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Chapter 12
Arbitrage Pricing Theory
(APT)
Road Map
Part A
Introduction to fnance.
Part B
Valuation oF assets, given discount rates.
Part C
Determination oF discount rates.
•
Historical asset returns.
•
Time value oF money.
•
Risk.
•
PortFolio theory.
•
Capital Asset Pricing Model (CAPM).
•
Arbitrage Pricing Theory (APT).
Part D
Introduction to corporate fnance.
Main Issues
1. ±actor Models oF Asset Returns
2. Arbitrage Pricing Model (APT)
3. Applications oF APT
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View Full Document 122
Arbitrage Pricing Theory (APT)
Chapter 12
Contents
1
In
t
r
odu
c
t
i
on .
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2
F
a
c
t
o
rM
od
e
l
so
fA
s
s
e
tR
e
tu
rn
s ................
1
2

4
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r
op
e
r
t
i
e
fF
a
c
t
o
e
l
s ..................
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4
APT .
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2

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5
Imp
l
em
en
t
a
t
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ono
fAPT .
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4
6
C
omm
t
sonAPT.
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H
om
ew
o
r
k ...........................
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8
15.407 Lecture Notes
Fall 2003
c
°
Jiang Wang
Chapter 12
Arbitrage Pricing Theory (APT)
123
1
Introduction
The CAPM and its extensions are based on specifc assumptions
on investors’ asset demand. For example:
•
Investors care only about mean return and variance.
•
Investors hold only traded assets.
The CAPM has several weakness (as discussed in Chapter 12),
which the APT attempts to overcome.
The Arbitrage Pricing Theory (APT) starts with specifc assump
tions on the distribution o± asset returns and relies on
approximate
arbitrage arguments.
In particular, APT assumes a “±actor model” o± asset returns.
c
°
Jiang Wang
Fall 2003
15.407 Lecture Notes
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View Full Document 124
Arbitrage Pricing Theory (APT)
Chapter 12
2
Factor Models of Asset Returns
Suppose that asset returns are driven by a few (
K
) common
factors and idiosyncratic noise:
˜
r
i
=¯
r
i
+
b
i
1
˜
f
1
+
···
+
b
iK
˜
f
K
+˜
u
i
(
i
=1
,
2
,...
)
(12.1)
where
•
¯
r
i
is the expected return on asset
i
•
˜
f
1
,
...
,
˜
f
K
are news on common factors driving all asset
returns:
˜
f
k
=
˜
F
k
−
E
[
˜
F
k
]
•
b
ik
gives how sensitive the return on asset
i
with respect to
news on the
k
th factor

b
ik
is called the factor loading of asset
i
on factor
˜
f
k
•
˜
u
i
is the idiosyncratic component in asset
i
’s return that is
unrelated to other asset returns
•
˜
f
1
,
˜
f
2
,
,
˜
f
K
and
˜
u
i
have zero means:
E
[
˜
f
k
]=0(
k
,...,K
)
E
[˜
u
i
i
)
.
15.407 Lecture Notes
Fall 2003
c
°
Jiang Wang
Chapter 12
Arbitrage Pricing Theory (APT)
125
Example.
Common factors driving asset returns may include
GNP, interest rates, inﬂation, etc.
Let
˜
f
int
b
et
h
en
ew
so
n
interest rates.
Before a board meeting of the Fed, the market
expects the Fed not to change the interest rate. After the meeting,
Greenspan announces that
•
There is no change in interest rate — “no news”:
˜
f
int
.
=0
.
•
Thereisa
1
4
%
increase in interest rate — “positive surprise”:
˜
f
int
.
.
25%
>
0
.
What should be the sign of factor loadings on
˜
f
int
.
for
•
±xed income securities
•
stocks
•
commodity futures, etc.?
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This note was uploaded on 01/19/2011 for the course 15 15.407 taught by Professor Wang during the Fall '03 term at MIT.
 Fall '03
 Wang

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