This preview shows pages 1–3. Sign up to view the full content.
Investment Science
Chapter 6
Solutions to Suggested Problems
Dr. James A. Tzitzouris
<jimt2@ams.jhu.edu>
6.1
The money invested is
X
0
. The money received at the end of a year is
X
0

X
1
+
X
0
. Hence,
R
=
2
X
0

X
1
X
0
.
6.3
For solution method, see solution to Problem 6.4 in this solution set.
(a)
α
= 19
/
23
(b) The minimum standard deviation is approximately 13
.
7%.
(c) The expected return of this portfolio is approximately 11
.
4%.
6.4
Let
α
and
β
equal the percent of investment in stock 1 and stock 2, respectively. The problem is:
min
α,β
α
2
σ
2
1
+ 2
αβσ
12
+
β
2
σ
2
2
s.t.
α
+
β
= 1
.
1
This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentSetting up the Lagrangian,
L
, we have:
L
=
α
2
σ
2
1
+ 2
αβσ
12
+
β
2
σ
2
2

λ
(
α
+
β

1)
.
The ﬁrst order necessary conditions are:
0 =
∂L
∂α
= 2
ασ
2
1
+ 2
βσ
12

λ,
0 =
∂L
∂β
= 2
βσ
2
2
+ 2
ασ
12

λ,
1 =
α
+
β,
which imply
α
=
σ
2
2

σ
12
σ
2
1
+
σ
2
2

2
σ
12
.
The mean rate of return is simply
This is the end of the preview. Sign up
to
access the rest of the document.
 Spring '10
 Won
 Electromagnet

Click to edit the document details