Asset Pricing Models
Tyler R. Henry
1
FINA 4310
Outline
Contents
1
CAPM
1
1.1
SML
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4
1.2
SCL
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7
1.3
Empirical Evidence
. . . . . . . . . . . . . . . . . . . . . . . . . . .
10
2
MultiFactor Models
13
2.1
APT
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
13
2.2
FF3
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
14
1
CAPM
Capital Asset Pricing Model (CAPM)
•
The CAPM is an equilibrium model of security markets that attempts to answer
the question: "What is the relationship between risk and expected returns?"
•
CAPM is a single factor asset pricing model, that describes the riskreturn rela
tionship for individual assets, where an asset’s risk is characterized by its contri
bution to the risk of an efficient, diversified portfolio.
•
The single factor is the market portfolio (more on that later), and an asset’s rele
vant risk is the risk that cannot be diversified away by including it in the market
portfolio.
1
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CAPM Assumptions
•
Investors are rational
meanvariance optimizers
: they form their portfolios based
on mean returns and variances.
•
Homogeneous expectations
: All investors possess the same probability distribu
tion of future asset returns. In other words, they all agree on the same means,
variances, and covariance of future asset returns.
•
Markets are perfectly competitive and investors are price takers.
•
Investors have a singleperiod investment horizon.
•
No market frictions such as taxes or transactions costs.
•
All investors can borrow and lend at the same riskfree rate.
Note: Clearly, these assumptions are not satisfied in reality. They are assumptions necessary to simplify the model’s approx
imation of reality. The success of a model is based on the accuracy of its predictions not on the realism of its assumptions.
CAPM Equilibrium Outcome
Under the assumptions of CAPM, all investors have the same investment opportunity set (e.g., they have
access to the same set of risky assets), and the same riskfree rate. Therefore, they will also have the same
optimal risky portfolio and the same efficient frontier. Under these conditions, the equilibrium outcome is:
•
All investors hold the same optimal risky portfolio, and this portfolio is called the
Market portfolio
(
M
).
•
The market portfolio will be on the efficient frontier, and is the optimal risky portfolio.
•
The CAL that runs from the riskfree rate through
M
is the best CAL, and is called the
Capital
Market Line
(CML).
Capital Market Line (CML)
Capital Market Line (CML)
(
)
P
E r
CML
All investors are on
th
CAL
hi h
M
(
)
M
E r
the same CAL, which
is the CML.
Where
they lie on the CML
depends on their risk
r
f
aversion, and is
reflected through the
proportion of their
wealth invested in the
P
σ
M
σ
wealth invested in the
riskfree asset versus
M
.
(
)
(
)
M
f
P
f
P
M
E r
r
E r
r
σ
σ
−
⎡
⎤
=
+
⎢
⎥
⎣
⎦
CML:
10/08/2007
FINA 4310
5
E
(
r
P
) =
r
f
+
E
(
r
M
)

r
f
σ
M
σ
P
2