the same
tangency portfolio. Further,
under the assumptions of
CMT
all investors agree on the
riskfree rate.
Borrowing
and lending possibilities, combined
with one portfolio of risky
assets M, offer an
investor
whatever riskexpected return
combination he or she seeks;
that is, investors can
be
anywhere
they choose on this line
depending on their riskreturn
preferences. An investor
could:
1.
Invest 100 percent of investable
funds in the riskfree
asset, providing an expected
return
of RF and zero risk.
2.
Invest 100 percent of investable
funds in riskyasset portfolioM,
offering E
(RM),
with
its risk σM.
3.
Invest in any combination of
return and risk between
these two points; obtained
by
varying
the proportion wRF invested in the riskfree
asset.
4.
Invest more than 100 percent
of investable funds in the
riskyasset portfolio M by
borrowing
money at the rate RF,
thereby increasing both the
expected return and the
risk
beyond that offered by
portfolio M.
Different
investors will choose different
portfolios because of their
risk preferences (they
have
different indifference curves),
but they will choose the
same combination of
risky
securities
as denoted by the tangency point M.
Investors will then borrow or
lend to achieve
various
positions on the linear
tradeoff, between expected return and
risk.
Unlike
the Markowitz analysis; it is
not necessary to match each
client's indifference
curves
with
a particular efficient portfolio,
because only one efficient
portfolio is held by
all
investors.
Rather each client will use
his or her indifference
curves to determine
where
along
the new efficient frontier
RFML he or she should be; In
effect, each client
must
determine
how much of investable funds
should be lend or borrowed at RF and
how much
should
be invested in portfolio M. This
result is referred to as a separation
property.
The
Security Market
Line:
The
capital market line depicts
the riskreturn tradeoff in
the financial markets
in
equilibrium.
However, it applies only to efficient
portfolios and cannot be used
toassess the
equilibrium
expected return for a single
security. What about
individual securities or
inefficient
portfolios?
Under
the CAPM all investors will
hold the market portfolio,
which is the
benchmark
portfolio
against which other portfolios
are measured. How does an
individual security
contribute
to the risk of the market
portfolio?
Investors
should expect a risk premium
for buying a risky asset
such as a, stock. The
greater
the
riskiness of that stock, the
higher the risk premium
should be. If investors hold
well
diversified
portfolios, they should be
interested in portfolio risk
rather than
individual
security
risk. Different stocks will affect a
welldiversified portfolio differently.
The
relevant
risk for an individual stock
is its contribution to the
riskiness of a welldiversified
portfolio.
And the risk of a
welldiversified portfolio is market
risk, or systematic
risk,
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Investment
Analysis & Portfolio Management
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which
is nondiversifiable.
Beta:
We
now know that investors
should hold diversified
portfolios to reduce the portfolio
risk.
When
an investor adds a security to a
portfolio what matters is
the security's
average
covariance
with the other securities in
the portfolio. We also now
know that under CMT
all
investors
will hold the same portfolio
of risky assets, the market
portfolio. Therefore,
the
risk
that matters when we
consider any security is its
covariance with the market
portfolio.
We
could relate the expected
return on a stock to its
covariance with the market
portfolio.
However,
it is more convenient to use a
standardized measure of the systematic
risk that
cannot
be avoided through diversification. Beta
is a relative measure of riskthe
risk of an
individual
stock relative to the market
portfolio of all stocks. If the
security's returns
move,
more
(less) than, the market's
returns as the latter changes,
the security's returns have
more
(less)
volatility (fluctuations in price)
than those of the market.
For example, a
security
whose
returns rise or fall on average 15
percent when the market
return rises or falls
10
percent
is said to be an aggressive or volatile
security.
CAPM's
Expected ReturnBeta
Relationship:
The
security market line (SML)
is the CAPM specification of
how risk and required rate
of
return
for any asset security, or
portfolio are related. This
theory posits a linear
relationship
between
an asset's risk and its
required rate of return. This
linear relationship, called
the
security
market line (SML). Required
rate of return is on the vertical
axis and beta, the
measure
of risk, is on the horizontal
axis. The slope of the line
is the difference between
the
required
rate of return on the market
index and RF, the riskfree
rate.
The
capital asset pricing model
(CAPM) formally relates the expected rate
of return for any
security
or portfolio with .the
relevant risk measure. The
CAPM's expected returnbeta
relationship
is the mostoften cited form
of the relationship. Beta is the
relevant measure of
risk
that cannot be diversified
away in a portfolio of securities and, as
such, is the measure
that
investors should consider in
their portfolio management decision
process.
The
CAPM in its expected returnbeta
relationship form is a simple
but elegant statement.
It
says
that the expected rate of return on an
asset is a function of the
two components of the
required
rate of returnthe riskfree rate and
the risk premium.
Thus;
ki = Riskfree rate + Risk
premium
= RF +
βi
[E (RM)  RF]
Where;
ki
= the
required rate of return on asset
i
E (RM) = the expected rate of return on
the market portfolio
βi
= the
beta coefficient for asset
i
This
relationship provides an explicit
measure of the risk premium.
It is the product of
the
beta
for a particular security i and
the market risk premium, E
(RM)  RF.
Thus,
Risk
premium for security i = βi
(market
risk premium)
=
βi
[E (RM)  RF]
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Investment
Analysis & Portfolio Management
(FIN630)
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The
CAPM's expected returnbeta relationship
is a simple but elegant
statement about
expected
(required) return and risk
for any security or
portfolio. It formalizes the
basis of
investments
which is that the greater
the risk assumed, the
greater the expected (required)
return
should be. This relationship
states that an investor
require (expects) a return on
arisky
asset
equal to the return on a
riskfree asset plus a risk
premium and the greater the
risk
assumed,
the greater the risk
premium.
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