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R
2
=
b
i
2
s
M
2
b
i
2
s
M
2
+
s
2
(
e
i
)
CAPM :
The CAPM (capital asset pricing model) is a theoretical model of equilibrium ex ante or expected
returns on risky assets; it is a valueweighted portfolio.
Each security is held in a proportion equal to its
market value divided by the total market value of all securities.
(Assumes that investors are singleperiod
planners who agree on a common input list form security analysis and seek meanvariance optimal portfolios).
•Recall the simplifying assumptions that lead to the basic version of the CAPM (necessary for all investors to
agree on risky portfolio)
1.Investors are “price takers” and act as if security prices are unaffected by their own
trades
no one can manipulate; price it is market determined; necessary to agree on optimal risky portfolio 2.
All investors have the same identical singleperiod planning horizon
heroic assumption 3.
Investments are
limited to publicly traded financial assets, and to riskfree borrowing and lending (most of the time borrow at a
higher rate than risk free) 4.
Investors pay no taxes and no transactions costs 5.
All investors are rational
meanvariance optimizers (very far off assumption)
6. Symmetric information and identical expectations
(means we all have the same info set, erroneous for one, then erroneous for all; everyone expects same
returns).
*Summary of the equilibrium that will prevail in this hypothetical world of securities and investors
*
1. All investors will choose to hold a portfolio of risky assets in proportions that duplicate representation of
the assets in the
market portfolio
(
M
), which includes all traded assets. 2.The market portfolio will be the
tangency portfolio to the optimal capital allocation line.
(This CAL is referred to as the capital market line, or
CML.) All investors therefore hold
M
as their optimal risky portfolio. 3. The risk premium on the market
portfolio will be proportional to its risk, and the degree of risk aversion of the representative investor:
E
(
r
M
) 
r
f
= (1)
A s
M
2
(times risk of market portfolio) Here A is the average level of risk aversion
across investors. &
σ
M
2
is the variance of the market portfolio
4. The risk premium on individual assets will
be proportional to the risk premium on the market portfolio (
M
), and the
β
coefficient of the security, where:
2
)
,
cov(
M
M
i
i
r
r
β
=
and
E
(
r
i
) 
r
f
=
b
i
[
E
(
r
M
) 
r
f
]
= 1 variance /variance
All Investors Hold
the Market Portfolio
: The contribution of the CAPM is to derive the fair price (in terms of the expected return)
at which investors are willing to hold each asset in the optimal risky portfolio
Expected Returns on Individual
Securities:
The CAPM is built on the insight that the appropriate risk premium on an individual asset will be
determined by its contribution to the risk of the investors’ overall portfolios
Recall first that the market portfolio has a risk premium of E(rM)  rf , and a riskreward ratio of:
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 Fall '08
 ChipRusher
 Capital Asset Pricing Model

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