INVESTMENT ANALYSIS 70492
Fall 2009
Suggested Solution to Midterm Exam
Professor Anisha Ghosh
1. CAPM
(a) Let
ω
1
denote the proportion of wealth invested in asset A and
ω
2
the proportion in asset B.
The tangency portfolio solves the following problem:
max
ω
1
,ω
2
E
(
r
T
)

r
f
σ
T
where
E
(
r
T
) =
ω
1
E
(
r
A
) +
ω
2
E
(
r
B
)
σ
T
=
q
ω
2
1
σ
2
A
+
ω
2
2
σ
2
B
+ 2
ω
1
ω
2
ρ
AB
σ
A
σ
B
ω
1
+
ω
2
= 1
This gives the following equations with 2 unknowns
z
1
and
z
2
:
±
z
1
z
2
²
=
±
σ
2
A
ρ
AB
σ
A
σ
B
ρ
AB
σ
A
σ
B
σ
2
B
²±
E
(
r
A
)

r
f
E
(
r
B
)

r
f
²
The composition of the tangency portfolio is obtained as
ω
*
1
=
z
1
z
1
+
z
2
ω
*
2
=
z
2
z
1
+
z
2
For the given problem, we have
ω
*
1
= 0
.
605
,ω
*
2
= 0
.
395.
(b) Plugging the composition obtained in part (a) yields
E
(
r
T
) = 0
.
605
×
0
.
02 + 0
.
395
×
0
.
09 = 0
.
048
.
σ
T
=
p
(0
.
605)
2
×
(0
.
02)
2
+ (0
.
395)
2
×
(0
.
07
2
) = 0
.
030
(c) If the CAPM is true, the market portfolio is the tangency portfolio and, hence, has the highest
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 Spring '08
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