1
U
NIVERSITY OF
N
ORTH
C
AROLINA
K
ENAN
-F
LAGLER
B
USINESS
S
CHOOL
BUSI 580: INVESTMENTS
P
ART
I:
P
ORTFOLIO
T
HEORY AND
A
SSET
P
RICING
Prof. Günter Strobl
Spring 2010
Solution to Problem Set 3
A.
The Arbitrage Pricing Theory
1.
(a) In a two-factor economy, the expected return of any well-diversified portfolio is
given by:
(
)
2
,
p
2
1
,
p
1
f
p
b
b
r
r
E
λ
λ
+
+
=
.
Thus, in order to find the factor risk premia, we have to solve the following
system of two equations in two unknowns:
2
1
4
.
3
2
.
1
%
5
%
1
.
13
λ
λ
×
+
×
+
=
2
1
6
.
2
6
.
2
%
5
%
4
.
15
λ
λ
×
+
×
+
=
The solution to this set of equations is
λ
1
= 2.5% (risk premium for factor F
1
) and
λ
2
= 1.5% (risk premium for factor F
2
).
(b)
If the risk premium for F
1
increases from 2.5% to 2.75%, then the expected
returns for portfolios X and Y are:
(
)
%
4
.
13
%
5
.
1
4
.
3
%
75
.
2
2
.
1
%
5
r
E
X
=
×
+
×
+
=
(
)
%
05
.
16
%
5
.
1
6
.
2
%
75
.
2
6
.
2
%
5
r
E
Y
=
×
+
×
+
=

This
** preview**
has intentionally

**sections.**

*blurred***to view the full version.**

*Sign up*