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Capital market

August 10th, 2017 admin
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

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