4
.
Given
E(X)
:
=
4
ELY)
,
=
2ar(x)
=
2
,
Var (Y)
=
4
,
Var(X + Y)
=
8
Computing Cov(X Y)
,
Using the identity
Var(X + Y)
,
8
:
,
w
=
,
V(w)
4w
=
5
2
.
-
(1
+
We want
V(w)
nw
:
:
-
462
w
-
-
6w
+h
60
60
6
=
-
36
=
-
6
-
-
w)2 4
.
2w +
g
1772
=
=
6
1
g
27 78
.
.
=
+
w)
+
4w + 26
+
4
0
4(4)( 46)
-
36 + 736
I
-
-
50
=
46
and (1-w) in stock Y.
5(1 w)
8
=
,
(1 w) ELY)
50
=
=
:
8
-
4-
=
z(a(x Y)
+
w
z + 4(1
4
+
+
=
=
,
1
=
E(X)
.
=
w2
=
Var(y) + 2 hor (x Y)
proportion invested in stock x
Expected return R(c)
,
+
4
2 +
=
,
Let w be the
Variance
Var(x)
Cov(X Y)
:
Now
=
2w(l w) -
+
zw
-
:
wi
and
wa
Therefore
There
=8
278
=
is
=
,
neither
no
=2
=
solution
-2
.
72
is in
the interval [0 1)
,
valid allocation w 20 1)
,
that
satisfies the variance constraint of 50.