Understanding the CAPM
1
The CAPM consists of two statements
1. The tangency portfolio is in fact the market portfolio.
2. In equilibrium the following relation must hold between excess returns and
β
:
¯
R
i
=
R
f
+
β
i
(
¯
R
M

R
f
)
.
(1)
The second statememt is known as the security market line. It says that, in equilib
rium, the return on security
i
is equal to the riskfree rate plus the excess return on
the market portfolio times the
β
of security
i
.
Proof of Statement 1
:
Assume all investors like mean and dislike variance, and assume that all investors
have homogenous beliefs about means, variances, and correlations.
Then everyone
holds some combination of the tangency portfolio and the riskfree asset.
•
Suppose that the weight of a stock (say IBM) in the tangency portfolio is 2%.
•
Now suppose that the market opens and IBM is worth 3% of total wealth in
risky assets.
•
It must be that some people have 3% of their risky asset portfolio in IBM. Those
people want to sell
•
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 Fall '09
 Finance, Capital Asset Pricing Model, Financial Markets, Modern portfolio theory, Ri, Tangency Portfolio

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