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August 10th, 2017 
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Suppose there are two factors,
F
1
and
F
2
, that determine asset returns. Assume that
the Arbitrage Pricing Theory (APT) holds. Both factors have zero expectations, i.e.,
E
[
F
1
] =
E
[
F
2
] = 0. There are two stocks A and B traded in the market whose returns
are given by the system of equations below. The risk-free rate is
r
f
= 5% and the
returns of the two stocks are given by
r
A
= 0
:
2 + 0
:
5
F
1
+ 2
F
2
r
B
= 0
:
25 + 1
:
5
F
1
+
F
2
Under the APT, the expected return of any asset i is given by
E
[
R
i
] =
r
f
+
i
1
1
+
i
2
2
Where
i
1
and
i
2
are the sensitivities of stock i to factor 1 and 2, respectively
(a) Find
1
and
2
implied by the APT.
(b) Construct a portfolio of risk-free asset, stock A, and stock B that only has exposure
to
F
1
with
p
1
= 1.
(c) What is the expected return of the portfolio constructed in part (b)?
(d) Suppose that we have another stock C with its return following
r
C
= 0
:
3 +
F
1
+
C;
2
F
2
What is the value of
C;
2
for there to be no arbitrage in the market?
(e) Assume that
C;
2
from part (d) is equal to 2. Construct a portfolio that eliminates
all risks and yields an arbitrage opportunity.
(f) Per dollar of stock C you buy or sell, how much of an arbitrage pro t are you able
to make?
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