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Fin3715 – Fall 07 – Kayhan
1
Lecture 15: Capital Asset Pricing Model
Reading: RWJ
Chapter 13
Outline
:
Derivation of the CAPM
The Security Market Line
Properties of Beta
Alternatives to the CAPM
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Summary
: Portfolio
Theory (1)
Assume:
Investors maximize expected return while minimizing
portfolio standard deviation, and
Investors can borrow and lend at riskfree rate.
Results:
each investor’s optimal portfolio is a combination
of only two portfolios
The riskfree asset
The market portfolio
The market portfolio
is the portfolio of all assets in
the economy.
In practice a broad stock market
index, such as the S&P 500, is often used to
represent the market.
Fin3715 – Fall 07 – Kayhan
3
Summary: Portfolio theory (2)
We analyze investors' asset demand given the
distribution of asset returns.
Investors hold portfolios to reduce risk
(Diversification).
``Nonsystematic risks'' of individual assets don't
matter.
Only ``systematic risks'' matter.
Investors hold portfolios that has eliminated the
unique risk and care only about portfolio risk.
An individual asset's contribution to portfolio risk
is its covariance with portfolio
.
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A “Standardized” Measure of Market
Risk for an Asset: beta (
)
If an individual asset's contribution to portfolio risk is its
covariance with portfolio, then we can define
as the
“standardized” measure of market risk of asset “i” with
respect to the market portfolio:
The main intuition is that due to diversification, only
nondiversifiable risk is priced.
We often refer to
β
iM
as
β
i
to simplify notation.
2
iM
σ
σ
)
var(
)
,
cov(
β
M
iM
M
M
i
r
r
r
=
=
β
iM
β
5
The Capital Asset Pricing Model (CAPM)
The general relationship between the risk and return of an
asset is therefore given by
)
(
f
M
i
f
i
r
r
r
r

+
=
β
CAPM
:
The CAPM is a model of assets’ riskreturn tradeoff.
In particular, the CAPM says that assets earn a risk premium
proportional to the market risk premium
,
, where the
constant of proportionality is the asset’s beta with respect to
the market.
f
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This note was uploaded on 05/06/2008 for the course FIN 3715 taught by Professor Stephens during the Spring '08 term at LSU.
 Spring '08
 Stephens
 Capital Asset Pricing Model

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