The two-asset case The expected return for asset A is 6.25% with a standard deviation of
5.00%, and the expected return for asset B is 4.50% with a standard deviation of 5.00%. Based
on your knowledge of efficient portfolis, fill in the blanks in the following table with the
appropriate answers. What is the efficient proportion of asset A within the portfolio for case II?
0.50 1.00 0.00 0.43
Solution
Answer
Answer 1
Security A
Security B
Expected portfolio return
Proportion
Expected Return
SD
Proportion
Expected Return
SD
A
B
C
D
E
F
(A*B)+(D*E)
1
6.25
5
0
4.5
5
6.25
0.75
6.25
5
0.25
4.5
5
5.81
0.5
6.25
5
0.5
4.5
5
5.38
0.25
6.25
5
0.75
4.5
5
4.94
0
6.25
5
1
4.5
5
4.50
CASE I
Security A
Security B
SD of Portfolio
Proportion
SD
Proportion
SD
Pab
A
M
C
N
O
D
P
F
Q
R
S
T
U
A*A
C*C
M*N
D*D
F*F
P*Q
2*A*C*D*F*S
O+R+T
Squreroot of U
1.00
1.0
5.0
25.0
25.0
0.00
0.0
5.0
25.0
0.0
-0.5
0.0
25.0
5.0
0.75
0.6
5.0
25.0
14.1
0.25
0.1
5.0
25.0
1.6
-0.5
-4.7
10.9
3.3
0.50
0.3
5.0
25.0
6.3
0.50
0.3
5.0
25.0
6.3
-0.5
-6.3
6.3
2.5
0.25
0.1
5.0
25.0
1.6
0.75
0.6
5.0
25.0
14.1
-0.5
-4.7
10.9
3.3
0.00
0.0
5.0
25.0
0.0
1.00
1.0
5.0
25.0
25.0
-0.5
0.0
25.0
5.0
CASE II
Security A
Security B
SD of Portfolio
Proportion
SD
Proportion
SD
Pab
A
M
C
N
O
D
P
F
Q
R
S
T
U
A*A
C*C
M*N
D*D
F*F
P*Q
2*A*C*D*F*S
O+R+T
Squreroot of U
1.00
1.0
5.0
25.0
25.0
0.00
0.0
5.0
25.0
0.0
0.4
0.0
25.0
5.0
0.75
0.6
5.0
25.0
14.1
0.25
0.1
5.0
25.0
1.6
0.4
3.8
19.4
4.4
0.50
0.3
5.0
25.0
6.3
0.50
0.3
5.0
25.0
6.3
0.4
5.0
17.5
4.2
0.25
0.1
5.0
25.0
1.6
0.75
0.6
5.0
25.0
14.1
0.4
3.8
19.4
4.4
0.00
0.0
5.0
25.0
0.0
1.00
1.0
5.0
25.0
25.0
0.4
0.0
25.0
5.0
CASE III
Security A
Security B
SD of Portfolio
Proportion
SD
Proportion
SD
Pab
A
M
C
N
O
D
P
F
Q
R
S
T
U
A*A
C*C
M*N
D*D
F*F
P*Q
2*A*C*D*F*S
O+R+T
Squreroot of U
1.00
1.0
5.0
25.0
25.0
0.00
0.0
5.0
25.0
0.0
0.7
0.0
25.0
5.0
0.75
0.6
5.0
25.0
14.1
0.25
0.1
5.0
25.0
1.6
0.7
6.6
22.2
4.7
0.50
0.3
5.0
25.0
6.3
0.50
0.3
5.0
25.0
6.3
0.7
8.8
21.3
4.6
0.25
0.1
5.0
25.0
1.6
0.75
0.6
5.0
25.0
14.1
0.7
6.6
22.2
4.7
0.00
0.0
5.0
25.0
0.0
1.00
1.0
5.0
25.0
25.0
0.7
0.0
25.0
5.0
Answer 2
What is the efficient proportion of asset A within the portfolio for CASE II?
Efficient portfolio offers the highest expected return for a defined level of risk or the lowest risk
for a given level of expected return.
Answer : efficient proportion of asset A is 0.5 ( Where standard deviation (SD) of portfolio is
lowest i.e. 4.2%)
Security A
Security B
Expected portfolio return
Proportion
Expected Return
SD
Proportion
Expected Return
SD
A
B
C
D
E
F
(A*B)+(D*E)
1
6.25
5
0
4.5
5
6.25
0.75
6.25
5
0.25
4.5
5
5.81
0.5
6.25
5
0.5
4.5
5
5.38
0.25
6.25
5
0.75
4.5
5
4.94
0
6.25
5
1
4.5
5
4.50.
The two-asset case The expected return for asset A is 6.25 with a s.pdf
1. The two-asset case The expected return for asset A is 6.25% with a standard deviation of
5.00%, and the expected return for asset B is 4.50% with a standard deviation of 5.00%. Based
on your knowledge of efficient portfolis, fill in the blanks in the following table with the
appropriate answers. What is the efficient proportion of asset A within the portfolio for case II?
0.50 1.00 0.00 0.43
Solution
Answer
Answer 1
Security A
Security B
Expected portfolio return
Proportion
Expected Return
SD
Proportion
Expected Return
SD
A
B
C
D
E
F
(A*B)+(D*E)
1
6.25
5
0
4.5
5
6.25
0.75
6.25
5
11. 0.7
0.0
25.0
5.0
Answer 2
What is the efficient proportion of asset A within the portfolio for CASE II?
Efficient portfolio offers the highest expected return for a defined level of risk or the lowest risk
for a given level of expected return.
Answer : efficient proportion of asset A is 0.5 ( Where standard deviation (SD) of portfolio is
lowest i.e. 4.2%)
Security A
Security B
Expected portfolio return
Proportion
Expected Return
SD
Proportion
Expected Return
SD
A
B
C
D
E
F
(A*B)+(D*E)
1
6.25
5
0
4.5
5
6.25
0.75
6.25
